Nanostructured metals and alloys - Processing, microstructure, mechanical properties and applications

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Nanostructured metals and alloys

i © Woodhead Publishing Limited, 2011

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Related titles: Fundamentals of aluminium metallurgy (ISBN 978-1-84569-654-2) This authoritative book reviews the latest advances in the study of the metallurgy of aluminium and how this knowledge is applied to the production, casting and processing of the metal and its alloys. It includes a comprehensive range of chapters on topics such as production, casting, alloys and heat treatments, through to physical metallurgy and applications. Corrosion of magnesium alloys (ISBN 978-1-84569-708-2) The book gives a comprehensive account of the corrosion of magnesium alloys. The book covers the better known methods of corrosion, such as atmospheric, as well as the lesser known processes such as corrosion in engine coolants and the corrosion mechanisms of implants. The use of magnesium alloys is increasing in a range of applications and their popularity is growing wherever lightweight materials are needed. The book covers the fundamentals of magnesium alloy corrosion, metallurgical effects, environment-affected behaviour and protected magnesium alloys. Welding and joining of magnesium alloys (ISBN 978-1-84569-692-4) This book covers all aspects of the welding and joining of magnesium alloys. Magnesium and its alloys have been used for many years and their use is increasing due to their superior properties and light weight. Part I includes welding metallurgy, preparation for welding and welding materials. Part II covers the various welding technologies that can be used for joining magnesium alloys and Part III includes other joining technologies, weld defects and corrosion protection. Details of these and other Woodhead Publishing materials books can be obtained by: • visiting our web site at www.woodheadpublishing.com • contacting Customer Services (e-mail: [email protected]; fax: +44 (0) 1223 832819; tel.: +44 (0) 1223 499410 ext. 130; address: Woodhead Publishing Limited, 80 High Street, Sawston, Cambridge CB22 3HJ, UK) If you would like to receive information on forthcoming titles, please send your address details to: Francis Dodds (address, tel. and fax as above; e-mail: francis. [email protected]). Please confirm which subject areas you are interested in.

ii © Woodhead Publishing Limited, 2011

Nanostructured metals and alloys Processing, microstructure, mechanical properties and applications Edited by Sung H. Whang

iii © Woodhead Publishing Limited, 2011

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Published by Woodhead Publishing Limited, 80 High Street, Sawston, Cambridge CB22 3HJ, UK www.woodheadpublishing.com Woodhead Publishing, 1518 Walnut Street, Suite 1100, Philadelphia, PA 19102-3406, USA Woodhead Publishing India Private Limited, G-2, Vardaan House, 7/28 Ansari Road, Daryaganj, New Delhi – 110002, India www.woodheadpublishingindia.com First published 2011, Woodhead Publishing Limited © Woodhead Publishing Limited, 2011 The authors have asserted their moral rights. This book contains information obtained from authentic and highly regarded sources. Reprinted material is quoted with permission, and sources are indicated. Reasonable efforts have been made to publish reliable data and information, but the authors and the publisher cannot assume responsibility for the validity of all materials. Neither the authors nor the publisher, nor anyone else associated with this publication, shall be liable for any loss, damage or liability directly or indirectly caused or alleged to be caused by this book. Neither this book nor any part may be reproduced or transmitted in any form or by any means, electronic or mechanical, including photocopying, microfilming and recording, or by any information storage or retrieval system, without permission in writing from Woodhead Publishing Limited. The consent of Woodhead Publishing Limited does not extend to copying for general distribution, for promotion, for creating new works, or for resale. Specific permission must be obtained in writing from Woodhead Publishing Limited for such copying. Trademark notice: Product or corporate names may be trademarks or registered trademarks, and are used only for identification and explanation, without intent to infringe. British Library Cataloguing in Publication Data A catalogue record for this book is available from the British Library. ISBN 978-1-84569-670-2 (print) ISBN 978-0-85709-112-3 (online) The publisher’s policy is to use permanent paper from mills that operate a sustainable forestry policy, and which has been manufactured from pulp which is processed using acid-free and elemental chlorine-free practices. Furthermore, the publisher ensures that the text paper and cover board used have met acceptable environmental accreditation standards. Typeset by RefineCatch Limited, Bungay, Suffolk, UK Printed by TJI Digital, Padstow, Cornwall, UK

iv © Woodhead Publishing Limited, 2011

Contents

Contributor contact details Introduction

xv xxi

S.H. Whang, New York University, USA

Part I Processing bulk nanostructured metals and alloys 1

Producing bulk nanostructured metals and alloys by severe plastic deformation (SPD)

1 3

R.Z. Valiev, Ufa State Aviation Technical University, Russia

1.1 1.2 1.3 1.4 1.5 1.6 1.7 2

Introduction The principles of severe plastic deformation (SPD) processing New trends in SPD processing for effective grain refinement Enhanced properties achieved using SPD processing Innovation potential of bulk nanostructured materials Conclusions References

3 4 8 22 33 34 35

Bulk nanostructured metals and alloys produced by accumulative roll-bonding

40

N. Tsuji, Kyoto University, Japan

2.1 2.2 2.3 2.4 2.5 2.6 2.7

Introduction The principle of accumulative roll-bonding (ARB) Processing details Change in microstructures during the process Mechanical properties of nanostructured metals fabricated by ARB Conclusions References

40 41 42 45 53 57 57

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Contents

3

Nanocrystalline metals and alloys prepared by mechanical attrition

59

S. Scudino and J. Eckert, IFW Dresden, Germany

3.1 3.2 3.3 3.4 3.5 3.6 3.7

Introduction Mechanical attrition Nanocrystalline phase formation by mechanical attrition Consolidation of nanocrystalline powders Conclusion and future trends Acknowledgements References

59 60 62 75 80 81 82

4

The processing of nanocrystalline steels by solid reaction

85

F.G. Caballero and C. García -Mateo , National Center for Metallurgical Research (CENIM-CSIC), Spain

4.1 4.2 4.3 4.4 4.5 4.6 4.7 4.8 4.9 4.10 4.11 5

Introduction The finest grain structures in steels Phase transformation theory: a powerful tool for the design of advanced steels, from micro to nano NANOBAIN steel: a material going to extremes Accelerating the bainite reaction at low temperatures Characterizing nanocrystalline bainitic steels at the atomic scale The mechanical properties of nanocrystalline bainitic steels Conclusion and future trends Sources of further information and advice Acknowledgements References

85 86

98 107 113 114 114 114

The processing of bulk nanocrystalline metals and alloys by electrodeposition

118

89 93 98

U. Erb , University of Toronto, Canada and G. Palumbo and J.L. Mc C rea , Integran Technologies Inc., Canada

5.1 5.2 5.3 5.4 5.5 5.6 5.7 5.8 5.9

Introduction Electrodeposition methods Examples of nanocrystalline metals and alloys prepared by electrodeposition Mechanical properties of nanocrystalline electrodeposits Corrosion properties of nanocrystalline electrodeposits Other properties of nanocrystalline electrodeposits Applications Acknowledgements References

© Woodhead Publishing Limited, 2011

118 119 128 136 141 143 145 146 146

6

Contents

Bulk nanocrystalline and nanocomposite alloys produced from amorphous phase

vii

152

A. Inoue and D.V. Louzguine , Tohoku University, Japan

6.1 6.2 6.3 6.4 6.5 6.6 6.7 6.8 7

Introduction The formation of bulk metallic glassy alloys The formation of a nanostructure by crystallization of the glassy phase, by deformation or directly from the melt on casting The formation of nano-quasicrystals The mechanical properties of nanocomposite alloys The magnetic properties of nanocomposite alloys Conclusions References

152 153 159 165 167 169 172 173

Severe plastic deformation and the production of nanostructured alloys by machining

178

J.B. Mann , M4 Sciences, USA, S. Chandrasekar , W.D. Compton , and K.P. Trumble , Purdue University, USA, C. Saldana , and S. Swaminathan , GE John F. Welch Technology Center, India, W. Moscoso and T.G. Murthy , Indian Institute of Science, India

7.1 7.2 7.3 7.4 7.5 7.6 7.7 7.8 7.9

Introduction The mechanics of severe plastic deformation (SPD) in machining A study of microstructure refinement Bulk forms with ultrafine-grained (UFG) microstructure Nanostructured particulate Surface nanostructuring Conclusions Acknowledgements References

Part II Microstructure 8

Deformation structures including twins in nanograined pure metals

178 179 189 196 200 205 207 207 208 211 213

K. Hattar , Sandia National Laboratories, USA

8.1 8.2 8.3 8.4 8.5 8.6 8.7 8.8

Introduction Classical defect structures in nanograined metals Classical defect structures absent in nanograined metals Novel defect structures in nanograined metals The effect of initial microstructure on deformation structures Future trends Acknowledgements References


213 214 221 224 230 236 239 239

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Contents

9

Microstructure and mechanical properties of nanostructured low-carbon steel prepared by equal-channel angular pressing

243

Y.G. Ko , Yeungnam University, Republic of Korea, and D.H. Shin , Hanyang University, Republic of Korea

9.1 9.2 9.3 9.4 9.5 9.6 9.7 10

Introduction The microstructural evolution of low-carbon steel (LCS) The mechanical response of a nanostructured LCS alloy Enhanced tensile properties by grain refinement and microstructural modification Continuous shear drawing: a new processing method Conclusion References

243 244 261 268 270 272 272

Characteristic structures and properties of nanostructured metals prepared by plastic deformation

276

X. Huang , Technical University of Denmark, Denmark

10.1 10.2 10.3 10.4 10.5 10.6 10.7

Introduction Characteristic microstructures Hardening by annealing and softening by deformation Optimisation of microstructure and mechanical properties Conclusions Acknowledgements References

276 277 286 289 290 294 294

Part III Mechanical properties

297

11

299

Strengthening mechanisms in nanocrystalline metals D.G. M orris , National Center for Metallurgical Research (CENIM-CSIC), Spain

11.1 11.2 11.3 11.4 11.5 11.6 11.7 11.8 11.9 11.10

Introduction The deformation of polycrystals; the Hall–Petch model for strengthening; typical strength and hardness data Hall–Petch breakdown: a fine grain size limit to models Hall–Petch breakdown: the importance of defective materials Alternative deformation mechanisms at very fine grain sizes Strengthening caused by second-phase particles Strengthening caused by other factors: solute, order, twin boundaries Strengthening mechanisms in materials with ultrafine microstructure prepared by severe plastic deformation Conclusion and future trends References


299 300 303 304 307 314 319 320 324 325

12

Contents

Elastic and plastic deformation in nanocrystalline metals

ix

329

M.Y. Gutkin , Russian Academy of Sciences, Russia

12.1 12.2 12.3 12.4 12.5 12.6 12.7

Introduction Elastic strains in nanocrystalline metals Plastic deformation in nanocrystalline metals Conclusions and future trends Sources of further information and advice Acknowledgements References

329 330 337 365 367 367 367

13

The mechanical properties of multi-scale metallic materials

375

Y.H. Zhao and E.J. Lavernia , University of California Davis, USA

13.1 13.2 13.3 13.4 13.5 13.6 13.7 14

Introduction Mechanical properties of multi-scale metallic materials Deformation and fracture mechanisms of multi-scale metallic materials Future trends Conclusions Acknowledgements References

375 383 405 425 425 426 426

Enhanced ductility and its mechanisms in nanocrystalline metallic materials

430

I.A. Ovid’ko, Russian Academy of Sciences, Russia

14.1 14.2 14.3 14.4 14.5 14.6 14.7 14.8 14.9

Introduction General aspects concerning the tensile ductility of materials Plastic flow mechanisms in coarse-grained metallic polycrystals, ultrafine-grained metals and nanocrystalline metals with intermediate grains Plastic flow mechanisms in nanocrystalline metals with the finest grains Specific features of crack nucleation and growth processes in nanocrystalline metallic materials Enhanced ductility of artifact-free nanocrystalline metals with narrow grain size distributions Enhanced ductility of nanocrystalline metals due to twin deformation and growth twins Enhanced ductility of nanocrystalline metals due to strain rate hardening Enhanced ductility of single-phase nanocrystalline metals with bimodal structures


430 431 435 436 440 444 446 448 449

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Contents

14.10

Enhanced ductility of nanocrystalline metallic composites with second-phase nanoparticles, dendrite-like inclusions and carbon nanotubes Conclusions and future trends Sources of further information and advice Acknowledgements References

451 452 454 455 455

The mechanical behavior of nanostructured metals based on molecular dynamics computer simulations

459

14.11 14.12 14.13 14.14 15

V.I. Yamakov , National Institute of Aerospace, USA

15.1 15.2 15.3 15.4 15.5 15.6 15.7 16

Introduction The structure and properties of grain boundaries in nanocrystalline (NC) metals by molecular dynamics (MD) simulation Deformation mechanisms in nanoscale grains Grain growth and microstructure evolution in NC metals Conclusions Acknowledgement References

459 461 465 472 476 477 477

The surface deformation and mechanical behavior in nanostructured alloys

481

L.L. Shaw , University of Connecticut, USA

16.1 16.2 16.3 16.4 16.5 16.6 16.7 16.8 16.9 17

Introduction Mechanics aspects during surface severe plastic deformation Changes in the microstructure and stress states induced by surface severe plastic deformation Tensile properties of metals with a nanocrystalline surface and hardened layer Fatigue resistance of metals with a nanocrystalline surface and hardened layer Wear resistance of metals with a nanocrystalline surface and hardened layer Conclusions Acknowledgements References Fatigue behaviour in nanostructured metals

481 482 484 493 499 501 502 504 504 507

H.W. Höppel and M. Göken , Friedrich-Alexander University of Erlangen-Nuremberg, Germany

17.1 17.2

Introduction and motivation General findings on the fatigue behaviour and the fatigue lives of nanostructured model materials


507 509

17.3 17.4 17.5 17.6 18

Contents

xi

Light metal alloys Fatigue behaviour and life of nanostructured steels Consequences and strategies for optimizing fatigue lives and cyclic deformation behaviour References

517 532 534 537

Superplastic deformation in nanocrystalline metals and alloys

542

A. Sergueeva , The Nanosteel Company, USA and A. Mukherjee , University of California Davis, USA

18.1 18.2 18.3 18.4 18.5 18.6 18.7 18.8 19

Introduction Theoretical predictions Superplasticity in nanocrystalline metals and alloys Specific features of superplasticity in nanocrystalline materials Deformation mechanisms Conclusions Acknowledgements References

542 543 546 568 578 587 590 590

Creep and high-temperature deformation in nanostructured metals and alloys

594

W. Yin , Williams Advanced Materials, USA

19.1 19.2 19.3 19.4 19.5 19.6

Introduction Temperature-dependent deformation in fine-grained pure metals Creep and high-temperature deformation in nanostructured alloys Deformation mechanisms and modeling Conclusions References

Part IV Applications 20

Processing nanostructured metal and metal-matrix coatings by thermal and cold spraying

594 595 601 603 609 610 613 615

G.E. Kim , Perpetual Technologies Inc., Canada, V.K. Champagne , and M. Trexler , US Army Research Laboratory AMSRD-ARL-WM-MC, USA and Y. Sohn , University of Central Florida, USA

20.1 20.2 20.3

Introduction Nanostructured metal-base feedstock Thermal spray processing


615 616 617

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Contents

20.4

Thermal spray processing of nanostructured coatings: tungsten carbide-cobalt (WC-Co) coatings Thermal spray processing of nanostructured coatings: alumina-titania (n-AT) coatings Thermal spray processing of nanostructured coatings: titanium oxide coatings Thermal spray processing of nanostructured coatings: MCrAlY and NiCrAlY coatings The cold spray process Characteristics of cold spray material Cold-sprayed processing of WC-Co Cold-sprayed processing of non-cryogenically milled n-WERKZ AA5083 Future trends Sources of further information and advice Acknowledgements References

20.5 20.6 20.7 20.8 20.9 20.10 20.11 20.12 20.13 20.14 20.15 21

Nanocoatings for commercial and industrial applications

620 621 622 627 644 647 648 651 657 658 658 658 663

J.L. Mc C rea and G. Palumbo , Integran Technologies, Canada and U. Erb , University of Toronto, Canada

21.1 21.2 21.3 21.4 21.5 21.6

Introduction Overview of nanostructured metals and alloys Commercialization of nanostructured materials Current and emerging applications Conclusions References

663 664 666 669 683 684

22

Applying nanostructured steel sheets to automotive body structures

687

Y. Okitsu and N. Tsuji , Honda R&D Co., Ltd., Japan

22.1 22.2 22.3 22.4 22.5 22.6 22.7 22.8

Introduction The potential demand for nanostructured steels for automotive body structures Fabricating nanostructured low-C steel sheets Improving elongation in nanostructured steel sheets Crash-worthiness of nanostructured steel sheets Conclusions References Appendix


687 688 689 699 706 711 712 713

23

Contents

Production processes for nanostructured wires, bars and strips

xiii

715

S. Torizuka , and E. Muramatsu , National Institute for Material Science, Japan, T. Komatsu , Komatsuseiki Kosakusho Co., Ltd., Japan and S. Nagayama , Tokushu Kinzoku Excel Co., Ltd., Japan

23.1 23.2 23.3 23.4 23.5 23.6 23.7 23.8 24

Introduction The production processes and properties of nanostructured steel bars The production processes and properties of nanostructured steel wire The production processes and properties of nanostructured steel strips Applications of nanostructured steels and their features Future trends Acknowledgements References Nanostructured plain carbon-manganese (C-Mn) steel sheets prepared by ultra-fast cooling and short interval multi-pass hot rolling

715 716 722 725 731 743 745 745

747

T. Tomida , K. Miyata , and H. Nishibata , Sumitomo Metal Industries Ltd., Japan

24.1 24.2 24.3 24.4 24.5 24.6 24.7 24.8

Introduction The concept of ultra-fast direct cooling and short interval multi-pass hot rolling (UDCSMR) and an experimental hot rolling mill Nanostructured carbon-manganese (C-Mn) steel sheets produced by UDCSMR Grain refinement mechanisms Deformation characteristics Welding and application to some prototype parts Conclusions References

Index

747 749 752 757 765 773 784 784 787


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Contributor contact details

(* = main contact)

Editor

Chapter 3

S. H. Whang Department of Mechanical Engineering Polytechnic Institute New York University NY 11201 USA

S. Scudino and J. Eckert* Institute for Complex Materials Leibniz Institute for Solid State and Materials Research Dresden (IFW Dresden) Helmholtzstr. 20 D-01069 Dresden Germany

E-mail: [email protected]

E-mail: [email protected] [email protected]

Chapter 1 R. Z. Valiev Institute of Physics of Advanced Materials Ufa State Aviation Technical University 12 K. Marx str. Ufa 450000 Russia E-mail: [email protected]

Chapter 4 F. G. Caballero* and C. García-Mateo National Center for Metallurgical Research (CENIM-CSIC) Avenida Gregorio del Amo, 8 Madrid 28040 Spain E-mail: [email protected]

Chapter 2 N. Tsuji Department of Materials Science and Engineering Graduate School of Engineering Kyoto University Yoshida-Honmachi, Sakyo-ku Kyoto 606-8501 Japan E-mail: [email protected]

Chapter 5 U. Erb* University of Toronto Dept. Materials Science & Engineering 184 College Street, Room 140 Toronto, ON M5S 3E4 Canada E-mail: [email protected]

xv © Woodhead Publishing Limited, 2011

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G. Palumbo and J. L. McCrea Integran Technologies Inc. 1 Meridian Road Toronto, ON M9W 4Z6 Canada E-mail: [email protected] [email protected]

Chapter 6 D. V. Louzguine* and A. Inoue WPI Advanced Institute for Materials Research Tohoku University 2-1-1 Katahira Aoba-Ku Sendai, 980-8577 Japan E-mail: dml@[email protected]

Chapter 7 J. B. Mann M4 Sciences West Lafayette IN 47906 USA

T. G. Murthy Department of Civil Engineering Indian Institute of Science Bangalore, India

Chapter 8 K. Hattar Sandia National Laboratories (505) 845-9859 PO Box 5800 Mail Stop 1056 Albuquerque NM 87185-1056 USA E-mail: [email protected]

Chapter 9 Y. G. Ko School of Materials Science and Engineering Yeungnam University Gyeongsan 712-749 Republic of Korea E-mail: [email protected]

S. Chandrasekar*, W. D. Compton, K. P. Trumble, C. Saldana, and W. Moscoso Center for Materials Processing and Tribology Purdue University West Lafayette IN 47907 USA E-mail: [email protected]

S. Swaminathan GE John F. Welch Technology Center Bangalore India

D. H. Shin* Department of Metallurgical and Materials Science Hanyang University Ansan 425-791 Republic of Korea E-mail: [email protected]

Chapter 10 X. Huang Danish-Chinese Center for Nanometals Materials Research Division Risø National Laboratory for Sustainable Energy Technical University of Denmark DK-4000 Roskilde Denmark E-mail: [email protected]



Chapter 11

Chapter 14

D. G. Morris National Center for Metallurgical Research (CENIM-CSIC) Avenida Gregorio del Amo, 8 Madrid 28040 Spain

I.A. Ovid’ko Institute of Problems of Mechanical Engineering Russian Academy of Sciences St. Petersburg Russia



Chapter 12

Chapter 15

M. Y. Gutkin Institute of Problems of Mechanical Engineering Russian Academy of Sciences Bolshoj 61 Vasilievskii Ostrov St. Petersburg 199178 Russia

V. I. Yamakov Durability and Damage Tolerance Branch NASA Langley Research Center Hampton VA 23681 USA


Chapter 13 Y. H. Zhao* Department of Chemical Engineering and Materials Science University of California, Davis 1231 Bainer Hall One Shields Avenue Davis CA 95616-5294 USA E-mail: [email protected]

E. J. Lavernia Department of Chemical Engineering and Materials Science University of California, Davis Davis CA 95616-5294 USA

xvii


Chapter 16 L. L. Shaw Department of Chemical, Materials and Biomolecular Engineering University of Connecticut Storrs CT 06269 USA E-mail: [email protected]

Chapter 17 H. W. Höppel* and M. Göken Department of Materials Science and Engineering Institute I: General Materials Properties Friedrich-Alexander University of Erlangen-Nuremberg 91058 Erlangen Germany E-mail: heinz-werner.hoeppel@ww. uni-erlangen.de

E-mail: [email protected] © Woodhead Publishing Limited, 2011

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Chapter 18 A. Sergueeva* The Nanosteel Company Idaho Falls ID 83402 USA E-mail: [email protected]

A. Mukherjee University of California Davis California USA E-mail: [email protected]

Chapter 19 W. Yin Williams Advanced Materials Inc., Thin Film Products 42 Mount Ebo Road South Brewster NY 10509 USA E-mail: [email protected]

Chapter 20 G. E. Kim* Perpetual Technologies, Inc. 38 Place du Commerce Suite 11-163 Ile des Soeurs Quebec H3E 1T8 Canada E-mail: [email protected]

V. K. Champagne US Army Research Laboratory AMSRD-ARL-WM-MC Building 4600 Aberdeen Proving Ground MD 21005-5069 USA

M. Trexler US Army Research Laboratory AMSRD-ARL-WM-MC Building 4600 Aberdeen Proving Ground MD 21005-5069 USAY. Sohn Advanced Materials Processing and Analysis Center and Department of Mechanical, Materials and Aerospace Engineering University of Central Florida 4000 Central Florida Blvd. Orlando FL 32816-2455 USA

Chapter 21 J. McCrea* and G. Palumbo Integran Technologies 1 Meridian Road Toronto, ON M9W 4Z6 Canada E-mail: [email protected] [email protected]

U. Erb University of Toronto Dept. Materials Science & Engineering 184 College Street, Room 140 Toronto, ON M5S 3E4 Canada E-mail: [email protected]



Chapter 22

T. Komatsu Komatsuseiki Kosakusho Co., Ltd. Production Department 942-2 Siga, Suwa Nagano 392-0012 Japan

Y. Okitsu* Automobile R&D Center Honda R&D Co., Ltd. 4930 Shimotakanezawa Haga-machi, Haga-gun Tochigi 321-3393 Japan E-mail: [email protected]. co.jp

N. Tsuji Department of Materials Science and Engineering Graduate School of Engineering Kyoto University Yoshida-Honmachi, Sakyo-ku Kyoto 606-8501 Japan E-mail: [email protected]

Chapter 23 S. Torizuka* and E. Muramatsu National Institute for Material Science Material Manufacturing and Engineering Station 1-2-1 Sengen, Tsukuba Ibaraki 305-0047 Japan

xix


S. Nagayama Tokushu Kinzoku Excel Co., Ltd. New Functional Materials R&D H.Q. 56 Tamagawa, Tokigawa Saitama 355-0342 Japan E-mail: [email protected]

Chapter 24 T. Tomida*, K. Miyata and H. Nishibata Sumitomo Metal Industries, LTD. Corporate R&D Laboratories 1-8, Fuso-Cho Amagasaki Hyogo, 660-0891 Japan E-mail: tomida-tsr@sumitomometals. co.jp



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Introduction S. H. WHANG, New York University, USA Recent nanotechnology for material applications deals with a very wide range of material groups and various aspects of materials problems. Since the volume of the accumulated knowledge and database for the subjects stemming from worldwide research and development has been rapidly escalating, this book intends to limit its coverage to the recent progress on nanostructured metallic materials for structural applications. Since ‘nanostructured materials’ were first defined by Gleiter,1,2 research and development in the fields of nanostuctured materials have flourished over the last two decades. Currently nanostructured materials are conveniently defined as materials made of a microstructure less than 100 nm in length in at least one dimension whereas ultrafine-grained materials (UFG) possess a grain size range between 200 nm and less than 1 µm in diameter. But, for practical reasons, nanostructured metallic materials that have been prepared for research and development contain a wide range of grain size distribution from tens of nanometers to a submicrometer. For example, research on optimizing the mechanical properties of nanostructured materials requires manipulation of its bimodal and multimodal grain size distribution. In this case, the grain size ranges from nano size (NG) to submicron size (UFG). Therefore, for practical structural applications, it is envisioned that nanostructured bulk metallic materials may contain both nanoscale as well as submicron-scale microstructures in the future. This book deals with metallic materials that have various grain size distributions: nanoscale grains or nanomicrostructure other than nanograins or submicron scale grains or submicron microstructure other than submicron grains or a combination of all these. The history of metallic materials shows that an appetite for higher strength/ specific strength, and better ductility and toughness for structural applications has been the main driving force for research and development for better and even better materials in the last century, as well as this century. Recent nanostructurizing approaches to the metallic material systems continue this effort. To achieve this desire, scientists and engineers always look into smaller-scale worlds from micron- to submicron-, and submicron- to nano-dimensions for their solutions. Long before such recent endeavors became a fashion among materials scientists and engineers, it was recognized that nanoscale microstructure has great potential for changing the landscape in advanced engineering materials and manufacturing. For example, new high-strength aluminum alloys were produced for the first time utilizing the nanoscale Guinier-Preston zone3 and ultrafine-layered wire with extremely high strength4 long before the current nanotechnology debut. The xxi © Woodhead Publishing Limited, 2011

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Introduction

discovery of the Hall–Petch relationship also suggested that new high-strength materials might be fabricated with materials with nanoscale grain sizes. In the last two decades, research and development into nanostructured metallic materials have been largely focused on metallic materials with two different microstructures: nanograined structures and embedded nanomicrostructures other than nanograins; and also the effort has been largely devoted to four different subject areas: processing and fabrication, characterization of material properties, microstructural characterization, and engineering design and development for new products and applications. The first hurdle to overcome in this effort has been the large-scale processing of high quality of nanomaterial for use in research and development. Of course, many technically challenging problems emerge in the course of processing of such nanomaterials. In general, the bulk forms prepared by different processes contain different structural defects and impurities. As a result, the mechanical properties of the specimens of an alloy prepared by different processing routes exhibit substantial deviation, particularly in structure-sensitive properties such as deformation behavior, ductility, fatigue, superplasticity and creep. This deviation poses serious problems for scientists in the analysis and interpretation of the experimental results and in arriving at meaningful conclusions. In addition, many of the processes face other challenging engineering problems that require each process to demonstrate the feasibility of scaling-up for industrial applications. As the nanomaterials research fields continue to expand and the accumulation of knowledge from the research escalates, it becomes clear that it is increasingly difficult to cover the progress made in these fields adequately in a single publication. Thus, the focus of the current book is placed on the recent progress on nanostructured metallic materials in bulk forms, in their processing, microstructure, mechanical properties and structural applications. For those who are interested in these subjects and want to know the depth and breath of the issues, there are references available for additional reading, which have reviewed and summarized the progress made in these areas in the past.5–7 This brief introduction on the subject areas is given for readers who come from other fields.

Processing It is imperative to provide nanostructured metallic materials of sufficient quality and quantity for research and development in order to realize the envisioned progress in this field. There have been many processing approaches available for producing a small quantity of nanostructured metals based on ‘top-down’, and ‘bottom-up’ approaches1 in three different phase forms – vapor, liquid or solid – utilizing all available technological means. The bottom-up approach includes inert gas condensation, chemical vapor condensation, pulse electron deposition,


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etc. Nevertheless, the structural application requires a substantial quantity of nanostructured materials in three dimensions, which eliminates the majority of possible bottom-up processing approaches as candidates for the current effort, at least at this stage. Currently, that leaves only a handful of potentially viable processes for research and development in bulk nanostructured metallic materials. For these reasons, this book includes only those processing methods that could be serious candidates for producing nanostructured metallic materials in the near future. This book introduces several promising processing approaches for nanostructured metallic materials, which include 1) solid deformation processing: equal channel angular pressing (ECAP), high pressure torsion (HPT), accumulative roll-bonding (ARB), mechanical attrition (MA) and mechanical machining process (MM); 2) solid reaction processing: ultrafine bainite or pearlite structure in carbon steels using a combination of deformation and thermal reaction; and 3) liquid– solid transformation: involving a transformation from liquid to solid phases, e.g. from the molten phase to metallic glass and subsequently to crystallization; electrodeposition processing; and thermal spray processing, from molten droplets to solidified droplets containing nanograins.

Severe plastic deformation processes Historically, a large plastic deformation and the resulting microstructural refinement in metals and alloys have been investigated by a number of researchers.8–11 Nevertheless, the concept of relating severe plastic deformation (SPD) to ultrafine microstructure as well as unique properties has been put to test by Valiev and co-workers in the 1980s and thereafter,12–14 which has contributed to the popularization of current SPD technology for nanostructured metallic materials. Both high pressure torsion (HPT) pressing and equal channel angular pressing (ECAP)11 use the same principle: that hydrostatic pressure permits a very large shear deformation in ductile metals, at a strain as high as strain of 4–5, which translates into the dislocation density up to 1014–17 mm–1.15,16 Repeating the process cycle in SPD results in ultrafine grains (100–300 nm). On the other hand, although the ARB process as another form of SPD generates fine-grained microstructure by a large accumulative deformation similar to ECAP, the approach is substantially different in that in ARB processing,17,18 a very large accumulative deformation is applied to a thin sheet by a series of repetitive fold-and-roll processes without hydrostatic pressure where the surfaces of sheets in the folded sides convert to grain boundaries by cold welding. In the processing, the ultrafine grain refinement occurs by the introduction of new grains in the old grains during dynamic recovery and post annealing. Both ARB and ECAP deformation generate new grains of high angle grain boundaries, and the fraction of such boundaries increases with an increasing number of cycles. ARB is particularly advantageous for producing a sheet form of nanostructured metallic material.


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There are many roadblocks in the way of ECAP and HPT becoming industrially viable processes. They include the inability to produce the desired dimensions – length, width and thickness of continuous bulk forms – at this stage. Nevertheless, in one area, the wire processing by a large acumulative deformation is successful in producing the required dimensions. For example, a fine wire of Mn steel is made by drawing 10 mm diameter rods of a dual-phase microstructure of martensite and ferrite and of the composition of Fe-0.2C-0.8Si-1Mn (wt-%) into individual strands of 8 µm diameter wire. This wire drawing amounts to a huge deformation of a true strain in excess of 9. The dislocation cell size in the deformed wires is found to be 10–15 nm.19,20 Another form of SPD is mechanical attrition, which is basically high impact ball-milling, and produces very large plastic deformation. Although an initial development aimed to produce new alloys by mechanical alloying,21 the same technique can be employed to produce microstructural refinement. In the process, metallic powders undergo fracture and plastic deformation in which the powders can form mechanical alloying or generate nanoscale microstructures such as fine grains or fine precipitates. The deformed nanograins in this process exhibit deformation shear bands22 like any other highly deformed nanograins produced by other processing techniques. Nevertheless, these nanostructured powders are not a final product, but a precursor material. The nanopowders may be consolidated into nanostructured bulk materials or they can be sprayed for nanostructured coatings. Consolidating powders into a bulk material is a challenging process because of pores or oxides or other potential contamination introduced into the matrix, some of which are produced during milling and consolidation; and second, these precursor powders undergo microstructural coarsening or grain growth during thermal consolidation. A recent approach using a cryogenic atmosphere in mechanical attrition shows clear improvement in effective milling and a reduction in contamination.23 SPD metals with UFG can be produced by a conventional machining process, whose microstructual refinement mechanisms have been known for some time. The grain size produced in machining depends on processing parameters, but it can be as low as 200 nm. Besides, the machining can produce bulk forms of UFG products such as foils, sheets, or rods, directly from the coarse-grained bulk metals.24 The challenging aspect of this approach is to control the microstructure via machining parameters such as strain, strain rate and temperature throughout the entire operation. Alternatively, individual UFG chips produced can be consolidated into a bulk form by various consolidation techniques, which are still in the early stage of development.

Solid reaction processes Nanomicrostructures other than nanograin structures can be generated and produced in a controlled manner by thermal reaction and diffusion. One recent interesting approach is to examine the possibility of creating nanostructure in


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conventional high-strength steel material, which is difficult to process using conventional SPD approaches due to its high flow stresses. In the past, bainite steels have been in use for a long time, and the nucleation and kinetics of bainite formation have also long been understood. In another recent approach, the bainite reaction can be made to produce nanoscale bainitic ferrite plates (20–40 nm) by heat-treating bainite steel at relatively low temperatures for a longer duration. This is only possible in steels with a relatively high concentration of carbon. For example, in Fe-0.78-0.98 C-Si-Mn-Cr-Mo alloys, an enhanced nucleation of ferrite in austenite after supercooling is possible at the low temperatures (125–325oC) for one to six days’ holding time during which grain growth is suppressed.25,26 This type of steel containing nanostructures exhibits an extremely high strength comparable with that of maraging steels. The advantage of bainite steels over martensitic steels is that martensite steel has limited dimensionality due to the fact that it needs a high cooling rate to produce martensite, while nanoscale bainite steels can be produced in larger dimensions due to their flexible heat treatment requirements and no requirement of high cooling. Highsilicon bainite steels also exhibit a combination of high strength and toughness.26

Liquid–solid transformation processes Liquid–solid transformation processes have two different approaches. First, a molten alloy is solidified into an amorphous phase, from which nanocrystalline precipitates or nanograins can be produced by controlled heat treatment for crystallization.27 The amorphous matrix turns into partially or fully nanocrystalline matrix depending on heat treatment conditions. The maximum dimensions of a bulk amorphous metal, however, are limited due to the fact that 1) a critical cooling rate is required for amorphous formation and 2) each alloy has its own glass forming ability. The second process includes thermal spray coating, in which the feed material is melted and broken into fine droplets before solidifying on the substrate surface. In this process, the stability of the molten phase is important during melting and flight.28 The feedstock could be powders or solid wires. A general rule of thumb is that any material that has a stable molten phase and can be processed into the appropriate feed specifications, can be thermal sprayed. The heat source used to heat and accelerate the feedstock is generated either chemically via oxygen-fuel combustion or electrically via an arc.

Mechanical properties One of the most pronounced mechanical properties of nanostructured metals is their extraordinary high yield strength compared to those of conventional coarsegrained metallic materials. But, the downside of this material is its well-known poor ductility. Earlier efforts to test the strengthening behavior of nanometals with respect to grain size led to the discovery of a breakdown of the Hall–Petch (H–P)


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relationship.29,30 This unexpected behavior was identified as the ‘inverse H–P relationship’. Since then, this unexpected softening behavior of nanostructured metals has been a subject of intensive research and the center of discussion. Furthermore, not only is strain hardening (the result of characteristic dislocation pile-ups in coarse-grained metals) absent in nanostructured metals with grain size less than approximately 20 nm, but also any dislocation pile-up in nanograins has not been observed using high-resolution microscopy. Thus, in nanograined metals, grain boundary (GB) deformation has to be the main mechanism for plastic deformation, considering the fact that 1) nanograins become an inactive component in deformation, and 2) the volume fraction of grain boundary and triple junction under the single-digit grain size matrix could be anywhere from 10% to as much as 30%. For these reasons, the focus of research moved from grain deformation to grain boundary deformation for nanograined metals. For the last two decades, unique deformation mechanisms of nanostructured metals and alloys based on grain boundary deformation mechanisms have been investigated, in which each of different deformation modes such as tensile deformation, superplastic deformation, creep and fatigue failure has been studied separately to capture a complete picture of the deformation mechanisms. Research results on these subjects are presented and discussed throughout various chapters in Parts II and III of this book.

Strength and ductility The Hall–Petch relationship tells us that we could achieve strength in materials that is as high as their own theoretical strength by reducing grain size. Indeed, their strength continues to increase with decreasing grain size to approximately 20–30 nm where the strength peaks. Indeed, the peak yield strength of pure nanostructured copper with grain size approaching approximately 20 nm can reach as high as 800– 900 MPa 29,31–33 compared to 200 MPa for coarse-grained copper. But decreasing grain size beyond 20 nm reverses the H–P effect: in other words the material starts to soften instead of further strengthening. In general, nanostructured metals are characterized as having very high strength with poor ductility. In other words, the strength increase trades off with ductility in nanostructured metallic materials. As an exception, artifact-free nanocrystalline copper with a grain size of 30–60 nm was found to possess a very high yield strength, and good ductility such as a fracture strain of 0.06 to 0.12 (Eng).34,35 Such relatively ductile behavior of nanocopper may be explained by a number of models: dislocations stored in larger grains, grain boundary sliding, Coble creep (GB diffusion), localized shear microbands, twinning, etc. For nanostructured metals with a wide distribution of grain size, none of the above models can be excluded. But, when the grain size distribution is narrow and its median value is close to 20 nm or less, only grain boundary deformation modes, i.e. grain boundary sliding, grain boundary rotation or Coble creep must


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be considered since the grains are regarded as plastically non-deformable islands that are embedded in the network of grain boundaries. For nanostructured metals, it may be possible that all these GB deformation models are operating in an optimized manner.36 Another important factor is the effect of impurities on GB deformation. For example, nano-copper with contaminants does not exhibit such ductile behavior, probably due to the fact that the impurity has a negative influence on GB deformation, which is a subject of future investigation.

Deformation mechanisms In the past, tensile testing of nanostructured metallic materials has been performed with various grain sizes from the ultrafine scale to the nanoscale, as small as 10 nm in diameter. In addition, the samples prepared by different processing routes have contained different levels of atomic as well as macro defects. Thus, one must be careful in analysing and interpreting the experimental results from such diversified material sources. In fact, this has been a challenging aspect for investigating deformation mechanisms of nanostructured metals in the past. In general, the tensile deformation of nanostructured metals shows that the flow stress starts to decline right after yielding, indicating an absence of strain hardening behavior. This is an indicative of the fact that the dislocation pile-up doesn’t occur beyond the yield point in nanostructured metals. To explain this behavior, it is proposed that the number of dislocations in the pile-up continues to decline with decreasing grain size.37,38 Thus, there must be a critical grain size where a single Frank–Read source can operate in a grain. Near such a critical grain size, the dislocation pile-up would no longer occur due to the very high shear stress required for the generation of any additional dislocation, and consequently, the Hall–Petch relationship cannot be established. This would explain why the H–P relationship breaks down in nanostructured metals. For these reasons, dislocation pile-up mechanisms would no longer be useful for nanostructured metals with a grain size less than 20–30 nm. Thus, the focus has been shifted to grain boundary deformation in recent years. The fact that the volume percentage of grain boundary and triple junction significantly increases and reaches as much as 30% for a grain size less 10 nm makes GB deformation more significant. But the details of GB deformation in nanostructured metals are very complex. Furthermore, direct observation of deformation defect structures using high-resolution microscopy is scarce. Therefore, research into GB deformation mechanisms has largely taken two tracks: 1) developing theoretical approaches that are based on classical deformation models for superplasticity; 2) performing computer simulations based on molecular dynamics under various stress and temperature conditions. The theoretical approach is considered to test the predetermined framework against experimental measurements whereas MD simulations let atoms and groups of atoms play the game without knowing the outcome.


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From this prospect, MD simulations could provide insightful information about the process and mechanisms of plastic deformation. Since, in nanograined metals, tensile deformation, superplastic deformation and creep have a common thread, i.e. grain boundary deformation, it may be possible to develop a unified model that can describe these three deformation modes in the future. GB deformation models Although the three different deformation modes – time-independent deformation, superplasticity and creep–are connected through grain boundary deformation mechanisms, conceptually it can be said that each of the modes is made of different levels of contributions by stress-induced GB deformation and thermally-induced GB deformation. In general, it is understood that grain boundary sliding in nanostructured metals occurs by GB dislocations if dislocations are available under applied shear stress, and by thermally activated local shear events, which occur by uncorrelated individual atomic jumps and the movement of small groups of atoms. In particular, nanostructured metals are made of grains whose boundaries are not only nanoscale, but also in the non-equilibrium state (majority). Thus, thermally induced GB deformation becomes important in this type of materials. With such a conceptual background, Conrad et al.39 proposed that the macroscopic shear occurs due to thermally activated atomic shear in the nanograin boundary, i.e. GB sliding. Fu et al., following the idea of a neighbor-grainexchange mechanism in superplastic deformation by Raj et al.,40 introduced a plastic accommodation term to the thermal shear stress in Core–Mantle nanograins.41 The results show that the strain rate in nano-copper with grain size less than 10 nm at 300K could reach a significant level indicating that GB sliding would be real possibility under diffusional sliding with plastic accommodation. In recent years, Wang et al.42 suggested that grain rotation and grain coalescence in the direction of shear would be possible during plastic deformation. Ovid’ko demonstrated that such a rotation of grains could be indeed possible by creating disclinations during such a rotation.43 Furthermore, Murayama et al.44 reported that TEM images from a milled Fe sample showed a partial disclination dipole. Another deformation structure reported was shear band formation as a localized deformation mode in ultrafine-grained iron.45 Another important issue is non-equilibrium GB,46 which is a center of dislocation sink and generation. The fraction of non-equilibrium boundary increases with decreasing grain size. It is important to understand the role of the non-equilibrium GB in deformation. For example, 1) the emission of partial dislocations from triple junctions and non-equilibrium GB as part of the accommodation mechanisms to local shear events would trigger the formation of stacking faults and twins in nanograins, and 2) non-equilibrium GB acts as a dislocation sink and may assist dynamic recovery during deformation. Despite the


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limited success of analytical models, it is not possible to understand the complex dynamic process of GB sliding by analytical modeling as the process is characterized by the evolution, annihilation and mutual interaction of various defect structures in the process. MD simulations Scientists have often been unable to observe the evolution of deformation microstructure on an atomic scale by high-resolution microscopy. In the past, numerous interesting pieces of defect structures in nanostructured metals have been reported. On the other hand, regular mechanical testing continues to generate a large volume of experimental results that were usually not provided with the related microstructures. Therefore, to establish the property–structure relationship, computer simulations must play a crucial role in bridging the two different types of observation. In addition, other unexpected microstructural evidence that has been observed needs to be explained by theory or demonstrated by MD simulations. For example, some interesting microstructures observed by highresolution microscopy include stacking faults, twins in face-centred cubic (fcc) metals such as Al, Cu with high stacking faults energy, stacking fault tetrahedral, and disclinations. The challenging task is to understand why these defect structures are present only in nanostructured metals. To answer these questions, numerous theoretical models and computer atomic simulation techniques have been employed. In the early stage of investigations, for example, finite element (FE) simulations by Kim et al.47 were used to reproduce experimental tensile test results as well as the H–P plot for nano-Cu with grain size of 10–1000 nm. Kim used a ‘phase mixture mode’ in which nanomaterial consisted of two distinctive phases: initially dislocation-free crystalline matter at the center and the surrounding grain boundary (amorphous-like). Thus, during simulations, the dislocation pile-up was allowed in the crystalline matter while diffusional flow occurred in the grain boundary. The H–P plot generated by this scheme is in good agreement with experimental data. Nevertheless, FE simulations are not equipped to investigate the role of various defects in GB deformation or to predict the evolution of unexpected defect structures. In recent years, however, molecular dynamic (MD) computer simulations have demonstrated that they are powerful tools in investigating the deformation mechanisms in nanostructured metals. For example, twinning in deformed nanostructured Al was predicted by MD simulations,48 and was confirmed later by experiment.49 The deformation mechanisms in both time-dependent and time-independent deformation have been studied by MD simulations in the past. For time-dependent deformation, MD simulations have been focused on grain boundary diffusion, grain boundary sliding and emission of dislocations, particular partial dislocations and twins from grain boundaries.


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Despite their inherent deficiencies (see Chapter 15), MD simulations have already made a significant contribution in elucidating deformation mechanisms of nanostructured materials this decade. Such important events by MD simulations this decade include 1) confirmation of the inverse Hall–Petch relationship;50 MD models reasonably explained the transition from the hardening mode to the softening mode in nanostructured metals using two competing mechanisms: grain boundary mediated mechanisms (GB sliding, diffusion)51,52 and transgranular dominant mechanisms (dislocation slip, twinning, etc.) depending on grain size; 2) MD simulations showed the existence of Coble creep in nanostructured metals at relatively low temperatures;53 3) elucidating grain boundary-mediated deformation mechanisms in which the Shockley partial dislocations emitting from triple junction and GB are also a part of GB sliding.51,54 Yet, there are unresolved problems regarding the fundamental understanding of GB sliding mechanisms. There are two views: either stress-induced free-volume migration or stress-induced long-range atomic migration (diffusion) causes the deformation of nanograined metals. The fact that both GB sliding and GB diffusion are influenced by applied stress and temperature makes it difficult to separate one from the other. Second, such MD simulations that have been performed on fcc metals are not or almost not available for other crystal structures such as body-centred cubic (bcc), hexgonal close packed (hcp) and tetragonal structures. Thus, it is desired to have MD simulations for other nanostructured metals with different crystal structures other than fcc in the future.

Superplasticity and creep Both superplasticity (SP) and creep were observed in nanostructured metallic materials and in course grained metallic materials. The differences between the two deformation modes lie in the loading conditions: applied stress, strain rate, time duration and temperature. Nevertheless, the main deformation mechanism for both deformation modes remains in the grain boundary deformation regime. Since SP deformation occurs at higher strain rates and higher stresses while creep occurs under relatively low applied stress for a longer time frame, diffusion carries out the bulk of grain boundary deformation. One of the theories about GB sliding in SP deformation is that GB sliding is an operation of the sliding and rotation of entire grain groups along common sliding surfaces. The evidence of such a group sliding is the existence of steps along shear planes on a surface of post-deformed materials. Such ‘cooperative grain boundary sliding’ (CGBS) was observed indirectly in Ni3Al,55 Pd56 and directly in Nano-Ni3Al.57 For example, Ti-6Al-4V with a grain size 100–200 nm deformed at 725° at a strain rate range 10–1 to 10–3 s–1 yielded an elongation more than 500%, which is much higher than that in the microcrystalline state.58 It is logical to assume that higher diffusion flux as a component of CGBS in nanostructured metallic materials would assist GB sliding while lack of intragranular dislocation activity in nanostructured


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metallic materials (NMM) may negatively influence the grain boundary sliding. But, the fundamental classical mechanisms for SP and creep appear to remain in NMM. Understanding of SP and creep mechanisms must start with an understanding of the GB sliding mechanisms in NMM. Nanostructured Ni (20–40 nm grains) exhibits creep at RT. The test results well fit into the models of grain boundary sliding aided by grain boundary diffusion.59,60 Yin et al.61 studied the creep of nano-Ni from RT to 473 K. The activation energy calculated from the temperature dependence curve was 92 kJ/mol, which is activation energy for GB diffusion in Ni. Thus, at the moment, both grain boundary sliding and grain boundary diffusion can be considered as candidates for creep in nano-Ni in the temperature range RT to 473k. On the other hand, Yamakov et al.53 performed MD simulations for nano-Pd at elevated temperatures under high stresses assuming no grain growth. The results show that the creep was characterized as a Coble-type creep and GB sliding is an accommodating mechanism for the creep. The simulations showed a linear dependence of the creep rate with the applied stress. But, the linear relationship was unable to extrapolate to a low temperature regime, e.g. RT. The questions remain whether conditions of high stress and high strain rates at high temperatures used in the simulations can duplicate the real creep situation under low stress, low strain rate at low temperatures because different conditions would alter deformation mechanisms. It would take for a while for MD simulations to carry out creep deformation under reasonable conditions, because currently the limitations imposed on the computations are too severe. Another complication in analysing experimental data for creep is that in fact grain growth occurs in nanometals even at relatively low temperatures where the time duration for creep testing is significant for grain growth. Although both GB diffusion and GB sliding are an integral part of the creep, it is difficult to determine which is the dominant mechanism for a given stress and temperature at this time.

Fatigue Investigating the fatigue behavior of nanograined metals has rarely been done, mainly due to inadequate nanomaterial supply, and thus the majority of investigation has been focused on ultrafine-grained (UFG) metals and alloys with a grain size range of 100 nm–1 µm.62 Nevertheless, an interesting earlier piece of work on fatigue in nanostructured Ni was reported by Hanlon et al.63 In the report, nanocrystalline (NC) Ni was compared with UFC Ni and microcrystalline (MC) Ni with respect to its stresslife (S-N) fatigue behavior. NC Ni sheets with grain size 20 to 40 nm and UFC Ni sheets with grain size 300 nm were prepared by electrodeposition technique. The results show that the endurance limit significantly increased from MC Ni to both UFC Ni and NC Ni. There is no appreciable difference between NC Ni and MC Ni in terms of fatigue resistance. However, the fatigue growth rate of NC Ni is


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higher than that of UFC Ni, and much higher than that of MC Ni. Depending on the grain size, the refinement has a negative influence on fatigue crack growth resistance. Despite some preliminary evidence for the fatigue properties of nanometals, it is critical to conduct similar experiments with specimens of artifactfree and controlled impurity concentration at GB to confirm these results. It is too early to draw conclusions with only limited information. Fatigue life based on a S-N plot for pure UFG metals – copper, nickel and aluminum – has been investigated. The results show a significant increase in fatigue life in all these UFG metals compared to those of the counterpart coarsegrained metals, primary due to the increase in strength in UFG metals. Nevertheless, when fatigue life is regarded with respect to the plastic strain amplitude. UFG metals exhibit a deteriorated fatigue life compared to their coarse-grained counterparts. For UFG metals crack initiation is mostly a result of shear band formation and localized plastic deformation along these shear bands. Shear band formation appears to be the dominant mechanism to SPD-processed materials at this grain size range.64 But the key is the history of material processing, which would determine the microstructural characteristics and in turn has an influence on fatigue life. For example, SPD-processed UFG metals with a post-heat treatment result in a bimodal microstructure, which has a positive influence on fatigue life.65

Applications In the coming decades, structural applications will require energy efficient materials, e.g. with high specific strength, light weight and excellent durability. From this vantage point, nanostructured metals should have a bright future. Nevertheless, the development of products requires long-term commitment by the industry, and the odds that a product under development successfully makes it into the marketplace are still statistically quite low. Currently, a few products of nanostructured metallic material have found their way into the marketplace. For example, nanosurface coatings for corrosion protection and wear-resistant applications that are processed by electrodeposition, thermal spray and cold spray are already available for special applications. New nanostructured coating of cobalt-phosphorus alloy,66 as alternative to conventional hard chrome coating, shows excellent wear and corrosion properties. Due to growing environmental concern about the health risks of hexavalent chromium, this alternative looks attractive for practical applications. Thermal spraying of hard metals such as WC-Co67 and Ti-oxide, NiCrAlY62 by the high-velocity Oxyfuel (HVOF) processing yields high dense nanostructured coatings for wear and corrosion applications. Nowadays, the structural materials for aerospace and automobile applications and any other applications that are tied to power consumption are increasingly required to be energy efficient. Riding the trend, there is considerable effort to develop nanostructured steels that will meet such demands. But current effort has


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been focused on ultrafine-grain (UFG) ferrite single-phase steels,69,70 multi-phase steels,71 and nanostructured Bainite steels.25 UFG ferrite steel can be processed by hot rolling, followed by cold rolling in a conventional way, and the rolled sheets recrystallized at 525–700°C for two minutes in a salt bath. This UFG ferrite steel has been further developed into UFG-multi-phase steel to optimize the strength and ductility balance for highstrength automobile body applications. The multi-phases in this steel include austenite, bainite and martensite, in addition to ferrite grains. For very high strength structural applications, nanostructured bainite steels containing Si, Mn and Cr would be economically attractive compared to expensive maraging steels. These bainite steels have a yield strength of 1.4 GPa, a tensile strength of 2.2 GPa and fracture toughness (K1c) of 25 MPam1/2 at room temperature. Other ultrafine-grained steel materials come in bar, wire and strip form.72 Ultrafine-grained bars of low-carbon steel can be processed by multiple caliber rolling at 550°C and water quenching. Ultrafine-grained wires were made using a starting wire of 6 mm in diameter and by oval-square rolling repeatedly at 500°C until its diameter was reduced to 3 mm. The UF wires show a yield strength of more than 800 MPa, compared to that of the starting wire of 400 MPa. All these steels are some of the examples currently under development.

References 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19

Gleiter H. Prog Mater Sci 1989;33: 223. Gleiter H. Acta Mater 2000;48: 1–29. Guinier, A., Preston, D.A. Nature 1938;142: 569–570. Embury J.D., Fisher R.M. Acta Metall 1966;14: 147–159. Valiev R.Z., Langdon T.G. Prog Mater Sci 2006;51: 881. Koch C.C., editor, Nanostructured Materials – processing, properties and applications, Noyes publications, William Andrew Publishing, Norwich, New York (2007). Meyers M.A., Mishra D.J., Benson D.J. Prog Mater Sci 2006;51: 427–556. Erbel S. Metals Tech 1979;6: 482. Langford G., Cohen M. Trans. ASM 1969;82: 623. Saunders I., Nutting J. Metal Sci 1984;18: 571. Segal V.M., Mater Sci Eng 1995;A197: 157. Valiev R.Z., Kaibyshev O.A., Kuznetsov R.I., Musalimov R.Sh., Tsenev N.K. Dokl Akad Nauk SSSR (Reports of USSR Academy of Sciences) 1988;301(4): 864. Valiev R.Z., Krasilnikov N.A., Tsenev N.K. Mater Sci Eng A 1991;137: 35. Valiev R.Z., Korznikov A.V., Mulyukov R.R. Mater Sci Eng A 1993;186: 141. Valiev R.Z., Islamgaliev R.K., Alexandrov I.V. Prog Mater Sci 2000;45: 103. Ungár T., Balogh L., Zhu Y.T., Horita Z., Xu C., Langdon T.G. Mater Sci Eng A 2007;444: 153. Saito Y., Utsunomiya H., Tsuji N. and Sakai T. 1999;47: 579. Tsuji T., Saito Y., Lee S.H., and Minamino Y. Adv. Eng. Mater, 2003;5: 338. Bhadeshia H.K.D.H. High strength steels. In Charles J.A., Greenwood G.W., Smith G.C., editors. Future Developments in Metals and Ceramics, London, Institute of Materials, 1992. p.25.


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Bhadeshia H.K.D.H., Harada H. Appl Sur Sci 1993; 67: 328. Benjamin J.S. Metall Trans 1970;1: 2943. Fecht H.J., Hellstern E., Fu Z., Johnson W.L. Metall Trans A 1990;21: 2333. Perez R.J., Huang B., Lavernia E.J. Nanostructure Mater 1996;7: 565. Brown T.L., Saldana C., Murthy T.G., Mann J.B., Compton W.D., Trumble K.P., King A.H., and Chandrasekar S. Acta Mater 2009;57: 5491. Caballero F.G., Bhadeshia H.K.D.H., Mawella J.A., Jones D.G., Brown P. Mater Sci Technol 2002;18: 279. García-Mateo C., Caballero F.G., Bhadeshia H.K.D.H. ISIJ Int 2003;43: 1238. Perepezko J.H. and Hebert R.J., J Metall 2002;5: 34. Kim G.E. Thermal Sprayed Nanostructured Coatings: Applications and Developments. In Koch C.C., editor, Chapter 3, Nanostructured Materials Processing, Properties, and Applications, 2nd Edition, William Andrew Publishing, 2007. Chokshi A.H., Rosen A., Karch J., Gleiter H. Scripta Mater 1989;23: 1679. Fougere G.E., Weertman J.R., Siegel R.W., Kim S. Scripta Metall Mater 1992;26: 1879. Embury J.D., Keh A.S., Fisher R.M. Trans Metall Soc AIME 1966;236: 1252. Hansen N., Ralph B. Acta Metall 1982;30: 411. Nieman G.W., Weertman J.R., Siegel R.W. Scripta Metall 1989;23: 2013. Youssef K.M., Scattergood R.O., Murty K.L., Horton J.A., Koch C.C. Appl Phys Lett 2005;87: 091904. Cheng S., Ma E., Wang Y.M., Kecskes L.J., Youssef K.M., Koch C.C., Trociewitz U.P., Han K. Acta Mater 2005;53: 1521. Ovid’ko I.A., Sheinerman A.G. Acta Mater 2009;57: 2217. Pande C.S., Masumura R.A., Armstrong W. Nanostruct Mater 1993;2: 323–331. Nieh T.G., Wadsworth J. Scripta Metall Mater 1991;25: 955–958. Conrad H., Narayan J. Scripta Mater 2000;42: 1025. Raj R., Ashby M. J Met Tans 1971;2A: 1113. Fu H.H., Benson D.J., Meyers M.A. Acta Mater 2001;49: 2567–2582. Wang Y.M., Ma E., Chen M.W. Appl Phys Lett 2002;80: 2395–2397. Ovid’ko I.A. Science 2002;295: 2386. Murayama M., Howe J.M., Hidaka H., Takaki S. Science 2002;295: 2433–2435. Wei Q., Kecskes L., Jiao T., Hartwig K.T., Ramesh K.T., Ma E. Acta Mater 2004;52: 1859–1869. Valiev R.Z., Islamgaliev R.K., Alexandrov I.V. Prog Mater Sci 2000;45: 103. Kim H.S., Estrin Y., Bush M.B. Acta Mater 2000;42: 493–504. Yamakov V., Wolf D., Phillpot S.R., Gleiter H. Acta Mater 2002;50: 5005. Chen M. et al. Science 2003;300: 1275. Kadau K. et al. Metall Mater Trans 2004; 35A: 2719. Shiiotz J., Di Tolla F.D., Jacobson K.W. Phys Rev B 1999;60: 11,971. Swygenhoven H.V., Spaczer M., Caro A., Farkas D. Phys Rev B 1999;60: 22. Yamakov V., Wolf D., Phillpot S.R., Gleiter H. Acta Mater 2002;50: 61. Swygenhoven H.V., Farkas D., Caro A. Phys Rev B 2000;62: 831. Zelin M.G., Mukherjee A.K., Acta Metall Mater 1995;45: 2359. Markmann J., Bunzel P., Rosner H. Scripta Mater 2003;49: 637. Sergueeva A.V., Mara N.A., Krasilnikov N.A., Valiev R.Z., Mukherjee A.K. Phil Mag 2006;86: 5797. Sergueeva A.V., Stolyarov V.V., Valiev R.Z., Mukherjee A.K. Mater Sci Eng A 2002;323: 318. Cai B., Kong Q.P., Cui P., Lu L., Lu K.. Scripta Mater 2001;45: 1407.


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60 Sanders P.G., Eastman J.A., Weertman J.R. Acta Mater 1997;10: 4019. 61 Yin W.M., Whang S.H. JOM 2005;1: 63. 62 Höppel H.W., Kautz M., Xu C., Murashkin M., Langdon T.G., Valiev R.Z., Mughrabi H.: Int J Fatigue 2006,28: 1001. 63 Hanlon T., Kwon Y.N., Suresh S. Scripta Mater 2003;49: 675–680. 64 Mughrabi H., Höppel H.W. In: Farkas D., Kung H., Mayo M., v. Swygenhoven H., Weertman J., editors. Structure and mechanical properties of nanophase materialstheory and computer simulation vs. experiment, Mat Res Soc Symp Proc Vol 634, Materials Research Society; 2001; p. B 2.1.1. 65 Höppel H.W., Valiev R.Z. Z Metallkunde 2002;93: 641. 66 Erb U., El-Sherik A.M. US Patent No. 5,352,266 (1994). 67 He J., Ice M., Dallek S., Lavernia E.J. Metall and Mater Trans A 2000;31A: 541. 68 Ajdelsztajn L., Picas J.A., Kim G.E., Bastian F.L., Schoenung J.M., Provenzano V. Mater Sci Eng 2002;A338: 33. 69 Tsuji N., Ito Y., Saito Y., Minamino Y. Scripta Mater 2002;47: 893. 70 Tsuji N., Okuno S., Koizum Y., Minamino Y. Mater Trans 2004:45: 2272. 71 Okitsu Y., Naito T., Takaki N., Sugiura T., Tsuji N. SAE Technical Paper 2010:201001-0438. 72 Ohmori A., Torizuka S., Nagai K., Koseki N., Kogo Y. Tetsu-to-Hagane, 8(2003): 781–788.


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1 Producing bulk nanostructured metals and alloys by severe plastic deformation (SPD) R.Z. VALIEV, Ufa State Aviation Technical University, Russia Abstract: Despite its promise, the use of nanostructured metals and alloys as a new generation of structural and functional materials has only recently been realized. Only in recent years has a breakthrough been made in this area, associated both with developing new methods for fabricating bulk nanostructured materials and with investigating the fundamental mechanisms that lead to novel properties in these materials. This chapter presents new concepts and principles in using severe plastic deformation (SPD) techniques to fabricate bulk nanostructured metals with advanced properties. Special emphasis is laid on analysing of the effect of the microstructural features of nanostructured materials fabricated by SPD on mechanical properties such as strength and ductility, fatigue strength and life, and superplasticity, as well as describing early examples of their innovative applications. Key words: bulk nanostructured materials, severe plastic deformation, advanced properties, strength and ductility, equal-channel angular pressing, high pressure torsion.

1.1

Introduction

The concept of ‘large plastic strains’, or deformations that are characterized by a high value of true accumulated strain (e ≥ 0.5) and are realized at relatively low temperature (≤ 0.4 melting point), is widely used in the branches of physics and mechanics that deal with the problems of strength and ductility of solid states.1–3 Large plastic deformations are actively engaged in practice, for example, in metal forming for shaping in the process of manufacturing semi-products and parts as well as for materials hardening. Traditionally, such methods of metal forming as drawing, extrusion, rolling and others are used for these purposes. Experimental methods for achieving very large strains are usually based on the rolling of strips or thin foils, e.g. with initial thickness of ~10 mm up to a final one of ~0.1 mm, which is equivalent to a 99% reduction in thickness (true strain e = 4.6). Therefore, true strains 4–4.5 are critical for shaping bulk billets by conventional metal forming methods, and as it was noticed in earlier works, the achievement of larger strains requires radically different processing techniques.4 It was suggested4,5 that such techniques may comprise the die-sets combining shear (torsion) and compression straining as they make it possible to deform the material without changing its form. Fracture in material is another problem encountered when achieving super-high strains. As is known, many metallic materials are exposed to quick fracture at room temperature even in the early stages of deformation. However, it is possible 3 © Woodhead Publishing Limited, 2011

4


to increase the deformability of metals and alloys by imposing hydrostatic pressure. The phenomenon was first studied in detail by P.W. Bridgman (Harvard University), who was awarded the Nobel Prize for Physics in 1946 for his works in the sphere of high pressure.6 In the 1980s these ideas were realized by Polish4 and Russian scientists from Yekaterinburg, (formerly Sverdlovsk, USSR)7 in creating experimental die-sets for combined torsion and compression. The application of these devices achieved very large strains with true strains exceeding 8–10, which resulted in strong grain refinement in metals. The basic work was performed by scientists in Ufa in 1988,8 where this method was demonstrated for the first time, of producing ultrafinegrained (UFG) metals and alloys with high-angle grain boundaries that led to new properties. The latter was evidenced by revealing the so-called ‘low-temperature superplasticity’ in an UFG Al alloy. Later, in 1991 UFG materials were first obtained by means of another technique – equal-channel angular pressing (ECAP),9 during which the billet shape is also preserved and therefore very large strains are achieved by multi-pass processing. As demonstrated below, ECAP allows the production of UFG structures in bulk billets from different metals and alloys. Moreover, the technique is very promising for practical applications. This new approach to grain refinement, based on the achievement of very large true strains with e ≥ 6–8 under high pressure, was termed ‘severe plastic deformation’ (SPD)10 and attracted much attention with the further development of many SPD techniques.11–13 Besides, SPD processing routes and regimes for grain refinement were established for various metals and alloys.14 More complete definitions of SPD processing and ultrafinegrained (UFG) materials are presented in several recent overviews.11,12,15,16 It is important to emphasize that SPD-produced UFG materials are fully dense and their large geometric dimensions make it possible to study their properties thoroughly by means of mechanical and other tests. As a result, the subject of bulk ultrafine-grained materials produced by severe plastic deformation was introduced into scientific literature. The next important step along with the formation of UFG was finding nanostructural features in SPD-processed metals (non-equilibrium grain boundaries, dislocation substructures, segregations and nanoparticles and other elements) resulting in novel properties16 (see also section 1.3.3, this chapter). At this time, the fabrication of bulk nanostructured materials by SPD is becoming one of the most actively developing areas in the field of nanomaterials.12,17 The present chapter considers new trends in the development of SPD techniques, basic requirements for processing nanostructured materials with enhanced properties by means of SPD, and prospects for their practical applications.

1.2

The principles of severe plastic deformation (SPD) processing

Since the pioneering work on tailoring ultrafine-grained structures by SPD processing,9,10 two SPD techniques have attracted close attention and have


Producing bulk nanostructured metals and alloys by SPD

5

recently been further developed. These techniques are high-pressure torsion (HPT)16,18 and equal-channel angular pressing (ECAP).16,19 In the last 10 to 15 years there have appeared a wide diversity of new SPD techniques: for example, accumulative roll bonding (ARB), multi-axial forging, twist extrusion and others (see other chapters for details). Nevertheless, processing by HPT and ECAP has remained the most popular approach and has recently acquired a new impulse for development through the modification of conventional die-sets and demonstrations that new opportunities are now available for involving these procedures in processing (see References 15, 18, 19). The fundamental principles of these two techniques are illustrated schematically in Fig. 1.1. Samples processed under HPT are disc-shaped (Fig. 1 (a) ). In this process, the sample, with a diameter ranging from 10–20 mm and thickness of 0.3–0.8 mm, is placed between anvils and compressed under an applied pressure (P) of several GPa. The lower anvil turns and friction forces lead to a shear straining of the sample. Under high pressure, the deforming sample does not break even at high strains.16 In HPT, an essential microstructural refinement is observed after deformation through one-half or one complete (360°) turn. But to produce a homogeneous nanostructure, with a typical grain size of about 100 nm or less, deformation by several turns is necessary (Fig. 1.2). The important role of applied pressure in the formation of a more homogeneous nanostructured state during HPT is also shown in recent work on nickel.20 Among different SPD techniques, HPT particularly

1.1 Principles of severe plastic deformation: (a) High-pressure torsion: a sample is held between anvils and strained in torsion under an applied pressure (P); (b) Equal-channel angular pressing: a work piece is repeatedly pressed through a special die.


6


1.2 Transmission electron microscopy images of ultrafine-grained copper: (a) Copper processed by HPT at room temperature (P = 6 GPa, 5 turns); (b) Copper processed by ECAP (12 passes).

enables a refinement of the microstructure with maximum efficiency and often forms a UFG structure with a grain size less than 100 nm.16,18 For this reason, HPT is now widely used as an experimental technique for grain refinement in different laboratories all over the world. Moreover, in recent years it has been further developed by enlarging the size of specimens21,22 and by processing ringshaped samples23. Processing by ECAP (Fig. 1.1 (b) ) is now also the most established procedure for use with different metals and alloys and it is a very attractive technique for several reasons. First, it is relatively easy to set up and use an ECAP die. Second, exceptionally high strains may be imposed either through repetitive pressing of the same sample or by developing special multi-pass dies,24 rotary dies25 or sideextrusion facilities.26 Third, although ECAP is generally used with samples in the form of bars or rods, the process may be applied also to plate samples: for example, a recent report described the application of ECAP to an aluminum plate.27 Fourth, ECAP can be incorporated into conventional rolling mills for use in continuous processing28–31 or into the ECAP-conform process for the production of longsized rods and wires.32 In view of these many advantages, special attention has been paid recently to the principles of processing through the use of ECAP (see the reviews16,19,33). The ECAP technique was introduced by V. Segal et al. in 1981 as a technique for straining by a simple shear,34 however, as noted above, it was developed and first applied for producing UFG metals only in the early 1990s.9,10 Figure 1.3 shows a schematic illustration of the ECAP procedure.35 A die is constructed containing a channel that is bent through an abrupt angle – this angle is 90° in Fig. 1.3. A sample is machined to fit in the channel and the sample is then pressed through the die using a plunger. It is apparent from the illustration that the sample has the same cross-sectional dimensions before and after pressing, thereby



7

1.3 The principle of ECAP processing, including a definition of the three orthogonal planes X, Y and Z.35

permitting repetitive pressings of the same sample. It is important to note also that retaining the same cross-sectional area differentiates processing by ECAP in a very significant way from more conventional industrial processes, such as rolling, extrusion or drawing, where the sample dimensions are reduced in each consecutive pass. Three orthogonal planes are illustrated in Fig. 1.3, where X is the transverse plane perpendicular to the flow direction, Y is the flow plane parallel to the side face at the point of exit from the die and Z is the longitudinal plane parallel to the top surface at the point of exit from the die. The strain imposed on the sample in each passage through the die depends primarily upon the angle, Φ, between the two parts of the channel (90° in Fig. 1.3) and also to a minor extent upon the angle of curvature, Ψ, representing the outer arc of curvature where the two channels intersect (0° in Fig. 1.3). To achieve optimum results, ECAP is generally conducted using a die having a channel angle of Φ = 90°19,36 and with this configuration it can be shown from first principles that for these angles the imposed strain on each pass is approximately equal to 1 with only a small, and almost insignificant, Ψ depending upon the arc of curvature.34,37


8


1.4 The four processing routes in ECAP.24

When samples are pressed repetitively, different slip systems may be introduced by rotating the samples about the X-axis between consecutive passes through the die. In practice, four separate processing routes have been identified for use in ECAP: route A in which the sample is pressed repetitively without rotation between passes; route BA in which the sample is rotated through 90° around the extrusion axis in alternate directions between each pass; route BC in which the sample is rotated by 90° in the same sense between each pass; and route C where the sample is rotated by 180° between passes.38 These different processing routes are illustrated schematically in Fig. 1.4 and the distinction between these routes is important because the various routes introduce different shearing patterns into the samples39 leading to variations both in the macroscopic distortions of the individual grains in polycrystalline matrices40 and in the capability to develop a reasonably homogeneous and equiaxed ultrafine-grained microstructure.16,19,41–43

1.3

New trends in SPD processing for effective grain refinement

1.3.1 Development of SPD techniques and routes Since high-pressure torsion and equal-channel angular pressing were first used to produce UFG metals and alloys,9,10 processing regimes and routes have been established for many metallic materials, including some low-ductility and hardto-deform materials. High-pressure torsion and ECAP die sets have also been essentially modernized.19,44,45



9

However, to date these techniques have been usually used for laboratory-scale research. The requirement of economically feasible production of ultrafine-grained metals and alloys essential to successful commercialization raises several new problems in the development of the SPD techniques. Highest priority tasks include reducing the material waste, obtaining uniform microstructure and properties in bulk billets and products, and increasing the efficiency of SPD processing. The solution for these tasks has been found by developing continuous ECA pressing32 and multi-step combined SPD processing46,47 for fabrication of longsized rods aimed at setting aimed at setting up production of nanostructured Ti materials for medical applications48 and, later, other metals. Some recent results of these works are presented below. Continuous equal-channel angular (ECA) pressing So far, of all SPD techniques, equal-channel angular pressing (ECAP), also known as equal-channel angular extrusion (ECAE),49 has attracted most attention, because it is very effective in producing UFG structures and can be used to produce UFG billets that are sufficiently large for various structural applications.16,19,44,45 However, the ECAP technique in its original design has some limitations, in particular, a relatively short length of work piece that makes ECAP a discontinuous process with low production efficiency and high cost. In addition, the ends of a work piece usually contain non-uniform microstructure or macro-cracks and have to be thrown away, thus a significant portion of the work piece is wasted and the cost of the UFG materials produced by ECAP is further increased. The key to wide commercialization of UFG materials is to lower their processing cost and waste through continuous processing. Several attempts have been made to this end. For example, repetitive corrugation and straightening50,51 have been developed recently to process metal sheets and rods in a continuous manner. The co-shearing process28 and the continuous constrained strip shearing process29 were recently also reported for continuous processing of thin strips and sheets with UFG structures. However, the question of further improving microstructure uniformity and properties remains topical in the development of these techniques. In our studies we have worked on combining the Conform process52 with ECAP to continuously process UFG materials for large-scale commercial production.32 In this invention, the principle used to generate frictional force to push a work piece through an ECAP die is similar to the Conform process, while a modified ECAP die design is used so that the work piece can be processed repetitively to produce UFG structures. We have designed and constructed an ECAP-Conform set-up that is schematically illustrated in Fig. 1.5. As shown in the figure, a rotating shaft in the center contains a groove, into which the work piece is fed. The work piece is driven forward by frictional forces on the three contact interfaces with the groove, which makes the work piece rotate with the shaft. The work piece is constrained to the groove by a


10


1.5 A schematic illustration of an ECAP-Conform set-up.

stationary constraint die. The stationary constraint die also stops the work piece and forces it to turn an angle by shear as in a regular ECAP process. In the current set-up, the angle is about 90°, which is the most commonly used channel intersection angle in ECAP. This set-up effectively makes ECAP continuous. Other ECAP parameters (die angle, strain rate, etc.) can also be used. In our recent work32 we used commercially pure (99.95%) coarse-grained long Al wire with a diameter of 3.4 mm and more than 1 m in length for processing at room temperature with 1–4 passes using ECAP with route C, i.e. the sample was rotated 180° between ECAP passes. The starting Al wire had a grain size of 5–7 µm. Figure 1.6 shows an Al work piece at each stage of the ECAP-Conform process, from the initial round feeding stock to rectangular Al rod after the first ECAP pass. As shown, the rectangular cross-section was formed shortly after the wire entered the groove (see the arrow mark). The change is driven by the frictional force between the groove wall and the Al work piece. The frictional force pushes the wire forward, and deforms the wire to make it conform to the groove shape. After the wire cross-section changes to the square shape, the frictional force per unit of wire length increases because of the greater contact area between the groove and the wire. The total frictional force pushes the wire forward from the groove into the stationary die channel, which intersects the groove at a 90° angle. This part of the straining process is similar to that in the conventional ECAP process. Transmission electron microscopy observations have shown that the ECAPConform has led to microstructure evolution typical of the ECAP process.41,53 Figure 1.7 clearly indicates that the ECAP-Conform process can effectively



11

1.6 An Al work piece in the process of ECAP-Conform.

1.7 A TEM micrograph from the longitudinal section of Al wire processed by ECAP-Conform with four passes.

refine grains and produce UFG structures in Al and now in CP (commercially pure) Ti.45 The tensile mechanical properties of the as-processed Al samples after 1 to 4 passes are listed in Table 1.1. It is obvious that the ECAP-Conform process has significantly increased the yield strength (σ0.2) and the ultimate tensile strength (σu),


12


Table 1.1 Yield strength σ0.2, ultimate tensile strength σu, elongation to failure δ, and cross-section reduction (necking) ψ of Al samples processed with 1 to 4 passes Processing state

σ0.2, (MPa)

σu, (MPa)

Initial Al rod 47 71 After 1 pass 130 160 After 2 passes 140 170 After 3 passes 130 160 After 4 passes 140 180

δ, (%)

ψ, (%)

28 13 12 14 14

86 73 72 76 76

while preserving a high elongation to failure (ductility) of 12–14%. These results are consistent with those of Al processed by conventional ECAP.41 We also found that for Ti, the strength increased by more than twice after the ECAP processing as compared to the untreated Ti, and the same is true for Ti subjected to conventional ECAP. Thus, the newly developed continuous SPD technique, ECAP-Conform can successfully produce UFG materials. The continuous nature of the process makes it promising for producing UFG materials on a large scale, in an efficient and costeffective manner. However, further study is needed to investigate its ability with respect to grain refinement and properties improvement of various UFG materials. Combined SPD processing In solving the problem of fabrication of nanostructured Ti materials for medical applications, we showed the advantage of combining ECAP with other techniques of metal forming such as rolling, forging or extrusion.54,55 The advantages include effective shaping of long semi-products such as sheets, rods, etc as well as further enhancement of mechanical properties of UFG materials. For example, in Grade 2 CP Ti high-strength (YS = 980 MPa, UTS = 1100 MPa) with elongation to failure δ = 12% was attained using ECAP and extrusion. Also the results of investigations on processing of Ti rods of over 800 mm in length and 6.5 mm in diameter by a combination of ECAP and thermomechanical treatment including forging and rolling are very impressive.46,47 Figure 1.8 presents TEM micrographs of commercially pure (CP) Ti subjected to ECAP and thermomechanical treatment at 80%. It can be seen that combined processing results in significant additional grain refinement down to 100 nm in comparison with 300–400 nm after ECAP; however, a considerable elongation of grains takes place. Mechanical testing showed (Table 1.2) that in CP Ti, thermomechanical treatment after ECAP results not only in an increase in strength and recorded values of σ0.2 and σu, but also sufficient ductility is preserved. It is important that these strength values of nanostructured CP Ti are visibly higher



13

1.8 Transmission electron microscopy micrographs displaying the microstructure of Grade 2 Ti after ECAP + TMT, 80%: (a) cross section; (b) longitudinal section. Table 1.2 Mechanical properties of the Ti billets at different stages of processing State

σu, (MPa)

σ0.2, (MPa)

Initial 440 370 ECAP 4 passes 630 545 ECAP 4 passes + 1150 1100 TMT ε = 80%


δ, (%)

ψ, (%)

38 22 11

60 51 56

14


than that of the Ti-6%Al-4%V alloy, which is widely used in structural and medical applications. It is also interesting that the microstructure and properties of the obtained rods are rather uniform, the dispersion of mechanical properties along the rod length does not exceed ±5%.47

1.3.2 Processing of bulk nanocrystalline materials Since the first works dating back to the early 1990s9,10 severe plastic deformation techniques have been used mostly for coarse-grained metals in order to produce ultrafine-grained materials through microstructure refinement. The final grain size produced depends strongly on both processing regimes and the type of material. For pure metals the mean grain size is typically about 100–200 nm after processing by HPT (high-pressure torsion) and about 200–300 nm after processing by ECAP. For alloys and intermetallics the grain size is usually even finer and in some cases as fine as 50–100 nm. However, it is very important for fundamental tasks and many advanced applications to have bulk nanocrystalline materials with a mean grain size less than 30–50 nm. Is it possible to produce such materials using SPD techniques? In recent years this problem has become the object of special investigations and two approaches have been proposed:16;56 SPD consolidation of nanopowders and SPD-induced nanocrystallization of amorphous alloys. SPD consolidation Already in the early work on SPD consolidation of powders57,58 it was revealed that HPT with high pressures of several GPa can provide a rather high density close to 100% in the processed disc-type nanostructured samples. For fabricating such samples via high-pressure torsion, the consolidation of both conventional powders and powders prepared by ball milling can be used. HPT consolidation of nanostructured Ni and Fe powders prepared by ball milling57,58 can be taken as an example. The conducted investigations showed that the density of the samples processed at room temperature was very high and close to 95% of the theoretical density of bulk coarse-grained metals. After HPT consolidation at 200° or 400°C the samples’ density was even higher and reached 98%. Transmission electron microscopy examinations showed the absence of porosity. The mean grain size is very small; it is equal to 17 nm and 20 nm for Ni and Fe, respectively. It is also very interesting to note that the value of microhardness of the Ni samples produced by HPT consolidation was 8.60 ± 0.17 GPa, the highest value of microhardness mentioned in literature for nanocrystalline Ni. SPD-induced nanocrystallization Recent investigations also show that SPD processing can control crystallization of amorphous alloys that may result in the formation of bulk nanocrystalline



15

alloys with an ultrafine grain size and new properties.56,59 Recently this approach has also been used to produce and investigate nanocrystalline Ti-Ni alloys, widely known as alloys with shape memory effects. For this investigation, two alloys of the Ti-Ni system were used: melt-spun Ti50Ni25Cu25 alloy59,60 and cast Ti49.4Ni50.6 alloy.61,62 The amorphous structure of Ti50Ni25Cu25 alloy was confirmed by TEM and X-ray diffraction (Fig. 1.9 and 1.10).59,60 However, when the alloy was HPT-ed at room temperature, the x-ray diffraction still indicated the presence of an amorphous structure in the alloy, but TEM studies showed a structure full of nanocrystals with grain sizes of about 2–3 nm in it (Fig. 1.9 (c) ). The essential difference between this alloy in the amorphous state and in its HPT-ed state was revealed during subsequent annealing. As it can be seen in Fig. 1.10, the amorphous alloy was crystallized at 450°C, and formed a martensite phase B19 during cooling. The TEM micrograph of the alloy after annealing shows that the grain structure was rather non-uniform and contained a mixture of small grains and large grains with a size of about 1 micron (Fig. 1.9 (c) ). At the same time after HPT, crystallization occurs below 390°C and its micrograph shows a uniform nanocrystalline structure with a grain size of less than 50 nm (Fig. 1.9 (d) ).

1.9 Transmission electron microscopy image of rapidly-quenched alloy Ti50Ni25Cu25: (a) initial state (dark field); (b) after annealing at 450°C 10 min; (c) after HPT (dark field); (d) after HPT and annealing at 390°C 10 min.


16


1.10 X-ray diffraction patterns of the Ti50(Ni, Cu)50 alloy: (a) initial rapidly quenched alloy (1); after annealing at 300°C 5 min (2); after annealing at 450°C 5 min (3) with the phase B19; (b) alloy after HPT(1); after HPT and annealing at 300°C 5 min (2); after HPT and annealing at 400°C 5 min, with the phase B2 (3).

It is interesting to note that the structure after cooling was an austenitic B2-phase; in other words, imposing severe plastic deformation on the amorphous alloy resulted in its crystallization during heating and changed its phase composition after further cooling to room temperature. In the coarse-grained alloy Ti50Ni25Cu25, the temperature of martensite transformation upon cooling equals ~80°C, which explains why there is a martensite phase in the alloy at room temperature. In this connection, the existence of only an austenitic phase after HPT and nanocrystallization can be related to the martensite transformation retard in the alloy with a nanocrystalline grain size. This finding was previously reported in the literature for ultrafine-grained Ti-Ni alloys.63 For the alloy Ti50Ni25Cu25, the critical grain size for martensite transformation is about 100 nm, below which the martensite transformation does not take place at room temperature. The amorphous state in Ti49.4Ni50.6 alloy can be obtained directly as a result of HPT processing (P = 6 GPa, n = 5 revolutions).61,62 Subsequently, the homogeneous nanocrystalline structure was produced by annealing of the HPT-ed material (Fig. 1.11). For instance, after annealing at 400°C for 0.5 h the mean grain size was about 20 nm (Fig. 1.11 (a), (b), and after annealing at 500°C, it was about 40 nm (Fig. 1.11 (c), (d). It is worth mention that according to HREM observations, such annealing removed the amorphous phase and produced welldefined grain boundaries, though there were still small distortions of the crystal lattice near some of the boundaries.



17

1.11 Transmission electron microscopy micrographs of Ti49.4Ni50.6 alloy after HPT and annealing at 400°C (a, b) and at 500°C (c, d) for 0.5 h: (a, c) bright field images; (b, d) dark field images.

Tensile mechanical tests showed that the amorphous nitinol produced by HPT had much higher strength than at the initial microcrystalline state,61 but it was essentially brittle. Nanocrystallization results in the recorded value of yield strength for this material equal to 2650 MPa and an elongation to failure of about 5%. Thus, SPD consolidation of powders and SPD-induced nanocrystallization can be considered new SPD processing routes for fabricating bulk nanocrystalline materials. One of the advantages of these techniques is the possibility of producing fully dense samples with a uniform ultrafine-grained structure having a grain size less than 40–50 nm. Studies of the properties of these materials are of great interest for ongoing research because deformation mechanisms and, as mentioned above, phase transformations can essentially change the properties of materials with a small grain size.64,65

1.3.3 Basic rules for grain refinement For the formation of UFG structures with primarily high-angle grain boundaries through SPD processing, there have been defined five basic rules for grain refinement,66 four of which are related to the requirements for SPD processing regimes and routes while the fifth one is related to the intrinsic nature of the


18


material under study. These rules are briefly considered below. A detailed description of SPD processing regimes and routes may be found in recent overviews on the subject.16,18,19 1. SPD processing at low temperatures (as a rule, less than 0.4 Tm) is referred to as a rather important requirement for its realization. Only under these conditions is it possible to achieve dislocation densities of 1014 m–2 or higher, up to the limiting values of 1016–1017 m–2,16,67 which are necessary for the formation of the UFG structure. Higher processing temperatures result in a lower accumulated dislocation density and an increase in grain size to more than 1 micron. 2. The degree of strain during processing (true strain) should exceed 6–8. Although the considerable refinement of the microstructure and the attainment of dislocation densities exceeding 1014 m–2 occur at a strain of 1–2,16 the formation of UFG structure with a majority of high-angle grain boundaries requires further straining. 3. High hydrostatic pressures, usually >1 GPa, are important for efficient SPD processing. High pressure contributes to the enhancement of deformability of the processed material and therefore, provides solidity of the billets even under high strain.11,19 Furthermore, the pressure affects the diffusion and thus suppresses the annihilation of deformation-induced lattice defects.68 4. The formation of equiaxed ultrafine grains depends on the vorticity of the metal flow. At the macrolevel, the vorticity is related to the non-monotonous character of deformation. For example, the ECAP route BC, in which the billet is rotated by 90° between each pass, is considerably more effective for grain refinement in comparison with route C, in which the billet position does not change.19 At the microlevel, the vorticity is associated with grain rotations and displacements.69 5. Grain refinement is also related to the atomic structure of the material processed. The ordering of alloys or low-stacking fault energy (SFE), all other conditions being equal, contributes to the enhancement of accumulated dislocation density and considerably reduces the grain size produced.16 For example, in Pd-20%Ag alloy with SFE = 125 mJ·m–2, in comparison with pure Pd with SFE = 190 mJ·m–2, during HPT (5 rotations and P = 6 GPa), the grain size produced equals 150 nm for Pd-20%Ag and 240 nm for Pd, respectively.70 These five rules are required and typically sufficient conditions for effective grain refinement by SPD processing.

1.3.4 Types of nanostructures Though it is possible to achieve a nanocrystalline structure with a grain size less than 100 nm in a number of metals and alloys by means of HPT, for SPD



19

processing the formation of ultrafine-grained (UFG) structures with a mean grain size within the submicron range (i.e. with grains 200–500 nm in size) is typical. However, in the process of SPD, including ECAP, the formation of other structural elements takes place as well – that is, dislocation substructures, twins, grain boundary segregations and precipitations, which also produce a considerable influence on the properties of the materials after processing. Moreover, semiproducts in the form of rods, wires and sheets are produced by deformation and thermal treatment in sequence after ECAP, which additionally refines their microstructure and enhances their properties. In general, we can single out four types of nanostructural elements in the metals and alloys produced by SPD. It is possible to observe such nanostructures by the application of modern techniques for structural analysis – high-resolution transmission electron microscopy (HRTEM), 3D-atom probe, etc.16,19,71,72 These four types of structures are as follows: 1. Non-equilibrium grain boundaries. For example, as illustrated in Fig. 1.12,73 an excessively high density of dislocations, facets and steps are observed at grain boundaries of the UFG Al-3%Mg alloy after HPT, illustrating the nonequilibrium state of grain boundaries with crystal lattice distortions of 5–7 nm in width near boundaries.16,66 Such non-equilibrium grain boundaries are typical for different materials after SPD processing and their role in the mechanical behavior of UFG materials has been stressed in a number of works.16,66,74 2. Nanotwins, stacking faults, intragranular cells. These nanostructural elements are typical for the materials after HPT or ECAP at lower temperatures and/or those subjected to additional cold rolling, extrusion, and drawing. Figure 1.13 shows the TEM image of atom resolution of UFG Cu after ECAP and cold

1.12 Transmission electron microscopy images of non-equilibrium grain boundaries in the UFG Al-3%Mg alloy73 illustrating highresolution photographs of regions A and B.


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1.13 (a) TEM images of typical grain with high density of deformation twins in UFG Cu processed by ECAP with consequent cold rolling; (b) high-resolution TEM image taken from the zone axis. Inset: twin relationship (white lines) and a Frank dislocation at a twin boundary, marked by arrow.75

rolling at liquid nitrogen temperature with clearly observed twins of 10–20 nm in size.75 Such nanostructured defects also have a considerable effect on material strength,75,76 for example increasing the yield stress in UFG Cu from 380 to 510 MPa.75 3. Segregation clusters, ‘clouds’. Recent investigations by a 3D atom probe directly testify the formation of impurity as well as alloying element segregations at grain boundaries in the UFG alloys processed by SPD,71,72,77 see e.g. Fig. 1.14.71



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1.14 Grain boundary segregations in the HPT-processed 6061 Al alloy (of system Al-Mg-Si): (a) TEM image of the 6061 Al alloy; (b) grain size distribution; (c) Mg, Cu and Si distribution in a 3D reconstructed volume analysed in the 6061 alloy by HPT (6 × 6 × 40 nm3).71

These segregations form ‘clouds’, and clusters 3–5 nm in size influence the formation and motion of dislocations, which provides additional strengthening of the alloys, in particular those based on aluminum, by more than 40%.71,78 4. Nano-sized particles – second-phase precipitations. The formation of particles has been observed in many alloys subjected to SPD after solution quenching.15,19 Figure 1.15 illustrates the example of such nanoparticles 10–20 nm in size pre cipitated in the UFG alloy Al 6061 after ECAP.79 The presence of nano-particles


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1.15 UFG structure of the alloy Al 6061 after ECAP with parallel channels (4 passes). The formation of nano-sized precipitations is clearly visible inside the grain after processing at selected areas A and B with larger magnification.79

originates from dynamic ageing and provides additional precipitation hardening of the alloys.19,79 Thus, the UFG metals and alloys processed by SPD techniques and, in particular, ECAP are characterized by a number of nanostructural elements that considerably influence their properties, as will be shown below. That is why these materials are referred to as the class of ‘bulk nanostructured materials’, and this definition is presently accepted by the international community (www. nanospd. org). It is important that the strength of such materials as shown in the next section may be considerably higher than that expected from the Hall–Petch relation.

1.4

Enhanced properties achieved using SPD processing

The ultrafine grain sizes and high-defect densities inherent in UFG materials processed by severe plastic deformation lead to much higher strengths than in their coarse-grained counterparts. Moreover, according to the constitutive relationship for superplasticity, it is reasonable to expect the appearance of low-temperature and/ or high-rate superplasticity in UFG metals.8,80–83 The realization of these capabilities is important for the future development of high-strength and wear-resistant materials, advanced superplastic alloys and metals of high fatigue life. The potential for achieving all of these qualities has raised a keen interest among scientists and engineers studying the mechanical and functional properties of these UFG materials. In this connection, the first works on the fabrication of bulk samples and billets using SPD were a crucial step in initiating investigations on the properties of



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UFG materials, because the use of SPD processing made it possible to conduct a series of systematic studies using various nanostructured metallic materials including commercial alloys.16,84–88

1.4.1 Strength and ductility at ambient temperature During the last decade it has been widely demonstrated that major grain refinement, down to the nanometer range, may lead to considerable hardness and strength in various metals and alloys but nevertheless these materials invariably exhibit low ductility under tensile testing.12,15,89,90 A similar tendency is well known for metals subjected to heavy straining by other processes such as rolling, extrusion or drawing. Strength and ductility are the key mechanical properties of any material, but these properties typically have opposing characteristics. Thus, materials may be strong or ductile but they rarely possess both characteristics. This dichotomy shown in properties is of a fundamental nature. As discussed in more detail in earlier reports,64 the plastic deformation mechanisms associated with the generation and movement of dislocations can be different in ultrafine grains or in strongly refined microstructures. This is generally equally true for SPD-processed materials. Thus, most of these materials have a relatively low ductility but they usually demonstrate significantly higher strength than their coarse-grained counterparts. High strength in SPD-processed materials is usually attributed to the formation of UFG structure via the classic Hall–Petch relationship, according to which the yield stress σy is calculated as:

σy = σ0 + ky * d –1/2,

[1.1]

where d is a grain size, σ0 and k are constant for the material. However, it has been found that in many cases the yield stress value in the UFG materials processed by SPD may be considerably higher than those calculated by the Hall–Petch relation.15,16,91 For example, this was shown in the studies of mechanical behavior of Ni subjected to ECAP and consequent rolling.91 Figure 1.1691,93–95 shows the difference in strength between the states of Ni, where grains contain dislocation substructures inside grains, and the states with grains without substructure. An attempt was made to describe the deviation quantitatively from the Hall– Petch rule by taking into account the presence of two types of boundaries: highangle boundaries (HAB) between grains, and low-angle cell boundaries (LAB) on the yield stress. Following,92 it was assumed that all type of boundaries including non-equilibrium grain boundaries with extrinsic dislocations contribute to the yield stress independently:

σy = σ0 + σLAB + σHAB + σNGBs and


[1.2]

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1.16 Yield stress as a function of a grain size for Ni. Note: Continuous line: material states with grains without substructure, dashed line: UFG Ni containing dislocation substructure.

σy = σ0 + Mα Gb((1.5Svθ/b)LAB )1/2 + ky * d –1/2 + Mα Gb(ρGBDs)1/2,

[1.3]

where σ0 is the threshold stress, M is the Taylor factor (M = 3), α is the constant (α = 0.24), G is the shear modulus (79 GPa), and b is the Burgers vector (0.249 nm). The Sv is associated with the cell size, θ is the misorientation angle of LAB, ky is the Hall–Petch constant. The d is the average grain size, ρGBDs is the density of extrinsic GB dislocations. Their numerical values are taken following references.91,92 The contributions of these different components for SPD Ni correspond well to the experimentally obtained data (Table 1.3). After HPT a homogeneous UFG structure was formed with mainly high-angle misorientations. So, after several passes, we neglect the contribution of low-angle boundaries. Thus, the analysis of mechanical test data shows that the presence of substructure and the nonequilibrium state of GB contributes stronger to the yield stress of SPD Ni than that predicted by the Hall–Petch rule. In addition to the dislocation substructure and non-equilibrium grain boundaries other nanostructural elements formed in the UFG materials processed by SPD, as it was shown above in section 1.2.3, may contribute to the change of yield stress and flow stress. This issue has recently been studied in detail for the case of super-strong UFG Al alloys,78 such as commercial Al alloys 1570 (Al-5.7Mg-0.32Sc-0.4Mn wt. %) and 7475 (Al-5.7Zn-2.2Mg-1.6Cu-0.25Cr, wt. %), with considerable magnesium content. Al-Mg system alloys are the basis for most popular commercial Al alloys. For grain refinement the solid-soluted alloys were subjected to high-pressure torsion (HPT), in which UFG structures were produced with applied pressure of 6 GPa and number of anvil rotations equaling to 10. The samples in the



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Table 1.3 The contribution in flow stress for SPD-processed Ni Processing of Ni

YS exp, (MPa)

YS calc, (MPa)

ECAP + rolling 990 980 HPT 1200 1190

σLAB , (MPa)

σHAB , (MPa)

σGBDs, (MPa)

510 –

280 460

170 710

Note: YS exp: experimental data, YS calc: calculated by means of equation [1.3].

form of disks 20 mm in diameter and 0.8 mm in width were cut out from the HPT-processed alloys for further tensile tests. Transmission electron microscopy analysis demonstrated that HPT leads to a complete transformation of the initial coarse-grained structure of the alloys into the UFG structure. In alloys 1570 and 7475, homogeneous UFG structures with a grain size of about 100 nm were formed after HPT (Fig. 1.17). It was also determined that HPT processing has a visible effect on the value of crystal lattice parameter a of Al alloys. For example, in the alloy 1570, its lattice parameter value after straining was reduced considerably in comparison with that at the initial state – from 4.0765 ± 0.0001 Å to 4.0692 ± 0.0003 Å, approaching the lattice parameter of pure Al, which resulted in the formation of Mg segregations at grain boundaries.78 Figure 1.18 shows the results of mechanical tests of the alloys 1570 and 7475. It can be seen that the UFG alloys after HPT at room temperature demonstrate recorded strength that exceeds more than two times the level of strength of the material subjected to standard hardening.

1.17 Typical UFG structure formed in the alloy 1570 after HPT processing at room temperature (dark field).


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1.18 Engineering stress–strain curves of the UFG alloys 1570 (a) and 7475 (b).

Figure 1.1978 shows the data for a number of Al alloys presented in the form of the Hall–Petch relation in which the yield stress (σ0.2) is plotted against the inverse square root of the grain size (d–1/2) for a UFG Al alloy 1100 produced by ARBrolling and consequent heat treatment96 as well as for an ECAP-processed alloy Al-3% Mg alloy.97 For the Hall–Petch relation in the 1100 alloy,96 the following



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1.19 The Hall–Petch relation for the alloys 1100,96 Al–3%Mg97 and data on the yield stresses of the UFG alloys 1570 and 7475.

parameters were set: σ0 = 6.0 MPa and ky = 105 (for the grain sizes in µm); for the ECAP-processed alloy Al-3% Mg,97 σ0 = 62 MPa and ky = 149. Figure 1.19 also shows the data obtained for the coarse-grained (CG) and UFG 1570 and 7475 alloys. From the available data it is seen that the YS values for the CG quenched alloys are close to the results for the Al-3% Mg alloy. However, for the UFG states with a grain size of 100–130 nm the value sy is considerably higher than calculated from the Hall–Petch relation for these grain sizes. The physical nature of this unusual effect of super-strength refers to the features of the GB states formed during SPD and, in particular, to the formation of GB segregation of alloying elements.71,77,78 The point is that in UFG materials with a grain size of about 100 nm the deformation mechanisms controlling the flow stress change.98,99 In the CG materials the generation of dislocations proceeds relatively easily and hardening is related to the hindering of their movement by various obstacles. In the UFG materials the process of dislocation generation occurs at the GBs and is the most difficult.74,99 In this connection, the change of GB states and the formation of GB segregants of alloying elements, in particular in Al alloys, may considerably harden the dislocation generation and result in the achievement of a high-strength state.78


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As is well known, the UFG materials are commonly defined as interfacecontrolled materials.100 At the same time in the UFG materials produced by the SPD techniques, grain boundaries may vary significantly depending on the regimes and routes of processing, and they can belong to high- and low-angle grain boundaries, special and random boundaries, equilibrium and non-equilibrium boundaries as well as containing GB segregations or precipitations.11,64,71,101–104 In this context there appears a possibility of controlling and enhancing the properties of UFG materials by varying the structure of GBs using SPD processing. This approach can be considered as an application of the principles of GB engineering to UFG metals and alloys.64,104,105 The concept of grain boundary engineering or grain boundary design was introduced by T. Watanabe,106 who had proposed that the properties of polycrystalline materials may be effectively changed by deliberate and careful tailoring of the distributions of boundary misorientation angles. This approach has been employed successfully in several studies including, for example, improving the susceptibility to intergranular stress corrosion cracking.107 However, there are generally difficulties in achieving different boundary distributions in conventional coarse-grained materials. In this connection, UFG materials in which GB structure features are associated with SPD processing regimes allow much more possibilities for GB engineering. The concept of GB engineering is also of special interest regarding recent findings of extraordinary high strength and good ductility in several bulk ultrafinegrained metals produced by severe plastic deformation.80,108–111 Let us consider in detail the three different approaches that were used in these investigations. In the first study, high-purity (99.996%) Cu was processed at room temperature using ECAP with a 90° clockwise rotation around the billet axis between consecutive passes in route BC.108 Cu samples, which were prepared in the initial coarse-grained condition as well as in three processed states (cold rolled, 2-pass ECAP and 16-pass ECAP 108), were uni-axial tensile-tested at room temperature. The resulting engineering stress–strain curves are shown in Fig. 1.20. It is apparent that the initial coarse-grained Cu, with a grain size of about 30 µm, typically has low-yield stress with significant strain hardening and a large elongation to failure. At the same time, cold rolling of copper to a thickness reduction of 60% significantly increases its strength, as shown by curve 2 in Fig. 1.20, but dramatically decreases its total elongation to failure. This result is consistent with the classical strain hardening behavior of metals. The same tendency is true also for Cu subjected to 2 passes of ECAP. However, further straining of Cu to 16 passes of ECAP, as shown by curve 4 in Fig. 1.20, simultaneously increases both the strength and the ductility. Furthermore, the increase in ductility is much more significant than the relatively minor increase in strength. Thus, the data for Cu processed by ECAP shown in Fig. 1.20 clearly demonstrate enhanced strength as well as ductility with accumulated deformation on increasing the number of passes from 2 to 16. At the time of the investigation in 2002, this was considered a very remarkable result, which had never been observed before in



29

1.20 Tensile engineering stress–strain curves for Cu tested at 22°C with a strain rate of 10–3s–1: the processing conditions for each curve are indicated.108

metals processed by plastic deformation. Accordingly, the effect was termed the ‘paradox of strength and ductility in SPD-processed metals’, and the principles of this paradox are illustrated in Fig. 1.21, where it is apparent that conventional metals lie within the lower shaded quadrant.108 As seen in Fig. 1.21 for Cu and Al, cold rolling (the reduction in thickness is marked by each datum point) increases the yield strength but decreases the elongation to failure or ductility. The extraordinary combination of high strength and high ductility shown in Fig. 1.21 for the nanostructured Cu and Ti after processing by SPD clearly sets them apart from the other coarse-grained metals. In recent years, a similar tendency has been reported in a number of metals including Al,114,115 Cu,116 Ni117 and Ti,80 after processing through various types of severe plastic deformation such as ECAP, high-pressure torsion or accumulative roll bonding. Concerning the origin of this phenomenon, it has been suggested that it is associated with an increase in the fraction of high-angle grain boundaries with increased straining and with a consequent change in the dominant deformation mechanisms due to an increasing tendency for grain boundary sliding and grain rotation.64,108 An increase in the fraction of high-angle grain boundaries is also an example of GB engineering.105 Another approach to the problem of ductility enhancement that was suggested was the introduction of a bimodal distribution of grain sizes.109 In this study, nanostructured copper was produced through a combination of ECAP and subsequent rolling at the low temperature of liquid nitrogen prior to heating to a temperature close to ~450 K. This procedure gave a bimodal structure of micrometersized grains, with a volume fraction of around 25%, embedded in a matrix of nanocrystalline grains. The material produced in this way exhibited an extraordinarily high ductility but also retained a very high strength. The reason for this behavior is


30


1.21 The paradox of strength and ductility in metals subjected to SPD (‘VAZL paradox’): the extraordinary combination of high strength and high ductility in nanostructured Cu and Ti processed by SPD (two upper points) clearly sets them apart from conventional coarse-grained metals (the lower points relating to metals of 99.5–99.9% purity).108

that, while the nanocrystalline grains provide strength, the embedded larger grains stabilize the tensile deformation of the material. Other evidence supporting the importance of grain size distribution comes from investigations on zinc,118 copper119 and an aluminum alloy.120 Furthermore, the investigation of copper119 showed that bimodal structures might increase ductility not only during tensile testing but also during cyclic deformation. This observation is important in improving the fatigue properties of materials. A third approach has been suggested for enhancing strength and ductility based on the formation of second-phase particles in the nanostructured metallic matrix,89 where it is anticipated that these particles will modify the shear band propagation during straining and thereby lead to an increase in ductility. The principle of achieving high strength and high ductility by introducing intermediate metastable phases was successfully realized recently in commercial Al-Zn-Mg-Cu-Zr121 and Al-10.8% Ag alloys after processing by ECAP and subsequent ageing.110 The principle of this approach is illustrated in Fig. 1.22 for the Al-Ag alloy where Vickers microhardness is plotted against the ageing time at 373 K for samples prepared by three different pretreatments: the solution-treated condition (ST), cold rolling (CR) and ECAP.110 For the solution-treated condition, the hardness is initially low but increases with ageing time and reaches a peak



31

1.22 Variation of Vickers microhardness with ageing time for the Al-10.8%Ag alloy after solution treatment (ST), cold rolling (CR) and ECAP.110

value after 100 hours (3.6 × 105 s). For the cold-rolled condition, the hardness is higher but there is only a minor increase with ageing. The hardness is even higher after ECAP and further increases with ageing to a peak value after 100 hours. The relatively low values of hardness recorded after cold rolling in contrast with those higher values of ECAP samples is because the equivalent strain imposed on the sample is ~1.4 for CR and ~8 for ECAP so that the microstructure after CR consisted of subgrains or cell boundaries having low angles of misorientation. It was shown, using scanning TEM, that the peak hardness achieved after ECAP and ageing for 100 hours is due to precipitation within the grains of spherical particles with diameters of ~10 nm and elongated precipitates with lengths of ~20 nm. The spherical particles were identified as η-zones consisting of arrays of solute atoms lying parallel to the (001) planes and the elongated precipitates were identified as the plate-like γ' particles. It was shown also that additional ageing up to 300 hours led to a growth in the γ' particles and a very significant reduction in the density of the fine η-zones, thereby giving a consequent loss in hardening at the longest ageing time recorded in Fig. 1.22. The introduction of ageing after ECAP has an important influence on the stress– strain behavior at room temperature, as demonstrated in Fig. 1.23 where the tensile stress–strain curves of Al-10.8 wt% Ag alloy processed under four different conditions: 1) ECAP only; 2) ECAP and subsequent 100 h annealing at 373 K; 3) cold rolling and subsequent 100 h annealing at 373 K; and 4) solution treatment and subsequent 100 h annealing at 373 K.110 Thus, a combination of solution


32


1.23 Tensile plots of stress versus strain at room temperature for the Al-10.8%Ag alloy after solution treatment (ST) or cold-rolling (CR) with ageing at 373 K for 100 h or ECAP without subsequent ageing and ECAP with ageing at 373 K for 100 h.110

treatment and ageing gives a reasonable tensile strength, an extensive region of uniform strain and good ductility, whereas CR and ageing gives an increased strength but very limited uniform strain and a marked reduction in the total ductility. For the ECAP-ed alloy, the strength is high in the absence of ageing but there is a negligible region of uniform strain and no significant strain hardening. By contrast, the sample processed by ECAP and aged for 100 h shows a similar high strength, a region of strain hardening and good ductility. In practice, the uniform strain of ~0.14 achieved in this specimen is similar to the uniform strain of ~0.17 in the sample after solution treatment and ageing. The elongation to failure of ~0.40 is comparable to, and even slightly exceeds, the elongation of ~0.37 recorded in the solution treatment and aged condition. These results demonstrate, therefore, the potential for producing high strength and good ductility in precipitation-hardened alloys. Thus, recent results show that grain refinement by ECAP can lead to a unique combination of strength and ductility in metallic materials. However, the achievement of these properties is associated with the tailoring of specific microstructures, which, in turn, are determined by the precise processing regimes and origin of any further treatments. In this case the concept of GB engineering plays also an important role in the enhancement of strength and ductility. That is why nowadays nanostructuring of metals for advanced properties comprises, as a rule, scientific as well as artistic aspects of tailoring of materials by means of SPD techniques. In return, strength and ductility are fundamental mechanical properties that are closely connected with many engineering properties of materials, in particular



33

fatigue, fracture toughness, durability, wear resistance as well as creep and superplasticity. Such superior mechanical properties are highly desirable for the development of advanced next-generation structural materials and this has been an object of numerous investigations in the sphere of nanoSPD materials in the last several years.15,19,122 In fact, closer attention is now being paid to work on the enhancement of functional properties such as magnetic, electrical, super-elastic ones, etc., in the UFG metals produced by SPD.15,123,124 All this is very important in view of innovative applications of bulk nanomaterials.

1.5

Innovation potential of bulk nanostructured materials

Recent reports documented more than 100 specific market areas for nanostructured metals122,125 and it is evident that many of these new structural applications involve extreme environments where exceptional strength is needed. Potential near-future applications are presented schematically in Fig. 1.24 demonstrating some specific examples.122

1.24 Assumed innovation probability in various sectors vs. specific strength. The highest potential may be seen in applications and products under ‘extreme environments and/or with extreme specific strength’ requirements.


34


Firstly, due to excellent biological compatibility combined with superior specific strength, it is probable that UFG titanium will enter the bio-medical market at an ever-increasing pace. Titanium and titanium alloys are currently used extensively as implant materials in traumatology, orthopaedics and dentistry.126 This is due to several characteristics including their excellent biocompatibility, good corrosion resistance and specific strength compared with other metals. The implant materials used in these areas are subjected to complex loads with additional biomedical and other technical requirements. Significant progress may be achieved here by increasing the specific strength of the implant materials, and thereby permitting the use of a smaller size with less invasive surgery. Recent investigations have shown that, due to nanostructuring, the fatigue strength of CP-Ti may be significantly increased to a level exceeding that of the coarse-grained Ti-6Al-4V alloy.48,127 Hence, there is also the potential to replace more expensive and less biocompatible alloys with commercial-purity titanium that is more biocompatible.48 Important requirements in all biomedical applications are corrosion resistance and excellent biocompatibility and both are fulfilled with titanium and most titanium alloys. Preliminary investigations of the corrosion behavior of nano-titanium suggest that corrosion resistance is improved by introducing a UFG microstructure.128 A second example with high innovative potential is the superplastic forming of light metals produced by SPD for the fabrication of products with both complex shapes and high specific strengths. It is anticipated that these products will have a wide range of applications in the aeronautic and automotive sectors as well as in the consumer product industry. The development of superplastic forming capabilities after SPD is now well established.129 Numerous experiments show that these superplastic properties are retained when large billets processed by SPD are subsequently rolled into thin sheets during superplastic forming operations.130–132 Furthermore, the ultrafine grain size is preserved after SPD forming and thus provides a very high strength at ambient temperatures, which is an important consideration for many structural applications. A third potential innovation lies in extreme low-temperature applications as in arctic environments and in the special processing applications associated with the oil and gas industries. This is especially important for low carbon and stainless ferritic steels where usually there is a sharp transition from ductile to brittle behavior with decreasing temperature. Extensive grain refinement due to SPD can significantly decrease the brittle–ductile transition temperature in these steels133,134 and this is especially important when undertaking construction work at high latitudes.

1.6

Conclusions

Processing by severe plastic deformation provides strong grain refinement and therefore an opportunity to enhance properties of metals and alloys making them



35

attractive for new structural and functional applications. However, finding solutions to these problems is a complex challenge requiring an individual approach to the choice of processing routes and regimes and formation of certain nanostructures. The recent progress witnessed in this trend and many new works demonstrate unique opportunities to successfully do this. Limitations on the use of SPDprocessed materials to date, which have arisen primarily from their processing costs and the inherent wastage in conventional processing methods, are now being overcome through the development of new and continuous processing techniques. As these procedures become more developed, it is reasonable to anticipate that there will be significant advances in the use of nanomaterials in different areas of engineering and bio-medical applications. There is already every reason to believe that this breakthrough will take place in the coming years.

1.7

References

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58 Shen H., Li Z., Guenther B., Korznikov A.V., Valiev R.Z. Nanostr Mater 1995;6: 385. 59 Wilde G., Boucharat N., Dinda G.P., Rösner H., Valiev R.Z. Mater Sci Forum 2006;503–504: 425. 60 Gunderov D.V., Pushin V.G., Valiev R.Z., Valiev E.Z. Deformation and Fracture of Materials 2006;4: 22. 61 Sergueeva A.V., Song C., Valiev R.Z., Mukherjee A.K. Mater Sci Eng A 2003;339: 159. 62 Huang J.Y., Zhu Y.T., Liao X.Z., Valiev R.Z.. Phil Mag Lett 2004;84: 183. 63 Waitz T., Kazykhanov V., Karnthaler H.P. Acta Mater 2004;52: 385. 64 Valiev R.Z. Nature Mat 2004;3: 511. 65 Zhu Y.T., Langdon T.G. JOM 2004;56(10): 58. 66 Valiev R.Z. Int J Mat Res (formerly Metallkd) 2009;100: 757 67 Ungár T., Balogh L., Zhu Y.T., Horita Z., Xu C., Langdon T.G. Mater Sci Eng A 2007;444: 153. 68 Zehetbauer M.J. (ed.). Advanced Engineering Materials, Special Issue on Nanomaterials by Severe Plastic Deformation (SPD), Vol. 5, 2003. 69 Gutkin M.Y., Ovidko I.A. Appl Phys Lett 2005;87: 251916-1. 70 Kurmanaeva L., Ivanisenko Y., Markmann J., Kübel C., Chuvilin A., Doyle S., Valiev R.Z., Fecht H-J. Mater Sci Eng A 2010;527: 1776. 71 Nurislamova G., Sauvage X., Murashkin M., Islamgaliev R., Valiev R.Z. Phil Mag Lett 2008;88: 459. 72 Sha G., Wang Y.B., Liao X.Z., Duan Z.C., Ringer S.P., Langdon T.G. Acta Mater 2009;57: 3123. 73 Horita Z., Smith D.J., Furukawa M., Nemoto M., Valiev R.Z., Langdon T.G. J Mater Res 1996;11: 1880. 74 Valiev R.Z., Kozlov E.V., Ivanov Y.F., Lian J., Nazarov A.A., Baudelet B. Acta Metall Mater 1994;42: 2467. 75 Zhao Y., Bingert J.F., Liao X., Cui B., Han K., Sergueeva A.V., Mukherjee A.K., Valiev R.Z., Langdon T.G., Zhu Y.T. Adv Mater 2006;18: 2949. 76 Chukin M.V., Koptseva H.V., Valiev R.Z., Yakovleva I.L., Zrnik J., Covarik T. Vestnik MGTU 2008;1 (in Russian). 77 Liddicoat P.V., Liao X.Z., Zhao Y., Zhu Y., Murashkin M.Y., Lavernia E.J., Valiev R.Z., Ringer S.P., 2010, submitted to Nat. Commun. 78 Valiev R.Z., Enikeev N.A., Murashkin M.Y., Alexandrov S.E., Goldshtein R.V. Doklady Physics 2010;55(6): 267. 79 Valiev R.Z, Murashkin M.Yu, Bobruk E.V., Raab G.I. Mater Trans 2009;50: 87. 80 Valiev R.Z., Sergueeva A.V., Mukherjee A.K. Scripta Mater 2003;49: 669. 81 McFadden S.X., Mishra R.S., Valiev R.Z., Zhilyaev A.P., Mukherjee A.K. Nature 1999;398: 684 82 Valiev R.Z., Salimonenko D.A., Tsenev N.K., Berbon P.B., Langdon T.G. Scripta Mater 1997;37: 1945. 83 Kawasaki M., Langdon T.G. J Mater Sci 2007;42: 1782. 84 Lowe T.C., Valiev R.Z. Investigations and applications of severe plastic deformation. Kluwer, Dordrecht, The Netherlands, 2000. 85 Zhu Y.T., Langdon T.G., Valiev R.Z., Semiatin S.L., Shin D.H., Lowe T.C. (eds.) Ultrafine-Grained Materials III, Minerals, Metals and Materials Society, Warrendale, PA, USA, 2004. 86 Zehetbauer M.J., Valiev R.Z. (eds.) Nanomaterials by severe plastic deformation. Wiley-VCH Verlag, Weinheim, Germany, 2004.


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87 Zhu Y.T., Varyukhin V. (eds.) Nanostructured materials by high-pressure severe plastic deformation. Springer, Dordrecht, The Netherlands, 2006. 88 Zhu Y.T., Langdon T.G., Horita Z., Zehetbauer M.J., Semiatin S.L., Lowe T.C. (eds.) Ultrafine-Grained Materials IV, Minerals, Metals and Materials Society, Warrendale, PA, USA, 2006. 89 Koch C.C. Scripta Mater 2003;49: 657. 90 Morris D.G. Mechanical behaviour of nanostructured materials. Trans Tech, UetikonZürich, 1998. 91 Krasilnikov N., Pakiela Z., Lojkowski V., Valiev R.Z. Sol St Phen 2005;101–102: 49. 92 Hugnes D.A., Hansen N. Acta Metall 2000;48: 2985. 93 Thompson A.W. Acta Metall 1975;23: 1337. 94 Xiao C., Mirshams R.A., Whang S.H., Yin W.M. Mater Sci Eng A 2001;301: 35. 95 Ebrahimi F., Bourne G.R., Kelly M.S., Matthews T.E. Nanostr Mater 1999;11: 343. 96 Tsuji N. Unique deformation behaviors of the ultrafine-grained aluminum alloys fabricated by accumulative roll bonding. In: Zhu Y.T., Varyukhin V. (eds.) Nanostructured materials by high-pressure severe plastic deformation. Springer Netherlands, 2006. p. 227. 97 Furukawa M., Horita Z., Nemoto M., Valiev R.Z., Langdon T.G. Phil Mag A 1998;78(1): 203. 98 Meyers M.A., Mishra A., Benson D.J. JOM 2006;58(4): 41. 99 Pande C.S., Cooper K.P. Prog Mater Sci 2009;54: 689. 100 Gleiter H. Prog Mater Sci 1989;33: 223. 101 Dobatkin S., Zrnik J., Nikulin S., Kovarik T., submitted to JPCS (Proc. of the 15th Int. Conf. on the Strength of Materials), 2009. 102 Zhao Y.H., Bingert J.F., Zhu Y.T., Liao X.Z., Valiev R.Z., Horita Z., Langdon T.G., Zhou Y.Z., Lavernia E.J. Appl Phys Lett 2008;92: 081903. 103 Furukawa M., Horita Z., Langdon T.G. J Mater Sci 2005;40: 909. 104 Valiev R. Mater Sci Forum 2008;584–586: 22. 105 Fujita T., Horita Z., Langdon T.G. Mater Sci Eng A 2004;371: 241. 106 Watanabe T. Res Mech 1984;11: 47. 107 Watanabe T., Fujii H., Oikawa H., Arai K.I. Acta Metall 1989;37: 941. 108 Valiev R.Z., Alexandrov I.V., Zhu Y.T., Lowe T.C. J Mater Res 2002;17: 5. 109 Wang Y., Chen M., Zhou F., Ma E. Nature 2002;419: 912. 110 Horita Z., Ohashi K., Fujita T., Kaneko K., Langdon T.G. Adv Mater 2005;17: 1599. 111 Zhao Y., Topping T., Bingert J.F., Thornton J.J., Dangelewicz A.M., Li Y., Zhu Y.T., Zhou Y., Lavernia E.J. Adv Mater 2008;20: 3028. 112 Parker E.R. Materials data book for engineers and scientists. McGraw-Hill, New York, NY, USA, 1967. 113 Brandes E.A., Brook G.B. Smithells metals reference book, 7th ed. ButterworthHeinemann, Oxford, UK, Ch. 22, 1992. 114 Höppel H.W., May J., Eisenlohr P., Göken M. Metallkd 2005;96: 566. 115 May J., Höppel H.W., Göken M. Scripta Mater 2005;53: 189. 116 Dalla Torre F., Lapovok R., Sandlin J., Thomson P.F., Davies C.H.J., Pereloma E.V. Acta Mater 2004;52: 4819. 117 Krasilnikov N., Lojkowski W., Pakiela Z., Valiev R. Mater Sci Eng A 2005;397: 330. 118 Zhang X., Wang H., Scattergood R.O., Narayan J, Koch C.C., Sergueeva A.V., Mukherjee A.K. Acta Mater 2002;50: 4823. 119 Mughrabi H., Höppel H.W., Kautz M., Valiev R.Z. Metallkd 2003;94: 1079. 120 Park Y.S., Chung K.H., Kim N.J., Lavernia E.J. Mater Sci Eng A 2004;374: 211.



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121 Islamgaliev R.K., Yunusova N.F., Sabirov I.N., Sergueeva A.V., Valiev R.Z. Mater Sci Eng A 2001;319–321: 877. 122 Valiev R.Z., Zehetbauer M.J., Estrin Y., Höppel H.W., Ivanisenko Y., Hahn H., Wilde G., Roven H.J., Sauvage X., Langdon T.G. Adv Eng Mater 2007;9: 527. 123 K. Suehiro, S. Nishimura, Z. Horita, Mater Trans, 2008;49: 102. 124 B. Straumal, S.G. Protasova, A.A. Mazilkin, B. Baretzky, D. Goll, D.V. Gunderov, R.Z. Valiev, Phil Mag Lett, 2009;89: 649. 125 Lowe T.C. JOM 2006;58(4): 28. 126 Brunette D.M., Tengvall P., Textor M., Thomsen P. Titanium in med. Springer, Heidelberg, 2001. 127 Stolyarov V.V., Zhu Y.T., Alexandrov I.V., Lowe T.C., Valiev R.Z. Mater Sci Eng A 2003;343: 43. 128 Balyanov A., Kutnyakova J., Amirkhanova N.A., Stolyarov V.V., Valiev R.Z., Liao X.Z., Zhao Y.H., Jiang Y.B., Xu H.F., Lowe T.C., Zhu Y.T. Scripta Mater 2004;51: 225. 129 Horita Z., Furukawa M., Nemoto M., Barnes A.J., Langdon T.G. Acta Mater 2000;48: 3633. 130 Akamatsu H., Fujinami T., Horita Z., Nemoto M., Langdon T.G. Scripta Mater 2001;44: 759. 131 Park K.T., Lee H.J., Lee C.S., Nam W.J., Shin D.H. Scripta Mater 2004;51: 479. 132 Nikulin I., Kaibyshev R., Sakai T. Mater Sci Eng A 2005;07: 62. 133 Korznikov A.V., Safarov I.M., Nazarov A.A., Valiev R.Z. Mater Sci Eng A 1996;206: 39. 134 Borisova M.Z., Yakovleva S.P., Ivanov A.M. Sol St Phen 2006;14: 97.


2 Bulk nanostructured metals and alloys produced by accumulative roll-bonding N. TSUJI, Kyoto University, Japan Abstract: This chapter introduces the fabrication of bulk nanostructured metals and alloys by the accumulative roll-bonding (ARB) process. The principles and processing details of ARB are presented and discussed. The formation of ultrafine-grained structures in single-phased metals during ARB is illustrated using original experimental results. This process is understood in terms of grain subdivision: the ultrafine-grains essentially have the characteristics of deformation microstructures, which include large misorientation grain boundaries. Post-ARB annealing of aluminum and ferritic steel cause relatively continuous changes in the grain structure by a combination of recovery and grain growth. The ARB process can also fabricate non-equilibrium nanostructured materials, such as a composite of nanocrystals and metallic glass in the Cu + Zr multi-stack metal system. Ultrafine-grained metals fabricated by ARB exhibit two to four times more strength than the same metals with conventionally coarse-grained structures, but they also show limited tensile ductility, due to early plastic instability that occurs in the nanostructured materials. This observation also suggests the possibility of maintaining both high strength and adequate ductility by making the nanostructures multi-phased. Key words: severe plastic deformation, accumulative roll-bonding, ultrafine grains, non-equilibrium structures, grain subdivision, bulk mechanical alloying, mechanical properties.

2.1

Introduction

Accumulative roll-bonding (ARB) is a kind of severe plastic deformation (SPD) process for fabricating bulk nanostructured metallic materials.1 It has been clarified that bulk nanostructured metals and alloys, which are composed of ultrafine grains (UFGs) with a mean grain size of several hundreds of nanometers or nanocrystals with mean grain size of several tens of nanometers, can be fabricated by plastic deformation up to a very high strain (above logarithmic equivalent strain of 4~5), which is often called SPD.2 Various kinds of unique SPD processes, such as equal-channel angular extrusion (ECAE), high-pressure torsion (HPT), cyclic extrusion and compression (CEC), etc., have been developed for realizing bulk nanostructured metals.1,2 Among the SPD processes, ARB is advantageous for continuous production of sheet materials, since it uses rolling deformation in principle. In laboratory scale, ARB has been applied to various kinds of metals and alloys and has succeeded in producing bulky sheets having nanostructures. In this chapter, the principle of the ARB process, 40 © Woodhead Publishing Limited, 2011

Bulk nanostructured metals and alloys

41

evolution of nanostructures during ARB, and mechanical properties of the nanostructured metals and alloys fabricated by ARB are introduced and summarized.

2.2

The principle of accumulative roll-bonding (ARB)

ARB was developed by Saito et al. in 1998.1,3 The principle of the ARB process is schematically illustrated in Fig. 2.1. ARB is a SPD process using rolling deformation. Rolling is the most advantageous metalworking process for continuous production of bulk materials with shapes of plates, sheets, bars, and so on. However, it is nearly impossible to achieve ultra-high plastic strain above a logarithmic equivalent strain of 4~5 by the conventional rolling, because the dimension of the materials (the thickness of sheets, for example) decreases with increasing total plastic strain applied. In the ARB process, for example, a sheet 2 mm thick is first rolled to a 50% reduction in thickness. The rolled sheet with a thickness of 1 mm and approximately twice the length of the original is cut into two, stacked together to make 2 mm thick material (initial thickness) (see Fig. 2.1), and the stack is rolled again. In order to obtain one-body solid material, the rolling in the ARB process is not only a deformation process but also a bonding process, which is known as roll-bonding, used for the production of clad sheets. To achieve good bonding between two stacked sheets, the contact surfaces of the sheets are degreased and wire-brushed typically before being subjected to rolling. Roll-bonding is sometimes carried out at elevated temperatures below the recrystallization temperature of the material, in order to make the bonding better and to reduce the rolling force. By repeating the procedure, one can apply a very large amount of plastic strain to the sheet material without changing the original dimensions. The von Mises equivalent strain (εeq) after n cycles of the ARB can be expressed as,

2.1 Schematic illustration showing the principle of the accumulative roll-bonding (ARB) process.


42


,

[2.1]

where t0, t, and r are initial thickness of the stacked sheets, the thickness after rollbonding, and the reduction in thickness per cycle, respectively. Geometrical changes of the materials in the ARB process using 50% reduction per cycle (r = 0.5 in equation (2.1)) are summarized in Table 2.1. An equivalent strain of 4 can be achieved by 5 ARB cycles in this case, and after 10 ARB cycles the 1 mm-thick sheet contains 1024 original layers.

2.3

Processing details

The ARB process does not require any special equipment except for a rolling mill with enough capacity, which is another advantage of this method. Figure 2.2

Table 2.1 Geometrical changes of the material during the ARB where two pieces of the 1 mm thick sheets are stacked and roll-bonded by 50% reduction per cycle No. of cycles

1

2

3

4

5

6

7

8

No. of layers

2

4

8

16

32

64

128

256

512 1024

2n

No. of bonded boundaries

1

3

7

15

31

63

127

255

511 1023

2n –1

7.8

3.9

1.9

Layer 500 250 125 62.5 31.3 15.6 interval (µm)

9

10

1000/2n (1 – 1/2n) × 100

50

75

87.5 93.8 96.9 98.4 99.2 99.6 99.8 99.9

Equivalent strain

0.8

1.6

2.4

4

4.8

5.6

6.4

7.2

n

0.96

Total reduction (%)

3.2

. . . . . . . . .

8

2.2 (a) The two-high rolling mill used for the ARB process in the author’s group. (b) A channel guide for the stacked sheets on the entrance side of the mill.


0.8n


43

shows the rolling mill that has been used for the ARB process in the author’s group. The rolling machine is a conventional two-high mill with 310 mm roll diameter. Because the large reduction in 1 pass is necessary to achieve good bonding4 and roll-bonding is often carried out without lubrication to realize quick UFG formation,5,6 the rolling force during ARB becomes very large. For instance, the rolling force for a commercial purity aluminum sheet 40 mm in width reaches to 49 tons force in the seventh cycle of ARB at room temperature (RT) without lubrication.2 Thus, the rolling mill is required to have enough capacity. The rolling mill shown in Fig. 2.2 (a) has a capacity of 150 tons. The ARB process has been successfully applied to various kinds of metallic materials and actually produced bulky sheets with nanostructures. In most materials, the ultrafine lamellar boundary structures or the pancake-shaped ultrafine grains, whose average boundary spacing or grain thickness is much smaller than 1 µm, were formed uniformly in the materials after 5~6 cycles of ARB.1,2 The ARB-processed sheets with ultrafine-grained structures exhibited very high strength, which is two to four times higher than that of the starting materials with conventional grain sizes, as will be shown in a later section. It has been found, rather unexpectedly, that roll-bonding in the ARB process was not difficult for most of the ductile metallic materials, although degreasing and wire-brushing the contact surfaces before stacking were an indispensable step for a good bonding. The minimum required rolling reduction in 1 pass exists to achieve a good bonding,4 which depends on the kind of materials in use and the rolling conditions. The critical 1-pass reduction in ARB at RT is roughly 40~50%. In case of Al alloys, for example, oxide layers quickly cover the surfaces of the sheet even if wire-brushing is conducted. However, the oxide layers are very thin and brittle, and will not survive rolling. When a 50% reduction is used in rollbonding, the surface area increases by 100%, which means that so many fresh metallic atoms behind the oxide layer come to the surface during roll-bonding, i.e. create virgin surfaces that are not covered with oxide layers. The fresh metallic atoms on both sides of the sheet surfaces make close contact with each other to achieve bonding under great pressure from the roll-bite. This is a possible mechanism of roll-bonding in the ARB process. During repeated ARB cycles, bonding at the interfaces becomes increasingly stronger, since the bonding interfaces are repeatedly elongated to the rolling direction. As a result, even after fracture in a tensile test, exfoliation of the bonded interfaces could be seen only at the center of the sheet, which corresponds to the bonded interface in the most recent ARB cycle. A serious potential problem in the ARB process is cracking during rolling in some kinds of metals and alloys. The typical appearance of the ARB-processed aluminum alloys is shown in Fig. 2.3. In very ductile materials, such as pure Al, pure Cu and ultra-low-carbon steel, almost no cracking occurs even after many cycles of ARB. As a result, sound and large sheets filled with the UFG structures can be obtained. Figure 2.3a is such an example of the 1100-Al (99%Al) sheet


44


2.3 Appearance of the ARB-processed Al alloy sheets. Thickness of the sheets is 1 mm. (a) 1100-Al ARB-processed by 5 cycles at RT. (b) 5083-Al ARB processed by 2 cycles at RT.

ARB-processed by 5 cycles at RT, whose dimensions are 1 mm thick, 55 mm wide and 320 mm long. On the other hand, some kinds of materials considerably lost workability with increasing ARB cycles. An example of severely cracked sheet of the 5083-Al (Al-4.7%Mg) ARB-processed by 2 cycles at RT is shown in Fig. 2.3 (b). The cracks generally start at the edges of the sheet due to tensile stress, and they sometimes propagate into the center of the sheet (Fig. 2.3 (b) ). Once such cracking occurs, it is difficult to proceed to the next cycle. However, there are some small techniques or know-how for avoiding cracking during rollbonding. As a result, the ARB process has been applicable to most of the metallic materials that can be deformed in rolling. The ARB process has been successfully applied to pure metals (Al, Fe, Cu, Ni, Ti and Zr), various kinds of Al alloys,



45

Al-matrix composites, low-carbon steels, ferritic stainless steels, duplex stainless steels, high-Ni austenitic steels, dilute Cu alloys, brass, Cu-Ag alloys, and even Mg alloys, and UFG microstructures have been obtained in all cases after ARB over 5~6 cycles.2,7–10

2.4

Change in microstructures during the process

2.4.1 Formation of ultrafine grains in ARB In this section, the evolution of UFG structures during the ARB in single-phase metals is shown and discussed. Figure 2.4 shows the boundary misorientation maps obtained by electron backscattering diffraction (EBSD) measurement in a field-emission type scanning electron microscope (FE-SEM) for the ultra-lowcarbon interstitial free (IF) steel ARB-processed by various cycles at 500°C.11 In Fig. 2.4, high-angle boundaries with misorientations larger than 15° were drawn in bold black lines, while low-angle boundaries whose misorientations were between 2° and 15° were drawn in narrow grey lines. After 1-cycle ARB corresponding to just a 50% reduction, elongated initial grains involving many low-angle boundaries are observed. This is a typical microstructure conventionally seen in deformed metals. It should be noted, however, that newly formed highangle boundaries appeared in the vicinity of initial grain boundaries. The number and the density of the deformation-induced high-angle boundaries increased with more ARB cycles (i.e. strain), and finally the specimen was filled with the elongated grain structure, mostly subdivided by high-angle boundaries. The misorientation distribution in the samples shown in Fig. 2.4 is represented in Fig. 2.5. The ‘fHAGB’ in Fig. 2.5 indicates the fraction of high-angle grain boundaries. The 1-cycle ARB-processed specimen that had a typical deformation microstructure (Fig. 2.4 (a)) was mostly filled with low-angle boundaries (64%). It should be noted that in the EBSD analysis the misorientations under 2° were cut off in order to remove inaccuracy due to measurement and analysis in automatic orientation mapping. That is, the actual fraction of the low-angle boundaries must be much larger than 64%. The fraction of high-angle boundaries increased with increasing strain, and more than 80% of the observed boundaries were already high-angle in the specimen ARB-processed by 5 cycles (Fig. 2.5 (d) ). Other ARB-processed materials showed similar microstructural evolution to that in the IF steel described above.12,13 It has been clarified in various metals that the ultrafine microstructures are quite uniform throughout the thickness of the ARB-processed sheets.14,15 Figure 2.6 shows TEM micrographs of the IF steel (a) and the 1100-Al (b) ARB-processed by 6 cycles. The microstructures were observed from TD. These are the typical microstructures in the single-phased materials that have been ARB-processed by many cycles. Both materials showed quite similar microstructures elongated along RD, which corresponds to Fig. 2.4 (d). These are so-called lamellar boundary (LB) structures, which have been observed in heavily


46


2.4 Boundary misorientation maps obtained by FE-SEM/EBSD measurements of the IF steel ARB-processed by (a) 1 cycle, (b) 2 cycles, (c) 3 cycles and (d) 5 cycles at 500°C without lubrication. The measurements were done on the longitudinal sections of the sheets.

rolled FCC metals.16 The mean spacing of the LBs was about 200 nm for both materials. As is shown statistically in Fig. 2.5, most of the boundaries in these microstructures are already high-angle ones, as has been also confirmed by FE-SEM/EBSD and Kikuchi-line analysis in TEM.



47

2.5 Misorientation distributions of the boundaries observed in the EBSD measurements of the IF steel ARB-processed by (a) 1 cycle, (b) 2 cycles, (c) 3 cycles and (d) 5 cycles at 500°C without lubrication. The data taken throughout thickness of the ARB-processed sheets were summarized.

2.6 Transmission electron microscopy microstructures of singlephased materials ARB-processed by 6 cycles without lubrication. The microstructures were observed from TD of the sheets. (a) IF steel processed at 500°C. (b) 1100-Al processed at RT.


48


2.7 Transmission electron microscopy micrograph (a) and corresponding boundary misorientation map (b) of the 1100-Al ARB-processed by 6 cycles at 200°C. Observed from TD. The misorientation angles (in degrees) superimposed in (b) were calculated from the precise orientation of each region measured by TEM/Kikuchi-line analysis.

Figure 2.7 is a TEM microstructure (a) of a commercial purity aluminum (1100-Al) ARB-processed by 6 cycles at 200°C together with the boundary map (b) of the identical area obtained through TEM/Kikuchi-line analysis.12,17 In the boundary map (Fig. 2.7 (b) ), the misorientations of the boundaries are also indicated in degrees. It is again shown that most of the observed boundaries (especially lamellar boundaries) are high-angle ones having quite large mis orientations. The boundaries between adjacent regions are not broad (or unclear) like dislocation-cell boundaries, but seem quite sharp. It can be concluded, therefore, that the elongated regions surrounded by high-angle boundaries are



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2.8 Schematic illustration showing grain subdivision mechanism during plastic deformation.

certainly ‘grains’ from a viewpoint of misorientation. At the same time, however, the morphology of the grains is elongated along the principal deformation direction, and the microstructure involves many low-angle boundaries and dislocations tangled within the grains. That is, the ultrafine grains fabricated by the ARB process (and by other SPD processes) are essentially deformation microstructures as well. The microstructural evolution during ARB (or during SPD in general) can be understood in terms of grain subdivision.18 The process of grain subdivision is illustrated in Fig. 2.8. Plastic deformation of metallic crystals is born basically by dislocation slips. In polycrystalline materials, the slip patterns (combination and number of slip systems operated) generally differ depending on locations even within an identical crystal. Different slip patterns result in different crystal rotation in producing misorientation between neighboring regions. The boundaries between such regions to bear the misorientation are called geometrically necessary boundaries (GNBs).16,18 In addition, the dislocations stored in the crystal tend to form low-energy configurations (LEC). The boundaries formed by such LEC dislocations are called incidental dislocation boundaries (IDBs).16,18 The original grain (crystal) is finely subdivided by the GNBs and IDBs with increasing plastic strain, which is the grain subdivision mechanism. The GNBs are especially important for UFG formation, as their misorientation increases with increasing plastic strain applied.16,18 So-called lamellar boundary structure has been reported in heavily cold-rolled aluminum,16 where lamellar boundaries are GNBs. The ultrafine lamellar structures observed in the present ARB specimens (Fig. 2.6) are quite similar to the lamellar boundary structure reported in heavily cold-rolled aluminum, though the proportion of high-angle boundaries in the ARB specimens is much higher than in the cold-rolled one.12 Because the mechanism of


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microstructure evolution is grain subdivision, the UFG structures produced by ultra-high straining are naturally deformation microstructures, though the subdivided regions (grains) have large misorientations to each other. This agrees well with the fact that the UFG microstructures obtained through the ARB involves many dislocations and low-angle grain boundaries (Figs. 2.4–2.7). It is also interesting that nano-sized deformation twins have been observed in UFG pure Cu19 and pure Al20 fabricated by the ARB process, as has been reported in the materials fabricated by other SPD processes.

2.4.2 Change in microstructures during subsequent heat treatments Subsequent annealing could change the microstructures of the ARB-processed materials.17,21,22 Figure 2.9 shows the TEM microstructures of the 1100-Al ARB processed and then annealed at various temperatures.21 During low temperature annealing, the recovery decreases the dislocation density inside the elongated ultrafine grains, and the ultrafine grains grow slightly. The specimen annealed at 225°C for 1.8 ks was found to contain equiaxed grains free from dislocations (Fig. 2.9 (d) ). It is quite difficult to distinguish these grains from conventionally recrystallized grains. It should be noted, however, that the mean grain size is still

2.9 Transmission electron microscopy microstructures of the 1100-Al ARB-processed by 6 cycles at 200°C without lubrication and then annealed at (a) 100°C, (b) 150°C, (c) 200°C, (d) 225°C, (e) 250°C and (f) 300°C for 1.8 ks. Observed from TD.



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around 1 µm, which cannot be achieved through a conventional deformation and recrystallization process. Further annealing causes grain growth, resulting in equiaxed grain structures having various mean grain sizes. Similar microstructural change has been observed in the ARB-processed IF steel as well.21,22 The changes in microstructures during annealing of ARB-processed pure Al and IF steel are fairly homogeneous and continuous. Such a continuous change of the grain structure is sometimes called continuous recrystallization,23 since it is greatly different from conventional recrystallization characterized by nucleation and growth of particular grains (discontinuous recrystallization). However, even in conventional recrystallization (discontinuous recrystallization), it is considered that no new recrystallized grains nucleate by thermal fluctuation of atoms, but potential nuclei existed in the deformed microstructure preferentially grow.24 In that sense, it might be confusing to use the term, continuous recrystallization. In the materials deformed to ultra-high strains, the finely subdivided structure is already full of high-angle grain boundaries, as is shown in Figs. 2.4, 2.5 and 2.7. Thus, it is reasonable to consider that the microstructural change during annealing of SPD processed materials (Fig. 2.9) can be a kind of normal grain growth accompanied by the recovery at grain interior. Here, it should be noted that both pure aluminum (face-centered cubic (fcc) metal with very high stacking fault energy) and IF steel (ferritic iron: body-centered cubic (bcc) metal) are the materials where recovery is enhanced to occur during annealing. In fact, recovery quickly occurs to decrease significantly the dislocation density at the grain interior in the ARB-processed and annealed Al (Fig. 2.9). In the case of the ARB-processed fcc metals having medium to low stacking fault energy, such as Cu and austenitic steels or the ARB-processed Ti, it has been found that as ARB-processed microstructures are similar to Al and IF steel, but recovery is difficult to achieve and discontinuous recrystallization happens during annealing.11,15,25 One example of discontinuous grow of ultrafine grains during annealing in the commercial purity Ti ARB-processed and annealed is shown in Fig. 2.10. Even in the ARB-processed pure Al, discontinuous growth of particular grains can be observed under certain annealing conditions.13 Figure 2.10 looks like conventional (discontinuous) recrystallization by nucleation and growth, or abnormal grain growth. On the other hand, the microstructural change shown in Fig. 2.9 are much more like normal grain growth. When the ARB process is carried out after solution treatment of materials, precipitation occurs during heat treatment (ageing) following the ARB. Since the ARB-processed specimens have UFG structures with a very high density of grain boundaries, the precipitation behaviors of the ARB-processed materials are significantly different from those of the conventional alloys with coarse-grained structures. For example, the precipitation kinetics from the UFG materials is much faster than that from coarse-grained ones, and sometimes stable phases directly appear during aging treatment, skipping the formation of the metastable phases that usually appear in conventional alloys.26,27


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2.10 Transmission electron microscopy microstructures of the commercial purity Ti ARB-processed by 6 cycles at RT with lubrication and then annealed at various temperatures for 1.8 ks. Observed from TD. (a) As ARB-processed. Annealed at (b) 200°C, (c) 300°C, (d) 400°C, (e) 450°C, and (f) 500°C.

2.4.3 Formation of non-equilibrium phases in ARB Processes similar to ARB had previously been carried out for bulk mechanical alloying of different metals or for fabricating multi-layered materials.28,29 However, roll-bonding was not used in such attempts, but diffusion bonding at elevated temperatures was carried out between each pressing or rolling procedure. Bulk mechanical alloying by the ARB process is of course possible, and nonequilibrium structures including an amorphous phase have been fabricated.30–32 An example of the formation of non-equilibrium nanostructures by the ARB process is introduced here. Sheets of pure Cu (99.96% purity) and pure Zr (99.2% purity), 200 mm in length, 50 mm in width, and 0.2 mm in thickness, were mutually stacked so that the total thickness becomes 1 mm. The overall composition of the multi-stacks was Cu-29at%Zr. The ARB process using 75% reduction per cycle was carried out at RT with lubrication. The ARB was repeated for up to 10 cycles, with an equivalent strain of 15.8, which corresponds to the conventional rolling of a huge plate with a thickness of 568 m down to 1 mm thickness. Figure 2.11 shows a high-resolution TEM microstructure of the Cu/Zr multi-stacks ARB-processed by 9 cycles at RT. A nano-lamellar structure



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2.11 High-resolution TEM microstructure of the Cu + Zr multi-stacks ARB-processed by 9 cycles (equivalent strain of 13.7) at RT. Observed from TD.

composed of mutual alignment of Cu layers and Zr layers is observed. The thickness of each Cu or Zr layer is below 10 nm. In some thinner Zr layers, no periodical contrast is recognized, indicating that an amorphous phase has been formed (indicated as ‘Amo’). Also at the interfaces between Cu layers and Zr layers, thin amorphous regions are observed. EDX analysis using nano-beam has clarified that atomistic scale mixing of Cu and Zr happens at interface regions during the ARB and eventually form an amorphous region.32 It has also been found that the subsequent heat treatment of ARB-processed stacks causes thermally induced amorphization to form sheets of nearly 100% metallic glass.33

2.5

Mechanical properties of nanostructured metals fabricated by ARB

Figure 2.12 shows the changes in the nominal stress–strain curves of the IF steel and 1100-Al during ARB. The ARB process for the IF and 1100-Al were carried out without lubrication at 500°C and RT, respectively. Both materials showed quite similar changes in the stress–strain curves. The strength and ductility were summarized in Fig. 2.13 as a function of the number of the ARB cycles. The strength of the materials increased roughly twice by one cycle of ARB, while the elongation greatly decreased. This is a typical mechanical property of strainhardened materials. The flow stress increased with increasing the ARB cycle, keeping similar shapes of the stress–strain curves. The elongation maintained nearly the same value after the second cycle. After seven cycles, the tensile strength reached 910 MPa in the IF steel and 340 MPa in the 1100-Al, respectively,


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2.12 Engineering stress–strain curves of the ARB-processed materials. (a) IF steel ARB processed at 500°C without lubrication. (b) 1100-Al ARB processed at RT without lubrication.

which were more than 3~4 times higher than those of the starting materials. In stress–strain curves, the ARB-processed specimens reached their maximum strength at early stage of the tensile test, followed by macroscopic necking. Consequently, the specimens had limited uniform elongation (about 1~3%), which is a common feature of the ultra-high strained materials independent of the SPD process.34 Actually, the same materials, deformed highly to the equivalent



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2.13 Strength (0.2% proof stress (s0.2) and tensile strength (sB)) and ductility (uniform elongation (eu) and total elongation (et)) obtained by tensile test at RT for the ARB-processed materials. (a) IF steel ARB processed at 500°C without lubrication. (b) 1100-Al ARB processed at RT without lubrication.

amount of strain, show nearly the same strength, regardless of the processes. Different elongation (ductility) has sometimes been reported in the nanostructured materials SPD-processed by different techniques, but we should note that tensile elongation is significantly affected by the shape and dimensions of the tensile specimens, and in many cases different types of specimens have been used in different groups. It should be emphasized, however, that the UFG materials fabricated by ARB (SPD) do not lose plasticity, because they can be rolled, compressed or bent to fairly high degrees of deformation. There have been many arguments on whether oxides formed at bonded interfaces affect the mechanical properties of the ARB-processed sheets or not. There must be a certain amount of oxides at bonded interfaces in the ARBprocessed materials. However, even after six ARB cycles that can produce a homogeneous UFG structure (Fig. 2.4), the number of bonded interfaces within the 1 mm sheet is only 63 and the interval of the bonded interfaces (the thickness of the original sheet) is 15.6 µm (Table 2.1), which is much larger than the mean grain size (~0.2 µm). The total volume of oxides would thus be relatively small. Therefore, it is believed that the effect of oxides on the mechanical properties of the ARB-processed sheets is not significant below about ten cycles, which is usually used for fabricating UFG structures. The stress–strain curves of commercial purity aluminum (ARB-processed and then annealed) are shown in Fig. 2.14. The change in microstructures during annealing has been already shown in Fig. 2.9. Flow stress of the material decreases with increasing annealing temperature, but tensile elongation, especially uniform elongation, recovers only after the mean grain size becomes larger than 1 µm. Quite similar changes in mechanical properties have been reported in the IF steel (ARB processed and annealed).21 The results show that even if the characteristics


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2.14 Engineering stress–strain curves of the 1100-Al ARB-processed by 6 cycles at 200°C without lubrication and then annealed at various temperatures indicated in the figure for 1.8 ks. Mean grain thickness (dt) in each specimen is also indicated.

of deformation microstructures in the ARB-processed specimens are diminished by annealing, the UFG specimens exhibit limited tensile ductility. The limited uniform elongation of the UFG materials is understood in terms of early plastic instability.21 Plastic instability condition, i.e. necking criteria in tensile test, can be simply expressed in the Considère equation shown below: [2.2]

Here, σ and ε are true stress and true strain, respectively. Grain refinement greatly increases flow stress, especially yield strength, of the material. On the other hand, strain-hardening is not enhanced by grain refinement. As a result, the plastic instability expressed in equation (2.2) is easily achieved in UFG materials. Therefore, it is necessary to enhance strain-hardening ability of the matrix in order to manage both high strength and ductility in nanostructured metals.35 Actually, a good balance of strength and ductility has been reported in multiphased nanostructured metals and alloys.35–39 It is noteworthy in Fig. 2.14 that the specimens having mean grain sizes smaller than 3 µm exhibit yield-point phenomena, nevertheless the material is pure aluminum. A number of such unique and unusual mechanical properties have been recently reported in nanostructured metals fabricated by ARB, such as an increase in tensile ductility with increasing ARB strain in particular Al alloys40



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and the hardening by annealing and softening by deformation phenomena, which are totally opposite to metallurgical common sense.41

2.6

Conclusions

In this chapter, the principles and processing details of the ARB process were explained, and further the nanostructure evolution and mechanical properties of the ARB-processed materials were presented and discussed. The ARB process is the only SPD process applicable to continuous production of large bulky materials, while another batch type SPD processes are disadvantageous for practical application. Although to adapt ARB into large-scale mass production of materials, such as those in the steel industry, is still difficult, very thin strips (~0.1 mm thick) of UFG stainless steel has already been already produced in a relatively smallscale industry using the principle of the ARB (see Chapter 23).42 The present manuscript clearly shows that the ARB is also a nice process at the laboratory scale for obtaining bulky samples having homogeneous nanostructures. By the use of the technique, we have been able to systematically acquire fundamental knowledge of bulk nanostructured metals and alloys.

2.7

References

1 Tsuji N., Saito Y., Lee S.H., and Minamino Y. Adv. Eng. Mater. 2003: 5: 338. 2 Altan B.S., editor. Severe Plastic Deformation toward Bulk Production of Nanostructured Materials. New York: Nova Science Publishers, 2006. 3 Saito Y., Tsuji N., Utsunomiya H., Sakai T., and Hong R.G. Scripta Mater. 1998: 47: 893. 4 Tylecote R.F. The Solid Phase Welding of Metals. London: Edward Arnold, 1968. 5 Lee S.H., Saito Y.,Tsuji N., Utsunomiya H., and Sakai T. Scripta Mater. 2002: 46: 281. 6 Kamikawa N., Sakai T., and Tsuji N. Acta Mater. 2007: 55: 5873. 7 Tsuji N. in,2 p.545. 8 Terada D., Inoue M., Kitahara H., and Tsuji N. Acta Mater. 2008: 49: 41. 9 Dinda G.P., Rosner H., and Wilde G. Scripta Mater. 2005: 52: 577. 10 Perez-Prado M.T., del Valle J.A., and Ruano O.A. Scripta Mater. 2004: 51: 1093. 11 Tsuji N., Kamikawa N., and Minamino Y. Mater. Sci. Forum 2004: 467–470: 341. 12 Huang X., Tsuji N., Hansen N., and Minamino Y. Mater. Sci. Eng. A 2003: 340: 265. 13 Tsuji N., and Kamikawa N. Proc. of the 12th Int. Conf. on Aluminum Alloys (ICAA 12), 2010, The Japan Institute of Light Metals, pp. 1134–1140. 14 Kamikawa N., Tsuji N., and Minamino Y. Sci. Tech. Adv. Mater. 2004: 5: 163. 15 Li B.L., Tsuji N., and Kamikawa N. Mater. Sci. Eng. A 2006: 423: 331. 16 Hansen N., and Juul Jensen D. Phil. Trans. R. Soc. London A 1999: 357: 1447. 17 Ito Y., Tsuji N., Saito Y., Utsunomiya H., and Sakai T.J. Jpn. Inst. Metals 2000: 64: 429. 18 Hansen N. Metall. Mater. Trans. A 2001: 32: 2917. 19 Ikeda K., Yamada K., Takata N., Yoshida F., Nakashima H. and Tsuji N. Mater. Trans. 2008: 49: 24. 20 Ii S., Takata N., Ikeda K., Nakashima H. and Tsuji N. unpublished data.


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21 Tsuji N., Ito Y., Saito Y., and Minamino Y. Scripta Mater. 2002: 47: 893. 22 Tsuji N., Okuno S., Koizumi Y., and Minamino Y. Mater. Trans. 2004: 45: 2272. 23 Humphreys F.J., Prangnell P.B., and Priestner R. Curr. Opinion Solid State Mater. Sci. 2001: 5: 15. 24 Humphreys F.J., and Hatherly M. Recrystallization and Related Annealing Phenomena. Oxford: Pergamon, 1995. 25 Takata N., Yamada K., Ikeda K., Yoshida F., Nakashima H., and Tsuji N. Mater. Trans. 2007: 48: 2043. 26 Tsuji N., Iwata T., Sato M., Fujimoto S., and Minamino Y. Sci. Tech. Adv. Mater. 2004: 5: 173. 27 Terada D., Sato T., and Tsuji N. Proc. of the 30th Risø Int. Symp. on Mater. Sci. Roskilde: Risø National Laboratory, 2009: 351. 28 Atzmon M., Unruh K.M., and Johnson W.L. J. Appl. Phys. 1985: 58: 3865. 29 Yasuna K., Terauchi M., Otsuki A., Ishihara K.N., and Singu P.H. J. Appl. Phys. 1997: 82: 2435. 30 Sieber H., Wilde G., and Perepzko J.H. J. Non-Cryst. Solid 1999: 250–252: 611. 31 Sieber H., Wilde G., Sagel A., and Perpezko J.H. J. Non-Cryst. Solid 1999: 250–252: 616. 32 Ohsaki S., Kato S., Tsuji N., Ohkubo T., and Hono K. Acta Mater. 2007: 55: 2885. 33 Sun Y.F., Todaka Y., Umemoto M., and Tsuji N. J. Mater. Sci. 2008: 23–24: 7457. 34 Iwahashi Y., Wang J., Horita Z., Nemoto M., and Langdon T.G. Metall. Mater. Trans. A 1998: 29: 2503. 35 Tsuji N., Kamikawa N., Ueji R., Takata N., Koyama H., and Terada D. ISIJ Int. 2008: 48: 1114. 36 Tsuji N., Ueji R., Minamino Y., and Saito Y. Scripta Mater. 2002: 46: 305. 37 Ueji R., Tsuji N., Minamino Y., and Koizumi Y. Acta Mater. 2002: 50: 4177. 38 Okitsu Y., Takata N., and Tsuji N. J. Mater. Sci. 2008: 23–24: 7391. 39 Takata N., Ohtake Y., Kita K., Kitagawa K., and Tsuji N. Scripta Mater. 2009: 60: 590. 40 Kim H.W., Kang S.B., Tsuji N., and Minamino Y. Acta Mater. 2005: 53: 1737. 41 Huang X., Hansen N., and Tsuji N. Science 2006: 312: 249. 42 Tsuji N. Adv. Eng. Mater. 2010: 12: 701.


3 Nanocrystalline metals and alloys prepared by mechanical attrition S. SCUDINO and J. ECKERT, IFW Dresden, Germany Abstract: This overview discusses the formation of nanocrystalline materials by mechanical attrition. The chapter starts with a description of the methods and the process variables typically employed for producing nanostructured phases by mechanical attrition. Experimental data for the resulting nanostructures obtained by mechanical milling of single phases as well as by mechanical alloying of phase mixtures are discussed for selected materials with an emphasis on the different mechanisms involved. Finally, problems and possible solutions for consolidating nanostructured powders are also addressed at the end of this chapter. Key words: mechanical attrition, mechanical alloying, powder metallurgy, nanocrystalline materials, consolidation.

3.1

Introduction

Nanocrystalline (also referred to as nanostructured or nanophase) materials are single- or multi-phase polycrystals with particle or grain sizes, layer thicknesses, or domain sizes in the nanometer range (typically less than 100 nm at least in one dimension). Due to their extremely small grain size, an appreciable fraction of the atoms in nanostructured materials are located in the grain boundaries.1 Such unique microstructural features lead to physical and chemical properties that may significantly differ from those of the corresponding coarse-grained materials with the same composition.2–5 In particular, a significant improvement of the mechanical properties, such as a substantial increase in strength and hardness with respect to conventional coarse-grained materials, has been observed in a number of alloys with nanoscale microstructures.2–5 However, one major drawback for the use of nanocrystalline materials in engineering applications is their often limited room temperature ductility.2–5 Nevertheless, recent findings have shown that grain refinement to the nanometer regime may also lead to enhanced plastic deformation,6 therefore, opening up new perspectives for the application of nanocrystalline phases as structural and functional materials. Two main strategies have been used for the preparation of nanocrystalline materials: (i) the bottom-up approach, which consists of building the nanostructure atom-by-atom or layer-by-layer and (ii) the top-down approach that consists of breaking down the microstructure into a nanostructure. Examples of the bottom-up approach are inert gas condensation, chemical vapor condensation and pulse electron deposition.1,7,8 The archetype technique of the top-down approach is 59 © Woodhead Publishing Limited, 2011

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mechanical attrition. This processing route has been widely used for the preparation of nanostructured materials and, different from the top-down approach, produces nanophase structures not by cluster assembly but by the structural decomposition of coarser-grained structures as the result of heavy cyclic plastic deformation.4,9 Mechanical attrition is one of the less sophisticated technologies and, in turn, also one of the most inexpensive to produce nanophase powders. In addition, it can be used for the processing of essentially all classes of materials.9 This, along with the additional advantage of the possible scaling up to tonnage quantities of processed material, has made mechanical attrition a very popular method for the synthesis of nanocrystalline materials, not only for the laboratory scale but also for potential industrial applications.9 In view of the importance of mechanical attrition as a method for nanocrystalline materials synthesis, this overview starts with a description of the methods and the process variables typically employed for producing nanostructured phases by mechanical attrition. Experimental data for the resulting nanostructures obtained by mechanical attrition of single- and multi-phase powders will be described for selected materials, and the mechanisms responsible for the formation of the different nanophase structures will be discussed. Consideration of the problems and challenges for the consolidation of nanostructured powders, as well as a discussion of the possible solutions, will also be addressed at the end of this chapter.

3.2

Mechanical attrition

Mechanical attrition of powders, first developed by Benjamin and coworkers10,11 in the 1970s, is a processing route that can successfully produce new alloys, phases and phase mixtures. This method for materials synthesis can circumvent many of the limitations of conventional alloying and allows the preparation of alloys and composites that cannot be synthesized via conventional casting or rapid solidification routes. Examples are uniform dispersions of ceramic particles in a metallic matrix or alloys of metals with rather different melting points with the aim of improving strength and corrosion resistance.10,11 Over the years, mechanical attrition has attracted enormous interest as a versatile non-equilibrium processing technique resulting in solid-state alloying beyond the equilibrium solubility limit and the formation of amorphous, quasicrystalline or nanostructured materials for a broad range of alloys, intermetallic compounds, ceramics and composites.4,9,12,13,14 Mechanical attrition is usually performed in ball mills capable of high-energy impact forces. For this purpose, a variety of different types of ball mills with different characteristics have been developed, including attrition mills, shaker mills, planetary mills, vibratory mills, etc.14 The milling process consists of loading the starting material and the grinding balls (typically steel or tungsten carbide) into a milling container (vial), which is violently shaken or rotated, depending on the



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mill used. The intensity of milling depends on the internal mechanics of the specific mill and, consequently, on the kinetic energy imparted to the grinding balls, as well as on mass, size and number of the balls. One serious problem in the processing of fine powders by mechanical attrition is potential contamination from the milling media or atmosphere.4,9,13 The small size of the powder particles and the consequent availability of large surface area, along with the continuous formation of new fresh surfaces during milling, contribute to the contamination of the powder.14 If, as in most cases, the milling vial and balls are made of steel, iron is the typical contaminant due to debris of the milling tools. The magnitude of contamination appears to depend on both the time and the intensity of milling.9,15 The other major source of contamination is from the milling atmosphere, i.e. oxygen or nitrogen. Atmospheric contamination is particularly severe for milling of reactive metals, such as titanium and zirconium,9,14 however, it can be drastically reduced by milling in an inert gas atmosphere (e.g. argon). Mostly, mechanical attrition is carried out under dry conditions but also milling with liquid or solid process control agents is possible,13,14 depending on the nature of the milled powders, in order to prevent sticking of the materials to the milling tools. The dynamics of mechanical attrition are extremely complex and strongly depend on the mill characteristics. However, for all types of ball mills the fundamental event of the milling process is the ball–powder collision, as schematically shown in Fig. 3.1. During milling the powder particles are trapped between the colliding balls and are subjected to repeated high-energy impacts, which induce heavy plastic deformations together with fracturing and cold-welding events. For a given composition, the deformation/fracture process, the potential phase transformations during milling and the final structure of the material depend on the powder material properties (e.g. hardness, fracture toughness, etc.), being different for single-phase materials or combinations of ductile/ductile, ductile/ brittle or brittle/brittle components,9 as well as on the milling parameters, i.e. the kinetic energy transferred to the powder and the local temperature during the impacts.9,12 The temperature that the powders experience during milling also depends on the type of mill used and on parameters such as vibration frequency or rotational velocity. Experimental observations and modeling of the mechanics, kinetics and the energy transfer during collision suggest that the temperature rise during milling is about ≤ 100–200 K.9,12 Adjusting or changing the milling conditions can affect the phase formation or can lead to phase transitions between different phases. Depending on the chosen experimental conditions (i.e. energy input, milling temperature), nanocrystalline and amorphous materials as well as quasicrystalline or crystalline phases can be synthesized by mechanical attrition. In addition, the different phases can be transformed into each other by additional milling at higher or lower milling intensity. In particular, this has been demonstrated for the crystal-to-quasicrystal transition, the crystal-to-amorphous transition, and the quasicrystal-to-amorphous transition.16–18


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3.1 Schematic illustration of the basic event occurring during mechanical attrition showing the trapping of powder particles between colliding balls.

3.3

Nanocrystalline phase formation by mechanical attrition

A fundamental feature of mechanical attrition is the development of nanoscale microstructures. As described above, during milling the powder particles are subjected to severe mechanical deformation from repeated high-energy impacts with the milling tools. Deformation occurs under shear conditions and high strain rates (~103–104 s–1), leading to the incorporation of lattice defects and to a continuous refinement of the initial structure of the powder particles to the nanometer regime.4,13 Extended milling may eventually lead to phase transformations, including nanocrystalline equilibrium and metastable phases.4,13 The final structure of a powder subjected to mechanical attrition may depend on the starting material used. Accordingly, mechanical attrition can be divided in two different routes depending on the starting material. The mechanical attrition of powders with different compositions (the mixture of elemental powders as well as



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of intermetallic compounds), in which material transfer occurs, is named mechanical alloying (MA), while the mechanical attrition of single composition powders, such as pure elements and single-phase intermetallic compounds, where material transfer is not required, has been termed mechanical milling (MM).19 In the following section, the evolution of nanocrystalline structures produced by mechanical milling of single phases as well as by mechanical alloying of phase mixtures is discussed with emphasis on the different mechanisms involved. Similarly, selected examples of phase transformation during milling of different starting materials are also presented.

3.3.1 Mechanical milling of single-phase materials Grain refinement to the nanometer regime is a universal phenomenon of the milling process and has been observed in almost all mechanically attrited materials, including pure metals, intermetallic compounds and multi-phase materials.4,9,13,14 The microstructural changes induced by mechanical attrition can be estimated by x-ray diffraction (XRD) methods. The XRD patterns exhibit increasing broadening of the diffraction peaks as a function of milling time, which is caused by size as well as internal strain effects.4,13 The individual contributions of these effects to the total broadening can be separated using standard techniques: the peak broadening due to the reduction of grain or crystallite size (the average coherently diffracting domain size) is inversely proportional to cos θ, whereas broadening due to lattice strain is proportional to tan θ.20,21 The characteristics of grain size refinement by mechanical attrition have been studied extensively in the past years with particular attention on mechanical milling of pure metallic elements. For example, Fecht et al.22–24 observed the continuous decrease of the grain size with increasing milling time down to about 9 nm for the body-centered cubic (bcc) metals and to about 13 nm for the hexagonal close packed (hcp) metals. Similar results in terms of grain refinement with milling time have been also reported for milling of a series of face-centered cubic (fcc) metals.25 Interestingly, the minimum grain size for the fcc elements was found to inversely scale with the melting temperature.25 A similar trend as observed for the fcc metals can be observed for milling of a series of hcp metals spanning over a wide range of melting temperatures (Fig. 3.2). On the other hand, MM bcc metals do not show any significant variation of minimum grain size with the melting temperature,22 probably because of the lack of milling experiments for bcc metals with low melting point. Along with the grain size refinement to the nanometer regime, milling of powders can introduce a considerable amount of lattice strain, which is most presumably linked to the dislocation density.25 In analogy with the minimum grain size, the maximum lattice strain introduced during milling is also meltingpoint dependent, and increases with the melting temperature of the specific metal (Fig. 3.3). The observed dependence of grain size and lattice strain on the melting temperature suggests that recovery rates during the milling process correlate with


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3.2 Minimum grain size obtained by mechanical milling for different fcc, hcp and bcc metals as a function of the melting temperature (data from Fecht et al.22, Eckert et al.25 and Nogales et al.31).

Lattice strain, %

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Minimum grain size, nm

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3.3 Lattice strain for different mechanically milled fcc metals versus melting temperature (adapted from Eckert et al.25).

the melting point of the specific metal, thus preventing very small grain sizes for low-melting elements.25 Another important aspect of nanostructure formation by milling is the stored enthalpy, which is accumulated in the material as a result of the heavy mechanical deformation. This energy is released during heating to elevated temperatures due



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Stored enthalpy, kJ/mol

to recovery, relaxation processes within the boundaries and grain growth24 and can be determined using differential scanning calorimetry (DSC) measurements. As a typical example of mechanically attrited metals, Fig. 3.4 shows the stored enthalpy of MM Ni as a function of the reciprocal grain size.25 The stored enthalpy increases to a maximum value (which does not occur at the minimum grain size) and then decreases during further grain refinement. A plausible explanation for this behavior might be the increase of the impurity content during milling;25 however, a clear motivation for this phenomenon is still missing. The final energies stored during mechanical attrition largely exceed those resulting from conventional cold working of metals and alloys, such as cold rolling or wire drawing.23,25 During conventional deformation the stored enthalpy never exceeds more than a small fraction of the heat of fusion. However, in the case of mechanical attrition the energy stored can reach values corresponding to about 40% of the heat of fusion.25 Point defects and dislocations can account for only a fraction of this energy and, most likely, the major energy contribution is stored in the form of grain boundaries, and related strains within the nanocrystalline grains that are induced through grain boundary stresses.4 The minimum grain size obtainable by milling has been attributed to the competition between the heavy mechanical deformation and recovery by thermal processes and, in turn, by the minimum grain size that can sustain a dislocation pile-up within a grain and by the rate of recovery during milling.25 An estimate for the minimum dislocation separation in a pile-up Lc is given by Lc = 3Gb/π(1–ν)h, with shear modulus G, Burgers vector b, Poisson ratio ν, and hardness h of the

3.4 Stored enthalpy in mechanically milled Ni versus reciprocal grain size d (adapted from Eckert et al.25).


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material. Applying this relation to the milled fcc metals shows that the minimum grain size of fcc metals (d) follows a linear relation with Lc (Fig. 3.5, solid symbols). This gives a lower bound for the grain size of pure metals and reveals that a small grain size itself provides a limit for further grain refinement by milling.25 In addition, the reduction of the grain size is also limited by the rate of recovery during milling, which may be significant for metals with low melting points. It has been found22,24 that in the early stages of milling the deformation of milled powders is localized in shear bands containing a high dislocation density. By increasing the milling time, the lattice strain increases due to the increasing dislocation density and, at a certain strain level, the dislocations annihilate and recombine to small angle grain boundaries, separating the individual grains. The subgrains formed via this route are already in the nanometer size range (about 20–30 nm). With a longer milling time the grain size decreases gradually and the structure finally evolves into nano-grains separated by high-angle grain boundaries. At this stage, no further grain refinement is possible but only grain boundary sliding can occur, which does not refine the microstructure any further.4 These findings indicate that a high initial dislocation density and, thus, a large lattice strain, is necessary for significant grain size refinement by mechanical attrition. This is opposed by the recovery processes whose driving force is the energy stored in the grain boundaries of the milled material. Grain refinement and recovery are closely related to the minimum grain size d through the rate of each

Minimum grain size, nm

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3.5 Minimum grain size obtained by milling of pure metals (solid symbols) and FexCu100–x solid solutions with different compositions (open symbols) versus the minimum distance between two dislocations Lc (adapted from Eckert32).



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process expressed as a function of the grain size, since d is the grain size at which the two rates are equal.32 In the case of metals with low melting temperatures, such as Al, the dislocation density is limited by recovery processes and, therefore, the minimum grain size achievable is most likely governed by the recovery rate. On the other hand, almost no recovery is expected to occur for refractory metals during milling, but a high level of internal strain is created due to the large number of dislocations and other deformation faults introduced. Therefore, the minimum grain size for these elements is limited by the stress required for plastic deformation via dislocation motion rather than by the recovery rate.25 Nanocrystalline phase formation can also be achieved by the mechanical milling of intermetallic compounds. For example, Hellstern et al.33,34 investigated the stability of several intermetallic compounds with CsCl (ordered bcc) structure under high-energy milling. Like the milling of pure metals, they observed a decrease of the grain size with increasing milling time to about 5–12 nm. This was accompanied by disordering of the lattice as shown by the decrease of the longrange order parameter, which became more pronounced with decreasing grain size and finally saturated at about 0.7.34 This indicates that the material does not disorder completely and that some residual chemical disorder (i.e. atoms on wrong sites. For example, in an A-B compound, A atoms on B sites and B atoms on A sites) is present within the nanocrystalline grains after milling. Still, an appreciable part of the strain will reside in the disorder, because atoms on the ‘wrong’ sublattice are to be accommodated on lattice sites, where they do not fit. This gives rise to strain.35 Indeed, MM of CsCl intermetallics introduces a lattice strain of about 2–3%, which is much larger than what is generally observed for pure metals (less than 1%). In addition, milling intermetallic compounds does not lead to a peak of the maximum stored enthalpy, as is typical for pure metals (Fig. 3.4), but the stored energy shows saturation to a maximum value.34 The degree of disordering during mechanical milling of intermetallic phases depends on the structure of the compound, as observed by Jang and Koch36 for the ordered fcc Ni3Al compound, which exhibits complete disordering during milling. Following grain refinement and lattice disordering, the mechanical attrition of intermetallics can lead to mechanically induced phase transformations, such as for the A-15 type Nb3Au compound,37 which exhibits the formation of a nanocrystalline bcc solid solution during milling. This behavior can be understood by considering the Au-Nb equilibrium phase diagram.35 The Nb3Au compound is stable at room temperature and transforms to the bcc solid solution of Au in Nb at elevated temperatures. The type of atomic disorder, obtained after milling, appears to be similar to that generated at high temperature. Similarly to high temperature treatments, milling introduces anti-site disorder in Nb3Au and brings the material into an increasingly higher disordered state, which corresponds to heat treatments at progressively higher temperatures.35 Therefore, in terms of disorder, milling is equivalent to an increase of temperature of the compound up to the point where the transition from Nb3Au to the bcc solid solution occurs.35 This was corroborated


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by the observation that the Au2Nb compound transforms to a nanostructured fcc solid solution of Nb in Au during milling, as predicted when considering the equilibrium phase diagram.38 Other possible phase transformations during milling involving intermetallic compounds include amorphization and the transformation into a different (complex) crystal structure (for a review see Bakker et al.35). Another interesting type of mechanically induced phase transition is the allotropic transformation of pure elements during milling. Examples are the elements of the Group IVB Ti, Zr, and Hf that undergo an hcp-to-fcc allotropic transformation during mechanical milling39–41 and Co,42 which shows a reversible hcp-to-fcc transformation that depends on the milling intensity used. Although recent results43 have shown that allotropic transformations in the Group IVB might be due to impurity contamination during milling, thus raising doubts about the real nature of these transformations, this type of transformation further demonstrates the versatility of mechanical attrition as a tool for the formation of new materials.

3.3.2 Mechanical alloying of phase mixtures Mechanical alloying of powders with different compositions (mixture of elemental powders as well as of intermetallic compounds) is perhaps the most used mechanical attrition technique for the preparation of a wide range of materials including supersaturated solid solutions, amorphous, quasicrystalline or nanostructured materials for a broad range of alloys, intermetallic compounds, ceramics and composites.4,9,12,13,14 The mechanism of nanocrystalline formation operating during MA is different with respect to MM of single phases since it involves material transfer during processing. Although the microstructural evolution during MA depends on the mechanical behavior of the powder components (i.e. ductile or brittle), the primary aspect of the process is the reduction of the diffusion distances between the different phases. For example, for MA of ductile/ductile components, in the early stages of mechanical alloying the particles are cold-welded and plastically deformed, leading to a characteristic layered structure consisting of various combinations of the starting constituents, as illustrated in Fig. 3.6.44 With increasing milling time the thickness of the individual layers decreases so much that it is no longer visible under an optical microscope.9,14 The structure undergoes severe deformation, work hardening and fracture. Fragments generated by this mechanism may continue to reduce in size, giving rise to a more and more refined microstructure.12 Alloying begins to occur at this stage due to the combination of decreased diffusion distances (interlayer spacing), increased lattice defect density, and any heating that may have occurred during the milling operation.14 This has been confirmed by Klassen et al.,45 who investigated the microstructure evolution during the early stages of MA of Ti-Al powder blends. For MA powder with composition Ti25Al75, transmission electron microscopy (TEM) investigations revealed that, after the



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3.6 Typical layered microstructure obtained during mechanical alloying.14

initial formation of an hcp solid solution by the diffusion of Al into Ti, a (partially) ordered Ll2 fcc phase with grain size of about 10–30 nm is formed between the alternating Ti and Al lamellae. The volume fraction of the Ll2 phase increases with increasing milling time until Al is entirely consumed. No additional phase transformation was observed upon further milling. The authors concluded that the Ll2 phase, observed in the final stage of milling, is already formed in the early stages of the phase reaction. In addition, the initial diffusion of Al into the Ti matrix and the resulting formation of the hcp solid solution permit to exclude that the formation of the Ll2 fcc phase at the interface occurs by the diffusion of Ti into the fcc Al. Therefore, the development of the nanocrystalline structure is not a result of a gradual grain refinement process, as observed during milling of pure metals, but it consists of numerous nucleation events at the Ti/Al interface followed by limited growth of the new phase.46 Another remarkable achievement of MA is the production of a homogeneous mixture of immiscible phases. For example, large non-equilibrium solid solubility has been attained by MA for a series of Fe-Cu powders,47 which are essentially


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immiscible and display a large positive enthalpy of mixing. The ultimate grain size of the binary Fe-Cu nanostructured solid solutions depends on the composition of the material (Fig. 3.7). The grain size can be reduced to only 20 nm for pure Cu, whereas it continuously decreases with increasing Fe content, reaching values below 10 nm for the Fe-rich fcc solid solutions. Similarly, the grain size decreases with increasing Cu content for single-phase bcc solid solutions. A second decrease of the bcc grain size occurs for samples with two-phase fcc/bcc microstructure, whereas the fcc grain size in this region is independent of composition. When the contributions of solution hardening and dispersion hardening are taken into account,32,48 the ultimate grain size of the Fe-Cu alloys scales with the minimum dislocation separation in a pile-up Lc (Fig. 3.5, open symbols) in the same manner as the data for pure fcc metals. This indicates that, similarly to MM of pure metals, the minimum grain size in MA Fe-Cu powders can also be attributed to the competition between the plastic deformation and the recovery behavior and demonstrates that both the alloy composition and the microstructure of the material determine the final grain size.32 Solid solubility extension far beyond the equilibrium values has also been reported for mechanically alloyed nanocrystalline Cu-M (M = Ti, Nb, Ni, Cr, Fe and Co),49 Ti-Ni,50 Ni-Nb51 and Al-Nb52 (for an exhaustive review on this topic see13). Among the different alloys characterized by extended solid solubility when prepared by MA, the Al-Mg system has been extensively investigated in recent years.53–60 The equilibrium solid solubility of Mg in Al is quite small at room temperature (about 1 at.%61). However, depending on the initial solute content in the elemental powder mixture, the milling parameters and the presence of control

3.7 Effect of composition on the minimum grain size achievable by mechanical alloying of FexCu100–x powders (adapted from Eckert32).



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processing agents, an extended solid solubility of Mg in Al can be achieved by MA of elemental powders. For example, Calka et al.53 showed that mechanical alloying allows to extend the solid solubility of Mg in Al up to 18 at.% in the case of Al70Mg30 and 45 at.% for Al50Mg50. Similarly, Zhang et al.54 and Schoenitz et al.56 observed for mechanically alloyed Al60Mg40 the formation of a solid solution containing 23 at.% and 20.8 at.% Mg, respectively. Recently, it was found that both MA of elemental powder mixtures and MM of the single-phase intermetallic compound with composition Al60Mg40 lead to the same product, i.e. a supersaturated Al(Mg) solid solution.60,62 Although MA and MM may lead to the formation of the same product (i.e. the Al(Mg) solid solution), the solid-state transformations induced by the two processing routes occur by different mechanisms due to the different starting materials used (phase mixtures and single-phase materials, respectively). MA is not a purely mechanical process but it involves interdiffusion, driven by the negative heat of mixing, of alternating thin layers as observed for the interdiffusion of thin films of pure metals.63,64 On the other hand, MM consists of energizing the equilibrium crystalline compound by the severe cyclic deformation provided by the milling process.19 Mechanical milling increases the energy of the compound by the generation of chemical disorder, point defects such as vacancies, and lattice defects (e.g. dislocations).14,21,35 In addition, an important contribution to the energy increase comes from the reduction of the grain size to the nanometer level and the consequent storage of energy in the grain boundaries, which constitute an appreciable fraction of the material volume.14,21,35 This energy is stored in the crystal up to a point at which it becomes unstable. The highly energized material then lowers its energy by transforming into a different atomic structural arrangement, e.g. the supersaturated solid solution. With this in mind, it is possible to draw a schematic illustration of the formation of the supersaturated Al(Mg) solid solution by MA and MM. Instead of lowering the Gibbs free energy of the system, such as for mechanical alloying, during mechanical milling the free energy of the equilibrium crystalline compound is raised to a level equal to or larger than that of the metastable phase. The process can be better understood by referring to Fig. 3.8, which schematically shows the Gibbs free energies for the different phases that may form during mechanical attrition of binary Al60Mg40. The straight line represents the free energy of the elemental powder mixture of the pure elements Al and Mg. The broad curve is the free energy of the metastable solid solution and the narrow curve is the free energy of the crystalline intermetallic compound β-Al3Mg2 with composition Al60Mg40. From thermodynamic point of view, the two processes are quite different. While for MA of the mixture of pure Al and Mg with a composition corresponding to that of the intermetallic compound β-Al3Mg2 (reaction [1] → [2]), the initial state has a Gibbs free energy larger than that of the final product (i.e. the solid solution), for MM of the intermetallic compound β-Al3Mg2 (reaction [3] → [2]), the initial state has a Gibbs free energy lower than that of the final product. In the first case the negative heat of mixing of the elemental powders provides the driving force for


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3.8 Schematic free energy diagram of the Al–Mg system for the different phases that may form during mechanical alloying of elemental powder mixtures and mechanical milling of the single-phase intermetallic compound (adapted from Scudino et al.60).

interdiffusion and eventually for metastable phase formation. On the other hand, no chemical driving force exists for the reaction [3] → [2] In this case, the free energy of the equilibrium intermetallic compound must be raised above that of the metastable solid solution by the mechanism previously mentioned. A microscopic model for MA, which explains intermixing in systems with positive mixing enthalpy, has been proposed by Schwarz.65 The model is based on dislocation-mediated intermixing through the diffusion of solutes along the dislocation cores (dislocation pipe diffusion). Mechanical alloying produces fresh metal/metal surfaces and a high density of dislocations. Due to the strong attractive interaction between solutes and dislocations, the solutes can diffuse along the dislocation cores with an activation energy which is about half of that needed for bulk diffusion. When a powder particle is trapped between colliding balls, for short time intervals on the order of milliseconds, it is subjected to a high stress pulse. As a result, some or all the dislocations in the particle are forced to glide and leave their previous positions. However, the solutes that have diffused along the dislocation cores are not able to follow the fast moving dislocations and, consequently, are left behind as strings of solutes in a highly supersaturated state, which have an excess chemical energy. Multiple repetition of this process leads to effective alloy intermixing and/or to stable and metastable phase formation.



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Besides thermodynamic considerations, kinetic aspects also play a central role on the phase selection during mechanical attrition. This is particularly important when different (stable and metastable) phases compete for the final product. Typical examples are the formation of amorphous or nanostructured quasicrystalline powders by mechanical alloying.12 The amorphous phase and most of the quasicrystalline materials are metastable with respect to the equilibrium crystalline phases, i.e. an energy barrier exists preventing these metastable phases from spontaneous crystallization.12,18 The thermodynamically stable state of a system is determined by a minimum in the Gibbs free energy G. In metallic systems, the Gibbs free energy of the equilibrium crystalline state Geq is always lower than that of the metastable phases Gmeta below the melting temperature. In order to form a metastable phase by mechanical attrition, the free energy of the equilibrium phase has to be firstly raised to a state G0 (Fig. 3.9). This high-energy state can be achieved by mechanical attrition through the mechanisms explained previously. The free energy of the system can be then lowered from G0 either by the formation of the metastable phase with free energy Gmeta or by the formation of the equilibrium phase. The equilibrium phase is thermodynamically favored, since the driving force ∆Geq = (G0 – Geq) is larger than that for metastable phase formation ∆Gmeta = (G0 – Gmeta). However, the formation of equilibrium or metastable phases depends on thermodynamic as well as on kinetic factors. The formation of the metastable phase is then possible if the system is kinetically restricted from reaching the equilibrium state of lower free energy, i.e. metastable phase formation proceeds considerably faster than the

3.9 Schematic representation of the basic principles of metastable phase formation by mechanical attrition.


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formation of the equilibrium phase from the initial state G0. At the same time, the metastable phase must not transform into the equilibrium phase as the reaction proceeds, i.e. the timescale for transformation of the metastable phase must be longer than that of metastable phase formation. These kinetic constraints can be summarized as12,18,66:

τ0→meta 3 GPa already exist.27 This kind of martensite is produced in fairly large steel samples by rapid cooling from the austenitic condition. However, the dimensions can be limited by the need to achieve a uniform microstructure, a fact implicit in the original concept of hardenability. To increase hardenability requires the addition of expensive alloying elements. The rapid cooling can lead to undesirable residual stresses28,29 that can ruin critical components and have to be accounted for in component life assessments. Recently, an innovative design procedure based on phase transformation theory30 has been successfully applied to design strong, tough and affordable nanocrystalline steel without using deformation, rapid heat-treatment or mechanical processing. Furthermore, the material can be produced in a form that is large in all its three dimensions. The new material relies on a microstructure called bainite, which has been known since 1930; the novelty is in the alloy design which leads to the fine scale and controlled response to heat treatment.

4.3

Phase transformation theory: a powerful tool for the design of advanced steels, from micro to nano

It has long been known that alloying the steel with about 2 wt.% of silicon can in appropriate circumstances yield a carbide-free microstructure, which is a mixture of bainitic ferrite and carbon-enriched residual austenite. The silicon does not dissolve in cementite and hence suppresses its precipitation from austenite. Cementite is a cleavage and void-initiating phase that is best eliminated from strong steels. However, the full benefits of this carbide-free bainitic microstructure have frequently not been realized. This is because the transformation to bainitic ferrite stops well before the equilibrium carbon concentration in austenite is reached.31–34 There remain large regions of untransformed austenite that decompose under stress to hard, brittle martensite. The problem, which is essentially thermodynamic in origin, can be solved by altering the relative stabilities of the austenite and ferrite phases. The essential principles governing the optimization of such microstructures are now well established. Everything must be done that encourages an increase in the amount of bainitic ferrite so as to consume the blocks of austenite.35,36 With careful design, impressive combinations of strength and toughness have been reported for highsilicon bainitic steels.35–39 More recently, it has been demonstrated experimentally


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that models based on the atomic mechanism of displacive transformation can be applied successfully to the design of carbide-free bainitic steels, the only experiments needed are those to validate the theoretical predictions.40,41 Toughness values of nearly 130 MPa m1/2 were obtained for strength in the range of 1.6–1.7 GPa. This compares well with maraging steels, which are at least ninety times more expensive. The details of the design method, which is based on the discipline with which the atoms move during transformation, are as follows. Bainite grows without diffusion in the form of tiny plates known as ‘sub-units’; each plate grows to a limited size, which is determined by the plastic accommodation of the shape deformation accompanying transformation. One consequence of diffusionless growth is that the plates can be supersaturated with carbon, in which case the carbon partitions into the residual austenite soon after the completion of bainite growth. Diffusionless growth of this kind can only occur if the carbon concentration of the parent austenite is less than that given by the T o′ curve. The To curve is the locus of all points, on a temperature versus carbon concentration plot, where austenite and ferrite of the same chemical composition have the same free energy. The T ′o curve is defined similarly, but taking into account the strain energy associated with the fact that the shape deformation accompanying the displacive transformation is accommodated, at least partially, by plastic relaxation. The carbon content of the austenite at the termination of phase transformation for different temperatures in different steels is shown in Fig. 4.2. The calculated values for T o′ and paraequilibrium Ae 3′ phase boundaries are also plotted. Likewise, the same types of calculation, but not considering the stored energies of the related phases, are presented as To and Ae3. The measured concentrations in austenite at temperatures below the BS temperature (see Fig. 4.2) lie closer to the T o′ or To value boundaries and far from the paraequilibrium phase boundaries (Ae3 and Ae 3′ lines) for all the steels. The results are consistent with a mechanism in which the bainite grows without diffusion, but with excess carbon partitioning into the austenite soon after transformation. The reaction is said to be incomplete since transformation stops before the phases achieve their equilibrium compositions. In contrast, the measured carbon content of retained austenite at temperatures above the BS temperature in steels with a carbon content of 0.3 wt.% corresponds to that given by the Ae3 and Ae 3′ lines. The presence of Widmanstätten ferrite formed at the highest temperatures in these steels suggests that this trend is consistent with the difference between the growth mechanisms for Widmanstätten and bainitic ferrite formation, the former involving carbon diffusion control with equilibrium partitioning of carbon, and the latter involving that bainite initially forms having a full supersaturation of carbon and grows by a mechanism essentially displacive in nature.42 It follows that the maximum amount of bainitic ferrite that can form in the absence of carbide precipitation is limited by the T o′ curve; this is a severe limitation if large quantities of blocky austenite remain in the microstructure at the point where transformation stops. The design procedure avoids this difficulty



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4.2 Calculated phase boundaries for different steel grades together with X-ray experimental data representing the carbon concentration of the austenite that is left untransformed after cessation of the bainite/ Widmanstätten reaction.

in three ways: by adjusting the T o′ curve to greater carbon concentrations using substitutional solutes, by controlling the mean carbon concentration, and by minimizing the transformation temperature. It is worth pointing out that attempts have been made to interpret the T o′ criterion differently. One theory argues that the reason why the bainite reaction stops © Woodhead Publishing Limited, 2011

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prematurely is because of the plastic work done as the plate grows by a displacive mechanism overwhelms the driving force for transformation.43,44 However, the theory is derived incorrectly in that the calculated work is divided by the fraction of remaining austenite, whereas it is in fact per unit quantity of bainite. Furthermore, there is an upper limit to the amount of work done in plastic accommodation; this is the strain energy associated with an elastically accommodated plate, amounting to 400 J mol–1.45 An alternative interpretation46 requires local equilibrium at the interface, contradicting atomic resolution experiments that show the absence of substitutional solute partitioning.47,48 Returning now to the design, it is known that blocky austenite should be avoided to ensure good toughness. The size of these blocks (which may transform to brittle martensite under stress) must be less than or comparable to that of other fracture initiating phases such as non-metallic inclusions. A reduction in the scale of the microstructure enhances both strength and toughness; this leads naturally to the conclusion that the microstructure is best generated at low temperatures. The question then arises, what is the lowest temperature at which bainite can be obtained? In order to answer this question, one must be able to reliably calculate the highest temperature at which bainite can form. This requires a consideration of both nucleation and growth. Bainite can only form below the T o′ temperature when:

[4.5]

∆Gγα

where GSB  400 J is the stored energy of is the free energy change accompanying the transformation of austenite into ferrite without any change in chemical composition. The first condition therefore describes the limit to growth. The second condition refers to nucleation; thus, ∆Gm is the maximum molar Gibbs free energy change accompanying the nucleation of bainite. GN is a universal nucleation function based on a dislocation mechanism of the kind associated with martensite.42,49–50 The variation of GN with temperature is well behaved even for the high carbon steels of interest here.51 Together with the growth condition, the function allows the calculation of the bainite start temperature, Bs , from knowledge of thermodynamics alone. An example calculation is presented in Fig. 4.3, which reveals the important result that extraordinarily low transformation temperatures can be achieved because the bainite and martensite start temperatures remain separated. The rate of reaction is also important since transformation must be achieved in a realistic time. For this purpose, a method34 developed to allow the estimation of isothermal transformation diagrams can be used, with the chemical composition as an input. Calculated time–temperature–transformation (TTT) diagrams indicate the time required to initiate transformation. Such calculations also help design the hardenability of the alloy so as to avoid interfering reactions such as allotriomorphic ferrite and pearlite. mol–1

bainite42;



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4.3 Computed martensite-start, Ms, and bainite-start, Bs, temperatures in Fe-2Si-3Mn-C alloy system.

4.4

NANOBAIN steel: a material going to extremes

Low transformation temperatures are associated with fine microstructures, which in turn possess strength and toughness. The theory described above has been used to develop steels that transform to bainite at temperatures as low as 125°C, in timescales that are practical (Table 4.1). The low Bs temperature is a consequence of the high carbon concentration and, to a lesser extent, solutes such as manganese or chromium, which in the present context increase the stability of austenite relative to ferrite. The molybdenum is added to ameliorate any temper-embrittlement phenomena due to inevitable impurities such as phosphorus. The alloys all contain sufficient silicon to suppress the precipitation of cementite from any austenite. In the steels designated NANOBAIN 1 and 2 (Table 4.1), bainite can take between 2 to some 60 days to complete transformation within the temperature range 125– 325°C.52,53 In a commercial scenario it may be useful to accelerate transformation without losing the ability to utilize low temperatures. Certain elements increase the free energy change when austenite transforms and hence should accelerate its decomposition; hence, the cobalt and aluminium containing alloys in Table 4.1. Table 4.1 Compositions of NANOBAIN alloys, wt.% Steel NANOBAIN NANOBAIN (at.%) NANOBAIN NANOBAIN

C 1 2 3 4

Si

Mn

Cr

Mo

V

0.79 1.59 1.94 1.33 0.30 0.11 0.98 1.46 1.89 1.26 0.26 0.09 (4.34) (2.76) (1.82) (1.28) (0.14) (0.09) 0.83 1.57 1.98 1.02 0.24 – 0.78 1.49 1.95 0.97 0.24 –


Co

Al

– –

– –

1.54 1.60

– 0.99

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4.4 Microstructure formed by isothermal transformation in NANOBAIN 2 at: (a) 200°C for a day; (b) 200°C for two days; and (c) 200°C for six days.

Micrographs after isothermal transformation of austenite to bainitic ferrite at 200°C at different time intervals in NANOBAIN 2 are illustrated in Fig. 4.4. After a day of holding time at 200°C, bainite transformation has not started and a mixture of martensite and retained austenite is obtained by quenching (Fig. 4.4 (a) ). © Woodhead Publishing Limited, 2011


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A longer annealing time (two days) at this temperature was required to obtain a significant amount of bainitic transformation, as shown in Fig. 4.4 (b). Transformation is completed after six days of holding time, when a fully bainitic microstructure (~90% bainite) is obtained (Fig. 4.4 (c) ). The calculated34,54,55 TTT diagrams for the initiation of transformation in NANOBAIN 1 and 2 are shown in Fig. 4.5, which also contain experimental data for the reaction times. The upper C-curve represents the onset of reconstructive transformations such as allotriomorphic ferrite and pearlite, whereas the lower curve is for bainite. The measured values for a detectable degree of transformation are in reasonable agreement with those calculated, except at the highest temperature (300–400°C) where the time period required is underestimated. X-ray analysis was used to estimate the quantities of retained austenite present at the point where transformation ceases (Fig. 4.6 (a) ). The retained austenite fraction is expected to increase for the higher transformation temperature because less bainite forms; this is in contrast to the situation with low-carbon alloys, where a larger fraction of bainite favours the retention of austenite because of the portioning of carbon into the austenite.

4.5 Calculated TTT diagrams for the initiation of transformation, and measured times for the commencement (filled points) and termination of reaction (open circles): (a) NANOBAIN 1; (b) NANOBAIN 2.


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The maximum amount of bainite that can be obtained at any temperature is limited because the carbon content of the residual austenite must not exceed that given by the T ′o curve. At that point, the enriched austenite can no longer transform into bainite. The carbon concentrations of the austenite and bainitic ferrite as determined from X-ray analysis for NANOBAIN 2 are also presented in Fig. 4.6. The evolution of carbon in austenite and bainitic ferrite during transformation at 200°C is shown in Fig. 4.6 (b). Similarly, the carbon content of the austenite and bainitic ferrite at the termination of bainite reaction for different transformation temperatures is shown in Fig. 4.6 (c). The measured carbon concentrations in austenite lie closer to the T o′ value boundary and far from the paraequilibrium phase boundary. This trend is

4.6 X-ray experimental data on: (a) volume fractions of retained austenite; (b) carbon content in bainitic ferrite and retained austenite of the microstructure obtained by isothermal transformation at 200°C for 2 to 10 days in NANOBAIN 2; and (c) X-ray results corresponding at the termination of bainite reaction for different transformation temperatures in NANOBAIN 2. Xo represents the overall carbon content of the steel. T o′ and the paraequilibrium A’3 curves were calculated according to Bhadeshia.55



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4.6 Continued.

consistent with a mechanism in which the bainite grows without any diffusion, but with excess carbon partitioning into the austenite soon after transformation. The reaction is said to be incomplete since transformation stops before the phases achieve their equilibrium compositions. The transmission electron micrograph in Fig. 4.7 illustrates a typical microstructure of low-temperature bainite, with slender plates that are incredibly thin and long, giving a most elegant fine scale structure, which is an intimate mixture of austenite and ferrite. Dislocation debris is evident in both the bainitic ferrite and the surrounding austenite. Extensive transmission microscopy failed to reveal carbides in the microstructure, only a few minute (20 nm wide and 175 nm long) cementite particles in the ferrite within NANOBAIN 1 transformed at

4.7 Transmission electron micrographs of microstructure obtained at 200°C for 15 days in NANOBAIN 2.


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190°C for two weeks.52 Quite remarkably, the plates formed at 200°C in Steel B (Fig. 4.7) have a width that is less than 50 nm, with each plate separated by an even finer film of retained austenite. It is this fine scale that is responsible for much of the tenacity of the microstructure, with hardness values in excess of 600 HV and strength in excess of 2.5 GPa.52 The dispersion of films of austenite undoubtedly helps render the steel tough. Analysis indicates that the largest effects on plate thickness are the strength of the austenite, the free energy change accompanying transformation and a small independent effect due to transformation temperature.56 In the present case, the observed refinement is a consequence mainly of high carbon content and the low transformation temperature on enhancing the strength of the austenite.

4.5

Accelerating the bainite reaction at low temperatures

Slow transformation gives the ability to transform large components to a uniform microstructure free from residual stresses or complex processing. Suppose, however, that there is a need for more rapid heat treatment. The transformation can easily be accelerated to complete the processing within hours (as opposed to days), by making controlled additions of substitutional solutes to the steel, such that the free energy change as austenite changes into ferrite is enhanced. There are essentially two choices: aluminium and cobalt, in concentrations less than 2 wt.%, have been shown to accelerate the transformation in the manner described.57 Both are effective, either on their own or in combination. They work by increasing the driving force for the transformation of austenite; they have therefore been added to make NANOBAIN 3 and 4, which should then transform more rapidly. Fig. 4.8 (a) shows the increase in the reaction rate due to the cobalt; the effect is particularly large when both elements are added. A further rate increment is possible by refining the austenite grain size (Fig. 4.8 (b)). An increase in the free energy change also means that a greater fraction of bainite is obtained, which may have the additional advantage of increasing the stability of the austenite.57

4.6

Characterizing nanocrystalline bainitic steels at the atomic scale

The complexity of bainite formation mechanism and kinetics, and the apparent diversity of its microstructural appearance, gives rise to disagreement in identifying its correct definition. However, the well-known difference in carbide distribution between bainite formed at high and low temperatures, viz. intralath and interlath respectively, appears to exist in a majority of steels and makes the classical nomenclature of upper and lower bainite useful, both in describing the microstructural appearance and in classifying the overall reaction mechanism.



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4.8 (a) Kinetics of bainite formation at 200°C in NANOBAIN 2–4 steels; (b) effect of prior austenite grain on bainite formation at 200°C in NANOBAIN 3 steel.

Both upper and lower bainite consist of plates of ferrite, known as sub-units, separated by cementite. The plates of ferrite grow in aggregates called sheaves of bainite. Within each sheaf, the plates of ferrite are parallel and share a common crystallographic orientation. The essential difference between upper and lower bainite is with respect to the carbide precipitation. In upper bainite, the bainitic ferrite is free of precipitation; carbides grow from the regions of carbon-enriched austenite, which are trapped between the sub-units of ferrite. In contrast, lower bainitic ferrite contains a fine dispersion of plate-like carbides within the bainitic ferrite plates. The carbide particles usually precipitate in a single crystallographic orientation such that their habit plane is inclined at ~60° to the plate axis. There are many observations that reveal that lower bainitic cementite forms within supersaturated ferrite by a displacive mechanism without the partitioning of substitutional solute.58 The cementite lattice is generated by the deformation of the ferrite crystal structure, at a rate controlled by the diffusion of carbon. The iron/substitutional solute content ratio thus remains constant everywhere and subject to that constraint, the carbon achieves equality of chemical potential; the cementite is then said to grow by paraequilibrium transformation. In contrast, the precipitation of carbides in upper bainite is a secondary process that does not interfere with the mechanism of formation of bainitic ferrite except


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in the sense that any precipitation from austenite will deplete its carbon content, thereby promoting further transformation. In fact, the precipitation of cementite from austenite during bainite formation can be suppressed using silicon as an alloying element because the driving force for precipitation is dramatically reduced when the cementite is forced to inherit the silicon present in the parent phase.59 The bainitic microstructure in high silicon steels, commonly known as carbide-free bainite, consists of fine plates of bainitic ferrite separated by carbonenriched regions of retained austenite. As mentioned above, extensive transmission electron microscopy (TEM) of this novel microstructure has failed to reveal carbide particles inside the bainitic ferrite. This is indeed an interesting observation, since at these temperatures, the steel with such high carbon levels would transform to a lower-bainitic microstructure. After extensive aging at 200°C for two weeks, just a few 20 nm wide and 175 nm long cementite particles have been observed inside a thicker bainitic ferrite plate in NANOBAIN 2.60 The difference between upper and lower bainite comes from a competition between the rate at which carbides can precipitate from ferrite and the rate with which carbon is partitioned from supersaturated ferrite into austenite.61 The precipitation of cementite from lower bainite can occur at temperatures below 125°C, in time periods too short to allow any substitutional diffusion of iron atoms. The long-range diffusion of carbon atoms is of course necessary, but because carbon resides in interstitial solution, it can be very mobile at temperatures as low as –60°C.62 The formation of cementite or other transition carbides of iron such as ε-carbide, in these circumstances of incredibly low atomic mobility, must differ from diffusional decomposition reactions. It has been suggested that63 the cementite lattice is generated by a displacive mechanism with paraequilibrium, i.e. a homogeneous deformation of supersaturated ferrite combined with the necessary diffusion of carbon. The X-ray diffraction analysis results in Fig. 4.6 (b) indicated that the carbon concentration in the bainitic ferrite was much higher than that expected from paraequilibrium thermodynamics between austenite and ferrite.60 This supersaturation was attributed to the trapping of carbon at the dislocations in the bainitic ferrite. Using transmission electron microscopy, Smith64 estimated a mean dislocation density of 4 × 1014 m–2 in a Fe-0.07C-0.23Ti wt.% alloy when isothermally transformed to bainite at 650°C. This relatively high dislocation density is attributed to the fact that shape deformation accompanying displacive transformations is accommodated partially by plastic relaxation.65 However, no direct observation has been yet reported of the interstitial carbon Cottrell atmosphere in bainitic ferrite. In this sense, atom probe tomography (APT) was used to characterize at the atomic scale bainitic microstructures formed at 200 and 300°C in NANOBAIN 2 bainitic steel. The large field of view and rapid analysis capability of this technique facilitated the analysis of dislocations in these materials.



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4.6.1 Solute distribution during transformation Five at.% carbon isoconcentration surface and concentration profiles from NANOBAIN 2 annealed at 200°C for four days are shown in Fig. 4.9. The distribution of carbon atoms in the analysis volume is not uniform and carbon-rich and carbon-depleted regions are clearly distinguishable. As no crystallographic information was available, the carbon-enriched regions of the atom maps are assumed to represent a region of austenite, as its carbon content is higher than the average value of 4.3 at.%, and the low carbon (< 1 at.%) regions indicate the ferrite phase. This figure shows an example of an austenite-ferrite interface for a transformation temperature of 200°C. For instance, comparison of APT results and the corresponding X-ray analysis for NANOBAIN 2 is presented in Table 4.2. In most cases, the APT results on carbon content of both bainitic ferrite and austenite are lower than those measured by X-ray. This is because APT estimate is a simple counting of atoms within the selected volume of matrix of ferrite or austenite that does not contain any carbon-enriched regions such as dislocations and boundaries, and not an average of a larger volume that may be enriched in carbon as in the X-ray estimate. However, both techniques confirm the small extent of carbon enrichment in the residual austenite compared to nominal carbon concentration of the steel and the high level of carbon in bainitic ferrite, well beyond that expected from paraequilibrium with austenite (~0.12 at.% C). APT results also indicate that the amount of carbon in bainitic ferrite increases as the transformation temperature decreases. It is also clear from the APT data in Fig. 4.9 that there is no significant segregation of either substitutional elements or carbon to the austenite–ferrite interface. Consistent with previous work,31 quantitative data confirms the absence of any partitioning of the substitutional elements between the phases involved. The results are fully consistent with the diffusionless transformation of austenite to bainite.66 The absence of any significant carbon build-up at the interface indicates that the interface must be semi-coherent, with a high degree of coherency, consistent with the shape change effect mentioned earlier. Thus, the interface may not provide a very large sink for carbon atoms.

Table 4.2 Carbon content in austenite and bainitic ferrite in NANOBAIN 2 steel Isothermal heat X-ray analysis Atom probe tomography treatment Austenite Bainitic Austenite Bainitic ferrite ferrite 200°C – 144 h 300°C – 8 h

(6.60 ± 0.44) at.% (2.92 ± 0.30) at.% (5.39 ± 0.18) at.% (0.62 ± 0.10) at.% (5.67 ± 0.44) at.% (1.37 ± 0.30) at.% (6.85 ± 0.22) at.% (0.52 ± 0.04) at.%


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4.9 Five at.% carbon isoconcentration surface and concentration profiles of selected volume showing austenite and ferrite regions obtained from NANOBAIN 2 transformed at 200°C during four days.



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4.6.2 Carbon trapped in defects A carbon atom map obtained from NANOBAIN 2 annealed at 200°C for two days is shown in Fig. 4.10. The carbon-enriched region at the top-left of the atom map represents austenite and the low carbon regions indicate the ferrite phase. Finally, the linear features with significant levels of carbon are speculated to be dislocations in the vicinity of a ferrite–austenite interface. The carbon, manganese, molybdenum and silicon atom maps of a selected volume orientated normal to a linear segment of the dislocation are also shown in Fig. 4.10. It is evident from these atom maps that dislocations only trap the carbon atoms, as originally suggested by Kalish and Cohen.67 The size of the Cottrell atmosphere in the vicinity of the dislocation was

4.10 Carbon atom map of dislocations in the vicinity of a ferrite– austenite interface (54 nm × 52 nm × 99 nm), and projected atom maps showing carbon segregation about dislocation in NANOBAIN 2 transformed at 200°C for two days.


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estimated from the envelope method68 to be approximately 5–6 nm. The average carbon level of the Cottrell atmosphere was estimated to be 7.4 ± 0.1 at.% C. This value is in good agreement with the prediction of Cochardt et al.69 of a saturation carbon concentration of 6–7 at.% in the region around the core. Wilde et al.70 also observed a maximum carbon concentration within a dislocation atmosphere of 8 at.% C from an energy-compensated optical position-sensitive atom probe analysis of a quenched and room temperature aged Fe-C alloy. The relatively high dislocation density associated with bainitic ferrite is often attributed to the fact that the shape deformation accompanying the displacive transformation is accommodated at least partially by plastic relaxation. Then the resulting dislocation debris introduced into the austenite can be inherited by any bainite that forms subsequently.65 Plastic relaxation may also follow in the bainite itself, since the yield stresses of both ferrite and austenite decrease with increasing transformation temperature. Plastic relaxation of the shape change has been observed experimentally, when pre-polished samples of austenite are transformed to bainite, the adjacent austenite surface does not remain planar but, instead, exhibits curvature that is characteristic of slip deformation.71 Observations of the transformation using hot-stage TEM revealed that the growth of bainite is accompanied by the formation of dislocations in and around the bainite,72 and direct observations of the austenite–ferrite interface also provide evidence of plastic accommodation in both phases.73 Sandvik and Nevalainen74 demonstrated that the austenite adjacent to the bainitic ferrite undergoes twinning deformation and that the density of twins increases as the transformation temperature decreases. It is known that impurities such as phosphorus, calcium and silicon boundaries can segregate on incoherent twin boundaries with high free volume.75–77 Carbon atom map in Fig. 4.11 shows a very fine scale modulation in NANOBAIN 2 transformed at 300°C for four hours. Results suggest that carbon is also segregated at microtwins in retained austenite (average carbon content of 5.3 at.%). It is believed that solute segregation on defects, as those presented in Figs. 4.10 and 4.11, plays an important role on carbon redistribution during bainite transformation. Dislocations associated with plastic relaxation in austenite are inherited by any bainite that forms subsequently, and segregation at dislocations is expected to bind and hence prevent or hinder the carbon atoms from diffusing out of the ferrite lattice. This explains the high level of carbon that exists in the bainitic ferrite after transformation and the small extent of carbon enrichment detected in the residual austenite. Moreover, the increase in the amount of carbon in bainitic ferrite as the transformation temperature decreases is consistent with the fact that the dislocation density of bainitic ferrite is higher the lower the reaction temperature.78

4.6.3 Cementite formation in lower bainite Matas and Hehemann79 first suggested that the initial carbide in lower bainite is ε-carbide, which is subsequently replaced by cementite. The rate at which the © Woodhead Publishing Limited, 2011


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4.11 Carbon atom map showing carbon segregation about microtwins in retained austenite for NANOBAIN 2 transformed at 300°C for four hours.

ε-carbide converts to cementite increases with temperature, but also depends on the steel composition. In fact, a high silicon concentration retards the reaction, as is commonly observed in the tempering of martensite.80 The detection of ε-carbide instead of cementite in lower bainite implies the existence of a carbon supersaturation in bainitic ferrite.81 However, ε-carbide is not always found as a precursor to the precipitation of cementite in lower bainite. Bhadeshia and Edmonds73 failed to detect ε-carbide in a high silicon medium carbon steel even during the early stages of the lower bainite transformation. This has been the case in the present investigation. Initially, TEM was unable to reveal carbide particles inside bainitic ferrite; however, after a large and equivalent set of accumulated APT results, cementite has been identified as the lower bainite carbide despite the high carbon and high silicon content of the steel. An example of carbide particle precipitated inside bainitic ferrite for NANOBAIN 2 transformed at 200°C for ten days is shown in carbon and silicon atoms maps presented in Fig. 4.12. The carbon level allows identifying the type of carbide precipitated inside bainitic ferrite (~25 at.% for cementite and ~30 at.% for ε-carbide). Beside the apparent low carbon concentration of cementite, it is clear from these results that paracementite is observed. In earlier APT works on steels, apparent low carbon


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4.12 Carbon and silicon atom maps showing cementite particle precipitated inside bainitic ferrite in NANOBAIN 2 transformed at 200°C for ten days.

concentrations of cementite were also reported.82–84 These results are consistent with those reported for cementite precipitation in martensite during the early stages of tempering.82,85 Although the carbon concentration changes at the cementite–ferrite interface, silicon does not change at all through the interface, indicating that the concentration of silicon is uniform throughout both phases. Since silicon does not partition and is expected to favour the precipitation of ε-carbide, the absence of ε-carbide precipitation in this high-carbon bainitic steel can be only rationalized in terms of carbon trapping at dislocations, as suggested by Kalish and Cohen.67 Thus, APT results confirm that the ε-carbide stage is missed in the precipitation sequence due to the high carbon tied up at the dislocations.



4.7

The mechanical properties of nanocrystalline bainitic steels

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The hardness of the nanostructured bainite can be as high as 690 HV, with tensile strengths in excess of 2.2 GPa, compressive strength in excess of 3 GPa, ductility in the range of 5–30% and fracture toughness (KIC ) values up to 45 MPa m1/2. A summary of the mechanical properties obtained for NANOBAIN 3 and 4 steels is illustrated in Fig. 4.13. The obtained microstructures exhibit an extraordinary combination of properties, with yield strengths (YS) greater than 1.2 GPa, and ultimate tensile strengths (UTS) ranging from 1.77 to 2.2 GPa (Fig. 4.13 (a)), the latter in the case of the 200°C microstructure. Such a combination of properties

4.13 Transformation temperature dependences of (a) UTS and YS; (b) total elongation; (c) fracture toughness K IC in NANOBAIN 3 and 4 steels; and (d) engineering stress–strain curves at room temperature, of NANOBAIN 4 microstructure obtained following transformation at the temperatures indicated. © Woodhead Publishing Limited, 2011

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has never before been achieved in bainitic steels. KIC values and ductility both decrease as the strength increases (Fig. 4.13 (b) and 4.13 (c) ). The microstructures obtained by transformation at 300°C exhibit total elongation ~30% and fracture toughness of 44 MPa m1/2 and 51 MPa m1/2 for NANOBAIN 3 and 4 respectively, very high values if compared with those obtained by transformation at 200°C, where elongation is reduced by ~20% and toughness by almost half. The transformation temperature dependence of engineering stress versus strain curves for NANOBAIN 4 is shown in Fig. 4.13 (d). Deformation of bainitic microstructures at room temperature is characterized by continuous yielding, as might be expected from microstructures with unlocked dislocations introduced by the plastic accommodation of the shape change. Although there is evidence that ferrite retains an excess concentration of carbon, even after annealing, the majority of dislocations are believed to be mobile. The gradual yielding behavior sometimes persists after stress-relief heat-treatments. There are a variety of obstacles to dislocation motion (solute atoms, boundaries, thin films of retained austenite), each with a different ability to obstruct plastic deformation. Many of the obstacles are not uniformly distributed, so dislocations can penetrate at low stresses into obstacle-free areas giving rise to a gradual deviation from elastic deformation. Another scale of heterogeneity can arise when a representative fraction of softer phase is included in the microstructure, such as blocks of retained austenite. Plastic deformation at first focuses in the softer phase; the hard phase only begins to deform when the softer phase has strain hardened sufficiently to transfer load, therefore leading to a continuous yielding. As is evident in Fig. 4.13 (d), plastic deformation is uniformly distributed along the gauge length of the samples, showing little or no necking; in other words, most or all of the total elongation achieved is uniform elongation. There are several operative strengthening mechanisms that are expected to contribute to the microstructure strength: the excess carbon concentration in ferrite, the thickness of the bainitic ferrite plates and the ferrite dislocation density (Fig. 4.14). It has been found that there is a strong correlation between the carbon content and the calculated dislocation density, Fig. 4.15, which corroborates that carbon must be trapped at dislocations in the bainitic ferrite, as ATP revealed. Therefore, there may be no independent contribution of carbon in solid solution, but rather, through its effect on the mobility of dislocations. Theory indicates that the contribution to strength due to the size of the plates is given by ∆σ 115(L)–1,86–88 where L2t is the mean linear intercept in micrometers, and that due to the dislocation density89 is given by ∆σ 7.3410–6(ρ)0.5, where ρ is in m–2, being ∆σ in MPa. Figure 4.16 represents the contributions of the two strengthening mechanisms in both alloys after correcting by the corresponding bainitic ferrite fractions. It is easily shown that much of the strength of lowtemperature bainite is due to the extremely fine plates of ferrite. Thus, at the lowest transformation temperatures (200°C) with >80% of the finest bainitic ferrite present in the microstructures, the contribution is about 1.6 and 1.1 GPa for NANOBAIN 3 and 4 respectively; on the other hand, the increment due to



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4.14 Quantitative microstructure results on NANOBAIN 3 and 4 steels: carbon content in bainitic ferrite, its plate thickness and dislocation density obtained after isothermal transformation at different temperatures and times, ensuring that bainitic transformation was finished.

4.15 Plot showing the relation between ferrite dislocation density and its carbon content following transformation.


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4.16 Strengthening contributions versus transformation temperature after correcting by their corresponding bainitic ferrite fractions.

dislocations is about 0.5 GPa for both alloys. As the transformation temperature increases and the microstructures become coarser and less dislocated, these contributions become weaker, as Fig. 4.16 illustrates for the microstructure obtained after transformation at 300°C in both steels. It is difficult to separate the effect of retained austenite on strength in these steel from other factors. Qualitatively, austenite can affect the strength by transforming to martensite during testing, the transformation-induced plasticity (TRIP) effect. The low yield/ultimate tensile strength ratios (YS/UTS) in Fig. 4.13 (a) are due to the presence of austenite and the large dislocation density in the microstructure.90 Consequently, retained austenite increases the strain-hardening rate of the steel. Similarly, toughness and ductility are controlled by the volume fraction of retained austenite,74 ductile phase compared to the bainitic ferrite, and its ability to transform to martensite under strain. This effect strongly depends on the chemical composition and morphology of the retained austenite.73,91 Thus the microstructures obtained after isothermal heat treatment at 300°C, with austenite fractions of 0.25 and 0.37 for NANOBAIN 3 and 4 respectively, exhibit the best results in terms of total elongation and fracture toughness (Fig. 4.13 (b) and (c)) © Woodhead Publishing Limited, 2011


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when compared with the microstructures obtained after transformation at 200°C, with austenite fractions of 0.13 and 0.17 for NANOBAIN 3 and 4 respectively. Strain hardening is characterized by the incremental strain-hardening exponent defined as n = d(ln σ)/d(ln εp), where σ = kε pn represents the flow curve in the region of uniform true plastic deformation (εp) and k is the strength coefficient. The variation of the incremental work hardening exponent n as a function of true strain in NANOBAIN 3 transformed at different temperatures is shown in Fig. 4.17. The straight line corresponds to the instability criterion εp = n. It appears that the different strength-ductility combinations in these advanced bainitic microstructures are associated with completely different work-hardening behaviors. The large true uniform strains of specimen treated at 300°C are due to a high retained austenite fraction that continuously increases the incremental work-hardening n after a sharp decrease at low plastic strains. In the microstructure obtained by transformation at 250°C, after reaching a maximum n smoothly decreases until the onset of necking. For the microstructures obtained at 200°C the situation completely differs from that previously described at higher transformation temperatures: a high increase of n during the first stages of plastic deformation is followed by a drastic drop that ends at low levels of plastic deformation. The mechanisms occurring during tensile deformation can be explained by the correlation between the shape of n versus true strain curves and the rate at which retained austenite transforms to martensite under strain.92–95 The 200°C microstructure, with low fractions and lowest stability of the austenite, rapidly transform at very small strains. As a result, there is little benefit of the straininduced transformation. The situation changes as the fraction of more stable

4.17 Curves of the incremental work hardening exponent, n, of bainitic microstructures obtained in NANOBAIN 3 steel by transformation at different temperatures (200, 250 and 300°C) and tested at room temperature. The straight line represents the instability criterion.


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austenite increases in the microstructure. For 250°C microstructure, retained austenite starts to transform immediately after the initial maximum n, and transformation proceeds until the instability criterion is reached. On the other hand, high fractions of very stable austenite are present at 300°C microstructures, as a result, transformation starts well after the maximum n and continues progressively up to necking. Finally, the properties of the present alloys are compared against published data in Fig. 4.18,39,96 highlighting the fact that novel bainitic steels exhibit an

4.18 Comparison of ultimate strength versus fracture toughness of: (a) conventional quenched and tempered steels (QT), maraging steels, other bainitic steels39 and NANOBAIN steels; and (b) strength versus total elongation of conventional steels96 and NANOBAIN steels. Note: IF: interstitial free, CMn: carbon manganese, BH: bake hardenable, IS: isotropic, DP: dual phase, CP: complex phase.



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exceptional combination of mechanical properties that places this new type of microstructures in an advantageous position for different applications such as transport, construction and offshore industries, as well as defence applications.

4.8

Conclusion and future trends

It is clear that bainite can be obtained by transforming at very low temperatures. There is then very a low possibility that iron or substitutional solutes will diffuse. A consequence of the low transformation temperature is that the plates of bainite are extremely fine, 20–40 nm thick, making the material very strong. This is a bulk nanocrystalline material that is cheap and can be obtained without severe deformation processing. When this feature is combined with the fact that the plates of ferrite are interspersed with austenite, it becomes possible to create novel strong and tough steels. In this regard, the potential for industrial application is large because the alloys are routinely manufactured. As is always the case, there remain many parameters that have yet to be characterized, for example the fatigue and stress corrosion properties. Moreover, the alloys designed so far either transform slowly over a period of many days, or have to be alloyed with cobalt and aluminium in order to accelerate transformation. In the future, it is possible that rapid transformation could be engineered by controlling the manganese concentration. The key will be to do this without compromising properties. Finally, high-carbon steels are difficult to weld because of the formation of untempered, brittle martensite in the coarse-grained heat-affected zones of the joints. The martensite fractures easily, leading to a gross deterioration in the structural integrity of the joint. For this reason, the vast majority of weldable steels have low-carbon concentrations. Therefore, it would be desirable to make the low-temperature bainite with a much reduced carbon concentration. Preliminary calculations indicate that carbon is much more effective in maintaining a difference between the MS and BS temperatures than are substitutional solutes which reduce ∆Gγα simultaneously for martensite and bainite. Substitutional solutes do not partition at any stage in the formation of martensite or bainite; therefore, both transformations are identically affected by the way in which the substitutional solute alters the thermodynamic driving force. It is the partitioning of carbon at the nucleation stage that is one of the distinguishing features of bainite when compared with martensite. This carbon partitioning allows bainite to form at a higher temperature than martensite. This advantage is diminished as the overall carbon concentration is reduced. These results are discouraging from the perspective of designing a low-carbon bainite with a fine microstructure obtained by transforming at low temperatures. However, the issue is worth investigating further since the original theory has a number of approximations. In the future, the Fe-Mn-Ni-C system should be explored in the context of these calculations, bearing in mind the desire to design low carbon alloys in which the BS temperature is suppressed.


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4.9

Sources of further information and advice

Research groups working on NANOBAIN MATERALIA Research Group, CENIM-CSIC, Madrid, Spain http://www. cenim.csic.es/materalia/PaginaWebEnglish/WebMateralia.html Phase Transformations & Complex Properties Research Group, University of Cambridge, Cambridge, UK http://www.msm.cam.ac.uk/phase-trans/

Key books to consult: R.W.K. Honeycombe and H.K.D.H. Bhadeshia: Steels, Microstructure and Properties. Edward Arnold, London (1995). H.K.D.H. Bhadeshia: Bainite in steels, 2nd ed. Institute of Materials, London (2001). M.K. Miller: Atom Probe Tomography. Kluwer Academic/Plenum Press, New York (2000).

4.10 Acknowledgements It is a special pleasure to acknowledge Professor H.K.D.H. Bhadeshia for his support guidelines on NANOBAIN research and development. Research at the Oak Ridge National Laboratory SHaRE User Facility was sponsored by the Scientific User Facilities Division, Office of Basic Energy Sciences, US Department of Energy.

4.11 References 1 Valiev R.Z., Islamgaliev R.K., Alexandrov I.V. Prog Mater Sci 2000; 45: 103. 2 Valiev R.Z., Zehetbauer M.J., Estrin Y., Hoppel H.W., Ivanisenko Y., Hahn H., Wilde G., Roven H.J., Sauvage, X. Langdon T.G. Adv Eng Mater 2007; 9: 527. 3 Ma E. JOM 2006; 58: 49. 4 Teplov V.A., Pilugin V.P., Gaviko V.S., Chernyshov E.G. Philos Mag 1993; 68: 877. 5 Senkov O.N., Froes F.H., Stolyarov V.V., Valiev R.Z., Liu J. Scr Mater 1998; 38: 1511. 6 Shabashov V.A., Litvinov A.V., Mukoseev A.G., Sagaradze V.V., Desyatkov D.V., Pilyugin V.P., Sagaradze I.V., Vildanova N.F. Mater Sci Eng A 2003; 361: 136. 7 Ivanisenko Y., Lojkowski W., Valiev R.Z., Fecht H.J. Acta Mater 2003; 51: 5555. 8 Sauvage X., Jessner P., Vurpillot F., Pippan R. Scr Mater 2008; 58: 1125. 9 Sauvage X., Ivanisenko Y. J Mater Sci 2007; 42: 1615. 10 Ohsaki S., Kato S., Tsuji N., Ohkubo T., Hono K. Acta Mater 2007; 55: 2885. 11 Embury J.D., Fisher R.M. Acta Metall 1966; 14: 147. 12 Languillaume J., Kapelski G., Baudelet B. Acta Mater 1997; 45: 1201. 13 Langford G. Metall Trans 1970; 1: 465. 14 Kobe Steel Ltd. Kobelco technology review No. 8, Japan, 1990.



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15 Bhadeshia H.K.D.H. High strength steels. In Charles J.A., Greenwood G.W., Smith G.C., editors. Future Developments in Metals and Ceramics, London, Institute of Materials, 1992; p. 25. 16 Bhadeshia H.K.D.H., Harada H. Appl Sur Sci 1993; 67: 328. 17 Segal V.M. Mater Sci Eng A 2002; 338A: 331. 18 Saito Y., Tsuji N., Utsunomiya H., Sakai T., Hone R.J. Scr Mater 1998; 39: 1221. 19 Tsuji N., Saito Y., Ustunomiya H., Tanigawa S. Scr Mater 1999; 40: 795. 20 Krauss G. Steels heat treatment and processing principles. Materials Park (OH): ASM International, 1995. 21 Maki T. Tetsu-to-Hagane 1995; 81: N547. 22 Niikura M., Fujioka M., Adachi Y., Matsukura A., Yokota T., Shirota Y., Hagiwara Y. J Mater Process Technol 2001; 117: 341. 23 Yokota T., Garcia-Mateo C., Bhadeshia H.K.D.H. Scr Mater 2004; 51: 767. 24 Das S.K., Thomas G. Metall Trans 1970; 1: 325. 25 Morito S., Huang X., Maki T., Hansen N. Acta Mater 2006; 54: 5323. 26 Morito S., Nishikawa J., Maki T. ISIJ Int 2003; 43: 1475. 27 Hornbogen E. Innovations in ultrahigh-strength steel technology. In Olson G.B., Azrin M., Wright E.S., editors. Proc. 34th Sagamore Army Conf, Boston (MA), 1987; p. 113. 28 Withers P.J., Bhadeshia H.K.D.H. Mater Sci Technol 2001; 17: 355. 29 Withers P.J., Bhadeshia H.K.D.H. Mater Sci Technol 2001; 17: 366. 30 Caballero F.G., Miller M.K., Garcia-Mateo C., Capdevila C., Garcia de Andrés C. JOM 2008; 60: 16. 31 Bhadeshia H.K.D.H., Waugh A.R. Acta Metall 1982; 30: 775. 32 Chang L.C., Bhadeshia H.K.D.H. Mater Sci Eng A 1994; A184: L17. 33 Self P., Bhadeshia H.K.D.H., Stobbs M. Ultramicroscopy 1981; 6: 29. 34 Bhadeshia H.K.D.H. Met Sci 1982; 16: 159. 35 Bhadeshia H.K.D.H., Edmonds D.V. Met Sci 1983; 17: 411. 36 Bhadeshia H.K.D.H., Edmonds D.V. Met Sci 1983; 17: 420. 37 Miihkinen V.T.T.D., Edmonds D.V. Mater Sci Technol 1987; 3: 422. 38 Miihkinen V.T.T.D., Edmonds D.V. Mater Sci Technol 1987; 3: 432. 39 Miihkinen V.T.T.D., Edmonds D.V. Mater Sci Technol 1987; 3: 441. 40 Caballero F.G., Bhadeshia H.K.D.H., Mawella J.A., Jones D.G., Brown P. Mater Sci Technol 2001; 17: 512. 41 Caballero F.G., Bhadeshia H.K.D.H., Mawella J.A., Jones D.G., Brown P. Mater Sci Technol 2001; 17: 517. 42 Bhadeshia H.K.D.H. Acta Metall 1981; 29: 1117. 43 Bouaziz O., Quidort D., Maugis P. Rev Metall Paris 2003; 100: 103. 44 Quidort D., Bouaziz O. Can Metall Quart 2004; 43: 25. 45 Bhadeshia H.K.D.H. Mat Sci Eng A 2004; A378: 34. 46 Hillert M. ISIJ Int 1995; 35: 1134. 47 Bhadeshia H.K.D.H., Waugh A.R. An atom-probe study of bainite. In Aaronson H.I., Laughlin D.E., Sekerka R.F., Wayman C.M., editors. Proc. Int. Conf. Solid-Solid Phase Trans, Warrendale: Metall Soc AIME, 1981; p. 993. 48 Stark I., Smith G.D.W., Bhadeshia H.K.D.H. The element redistribution associated with the incomplete-reaction phenomenon in bainitic steels: an atom-probe investigation. In Lorimer G editor. Proc. Int. Conf. Solid-Solid Phase Trans, London: Inst. of Metals, 1988. p. 211. 49 Bhadeshia H.K.D.H. Bainite in steels. 2nd ed., London: Institute of Materials, 2001. p. 132.


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50 Olson G.B., Cohen M. Metall Trans 1976; 7A: 1897. 51 García-Mateo C., Bhadeshia H.K.D.H. Mat Sci Eng A 2004; A378: 289. 52 Caballero F.G., Bhadeshia H.K.D.H., Mawella J.A., Jones D.G., Brown P. Mater Sci Technol 2002; 18: 279. 53 García-Mateo C., Caballero F.G., Bhadeshia H.K.D.H. ISIJ Int 2003; 43: 1238. 54 Lee J.L., Bhadeshia H.K.D.H. Mat Sci Eng A 1993; A171: 223. 55 Bhadeshia H.K.D.H. Program MAP_STEEL_MUCG46, Cambridge, Materials Algorithms Project. Available from: http://www.msm.cam.ac.uk/map/steel/programs/ mucg46-b.html [accessed 30 June 2009]. 56 Singh S.B., Bhadeshia H.K.D.H. Mat Sci Eng A 1998; 245: 72. 57 García-Mateo C., Caballero F.G., Bhadeshia H.K.D.H. ISIJ Int 2003; 43: 1821. 58 Bhadeshia H.K.D.H. Acta Metall 1980; 28: 1103. 59 Kozeschnik E., Bhadeshia H.K.D.H. Mater Sci Technol 2008; 24: 343. 60 Caballero F.G., Bhadeshia H.K.D.H. Curr Opin Solid State Mater Sci 2004; 8: 251. 61 Takahashi M., Bhadeshia H.K.D.H. Mater Sci Tech 1990; 6: 592. 62 Winchell P.G., Cohen M. Trans ASM 1962; 55: 347. 63 Yakel H.C. Int Met Rev 1985; 30: 17. 64 Smith G.M. The microstructure and yielding behaviour of some Ti steels, Cambridge (UK): University of Cambridge, 1984. 65 Bhadeshia H.K.D.H., Christian J.W. Metall Trans 1990; 21A: 767. 66 Bhadeshia H.K.D.H., Edmonds D.V. Acta Metall 1980; 28: 1265. 67 Kalish D., Cohen M. Mater Sci Eng 1970; 6: 156. 68 Miller M.K. Atom probe tomography. New York, Kluwer Academic/Plenum Press, 2000; p. 158. 69 Cochardt A., Schoeck G., Wiedersich H. Acta Metall 1955; 3: 533. 70 Wilde J., Cerezo A., Smith G.D.W. Scr Mater 2000; 43: 39. 71 Srinivasan G.R., Wayman C.M. Acta Metall 1968; 16: 621. 72 Nemoto M. High voltage electron microscopy, New York, Academic Press, 1974; p. 230. 73 Bhadeshia H.K.D.H., Edmonds D.V. Metall Trans 1979; 10A: 895. 74 Sandvik B.P.J., Nevalainen H.P. Met Technol 1981; 15: 213. 75 Ogura T., McMahon C.J., Feng H.C., Vitek V. Acta Metall 1978; 26: 1317. 76 Ogura T., Watanabe T., Karashima S., Masumoto T. Acta Metall 1987; 35: 1807. 77 Swiatnicki W., Lartigue-Korinek S., Laval J.Y. Acta Metall Mater 1995; 43: 795. 78 Fondekar M.K., Rao A.M., Mallik A.K. Metall Trans 1970; 1: 885. 79 Matas S.J., Hehemann R.F. Trans Met Soc AIME 1968; 221: 179. 80 Owen W.S. Trans ASM 1954; 46: 812. 81 Roberts C.S., Averbach B.L., Cohen M. Trans ASM 1953; 45: 576. 82 Babu S.S., Hono K., Sakurai T. Metall Mater Trans 1994; 25A: 499. 83 Miller M.K., Beaven P.A., Brenner S.S., Smith G.D.W. Metall Trans 1983; 14: 1021. 84 Sha W., Chang L., Smith G.D.W., Cheng L., Mittemeijer E.J. Surf Sci 1992; 266: 416. 85 Thomson R.C., Miller M.K. Acta Mater 1998; 46: 2203. 86 Bhadeshia H.K.D.H. Mathematical modelling of weld phenomena III. London, Institute of Materials, 1997; p. 229. 87 Langford G., Cohen M. Trans ASM 1969; 62: 623. 88 Langford G., Cohen M. Metall Trans 1970; 1: 1478. 89 Honeycombe R.W.K., Bhadeshia H.K.D.H. Steels. Microstructure and Properties. London, Edward Arnold, 1995; p. 311. 90 Coldren A.P., Cryderman R.L., Semchysen M. Steel Strengthening Mechanisms. Ann Arbor (MI): Climax Molybdenum, 1969; p. 17.


91 92 93 94 95 96


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Ballinger N.K., Gladman T. Met Sci 1981; 15: 95. Jacques P.J., Girault E., Harlet P., Delannay F. ISIJ Int 2001; 41: 1061. Itami A., Takahashi M., Ushioda K. ISIJ Int 1995; 35: 1121. Sakuma Y., Matlock D.K., Krauss G. Metall Trans 1992; 23A: 1233. Sugimoto K., Kobayashi M., Hashimoto S. Metall Trans 1992; 23A: 3085. World Auto Steel. World Steel Association. Middletown (OH): Available from: http:// www.worldautosteel.org [accessed 1 July 2009].


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5 The processing of bulk nanocrystalline metals and alloys by electrodeposition U. ERB, University of Toronto, Canada, G. PALUMBO and J.L. McCREA, Integran Technologies Inc., Canada Abstract: This chapter deals with the synthesis of nanocrystalline metals, alloys and metal matrix composites using the electrodeposition method. The first part of the chapter covers the fundamentals of electrodeposition from aqueous solutions and reviews experimental details for several specific nanomaterials. This will be followed by a summary of mechanical, corrosion and other properties reported for these materials over the past two decades. The chapter includes several examples of industrial applications for these advanced materials. Key words: electrodeposition of nanomaterials, metals, alloys and composites, mechanical, corrosion, electrical, thermal and magnetic properties, industrial applications.

5.1

Introduction

There are five general approaches to making nanocrystalline materials: solid state processing, liquid phase processing, vapor phase processing, chemical synthesis and electrochemical synthesis. For each general approach, many different specific methods have been developed to produce nanomaterials in different shapes including thin films, powders, nanodots and nanowires or compact three-dimensional bulk nanomaterials. This chapter deals with electrodeposited bulk nanomaterials. Electrodeposition belongs to the general group of electrochemical synthesis methods. Other methods in this group of techniques include electroless deposition, galvanic displacement deposition or immersion plating, and electrodeposition under oxidizing conditions. The chapter will focus on recent advances in electrodeposition from aqueous solutions. Electrodeposition from organic solutions, molten salts or ionic liquids will not be covered here. Furthermore, the main focus of this review will be on metals, alloys and metal-matrix composites. Electrodeposition of organic films, conductive polymers, semiconductors and oxides will not be included in this chapter. Electrodeposition has been used for more than a century in several application areas including primary metal production (e.g. electrowinning and electrorefining), direct manufacturing (e.g. electroforming of large structural objects or small components for microelectromechanical systems) and surface finishing (e.g. decorative coatings, corrosion and wear-resistant coatings, functional coatings).1–3 118 © Woodhead Publishing Limited, 2011

The processing of bulk nanocrystalline metals and alloys

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There are numerous reports in the literature that have dealt with electrodeposits with extremely small crystal size and the property enhancements that can be achieved in such materials by grain size reduction. However, it was only throughout the 1980s that the full potential of electrodeposition as a production route for nanocrystalline materials was recognized.4,5 The earliest patents on nanomaterials made by electrodeposition were issued in the mid 1990s.6,7 The superior properties first observed on nanocrystalline nickel electrodeposits resulted in one of the world’s earliest large-scale industrial applications of nanomaterials in 1994: the so-called electrosleeve process for in situ repair of nuclear steam generator tubing.8–10 This process has been implemented in both Canadian CANDU and US pressurized water reactors. Essentially, this application is a nanocrystalline Ni-P microalloy electroform (~ 1 mm in thickness, 50–100 nm grain size) deposited on the inside of steam generator tubes to effect a complete structural repair at sites where corrosion, stress corrosion cracking and other degradation phenomena compromised the structural integrity of the tubes. The early success of nanocrystalline metal electrodeposits accelerated 1) research efforts in this area by numerous groups around the world, and 2) the development of applications in several sectors, including energy, automotive, aerospace, consumer product and defense industries.11–18 Several review articles on the electrodeposition method have been published over the past decade.19–25

5.2

Electrodeposition methods

The four most important components of a typical electroplating system are 1) an appropriate electrolyte, often referred to as the plating bath, 2) a power supply, usually either a direct current (DC) or pulsed current (PC) power supply, 3) the cathode onto which the material is electrodeposited and 4) the anode. Figure 5.1 shows that, in addition, a heater and electrolyte stirring are often used, mainly to enhance the diffusion of metal ions and other species in the plating bath.

5.2.1 Electrolyte The electrolyte is an aqueous solution containing several ingredients. The most important is the salt of the metal to be deposited on the cathode. Metal salts include sulfamates, sulfates, chlorides, cyanides, fluoroborates, pyrophosphates and others. These salts provide the initial metal ion concentration in the plating bath. Many baths contain several salts of the same metal. For example, in the so-called Watts nickel plating bath both nickel sulfate and nickel chloride are used, the latter in a much smaller concentration. In addition to providing some Ni2+ ions, the main role of the nickel chloride is to increase the bath conductivity and to aid in the nickel anode dissolution. For alloy deposits that contain two or more metals, salts of each component are added to the bath. For example, to electrodeposit Zn-Ni binary alloys a bath


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5.1 Schematic diagrams showing experimental set-up (top) and current versus time curve (bottom) for conventional direct current plating.

containing both zinc chloride and nickel chloride can be used. Other alloying elements include non-metals such as phosphorus or boron, which must also be added to the bath in the right concentration. An example is Ni-P deposited from a plating bath containing nickel sulfate and phosphorous acid, the latter as the source of phosphorus. Composite deposits can be made by adding a second phase in the form of fine particles, whiskers or fibres to the electroplating bath. The second phase is then codeposited with the metal matrix to form the composite material. Examples are Ni-SiC, Ni-carbon nanotubes, Cu-Al2O3, etc. Many plating baths contain buffers. Buffers have the property that they maintain the plating bath pH by neutralizing both acid and base changes in the solution. Examples of buffers used in metal plating are boric acid (H3BO 3) for nickel or zinc–nickel plating at low pH or potassium orthophosphate/phosphate (KH 2PO 4/ K3PO 4) mixtures for plating of palladium from high pH solutions.1



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Metal ions in an aqueous solution are usually hydrated, i.e. surrounded by several water molecules (solvation sheath), usually expressed as shown in equation 5.1.

[5.1]

For example, for Ni2+ the number x is either 4 or 6.1 When water molecules are replaced by other ions or molecules (i.e. complexing agents) the metal is referred to as a metal ion complex. Complex formation can considerably change the properties of the metal ions in the solution and in particular the metal ion deposition, which involves complex dissociation to form free metal ions. Complexing agents, also referred to as ligands, are particularly important in the co-deposition of alloys where they help to bring the deposition potentials/activities of the individual metals closer together. Complexed ions are usually written as follows:

[5.2]

Examples are:

[5.3]

[5.4]

Many complexing agents have been used in alloy plating. For example, for Ni-Fe-Cr ternary alloys alone, the list is very large, including di-methyl formamide (DMF, HCON(CH 3)2), ethylene-diamine-tetra-acetate (EDTA, (HO 2CCH 2)2 NCH 2CH 2N(CH 2CO 2H)2), sodium citrate (Na3C6H5O7 × 2 H2O), urea (NH 2 CONH 2) and glycolic acid (HOCH 2CO 2H). Other bath ingredients include addition agents to achieve specific deposit properties in terms of brightening, stress relief, hardening, leveling, grain refining or surface smoothing. One particular example is the use of saccharin (benzoic sulfimide (C7H5NO 3S)) in nickel electroplating. Saccharin in this plating bath has a dual purpose. It is a grain refiner and stress reliever at the same time, typically added to the plating bath in low concentrations of about a few grams per liter.1

5.2.2 Power supplies in conventional electroplating Most electroplating operations use direct current plating as shown in Fig. 5.1. Direct current is usually supplied from rectifiers, although older rotating DC generators may still be in operation in some industries. In direct current plating, an important plating variable is the current density, I, usually expressed in units of mA/cm.2 Electrodeposition often involves more than one single electrochemical reaction at each the anode and cathode. For example, during the electrodeposition from a low pH bath containing Mez+ and H+ ions, the following reactions occur at the cathode:


122


[5.5]

[5.6]

The metal deposition process involves various steps including diffusion of ions from the bulk of the electrolyte to the cathode and through the Nernst diffusion layer, formation of the first adions on the cathode surface, surface diffusion of the adions, nucleation of the crystals and growth of the crystals. When charge transfer associated with the metal ion deposition is the slow, rate-determining step, equation 5.7 gives the limit in terms of current density, IL , which is controlled by the transport of Mez+ ions from the bulk of the electrolyte to the cathode:1

[5.7]

where D is the diffusion coefficient of the deposited Mez+ species, F is the Faraday constant, z the number of electrons involved in the metal ion reduction, Cb the concentration of Mez+ ions in the bulk electrolyte and δ the diffusion layer thickness. Direct current electrodeposition at current densities higher than the limiting current density usually produces poor deposits as the process then involves cathodic reactions other than metal ion deposition. The limiting current density is strongly dependent on solution agitation. For example, for the case of a rotating electrode it has been shown1 that the limiting current density changes with the angular speed of rotation (ω) as follows:

[5.8]

where ν is the kinematic viscosity of the electrolyte, Cb the concentration of the solution and a is the rotating disk surface area. The weight of the deposit is given by the following equation:

[5.9]

where I is the applied current density, t is the plating time, A is the atomic weight of the deposited metal, z the number of electrons, and F is the Faraday constant. The current efficiency (CE) of a plating process is a measure of the actual metal deposition (Wmetal) relative to the theoretically possible metal deposition (Wtotal), when no other reactions occur at the cathode.

[5.10]

In most cases the current efficiency is less than 100%, indicating that other reactions do indeed occur at the cathode such as the hydrogen evolution reaction given in equation 5.6. For example, nickel plating from a Watts-type bath has a high current © Woodhead Publishing Limited, 2011


123

efficiency of more than 90%, which means that less than 10% of all electrons in the process are used to produce hydrogen gas. On the other hand, the current efficiency for chromium plating is much lower, typically of the order of 10–30%.26

5.2.3 Cathodes and cathodic reactions When the purpose of electrodeposition is to create a permanently modified surface, the cathode is usually the finished workpiece. Electroplating is then carried out until the required coating thickness is reached. Subsequently the workpiece is removed from the plating bath, rinsed and dried. Typical plating operations include rack plating, barrel plating, reel-to-reel plating and brush plating. On the other hand, in processes such as electroforming27–29 the cathode is used only as a temporary mandrel or mold to deposit the material in the shape of a specific final object. Following the electrodeposition process the electroformed object is separated from the mold by mechanical means. The mold can then be reused to deposit the next piece either in batch processing (Fig. 5.2) or as a continuous process such as in foil plating (Fig. 5.3). Titanium or steel cathodes are frequently used in such processes. The cathodic reactions in terms of overall metal deposition are often given as in equation 5.5. However, it should be noted that the reactions can be much more complex involving several intermediate steps. For example, for the electrodeposition of Ni from a Watts-type bath, the cathodic reaction given in equation 5.11 is usually presented:

[5.11]

However, it is more likely that deposition involves the following reactions:30,31

5.2 Schematic diagram showing net-shape manufacturing of an electroformed product. Source: Courtesy of Nickel Development Institute, Toronto, Canada.


[5.12] [5.13]

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5.3 Schematic diagram showing continuous electrodeposition of nanocrystalline sheet/foil. Source: Courtesy of Integran Technologies, Inc., Toronto, Canada.

[5.14]

5.2.4 Anodes The anode completes the electric circuit in the plating cell (Fig. 5.1). Two types of anodes are typically used. The first type is a dissolvable anode of the same material as the electroplate, which replenishes the bath with metal ions as they are deposited on the cathode. Often the anode material is contained in a mesh basket made of titanium (Fig. 5.1), the latter being inert in many electroplating baths because of the protective titanium oxide layer on the surface. Anode material is periodically replenished in the anode basket. The second type of anode is referred to as the dimensionally stable anode (DSA). Supplied as sheet or mesh, these anodes are made of platinum coated/clad titanium or niobium with platinum thicknesses typically of the order of 0.1–0.25 mm. These anodes are chemically inert and do not replenish the plating bath with metal ions. Therefore, periodic additions of metal salts to the plating bath are required to maintain the ion concentration within a certain operating range.



125

5.2.5 Structure evolution in conventional electrodeposits Under conventional electroplating conditions, the microstructural evolution with increasing deposit thickness is as shown in Fig. 5.4. Initially, numerous crystals are nucleated on the cathode, which usually have different crystallographic orientations with respect to the substrate material. With increasing deposit thickness there is a competition between nucleation of new crystals and growth of existing crystals. Many operating conditions (e.g. low current density) promote crystal growth where certain crystal orientations grow faster than others. As a result, the initial fine-grained structure changes with increasing deposit thickness to a large-grained, often columnar grain structure as seen in Fig. 5.4 (b) for an iron deposit. The grain size in the initial layer is very small and cannot be easily resolved in the etched cross-section. However, the columnar large grained structure that developed with increasing deposit thickness is clearly visible in Fig. 5.4 (b). It should be noted that the thickness of the initial fine-grained structure is often found to be strongly dependent on the pH of the electrolyte. For example, for nickel deposited from a Watts-type bath, the thickness decreased from about 150 µm at a pH of 0.5 to about 20 µm at a pH of 3.0 and completely disappeared at a pH of 3.5.32

5.2.6 Structure evolution in nanocrystalline electrodeposits It has been shown that nanocrystalline metals can be produced by electrodeposition under electrochemical conditions that promote crystal nucleation and suppress crystal growth.6,7,33,34 The conditions leading to massive nucleation of crystals can be achieved by selecting plating parameters that 1) allow for very high

5.4 Schematic diagram (a) and cross-sectional scanning electron micrograph (b) of an iron electrodeposit showing grain size and shape evolution with increasing deposit thickness. Arrows indicate growth direction.


126


deposition rates and 2) reduce the diffusion of adatoms over the surface of the growing deposit. The current density applied during plating has two important effects on electrocrystallization. It increases the rate of metal ion reduction on the surface and reduces the critical crystal nucleation size, rc, which is inversely proportional to overpotential, η/current density, I, as shown in the classical Gibbs–Kelvin equation:35

[5.15]

where σ is the interfacial tension of the metal/solution interface, M the molecular weight, ρ the density and z · F the molar charge. The effect of over-potential/ current density on the critical crystal size is shown schematically in Fig. 5.5 in the form of free energy versus crystal size graphs. Figure 5.5 clearly shows that higher current density results in smaller crystal sizes. However, conventional DC plating is limited by the limiting current density (equation 5.7) above which electrochemical reactions other than metal deposition

5.5 Effect of over-potential/current density on critical crystal nucleation size.



127

occur on the cathode. For this reason, pulsed current electrodeposition was introduced,6,7,33 as shown schematically in Fig. 5.6. In this case the current, Ipeak, during the current on time (Ton) can be significantly higher than the limiting DC current density. However, in order to replenish the double layer with metal ions by diffusion from the bulk of the electrolyte before other cathode reactions begin to dominate, the current is turned off for a certain period of time, Toff. Usually Toff is longer than Ton. The important electrical parameters during pulse plating include the pulse frequency, f, the duty cycle, θ, and the average current density, Iave:

[5.16]

5.6 Schematic diagrams showing experimental set-up (top) and current versus time curve (bottom) for pulsed current plating.


128

Nanostructured metals and alloys [5.17]

[5.18]

More recent research efforts have concentrated on producing electrodeposited nanomaterials with different structure types. These include structurally graded materials in which the grain size changes in cross-section, materials with broader or bimodal grain size distribution and nanocomposites consisting of two or several distinct phases36 or nanotwinned electrodeposits.37 Such structures allow for interesting property optimizations, such as high strength combined with high ductility or high electrical conductivity.

5.3

Examples of nanocrystalline metals and alloys prepared by electrodeposition

As pointed out in section 5.1, there have been numerous early studies on electrodeposited metals with extremely fine grain size, however, without particular emphasis on identifying in a systematic way those plating parameters that would lead to nanocrystalline materials. The first alloys that were studied with emphasis on nanocrystalline material formation were Ni-P electrodeposits.4,5 Earlier studies had shown that these alloys could be produced with both conventional polycrystalline and amorphous structures.38 An electrolyte and plating conditions as shown in Table 5.1 were used to study nanocrystal formation.4,5 As can be seen from this table, electrodeposition was carried out using DC plating and the main variable was the concentration of phosphorous acid (H3PO 3) in the plating bath. It was shown that the phosphorus content in the electrodeposit increased with increasing phosphorous acid concentration in the plating bath, likely by the following reactions39 in addition to the reactions for Ni reduction given in equations 5.11 through 5.14:

[5.19]

Table 5.1 Electrolyte composition and plating conditions used for the synthesis of nanocrystalline Ni-P alloy deposits4,5 Compound

Concentration (g/l)

Plating conditions

Ni2SO 4 × 7H2O NiCl2 × 6H2O

150 45

pH T (°C)

1.5 80

IDC (mA/cm2) Ipeak(mA/cm2) Ton(msec) Toff (msec)

100 – – –

H3PO 4 50 H3PO 3 0–40



129

[5.20]

[5.21]

The resulting deposits were supersaturated solid solutions of P in Ni, with P concentrations up to 24 at.% for the highest concentration of phosphorous acid in the plating bath. It was further shown that the structures of the deposits were crystalline for low P-concentrations in the deposit, less than 4 at.%. On the other hand, deposits containing more than ~ 15 at.% P were amorphous. For the intermediate concentration range, rapid grain size reduction was observed and nanocrystalline deposits with grain sizes down to less than 3 nm and towards the amorphous limit were observed with increasing phosphorus content. Figure 5.7 shows brightfield and darkfield transmission electron micrographs of a Ni-5.2 at.% P deposit with an average grain size of 6.1 nm. Since the early 1990s numerous other nanomaterials have been produced by electrodeposition, many of which are summarized in Table 5.2. These include pure metals such as Ni, Co, Pd, Cu and Zn, binary and ternary alloys including Ni-Zn, Co-W, Co-Fe, Ni-F-Cr and Ni-Zn-P, and composite materials, for example Ni-Al2O3, Ni-SiC, Ni-P-BN or Ni-carbon nanotubes. It should be noted that many bath formulations and electroplating parameters have been developed for different materials by various research groups. In the following examples details will be given for several specific materials produced in our laboratories over the past 20 years. Table 5.3 summarizes the important electrochemical conditions used in the synthesis of nanocrystalline nickel produced from a Watts-type electrolyte.33 Note that these materials were produced by pulsed current deposition using a peak current density of 1900 mA/cm2, which is about 4–5 times higher than the limiting DC current density for nickel plating. In addition, the plating baths contained

5.7 Brightfield (a) and darkfield (b) transmission electron micrographs of a Ni – 5.2 at.% P electrodeposit with an average grain size of 6.1 nm in planar section.


130

Nanostructured metals and alloys Table 5.2 Examples of nanocrystalline metals, alloys and metal matrix composites that have been produced by electrodeposition Material

References

Material

References

Ni Co Pd Cu Zn Ni-P Ni-Fe Ni-Zn Co-W Co-Fe Pd-Fe

[6, 33] [6, 40] [41] [40, 42] [43] [4, 5] [44, 45] [46, 47] [48] [49] [50]

Ni-Fe-Cr Ni-Zn-P Co-Fe-P Ni-SiC Ni-Al2O3 Cu-Al2O3 Ni-P-BN Ni-MoS2 Ni-Al (particles) Ni-Nanocarbon tubes

[51–53] [54] [55] [56, 57] [58, 59] [60] [18] [18] [61] [62]

Table 5.3 Electrolyte composition and plating conditions used for the synthesis of nanocrystalline Ni deposits33 Compound

Concentration (g/l)

Ni2SO 4 × 7H2O 300 NiCl2 × 6H2O 45 H3BO 3 45 C7H5NO 3S 0–10

Plating conditions pH T (°C) IDC (mA/cm2) Ipeak(mA/cm2) Ton(msec) Toff (msec)

2.5 65 – 1900 2.5 45.0

saccharin (C7H5NO 3S) in various concentrations (0–10 g/l) as a grain refiner. Figure 5.8 presents scanning electron microscope (SEM) micrographs showing the surface morphology of deposits without and with saccharin additions. These micrographs clearly show that in the absence of saccharin (Fig. 5.8 (a) ) large crystals with sizes in the micrometer range are obtained. These deposits exhibited a relatively large surface roughness and dull appearance. With increasing saccharin concentration the surface morphology changed to a more colony-type structure in which individual grains cannot be resolved in the SEM (Fig. 5.8 (b) ). Transmission electron microscopy was used to determine the grain size of the deposit as a function of saccharin concentration in the bath; the results are given in Table 5.4. A small addition (0.5 g/l) of saccharin is sufficient to reduce the crystal size from >1µm to about 40 nm. Further increases in saccharin additions to 5 g/l reduced the grain size further to about 10 nm. Even higher saccharin concentrations (10 g/l) had no major additional effect on grain size. Figure 5.9 shows a schematic diagram and a brightfield transmission electron micrograph of a nanocrystalline nickel electrodeposit in cross-section through the



131

5.8 Scanning electron micrographs showing surface structure of electrodeposited polycrystalline nickel without saccharin (a) and nanocrystalline nickel with a saccharin addition of 5.0 g/l in the plating bath (b). Table 5.4 Effect of saccharin concentration on grain size and sulfur content of nanocrystalline nickel electrodeposits produced from a Wattstype plating bath33 Saccharin concentration (g/l) Grain size (nm)

Sulfur concentration (ppm)

0 >1000 0.5 40 2.5 20 5.0 10 10.0 9

5%) ductility to sustain tensile deformation to


140


a discernable peak load, equation [5.28] can be used to estimate tensile strength from hardness measurements. For more brittle materials with tensile elongations less than 5%, the relationship given in equation [5.28] was also found to be invalid. Both abrasive and adhesive wear studies have shown that the wear resistance of nanocrystalline nickel increases with decreasing grain size.65,71 Table 5.8 shows the effect of grain size on the abrasive wear resistance (Taber wear index). This behavior is in agreement with Archard’s law, which states that the wear resistance is inversely proportional to the hardness of the material, which in turn initially increases with decreasing grain sizes. It is interesting to note that according to Archard’s law the wear resistance should decrease in nanomaterials that show the negative Hall–Petch behavior. This was indeed observed for both Ni-P111 and Ni-W73 electrodeposits.

5.4.3 Ultimate tensile strength and tensile ductility Because of the initial material size and shape limitations and the impurity problems mentioned earlier in this section, it is currently impossible to predict the intrinsic ultimate tensile strengths and ductilities that could potentially be achieved by grain size control in nanocrystalline electrodeposits. Early results were very disappointing in terms of ductility. For example, the ductility of Ni was observed to decrease from over 50% at a grain size of 100 µm to about 1% at a grain size of ~10 nm.16 Many other studies also found very low ductilities and many electrodeposits failed in a completely brittle fashion without onset of necking instability. Over the past several years considerable progress has been made in producing nanocrystalline electrodeposits which much improved ductility and very high ultimate tensile strength in cobalt,120,121 nickel-based alloys89 and copper.37,118 For example, for cobalt and some nickel–iron nanodeposits ultimate tensile strength values in excess of 2000 MPa and ductilities in the 5–15% range can now be achieved. There are several contributing factors for the higher ductility/ultimate tensile strength values observed in more recent studies. First, improved synthesis methods have been developed with much better control of impurities and other deposition defects such as hydrogen pits or co-deposited hydroxides.89 Second, thicker and larger samples are now available for testing following standard testing procedures. Early testing was often done on very thin specimens very close to plane stress conditions, which usually yield lower ductility values. Third, the development of nanotwinned electrodeposits has shown that the high density of twin boundaries can produce a unique combination of high strength and high ductility.37,118 Fourth, there is now considerable evidence that wide/bimodal grain size distributions,87 and co-deposited second phase particles can enhance ultimate tensile strength and ductility of nanomaterials57 and even produce superplastic



141

behavior in some cases131,132 when the nickel matrix grain size was in the range of 50–200 nm. Superplasticity was also observed in electrodeposited nickel containing sulfur impurities, deformed at temperatures between 350 and 400°C.68,84 However, the interpretation of these results is difficult because of 1) the substantial grain growth before and during high-temperature deformation that produced grain sizes in the micrometer range, and 2) the formation of sulfurenriched grain boundaries that may have resulted in a liquid grain boundary phase.

5.5

Corrosion properties of nanocrystalline electrodeposits

The corrosion properties of electrodeposited nanomaterials have been reported in many studies dealing with Ni and Ni-based alloys,135–153 nanocrystalline Co,154–157 Zn and Zn-Ni alloys158,159 and nanocrystalline Cu.160–162 A detailed analysis of the findings reported in the various investigations is beyond the scope of this review. However, the main results of these studies have shown the following. First, contrary to earlier concerns, the high grain boundary and triple junction densities found on the surfaces of electrodeposited nanomaterials do not compromise their corrosion performance. The general shapes of the potentiodynamic polarization curves for various materials in acidic, basic or neutral chloride solutions were not significantly affected by grain size in most cases. Materials that show passivity in the polycrystalline form also showed passivity in the nanocrystalline form. Some materials showed slightly higher or lower current densities in some regions of the active, passive and trans-passive portions in the polarization curves, but overall the nanomaterials and their polycrystalline counterparts showed very similar behavior. Some materials also displayed a shift in open circuit potential indicating that the nanostructure catalyzes the hydrogen evolution reaction on some materials. Second, for materials that do show passivity, the structure and chemical composition of the passive layers were found to depend on grain size. This is due to the high density of defects (grain boundaries and triple junctions) that intersect the free surface of the nanomaterials. The defect structure that forms in the passive layer is strongly influenced by the substrate defects. It was also found that impurity atoms in the nanomaterials could have a substantial effect on the nature of the passive film. However, even with a defective structure, the passive films on nanomaterials still provide considerable protection for the material exposed to various electrochemical conditions. Third, materials that are susceptible to preferential attack along grain boundaries can benefit enormously by grain size reduction. This is clearly seen in Fig. 5.14 which shows cross-sectional micrographs of polycrystalline and nanocrystalline (grain size 20–30 nm) nickel both containing about 1000 ppm by weight of sulfur after potentiodynamic polarization in a 0.25M Na2SO 4 solution at a pH of 6.5.145 The polycrystalline material shows excessive attack along the grain boundaries with considerable weakening of the structure deep inside the material. On the other hand,


142


5.14 Scanning electron micrographs of cross-sectional corrosion morphologies in polycrystalline (top) and nanocrystalline (bottom) nickel containing 1000 ppm sulfur. Note that σ represents either internal or externally applied stresses.

corrosion attack on the nanocrystalline nickel shows numerous, but only superficial, surface pits with no deep penetration into the bulk of the material. In other words, for nanocrystalline nickel, the corrosion attack is more or less spread out over the entire surface rather than being concentrated along the grain boundaries as seen for polycrystalline nickel. This has a tremendous effect on the performance of the materials in service. Many components in application have either internal stresses or are subjected to external stresses, both schematically indicated by the σ arrows in Fig. 5.14. For the polycrystalline material, extensive grain boundary corrosion has not only reduced the effective cross-sectional load-bearing capacity, the deep corrosion grooves at the grain boundaries also can act as stress concentrations; both factors contributing to conditions that can lead to unpredictable and catastrophic failures. On the other hand, the more or less uniform corrosion of the nanocrystalline material results in predictable overall thickness reduction. Therefore a component’s lifetime can be easily estimated as long as the average corrosion rate of the nanomaterial is known, for example, from polarization or immersion tests.



143

The effect of sulfur impurities on the corrosion behavior of nanocrystalline and polycrystalline nickel was discussed by Kim et al.145 One of the critical points to consider is the distribution of sulfur throughout the material. For constant overall sulfur content, the sulfur concentration per unit grain boundary area is much smaller in nanocrystalline nickel compared to polycrystalline nickel. For example, if it is assumed that all impurities segregate to grain boundaries, it can be shown that the maximum grain boundary sulfur concentration decreases by three orders of magnitude when the grain size is reduced from 10 µm to 10 nm. In other words, at constant bulk sulfur concentration, nanocrystalline nickel is expected to have cleaner boundaries than polycrystalline nickel.

5.6

Other properties of nanocrystalline electrodeposits

The physical properties of conventional metals and alloys are either structuresensitive or structure-insensitive.163 Structure-sensitive properties include tensile strength, hardness, electrical resistivity and thermal conductivity at low temperatures, coercivity, magnetostrictiction and magnetic permeability. On the other hand, density, elastic moduli, thermal expansion, specific heat, heat of fusion and saturation magnetization belong to the group of properties that are relatively structureinsensitive. Sensitivity and insensitivity are with respect to structural changes, for example by grain size reduction, increases in dislocation density or low concentrations of solute additions. In section 5.4 on the mechanical properties of nanocrystalline electrodeposits, it has already been shown that tensile strength and hardness are strongly dependent on grain size, while the Young’s modulus is relatively grain size independent. Table 5.9 shows how grain size and intercrystalline volume fraction affect room temperature electrical resistivity, ρ, saturation magnetization, MS, and thermal expansion, α, of nickel over a grain size range from 10 µm to 10 nm. The values given in Table 5.9 were again taken from grain size–property graphs presented earlier.16 Table 5.9 Electrical resistivity (ρ), saturation magnetization (MS), and thermal expansion coefficient (α) for nickel as a function of grain size and intercrystalline volume fraction Grain size (nm)

Vic (%)

ρ (µΩ cm)

MS (kA/m)

α (x 10–6/K)

10 000 1 000 100 50 20 10

0.03 0.29 2.97 5.88 14.26 27.10

8.5 8.5 8.8 9.0 13.0 20.0

502 500 500 495 489 488

11.2 11.1 11.0 10.8 10.7 10.6


144


Table 5.9 shows that the room temperature electrical resistivity is strongly dependend on grain size, in particular for grain sizes less than 100 nm for which the intercrystalline volume fractions rapidly increase. This is as expected because grain boundaries and triple junctions are very effective electron scattering centers. The grain size dependence for the room temperature electrical resistivity of nickel was given by the following equation:164

[5.29]

where d is the grain size. In this equation the factor 2.37 comes from the grain shape of the 14-sided tetrakaidecahedron, 2.82 × 10–6 µΩ cm2 is the specific grain boundary resistivity term and 8.33 µΩ cm is the resistivity due to electron scattering on phonons and other defects in the material including vacancies, dislocations and impurities. On the other hand, Table 5.9 shows that saturation magnetization, MS, changes very little with grain size in nickel.165 This is consistent with results obtained in linear muffin-tin orbital atomic sphere approximation calculations that evaluated the effect of structural disorder introduced by grain boundaries on the local magnetic moments in nickel.166,167 These studies have shown that the magnetic moments in different types of grain boundaries (e.g. several coincidence site lattice boundaries and a completely amorphous boundary) are not strongly affected by the structure of boundary defects. Similarly, grain size had very little effect on the saturation magnetization in nanocrystalline Co, Co-Fe, Co-W, Ni-Fe and Ni-P electrodeposits.168–170 In alloy deposits it is only the composition that controls the saturation magnetization. Table 5.9 further shows that grain size and intercrystalline volume fraction have no significant effect on the thermal expansion of electrodeposited nickel.171 Again this is consistent with results from a molecular-dynamics simulation study,172 which showed that grain boundaries have only a small effect on the thermal expansion of a material. Other structure-insensitive properties in nanocrystalline nickel include density173 and specific heat,171 two properties that show structure-insensitivity also for conventional materials. From the property examples shown in Tables 5.8 and 5.9 it is interesting to note that structure-sensitivity and structure-insensitivity observed in conventional materials are largely maintained when the grain size is reduced to the nanometer range in electrodeposited materials in which the main structural defects are the high volume fractions of grain boundaries and triple junctions. This is in contrast to nanomaterials produced by other synthesis methods such as inert gas condensation, ball milling or crystallization of amorphous precursors that often contain other defects such as porosity or residual amorphous phase. In these materials considerable changes have been observed for several structureinsensitive properties such as thermal expansion, specific heat, Young’s modulus



145

and saturation magnetization. These differences have been discussed elsewhere in more detail.22,174,175

5.7

Applications

Electrodeposition is a relatively low-cost production route to make nanocrystalline metals, alloys and composite materials. It is a low-temperature, single-step process and produces fully dense nanostructures, free of porosity often found in materials made from nanocrystalline powder precursors. The electrodeposition method for nanomaterials is a drop-in technology that can make use of existing electroplating and electroforming infrastructure and electrolyte ingredients such as metal salts and bath additions. Switching from conventional electroplating to nanoplating requires only modest capital investment, for example for a change over from DC plating to pulse plating. From an engineering point of view, electrodeposition is an extremely versatile and flexible technology. First, there are many different metals, alloys and composites that can be readily deposited in nanocrystalline form to meet specific application needs. Second, these materials can be deposited in a variety of different product shapes and forms including thin and thick coatings, free-standing sheet, foil, tubes, wires, plates, molds and even powders for some applications. Table 5.10 Table 5.10 Various shapes and applications of nanocrystalline products made by electrodeposition and electroforming Shapes

Applications

Thin coatings Surface modification for wear and corrosion resistance; catalytic surfaces Thick coatings ElectrosleeveTM ; repair of worn components Sheet, foil Gaskets; pressure control membranes; hydrogen purification membranes; thermal barriers; solar energy absorbers; microfoils; soft magnets Tubes, wire Surgical tools; missile guidance systems; miniature gamma radiation sources Mesh Filters; precision sieve screens; razor foils; printing screens; centrifuge screens Plate Structural applications Foam Filters; electromagnetic shielding; battery electrodes; catalyst carriers Molds Embossing tools for holograms; compression, injection and pattern molds Free forms Precision bellows; erosion shields for helicopters; trust chambers for rocket engines; components for micromagnetic motors, micro-optics, microactuators and microfiltration; shaped charge liners; precision reflectors and mirrors; nozzles Powder Catalysts; reinforcements


146


summarizes typical applications for the various product shapes of nanocrystalline electrodeposits. Many of these applications have been previously discussed in more detail.11–13,15,18,20,22,55 Chapter 22 will discuss several of these applications with emphasis on some of the more recently developed nanometal-enabled hybrid materials.

5.8

Acknowledgements

Financial support from the Natural Sciences and Engineering Research Council of Canada (NSERC) and the Ontario Research Fund (ORF) is gratefully acknowledged.

5.9

References

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6 Bulk nanocrystalline and nanocomposite alloys produced from amorphous phase A. INOUE and D.V. LOUZGUINE, Tohoku University, Japan Abstract In this chapter we review a large set of the research results related to formation and characterization of bulk nanocrystalline and nanocomposite alloys produced by crystallization of an amorphous/glassy phase or directly from the melt on cooling. The formation of bulk glassy alloys and their processing routes are also outlined. Nanocrystallizing glassy samples leads to the formation of composites containing nanoscale crystalline or quasicrystalline particles. The structure, general physical, thermal, mechanical and magnetic properties of these nanostructured materials are discussed. Some of these composites possess a better combination of mechanical properties than those of fully glassy or crystalline alloys. For example, nanoscale crystalline and quasicrystalline phases play a very important role in ductilization of bulk glassy alloys. Nanostructured ferromagnetic alloys and glassy-nanocrystal composites possess good soft magnetic properties and create an important application area for such materials. Key words: bulk, nano, crystalline, composite, alloy, amorphous, glassy, magnetic, material.

6.1

Introduction

As a rule bulk metallic alloy samples have a polycrystalline structure after solidification. Even casting of commercial alloys into a thin mould (with a cavity thickness of about 1 mm) produces a crystalline structure that is typical for metallic materials. Although oxide glasses have been known long ago, active research activities on metallic glassy alloys started after the formation of the first Au-Si sample with an amorphous structure in 1960.1 This became possible by using a rapid solidification technique for casting of metallic liquids at a very high cooling rate of 106 K/s when molten Au-Si and Pd-Si alloys undergo glass transition (vitrification) on cooling. Such alloys required extremely high cooling rate (from metallurgical viewpoint) for vitrification. For a long time Pd-Cu-Si and Pd-Ni-P system glassy alloys produced in a bulk form after flux treatment, which helps to suppress heterogeneous nucleation, were known to be the best metallic glass formers2,3 but remained a laboratory curiosity. However, a large number of bulk glassy alloys (also called bulk metallic glasses) defined as 3-dimensional massive glassy (amorphous) objects with a size not less than 1 mm in any dimension (by other definition 10 mm) have been produced since the end of the 1980s. The high glass forming ability of some alloy compositions has enabled the 152 © Woodhead Publishing Limited, 2011

Bulk nanocrystalline and nanocomposite alloys

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production of bulk metallic glasses in the thickness range of 100–102 mm by using various casting processes.4,5,6 Metallic glasses obtained in thin film, ribbon or bulk forms are metastable at room temperature and devitrify/crystallize on heating. Such a devitrification process leads to the formation of a nanostructure in many alloys. Nanostructured material can be defined as a substance that contains very small grains or particles of typically 1 to 100 nm in size (more strictly speaking in one or more dimensions). These nanostructured materials exhibit unique and superior properties, and for this reason they are subjects of high interest to scientists in various fields of physics, chemistry and materials science.7,8 Although the same nanomaterial can be produced using different techniques, the production technique often significantly influences the properties of metallic glass-originated nanomaterials. If the process involves nucleation and growth then a high nucleation rate and a low growth rate of the precipitating phase are required in order to obtain a nanostructure. Such conditions are usually obtained under primary crystallization/devitrification with a long-range diffusioncontrolled growth.

6.2

The formation of bulk metallic glassy alloys

Depending upon their glass-forming ability (GFA), glassy (amorphous) alloys can be produced using various processing methods. Alloys having a low GFA can be prepared in an amorphous state by condensation from a vapor phase.9 This method is, however, high on power consumption and not efficient for the preparation of bulk glassy metals. Some glassy alloys can be produced by a solid-state reaction using mechanical attrition10 such as ball milling11 or by severe plastic deformation.12,13 Another method for producing glassy metals is electrodeposition from a solution.14,15 The two methods mentioned above are efficient but also heavy on power consumption. Much more productive is rapid solidification from a liquid phase16 by melt-spinning or Cu-mold casting, for example, or from quartz crucible through a nozzle (Fig. 6.1), liquid forging and so on. Bulk glassy alloys with an extraordinarily high GFA 4–6,17 among metallic alloys have been widely produced since the breakthrough achieved in the end of 1980s and the beginning of the 1990s.18,19 They are greater in size compared to melt-spun ribbons or thin films, and thus represent higher commercial interest as structural materials. Since these discoveries, many other bulk glassy alloys have been produced.20–24 They can be produced at cooling rates of the order of 100, 10, 1 K/s and even less, which is much lower than those of 104–106 K/s required for vitrification of marginal glassformers using a rapid solidification technique. The bulk glassy alloys possess three common features summarized in,4 i.e. 1) the alloys belong to multicomponent systems, 2) the constituent elements have significant atomic size ratios above 12%, and 3) most of the alloying elements in such alloys have a large and negative mixing enthalpy with each other (although


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6.1 Bulk glassy sample casting technique, scheme.

some of the alloying elements like Ni and Cu, often presenting in the bulk glassy alloys, for example, have a moderately positive mixing enthalpy with each other). At present bulk metallic glasses already have some important applications4,6,25 and it is believed that these will increase in the near future.26,27 On the other hand, if the GFA of the alloy is insufficiently glassy or amorphous, powder samples can be produced by mechanical alloying or gas atomization techniques,28 for example, and then consolidated into bulk form by hot pressing in a WC die,29 spark plasma sintering (SPS)30 technique by applying pulsed direct current (Fig. 6.2) or some other techniques. For example, Ni-based bulk metallic glassy samples31,32 with a size of 20 mm were fabricated by spark plasma sintering of gas-atomized Ni52.5Nb10Zr15Ti15Pt7.5 glassy powders (Fig. 6.3 and Fig. 6.4). The structure, thermal stability and interface characteristics of the powder particles in the sintered specimens were investigated. Sintered glassy specimens with nearly 100% relative density were obtained by the SPS process at



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6.2 Schematic representation of spark plasma sintering technique.

6.3 Scanning electron microscope micrograph of the cross section of the sintered Ni52.5Nb10Zr15Ti15Pt7.5 specimen obtained at a sintering temperature of 773 K.


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6.4 Dimensions of the SPS compact.

the sintering temperature of 773 K under a loading pressure of 600 MPa. The consolidation was achieved with a relatively low sintering temperature, a short holding time and rapid cooling during the SPS process. Spark plasma sintering, as a newly developed rapid sintering technique, has great potential for producing dense glassy specimens or nanocrystalline materials in a short sintering time. In the SPS process, pulsed electrical current flows directly through the powder material being sintered, and high heating efficiency is achieved (Fig. 6.2). The application of pulsed DC voltage induces various phenomena caused by electrical and thermal effects, providing advantages that could not be obtained using conventional sintering processes. Aluminum-based bulk glassy samples of high relative density were obtained by warm extrusion of atomized amorphous powders33 though they have rather low GFA owing to a high density of so-called quenched-in nuclei in some glasses. This fact, as well as a low reduced glass-transition and devitrification temperature,34 limits the glassy sample’s critical thickness below 1 mm. Owing to the absence of crystalline lattice and dislocations, a unique deformation mechanism35,36 is realized in bulk glassy alloys, which thus exhibit high strength37 (~2 GPa for Cu-, Ti-, Zr-based, ~3 GPa for Ni-based, ~4 GPa for Fe-based, ~5 GPa for Co-based alloys), high hardness, good wear resistance38 and large elastic deformation. For example, (Fe, Co)-Cr-Mo-C-B-Tm glassy alloys prepared in a cylindrical form with a diameter of 18 mm demonstrate an excellent GFA and high strength exceeding 4 GPa.39 Some bulk metallic glasses exhibit significantly higher compressive ductility40,41 compared to the others. Their ductility can be related to Poisson’s ratio ν,42 in situ nanocrystallization43 or glassy phase separation.44 Nevertheless localized shear deformation is a dominant plastic-deformation mode at room temperature.45 The fatigue-endurance limits of some Zr-based alloys are comparable with those of high-strength structural alloys.46 Many of the metallic glassy alloys have a high corrosion resistance.47,48 Iron- and cobalt-based alloys exhibit good soft magnetic properties,49,50 while Nd-based alloys show hard magnetic properties.



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One should also mention that some bulk glassy alloys contain clear mediumrange order (MRO) zones51 or nanoscale particles52 in an as-solidified state, even though these precipitates do not produce diffraction peaks in the XRD and selected-area electron diffraction pattern (SAED) due to their small volume fraction. An example of MRO zones is shown in Fig. 6.5. Although binary bulk glassy alloys exist,53,54,55 their GFA is low (a critical thickness of the sample that achieves the glassy state without crystallization does not exceed 2 mm), some of them were reported to contain nanoparticles and they are formed in narrow composition ranges. On the other hand, an addition of a third element56 enhances their GFA. Bulk glassy alloys can be thermo-mechanically shaped or welded in the supercooled liquid regions by electromechanical shaping technology at low applied stresses due to the high electrical resistivity of glassy alloys.57 Some of the glassy alloys exhibit ‘superplasticity’ (actually good fluidity) on being heated to a supercooled liquid region.58 Bonding of glassy alloys can be achieved by laser,59 electron-beam60 and friction welding.61 Several attempts have also been made to explain the GFA of these alloys based on different criteria. These include the reduced glass transition temperature, Trg = Tg/Tl62 where Tg is the glass-transition temperature and Tl is the liquidus temperature (though overall validity of this criterion has been questioned recently);63,64 the width of the supercooled liquid region (∆Tx) defined as Tx – Tg where Tx is the crystallization onset temperature;65 and the γ = Tx/(Tg + Tl)

6.5 Medium range order zones in Ni50Pd30P20 alloy, encircled in the HRTEM image. The insert in the top left corner is a Fast Fourier Transform of the area encircled in the center. One can admit the existence of sharp spots.


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parameter,66 which somehow combines both ∆Tx and Tg/Tl criteria into a single parameter and many other criteria.67 It has also been clearly shown that purely extrinsic factors also have a significant influence on the GFA.68 The role of minor additions in the formation of metallic glasses was also discussed.69 Another important point relates to the nonequilibrium eutectic, as the best glass-forming compositions are found not exactly at the equilibrium eutectic point but somewhat shifted usually towards a more refractory eutectic component,70 while Tg is not significantly different in the observed range. This most likely takes place owing to the shift of the eutectic point with supercooling/undercooling at a high enough cooling rate because casting conditions of bulk glassy samples are far from equilibrium.71 However, binary (Si or Ge)-Ni and ternary (Si or Ge)-Ni-Nd alloys showed that the principles for achieving a good GFA known so far are necessary conditions, but not always sufficient conditions.72 It was found that the higher GFA of the Ge-Ni-Nd alloy compared to the Si-Ni-Nd alloy cannot be explained on the basis of the widely used parameters such as geometrical and chemical factors, viscosity and diffusion data. It was suggested that the electronic structure characteristics,72,73 for example electronegativity difference, should be taken into consideration. The electronegativity of the constituent elements is an important factor influencing the GFA and the temperature interval of the supercooled liquid region of the glass-forming alloys.74 The atomic packing density for non-crystalline structures is a geometrical factor influencing GFA.75 A mixture of atoms with different sizes enables their dense packing. The importance of efficient atomic packing for the formation of metallic glasses was shown recently,76,77 as the specific radius ratios are preferred in the compositions of metallic glasses. These features are also closely connected with so-called λ criterion for good GFA.78 It has been also postulated that electron concentration: number of valence electrons per atom (e/a value) affects the GFA79 by analogy with Hume–Rothery phases related to certain valence electron concentration. However, as many glassy alloys contain transition metals which have multiple valences, it is difficult to decide which valency value should be taken into consideration in a particular case. The glass-transition phenomenon in metallic glasses has been studied extensively. Three kinds of approaches have been formulated:80,81,82 the glassy phase is just a frozen liquid, and thus, glass-transition is a kinetic phenomenon and no thermodynamic phase transformation takes place; glass transition may be a secondorder transformation as follows from the shape of the curves for the thermodynamic parameters, for example, specific volume or enthalpy, which exhibit a continuity at the glass-transition temperature while their derivatives like thermal expansion coefficient or heat capacity exhibit a discontinuity (in a certain approximation) at the glass-transition temperature; glass transition may be a first-order transformation. A thermodynamic aspect of glass transition is known as the Kauzmann paradox.83


6.3


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The formation of a nanostructure by crystallization of the glassy phase, by deformation or directly from the melt on casting

Nanoscale particles of a crystalline or a quasicrystalline phase can be readily formed by crystallization/devitrification of the glassy alloys. This indirect method of production of the nanostructure requires formation of the glassy phase in the initial stage and its subsequent full or partial devitrification on heating. Such a method leads to the formation of a highly homogeneous dispersion of nanoparticles in various alloys. The difference in the devitrification pathways of glassy alloys is often connected with the state of the matrix phase prior to devitrification. It can be amorphous, glassy or supercooled liquid. Amorphous alloys like Al-Nd-Ni-Co do not transform to a supercooled liquid before crystallization (Fig. 6.6) upon conventional heating rate. Glassy alloys like Al-YNi-Co form the supercooled liquid region on heating prior to crystallization (Fig. 6.6) and in general have a better GFA compared to amorphous alloys which do not exhibit Tg on heating. Marginal glass-formers like Al-Y-Ni-Co-Cu (Fig. 6.6) have pre-existing nuclei84 or even nanoparticles in the amorphous matrix, and thus the initial heat flow signal in the DSC, marked as A, is related to the beginning of growth of these nuclei or particles. Although it might be difficult to establish an intrinsic physical difference between amorphous and glassy alloys such a slightly arbitrary differentiation in relation with the devitrification behavior is useful. The formation of a supercooled liquid has a significant influence on the devitrification process in metallic glasses.85 Alloys devitrifying from the supercooled liquid exhibit a tendency to form metastable phases and phases with high crystallographic symmetry on devitrification compared to similar alloys that crystallize.86 This may be connected with the change of the local atomic structure in the supercooled liquid region due to higher atomic mobility compared to that in the glassy phase. Below Tg the crystalline products of devitrification in some alloys inherit the as-solidified structure of the metallic glass. Four types of phase transformations were found to occur during devitrification of the glassy alloys: 1) polymorphous (a product phase has the same composition as the glassy phase), 2) primary (a product phase has a composition different from that of the glassy phase), 3) eutectic (eutectoid) transformation (two or more phases nucleate and grow conjointly) and 4) spinodal/binodal decomposition involving a phase separation of the glassy phase prior to crystallization/devitrification.87 When the devitrification occurs by nucleation and growth mechanism (amorphous alloy does not have pre-existing nuclei), a high nucleation rate leading to a high number density of the precipitates in the order of more than 1021 m–3 and low growth rate of the precipitating phase are required in order to obtain a nanostructure88 in many alloys. The kinetics of the devitrification process has been also analyzed. It is also


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6.6 Differential scanning calorimetry traces of three representative Al-based alloys exhibiting glass-transition on heating (alloyed with Y), crystallization without glass-transition (alloyed with Nd) and marginal glass-forming alloy which has pre-existing nuclei and nanoparticles (Cu-bearing alloy).

found that about 1 MHz frequency ultrasonic vibrations promote the crystallization of Pd40Ni40P20 bulk glass.89 Devitrification of glassy alloys can be analyzed by the Kolmogorov–Johnson– Mehl–Avrami general exponential equation for the fraction transformed x(t):90 X(t) = 1 − exp(−Kt n),

[6.1]

where t is time and n is the Avrami exponent in the case of a single-stage reaction and steady-state nucleation. Crystallization kinetics of many glassy alloys obeys this mechanism. For example, Fig. 6.7 shows the Avrami plot for a Cu45Zr45Ag10 glassy alloy, which exhibited eutectic-type crystallization causing simultaneous formation of oC68 (Cu,Ag)10Zr7 and tP4 (Ag,Cu)Zr solid-solution phases by nucleation and



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6.7 The Avrami plot for Cu45Zr45Ag10 glassy alloy heat-treated isothermally at 717 K in a DSC device. Coefficient of determination (R2) for linear function fitting is 0.99998. Only every 5th data point is shown as a filled circle for better visibility of the linearity of the plot.

3-dimensional interface-controlled growth. As expected, the Avrami exponent for this process is close to 4. Nanostructured alloys are readily obtained from the primary devitrification of glasses with a long-range diffusion-controlled growth. The primary devitrification process of a highly supercooled liquid or amorphous phase often has high nucleation frequency, low crystal growth rate, high concentration gradient of solute element at liquid/solid interface resulting from low atomic diffusivity, formation of metastable phases, formation of a residual amorphous phase with high solute concentration, and so on. Another type of phase transformation in an amorphous solid leading to the formation of a nanostructure is spinodal decomposition.91 There are some data suggesting that in particular cases nanocrystalline structure can be obtained after eutectic92 and polymorphous93 devitrification of glassy alloys. Nevertheless, the most common mechanism leading to formation of a nanostructure is primary crystallization. Different Al-RE-TM glasses (where RE: rare earth; TM: transition metals) show primary precipitation of the Al solid solution (α-Al) nanoparticles on heating94 with a high nucleation rate exceeding 1020–1021 m–3s–1.95 The formation of α-Al at the primary crystallization stage is quite typical for Al-based amorphous alloys and glass-formers, for example: Al-Y-Ni-Co,96 Al-Fe-Y, Al-Fe-Nd97 and others. The investigations showed very low concentration of the alloying elements in nanocrystalline98 Al in accordance with the phase diagrams of Al-RE and Al-TM.99 Segregation of the RE metal having low trace diffusivity in Al to the α-Al/amorphous phase interface is considered to be one of the most important reasons for their low growth rate. Extended X-ray absorption fine structure analysis of grain boundaries in the nanocrystalline Fe85Zr7B6Cu2 alloys also showed a low Fe content in the grain boundaries between the bcc (body-centered cubic) Fe solid solution nanograins. Although in most of the alloys the


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nanocrystalline precipitates were found not to contain dislocations the addition of Pd to Al-Y-Ni-Co alloys caused formation of the highly dispersed primary α-Al nanoparticles about 3–7 nm in size upon solidification homogeneously embedded in the glassy matrix, and the direct observation of micro-strain and dislocations quenched in nanoparticles with a size below 7 nm is provided.100 Clearly heterogeneous nucleation was observed during formation of the Fe nanocrystals.101 The structure of Fe-based soft magnetic alloys like: Fe73.5Cu1Nb3Si13.5B9102 and Fe84Zr3.5Nb3.5B8Cu1103 after annealing consist of bcc Fe nanocrystals below 20 nm in size well dispersed in the amorphous matrix. The devitrification of the Fe73.5Cu1Nb3Si13.5B9 alloy starts from the formation of Cu-enriched zones.104 Precipitation of a nanoscale α-(Fe,Co) phase105 was observed in the Fe40Co40Cu0.5Zr9Al2Si4B4.5 alloy (Fig. 6.8). As has been shown by means of atom probe field ion microscopy as well as by high-resolution transmission electron microscopy106 Cu atoms form nanoclusters in the Fe73.5Si13.5B9Nb3Cu1 amorphous matrix, which act as the nucleating sites for heterogeneous nucleation of the bcc Fe particles on devitrification.107 The density of the clusters estimated by 3-dimensional atom probe is in the order of 1024 m–3 at the average cluster size of about 2–3 nm. Yavari and Negri108 discussed nanocrystallization process of soft magnetic Fe-based amorphous alloys using the concentration gradients of the elements that are insoluble in the primary crystalline phase. The transformation of the glassy phase to a supercooled liquid region altered the crystallization behavior of Al85Y4Nd4Ni5Co2,109 Al85Y8Ni5Co2 as well as some other Al-based glassy alloys110,111 which exhibited different devitrification

6.8 Bright-field TEM image of Fe40Co40Cu0.5Zr9Al2Si4B4.5 alloy annealed for 15 min at 873 K showing the formation of nanoparticles. Inset shows the selected-area electron diffraction pattern.



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behavior above and below the onset glass-transition temperature (Tg), while no such a feature was found in the Al-RE-Ni-Co amorphous alloys (glassy alloys exhibit glass-transition on heating while amorphous do not) showing no Tg. Thus, the devitrification behavior of Al-RE-Ni-Co metallic glasses can be classified as follows: (1) If an alloy does not show Tg on heating prior to devitrification (crystallization) and exhibits nucleation and growth transformation mechanism, it forms intermetallic compound(s) (IM) or IM + nanoscale Al particles. (2) If an alloy does not show glass transition on heating prior to devitrification and has pre-existing nuclei, it forms nanoscale primary Al grains. (3) If an alloy shows glass transition on heating and exhibits nucleation and growth transformation mechanism, it forms nanoscale Al particles above Tg and IM + Al or IM below Tg. The exception found in Ref.112 with large ribbon thickness of about 40 µm is more likely related to the pre-existing α-Al nuclei. The devitrification behavior of Al-based glassy and amorphous alloys was also recently associated with a topological empirical criterion (λ) defined as:78,113

[6.2]

where Ci is concentration of the i-th alloying element while ri is a solute atom radius and rAl is Al atom radius. The λ parameter predicts whether the compositions exhibit supercooled liquid region (λ > 0.1) or not (λ < 0.1). Such a transition at different Ni/RE ratio has been also observed in Al-Y-Ni114 and Al-La-Ni alloys.115 Intermetallic compounds can also be formed into a nanoscale size of precipitates. For example, the devitrification of the Ti50Ni20Cu23Sn7 alloy begins from the primary precipitation of nanoscale equiaxed particles of cF96 (Pearson Symbol) Ti2Ni solid solution.116,117 Formation of such a nanoscale cF96 phase has also been observed in the Zr- and Hf-based alloys.118 The growth rate of cF96 phase at a constant temperature is non-linear which indicates the diffusion-controlled growth mechanism. An extremely low growth rate of cF96 crystals was observed on the primary crystallization of the Hf55Co25Al20 glassy alloy.119 Very small cF96 Hf2Co clusters of 2–5 nm in size are formed in the sample annealed at 907 K for 0.9 ks, which causes appearance of the broad diffraction peaks (Fig. 6.9). These clusters are not visible in the bright-field TEM images,119 while XRD pattern of the sample annealed for 0.9 ks at 907 K is already different from that of the as-solidified state: the broad diffraction peak from about 30 to 45 degrees 2θ splits into five narrower peaks. The factors leading to nano-devitrification can be connected with the occurrence of heterogeneities such as oxygen impurity-enriched clusters, spinodal


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6.9 X-ray diffraction pattern of the Hf55Co25Al20 glassy alloy annealed at 907 K for 0.9 ks. The location of the five strong peaks (Gaussian fitting) corresponds to that of cF96 Hf2Co phase. Source: Louzguine et al.119 reprinted with permission from Elsevier Science.

decomposition in the liquid or glass120 and homogeneous nucleation in partitioning systems.121 In many cases diffusive redistribution of the alloying elements on a short scale precedes crystallization. Mg-Ni-Mm and Mg-Ni-Y-Mm (where Mm denotes Mischmetal – a natural mixture of several rare-earth metals) glassy alloys show a multistage crystallization behavior.122 The local structure of the as-solidified Mg86Ni10Y2Mm2 and Mg82Ni14Y2Mm2 metallic glasses containing MRO zones changes prior to the formation of the crystalline phases. Changes in the amorphous halo peak occur after heating to the first DSC exothermic peak, which indicates redistribution of the alloying elements in the amorphous matrix forming Mg-enriched zones. This process occurs without an incubation period. Comparison of the long-term thermal stabilities of different metallic glasses has been carried out using continuous heating transformation (CHT) diagrams123 constructed by applying a corollary from the Kissinger analysis method. Continuous heating transformation diagrams also can be recalculated from the isothermal ones using a method close to that used for steels. Nanoparticles in the glassy matrix can be produced directly from the melt. A nanomaterial consisting of icosahedral particles with a diameter below 10 nm was obtained in Zr-Pt alloy124 by casting. The formation of the nanoscale icosahedral phase during casting may indicate that the icosahedral short-range order exists in the melt of Zr-Pt binary alloy. Plastic deformation can cause nanoscale devitrification of a glassy phase. For example, deformation of some Al-RE-TM amorphous alloys at room



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temperature causes precipitation of deformation-induced α-Al particles of 7–10 nm in diameter within the shear bands on bending125 or nano-indentation.126 This effect was also observed in a Ni-based glassy alloy.127 It has been suggested that a local temperature rise can play a role in mechanically induced devitrification.128 One should also mention electron-beam irradiation induced crystallization.129,130 A general observation is that it causes primary nanocrystallization even in alloys that exhibit eutectic transformation mechanism on heating. However, it tends to indicate a non-thermal crystallization.

6.4

The formation of nano-quasicrystals

Nanoscale quasicrystals are formed on devitrification in various metallic glassy alloys.131 An icosahedral quasicrystalline phase (a 3-dimensional quasicrystal while 2- and 1-dimensional quasiperiodic structures also exist) having a longrange quasiperiodic translational and an icosahedral orientational order, but with no 3-dimensional translational periodicity, was initially discovered in Al-Mn alloys132 and later in some other binary Al-TM alloys and different ternary Al-based alloys.133 After that the icosahedral phase was observed in Ga-, Ti-, Mg- and Pd-based alloys as well as Cd-, rare earth- and Zn-based alloys.134,135 It has been found that reduced supercooling before crystallization from the melt was found to be the lowest for quasicrystals, larger for crystal approximants (crystals which structure is somewhat similar to those of certain quasicrystals) and largest for the crystalline phases. The nucleation barrier scales with the supercooling, and thus, local icosahedral order is considered to exist in some supercooled liquids and glasses. A low energy barrier for nucleation of the icosahedral phase may explain the fact that only growth of the pre-existed icosahedral nuclei was observed in the Zr65Ni10Al7.5Cu7.5Ti10Ta10 alloy.136 Formation of the nanoscale icosahedral phase was observed in the devitrified Zr-Cu-Al, Zr-Al-Ni-Cu137 and Zr-Ti-Ni-Cu-Al138 glassy alloys containing an impurity of oxygen above about 1800 mass ppm, although no icosahedral phase is formed if oxygen content is lower than 1700 mass ppm. The nanoscale icosahedral phase was obtained in devitrified Zr-Al-Ni-Cu-Pd,139 Zr-Pd, Zr-Pt140 and other system alloys at much lower (about 800 mass ppm) oxygen content. The nanoscale icosahedral phase has been produced in the NM (noble metals)-free Zr-Cu-Ti-Ni141 and Zr-Al-Ni-Cu142 glassy alloys with low oxygen content, below 500 mass ppm. The icosahedral phase in Zr-based alloys is often formed in cooperation with cF96 phase and cI2 βZr solid solution phase.143 In the rapidly solidified TixZryHfzNi20 system alloys the nanoscale icosahedral phase forms in the composition ranges close to that of the cI2 β solid solution phase and complex cF96 phase formation ranges.144 Moreover, cI2 β solid solution and icosahedral phases were found to have close chemical compositions. A transformation from glassy + β-Zr to glassy + icosahedral structure was observed in Zr65Ni10Al7.5Cu7.5Ti5Nb5 alloy on heating by a single-stage transformation with


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diffusion control. β-Zr solid solution particles were found to dissolve in the glassy phase, while the nanoscale particles of the icosahedral phase precipitate after the completion of the first exothermic reaction,145 which is considered to be a singletype reaction somewhat similar to peritectic one. The nanoscale icosahedral quasicrystalline phase has been also produced upon heating glassy Hf-based alloys containing Pd146,147 or Au. Hafnium-based alloys have a higher tendency to form a cubic cF96 phase compared to Zr-based ones. The alloys in the systems in which an equilibrium Hf-based cF96 phase exists do not show the formation of the icosahedral phase from the amorphous matrix. The metastable cF96 phase and the icosahedral phase are formed by primary devitrification from the amorphous phase inheriting the structure of the icosahedral clusters. As these two phases are obtained in the alloys with similar compositions and due to local structural similarities between these two phases, one can say that these phases are produced from the same clusters and the free energy difference is a leading factor for the formation of one phase or another. The formation of the nanoscale icosahedral phase was observed in the Cu-based alloys containing Pd148 and Au while Ag- and Pt-bearing alloys did not form the icosahedral phase. Palladium in the Cu60Zr30Ti10 glass-former changes its devitrification pathway,149 inducing nucleation and diffusion-controlled growth of a nanoicosahedral phase (Fig. 6.10) from the supercooled liquid region in the initial stage of the devitrification process.

6.10 Transmission electron microscopy image of the Cu55Zr30Ti10Pd5 alloy annealed at 750 K for 1.2 ks. (a) Bright-field image, (b) dark-field image, and (c) selected-area electron diffraction pattern. The dark-field image was taken with the sharp rings in (c). Nanobeam diffraction patterns of 5-, 3- and 2-fold symmetries are inserted in (a), (b) and (c), respectively. Source: Data taken from Louzguine et al.148 with permission from Elsevier Science.



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A bulk glassy alloy sample of Cu-Zr-Ti was reported to contain nanoscale crystalline particles (about 5 nm size)150 in as-solidified state whereas the samples of the Cu-Zr-Ti-Pd alloy containing 5 at.% Pd were glassy. The nanoscale particles of the cP2 (Pearson Symbol) CuZr phase were observed in the as-solidified Cu50Zr30Ti10Pd10 bulk glassy sample. The dissolution of the CuZr nanoparticles took place on heating up to supercooled liquid region owing to the instability of the CuZr phase below 988 K.149,151 According to the Cu-Zr phase diagram, the CuZr phase undergoes eutectoid transformation at 988 K, which is above the supercooled liquid region of the Cu50Zr30Ti10Pd10 alloy (about 750–800 K). The nanoscale CuZr phase becomes thermodynamically unstable and dissolves on heating in the supercooled liquid above Tg when atomic diffusion is enhanced by temperature.

6.5

The mechanical properties of nanocomposite alloys

Bulk glassy alloys demonstrate high yield strength (σy), nearly 2% elastic strain and relatively low Young’s modulus (E). Thus, they have a high performance index σy2/E.152 However, highly inhomogeneous deformation localized in shear bands153 limits their ductility. Thus, the ductilization of bulk metallic glasses is an important technological challenge. Devitrification of the glassy alloys leads to the formation of the composite nanomaterials containing crystalline phase precipitates in the residual glassy phase matrix. Mechanical strength and ductility of glassy alloys can be improved by the precipitates of nanocrystalline or nanoquasicrystalline phase. For example, a Zr65Al7.5Cu7.5Ni10Pd10 alloy having nanoscale icosahedral phase particles embedded in the glassy matrix showed a better combination of the mechanical properties compared to the as-cast glassy sample154 without precipitates. Its Young’s modulus, 0.2% proof stress, ultimate tensile strength, total percentage deformation including elastic deformation are 85 GPa, 1640 MPa, 1750 MPa, and 2.2%, respectively, in the bulk glassy form and 88 GPa, 1780 MPa, 1830 MPa, and 3.1%, respectively, in the 2-phase (nanoquasicrystalline + glassy phase) form. The inclusion of a precipitating phase in this alloy causes deviation and blockage of the operating shear bands, which thus improves the plasticity of the alloy. However, because the single-phase icosahedral phase alloys are extremely brittle155 it is difficult to consider that the icosahedral phase itself has plastic deformability. Thus, its good mechanical properties are attributed to the existence of the residual intergranular glassy phase, while the icosahedral particles can act as a resisting medium against the shear deformation. Also, nanocrystalline precipitates increase the room-temperature mechanical strength of the Zr-AlCu-Pd,156 Zr-Al-Cu-Pd-Fe and (Zr/Ti)-Cu-Al-Ni157 bulk glassy alloys. Some bulk glassy-crystal composites with enhanced ductility have been produced by proper alloying in other Zr-158,159 and Cu-based alloys.160,161 The nanoscale icosahedral


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(Fig. 6.10) or crystalline particles can act as a resistant agent against the shear deformation. Amorphous alloys of Al-RE-TM possess a high tensile strength exceeding 1200 MPa162 and good bend ductility, that is, showing ability of being bent through 180° without fracture.163,164 The homogeneous dispersion of the nanoscale fcc (face-centered cubic) α-Al particles in the amorphous matrix causes a drastic increase in the tensile fracture strength to 1560 MPa165 which is a record number for the high strength Al-based glassy or crystalline alloys. The Al88Y2Ni9Fe1 amorphous alloy containing 7% volume fraction of the fcc-Al particles with a size of about 3–7 nm has a high tensile fracture strength of 1320 MPa and 1260 MPa with the particle volume fraction of 24%, respectively.166 These particles can be formed by controlling the cooling rate upon solidification or by annealing glassy alloys. The largest strength value was obtained when the volume fraction of α-Al phase reached 25%.167 The significant decrease in tensile fracture strength by the further increase in Vf is due to the embrittlement of the remaining amorphous phase by the progress of structural relaxation and enrichment in the solute elements.168 The (Al0.84Y0.09Ni0.05Co0.02)95Sc5 amorphous alloy has an ultra-high tensile fracture strength slightly exceeding 1500 MPa, which surpasses those for all other Al-based fully crystalline and fully amorphous alloys reported to date.169 It opens the possibility of further strengthening such an alloy by nanoscale crystallization. In metallic glasses the deformation is concentrated in the shear bands of maximum shear stress, which maintain about 45° with the load (tensile or compressive) direction. The width of the shear bands is about 10–20 nm. It is considered that the nanoscale α-Al particles can act as an effective barrier against the shear deformation of an amorphous matrix.170 At the same time, it was also suggested171 that the hardening could be attributed mainly to solute enrichment of the residual glassy matrix due to lowering of the Al content. This theory well describes the hardening of the material. As the hardness of fully amorphous or partially crystalline alloys correlates well with the solute content in the amorphous phase, it is suggested that not only α-Al particles but also the amorphous matrix has some role in the hardening and embrittlement of the alloy. However, in some cases, formation of the primary α-Al particles was found to deteriorate mechanical properties and decrease the tensile strength and hardness. Partial substitution of Ni by Cu in the Al85Y8Ni5Co2 metallic glass causes formation of the nanoscale α-Al particles and drastically decreases the tensile strength and hardness values of the alloy.172 Copper, which has a much lower absolute value of heat of mixing with Al, Y and Co than Ni has with these metals, may be responsible for such a decrease in the properties. Thus, Cu may weaken the interaction needed for the stability of the glass, thus resulting in the disappearance of Tg and precipitation of α-Al nanocrystals. In addition, the volume fraction of the α-Al nanocrystals in Al85Y8Ni3Co2Cu2, for example, is



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much lower than that in the primarily devitrified Al85Y8Ni5Co2 metallic glass. It was found that the α-Al inter-particular distances in the Al85Y8Ni3Co2Cu2 metallic glass significantly exceed the particle size itself. Thus, α-Al particles cannot act as an effective barrier against the shear deformation in the amorphous matrix.

6.6

The magnetic properties of nanocomposite alloys

Magnetic materials compose another very important and developing application field of nanostructured alloys. The connection between nanostructure and magnetic properties is a topic of intensive investigations. Ferromagnetic alloys can exhibit hard or soft magnetism depending on their coercivity. Magnetic materials having coercivity above about 104 A/m are considered to be hard while soft magnetic materials have a coercivity below 103 A/m.

6.6.1 Soft magnetic alloys A typical magnetization curve of a soft magnetic alloy (also called a magnetically soft alloy) is given in Fig. 6.11. Classical examples of Fe-based soft magnetic materials with mixed nanocrystalline and amorphous structure, as shown in Fig. 6.7, for example, are Finemet Fe73.5Cu1Nb3Si13.5B9102 and Nanoperm Fe84Zr3.5Nb3.5B8Cu1103 alloys. The structure consists of bcc Fe nanocrystals below 20 nm in size finely dispersed in the amorphous matrix. The addition of Cu, Nb or Zr is responsible for bcc Fe grain refinement and formation of a nanostructure in these alloys.

6.11 Magnetization curve of a Co-Fe-Ta-B glassy sample. Source: Courtesy of P. Sharma.


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Atom probe field ion microscopy and high-resolution TEM studies showed173 that Cu formed nanoclusters in the Fe73.5Si13.5B9Nb3Cu1 amorphous matrix, which work as heterogeneous nucleation sites for bcc Fe particles on devitrification. The studies by X-ray absorption fine structure (XAFS) also showed that Cu clusters with near-fcc structure were present from the very early stages of the devitrification process.174 The density of the clusters is of the order of 10–24 m–3 while the average cluster size is about 2 nm.175 The above-mentioned alloys show high permeability, for example, 100 000 in the case of Fe84Zr3.5Nb3.5B8Cu1 alloy, high magnetization saturation up to 1.5 T and low hysteresis losses.176 Soft magnetic materials of Fe-Zr-B also exhibit high magnetization saturation (Ms) of 1.60–1.70 T under an applied field of 800 kA/m as well as high effective permeability of 13 000–15 000 at 1 kHz. Typical nanocrystalline bcc Fe89Hf7B4 and Fe84Nb7B9 alloys subjected to the optimum annealing exhibit high magnetization saturation above 1.5 T, as well as high effective permeability at 1 kHz above 20,000. For a long time soft magnetic alloys were limited to marginal glass-formers. Soft magnetic properties of thick (Fe, Co)-RE-B glassy alloys were studied.177 Bulk glassy alloys exhibiting a wide supercooled liquid region before crystallization were found in Fe-(Co,Ni)-(Zr,Nb,Ta)-(Mo,W)-B system.178 These alloys have a high Tg of about 870 K and the supercooled liquid region close to 90 K. The high thermal stability of the supercooled liquid enabled the production of bulk glassy alloys with diameters up to 6 mm, which exhibit a high compressive strength of 3800 MPa, high Vickers hardness of 1360, and high corrosion resistance. These glassy alloys exhibit a large magnetization saturation of 0.74–0.96 T, low coercivity of 1.1–3.2 A/m, high permeability exceeding 1.2 × 104 at 1 kHz, and low magnetostriction of about 12 × 10–6. Boron addition is reported to suppress growth of bcc-Fe grains and to stabilize the amorphous matrix. Alloys of Fe82(Zr,Hf,Nb)7B10Cu1 exhibit good soft magnetic properties especially in the high-frequency range.179 Nanocrystalline Fe42.5Co42.5Nb7B8 alloys with a structure consisting of nearly spherical bcc grains with size from 5–10 nm dispersed in the residual amorphous matrix exhibit a high saturation magnetization of 1.90 T and a low coercivity (Hc) of 60 A/m.180 It also exhibits a high Curie temperature (Tc) exceeding 1173 K. The segregation of Nb element in the intergranular amorphous phase increases the thermal stability of the amorphous phase and suppresses the grain growth of the bcc phase. The high thermal stability of the structure and the high Curie temperature are necessary properties of a soft magnetic material for high-temperature application. The Fe-M-B (M = Zr, Hf, or Nb) alloys also show low core losses.181 The Fe66Nb4B30 ferromagnetic bulk glassy alloy with high B content was produced by fluxing and casting.182 It also forms a nanostructure upon initial crystallization on heating. Soft magnetic properties are determined by the nature of the nanocrystal-glassy phase coupling. The origin of the good soft magnetic properties is connected with the formation of the nanoscale bcc-Fe structure and the achievement of rather



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strong magnetic coupling between the bcc grains through the intergranular ferromagnetic amorphous phase.

6.6.2 Hard magnetic alloys Hard magnetic alloys (also called magnetically hard alloys) have sufficiently high coercive force as a resistance to demagnetizing fields with coercivities exceeding 10 kA m–1. These alloys can be used as permanent magnet materials with high magnetic induction that is retained because of a strong resistance to demagnetization, for example, as a result of high anisotropy. Hard magnetic alloys can be produced by crystallization of the glassy phase. For example, permanent magnetic materials consisting mainly of Fe3B with Nd2Fe14B phase were obtained by annealing Nd4.5Fe77B18.5 rapidly solidified alloys.183 The microstructure is composed of magnetically soft Fe3B nanoscale grains and magnetically hard Nd2Fe14B phases. High remanence (Br) of 0.8 T is obtained due to the remanence enhancement effect of exchange-coupled magnetic grains. The remanent polarization (Jr) of this material is 1.2 T and the maximum energy product (BH)max = 97 kJ/m3 while its coercivity Hc = 240 kJ/m. The influence of the heating rate on the microstructure of Fe3B/Nd2Fe14B nanocomposite magnets has also recently been studied.184,185 High coercivity values exceeding 300 kA/m were obtained in amorphous Nd5Fe72Cr5B18 crystallized into Fe3B/Nd2Fe14B state.186 Amorphous alloys of Fe-Nd-B containing 88–90 at.% Fe at 923–1023 K form a nanostructure consisting of bcc-Fe, Fe14Nd2B and the residual amorphous phase. They exhibit good hard magnetic properties, i.e. Br of 1.28 T, coercive field (iHc) of 252 kA/m and (BH)max of 146 kJ/m3 for Fe89Nd7B4.187 Ferromagnetic Nd90-xFexAl10 bulk amorphous alloys with high coercive force at room temperature were obtained by a copper mold casting method. The maximum diameter of the cylindrical amorphous samples with a length of 50 mm is about 7 mm. Neither glass transition nor supercooled liquid region was observed in these alloys in the temperature range before crystallization, which makes them different from previous bulk glassy alloys exhibiting a wide supercooled liquid region before crystallization. The bulk amorphous Nd70Fe20Al10 alloy has ferromagnetism with the Curie temperature (Tc) of about 600 K, which is much higher than the highest Tc (about 480 K) for the Nd-Fe binary amorphous alloy ribbons. The remanence (Br) and intrinsic coercive force (iHc) for the bulk Nd60Fe30Al10 alloy are 0.122 T and 277 kA/m, respectively, in the as-cast state and 0.128 T and 277 kA/m, respectively, in the annealed state for 600 s at 600 K. The Br and iHc decrease to 0.045 T and 265 kA/m, respectively, for the crystallized sample. The hard magnetic properties for the bulk amorphous alloys are presumably due to the homogeneous development of ferromagnetic clusters with large random magnetic anisotropy.188 The low coercivity of Fe3B/Nd2Fe14B magnets imposes a limit on their application. The bcc-Fe/Nd2Fe14B nanomaterials have higher coercivity than


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those for Fe3B/Nd2Fe14B magnets. Coercivity Hc of 480 kA/m and (BH)max of 160 kJ/m3 are reported for bcc-Fe/Nd2Fe14B nanomaterials. The structure consists of two phases: magnetically hard Nd2Fe14B with nanoparticles of α-iron on grain boundaries. Grain size of the Nd2Fe14B is below 30 nm and particle size of the α-iron is below 10 nm.189 The α-Fe/Nd2Fe14B nanostructured magnet of Fe89Nd7B4 composition contains residual amorphous phase and shows Br = 1.22 T, Hc = 240 kA/m and (BH)max = 130 kJ/m3. This alloy has high iron and low boron concentration.190 It has been also found that the rapidly solidified (Fe0.65Pt0.35)83B17 alloy possesses higher coercivity in the annealed state compared to binary Fe-Pt alloys.191 Remanence (Br), Mr /Ms, Hc, and (BH)max of the rapidly solidified Fe80-xPtxB20 (x = 20,22,24) ribbons in the annealed state are in the range of 0.93– 1.05 T, 0.79–0.82, 375–487 kA/m, and 118–127 kJ/m3, respectively (Br is remanence, Hc is coercivity, Ms is magnetization saturation, (BH)max is maximum energy product). Good hard magnetic properties result from the exchange magnetic coupling between the nanoscale magnetically hard γ1 tP4 FePt and magnetically soft γ cF4 Fe(Pt) solid solution as well as Fe2B phases.192 Rapidly solidified alloys of Fe-Pt-P were also found to possess good magnetic properties.193 Although these are rapidly solidified samples, they can be compacted by SPS or hot pressing. Alloys of (Fe0.75Pt0.25)75–70B25–30 were also found to possess good hard magnetic properties including high intrinsic coercivity values up to 400 kA/m in the nanocrystallized state.194 They are promising candidates for nanocomposite permanent magnets. The structure of the rapidly solidified (Fe0.75Pt0.25)75B25 alloy contains a limited volume fraction of the nanoscale cubic cF4 Fe(Pt) solid solution particles of about 4 nm in size embedded in the amorphous matrix. The nanoparticles of cF4 Fe(Pt) phase start growing at the elevated temperatures and then undergo forming of the tP4 FePt compound of about 15 nm in size which is followed by the formation of the tI12 Fe2B phase from the residual amorphous matrix.

6.7

Conclusions

Nanocrystallization on heating that is observed in various bulk metallic glassy alloys leads to the formation of the composites containing nanoscale crystalline or quasicrystalline particles. The formation of the nanocomposites leads to a better combination of mechanical properties than those of fully glassy and fully crystalline alloys. Nanoscale crystalline and quasicrystalline phases play a very important role in ductilization of bulk glassy alloys as they act as the effective barriers for shear bands propagation. This can open an area for future applications of these alloys as structural materials. Magnetic materials are another very important field of applications of nanostructured and composite metallic materials that are produced by partial crystallization of bulk glassy alloys.



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7 Severe plastic deformation and the production of nanostructured alloys by machining J.B. MANN M4 Sciences, USA, S. CHANDRASEKAR, W.D. COMPTON, K.P. TRUMBLE, Purdue University, USA, C. SALDANA and S. SWAMINATHAN, GE John F. Welch Technology Center, India and W. MOSCOSO and T.G. MURTHY, Indian Institute of Science, India Abstract: This chapter describes the production of nanostructured materials using severe plastic deformation (SPD) inherent to machining. The SPD can be controlled, in situ, to access a range of strains, strain rates and temperatures, enabling deformation-microstructure maps to be created. By tuning the SPD parameters, various nanoscale microstructures (e.g. nanocrystalline, nanotwinned, bimodal) can be engineered; and by constraining the chip formation, bulk forms (e.g. foil, sheet and rod) with nanocrystalline and ultrafinegrained microstructures are produced. Chip formation in the presence of a superimposed modulation enables the production of nanostructured particulate with controlled shapes including fiber, equiaxed and platelet types. SPD conditions also determine the deformation history of the machined surface, enabling microstructural engineering of surfaces. These diverse nanostructuring characteristics of machining are united by their common origins in the SPD phenomena prevailing in the deformation zone. Implications for large-scale manufacturing of nanostructured alloys, optimization of SPD microstructures, and consolidation–recycling of industrial machining chips are also briefly discussed. Key words: machining, severe plastic deformation, nanostructured alloys.

7.1

Introduction

The common applications of machining are in producing components with desired geometry and surface topography by the removal of unwanted material in the form of chips. Inherent to this chip formation is a condition of severe plastic deformation (SPD) that is characterized by the development of large plastic strains under controllable strain rates and temperatures. An important consequence of this SPD is the extensive change to the micro- and nanoscale structure of both the chip and machined surface.1 The SPD in machining can be controlled to access a far wider range of deformation parameters than is feasible with conventional SPD methods such as Equal-Channel Angular Pressing (ECAP) and High-Pressure Torsion (HPT), or even by more specialized techniques such as Dynamic Plastic Deformation (DPD). This enhanced control enables broader studies of the individual and interactive effects of strain, strain rate and temperature 178 © Woodhead Publishing Limited, 2011

Severe plastic deformation and production of nanostructured alloys 179 on large-strain deformation phenomena. After a brief review of the underlying mechanics, this chapter will give examples of the employ of machining-based SPD for a host of applications, including fundamental studies of microstructure refinement and bulk-form manufacture of nanostructured materials. First considered are the unique capabilities that chip formation affords to investigations of microstructure refinement, as deformation parameter control vis-à-vis tunable machining process parameters can be used to engineer novel nanoscale microstructures (e.g. nanostructured, bimodal, nano-twinned) that may otherwise be inaccessible with the usual SPD routes. Important aspects of the associated microstructures developed in these studies are highlighted, while correlating low deformation rate microstructures produced by machining with those of conventional SPD methods. As will be seen in the ensuing, this has particular relevance for the construction of deformation-microstructure maps that are likely of interest to materials researchers and structural designers alike. This is followed by consideration of the design of various machining-based SPD platforms for the creation of nanostructured materials in bulk and particulate forms and the application of such configurations to a host of alloy systems. Finally, controlled surface nanostructuring is presented as an emerging area for which the application of machining-based SPD techniques offers promise.

7.2

The mechanics of severe plastic deformation (SPD) in machining

The role of deformation in microstructure refinement is best illustrated in the seminal work of Embury and Fisher2 on deformation of pearlite and Langford and Cohen3 on iron. For example, Langford and Cohen achieved large plastic strains by repeated wire drawing and found the microstructure of deformed iron wire to be composed of grains in the sub-micrometer size range; these microstructure changes yielded a significant increase in the flow stress of the wire. The use of deformation to study microstructure refinement has received a major impetus in the last two decades as a result of the development of various Severe Plastic Deformation (SPD) methods. The most well studied among these are Equal-Channel Angular Pressing (ECAP), Accumulative Roll-Bonding (ARB) and High-Pressure Torsion (HPT), all of which are designed to impose large plastic strains by the cumulative application of deformation in multiple passes. These methods have been quite effective at producing bulk ultrafine-grained (UFG) materials, and have provided significant insights into the mechanisms of microstructure refinement. Perhaps more importantly, their emergence has established SPD as the primary route for developing UFG microstructures in bulk metals and alloys.2–5 However, they are not without limitations. Firstly, the physical configurations used to realize these methods typically limit deformation to small strain rates ( 100 mm/s, a fact established by PIV, metallography and microstructure/hardness characterization,7,12–15 and by slip line field (SLF) and finite element analyses.13–14,16 Even when the deformation zone is somewhat thicker, the largest strain increments remain highly localized in a narrow region reminiscent of the shear plane.10,13–14,16–18 Thus, in general, the approximation of the deformation zone as a shear plane is not unreasonable and is used in the present study to estimate thermo-mechanical SPD parameters of strain rate, temperature and strain. The effect of SPD by machining in imposing microstructure changes in the chip is revealed in the optical micrographs of partially formed pure copper and titanium chips, shown in Fig. 7.3 (a) and 7.3 (b) respectively. These chips were created in specially devised ‘quick-stop’ experiments wherein the machining was suddenly interrupted. While large grains are visible in the bulk, the chips reveal only flow lines indicative of large-strain deformation. Furthermore, the lack of a


Severe plastic deformation and production of nanostructured alloys 183

7.3 Quick-stop images of machining process with copper (right) and titanium (left).

visible grain structure in the polished and etched chip portions suggests that the grain size is in the sub-micrometer range. The change in the microstructure from that of the bulk to that of the chip is seen to be quite abrupt, occurring over a narrow zone – the shear plane. Figure 7.3 (a) also lists the Vickers hardness values in different regions of the partially formed copper chip sample. The hardness shows more than a two-fold increase across the shear plane, consistent with refinement of the microstructure.

7.2.1 Strain rate In contrast to the conventional SPD methods, machining provides a framework in which the effective strain rate in the deformation zone can be varied over a broad range by varying the deformation rate, V0.1,19 From PIV measurements, such as those shown in Fig. 7.2, dε/dt in the deformation zone can be directly measured and a representative value assigned to this deformation parameter for a given set of machining conditions.10 For example, dε/dt is ~20 s–1 in the machining of pure copper at V0 = 5 mm/s (Fig. 7.2 (b)). When SPD is carried out with a tool of fixed α, typically a condition of constant strain, then the PIV measurements show that dε/dt increases approximately linearly with V0 as dε/dt = KV0, for V0 < 100 mm/s. Similar inferences have been made from grid-based deformation analysis at low speeds.13–14 This range of deformation rates may be termed as low-strain rate deformation with dε/dt values typically in the range of 1 s–1 to 10 3 s–1. While the PIV measurements can be carried out at larger deformation rates of up to a few meters per second, such data are only now becoming available. Nevertheless, the linear dependence of dε/dt on V0 may be used to estimate strain rate at these higher speeds, as this relationship has been shown to be equally valid at larger deformation rates based on metallographic characterization of the deformation zone thickness and SLF analysis.8,13–15 This is based on the fact that:


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[7.4]

where ∆ is the thickness of the deformation zone, usually determined by one of the aforementioned characterization methods, and γ is estimated using Eq. (7.3). Observations have shown that, to first order, ∆ is essentially constant (~ 50 µm) over a wide range of deformation rates, particularly at the higher V0, supporting the linear dependence of dε/dt on V0. These conclusions have been further confirmed by finite element characterization of the deformation zone in machining.16 Thus, dε/dt can be estimated by taking Eq. (7.4) together with Eq. (7.3) and measurements of ∆, or by extrapolating the PIV measurements to higher V0. Based on PIV results and hardness/microstructure characterization of the deformation, ∆ is taken to be 50 µm for V0 > 100 mm/s and 100 µm otherwise. The strain rate in ECAP corresponds to that observed at the lower deformation rates in machining. This is due to the similarity in the deformation rates in ECAP (1 mm/s to 10 mm/s) and low-speed machining, and the close correspondence between their respective deformation fields, as confirmed by PIV measurements of the deformation.20 Contours of constant (iso) strain rate in γ – V0 space can be derived from Eq. (7.4). When ∆ is taken as 50 µm for V0 > 100 mm/s and 100 µm otherwise, as in the illustrative example with copper below, the constant dε/dt contours are hyperbolae in these two velocity regions.

7.2.2 Temperature Estimates of the deformation zone temperature can be made using established thermal analyses that are based on the upper-bound model, and which use measured deformation forces and deformation rates as inputs.8,21–22 Typically, these analyses assume heat generation to arise from plastic dissipation at the shear plane and generally all yield similar values for T. Indeed, these analytical temperature estimates agree well with temperatures measured directly using infra-red (IR) thermographic and thermocouple methods.21,23–25 The analysis of Boothroyd21 may be used to estimate the deformation zone temperature as a function of the machining (SPD) variables. This analysis gives:

[7.5a]

where Γ is the fraction of shear plane heat flowing into the work material, us is the specific cutting energy (energy/volume) due to shear, c is the heat capacity and ρ is the density of the work material, tw is the chip width and Fs is the shear component of the resultant force, FR, as defined in Fig. 7.1. Γ is obtained as:22



[7.5b]

where k is the thermal conductivity of the work material. Eq. (7.5) in the form above assumes that all of the plastic work at the shear plane is converted into heat. In practice, this is a good approximation since typically the fraction converted is measured to be in excess of 0.9 (90%) for a variety of metals. Direct measurements of the stored energy of cold work carried out using differential scanning calorimetry in copper chips also are in good agreement with this fraction, so Eq. (7.5) can be used in practice to estimate T. The duration that an elemental volume is exposed to this temperature is 0.1 ms to 10 ms for the conditions discussed herein.1 Since T is directly determined by the intrinsic plastic deformation-induced heating, the principal variables controlling it are V0 and α in Eq. (7.5a). While these parameters also affect the strain rate in Eq. (7.4), the specific values of dε/dt and T prevailing during the SPD can be determined as a function of V0 and α using Eqs. (7.3)–(7.5) and, hence, can be varied in a systematic way. Additional independent control of this temperature is possible through local heating or cooling of the workpiece prior to the deformation, an example of which will be seen in the cryo-SPD experiment presented.

7.2.3 Zener–Hollomon parameter The temperature and strain rate dependence of plastic deformation can be analyzed using the Zener–Hollomon parameter (Z ), which incorporates both of these variables as:

[7.6]

where T is the deformation temperature, Q is the activation energy for the operative thermally activated process and R is the gas constant. The Zener–Hollomon parameter was originally proposed to describe the combined effect of strain rate and temperature on flow stress of metals for deformation at or below room temperature.26–27 Z increases with increasing dε/dt and with decreasing T, containing within it the observed equivalence between higher strain rates and lower temperatures. Certain deformation-induced microstructure changes which are influenced by strain rate and temperature could also be interpreted in terms of this parameter. For example, the equivalence of high strain rates and low temperatures has been postulated to hold as well for dynamic recovery involving dislocation annihilation.27–28 Recently, deformation


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twinning in SPD of copper and titanium has been interpreted using the Z parameter.29,30 The selection of an appropriate activation energy in Eq. (7.6), however, requires careful consideration. When deformation conditions and microstructure vary significantly across a narrow deformation zone, as in SPD, it is difficult to justify a specific value for Q that is unambiguously characteristic of the deformation. In such conditions, the use of smaller Q values characteristic of the deformation has been suggested.27 In the ensuing analysis, Q for grain boundary diffusion has been used.

7.2.4 Texture When chip formation occurs by shear in a deformation zone of small width, the direction of maximum elongation in a sheared element of the chip is oriented at an angle ψ with respect to the shear plane, as shown in Fig. 7.1. This causes a circle or square element in the initial bulk material to be deformed into an ellipse or parallelogram, respectively, in the chip (Fig. 1.2 (b) ). The ‘texture’ angle (ψ) may be used to describe the ‘macroscopic texture’ in the chip created by the SPD and can be estimated as:31,32

[7.7]

The texture angle can be varied within limits by appropriate selection of the machining variables α and λ, highlighting another aspect of SPD by machining. Direct measurement of ψ is possible from PIV characterization of the strain tensor, as the direction of the largest principal strain is the direction of maximum elongation. For the SPD condition corresponding to Fig. 7.2, the PIV analysis gives an angle of 50.7° for ϕ + ψ; this is the angle between one of the principal directions and the direction of V0. The corresponding value for ϕ + ψ estimated using Eqs. (7.1–7.3) and (7.7) is 44.3° (ϕ = 23.9° and ψ = 20.4°), which is reasonably close. By combining such estimates with microstructure analysis, correlations can be established between the deformation path and evolution of texture.

7.2.5 Constrained chip formation – Large Strain Extrusion Machining Precise control of the deformation parameters (dε/dt, T and γ ) in conventional machining is limited in that the input variable λ in Eq. (7.3) is only partially controllable. In this regard, a constrained variant of the chip formation process – Large Strain Extrusion Machining (LSEM) – offers capability beyond conventional machining as a controlled method of SPD.33,34 Figure 7.4 (a) shows a configuration of LSEM in which the thickness of the chip after deformation is controlled a priori by a constraining tool edge. An analogous rotary configuration



7.4 Mechanics of large strain extrusion machining (LSEM): (a) schematic showing geometry of constrained chip formation in a linear press configuration; (b) constrained chip formation in a turning configuration; and (c) variation of shear strain and normalized hydrostatic pressure (p/2k) in the deformation zone with chip thickness ratio (λ). k is the shear yield strength of the material.

is shown in Fig. 7.4 (b). The position of the constraining edge can be set such that the chip thickness at the die exit (tc) can be greater or less than that the thickness of the material entering the deformation zone (t0). This affords LSEM full control of strain through the chip thickness ratio, λ, unlike in conventional machining where λ cannot be fixed a priori. Furthermore, Eqs. (7.3)–(7.5), which relate the deformation parameters to the controllable variables in machining, apply equally as well to SPD by LSEM. These relationships can also be used to estimate the deformation parameters in a single pass of ECAP, with V0 as the pressing speed, tc = t0, and α set equal to the die inclination angle minus 90°. Figure 7.4 (c) shows that the strain in LSEM is independently controlled by λ and α. Indeed, a 2-parameter dependence of strain enables a final deformation state to be realized by multiple deformation paths, each of which should results in a unique flow field and texture. This provides for flexibility in control of strain, microstructure and texture. Furthermore, the microstructure of samples created using LSEM has shown a one-to-one correlation with the microstructures


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produced by conventional machining under equivalent SPD conditions. Fig. 7.4 (c) also shows that extraordinarily high levels of strain can be imposed in a single pass by LSEM at small λ. The hydrostatic pressure (p/2k) in the deformation zone is also quite large under such conditions, decreasing with increasing λ, based on a slip line field analysis. The combination of large strain and hydrostatic pressure at small λ makes this process condition somewhat akin to that in HPT, and especially valuable for deformation of alloys of limited workability (e.g. Ti, Mg, cast materials).

7.2.6 Comparison of the deformation field in SPD by machining versus other methods The deformation field in machining is a steady-state field that involves the flow of material and heat through the deformation zone. In comparison, the deformation conditions in ECAP represent a relatively narrow band about V0 ~ 1 mm/s in γ – V0 space (see also Fig. 7.5 and the associated discussion). Particle Image Velocimetry (PIV) measurements of the ECAP deformation zone show that it is quite similar to that observed in machining at small deformation rates (Fig. 7.2). The use of larger deformation rates in ECAP is non-trivial given the layout of typical ECAP configurations and inertial effects, which limit the exploration of

7.5 Deformation conditions accessed in the SPD of pure copper. Contours of constant strain rate (d/dt) are shown overlaid on the graph. The ‘coordinates’ (a, b) of the points represent the strain rate, d/dt, and the deformation zone temperature, T, respectively.


Severe plastic deformation and production of nanostructured alloys 189 the combined effects of strain rate and temperature. However, ECAP can be used to explore strains in excess of machining, albeit using multiple passes of deformation at small deformation rates.35 The deformation rate in HPT can be varied within some range, though much less widely than in machining, by varying the platen rotation speed.35 Furthermore, the strains that can be realized by HPT are much larger than even those of ECAP. However, the deformation field is not steady state, depending on the twist of the sample. The deformation field also is inhomogeneous and is characterized by gradations in strain rate and strain across the sample. Regarding DPD, moderate strain rates of ~103 s–1 can be imposed at smaller strains (~3) by using multiple deformation passes.29 The DPD deformation field also is not steady state, and inertial effects likely hinder imposition of large strains and strain rates.

7.2.7 Machining as an experimental platform As outlined in Sections 7.2.1–7.2.4, the thermo-mechanical deformation parameters of strain, strain rate and temperature in the deformation zone can be systematically varied by appropriate selection of α, λ and V0. This controllability can be leveraged to study material property changes arising in SPD. While this notion has been recognized for some time in the context of using machining as a property test for estimating constitutive mechanical properties,8,36 it also is the subject of recent interest.37,38 What has not been considered thus far are the applications of machining to study microstructure development. Their use to manufacture bulk material forms has only been considered recently.6,7 These applications are reviewed below.

7.3

A study of microstructure refinement

The versatility of machining to study microstructure development over a wide range of deformation parameter space is illustrated by the results of SPD experiments carried out with copper of high purity (99.999%, Alfa Aesar) as a model material system (Fig. 7.5 and Fig. 7.6). The physical properties of the copper were an initial grain size of 0.9 mm, Vickers hardness of 73 ± 3 kg/mm,2 specific heat c = 385 J/kg·K, density ρ = 8900 kg/m3 and thermal conductivity k = 400 W/m·K. A range of deformation conditions – shear strains of 1 to 15, strain rates of 10 s–1 to 105 s–1 and deformation temperatures up to 250°C (0.4 TM) – were imposed in the copper by appropriate selection of the machining input variables, a from –30° to 50° and V0 from 10 mm/s to 5 m/s; Eqs. (7.3)–(7.5) were used to correlate these variables with the SPD conditions.1,19 Microstructure refinement at temperatures well below room temperature (cryo-SPD) was explored by immersing the deformation setup in liquid nitrogen at –196°C.1,19 Chip samples were typically 50 mm in length, 4 mm in width and 0.5 to 2.5 mm in thickness. The microstructure of the samples was characterized by transmission


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7.6 Transmission electron microscopy images of the microstructure of copper at select experimental conditions of strain and deformation rate. The points A, C, etc. correspond to the identically labeled points in Fig. 7.5, so as to facilitate mapping of the experimental deformation conditions on to the microstructures.

electron microscopy (TEM), orientation imaging microscopy (OIM) and optical microscopy, and hardness by Vickers indentation.1,19,39 Figure 7.5 shows the range of SPD conditions, including temperature and strain rate, mapped in γ – V0 space for copper. The shear strain ranges from about 1 to 15 over the different sets of SPD conditions that are represented in the experimental data. The strain rate (dε/dt) and deformation zone temperature are listed as coordinates (dε/dt, T ) beside each of the experimental points in Fig. 7.5, with higher values of V0 corresponding to larger values of dε/dt and T. Contours of constant strain rate are also shown in the figure (see discussion in Section 7.2.1 regarding estimation of dε/dt). The dε/dt values range from about 10 to 3 × 105 s–1 and T values range between 30°C and 250°C for V0 between 10 mm/s to 5 m/s. The corresponding ln Z values are in the range of 20 to 100.1 The extreme left hand side of Fig. 7.5 represents the deformation conditions typically accessible in ECAP.1,5,19,40 The microstructure and hardness were analyzed as a function of the deformation rate and strain, and also in terms of strain rate and temperature. Figure 7.6 shows TEM micrographs of the microstructure of the copper after the SPD at select


Severe plastic deformation and production of nanostructured alloys 191 conditions of V0 and γ. These conditions were selected to highlight key aspects of the microstructure at different combinations of SPD parameters; the points corresponding to these micrographs are labeled with the same corresponding letters as in Fig. 7.5 to facilitate direct comparison with the associated deformation parameters. The general range of hardness values in the different SPD regions are shown in the γ – V0 plane in Fig. 7.7; specific values at select deformation conditions are reported and discussed in detail elsewhere.1 The coefficient of variation (CV) on the hardness, which is the ratio of the standard deviation to the mean, is also provided in Fig. 7.7.

7.3.1 Microstructure evolution at small deformation rates A broad range of UFG microstructures can be seen in the images in Fig. 7.6. At γ ~ 2.1 and V0 = 13 mm/s, the lowest strain and smallest deformation rate used, the microstructure consists of cellular structures and elongated subgrains having broad, diffuse boundaries consisting of forest dislocations (point A in Fig. 7.6). Geometrically necessary boundaries (GNBs)41 are also seen to be forming, these indicated by arrows in the micrographs. At this SPD condition, the SAD pattern resembles more of a single-crystal type pattern that is indicative of substructures with very small misorientations. The hardness of this microstructure

7.7 Deformation-microstructure map for copper showing schematically, microstructures characteristic of the different SPD conditions. The dotted curves demarcate, roughly, regions with different microstructures. Average and variance of hardness for these microstructures are also provided.


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(~142 kg/mm2) is substantially greater than that of the bulk material. This suggests rapid initial hardening at low strains (Fig. 7.7). Indeed, this steep initial increase in strength for copper has been noted in ECAP,42 uniaxial compression43 and machining.44 At a higher γ of ~5, the microstructure is composed of elongated subgrains with sharper boundaries (point C, Fig. 7.6) and the distance between the GNBs decreases from ~190 nm to ~170 nm. The SAD pattern also indicates an increase in misorientation between the dislocation substructures. Higher strains at V0 = 13 mm/s give grain and subgrain structures with equiaxed morphology and larger misorientations (points D and E, Fig. 7.6), the development of which likely involves continuous dynamic recrystallization45 at the relatively small deformation temperatures (T ~ 40°C) characteristic of this set of SPD conditions. Furthermore, the equiaxed structures at γ ~ 12 (point E) are somewhat larger (345 nm) than those at γ ~ 8 (270 nm, point D), This likely due to growth associated with increases in strain energy and somewhat higher deformation temperatures.1 This microstructure evolution with increasing strain at small deformation rates, including a switchover from elongated substructures to the highly misoriented equiaxed grain structures, is consistent with what has been demonstrated in SPD of OFHC copper (99.95%) by machining.44 It is also consistent with multi-pass SPD of copper by ECAP.40,42 For these conditions, the hardness saturates at 150– 160 kg/mm2 with small variations (CV ~5%), see also Fig. 7.7.1

7.3.2 Deformation twinning Next we consider the microstructures developed at low strains when the strain rate is varied from about 102 s–1 to 105 s–1 by examining a portion of the γ – V0 space along a horizontal line through γ ~ 1.5 in Fig. 7.6. At the higher strain rates, deformation twinning is prevalent, characterized by a dense array of nanoscale twins of width ~20 nm. The twinning was observed at both V0 = 1.67 m/s and 4.4 m/s (points L and S in Fig. 7.6), corresponding to dε/dt of about 2 × 104 s–1 and 7 × 104 s–1, respectively. The overall microstructure at V0 = 1.67 m/s is heterogeneous, with some regions consisting of a high density of nanoscale twins and other regions exhibiting low-misorientation dislocation substructures interspersed with twins (point L in Fig. 7.5 and 7.6). A similar dense array of nanoscale twins was observed at V0 = 4.4 m/s. The twin density in this microstructure is somewhat lower, possibly due to a higher deformation zone temperature that promoted dislocation slip at the expense of twin formation (T ~ 160°C, Fig. 7.5). The hardness of the twinned microstructures corresponding to points L and S is in the range of 120–140 kg/mm2 (Fig. 7.7). While this is lower than the peak hardness levels recorded in copper, it is not significantly different from that of the subgrain microstructures produced at the same strain levels under the small deformation rate condition. Similar nanoscale twinning was observed in cryogenic SPD of copper, with the degree of twinning increasing with increasing strain rate. Figure 7.8 shows a cryoSPD microstructure at dε/dt ~ 103 s–1 and γ ~ 1.6 that is more homogeneous than



7.8 Transmission electron microscopy images of the copper microstructure after cryo-SPD at γ ~ 1.6 and strain rate of ~103 s–1 showing dense nano-twinning.

that corresponding to points L and S in Fig. 7.6, with most of the grains showing significant nanoscale twinning and average twin widths of ~20 nm. The hardness of this highly twinned microstructure is 175–200 kg/mm,2 substantially greater than that of the twinned structures of Fig. 7.6. Nano-twinned microstructures are of considerable interest since they exhibit Hall–Petch strengthening analogous to conventional nanostructured materials while also maintaining appreciable ductility.46 Furthermore, they have been found to exhibit unusual thermal stability characteristics.47

7.3.3 Discontinuous dynamic recrystallization and bimodal microstructures The unique combination of deformation parameters realized in SPD by machining enabled characterization of the onset and evolution of discontinuous dynamic recrystallization in copper. This can be seen in the microstructure evolution as a function of γ at V0 = 1.67 m/s (points L, M, N and O in Fig. 7.6). In this strain rate range of 104 s–1 to 105 s–1, the twinned microstructure gives way to an elongated subgrain structure with small misorientations (point M) at γ ~ 5, followed by the onset of a discontinuous type of recrystallization at γ ~ 7 (T ~ 200°C) at point N. The deformation-induced heating is important, in conjunction with the strain, for facilitating this type of recrystallization.45 Indeed, further increase in strain and


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deformation temperature results in large micron-sized grains, as at point O (Fig. 7.6). Figure 7.7 shows that the onset and progression of dynamic recrystallization is also accompanied by a dramatic loss in strength, with hardness values decreasing from about 140 kg/mm2 to 75 kg/mm2 at strains of 7 and higher. The deformation zone temperature corresponding to the onset of recrystallization is in the range of 200–250°C (Fig. 7.5), with the lower temperatures associated with larger strains. Dynamic recrystallization accompanying a similar evolution of microstructure with strain was also observed at larger deformation rates, as in point Q in Fig. 7.6, at V0 = 2.5 m/s. An intriguing feature of this evolution is the occurrence of a bimodal (composite) type of microstructure, composed of ultrafine subgrains and micron-sized grains at γ ~ 4. This microstructure has a hardness of 127 kg/mm2 with a large variation (CV ~ 25%) compared to that of the other microstructures (Fig. 7.7). This large CV is consistent with a partially recrystallized microstructure consisting of ‘hard’ and ‘soft’ regions. This was also evident in two distinct distributions of hardness with 70% of the points centered at 145 kg/mm2 and the remainder distributed about 85 kg/mm.2 Similar large hardness variations were observed at other similar deformation conditions. Bimodal microstructures, composed of a mixture of ultrafine and micron-sized grains, are of interest as they have been observed to possess potentially attractive combinations of ductility and strength.48 The most interesting aspect of the current processing, however, is that this microstructure was engineered, in situ, during the SPD by using the intrinsic deformation-induced heating. The creation of bimodal UFG microstructures, to date, has generally involved complex, multi-stage thermo-mechanical deformation processing routes.48,49

7.3.4 Fully recrystallized microstructures When the deformation conditions of temperature and strain exceed threshold levels, recrystallization of the copper is expected to occur in situ. These thresholds for complete dynamic recrystallization can be identified from Fig. 7.6 and 7.7. The microstructure in this region is seen to be composed of a mixture of large and small grains, several micrometers in size (Fig. 7.9). As in the partially recrystallized microstructure of point Q, annealing twins are seen in fully recrystallized microstructures corresponding to points N and O (Fig. 7.6). The hardness values of these microstructures are ~75 kg/mm,2 similar to those of the copper in an annealed condition. For a given strain rate, the threshold strain for recrystallization decreases with increasing deformation temperature (Fig. 7.6 and 7.7), typical of classical deformation-induced recrystallization.27

7.3.5 Homogeneity of microstructure Figure 7.10 shows OIM data for copper chips created at near-ambient deformation conditions39 for three different strains (γ ~ 3, 7 and 11). The inverse pole



7.9 Optical micrograph corresponding to point R(V0 = 2.5 m/s, = 6.7) showing some large recrystallized grains (>50 µm) interspersed with smaller micrometer-sized grains.

7.10 Orientation imaging microscopy (OIM) analysis, including inverse pole figure (IPF) map, pole figure and misorientation distribution, for copper subjected to shear strain of (a) 3, (b) 7 and (c) 11 (based on Swaninathan et al.39).


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figure (IPF) map for a strain of 3 shows elongated grains containing dislocation structures within as evident from the color changes within the grain (Fig. 7.10 (a)). The high-angle boundaries (>15°) are marked by black lines in the IPF map. The pole figure shows the presence of rotated (from the initial material) cube texture components, as well as two variants of the B-fiber shear texture component. At still larger strains, γ ~ 7, the IPF map shows presence of ultrafine elongated structures (Fig. 7.10 (b)). The pole figures at this strain show continuous distributions along A and B shear texture fibers and absence of any cube texture components.39 The IPF map at a strain level of 11, however, shows only equiaxed ultrafine grains along with a well-developed shear texture containing B-fiber and the C component. The misorientation distributions show an increase in the population of high-angle boundaries as the strain level increases. An OIM study of the deformation along three mutually orthogonal flow directions in the chip showed uniformity of microstructure throughout the chip volume.39 The development of such a homogeneous microstructure is consistent with a relatively uniform deformation field at the micro-scale, as confirmed by PIV 1,19,50 and evident in Fig. 7.2. Inverse pole figure maps determined for each of the chip faces using OIM (Fig. 7.10) show characteristic shear deformation components with nearly homogeneous texture in the volume of the chip. These observations of uniformity, both in microstructure and texture, throughout the chip volume are particularly encouraging for production of bulk nanostructured alloys.

7.3.6 Deformation-microstructure map The interactive effects of strain, strain rate and temperature on microstructure development could be extensively explored by using machining to probe the envelope of deformation conditions in Fig. 7.5, a range of conditions substantially more diverse than is achievable in ECAP, HPT or DPD. This has been done to develop a deformation-microstructure map for copper.19 Figure 7.7 shows such a map that identifies the microstructures observed in different portions of deformation parameter space. Among other uses, this type of map can guide selection and/or optimization of SPD conditions to realize specific nanoscale microstructures (e.g. nano-twinned, equiaxed, bimodal and combinations thereof). Machining also can be used to develop similar maps for other metals and alloys, even alloys of higher strength that are difficult to deform to large plastic strains over a range of deformation rates by conventional multi-pass SPD methods.

7.4

Bulk forms with ultrafine-grained (UFG) microstructure

Chip formation by machining, as demonstrated in the above results for Cu, offers a means for producing nanostructured materials with controllable microstructures. While chips of macroscopic dimensions can be created by the unconstrained chip


Severe plastic deformation and production of nanostructured alloys 197 formation in machining, shape and size control of the chips would be advantageous and could complement the microstructure control earlier demonstrated. It is in this regard that the constrained chip formation process – LSEM (see Section 7.2.5) – offers capability for applying controlled SPD in the production of geometrically defined bulk forms, including sheet, foil and wire.34 LSEM has been implemented in a rotary configuration for production of continuous foil34 and in a linear configuration for production of sheet.1 The linear configuration enables manufacture of larger-sized samples due to the increased load capacity of the press equipment used in this configuration. Additionally, a non-plane–strain rotary configuration has been used to produce nanostructured samples in wire and rod forms. Figure 7.11 shows examples of sheet, rod and foil created by LSEM in a diverse set of material systems, including pure metals (Ta, Ti and Cu) and alloys (e.g. Al 6061-T6) with a range of properties in terms of workability and strength. The microstructure of several of these metal and alloy samples are shown in Fig. 7.12 and 7.13, with the Inconel 718, Ti and Al 6061-T6 composed of sub-100 nm grains at higher strains. All of these samples have substantially higher hardness than the corresponding microcrystalline bulk material,51,52 a consequence of the nanoscale microstructure. Figure 7.14 shows the hardness values for the initial microcrystalline bulk alloy and the nanostructured chips. The microstructure in each case is determined by the interactive effects of strain, strain rate and temperature, as illustrated in the SPD results for copper earlier. In the steels, the refinement is reflected in the reduction of interlamellar spacing of

7.11 Bulk forms produced by LSEM using a linear press configuration (left) and a rotary lathe configuration (right).


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7.12 Bright-field TEM micrographs of chips cut from (a) commercially pure Ti, γ ~ 3, grain size: 80 nm, (b) 52100 steel with equi-axed nanoscale ferrite grains [330 nm] and dispersed carbide particles, (c) Al 6061-T6, γ ~ 3, grain size: 200 nm and (d) Inconel 718, γ ~ 8, grain size: 120 nm.

7.13 (a) An optical micrograph of bulk 1080 steel showing a coarse pearlite microstructure; (b) microstructure of 1080 steel chip with occurrence of two distinct pearlitic ensembles – refined pearlite and broken pearlite, as a result of the SPD by machining (based on Shankar et al.53).


HV, kg/mm2


7.14 Bar chart showing increases in hardness for a variety of material systems after deformation by machining.

pearlite, including break-up of the cementite at large strains (Fig. 7.13).53 Through single-pass machining-SPD of eutectoid (1080) steel, it has been possible to reproduce the microstructure evolution as a function of strain (up to shear strain of ~6.5) achieved through incremental SPD, as in the pioneering drawing experiments of Embury and Fisher to shear strains of ~7.2 The machining route has also demonstrated the creation of precipitation-treatable alloys (Ni-based alloys, Al 6061) with enhanced strength, thermal stability and ageing kinetics. This was achieved by combining SPD of these alloys in the solution-treated and homogenized condition, followed by suitable thermal treatments.17,54 These early results demonstrate the capability to produce bulk forms with nanoscale microstructure in material systems of commercial interest using LSEM. Furthermore, the transformation of an ‘undeformed chip’ of rectangular crosssection into a rod of circular cross-section, as is the case in the rod and wire, indeed shows that large shape transformations can be achieved by LSEM, a likely consequence of the unique (controllable) thermo-mechanical conditions prevailing in the deformation zone. Optimization of microstructure for specific performance characteristics (e.g. strength, ductility, thermal stability) once completed, will provide the basis for setting the LSEM parameters needed to attain specific nanoscale microstructures in these bulk forms. These nanocrystalline bulk forms can be used as precursor materials for structural components with enhanced strength and wear resistance. Micro- or macro-manufacturing processes such as EDM, laser machining, punching and stamping, micro-turning and micro-milling55 can be used to ‘cut out’ components from the bulk forms for these components. Figure 7.15 shows a set of small gears for a micro-power system produced from one of the nanostructured Inconel 718 foils using micro-EDM.51 This approach to making micro-scale components from


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7.15 A pair of micro-scale gears created from nanostructured Inconel 718 foil using micro-EDM (Agie AC Vertex 2F). The foil was produced by LSEM with λ = 3.5, γ ~ 4, V0 = 0.5 m/s (based on Saldana et al.51).

nanostructured alloys is quite versatile as it can be applied to manufacture microelectromechanical system (MEMS) components from functional materials, including those suited to withstand severe operating environments.

7.5

Nanostructured particulate

The chip formation process may be scaled down to produce particulate of controlled geometry with ultrafine-grained (UFG) microstructures. Potential applications for such materials include reinforcements in structural composites and precursors for powder metallurgy components. These metal particulates are currently produced by a range of processes that imparts characteristic morphology and microstructure to the particles.56 These processes generally yield broad size distributions that require classification. Furthermore, particle morphology and microstructure are highly process-dependent. For example, the evolution of particle size, shape and microstructure in high-energy milling is a consequence of several factors including, milling media, initial charge characteristics, environmental conditions and milling time.57 The milling process is also limited by the contamination associated with the high surface area exposed during repetitive comminution steps and limited control of the particle/agglomerate size. Particulate metals also can be produced through a variant of the machining process – modulation-assisted machining (MAM) – that superimposes a lowfrequency modulation ( 5) and decay with depth into the sub-surface.1 Similar inferences pertaining to the strain field have come from metallography, grid deformation13 and electron microscopy.67 As such, a fine-scale microstructure may be expected on the machined surface. Indeed, UFG microstructures have been observed on surfaces created by a number of different material removal processes.15 For example, copper surfaces created by abrasive machining have been shown to be comprised of equiaxed grains, ~30 nm, with an orientation texture similar to that of rolling.68 A microstructure consisting of ~100 nm grains has also been observed on hard steel surfaces generated under select machining conditions.69–72 These UFG microstructures are analogous to those found in sliding,73 rolling,74 mechanical attrition,75 and HPT. While the occurrence of such features on machined surfaces has long been recognized, what has not been explored is the possibility of systematically engineering specific microstructures in the surface. For machining, this concept is based on the close correspondence between the deformation histories of the material evolving into the machined surface and that of the chip.66,76 To demonstrate nanostructuring of surfaces by controlled machining SPD, oxygen-free high conductivity (OFHC) copper (99.95%, Goodfellow) and brass (70% Cu–30% Zn) samples were machined at near-ambient temperature and at –196°C under plane-strain conditions using a sharp, high-speed steel tool.1,66 The samples were sheets, 3 mm in width, with initial grain sizes of 35 µm (Cu) and 200 µm (brass), and Vickers hardness of 77 ± 3 kg/mm2 (Cu) and 80 ± 5 kg/mm2 (brass). An undeformed chip thickness of 100 µm to 200 µm and machining speeds of up to 500 mm/s were used. The strain imposed in the deformation zone was varied by using tool rake angles of –30° to +50°. Figure 7.20 shows PIV measurements of strain with depth from the machined surface for brass and copper. The strain values at the surface were estimated as ~5 (+20° rake) in the Cu and ~3 (+10° rake) and ~10 (–30° rake) in the brass. The strains in the corresponding chips were determined by PIV and are shown by points A, B and C.1,47,66 The close correspondence between the chip and surface strains is not surprising, given that the material constituting the bulk of the chip and the machined surface experience similar deformation history. Similar arguments may be made using analysis of particle trajectories in grid deformation experiments.13,67 Further evidence for the similarity between the deformation levels on the machined surface and chip comes from the hardness data for copper presented.66 The hardness of the machined surface is substantially greater than that of the bulk material prior to machining (dotted line in the figure). Furthermore, the hardness values at the surface and of the corresponding chip are essentially the same for different machining conditions. This equivalence is especially striking at


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7.20 Variation of strain with depth from the machined surface in copper and brass. The dotted curves are extrapolations used to estimate the strains at the surface. The strain values in the chip are marked as A (brass, +10° rake), B (copper, +20° rake) and C (brass, –30° rake). Inset shows TEM pictures of a microstructure on the machined surface and of a chip created under a similar deformation condition (γ ~ 8). Both of these microstructures are seen to be very similar, highlighting the equivalence between chip and surface microstructures for the same process conditions.

some of the more special deformation conditions, such as in the cryo-SPD and machining with a +50° rake angle tool. The cryo-SPD condition shows very high hardness values (~180 kg/mm2) for both the chip and machined surface, undoubtedly a consequence of the enhanced refinement occurring in both of these regions at this condition. When machining with the +50° rake angle tool at nearambient temperature, the deformation strain is much smaller (γ ~ 1) than with the –10° rake tool (γ ~ 8), resulting in smaller levels of microstructure refinement on the machined surface and in the chip.1 The inset TEM images in Fig. 7.20 also show a high degree of similarity between the chip and near-surface microstructures, in this case equiaxed UFG microstructures with grain size of ~200 nm, reflective of essentially identical deformation histories. Electron Backscatter Diffraction (EBSD) of the material on the work surface and deformation zone also supports this microstructure equivalence.18,66


Severe plastic deformation and production of nanostructured alloys 207 The basis for controlling microstructure and mechanical properties of surfaces created by machining is provided by the close correspondence between the strains on the machined surface and chip. The SPD parameters can be reasonably estimated using the shear plane model described in Section 7.2, enabling correlation with the controllable machining variables of cutting speed, rake angle and chip thickness ratio. Taken together with a deformation-microstructure map, such as that outlined for copper in Fig. 7.7, the controllable machining variables may be tuned to set appropriate SPD conditions for generating specific surface microstructures.

7.7

Conclusions

The deformation that occurs during chip formation can be controlled, in situ, to access a wide range of strains, strain rates and temperatures. This is used in the present study to demonstrate the creation of a variety of nanoscale microstructures in the chip including equiaxed, bimodal and nano-twinned structures. A map is outlined for SPD of copper that describes the interactive effects of strain, strain rate and temperature on microstructure. This type of map is may be used to optimize process parameters to engineer materials with interesting combinations of microstructure, texture and mechanical properties. By adding dimensional control to the chip formation process through LSEM, bulk forms such as foil, sheet and rod are produced with controllable nanocrystalline and UFG microstructures. A newly developed chip formation process, modulation-assisted machining (MAM), enables the production of nanostructured particulate with controlled particle shapes (e.g. fiber, equiaxed and platelet). Large-scale manufacturing of nanomaterials by LSEM and MAM in structural alloy systems of interest is currently being explored. Lastly, the SPD conditions prevailing in the deformation zone are shown to determine the deformation history of the machined surface and, consequently, also the microstructure. This suggests that machining can also be used to engineer surfaces with specific micro- and nanoscale structures. The uses of machining for materials manufacturing represent deformation processing applications of this class of processes. While these applications are diverse, they are united by their foundation in the SPD phenomena that prevails in the deformation zone during chip formation. Furthermore, these newer applications likely are subject to processing constraints similar to those of component manufacture, including those related to tool wear, workability of materials and equipment capability.

7.8

Acknowledgements

This work was supported in part by NSF grants CMMI-0626047 and CMMI0800481; the Oak Ridge National Laboratory; the U.S. Department of Energy’s


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FreedomCAR Program via Pacific Northwest National Laboratories contract DE-AC06–76RL01830; and a Ford University Research Program award all to Purdue University; NSF grants STTR-0944980 and SBIR-0822879 to M4 Sciences LLC; and an NSF Graduate Research Fellowship to CS. Microscopy work at the Oak Ridge National Laboratory’s High Temperature Materials Laboratory was sponsored by the US Department of Energy, Office of Energy Efficiency and Renewable Energy, Vehicle Technologies Program. We are grateful to Dr Larry Allard of Oak Ridge for assistance with some of the transmission electron microscopy. Drs S. Lee, B.C. Rao (IIT Madras, India), and M. Ravi Shankar (University of Pittsburgh, Pittsburgh, USA); and T.L. Brown and Y. Guo (Purdue University) are acknowledged for their contributions to some of the results reported herein. We also appreciate the support of Professor Terry R. McNelley, Naval Postgraduate School, Monterrey, CA, with the OIM analysis.

7.9

References

1 Brown T.L., Saldana C., Murthy T.G., Mann J.B., Compton W.D., Trumble K.P., King A.H., and Chandrasekar S. Acta Mater, 2009; 57:5491. 2 Embury J.D., Fisher R.M. Acta Metall 1966; 14:147. 3 Langford G., Cohen M. Trans ASME 1969; 62:623. 4 Segal V.M., Reznikov V.I., Drobyshevskiy A.E., Kopylov V. Rus Metall 1981; 1:99. 5 Valiev R.Z., Islamgaliev R.K., Alexandrov I.V. Prog Mater Sci 2000; 45:103. 6 Brown T.L., Swaminathan S., Chandrasekar S., Compton W.D., Trumble K.P., King A.H. J Mater Res 2002; 17:2484. 7 Swaminathan S., Shankar M.R., Lee S., Hwang J., King A.H., Kezar R., Rao B.C., Brown T.L., Chandrasekar S., Compton W.D., Trumble K.P. Mat Sci Eng A 2005; 410:358. 8 Shaw M.C. Metal cutting principles. Oxford University Press, New York, 1984. 9 Gnanamanickam E.P., Lee S., Sullivan J.P., Chandrasekar S. Proceedings of the Society for Experimental Mechanics Annual Conference and Exposition on Experimental and Applied Mechanics 2007; 1080. 10 Lee S., Hwang J., Shankar M.R., Chandrasekar S., Compton W.D. Metall Mater Trans A 2006; 37:1633. 11 Thomsen E.G. Yang C.T., Kobayashi S. Mechanics of plastic deformation in metal processing. Macmillan, 1965. 12 Keciouglu D. Trans ASME 1958; 80:158. 13 Oxley P.L.B. Mechanics of machining. Ellis Horwood, New York, 1989. 14 Oxley P.L.B., Hastings W.F. Proc R Soc Lond A 1977; 356:395. 15 Samuels L.E. Metallographic polishing by mechanical methods (4th ed). American Society for Materials International, 2003. 16 Sevier M., Yang H.T.Y., Lee S., Chandrasekar S. Metall Mater Trans B 2007; 38:927. 17 Shankar M.R., Chandrasekar S., King A.H., Compton W.D. Acta Mater 2005; 53:4781. 18 M’Saoubi R. and Ryde L. Mat Sci Eng A 2005; 405:339. 19 Saldana C., Swaminathan S., Brown T.L., Mann J.B., Compton W.D. and Chandrasekar S. ASME J Mfg Sci Eng 2010; 132:030908. 20 Lee S. Ph.D thesis, Purdue University, 2006. See also Chandrasekar S. and Trumble K.P., In situ characterization of large strain deformation field in severe plastic


Severe plastic deformation and production of nanostructured alloys 209 deformation, presentation at Ultrafine Grained Materials (UFG) 2006, Kloster Irsee, Germany, September 24–26, 2006. 21 Boothroyd G. Proc I Mech E 1963; 177:789. 22 Weiner J.H. Trans ASME 1955; 77:1331. 23 Hwang J., Kompella S., Chandrasekar S., Farris T.N. ASME J Trib 2003; 125:377. 24 Narayanan V., Krishnamurthy K., Hwang J., Chandrasekar S., T.N. Farris, Madhavan V. Measurement of Temperature Field at the Tool–Chip Interface in Machining, NSF Workshop on Research Needs in Thermal Aspects of Material Removal Advanced Technology Research Center, Oklahoma State University, June 10–12, 2003. 25 Davies M.A., Ueda T., M’Saoubi R., Mullany B., Cooke A.L. CIRP Ann 2007; 56:581. 26 Zener C., Hollomon J.H. J Appl Phys 1944; 15:22. 27 Backofen W.A. Deformation processing. Addison-Wesley, 1972. 28 Christian J.W., Mahajan S. Prog Mater Sci 1995; 39:1. 29 Li Y.S., Zhang Y., Tao N.R., Lu K. Acta Mater 2009; 57:761. 30 Saldana C., Shankar M.R., Murthy T.G., Huang C., Gnanamanickam E., Chandrasekar S. Proceedings of the 11th CIRP conference on Modeling of Machining Operations, NIST, 2008. 31 Dautzenberg J.H., Zaat J.H. Wear 1973; 23:9. 32 Townend G.H. J Appl Phys 1947; 18:784. 33 De Chiffre L. Int J Mac Tool Des Res 1976; 16:137. 34 Moscoso W., Shankar M.R., Mann J.B., Compton W.D., Chandrasekar S. J Mater Res 2007; 22:201. 35 Valiev R.Z. and Langdon T.G. Prog Mater Sci 2006; 51:881. 36 Drucker D.C. J Appl Phys 1949; 20:1013. 37 Maekawa, K., Obikawa, T., Yamane, Y., Childs, T.H.C., 2000, Metal Machining: Theory and Applications. Butterworth-Heinemann, UK. 38 Adibi-Sedeh A.H., Madhavan V. and Bahr B.J. ASME J Mfg Sci Eng 2003; 125:656. 39 Swaminathan S., Brown T.L., Chandrasekar S., McNelley T.R. and Compton W.D. Scrip Mater 2007; 56:1047. 40 Mishra A., Kad B.K., Gregoric F., Meyer M.A. Acta Mater 2007; 55:13. 41 Hughes D.A., Hansen N., Bamman D.J. Scrip Mater 2003; 48:147. 42 Torre F.D., Lapovok R., Sandlin J., Thomson P.F., Davies C.H.J., Pereloma E.V. Acta Mater 2004; 52:4819. 43 Steeds J.W. Proc R Soc Lond A 1966; 292:343. 44 Swaminathan S., Shankar M.R., Rao B.C., Compton W.D., Chandrasekar S., King A.H., Trumble K.P. J Mater Sci 2007; 42:1529. 45 Humphreys F.J., Hatherly M. Recrystallization and related annealing phenomena (2nd ed). Elsevier, Oxford, 2004. 46 Lu L., Shen Y.F., Chen X.H., Qian L.H. and Lu K. Science 2004; 304:422. 47 Saldana C., Murthy T.G., Shankar M.R., Stach E.A., Chandrasekar S. Appl Phys Lett 2009; 94:021910. 48 Wang Y.M., Ma E. Acta Mater 2004; 52:1699. 49 Wang Y.M., Chen M., Zhou F., Ma E. Nature 2002; 419:912. 50 Gnanamanickam E.P., Lee S., Sullivan J.P. and Chandrasekar S., Meas Sci Tech 2009; 20:095710. 51 Saldana C., Yang P., Mann J.B., Moscoso W., Gill D.D., Chandrasekar S. and Trumble K.P. Mat Sci Eng A 2009; 503:172. 52 Swaminathan S., Shankar M.R., Rao B.C., Compton W.D., Chandrasekar S., King A.H. and Trumble K.P. J Mater Sci 2007; 42:1529.


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53 Shankar M.R., Verma R., Rao B.C., Chandrasekar S., Compton W.D., King A.H. and Trumble K.P. Metall Mater Trans A 2007; 38:1899. 54 Shankar M.R., Rao B.C., Chandrasekar S., Compton W.D. and King A.H. Scrip Mater 2008; 58:675. 55 Rajurkar K.P., Levy G., Malshe A., Sundaram M.M., McGeough J., Hu X., Resnick R. and DeSilva A., CIRP Ann 2006; 55:643. 56 Lenel F.V. Powder Metallurgy: Principles and Applications, Metal Powder Industries Federation, Princeton, NJ, 1980. 57 Witkin D.B. and Lavernia E.J., Prog Mater Sci 2006; 51:1. 58 Mann J.B., Shankar M.R., Chandrasekar S., Compton W.D. and Moscoso W, Machining Method to Controllably Produce Chips with Determinable Shapes and Sizes, US Patent 7,628,099, December 8, 2009. See also Mann J.B., Chandrasekar S. and Compton W.D., Tool-Holder Assembly and Method for Modulation-Assisted Machining, US Patent 7,587,965, September 15, 2009. 59 Toews H.G., Compton W.D. and Chandrasekar S., Prec Engg 1998; 22:1–9. 60 Chhabra P.N, Ackroyd B., Compton W.D., Chandrasekar S. Proc Inst Mech Engrs B 2002; 216:321. 61 Mann J.B., Saldana C., Chandrasekar S., Compton W.D. and Trumble K.P. Scrip Mater 2007; 57:909. 62 Lenel, F.V. Powder Metallurgy Principles and Applications, Metal Powder Industries Federation, Princeton, NJ, 1980. 63 Sanders, P.G., Fougere, G.E., Thompson, L.J., Eastman, J.A. and Weertman, J.R. Improvements in the synthesis and compaction of nanocrystalline materials. Nanostruct Mater 1997; 8:3, 243–252. 64 Roberts, P.R. and Ferguson, B.I. Extrusion of Metal Powders, Inter Mater Rev 1991 36:2, 62–79. 65 Clyne, T.W. and Withers, P.J. An Introduction to Metal–Matrix Composites, Cambridge, 1995. 66 Calistes R., Swaminathan S., Murthy T.G., Huang C., Saldana C., Shankar M.R., Chandrasekar. S. Scripta Mater 2009; 60:17. 67 Ramalingam S., 1967, Plastic Deformation in Metal Cutting, Ph.D. Thesis, University of Illinois. 68 Turley D.M., Samuels L.E. Metallog 1981; 14:275. 69 Rogers H.C. Ann Rev Mater Sci 1979; 9:283. 70 Matsumoto Y., Barash M.M. and Liu C.R. J Eng Indus 1986; 108:169. 71 Akcan S., Shah S., Moylan S.P., Chhabra P.N., Chandrasekar S. and Yang H.T.Y. Metall Mater Trans A 2002; 33:1245. 72 Ramesh A., Melkote S.N., Allard L.F., Riester L. and Watkins T.R. Mat Sci Eng A 2005; 390:88. 73 Rigney D.A. Wear 2000; 245:1. 74 Hughes D.A., Chrzan D.C., Liu Q., Hansen N. Phys Rev Lett 1998; 81:4664. 75 Zhu K.Y., Vassel A., Brisset F., Lu K., Lu J. Acta Mater 2004; 52:4101. 76 Mann J.B., Saldana C., Moscoso W., Murthy T.G., Huang C., Swaminathan S., Rao B.C., Shankar M.R., Compton W.D., Trumble K.P., Chandrasekar S. 2008, Unusual Applications of Machining, Proc 23rd All India Int Ind Manf Tech Des Res Conf, pp. 47–55.


8 Deformation structures including twins in nanograined pure metals K. HATTAR, Sandia National Laboratories, USA Abstract: This chapter discusses deformation structures observed in nanograined metals and the proposed formation mechanisms associated with each defect structure. This review is limited to experimental observations in pure metals and predominately to transmission electron microscopy studies due to the length scale of interest. The defect structures that have been observed and will be discussed include: perfect and partial dislocation structures, twins, dislocation loops, disclinations, and other unexpected defect structures. Several of these defects are not observed or are not present at equivalent densities in coarse-grained metals, suggesting the activation of alternative deformation mechanisms. These effects will be highlighted by a few key experiments. Theory and modeling will be used to aid the interpretation of the experimental results, particularly in cases in which time-resolved results at the appropriate spatial resolution are not available. Key words: deformation structures, transmission electron microscopy (TEM), deformation mechanisms.

8.1

Introduction

8.1.1 Nanograined defects in historical perspective Despite the fact that mechanical deformation and metallurgy date back to antiquity, the study of deformation defect structures in metals began in the 1930s when Orowan, Taylor, and Polanyi proposed the concept of edge dislocations. Since that discovery, extensive research along with new experimental and modeling tools has resulted in the discovery of a multitude of deformation defects in metals. Great advances in the discovery and characterization of defect structures in metals resulted from the introduction of the transmission electron microscope (TEM), which permitted direct observation of these defects and their interactions with each other. The type, size, and density of the defect structures found in structural metals, which vary from nearly perfect single crystals to severely plastically deformed structures, are a result of the materials processing history and composition. In this chapter, we will discuss the defect structures observed in high purity nanograined metals that are 1–100 nm in grain size and produced by a variety of methods. Most of the observations will be limited to a variety of TEM characterization techniques due to the resolution needed for the characterization of nanoscale defects in nanograined metals. Real-time TEM observations of the 213 © Woodhead Publishing Limited, 2011

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deformation dynamics will be referenced heavily, as they often provide the greatest insight into the formation and destruction of the deformation structures. This chapter will begin with a characterization of the classical defect structures observed in nanograined metals including: grain boundaries, twins, and dislocations. Classical deformation structures, which are absent from nanograined metals such as dislocation networks, cell structures, and pile-ups, will be discussed next. The third main topic to be discussed is the unique defect structures that have been reported in nanograined metals, but are uncommon in coarse-grained metals. These uncommon defects include five-fold twin formations, disclinations, and agglomerated grains. The effect of initial microstructure on the active deformation mechanisms and the resulting deformation defect structure will be emphasized. Finally, the chapter will end with a brief description of the potential future trends in the field and suggested literature for the reader with further interest in this area.

8.1.2 Short review of well established structures Before discussing the defect structures in nanograined metals, a basic understanding of the common defect structures present in coarse-grained metallic structures is necessary. The defect structures present in metals can be defined by either their dimensionality or the process by which they were introduced into the crystal structure. Using a bubble raft model, Table 8.1 illustrates the classical defects commonly found in metal systems based on their dimensionality. The top row has 0-D defects that include the omission of an atom, vacancy, the inclusion of either an atom larger, smaller, or different in some capacity from the matrix, interstitial or substitutional atom. The second row shows an individual edge dislocation, a 1-D defect, which is identified by the Burgers vector arrowed. The third row shows a grain boundary, a misorientation of the same lattice structure, and an interface between different lattice structures. Two-dimensional defects are the most common defect in nanograined metals. Three-dimensional defects include voids, as illustrated in the last row of Table 8.1, and precipitates. The distinction of defect structures produced by process route is not as definitive, although a general trend suggests that the greater the energy put into deformation, the more complex the defect structure. The combination of the defect dimensionality, density, and character has a direct effect on the properties and performance of any material and is thus worthy of investigation. Readers new to this field are referred to the classical and introductory literature.1–9 The details of the formation and destruction active in many of these structures are still under investigation, although much progress has been made through a combination of in situ TEM investigations and computational models.

8.2

Classical defect structures in nanograined metals

Several defect structures that have been experimentally observed in nanograined metals are also commonly observed in coarse-grained metals, but at densities and


Deformation structures including twins in nanograined pure metals 215 Table 8.1 Potential defect structures in crystalline lattices arranged by dimensionality


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under circumstances not regularly seen in coarse-grained metals. These defects include dislocations, stacking faults, twins, grain boundaries, and point defect agglomerations. A comparison will be made of the character and density of these defects as a function of grain size.

8.2.1 Perfect dislocations Dislocation motion and interactions are at the core of all deformation and failure mechanisms in ductile metallic systems. As has been discussed throughout the chapters of this book, much of the study of nanograined metals has emphasized the effects of limited grain volume on the hindrance or absence of classical dislocation mechanisms and processes. Dislocation density and dislocation structures are commonly identified by TEM using a variety of imaging conditions. Identification of dislocations becomes more difficult as the grain size decreases and multiple grains are present through the thickness of the TEM foil. Despite these difficulties, dislocations have been observed in nanograined metals with grains as small as 10 nm.10 Figure 8.1 (a) illustrates a common dislocation structure seen in a coarse grained Al-Mg-Sc alloy. As is often the case in coarse-grained alloys, the dislocations interact with themselves as well as with grain boundaries, particles, and any other structural defects in the material. As the grain size decreases, the time for which a mobile dislocation is present within a grain decreases; this decreases the probability that the dislocation will have time to interact with other dislocations and limits the interactions with the surrounding grain boundaries. The interaction of a limited number of dislocations on at least two slip systems can be seen in Fig. 8.1 (b). When the grain size decreases to 10 nm, the number of dislocations present in the film decreases substantially due to dislocation repulsion forces. These dislocations are often reported as dislocation dipoles indicated in Fig. 8.1 (c) from Shan et al.’s work on nanograined Ni. The decreased presence of dislocations and, more importantly, of dislocation interactions has a significant effect on the mechanical properties of nanograined metals. This decreased presence will be discussed in more detail in Section 8.3.

8.1 (a) Common dislocation structure seen in Al-Mg-Sc alloy. (b) Dislocation present within a 1 µm grain of high-purity Al. (c) Dislocation present in a 10 nm diameter grain in Ni.10


Deformation structures including twins in nanograined pure metals 217

8.2.2 Partial dislocations (stacking faults) Partial dislocations are commonly observed in coarse-grained metals and alloys with low stacking-fault energy. The interactions of these partial dislocations have been found to play a significant role in the deformation and failure processes. It has been suggested from the theory and computational models that as grain size decreases, perfect dislocations become less dominant and partial dislocations occur more frequently. In order to understand the potential difference in defect structure, Yamakov et al.11 developed a deformation map for nanograined metals in which the deformation mechanism is determined to be simply a function of stress, grain size, and stacking-fault energy, as seen in Fig. 8.2.11 The three dominant mechanisms were determined to be grain boundary mediated deformation, partial dislocation slip, and full dislocation slip. These mechanisms were identified by simulating strain in nanograined Al with an average grain size of 32 nm and varying the stacking-fault energy. The change in deformation mechanism to grain boundary mediated processes results in a change in the Hall– Petch relationship as the grain size decreases. At the smallest grain size, this results in an inverse relationship between grain size (d ) and yield stress (σ ):

.

[8.1]

8.2 Deformation map delineating the active deformation mechanism as a function of grain size based on MD computer simulations,11 where r and d are defined in equation 8.2.


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This proposed mechanism and the associated deformation map, Fig. 8.2,11 have resulted in intense discussions within the field and have been accepted as incomplete due to recent experimental studies. This model does not take into account any deformation mechanisms associated with grain growth that have recently been reported to be active in nanograined metals during deformation.10,12,13 Normalized values of stress (σ∞ /σ∞ ) and grain size (r/d ) make Yamakov et al.’s deformation map applicable to a wide variety of metals.

[8.2]

The applied stress (σ ) is normalized by the resolved shear stress at which the dislocation splitting distance is infinity (σ∞). This resolved shear stress is the stacking-fault energy (γ ) and a set of constants based on the elastic modulus and the Shockley partial dislocation type. The grain diameter is normalized by the placement of the equilibrium dislocation splitting distance (r0) in the numerator of the abscissa. The term r0, as shown in Equation 8.2, is based on the elastic modulus and the Shockley partial dislocation type, as well as the Burgers vector (b), and the stacking-fault energy (γ ). The mechanism demarcation lines indicated in Fig. 8.2 are dependent on a variable (r) that is a function of the equilibrium dislocation splitting distance (r0 ), the applied stress (σ ), and the resolved shear stress at which the dislocation splitting distance is infinity (σ∞). Although the motion of partial dislocations has been proposed to dominate in many nanograined metals, limited experimental research exists showing the presence of either partial dislocations or partial dislocation structures.14 Complex partial dislocation structures are known to exist in coarse-grained low stackingfault energy metals; these structures include dislocation node structures that result in interacting partial dislocations. This is in contrast to the structures seen in deformed nanograined Au, a low stacking-fault metal that does not show significant signs of partial dislocation structures.15 Partial dislocations and the subsequent stacking faults have been reported in nanograined metals. For example, Liao et al. observed both deformation twins and stacking faults as wide as 6.8 nm in cryogenically ball-milled Al, despite a bulk stacking-fault energy of 166 mJ m–2.16,17 In general, partial dislocations and stacking faults do not appear to play a major role in the deformation structure formed in nanograined metals.

8.2.3 Twins Deformation twins are a significant defect structure in many face-centered cubic (FCC) metals with low stacking-fault energy. Several suggested mechanisms



8.3 Image of a deformation twin in Al near crack tip.18

exist for the formation of twins from deformation. Figure 8.3 shows frames captured from an in situ TEM video of the deformation and failure of sputterdeposited Al thin films.18 An interesting aspect of this experiment is the presence of a twin in the grain adjacent to the one responsible for blocking the crack. Although the twin is ahead of the blunting crack tip and may have formed because of the stress field associated with the crack, its formation was not observed dynamically. The density of twins around the fracture surface was greater than in the rest of the gauge section, suggesting that deformation twinning occurred in association with crack blunting.18 These twins have been observed in nanograined and ultra-fine grained FCC metals with low and high stacking-fault energy.17,19–22 Several models suggested that a change in activation volume, strain rate sensitivity, or confining pressure as grain size decreases would result in an increased propensity for twinning.23–26 The addition of twins during the deformation process may act to both relieve stress in a given grain and provide an additional defect structure to limit continued slip activity by providing an additional boundary.27 Deformation twinning is therefore an active mechanism in many nanograined metals and may play a significant role in the mechanical properties.

8.2.4 Grain boundaries The essential defects of nanograined metals are two-dimensional defect structures known as grain boundaries. The dynamics of grain boundaries and resulting defect structures dictate the mechanical properties of nanograined metals. The types and structures of these grain boundaries are highly dependent on the alloy composition and processing steps in the manufacturing of nanograined metals. In general, nanograined structures produced using bottom-up approaches are more


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prone to possessing voids and greater free volume at the grain boundaries.28,29 In contrast, nanograined and ultra-fine grained metals formed by severe plastic deformation and other top-down approaches often contain dislocations in or near the grain boundary.30 In either case, the multitude and often the types of grain boundaries found in nanograined metals are far-from-equilibrium and thus not always stable under standard temperature and pressure. Recent studies have begun to investigate the effects of controlling both the grain size and grain boundary type in an effort to completely engineer a material from the grain boundary up.31,32 Understanding and controlling the response of grain boundaries during plastic deformation is essential for predicting the mechanical properties of nanograined metals and determining potential applications of these materials. One investigation into the understanding of these instabilities and how they may be controlled, deformation-induced grain growth, will be discussed extensively in Section 8.4.1.

8.2.5 Point defects and resulting structures: dislocation loops and stacking-fault tetrahedra Dislocation loops and stacking-fault tetrahedra are defects associated with the collapse of a large number of point defects into lower energy defect structures. Dislocation loops can either be the absence or addition of an extra plane of atoms within a crystalline structure. Stacking-fault tetrahedra are pyramidal structures formed in FCC metals in which the faces of the pyramid are stacking faults that lie on intersecting {111} planes. Dislocation loops have been proposed to be formed from a variety of techniques including dislocation– dislocation interactions during extensive deformation.1,33 The high concentration of vacancies that are needed to form stacking-fault tetrahedra have been reportedly produced by a variety of means including rapid quenching from temperatures near Tm,34,35 irradiation with energetic particles,36 dislocation– dislocation interactions,37 diffusion-induced grain boundary migration under specific temperatures and migration rates,38 annealing and recrystallization following severe plastic deformation,39 and high strain rate (as high as 108 s–1) deformation.40 In severe plastic deformation used to form ultra-fine grained and nanograined metals, it appears that both dislocation loops and stacking-fault tetrahedra can form from mechanical deformation at room temperature. This suggests that the extensive plasticity of either nanograined or ultra-fine grained metals provides a source for a supersaturation of vacancies that results in the formation of dislocation loops and stacking-fault tetrahedra. Dislocation loops and stacking-fault tetrahedra were identified by Dalla Torre et al. in equalchannel angular pressed Cu that was neither irradiated nor quenched. The stacking-fault tetrahedra are black triangles and the dislocation loops are black dots or black and white lobes under the bright-field imaging conditions used in Fig. 8.4.39



8.4 Stacking-fault tetrahedra (arrowed) and dislocation loops in ECAP Cu.39

8.3

Classical defect structures absent in nanograined metals

Greater insight into the properties of nanograined metals may be gained from the classical defect structures absent, rather than those present. This section will detail the defect structures that are commonly seen in bulk deformed metals, but are seldom, if ever, reported in nanograined metals. This discussion will include the description of dislocation locks, cell structures, and intergrain sources. A comparison between the microstructure commonly seen in deformed coarsegrained and nanograined metals will be made on the possible mechanistic differences and resulting alteration to the mechanical properties.

8.3.1 Classical structures absent The variety of classical structures commonly seen in deformed coarse-grained FCC metals is not present in nanograined metals and thus warrants discussion. These structures include dislocation locks, dislocation pile-ups, dislocation tangles, dislocation cell structures, and intergrain dislocation sources. Although all of these structures are different and play significantly different roles in the deformation and failure mechanisms as well as the mechanical properties of metals, they all have in common multiple dislocation interactions, which are needed to form them. Much of what has been discussed thus far relates to the possible breakdown of the Hall–Petch relationship between yield strength and grain size. The Hall–Petch relationship is an empirical observation that has been associated with many of the mobile defect structures that are often absent in nanograined metals.7,41–45 There are a variety of potential dislocation lock


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8.5 A series of micrographs showing (a) dislocation pile-up at a grain boundary; (b) dislocation emission from a grain boundary in stainless steel.46

structures possible in FCC metals; all of which combine two or more dislocations of different slip character within a grain or grain boundary to form sessile dislocation structures from glissile dislocation combinations. Once locks are formed, they provide an impediment to dislocation motion within a grain. This significantly decreases the free path along which the dislocation can proceed. Dislocation pile-ups are arrays of dislocations on the same slip plane and of similar character that apply a local stress on an immobile feature in the microstructure. The pile-up can contain a multitude of dislocations, which can result in a significant stress concentration as is illustrated in Fig. 8.5 (a). The dislocations produced during deformation can either originate from a grain boundary as shown in Fig. 8.5 (b) or internally within a grain by Frank–Read sources.46 Dislocation sources provide the slip and thereby deformation necessary in the crystal without inducing failure. The hindrance of these sources was the first mechanistic explanation for the empirical Hall–Petch effect. Dislocation tangles and cell structures are more complex structures, which evolve to contain a large number of dislocations. These structures will often include dislocation locks and pile-ups. The range of dislocation structures that include locks, pile-ups, and cell structures is complex and important to many of the properties of ductile metals, but appears to be absent from most nanograined systems.

8.3.2 Reasons for the absence of classical structures in nanograined metals The absence of these features can be directly correlated with the lack of space available for their development within a nanograined structure. This lack of defect-free volume often found in nanograined metals in combination with the short mean free path between boundaries means that the probability of dislocation– dislocation interactions occurring during the time it takes for these defects to proceed from one grain boundary to the other is significantly less than in coarsegrained metals. This decreased probability of dislocation–dislocation interaction


Deformation structures including twins in nanograined pure metals 223 results in fewer dislocation locks and other complex multiple dislocation structures forming within the matrix of nanograined metals. Dislocation pile-ups containing a few dislocations have been observed in nanograined metals,13,30 but pile-ups of the size seen in Fig. 8.5 (a) are physically impossible in nanograined metals due to dislocation–dislocation repulsion.47 The limitation of pile-up size results in a limit on the stress applied to the grain boundary and a limit on the slip transferred from one side of the grain to the other.48 This lack of pile-up stress hinders the cross-slip of dislocations in the pile-up that results in both slip on other slip systems and the formation of more complex dislocation structures resulting from dislocation–dislocation interactions.46 The large amount of stress that is applied from large dislocation pile-ups can result in some of the strain being transferred across the grain boundary in the form of new dislocations being generated from the grain boundary. An example of dislocation cross-slip and slip transfer across the grain boundary can be seen in Fig. 8.6.46 The lack of defects, mainly dislocations, within the grains, including dislocation locks to pin the grain boundaries on, means that if dislocations were to move across a grain it would occur very rapidly. This type of dislocation motion would

8.6 A series of micrographs showing (a) cross-slip and (b) slip transfer due to the large dislocation pile-up seen in Fig. 8.5 (a) in stainless steel.46


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not result in the development of complex microstructure within the grains, but may have a significant effect on the grain boundary character. As a result, the grain boundaries are expected to be the location for all the complex interactions that occur during the plastic deformation of nanograined metals.

8.3.3 The effect of missing structures on mechanical properties The lack of these complex defect structures that result from dislocation–dislocation interaction in deformed nanograined metals has a substantial impact on the deformation and failure mechanisms. In coarse-grained metals, these defect structures increase in density as the number of dislocations and thus the probability of their interaction increases. The resulting increase in new structures to pin dislocation motion leads to work hardening, which can significantly prolong the time between initial deformation and final failure. However, in nanograined metals, the lower probability of interaction results in little to no work hardening. Most nanograined metals show minimal ductility prior to catastrophic failure, significantly limiting their application.49–51

8.4

Novel defect structures in nanograined metals

The final class of defect structures in nanograined high purity metals is the completely unexpected defect structures seen in nanograined metals that are not common or have never been reported in traditional coarse-grained metals. The three structures related to deformation are: larger agglomerated grains, five-fold twin structures, and disclinations.

8.4.1 Agglomerated grains A coarsened microstructure commonly results from deformation processes in high-purity nanograined metals. Deformed metals with an initially nanograined microstructure will often have regions containing larger grains that can be correlated to the regions of the highest stress during deformation.52 These grains come in a variety of shapes and sizes with occasional indications for oblong grains in the direction of the greatest stress.52,53 These structures have been identified by both in situ TEM deformation studies and post-mortem TEM analysis.12,53,54 This coarsening of grains during deformation is in direct contrast to the refinement of grain structure during the room temperature deformation of coarse-grained metals. Three possible mechanisms have been proposed for grain growth in nanograined metals. The traditional mechanism is that grain boundaries migrate by the transfer of atoms across the grain boundary, resulting in a change in the dominant grain orientation. The driving force for this change is often associated with grain


Deformation structures including twins in nanograined pure metals 225 boundary curvature.55 This mechanism is highlighted in Fig. 8.7 (a) and 8.7 (b). In Fig. 8.7 (a), a small concave grain with four sides is present in a microstructure dominated by stable six-sided grains. The shape of the grains produces an instability that results in the shrinkage and elimination of the grain. This likely occurs through atomic shuffling across the grain boundaries resulting in the progression of the grain boundary in the direction highlighted by the arrows. The collapse of this grain boundary results in the formation of two triple junctions with angles of 120°56 that are indistinguishable from the surrounding stable grain boundary structure, Fig. 8.7 (b). It should be noted that all polycrystalline systems are theoretically unstable in comparison to single crystals with certain grain boundary types and structures having an energetic local minimum.57–59 Recently, it has been suggested by Molecular Dynamics computer simulations and reported experimentally that grain growth in nanograined materials can occur via grain rotation at room temperature under an applied load.10,60,61 In order for this mechanism to occur, a large amount of free volume must be present in the

8.7 Proposed grain boundary migration mechanisms: (a) grain boundary migration and (b) the resulting microstructure; (c) grain rotation and (d) the resulting microstructure; (e) grain boundary elimination and (f) the resulting microstructure.


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grain boundaries of a far-from-equilibrium structure as illustrated by the thicker grain boundaries and the atypical grain shape shown in Fig. 8.7 (c). A small grain with extensive free-volume at the grain boundaries is highlighted. Local stresses applied to the grain can result in atomistic shuffling in the grain boundaries that has been predicted to result in grain boundary rotation along the direction of the arrow in Fig. 8.7 (c). If the grains to the left and the right of the grain are of the same orientation, then the rotation of the grain can result in the formation of an oblong grain as seen in Fig. 8.7 (d). Cahn and Taylor developed a mathematical model to explain the combination of grain boundary sliding and grain rotation.62 In this model, the tangential motion of grain boundaries was a result of biased grain boundary diffusion.62 Another explanation of grain growth via grain rotation was proposed by Rath et al.63 In their model, introducing a simple stable dislocation structure produces a small-angle grain boundary encircling a region that is rotated relative to the surrounding matrix. This dislocation-based model shows that grain boundary motion may produce grain rotation if the necessary grain misorientation and grain boundary structure are present.63 In another proposed model, grain growth is caused by grain boundary annihilation or alteration due to the bombardment and accommodation of a large number of mobile dislocations.64–66 Figures 8.7 (e) and 8.7 (f ) illustrate the proposed mechanism for dislocation mediated grain growth. This mechanism is associated with a large active dislocation density and thus is thought to occur in samples under extreme stress states. Figure 8.7 (e) shows an unstable grain structure in which a high density of dislocations is piled up on a weak or lowangle grain boundary as indicated. After continued build-up of local stresses, the grain boundary absorbs and emits dislocations into the matrix and potentially along the grain boundary to the extent that the grain boundary structure can no longer be clearly identified. Instead, the orientation between the grains becomes a general transition associated with high dislocation density and without the clear demarcation of grain orientation found with grain boundaries,1 as is illustrated in Fig. 8.7 (f ). The grain coarsening observed here is in stark contrast to the deformation structures observed in coarse-grained metals after deformation at room temperature. It is typical for intense deformation in coarse-grained microstructures to result in the refinement of the grains. This can be seen in the formation of complex dislocation cell structures that form barriers to further dislocation motion. The 3D structures formed from fatigue deformation of Cu-16%Al single crystals at 28 MPa, 34 MPa, and 41 MPa are seen in Fig. 8.8.67 The initial structure seen in the Cu alloy after 28 MPa shows dislocation activity on two slip systems. As the extent of fatigue increases, the densities of dislocations and structures resulting from dislocation–dislocation interaction increase. These defects include dislocation loops, dense dislocation arrays. This type of refinement is assumed to be the mechanism that is used for the formation of ultra-fine and nanograined structures by severe plastic deformation processes. Grain boundaries are known to be



8.8 Three-dimensional view of dislocation structures in Cu-16%Al after fatigue deformation at (a) 28 MPa, (b) 34 MPa and (c) 41 MPa. The planes are indexed and in (d) the {111} planes are indicated.67

destroyed in coarse-grained metals during dynamic recrystallization. This process can be seen in Fig. 8.9, in which a triple boundary in an aluminum alloy is destroyed. This process is associated with superplastic forming and is a result of applied load, while at elevated temperature. The grain structure in metals can be refined to an ultra-fine or nanograined structure using severe plasticity,68 but it has also been shown to undergo grain growth at room temperature from an applied load.53 It is hypothesized that this grain growth due to applied load is seen in nanograined structures deformed at room temperature because of the lack of complex dislocation interactions necessary for grain boundary formation and the high amounts of stress applied to far-from-equilibrium boundaries. An example of grain growth both directly ahead of the crack tip and in the plastic zone due to room temperature straining will be discussed in Section 8.5. The formation of a coarse-grained structure, as a result of deformation in nanograined metals, has a significant effect on the properties and performance of


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8.9 Series of micrographs showing the destruction of a triple junction in Al-4Mg-0.3Sc alloy at nominally the superplastic deformation temperature.69

nanograined metals. Large grains found in localized regions of high stress reduce the strength significantly in the local region and increase local dislocation slip promoting failure to occur within this region.70 The localized deformation in these large grain regions results in localized plasticity and failure with limited global deformation resulting in premature failure of traditionally ductile metals. The lack of knowledge on the factors controlling the formation of the agglomerated grain deformation structure represents a significant hindrance to the application of nanograined materials and is thus an area of intense investigation.12,71

8.4.2 Star twins Another defect structure not observed in coarse-grained metals, but occasionally observed in nanograined metals, is the five-fold twin structure, also known as star twins. This structure entails the union at a single junction of five twins and was first observed in Au and other FCC nanoparticles.69–72 An example of such structure in a gold nanoparticle which is undergoing sintering at elevated temperatures is shown in Fig. 8.10.72 These structures in the nanoparticles have been well studied and have been accredited to the decreased surface energy gained by the formation of the far-from-equilibrium five-fold twin structure. These structures have been observed in nanograined metals produced by various methods.73,74 Similar to nanoparticles with five-fold symmetry, the formation of these non-equilibrium structures in bulk metals has also been associated with the decreased energy gained by the formation relative to the grain boundary energy.73 In grains of 20 nm or less produced by severe plastic deformation, five-fold deformation twins were observed. These defects are present only in nanograined metals, due to the increasing geometrically necessary lattice strain imposed by the



8.10 High resolution TEM of a five-fold twinned Au nanoparticle as it undergoes sintering with a neighboring particle.72

increased lattice mismatch as the structure increases in size. From these results, Zhu et al. were able to develop a proposed mechanism that would permit the formation of five-fold twins from severe plastic deformation.74,75 Five-fold twin structures are not commonly observed in nanograined metals and as a result are not believed to have a significant effect on their mechanical properties.

8.4.3 Disclinations Disclinations are line defects similar to dislocations and will be the final defect structure discussed in this chapter. In contrast to dislocations that displace a local region, disclinations are violations in rotation symmetry of the crystal. Disclinations are defects that are not commonly associated with deformation in coarse-grained metals. High-resolution TEM has been used to identify disclination dipoles in mechanically milled nanocrystalline Fe.76,77 The formation of these rotational defects, seen in Fig. 8.11, is theorized to permit turbulent behavior in the solid metal during severe plastic deformation. It has been stipulated that these defects are present in nanograined metals not only as a result of severe plastic deformation, but also as a result of the increased reliance on intergrain sliding during the deformation process. The observation of disclinations in nanograined metals supports the hypothesis that nanograined metals deform predominantly via grain boundary mechanisms rather than dislocation slip.76,77


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8.11 (a) Transmission electron microscopy micrograph of nanocrystalline Fe powder. (b) Same micrograph with overlaying lines indicating planes of atoms. (c) Schematic of the plane structure with the location of the two disclinations identified.76

8.5

The effect of initial microstructure on deformation structures

The deformation structure formed in a given nanograined metal is highly dependent on the processing history of the metal and the resulting microstructure. This effect is true for all materials, but is of greater significance in nanograined structures due to their very high percentage of atoms not in stable lattice correlation. The variety of possible processing histories that can form nanograined structures can result in various percentages of free volume and types of grain boundaries within the microstructure. Characterization and testing of nanograined metals with the same purity and average grain size but created by different processing routes have shown that neither the microstructure nor the resulting mechanical properties of the two metals are equivalent.28 This suggests that the grain size distribution, types of defects present in the grains, and grain boundaries have a significant effect on the active deformation mechanisms and resulting mechanical properties. The microstructures formed during the production of nanograined materials can be controlled to contain many non-equilibrium structures, as demonstrated below. This effect can be clearly observed in a detailed study of the active deformation and failure mechanisms and properties of nanograined pulsed-laser deposited (PLD) Ni as a function of grain size. The three microstructures, seen in Fig. 8.12, chosen for investigation were nearly monodispersed nanograined Ni film present in the as-released freestanding condition, Fig. 8.12 (a) and 8.12 (b), the micro structure with maximized bimodal distribution, Fig. 8.12 (c) and 8.12 (d), and the ultra-fine grained Ni films, Fig. 8.12 (e) and 8.12 (f ). The bright-field image, Fig. 8.12 (a), of the as-released microstructure contains only nanograined Ni grains as confirmed by the select area diffraction (SAD) pattern insert that contains uniform rings of constant brightness, which is typical of fine-grained metals with no preferred texture. The histogram associated with Fig. 8.12 (a), which quantifies the grain size distribution, is presented in Fig. 8.12 (b). The average grain size ranged from 4 nm to 39 nm with a mean of 13 nm. This resulted



8.12 The microfabricated structure: (a) The initial nanograined microstructure of Ni film after release from Si; (b) Associated histogram of grain size distribution of the nanograined structure; (c) The bimodal microstructure of Ni film after annealing for 1 hour at 548 K; (d) Associated histogram of the mixed structure; (e) The ultra-fine grained microstructure of Ni film after annealing for 1 hour at 598 K; (f) Associated histogram of the ultra-fine grained structure.


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in a standard deviation of 5.3 nm as can be seen in Table 8.2. The vast majority of the 960 grains measured, 90%, are within the range of 5 nm and 20 nm. This results in a maximum grain size to average grain size ratio of 2.9. For comparison, the average grain size in these microfabricated samples is larger, and the distribution broader, than that in the as-deposited Ni films.78 For example, a 90 nm-thick film deposited on rock salt and not subject to microfabrication was found to have an average grain size of 9 nm with a standard deviation of 3 nm, suggesting that despite both being monodispersed high-purity nanograined metals, the process history associated with microfabrication altered the grain size distribution. A bimodal grain size distribution, seen in Fig. 8.12 (b), was achieved through a one-hour anneal at 548 K. The microstructure contains several large grains with scalloped grain boundaries and a myriad of unexpected internal defects. The SAD pattern inserted in Fig. 8.12 (c) shows that continuous rings are maintained due to the nanograined matrix, but the rings are no longer of uniform intensity due to the presence of these large grains. The histogram of grain size distribution presented in Fig. 8.12 (d) shows that the average grain size has nearly doubled to 25 nm from the initial grain size. The range of grain sizes has increased significantly, varying from 4 nm to 435 nm, resulting in a standard deviation of 40 nm as seen in Table 8.2. The ratio of maximum grain size measured to average grain size is 17.2, yet 70% of the grains remain in the range of 5 nm and 20 nm. The line-intercept method identified 25 ultra-fine grains, larger than 100 nm, in the region analyzed. This accounts for only 3.7% of the 681 grains measured as seen in Table 8.3. The initial microstructure was completely eliminated after annealing for one hour at 598 K and developed into large nanograins and small ultra-fine grains, as can be seen in Fig. 8.12 (e). The SAD pattern, Fig. 8.12 (e) insert, is now neither uniform in brightness nor continuous, and is typical of ultra-fine grained crystalline structures. The grain size distribution shown in Fig. 8.12 (f ) is significantly different from the as-deposited distribution, Fig. 8.12 (b). The average grain size has increased by nearly an order of magnitude of 150 nm with a broad distribution Table 8.2 The mean, median, largest, and smallest grain size, as well as the total number of grains for annealing treatments applied to 90 nm-thick PLD Ni films for in situ TEM straining Condition

Total number of grains

Mean (nm)

Median Standard Maximum Minimum Max (nm) deviation (nm) (nm) mean (nm)

As-deposited

960

13

12

5

39

4

3

548 K 1 hr

681

25

15

40

435

4

17

598 K 1 hr

116

150

145

81

436

23

3


Deformation structures including twins in nanograined pure metals 233 Table 8.3 Ratios derived from the grain size distribution annealing treatments applied to 90 nm-thick PLD Ni films for in situ TEM straining. The 10 × initial average, ultra-fine grain, 5 × average, and Tukey outliers are normalized by the total number of grains per histogram. The deviation from as-deposited and log normality are based on the Kolmogorov–Smirnov analysis Condition 10x average (%)

10x Ultra-fine 5x Tukey Log initial grains average outliers normality average (%) (%) (%) (%) (%)

Deviation from asdeposited (%)

As-deposited 0.0 548 K 0.6 598 K 0.0

0.0 3.1 54.3

0.0 20.6 42.2

0.0 3.7 69.8

0.0 3.2 0.0

3.3 9.5 0.9

0.0 0.0 1.0

ranging from 23 nm to 436 nm (Fig. 8.12 (f ) ). This resulted in a standard deviation of 81 nm, seen in Table 8.2. The maximum grain size to average grain size ratio is 2.9, comparable to that of the as-released films. No grains remain in the 5 nm to 20 nm range and ultra-fine grains account for 70% of the 116 grains measured in an area of identical size to the previous histograms. This distribution is only one of the three to show any similarity to a log normal distribution based on the Kolmogorov–Simirnov test as seen in Table 8.3 and described by Kirkman.79 This control of microstructure permits the study into the relationship of grain size distributions, not just average grain size, with deformation and failure mechanisms active during straining. The deformation and failure of a PLD Ni freestanding film annealed at 548 K for 1 hour was observed during in situ TEM pulsed straining experiments using a custom-built straining device. The bimodal grain size distribution produced by annealing of these films, evident in Fig. 8.12 (c) and 8.12 (d), provides the opportunity for a multitude of deformation mechanisms. Evidence for a variety of mechanisms including dislocation pile-ups, twinning, stress-driven grain growth, localized thinning, crack blunting, ligament necking, and even what is interpreted to be grain agglomeration were present during the deformation and failure of the films with a bimodal structure. Plasticity was observed up to 2 µm in front of the crack tip with extensive plasticity observed in a region up to 500 nm directly vicinal to the tip, as will be discussed in Fig. 8.13 and Fig. 8.14. Dislocation activity was observed in the large grains within the plastic zone without any observable change in the small surrounding grains. The solidified Ni droplets, or splats, present in the film were found to have no observable interaction with crack propagation despite it propagating within 100 nm of the splat. Closer to the crack tip, severe microstructural rearrangement occurred in both the large grains and the nanograins. In the region of the Ni film directly ahead of the crack tip undergoing thinning, the large grains contained active full dislocations whereas the nanograins underwent the process termed grain agglomeration by Shan et al.10 The combination of these processes resulted in a thinning and


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8.13 Still frames taken from an in situ TEM deformation experiment of a custom-built PLD Ni device annealed at 548 K for 1 hour showing grain growth 240 nm ahead of the crack tip: (a) A still frame with migrating boundary outlined; (b) The same region 0.10 seconds later with the new boundary demarked.

eventual local failure of the film. No observation of deformation or failure was observed to occur in any grains identified as being metastable hexagonal closepacked (HCP) phased despite a portion of the large grains being of this character. Deformation was seen in a grain containing a rich debris field. Despite these observations, no interactions of dislocations with stacking-fault tetrahedra were discernable. This work also provided direct evidence for stress-driven grain growth. An example of this effect is shown in the images presented in Fig. 8.13. To illustrate the grain growth, a portion of the grain boundary of a grain 240 nm from the nearest crack is highlighted. The new position of the boundary after stress-driven grain growth is highlighted in Fig. 8.13 (b). The grain boundary sweeps out an area of 250 nm2 in less than 0.1 s. Grain growth of this nature was observed in several grains within the plastic zone. The progression of the crack through the film was often halted due to the large grains present in the bimodal microstructure, as is shown in Fig. 8.14 (a). In this image, a crack that was progressing from left to right was halted on the two large grains indicated. The left-most large grain indicated in Fig. 8.14 (a) separates the primary crack from the microcrack, formed on the other side of the grain. The second large grain present in front of the secondary crack also hindered crack progression. In situ TEM observations of this region showed dislocation activity in both grains during pulse straining followed by extensive necking in the thinned region between the crack and microcrack. Figure 8.14 (b) and 8.14 (c) are postmortem micrographs of the fracture surface. A set of large grains along the fracture surface indicates severe plasticity including necking down to nearly a point. One of the large grains contains two dislocation pile-ups present on opposite planes



8.14 Fracture surface of PLD Ni device annealed at 548 K for 1 hour: (a) A crack temporarily halted with one large grain spanning crack spacing and the other in front of the crack tip; (b) Necked region containing two dislocation pile-ups; (c) Large grain containing both dislocations and a twin.

and originating near the same region containing slightly more than 15 dislocations each in a grain with a length of 130 nm. Figure 8.14 (c) shows another region of large grains along the fracture surface. In this micrograph, both a dislocation pile-up and a twin are labeled. The dislocation pile-up contains 12 identifiable dislocations. The thin twin, near an area previously exposed to high stresses, was confirmed by SAD. Significant necking was evident along the fracture surface of the PLD Ni film annealed at 548 K for one hour, but not on the fracture surface of the as-deposited Ni film. Analysis of the fracture surface of the annealed PLD Ni films by both the scanning electron microscope (SEM) and TEM revealed


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extensive dislocation activity in the large grains that resulted in significant plasticity along the fracture. Further insight into the mechanisms active in the film as a function of grain size and distribution can be gained from the comparison of the fracture surfaces in the three freestanding PLD Ni films produced by microfabrication and annealed to varying conditions (Fig. 8.15). In Fig. 8.15 (a), the film, after release from the substrate, failed during straining in the TEM. The location of crack initiation and propagation was not observed at the time of failure. Cross-sectional SEM images of the film show no sign of necking in the film. The fracture surface of this film shows limited signs of plasticity. On the fracture surface of a PLD Ni film annealed at 548 K and shown in Fig. 8.15 (b), three different microstructures are encountered. In the center of the image, the fracture surface intersects a nanograined region in which the surface appears similar to that seen in Fig. 8.15 (a). To the left of this region, a cusp is observed along the fracture surface as it cuts through a large grain. Detailed observation of this grain and other large grains along the fracture surface reveals limited necking within the large grains. In the far right of Fig. 8.15 (b), a region is seen in which the fracture surface passes through a nanograined region vicinal to a large grain present in the film. The crack propagated through these three regions with no tendency to avoid any of them. The fracture surface of the PLD Ni sample annealed at 598 K for one hour, Fig. 8.15, is dominated by dislocation motion within a plastic region. Necking of the film can be seen in multiple grains in Fig. 8.15 (c). The plasticity observed in this film is similar to the classical expectation for coarse-grained foils.1,80,81 The combination of dynamic observation of deformation and failure in bimodal PLD Ni and detailed observation of the fracture surface have shown that a variety of mechanisms can be operative in the same region of the film simultaneously dependent on the processing history of the metal.

8.6

Future trends

Current trends in the field would suggest the maturation of studies into nanograined FCC metals. Since Gleiter’s first suggestion that nanograined metals may have unique properties over 20 years ago,82 intensive research has been undertaken to develop processing, characterization, and testing tools, and evaluate the structure of nanograined metals. As such, the field is beginning to lose its novelty and the research is becoming less ground-breaking and more detailed in nature. This is exemplified in the decreased interest in the inverse Hall–Petch relationship by leading research groups. Likewise, a trend is observed in the expansion of the field to pure BCC, HCP, and alloy systems being tested by increasing the number of methods for a greater variety of electrical, thermal, mechanical, and other properties.



8.15 Fracture surfaces of the PLD Ni films produced by microfabrication with: (a) the initial nanograined microstructure; (b) the bimodal grain size distribution from annealing for 1 hour at 548 K, and (c) ultra-fine grained microstructure from annealing for 1 hour at 598 K.

A promising trend in the field is the publishing of more thorough studies into the governing mechanisms and controlling factors that determine the deformation structures formed in nanograined metals. One of the greatest advances in recent history is the development and refinement of processes for producing nanograined


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metals with lower contamination levels and well-controlled grain boundary structures. The advancement in the processing-microstructure correlation has resulted in a split in the nanograined field between the metals produced by topdown approaches and those produced by the bottom-up approaches. It is generally accepted that these sets of materials have very different initial microstructure, and as a result, will likely have differing active deformation mechanisms and resulting deformation defects. Along with studies of greater depth, the research into deformation defects in nanograined metals should expand in all dimensions to include investigations employing a greater range of techniques and materials systems. These material systems should include alloy systems with both solutes and precipitates, as strengthening and grain size stabilizing elements; more applied systems such as nanograined titanium alloys and oxide-dispersed steels; and various crystal systems. The investigation into different crystal systems, alloy compositions, and processing history will assist in the settlement of debate on the effect length-scale transitions have on the active mechanisms and resulting structures, as well as result in a better understanding of the defect structure and the active mechanisms, and development of nanograined metal applications in industry. Beyond the development in processing and analysis, the greatest potential in the identification of defect structures may come from the recent advances in highresolution microscopy. Three recent techniques that have undergone significant development are aberration-corrected TEM, tomography, and atom probe microscopy. Recent developments in spherical and chromatic aberration-corrected TEM provides increased resolution and chemical mapping, which are essential for detailed analysis of nanograined structures. The further potential for increased resolution and a widened pole piece gap offered by spherical and chromatic aberration corrected TEM provides the opportunity to include a wide range of in situ techniques not previously possible. This should result in techniques for better understanding of the unique deformation structures in nanograined metals and the related formation mechanisms. Three-dimensional electron tomography is another technique that has progressed significantly and also has a potential for continued development. The automation of this technique provides three-dimensional structural information with relative ease to a wide variety of sample geometries, microstructures, and chemistries. The final technique that could potentially have a large impact on defect structures in nanograined metals research is atom probe microscopy. This technique identifies the location and type of element present in a material. With sufficient increases in resolution, it would be able to determine the exact relationship between local chemistry and microstructure within complex nanograined alloys. One piece of equipment that would be of great benefit to the field, but is not currently available is a non-destructive tool capable of rapid evaluation of the internal and grain boundary defects in bulk nanograined metals. It is also foreseen that current trends in computation capabilities will continue to increase greatly. This will result in the development of more robust computer


Deformation structures including twins in nanograined pure metals 239 models that should then be able to predict the evolution of more complex structures over greater time periods. Overall, it appears that understanding of nanograined deformation and deformation structures through advances in new tools is progressing out of its infancy and expanding into a broad range of fields. For greater depth in mechanical properties,1,47,83 grain boundary structure,84 or electron microscopy85,86 the reader should consult the classical text on the subject referenced.

8.7

Acknowledgements

This work is supported by the Division of Materials Science and Engineering, Office of Basic Energy Sciences, US Department of Energy both at Sandia and under grant DE-FG02–07ER46443. Sandia National Laboratories is a multiprogram laboratory operated by Sandia Corporation, a wholly owned subsidiary of Lockheed Martin Corporation, for the US Department of Energy’s National Nuclear Security Administration under contract DE-AC04–94AL85000.

8.8

References

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Deformation structures including twins in nanograined pure metals 241 48 I.M. Robertson, A. Beaudoin, K. Al-Fadhalah, L. Chun-Ming, J. Robach, B.D. Wirth, A. Arsenlis, D. Ahn and P. Sofronis, Materials Science and Engineering A 400–401 (2005) 245. 49 Y. Wang, M. Chen, F. Zhou and E. Ma, Nature 419 (2002) 912. 50 D. Farkas, H. Van Swygenhoven and P.M. Derlet, Physical Review B (Condensed Matter and Materials Physics) 66 (2002) 060101. 51 H. Huang and F. Spaepen, Acta Materialia 48 (2000) 3261. 52 F.R.N. Nabarro, Scripta Materialia v 39 (1998) p 1681. 53 D.S. Gianola, S. Van Petegem, M. Legros, S. Brandstetter, H. Van Swygenhoven and K. J. Hemker, Acta Materialia 54 (2006) 2253. 54 K. Hattar, D.M. Follstaedt, J.A. Knapp and I.M. Robertson, In situ TEM observation of Stress-Induced Grain Growth, (2010). 55 T. Gladman, Grain Size Control (Maney Publishing, London, 2004). 56 A.C. Ferro and M.A. Fortes, Interface Science 5 (1997) 263. 57 E.M. Bringa, A. Caro, Y. Wang, M. Victoria, J.M. McNaney, B.A. Remington, R.F. Smith, B.R. Torralva and H. Van Swygenhoven, Science 309 (2005) 1838. 58 H. Van Swygenhoven, A. Caro and D. Farkas, Scripta Materialia, 5th International Conference on Nanostructured Materials (NANO 2000), Aug. 20–25, 2000 44 (2001) 1513. 59 H. Van Swygenhoven, M. Spaczer and A. Caro, Nanostructured Materials, Proceedings of the 1998 TMS Annual Meeting & Exposition, Feb. 15–19, 1998 10 (1998) 819. 60 A.J. Haslam, S.R. Phillpot, D. Wolf, D. Moldovan and H. Gleiter, Materials Science & Engineering A (Structural Materials: Properties, Microstructure and Processing) A318 (2001) 293. 61 H. Li, Advanced Engineering Materials 7 (2005) 1109. 62 J.W. Cahn and J.E. Taylor, 52 4887. 63 B.B. Rath, M. Winning and J.C.M. Li, Applied Physics Letters 90 (2007) 161915. 64 V. Bata and E.V. Pereloma, Acta Materialia 52 (2004) 657. 65 V. Bata and E.V. Pereloma, Scripta Materialia 51 (2004) 927. 66 J.A. Wert, Scripta Materialia 50 (2004) 1487. 67 H. Inui, S.I. Hong and C. Laird, Acta Metallurgica 38 (1990) 2261. 68 R.Z. Valiev and I.V. Alexandrov, 58 1003. 69 L.M. Dougherty, I.M. Robertson and J.S. Vetrano, Acta Materialia 51 (2003) 4367. 70 B.L. Boyce, Proceedings of the SPIE – The International Society for Optical Engineering Reliability, Testing, and Characterization of MEMS/MOEMS II, Jan. 27–29, 2003 4980 (2003) 175. 71 S.M. Allameh, Journal of Materials Science 38 (2003) 4115. 72 M. Briceno, K. Hattar, J. Damiano, D. Nackashi and I.M. Robertson, In-situ TEM study of the sintering process of gold nanoparticles using ultra-fast heating stage (2010). 73 J. Urban, 33 1009. 74 Y.T. Zhu, X.Z. Liao and R.Z. Valiev, Applied Physics Letters 86 (2005). 75 Y.T. Zhu, X.Z. Liao and R.Z. Valiev, Applied Physics Letters 86 (2005) 103112. 76 M. Murayama, J.M. Howe, H. Hidaka and S. Takaki, Science 295 (2002) 2433. 77 I.A. Ovid’ko, Science 295 (2002) 2386. 78 K. Hattar, D.M. Follstaedt, J.A. Knapp and I.M. Robertson, 56 794. 79 T.W. Kirkman, Statistists to Use, at http://www.physics.csbsju.edu/stats/ (1996). 80 M.P. Dewald and W.A. Curtin, Modelling and Simulation in Materials Science and Engineering 15 (2007) 193.


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9 Microstructure and mechanical properties of nanostructured low-carbon steel prepared by equal-channel angular pressing Y.G. KO, Yeungnam University, Republic of Korea and D. H. SHIN, Hanyang University, Republic of Korea Abstract: This chapter reviews the microstructural evolution of nanostructured low-carbon steels during equal-channel angular pressing (ECAP) and subsequent heat treatments. Regarding microstructural evolution, most ferrite phase grains are significantly refined by grain subdivision related to various slip systems of {110}, {112} and {123}, which are mainly operated by ECAP shear strain, while pearlite colonies are deformed by mechanical fragmentation. When appropriate subsequent heat treatments are selected, a significant portion of carbon atoms are redistributed uniformly during ECAP deformation, leading to a uniform distribution of nanoscale cementite particles. The mechanical properties of the nanostructured steel samples are also examined, focusing on microstructural modifications to overcome their inherent mechanical drawbacks arising from dynamic recovery and nanoscale grains. Key words: nanostructured low-carbon steel, equal-channel angular pressing (ECAP), microstructural evolution, mechanical properties.

9.1

Introduction

Over the past decade, the materials science and engineering community has paid considerable attention to nanostructured metallic materials due to their unique properties, particularly their superior mechanical properties, which offer opportunities for a variety of structural applications.1–14 Previous studies have shown that the mechanical properties of nanostructured metallic materials differ greatly from those of traditional coarse- and fine-grained metallic materials.15–20 Since the milestone work by Segal et al.,21 equal-channel angular pressing (ECAP) has been regarded as one of the most promising processes for fabricating advanced metallic materials with nanoscale grains. Its advantages have spurred a great deal of research on ECAPed metallic materials, which have found successful applications in metallic systems such as aluminum,22 iron,23–25 and titanium10,14 alloys. Among these materials, a special focus is placed here on the microstructure and mechanical properties of nanostructured low-carbon steel (LCS) in light of two main considerations. In conventional LCS steels, structural refinement of the grain size from ~10 to ~1 µm led to an increase in yield strength by as much as ~500 MPa, and a decrease in the ductile–brittle transition temperature below roughly –350 K. Thus, extensive efforts have been devoted to the development of 243 © Woodhead Publishing Limited, 2011

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ferrous alloys with submicron-level grain sizes by the aforementioned processing technologies. Considering the enhanced mechanical properties and concomitant commercial potential of nanostructured low-carbon steel (LCS), an overall review would provide a fundamental understanding along with assessing the current development of new types of ferrous alloys. Second, since an LCS alloy consists of two phases, i.e. ferrite and pearlite, its deformation behavior differs markedly from that of single-phase materials. Although pearlite has a much smaller volume fraction than ferrite in LCS, its effect on the mechanical properties of steel is disproportionately large. In addition, the microstructural evolution of pearlite during ECAP is expected to be complex due to the existence of hard cementite lamellar plates. In this chapter, we reviewed recent progress on microstructural evolution and the resulting mechanical properties of nanostructured LCS samples, which were analyzed through transmission electron microscopy (TEM) based and theoretical approaches. We also reviewed several metallurgical strategies that had intended to overcome the shortcomings of mechanical properties of nanostructured LCS, such as a lack of strain hardenability.

9.2

The microstructural evolution of low-carbon steel (LCS)

9.2.1 The microstructural evolution of LCS by equal-channel angular pressing (ECAP) Figure 9.1 displays the optical microstructure of an ECAPed LCS as a function of the number of ECAP passes with route C where the sample is rotated 180° along its longitudinal axis. The X-plane is the plane perpendicular to the longitudinal axis of the sample, and the Y- and Z-planes denote the side-viewed and top-viewed planes along the longitudinal axis of the sample, respectively. The initial sample reviewed here is a LCS sample consisting of pearlite of approximately 15% (dark phase) with the remainder being ferrite (bright phase) shown in Fig. 9.1 (a). Both phases are nearly globular and their size is ~30 µm. Several common microstructural changes with ECAP deformation were noted regardless of the planes: 1) the constituent phases became smaller and more irregular with repetition of pressing as can be seen from Fig. 9.1 (b)–(e); 2) the ferrite grain boundaries of the sample after a single pass were visible as shown in Fig. 9.1 (b), but there existed many dim contours inside them, likely indicative of the fragmentation of ferrite grains due to extensive strain;26 and 3) it is difficult to identify the initial ferrite grain boundaries, and the dim contours became extensive beyond two or more passes of the pressing as shown in Fig. 9.1 (c)–(f ). Referring to the pearlite colony size as a qualitative measure of the mechanical fragmentation, the fragmentation on the X-plane was even more severe than that on the Y-planes. With an odd number of passes, the micrographs of the Y-plane showed that the grains were severely elongated along the direction of ~30° inclined to its


Microstructure and mechanical properties

245

9.1 Optical micrographs of (a) the initial sample, (b) one-pass, (c) two-pass, (d) three-pass, and (e) four-pass ECAP-deformed samples with respect to the viewing planes (X, Y, and Z planes).24

longitudinal axis, which was fairly similar to the macro-shear direction imposed by ECAP as shown in Fig. 9.1 (b) and (d). With a subsequent even number of passes, both phases restored the near-equiaxed shape as shown in Figs. 9.1 (c) and (e). These microstructural changes were anticipated when route C was used.27–29 Despite the significant inherent difference in yield strength and plastic deformation between pearlite and ferrite phases, the presence of severely elongated phases after an odd number of passes and the restoration of their equiaxed shape after a subsequent even number of passes were observable. Under severe plastic deformation conditions, the macroscopic deformation behavior of pearlite was quite similar to that of ferrite. In terms of deformability, no cracking was observed in the LCS samples that were subjected to severe plastic straining while the strength and plastic deformation behaviors of pearlite and ferrite all vary. Two factors could account for this observation: 1) a soft ferrite phase with a large


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volume fraction could accommodate plastic incompatibility between two phases, and 2) a hard pearlite phase is capable of sustaining plastic deformation to some extent. Figure 9.2 (a) presents a TEM image of ferrite in the deformed samples viewed from the Y-plane. The initial microstructure exhibited a relatively low dislocation density. After a single pass, the microstructure mainly consisted of parallel shear bands of elongated grains with a length of ~2 µm and width of ~0.5 µm, showing considerable grain refinement (Fig. 9.2 (b) ). The corresponding selected-area electron diffraction (SAED) pattern was characterized by individual spots, implying that most of the boundaries of fine grains formed by a single pass would be of low angle. The microstructure after two passes (Fig. 9.2 (c) ) contained fairly equiaxed grains with widths comparable to those of grains obtained by the first pass. However, the SAED pattern showed the appearance of additional rings and extra spots, indicating the formation of high-angle grain boundaries. Near-equiaxed ultra-fine grains of 0.2–0.3 µm diameter, which were finer than those obtained at two passes, resulted from four-pass treatment (Fig. 9.2 (d) ). In addition, the number of rings in the SAED

9.2 Transmission electron microscopy images of ferrite phase grains in (a) the initial sample, (b) one-pass, (c) two-pass, and (d) four-pass ECAPed LCS samples taken from the Y-plane presenting main shear deformation.24



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pattern increased and the spots became more diffused as compared to the previous observations. The increase in the number of the rings and the spots with repeated passes indicates that the grain size reduction rose with increasing number of pressings by evolution from low-angle boundaries, which appeared after the first pass, to highangle boundaries. From TEM observations, however, ferrite grain boundaries after ECAP were not well defined and the existence of extensive extinction contours along grain boundaries was evident. These observations indicated that ferrite grain boundaries formed by ECAP were in a non-equilibrium state having a high internal stress due to long-range order lattice distortion. These general features associated with the microstructural changes observed in ferrite phases are consistent with those in ECAP-deformed aluminum alloys reported in the literature.7,26,30–32 On the other hand, the deformation behavior of pearlite differed from that of the ferrite phase during ECAP. The initial morphology of pearlite in the LCS sample consisted of a well-developed continuous lamellar structure, as shown in Fig. 9.3 (a).

9.3 Transmission electron microscopy images of pearlite colonies in the initial and ECAP-deformed LCS samples showing the morphological changes in cementite: (a) the initial sample, (b) severely necked cementite after four-pass, (c) mechanically curled and wavy cementite plates after four-pass, and (d) globular cementite and sharp slip lines (marked by two black arrows) after four-pass.24


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After four-pass ECAP, the microstructure of the pearlite phase is represented by two typical features according to cementite morphology. The first feature is that cementite plates remained parallel to each other but were in a discrete form, indicating the occurrence of a breakage of cementite lamellae during ECAP (Fig. 9.3 (b) ). The second feature is that the discrete cementite lamellae were severely curled and wavy (Fig. 9.3 (c) ). The occurrence of severe necking was also evident along the cementite plate length. In some cases, as shown in Fig. 9.3 (d), a globular cementite33,34 and a sharp slip line35 were observed. The observation of both severe necking and a sharp slip line indicated that a breakage of the cementite lamellae occurred. It is of interest that the cementite lamellae exhibited a considerable capability for plastic deformation as shown in Fig. 9.3 (b)–(d), given that the cementite is prone to fracture with ease in a brittle manner under uni-axial tensile mode on account of the few slip systems available.36 Such plastic deformation behavior of cementite could be attributed to the presence of severely elongated pearlite after an odd number of passes and the restoration of its equiaxed shape after a subsequent even number of passes. To shed light on this unusual behavior, a comparison with the earlier work on a pearlitic steel wire deformed via conventional drawing would be helpful.33 Under the nearly same effective strain, severely ECAP-deformed cementite in the pearlite phase was quite similar to that observed in a heavily cold drawn pearlitic steel wire.33,34 For the heavily cold drawn pearlitic steel wire, it is generally accepted that severely deformed cementite plates are found on the planes of the lamellae aligned along the drawing axis while curled wavy cementite plates are observed on the planes of the lamellae, which are not aligned along the drawing axis. When cementite was subjected to uni-axial tensile deformation, (001)[010], (010)[001] and (100)[010] slip systems were operative, but they were insufficient for cementite to deform plastically without inducing significant cracks.37 Accordingly, the TEM observations showing considerable plastic deformation of cementite suggested that the additional slip systems might operate under the deformation mode accompanied by ECAP, the deformation mode of which was documented to be shear. In the cold drawing process, pearlite was subjected to a hydrostatic stress state. Under the hydrostatic stress state, – – additional slip systems of (110)[111] and (011)[111] became active. Cementite thereupon possessed a number of slip systems sufficient for homogeneous plastic deformation.21,38 Still, it is doubtful whether the stress state induced by ECAP is comparable to that induced by the cold drawing process. Based on the observation that cementite deformed plastically in Fig. 9.3 (b)–(d), however, it is likely that ECAP deformation could develop a complex stress state where a sufficient number of slip systems for the plastic deformation of cementite are in operation.

9.2.2 Grain refinement mechanism Slip system at the first pass of ECAP Figure 9.4 (a) presents a TEM micrograph of a LCS sample viewed from the zone axis after the first pass of ECAP. The ferrite microstructure mainly consists of



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parallel bands of elongated grains having a width of 0.3 µm. The extended parallel band boundaries are called lamellar-type boundaries (LBs). The corresponding SAED pattern shows that LBs are mainly low-angled and the direction of the bands is primarily parallel to the direction. Inside the band interior, dislocation cell boundaries (DCBs) were also detected. The dislocation density inside a cell enclosed by DCBs is relatively low. DBs were typically found to be either normal to LBs or 30° and 60° inclined to LBs. This kind of boundary structure was reported to be typical for heavily deformed metallic materials. In order to identify the slip system operating during ECAP, first it is important to recognize that the direction of the deformation band should be parallel to the intersecting line between the viewing plane normal to the selected zone axis and the slip plane on which deformation occurred. The direction of the deformation band is thus equivalent to that of the projection of the slip plane, which contains both the slip direction and the direction of the deformation band, on the viewing plane. Figure 9.4 (b) suggests a probable grain refinement mechanism of a LCS alloy from the standpoint of dislocation slip activities based on analysis of TEM data. A pictorial illustration satisfying this condition is presented in order to –– identify the slip systems operating at the first pass of ECAP. When the [111] – direction was selected as the viewing direction, two of the slip planes (110) and –– (112) in the body-centered cubic (bcc) crystal system could contain the [110] deformation band direction, which was the major deformation band direction formed at the first pass. In order to identify the slip plane more definitively, it was necessary to rotate the viewing direction in TEM. Using this tilting method, the –– – (112) plane with the [111] slip direction was characterized as the slip plane. It was noted that, in a different region, planes belonging to the {110} family were also identified as the slip plane. Accordingly, it was evident that the slip systems of

9.4 (a) Transmission electron microscopy micrograph of the first pass ECAPed LCS sample and (b) pictorial illustration for formation of the deformation band and identification of the corresponding slip systems operating at the first pass.39


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{110} and {112}, which are typical in a bcc crystal system, were the major slip systems operating in the LCS alloy during the first pass of ECAP. Slip system at the second pass of ECAP Figure 9.5 (a) shows a TEM micrograph of a LCS sample viewed from the zone axis after the second pass of ECAP. Equiaxed grains were formed by the second pass, but their average size of ~0.5 µm was slightly larger than the width of the subgrain bands formed by the first pass. From the SAED pattern, it was obvious that, at least in this area, the misorientation between sub-grains increased compared with that of the sample deformed by a single pass. Even though the portion of ultra-fine equiaxed grains was large, some sub-grain bands remained. This implies that twopass ECAP was insufficient to produce a homogeneous structure despite the considerable grain refinement. Many boundaries were aligned along either the or directions, similar to those in the sample after a single pass. However, detailed inspection of Fig. 9.5 (a) reveals the presence of additional boundaries having several different angles with respect to the direction. The direction is the alignment direction of LBs as well as sub-grain bands. The observation of sub-grain boundaries with other directions reveals that new slip systems operated in the course of the following deformation. Accordingly, the boundaries appeared to be serrated as shown in regions 1 and 2 in Fig. 9.5 (a). A TEM analysis was conducted on the two-pass ECAPed sample. In addition to the and directions, the boundaries having several different angles with respect to the direction were observed. This reflects that dislocations belonging to several different slip systems moved and, thereby, formed cell boundaries inside the initial sub-grain bands to accommodate the strain energy. To understand the deformation characteristics induced by the second pass, a pictorial illustration is

9.5 (a) Transmission electron microscopy micrograph of the second pass ECAPed LCS sample and (b) pictorial illustration for formation of the deformation band and identification of the corresponding slip systems operating at the second pass.39



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– provided in Fig. 9.5 (b). In the second pass, the [111] direction became the slip – direction if the [111] direction could be the slip direction operating at the first pass. – The intersection between the viewing plane of (111) and the slip plane of (110) – – – containing the [111] slip direction was aligned along the [112] direction, displaying the direction of the new deformation band. It was noted that, on the viewing plane of – – – (111), the [112] direction was normal to the [110] direction, which coincides with the direction of deformation bands formed by the first pass. Accordingly, based on the –– – – TEM image observed in the direction of [111], the boundaries aligned along the [112] direction appeared to be normal to the LBs formed by the first pass. By the same – logic, boundaries representing the [213] and [101] deformation bands appeared to be – inclined 79° and 60°, respectively, to the LBs formed by the first pass. The [213] and – – – – [101] deformation bands were associated with the (211) and (101) slip systems, respectively. Figure 9.6 (a) provides a TEM micrograph of the serrated

9.6 Transmission electron microscopy micrograph showing an example of the serrated boundaries found in (a) the two-pass ECAPed LCS sample, viewed by a zone axis, and (b) its schematic description including the slip system corresponding to the individual bands and the angular relationship between them.39


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boundary observed in the two-pass ECAPed sample, viewed by the zone axis, as well as its schematic description, including the slip system corresponding to the individual bands and the angular relationship between bands. The angular relationship between deformation bands formed by the first and second passes described above was in excellent accordance with that measured experimentally in Fig. 9.6 (b). Thus, similar to the first pass, the {112} and {110} systems could be considered as slip systems operating at the second pass. However, the initial shear bands formed at the first pass inhibited dislocations on other slip systems from crossing the bands. As a result, all of the possible slip systems belonging to the {112} and {110} slip system families should operate to accommodate deformation during the second pass. Hence, nanoscale dislocation cells enclosed by the {112} and {110} planes were formed.39–41 Formation of high-angle grain boundary The microstructures after four-pass ECAP are shown in Fig. 9.7, in which equiaxed grains with an average grain size of 0.2–0.3 µm were formed. Similar to previous findings,42–45 this confirms that grain refinement was most pronounced at the initial stage of ECAP but was not significant at large strains. This is because, with an increment in the amount of applied strain, the dislocation movement on the new slip systems would be restricted by the presence of the initial shear bands and, thus, they should rotate so as not only to accommodate strain but also to maintain an even shear strain distribution at grain boundaries once sub-grains appear. In order to examine the grain orientation relationship between two adjacent nanostructured grains, a Kikuchi pattern analysis was carried out. Some examples

9.7 Transmission electron microscopy micrograph of the four-pass ECAPed LCS sample.39 (Hereafter, all samples were subjected to four-pass ECAP).



253

9.8 Transmission electron microscopy Kikuchi patterns showing the misorientation relationship between adjacent nanostructured ferrite grains of the ECAPed LCS sample.39

of the Kikuchi patterns of the four-pass ECAPed sample viewed from the zone axis are shown in Fig. 9.8. As illustrated above, the directions of the grain boundaries in grain 1 were aligned along the and directions. The average misorientation angles across the boundaries aligned along the and directions were ~15° and ~10°, respectively. The Kikuchi patterns and the SAED patterns at large strains confirmed that the portion of high-angle boundaries increased with increasing the number of the pressing passes and that, thereby, they became the dominant structure at the large deformation strain.39

9.2.3 Microstructural evolution of LCS alloy by post-ECAP annealing Annealing behavior of ferrite phase The microstructural changes of ferrite phase in LCS alloy processed by ECAP and post-ECAP annealing treatments are shown in Fig. 9.9. Little grain growth


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9.9 Transmission electron microscopy and optical images showing the annealing behavior of nanostructured ferrite grains in the ECAPed LCS sample annealed for 1 h at various temperatures of (a) 723, (b) 753, (c) 783, (d) 813 K, and (e) 873 K.25

occurred at relatively low annealing temperatures of 693–783 K. As shown in Fig. 9.9 (a), however, the portion of well-defined grain boundaries increased and a considerable annihilation of lattice dislocations was noticed. Several interesting features were noticed in the sample annealed at 753 K (Fig. 9.9 (b) ): 1) slight but notable grain growth took place; 2) most grain boundaries were well defined; 3) in some grains (marked by grain A), dislocation cells were observed; and 4) dislocation density inside individual grains became low. By annealing at 783 K (Fig. 9.9 (c) ), most boundaries became well defined, but their appearance was



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somewhat different from that observed in the sample annealed at 753 K (Fig. 9.9 (b) ). In addition, the existence of a dislocation wall (marked by arrows) was found, but extinction contours remained. These facts indicate that recovery was still in process. At 813 K (Fig. 9.9 (d) ), large, dislocation-free grains were observed and recrystallization was virtually completed at the annealing temperature of 873 K (Fig. 9.9 (e) ). The variation of ferrite grain size in 4 ECAPed LCS sample with annealing temperature is presented in Fig. 9.10. From Fig. 9.10, it is noticed that annealing behavior is different with respect to annealing temperature, resulting in two different regions whose boundary is determined at 783 K. This fact is mainly due to two different mechanisms such as recovery and recrystallization operated during heat treatments. Below 783 K, the microstructural change during annealing showed that a recovery process was dominant and indicated that recovery could be attributed to a process associated with the dissociation of lattice dislocations into extrinsic boundary dislocations during annealing. This finding is consistent with the experimental observation of an earlier high-resolution electron microscopy (HREM) study on an ECAPed aluminum alloy37 showing the existence of a large number of extrinsic dislocations at the non-equilibrium grain boundary region. At this temperature range, the grain size did not increase significantly with increasing annealing temperature. As a first approximation, the grain growth behavior in this regime was examined by applying the general equation for grain growth:

9.10 A grain size variation of ferrite phase with annealing temperatures.25


[9.1]

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where d is the grain size at a given annealing time, d0 is the initial grain size, K0 is a constant, t is the annealing time, n is a constant with a value close to a unity, Q is the activation energy for grain growth and RT has its usual meaning. Using Eq. [9.1], Q can be obtained by plotting (d2–d02) against (1/T) in a semi-logarithmic scale at the same annealing time. Such a plot is depicted in Fig. 9.11 where d0 was taken as ~0.3 µm. The value of the activation energy was calculated to be ~106 kJ/mol. This value was lower than the activation energies for several kinetic processes associated with ferrite grain growth such as volume diffusion (~280 kJ/mol), grain boundary diffusion (~164 kJ/mol) of Fe in alpha-iron,46 grain boundary mobility of pure iron (~147 kJ/mol),47 and carbon diffusion in alpha-iron above 673 K (~141 kJ/ mol)46 Wang et al.48 reported that the activation energy for grain growth of an ECAPed Al-Mg alloy in the unrecrystallized regime was only 20% of that for self-diffusion of pure aluminum. Indeed, activation energy for grain growth in the unrecrystallized regime was ~0.35. This agrees well with the suggestion that nonequilibrium grain boundaries induced by severe plastic straining show higher mobility compared with those subjected to little or less plastic strain.49,50 Above 783 K, the ferrite phase of the LCS sample consisted of an unrecrystallized area and a recrystallized area, resulting in a bimodal grain size distribution. The

9.11 A plot of log (d 2–d02) vs. 1/T for the estimation of the apparent activation energy for grain growth of ferrite phase in the ECAPed LCS samples.25



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activation energy for grain growth in this regime was estimated as ~230 kJ/mol by taking, as a first approximation, the average value of the recrystallized ferrite grain size at each temperature and d0 = 0.3 µm. This value was lower than that for volume diffusion (~280 kJ/mol) of Fe in alpha-iron. However, it is worth mentioning that the estimation of activation energy for grain growth in this regime is less meaningful than that for the regime below 783 K due to the non-uniform distribution of the recrystallized ferrite grain size and the difficulty of determining the initial value of the recrystallized ferrite grain. In conclusion, up to 783 K, the grains were relatively stable and grain growth took place slowly with increasing annealing temperature. Above 783 K, the grains seemed to be unstable, showing a bimodal grain size distribution, i.e. coexistence of coarse grains and nanoscale grains.25,51 Annealing behavior of pearlite structure For the pearlite structure, no significant morphological change was observed below 753 K compared to the as-ECAPed sample (Fig. 9.3). However, the spheroidization of a large portion of cementite started to appear at 783 K (Fig. 9.12 (a) ). The spheroidized cementite particles remained at the initial cementite lamellar domain. In addition, some images of spheroidized cementite particles were not definite but relatively dim and diffused. This indicates that carbon in cementite dissolved locally into the pearlitic ferrite. At the same annealing temperature of 783 K, the dislocation density in pearlitic ferrite remained high compared to that in the ferrite phase (Fig. 9.9 (c) ). At 813 K (Fig. 9.12 (b) ), the microstructure of pearlite consisted of nearly spheroidal cementite particles with an average aspect ratio of ~2 and fine ferrite grains. It is worth noting that, under the same annealing conditions, the size of recrystallized ferrite grains within the pearlite structure was smaller than that in the group of ferrite grains (Fig. 9.9 (d) ); this is mainly due to a grain boundary pinning effect by fine cementite particles.

9.12 Transmission electron microscopy images showing the microstructure change of pearlite in the ECAPed LCS samples annealed for 1 h at various temperatures of (a) 783 and (b) 813 K.25


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As explained above, the spheroidization of cementite was clearly observed above 753 K and nearly completed at 813 K. This result was consistent with the morphological changes of cementite in heavily cold drawn pearlitic steel wire.33 To examine the influence of intense plastic strain on the enhancement of the spheroidization behavior of cementite, the initial sample prior to ECAP was annealed at 783 K and its pearlite structure is shown in Fig. 9.13. Comparison of Fig. 9.12 (a) (ECAPed alloy) and Fig. 9.13 (initial pre-ECAPed alloy), where both alloy samples were annealed under the same conditions, led to the conclusion that the kinetics of spheroidization occurred only in the ECAPed sample. It has been established that, in the case of heavily cold drawn pearlitic steel wire, severe plastic strain leads to enhanced spheroidization of cementite due to relatively easy carbon dissolution from deformed cementite into pearlitic ferrite during bluing treatment.52–55 Gridnev and Garririlyuk56 proposed that easy carbon dissolution during the bluing treatment of heavily cold drawn pearlitic steel wire could be attributed to higher binding energy between dislocations in pearlitic ferrite and carbon atoms than that between the Fe atoms in cementite and the carbon atoms. However, researchers find fault with this suggestion since both binding energies are roughly the same: the former and the latter are 0.55 and 0.50 eV, respectively.57,58 Languillaume et al.59 explained the easy carbon dissolution behavior by suggesting that the driving force for carbon dissolution was increased by an increase in the cementite/pearlitic ferrite interfacial energy due to the formation of slip steps at the cementite/pearlitic ferrite interface during the heavy cold drawing process. In addition, Hong et al.60 suggested that, in the same LCS materials, excessive imperfections would be introduced into cementite

9.13 Transmission electron microscopy image of pearlite in the initial LCS sample without ECAP annealed at 783 K for 1 h.25



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by severe plastic deformation and their existence resulted in a comprised nonstoichiometric cementite composition, facilitating easy carbon dissolution. Accordingly, given that the microstructural change of pearlite in the ECAPed LCS alloy during annealing was very similar to that observed during the bluing treatment of the heavily cold drawn pearlitic steel wire, the enhanced spheroidization of cementite here could be attributed to easy carbon dissolution from cementite into pearlitic ferrite caused by severe plastic deformation of cementite.

9.2.4 Formation of fine cementite precipitates The TEM micrograph of the LCS sample after annealing at 813 K for 1 h presented in Fig. 9.14 reveals a number of spherical cementite precipitations within a pearlite colony. In some of the colonies, depending on their inclinations to the main shear direction, rod-like cementite particles were restored, whereas they successfully transformed into spherical precipitates during the annealing. From the TEM images taken of the annealed sample, the dislocation density was observed to be of the order of 1014 to 1016 m–2, although it was expected that the dislocation density within ferrite grains of the annealed sample would reduced due to the static recovery. As discussed earlier by several researchers,1,61 the decomposition reaction occurred not only during the deformation stage but also during the annealing stage. As such, static annealing of the ECAPed ferrous alloy at 813 K for 1 h would be beneficial for the decomposition of the entire pearlite colonies and the uniform precipitation of cementite particles. This extraordinary phenomenon demonstrates a potential new processing route of forming fine precipitates by

9.14 Transmission electron microscopy image of a spheroidized pearlite colony in the ECAPed LCS sample annealed at 813 K for 1 h.61


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the static annealing of severely deformed steel, instead of the conventional heat treatment route including normalizing, quenching and aging treatment. As the formation energy of cementite is relatively low and the dislocationcementite interaction energy was estimated to be approximately ~0.5 eV,62 the cementite might be decomposed by the interaction with the stress field of dislocations, as indicated in a previous report.60 In the presence of the internal stress field of dislocation, the net number of extra carbon atoms segregated per unit length of a dislocation (N/L) was estimated by the following Eq. [9.2]:63 ,

[9.2]

where C0 is the equilibrium concentration in the matrix, b the Burgers vector of the edge component, ν Poisson’s ratio, G equals E/2(1 + ν), E Young’s modulus, Vs the atomic volume of carbon and Va the interstitial site volume of ferrite steel. As the cementite became nano-sized, the experimentally determined C0 value64 was adjusted using the Gibbs–Thompson relationship.65 For the adjustment, the cementite was assumed to be a sphere of ~20 nm in diameter and has a surface energy of 1 J/m2.66 Using the above equation, the excess carbon concentration (ECC) was calculated as a function of temperature at different dislocation densities (1014–1016m–2). As shown in Fig. 9.15, the ECC value was a strong

9.15 Excess carbon concentration calculated as a function of annealing temperature. The dislocation density changed from 1014 to 1016 m–2.65



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function of the dislocation density and became negligible as the density decreased to less than 1014 m–2. Although the rate constant for the decomposition reaction was not determined, the calculated ECC value, which was 10–20% of the equilibrium concentration, was considered to be large enough for the decomposition reaction to proceed at a reasonable rate. Therefore, a group of high dislocation density might promote the decomposition of the cementite via interaction with the dislocations. For a uniform distribution of cementite particles, the carbon atoms released from the decomposition reaction should diffuse away from the colonies toward ferrite grains and precipitate during the static annealing treatment. On the basis of a microstructural analysis utilizing TEM, the dislocation density in the pearlite colony was much higher than that inside the ferrite grains. As the ECC value was sensitive to the dislocation density as shown in Fig. 9.15, the ECC value in the colony was relatively higher, as compared to that inside the ferrite grain, which would induce a diffusion flux towards the ferrite grains. With the carbon diffused away from the colony towards the ferrite grains of low dislocation density, the grain would became supersaturated with carbon atoms, providing a favorable condition for precipitation.

9.3

The mechanical response of a nanostructured LCS alloy

9.3.1 Mechanical properties Figure 9.16 shows the deformation behavior of the ECAPed LSC alloy with respect to the number of ECAP operations, corresponding to effective strain. The increase in hardness was most pronounced at the first pass and thereafter, the strengthening became less significant for further deformation. This finding is in line with the observation of microstructural evolution that grain refinement was most significant at the first pass. It is also consistent with previous observations reported for various ECAPed materials.14–16 After the initial pressing, the hardening behavior of the ferrite phase was more considerable than that of pearlite. With an increasing number of passes, however, the hardening tendency in both grains was toward saturation. Tensile properties of the ECAPed LCS alloy are shown in Fig. 9.17. The trend of the variation of yield strength and ultimate tensile strength with the pass number agreed with that of the hardness data (Fig. 9.16). It was found that, without the aid of compositional changes, the nanostructured grains could give rise to tensile strength higher than 900 MPa together with reasonable elongation of ~10%. This suggested that, among strengthening mechanisms, inducing a nano-grained structure is advantageous for improving strength without significant loss of ductility.17 Stress–strain curves of the initial, ECAPed and ECAPed-annealed LCS samples are shown in Fig. 9.18, and the values of their tensile properties are listed


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Microhardness, Hv

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9.16 A plot of micro-hardness vs. the pass number for each of the constituent phases of the ECAPed LCS sample.17

9.17 Tensile properties of the ECAPed LCS samples with increasing number of operation.17

in Table 9.1. Particular attention should be paid to strain hardening behavior. The initial samples exhibited moderate strain hardenability with large uniform ductility after Lüders strain, whereas the as-pressed and annealed samples exhibited no strain hardening behavior, a general feature of nanostructured metals reported



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9.18 Engineering stress–strain curves of the initial, ECAPed, and ECAPed-annealed LCS samples.18

Table 9.1 Ferrite grain sizes and tensile properties of the LCS samples Treatments

d (µm)

YS (MPa)

UTS (MPa)

ef (%)

As-received As-ECAPed ECAP + Annealed at 753 K for 72 hrs

30 0.2 ~ 0.3 0.45

310 937 683

480 943 720

29.9 10.9 20.2

previously.25,27,39,61 Depending upon the annealing condition, however, this strain hardenability was successfully restored with a sacrifice of strength.

9.3.2 Deformation mechanism Ultra-high strength Similar to the case of other nanostructured metals, the tensile deformation behavior of the nanostructured LCS alloy was characterized by the absence of strain hardening as well as ultra-high strength. Since the nanostructured LCS samples exhibited negligible strain hardening, their ultra-high strength could not be explained solely by the dislocation pile-up mechanism. However, as noted by Valiev et al.,50 the


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dislocation bow-out model, which was used to explain the mechanical behavior of nanostructured materials, is applicable. In the context of the dislocation bow-out model,67,68 yielding occurred when the dislocation configuration reached a semicircle and the critical stress for this condition was approximated by the following expression: ,

[9.3]

where G is the shear modulus, b is the Burgers vector, ν is Poisson’s ratio and L is the average dislocation length. For grain size larger than 100 nm, L was equivalent to ρ–½ where ρ is the dislocation density.69 With the aid of Eq. [9.3], the yield stress of nanostructured materials could be expressed as: ,

[9.4]

where σ0 is the friction stress and M is the Taylor factor. Using equations [9.3] and [9.4], the yield strength of ferrite phase in the ECAPed LCS sample was estimated as 728 MPa with the following values: G = 78 GPa, b = 2.48 × 10–10 m, ρ = 1015 m–2, ν = 0.33, M = 2.78 for bcc structure, and σ0 = 76 MPa.8 Although there existed some variation in dislocation density when TEM was used, the use of the value of 1015 m–2 does not appear to be erroneous since ρ for several nanostructured materials by the ECAP process was reported to be on the order of 1015 m–2.7,49 It is also important to consider that the LCS sample consisted of ~85% of ferrite phase with the remainder being pearlite phase. Hence, the yield stress of the ECAPed LCS sample could be approximated by the rule of mixture: ,

[9.5]

where V is the volume fraction and the superscripts f and p denote ferrite and pearlite, respectively. Due to a lack of reliable data on the application of ECAP to high-carbon steel consisting of a fully pearlite structure, σ ysp should be deduced from that of a cold drawn pearlitic steel. Under the same amount of effective strain, σ ysp of the heavily drawn pearlitic steel was in a range of 1800–2000 MPa.34 Our estimation showed a yield stress of 850–880 MPa, which was still lower than obtained above (937 MPa). Valiev et al.49 also used the dislocation bow-out model to predict the strength of nanostructured pure copper at ambient temperature. They argued that some deviation of the estimated value based on dislocation bowout from the experimental value could be attributed to 1) the actual dislocation density and 2) the supplementary effect of internal stress. A lack of strain hardenability: dynamic recovery As shown in Fig. 9.18, the nanostructured LCS sample exhibited no strain hardening under tension deformation. The absence of strain hardening in ultrafine grained (UFG) steels was examined in terms of dynamic recovery. During



265

tensile deformation, dislocations causing intragranular strain are trapped at the grain boundaries if no strong obstacles for lattice dislocation motion existed inside the grains. The kinetics of dynamic recovery is closely related to the spreading of trapped lattice dislocations (TLDs) into the grain boundaries.49,70,71 The change of dislocation density owing to dynamic recovery by TLD spreading into the grain boundaries could be described by the following generalized equation

[9.6]

. where ρ is the dislocation density, t is the time, α is a constant, ε is the strain rate, b is the Burgers vector, d is the grain size and ξ is the characteristic time for TLD spreading into the grain boundaries. At steady state deformation, i.e. (∂ρ/∂t) = 0:

[9.7]

For the ECAPed sample, ξ was ~21 s with ρ = 1015 m–2, b = 2.48 × 10–10 m, . d = 0.25 × 10–6 m, α = 2.4 and ε = 1.33 × 10–3 s–1. The deformation time to reach the maximum point in stress was ~22 s. Therefore, lattice dislocations contributing to intragranular strain were trapped at interfaces, and they subsequently spread into the grain boundary concurrently during deformation. As a result, there is no accumulation of lattice dislocations and, consequently, no strain hardening is expected. For a sample annealed at 753 K for 72 hrs, the dislocation density decreased by several orders of magnitude, but the ferrite grain size increased only by a factor of 2. In this case, the value of ξ decreased drastically but the deformation time became more prolonged due to the larger elongation. Accordingly, it was natural that strain hardening was observed to some extent in the sample annealed at 753 K for 72 hrs.18,19 A lack of strain hardenability: mean free length of dislocation Figure 9.19 shows the dislocation distribution observed in tensile-deformed steel without ECAP (d = 30 µm) at different strain levels. Prior to the tension test, the dislocation density was relatively low (Fig. 9.19 (a) ); but after 5% deformation (Fig.9.19 (b) ) the dislocations were distributed randomly inside grains with high density. A dislocation cell structure with an average diameter of 0.35 µm was formed at the engineering strain of 15% (Fig. 9.19 (c) ). The tensile deformed microstructure of the steel annealed at 753 K for 72 hrs after ECAP is shown in Fig. 9.20. Most ferrite grains in the ECAP-deformed sample were elongated (Fig. 9.20 (a) ), indicating that considerable intragranular strain was induced during deformation. In addition, an inspection with higher magnification (Fig. 9.20 (b) ) revealed that the dislocations were not distributed uniformly inside the grains but were localized in the vicinity of the grain boundaries.


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9.19 Transmission electron microscopy images showing the distribution and density of lattice dislocation in tensile-deformed LCS sample without ECAP at different strain levels: (a) before testing, (b) e = 5% and (c) e = 15%.18

9.20 (a) Transmission electron microscopy image showing tensiledeformed LCS sample annealed at 753 K for 72 hrs after ECAP and (b) magnified image of the same sample showing dislocation distribution near to grain boundaries.18

At the initial stage of plastic deformation, the dislocation density increased and its distribution was relatively uniform at the grain interior, causing strain hardening. As plastic deformation proceeds, a dislocation cell structure was formed due to dislocation entanglement. Under these conditions, the cell size was equivalent to



267

the mean free dislocation length (L).72 The mean free dislocation length was inversely proportional to the shear stress (τ).

[9.8]

The cell size at different stress levels could then be approximated by the following simple relationship for the same material:

[9.9]

With the cell size (δ1 = 0.35 µm) measured from the deformed sample without ECAP and the stresses inferred from Fig. 9.18, the cell size (δ2) of the other sample is estimated from Eq. [9.9] and listed in Table 9.2. In the estimation, the engineering stress in Fig. 9.18 was converted to the corresponding shear stress by the generalized relationships. Two findings are noted from Table 9.2. First, for the ECAP-deformed sample annealed at 753 K for 72 hrs, the measured cell size, 0.35 µm, is almost identical with that estimated from Eq. [9.9], 0.24 µm, thus demonstrating the validity of Eq. [9.9]. Second, the ferrite grain sizes of nanostructured LCS samples were comparable to the estimated cell sizes within a factor of 2 at the corresponding stress levels. The negligible strain hardening during tensile deformation of the nanostructured LCS sample could be attributed to the mean free dislocation length at the corresponding stress level being comparable to the ferrite grain size. Consequently, dislocation entanglement largely took place at the grain interior of nanoscale grains, thus affecting strain hardenability. In coarse-grained LCS materials, the equiaxed dislocation cells were not subjected to shape changes even at relatively high strains. This indicates that the cell formation occurred continuously during deformation, implying that the cell formation is a kind of relaxation process that causes a reduction in the strainhardening rate.73 The uniform distribution of lattice dislocation with high density

Table 9.2 Dislocation cell sizes calculated by Eq. 1.9 and ferrite grain sizes of the LCS samples

τ1

τ2

As-received

276

δ1

δ2

0.35

δ

Remarks

30

Strain hardening

As-ECAPed 486 0.20 0.2 ~ 0.3

Weak strain hardening

ECAP + Annealed 396 0.24 0.45 at 753 K for 72 hrs

Slight strain hardening


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at the initial stage of deformation, but with further deformation, it changed into a cell structure consisting of hard and soft regions. For the cell structure the hard region is the cell wall region with tangled dislocations while the soft region is the dislocation-free cell interior. In nanostructured materials, the TLDs at the grain boundaries, one of the relaxation processes, occurred at the onset of plastic deformation without a uniform distribution of lattice dislocation, since the grain size is comparable or even smaller than the mean free dislocation length. This analysis indicates that the strain-hardening rate would be negligible during plastic flow of nanostructured metallic materials, but the hardening rate would be restored with post-ECAP annealing.

9.4

Enhanced tensile properties by grain refinement and microstructural modification

9.4.1 LCS alloy containing vanadium carbides Since strain-hardening characteristics rapidly diminish with a decreasing of grain size down to a nanometer level, we introduced fine vanadium carbides to the nanostructured LCS sample in order to alleviate the inherent mechanical drawback discussed above. A LCS sample with an addition of 0.34 wt% vanadium was prepared and deformed by ECAP with the same working conditions. Details of the procedures have been described elsewhere.20 As indicated by the arrows in Fig. 9.21 (a), nanoscale precipitates of 5–10 nm were observed at the area of high dislocation density in the ECAPed LCS sample, which did not contain precipitates prior to ECAP operation. These precipitates formed during ECAP at 623 K were identified as V3C4 by an energy dispersive spectra analysis (Fig. 9.21 (b) ). The precipitates are believed to have originated from strain-induced precipitation,

9.21 (a) Transmission electron microscopy image showing the existence of nanoscale vanadium carbides at the area of high dislocation density in the ECAPed LCS sample and (b) qualitative chemical analysis of them.20



269

where nucleation sites are the heterogeneous regions such as dislocations of high density formed by ECAP.

9.4.2 Dual-phase LCS alloy Within the framework of strain gradient plasticity, two different kinds of dislocations played different roles on plastic deformation; that is, statistically stored dislocations influence deformation itself, whereas geometrically necessary dislocations (GNDs) operate for strain hardening.74 Among a variety of ferrous alloys, a dual phase structure consisting of ferrite and martensite is a representative structure having a large number of GNDs. It is well established that the excellent strain hardenability of dual phase steel is mainly due to the existence of glissile dislocations newly formed during intercritical annealing followed by water quenching after ECAP.75–79 These dislocations, which have been observed at ferrite grains close to martensite, act as GNDs, making it possible to achieve high strain hardenability.80 Details of processing conditions can be found in Ref.81 As shown in Fig. 9.22 (a), the microstructure of the nanostructured dual-phase steel consisted of equiaxed ferrite grains (0.8 µm in size) and martensite grains (0.9 µm in size). Both ferrite grain size and martensite island size were found to have a submicrometer scale and the volume fraction of martensite was about ~30%. A SEM micrograph with higher magnification (Fig. 9.22 (b) ) revealed that the martensite ('M' in Fig. 9.22 (b) ) was in an isolated blocky type82 and existed in minute quantities at ferrite/ferrite boundaries. Again, a nanostructured dual phase microstructure with a uniform distribution of each constituent phase could be attained by three distinctive steps associated with thermo-mechanical treatment. First, during ECAP, carbon atoms from pearlitic cementite were dissolved and, thereby, diffused toward ferrite phase grains. This uniform distribution of equilibrium/excessive carbon atoms allowed an austenite phase to form uniformly during intercritical annealing. During water quenching, austenite grains were

9.22 Scanning electron microscopy images of (a) the nanostructured dual-phase steel and (b) nanostructured dual-phase steel with higher magnification.81


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transformed into martensite islands, generating a number of mobile dislocations in ferrite grains adjacent to martensite by volume expansion. Tensile testing of the nanostructured dual phase steel showed that, unlike most nanostructured materials that show a poor strain-hardening rate, the dual phase exhibited a good combination of high strength and ductility (extensive strain hardenability). This demonstrates that strain gradient plasticity has a high potential to enhance the strain hardenability of nanostructured materials.

9.5

Continuous shear drawing: a new processing method

Although severe plastic deformation of metals and alloys utilizing ECAP has recently been regarded as a promising method for tailoring nanostructure as well as decomposing lamellar or dendrite structure, the batch process of ECAP generated a technical problem, which limits its actual applications. Thus, one of the approaches currently being considered to develop a method that is suitable for the continuous processing is the use of equal-channel angular drawing (ECAD), where samples are deformed in a drawing fashion instead of pressing, as the length of sample would likely no longer be limited by the buckling instability during deformation.83–86 However, Luis et al.,86 based on finite element method (FEM) calculations, validated what was found by actual experiments, that the deformation of ECAD is inevitably accompanied by both appreciable corner gap and severely localized necking. This is presumably due to the fact that the deformation is more dominated by drawing than by shearing when the sample passes through the shear plane. We suggested a new type of ECAD termed continuous shear drawing (CSD) in conjunction with an effort to modify the design of the die in order to avoid dimensional inhomogeniety of the sample during deformation. According to an upper bound analysis84 and FEM results,85 the use of ECAD clearly caused unstable deformation of a number of fine meshes when the inner angles became less than 120°. As shown in Fig. 9.23, a die with an inner angle of 135° was designed to avoid the formation of pronounced necking, which is noxious to further deformation. A CSD die was also prepared by reducing the diameter of the exit channel so as to impose higher strain compared to ECAD. Considering the reduced geometry of the exit channel, an additional strain was imparted to samples when the samples experienced one passage. The total effective stain (εT) accumulated from the CSD process was the sum of the shear strain87 and the drawing strain: ,

[9.10]

where φ, li and lf are the half of inner angle in die and the initial and the final diameters of sample, respectively. The annealing behavior of three different samples with no deformation, drawing and CSD is shown in Fig. 9.24 (a). The annealed sample without deformation



271

9.23 Schematic description of the proposed die used for CSD technique.

9.24 Scanning electron microscopy images showing spheroidization behavior at a subcritical temperature of 973 K (a) for 10 hrs in sample with no prior deformation, (b) for 5 hrs in sample deformed via conventional drawing and (c) for 1 h in sample deformed via CSD method.

shows remnant thin-striped cementite phases. The other samples deformed via drawing and CSD methods required 5 hrs and 1 h, respectively in order to achieve a uniform microstructure with fine cementite (Fig. 9.24 (b) and 9.24 (c) ). From these results, the CSD method is thought to possess a commercial potential for


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use as an intermediate step of wire manufacture, as it could reduce annealing time by promoting the rate of spheroidization of the pearlitic-cementite phase. Moreover, as compared to the result yielded by conventional drawing, the use of the CSD technique combined with an annealing treatment led to a microstructure having fine cementite dispersed uniformly in the ferrite matrix due to straininduced spheroidization.

9.6

Conclusion

The change in microstructure and the variations in tensile properties of nanostructured LSD alloy fabricated by ECAP together without/with various post-ECAP annealing treatments have been reviewed. The grain refinement of LSD alloy was achieved by grain subdivision due to the operation of multiple slip systems of {110}, {112} and {123}. A comparison between the ferrite grain size of a nanostructured LCS sample and the dislocation cell size of its coarse-grained counterpart formed during tensile deformation revealed that the cell formation was unlikely to occur in the former, thus implying that the low strain hardening rate could be attributed to two factors: dynamic recovery and nanoscale grains comparable to the mean free length of dislocations. First, the feasibility of enhancing the strain hardenability of the nanostructured LCS sample was explored by comparing the microstructure and stress–strain behavior of two LCS samples without/with vanadium carbides. Second, the strain hardening behavior of a dual-phase steel via both ECAP and intercritical annealing followed by water quenching was investigated. In addition, we developed a continuous approach based upon CSD in which shear and drawing deformation are conjugated. It appears that the use of CSD would be advantageous for achieving a microstructure incorporating fine cementite particles, which are dispersed uniformly throughout the matrix due to strain-induced spheroidization.

9.7

References

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10 Characteristic structures and properties of nanostructured metals prepared by plastic deformation X. HUANG, Technical University of Denmark, Denmark Abstract: This chapter focuses on describing the characteristic microstructures of nanostructured metals produced by plastic deformation to ultrahigh strains and their correlation with hardening by annealing and softening by deformation. The results suggest that optimising microstructure and the mechanical properties of nanostructured metals can be achieved by a combination of post-process heat treatment and deformation. Key words: nanostructured metals, transmission electron microscopy (TEM), boundary spacing and misorientation, dislocation density, unusual mechanical behaviours.

10.1 Introduction Nanostructured metals produced by plastic deformation to ultrahigh strains constitute a special class of nanomaterials with characteristic microstructures and properties. Over the last decades progress has been made in many areas: • New processes have been introduced, such as high-pressure torsion (HPT), equal-channel angular pressing (ECAP), and accumulative roll bonding (ARB), which enable the researcher to impose extremely high strains to a metal without change in the sample geometry. • Characteristic microstructural parameters and their distribution have been quantified including grain size, boundary misorientation and dislocation density. • Characteristic mechanical properties have been analysed such as strength, tensile ductility, strain rate sensitivity and flow instabilities, and the effect of post-process annealing and deformation on these properties. • Strengthening mechanisms and the relationship between microstructural parameters and mechanical properties have been explored. • New approaches for optimising mechanical properties by manipulating the microstructure have been investigated. Some of these areas are reviewed and discussed in other chapters of this book. This chapter will focus on characteristic microstructural parameters in nanostructured face-centred cubic (fcc) Al and body-centred cubic (bcc) interstitialfree (IF) steel produced by ARB at room temperature and 500°C, respectively, and fcc Ni produced by HPT at room temperature. The compositions of these metals 276 © Woodhead Publishing Limited, 2011

Characteristic structures and properties of nanostructured metals

277

Table 10.1 Chemical composition of a commercial purity Al (JIS1100) (mass%) Si 0.11

Fe 0.55

Cu 0.11

Mn 0.01

Mg 0.02

Ti 0.02

B 0.0007

V Ni Al 0.011 0.003 Bal.

Table 10.2 Chemical composition of an IF steel (mass%) C 0.002

N 0.003

Si 0.01

Mn 0.17

P 0.012

Cu 0.01

Ni 0.02

Ti 0.072

Fe Bal.

Table 10.3 Chemical composition of a commercial purity Ni (mass%) C Si Mn P S Cr Fe Al Co Cu Ti Mg Ni 0.006 0.003 0.015 0.025 0.001 0.001 0.44 0.004 0.035 0.012 0.002 0.003 Bal.

are shown in Tables 10.1–10.3. Then the correlation between microstructural characteristics and mechanical properties is discussed with an emphasis on recent observations of unusual mechanical behaviours. The observations and analyses lead to suggestions for new approaches for optimisation of microstructure and properties of nanostructured metals.

10.2 Characteristic microstructures 10.2.1 Microstructural parameters The key microstructural parameters characterising nanostructured metals are microstructural morphology, spacing between boundaries, misorientation across boundaries, fraction of high-angle boundaries, and density of dislocations present in dislocation boundaries (15°) are listed in Table 10.4. Similar bimodal distributions have also been reported for the nanostructured pure Al produced by cold rolling3 and ECAP 14–16 and the relationship between the boundary angle distribution and the evolution of microstructure and texture during deformation to large strain has been analysed.17 Within the volume between the boundaries, the presence of individual dislocations



279

10.1 (a) Transmission electron microscopy image showing a lamellar structural morphology and dislocation configurations in the nanostructured Al (JIS1100, 99.2% pure) processed by six-cycle ARB to εvM = 4.8. (b) Histogram showing the distribution of boundary misorientation angles.13 Table 10.4 Structural parameters of nanostructured commercial purity Al 1100 (99.2%) and IF steel processed by non-lubricated ARB to 6 cycles19 Material

dt(nm) dl(nm) dl /dt

Al (JIS1100) 180 IF Steel 210

600 620

3.3 3.0

θav (°) f(θ ≥ 15°) (%) t(θ < 3°) (%) ρ0(m–2) 27.3 24.2

66.3 59.8


17.5 15.7

1.3 × 1014 6.3 × 1013

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and dislocation tangles is observed. Sample tilting in the TEM confirmed that almost all lamellae contain dislocations although the dislocation density varies from lamella to lamella. The average dislocation density was measured to be about 1.3 × 1014 m–2.18

10.2.3 Nanostructured interstitial-free (IF) steel by ARB Figure 10.2 shows the TEM microstructure and the misorientation angle distribution for an IF steel (see Table 10.2) processed by ARB at 500°C for six cycles.19 The microstructure exhibits a lamellar morphology, Fig. 10.2 (a), similar to that observed in the nanostructured Al sample (Fig. 10.1 (a) ). The presence of loose dislocations and dislocation tangles in the volume between the lamellar boundaries is also clearly seen in the micrograph. Figure 10.2 (b) illustrates a bimodal distribution of misorientation angles, resembling that obtained in

10.2 (a) Transmission electron microscopy image showing a lamellar structural morphology and dislocation configurations in the nanostructured IF steel processed by six-cycle ARB at 500°C to εvM = 4.8. (b) Histogram showing the distribution of boundary misorientation angles.19



281

10.2 Continued.

the nanostructured Al (Fig. 10.1 (b) ). The average spacing between the lamellar boundaries and interconnecting boundaries and the density of loose dislocations are given in Table 10.4.

10.2.4 Nanostructured Ni by high-pressure torsion (HPT) The microstructure in a commercial purity Ni (99.5% pure, see Table 10.3) processed by HPT up to a strain of 300 has been analysed in detail by TEM.6 The TEM results were obtained from the longitudinal section parallel to the torsion axis (see Fig. 10.3) rather than from the torsion plane as investigated in previous studies.20,21 Figure 10.3 shows the microstructure at a strain of 8.7. A typical lamellar microstructure is seen, where the lamellar boundaries are nearly parallel to the torsion plane (±10°). In the volumes between the lamellar and interconnecting boundaries, dislocation clusters and individual dislocations can be observed. These types of microstructural features are maintained at higher strains up to 300, as shown in Fig. 10.4. However, with increasing strain, the lamellar boundaries sharpen and decrease their width. There is a clear tendency for the microstructural morphology to be more equiaxed at extremely high strains (see Fig. 10.4(b) ) while maintaining some directional appearance characteristic of microstructures at lower strains. In addition to the lamellar boundaries, interconnecting boundaries and loose dislocations, two new microstructural features, namely small equiaxed crystallites (Fig. 10.5(a) ) and deformation twins (Fig. 10.5(b) ), were also observed in samples deformed to strains ≥12. The equiaxed crystallites are isolated in the microstructure: they form at triple junctions and are in general surrounded by high-angle boundaries. The sizes of these equiaxed crystallites range from


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10.3 (a) A schematic drawing showing the sampling for TEM observation. (b) Transmission electron microscopy micrograph showing a typical lamellar structure formed in pure Ni deformed by HPT to εvM = 8.7. The shear direction is marked by the double arrows.6

30–130 nm. The deformation twins are in general only 10–50 nm wide and they are inclined with respect to the lamellar boundaries (Fig. 10.5 (b) ). The total volume fraction of equiaxed crystallites and deformation twins is quite low ( φ, can be described as:

[11.13]

where m is the Taylor factor, G the shear modulus, b the Burgers vector and λ the separation of particles on the shear plane.84 The parameter λ is related to particle size as λ = φ / √ f. Since particles tend to pin grain boundaries, for materials in quasiequilibrium after preparation by annealing (for powder consolidation, precipitation, coarsening, etc.) grain size and particle size are related, for example by the Zener relation, d = 0.66 φ/f, and hence grain size and particle separation are related:

[11.14]

As such, it is clear that Orowan strengthening models can only be used for materials containing a small volume fraction of second-phase particles, say less than 10%, and then the model applies independently of the grain size, nanoscale to microscale. Figure 11.5 shows an analysis of strengthening in copper alloys containing secondphase particles,84 where strength is related, via equation 11.13, through the Orowan mechanism. A good description of the particle strengthening, i.e. σOR proportional to {1/(λ–φ).ln(φ /2b)}, is seen down to particle sizes of about 7 nm. Figure 11.6 shows some microstructures of these deformed particle-strengthened copper materials, where particle-dislocation interaction is clear. Since particle size can be related to grain size, equation 11.14, the strengthening may be re-expressed in terms of grain

11.5 Analysis of strengthening in Cu-bcc particle materials in terms of the Orowan strengthening model, see text for details. Source: Morris and Morris.84


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11.6 Transmission electron micrographs illustrating dislocation– particle interactions in Cu-bcc particle materials of fine grain size. Source: Morris and Morris.84

size, by the Hall–Petch equation (equation 11.1, σ y = σ0 + k d –1/2) with relatively good agreement found. The numerical value of the Hall–Petch slope, k, is 0.28 MPa√ m, however, much greater than the accepted values for a Cu matrix.85,86 This analysis confirms that the major strengthening is due, in this case, to the particles present, and grain boundary strengthening is less important. A quantitative evaluation of Hall–Petch strengthening (equation 11.1) and Orowan hardening (equation 11.13), making use of the particle–grain size relation (equation 11.14) confirms that Orowan particle strengthening will dominate strengthening in Cu for particle sizes below about 20 nm and grain sizes below about 200 nm (for material with 5–10% second phase). The slower strengthening observed in Fig. 11.5 as the second-phase particles refine to very fine sizes (the near saturation in Fig. 11.5) may be due to particles shearing or to the loss of a homogeneous particle distribution with many particles trapped at the grain boundaries. Another study examined hardening in nanocrystalline FeAl alloys and related strength to grain size87,88 (Fig. 11.7), with data characterised by exactly the same


Strengthening mechanisms in nanocrystalline metals

317

Hall–Petch slope as Fe (Fig. 11.1). These materials also contained fine Al2O3 particles, from oxidation during powder milling and during hot consolidation to solid material. The oxide particles are very fine here, less than 3 nm (see Fig. 11.8) and dislocations propagate with little effort since, presumably, they can shear the weak particles. Oxide particle coarsening on heat treating this material leads to initial strengthening, before softening through particle and grain coarsening – this evolution is indicated by the sequence of arrows in Fig. 11.7. More significant hardening has been produced in FeAl intermetallic by the addition of 30%TiC to the material, as indicated by the high-pressure data in Fig. 11.7.89–91 These materials retained fine grain size, 20–30 nm, after high-temperature, high-pressure

11.7 Hardness of several FeAl materials related to grain size by the Hall–Petch relationship. Data points connected by arrows indicate the hardness evolution on ageing, as oxide precipitates form.88 Highest hardness is achieved after high pressure, high temperature consolidation of FeAl-TiC composites.89–91

11.8 Transmission electron micrograph illustrating dislocation–particle interactions (arrowed) in FeAl.88


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consolidation, but hardness can no longer be analysed by the Orowan model since both FeAl and TiC are of similar size and the material should be considered as a composite with mixed grains of the two phases. When second-phase particles are present in large volume proportion (>10%) or the particles have a similar or larger size than the matrix grains, it is better to analyse material and hardness as a composite, where the rule of mixtures provides a good description (hardness is an area or volume-adjusted average of the hardness of the components). He and Ma92 examined hardness in Cu-Fe composites, with an Fe content between 15 and 90%, and grain sizes of 25–45 nm for both phases, to find material hardnesses significantly greater than expected from the rule of mixtures, considering nanocrystalline Cu and nanocrystalline Fe. They concluded that the bcc–fcc interphase boundaries were much stronger than usual grain boundaries in either single phase Cu or single phase Fe. On the other hand, in studies on materials of Cu matrix and bcc second-phase additions,93,94 the hardness observed for mixtures with Cu grain sizes between 10 and 60 nm fit well to the Hall–Petch relationship with a good value for the slope, k (0.16 MPa√ m). In these cases, however, the volume fraction of bcc phase was small (5–10%) and bcc particles were somewhat larger than the Cu grain size, such that most boundaries present were standard fcc–fcc grain boundaries, and only few were bcc–fcc interphase boundaries. Guduru et al.13 also studied Fe mixed with Al2O3 and analysed hardness in terms of the rule of mixtures. This was justified since the Fe matrix grain size was about 10 nm but the Al2O3 particles about 50 nm. The experimental hardness was much greater than predicted by the rule of mixtures, see Fig. 11.9, and it was

11.9 Hardness of Fe milled with Al2O3 and with Pb, indicating that the data do not fit to the composite rule of mixtures.13 © Woodhead Publishing Limited, 2011


319

argued that the much harder Al2O3 particles created a local heavily work-hardened zone in the neighbouring Fe grains due to the large number of geometrically necessary dislocations that formed there during deformation. While most attention is given to strengthening by second-phase additions, and large second-phase particles seem generally associated with poorer ductility, there is some evidence that correctly sized and distributed second-phase particles might improve ductility. Dutta et al.95 found that spherical second-phase particles of size slightly smaller than the matrix grain size, arranged on grain boundaries, might improve ductility by homogenising strain distribution during deformation. Finally, reiterating Koch,96 relatively little has been studied about the role of second-phase particles in affecting strength, toughness and ductility of nanocrystalline materials. There appears to be ample scope for improvement, and this area is one worthy of further investigation.

11.7 Strengthening caused by other factors: solute, order, twin boundaries There are few studies that explicitly examine the role of solute or order of the nanocrystalline matrix in affecting mechanical behaviour. Guduru et al.13 examined nanocrystalline Fe-Pb mixtures prepared by milling, using X-ray diffraction to confirm that the Pb had been dissolved. The disappearance, following milling, of diffraction peaks corresponding to Pb is insufficient, as such, to confirm Pb dissolution since X-ray diffraction is insensitive to the presence of small amounts of second phase present as fine particles. At the same time, however, the researchers observed a significant displacement of the matrix reflections, confirming the likely solution of up to about 5% Pb. Similar results on Pb dissolution during milling have also been observed by other researchers, see13 for details. Fig. 11.9 shows the evolution of hardness with Pb addition, with a large increase with the 5% Pb addition. Hardness would be expected to fall if the Pb were present as secondphase particles, according to the composite rule of mixtures, indicated in Fig. 11.9. Examination of expected hardening by the large Pb atoms in the Fe matrix according to the Fleischer solution-hardening model showed, however, that even greater hardening should be expected. The authors speculated that the Pb atoms were not all uniformly distributed in solution and that some Pb could be present as segregation at grain boundaries or as sub-nanometric clusters, too small to be detected by standard diffraction methods. Preparation of nanomaterials by milling techniques often leads to disordering of many intermetallics,97,98 which can modify mechanical behaviour. For nanocrystalline FeAl, subsequent annealing at 150–250°C leads to reordering87,88,98 but, as indicated in Fig. 11.7 by the arrows showing hardness evolution on annealing, there is no noticeable hardness change during this re-ordering.88 One possible explanation is that the super-partial dislocation separation is so large for many such intermetallics that it is similar to the


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nanocrystalline grain size and deformation is then accomplished by the partial dislocations that characterise the disordered matrix, somewhat analogous to the operation of partial dislocation sources (Shockley dislocations or twinning dislocations) suggested by molecular dynamics modelling. Finally, while the theoretical models (Hall–Petch/Core-and-Mantle/Molecular Dynamics) do not clearly explain the role of solution additions on hardening, the evolution from a single perfect dislocation source to a single partial dislocation or twinning dislocation source, however, is clearly eased by alloying to lower stacking fault energy. Improved strength is found also with finely spaced twins introduced by electrodeposition99 or by rapid straining, especially at low temperatures100–102 in materials with low stacking fault energy. Such twin strengthening can be found in grains of any size with the strengthening now determined by twin spacing instead of grain boundary spacing.99 A significant advantage of nanospaced twin boundaries appears to be that ductility or toughness can remain high at the same time as strengthening is achieved.101,103 Twins appear to act as barriers to dislocation slip operating in the parent grain, in much the same way as grain boundaries, requiring new slip activation in the twinned region or the parentoriented region found behind the subsequent twin boundary.104 Strengthening should then be described by the same formulation as for grain boundaries, such as the Hall–Petch approach. An alternative approach is to consider the twinned regions, which have nanoscale thickness determined by the close spacing of the pairs of bounding parent–twin interfaces, as hard regions of a composite, and then the overall material strength is given by a composite model of mixed hard and soft regions.101 The low-energy, coherent twin boundaries appear, however, to be able to spread stress concentrations much more than occurs at grain boundaries, and hence are not the sites for crack or cavity nucleation as are grain boundaries or their triple points. This ability to suffer plastic deformation and store dislocations means also that the twin-strengthened materials possess some work hardening,101,103 more than for nanoscale grainboundary-strengthened materials, which is a second reason for the improved ductility of these materials.

11.8 Strengthening mechanisms in materials with ultrafine microstructure prepared by severe plastic deformation Techniques of severe plastic deformation have been developed over the past about 20 years and shown to lead to microstructural refinement, towards the nanoscale, and to significant strengthening.105,106 Techniques such as Equal-Channel Angular Pressing (ECAP) and High-Pressure Torsion (HPT) have been used to impose strains to of the order of (true strain) and above 100 for ECAP and HPT, respectively. Submicron or nanostructures can eventually be achieved at very high



321

strains in materials where recovery is slow or where multiple phase components impose strong microstructural refinement. At the relatively low strains (2–8) generally achieved by the popular ECAP technique, however, the microstructure is composed of random dislocations within dislocation cell walls or low-angle grain boundaries (LAGB), contained within a smaller density of grain boundaries, or high-angle grain boundaries (HAGB). For example, deforming Al or Cu by ECAP to strains of 1–2 produces elongated dislocation cells; deforming to strains of 4 produces more equiaxed dislocation cell/subgrains; while deforming to strains of 10 produces microstructures of scale about 100–500 nm, where 50–70% of the boundaries have misorientations above 15°, i.e. are defined as HAGB.105–107 Gubizca et al.108 obtained similar dislocation cell structures in Al and Al-Mg alloy of size about 250–75 nm, respectively, after deforming to a strain of 2–8, where a dislocation density of 2 × 1014 – 2 × 1015/m2, respectively, was measured. Similar structures are obtained in Fe and FeAl intermetallics,109,110 where dislocation cellular structures are obtained after strains below 10, and nanocrystalline structures after strains above 100 imposed by HPT. After strains of about 3, the microstructure shows many randomly arranged dislocations inside a dislocation cell structure of size 200 nm with an average misorientation of 10° and 15% of boundaries being HAGB. A histogram of the distribution of boundary misorientations in this material, FeAl rolled to a strain near 3, is illustrated in Fig. 11.10. Various explanations of strengthening during such severe plastic deformation have been proposed. Valiev et al.109 argued that strengthening was caused by the many grain boundaries, i.e. by Hall–Petch strengthening, after heavy deformation

11.10 Histogram showing distribution of boundary misorientations in Fe3Al rolled to a true strain of 3.3. Analysis by Electron Back-Scatter Diffraction in a Scanning Electron Microscope. Source: Adapted from Morris et al.110


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to a nanocrystalline state. Gubizca et al.,108 however, related strengthening (∆σρ), through the Taylor equation, to the measured dislocation density (ρloose) as:

[11.15]

where α is a factor of value about 0.3, M the Taylor factor, G the shear modulus, and b the Burgers vector. Leseur et al.111 examined milled Fe and argued that a Hall–Petch dependence of hardening, i.e. ∆H α 1/√ d, could be expected for grain size d above 1 µm, but a subgrain size dependence, i.e. ∆H α 1/d, for cells or subgrains smaller than 1 µm, i.e. about 50–1000 nm. In addition, they noted that hardening could be increased by nanosized oxide particles introduced during milling. Hansen85,86 has discussed how dislocation cell boundaries can be regarded essentially as additional dislocations, producing Taylor hardening, by converting cell boundary area and misorientation into equivalent dislocation density, ρeff. This approach seems reasonable but does not take complete account of the interaction of dislocation stress fields of closely spaced dislocations of different types, which will partially annihilate and reduce overall effectiveness as a barrier. With this approach, the strengthening from dislocation cell boundaries (LAGB) can be written:

[11.16]

with ρeff = Svθ/b = 3θ/dcb, and hence:

[11.17]

where ρeff is the effective dislocation density inside cell walls, Sv the surface area of boundaries per volume, θ the boundary misorientation, and dc the cell size. Note that equation 11.17 has the same dependency of strengthening on reciprocal square root of size as the Hall–Petch equation, with the effective Hall–Petch slope given by kcell = MαG√ (3θb). For small-cell boundary misorientations, the boundaries are much weaker than usual grain boundaries, but for misorientations reaching about 15° the value of kcell is approximately that of kH-P, justifying the common consideration that this misorientation marks the distinction between LAGB and HAGB. Based on these arguments, the strength of a moderately deformed material should be seen as the sum of matrix friction stress σ0, including any particle or solution terms, a loose dislocation term ∆σρ taking account of dislocations inside cells, a dislocation cell term ∆σcell, and a Hall–Petch term ∆σHP taking account of HAGB strengthening, thus:

[11.18]

An analysis of strengthening in heavily rolled Fe3Al as strain level increases is shown in Fig. 11.11, where the dislocation hardening term ∆σρ and the



323

11.11 Analysis of hardening taking place during heavy rolling of Fe3Al. Flow stress is interpreted as the sum of the initial, undeformed strength, an increase due to dislocation hardening, and hardening by cell boundaries (LAGB) created by deformation. Source: Taken from Morris et al.110,112

cell-LAGB hardening term ∆σcell are seen to add to the initial material strength (σ0 + ∆σHP ) to provide a good description of the experimental strength.110,112 It can thus be understood that initial structural changes during deformation will cause rapid hardening as loose dislocations and dislocation cells are introduced, and only later will grain size hardening be significant as grain size is reduced significantly when LAGB (cell walls) slowly transition to HAGB (grain boundaries). Eventually, at nanoscale grain sizes, dislocation and cell hardening will be lost. A simple description of hardness as related to grain size (i.e. ∆H ∝ 1/√ d) or as related to dislocation cell size (i.e. ∆H ∝ 1/dc) will have some validity, each in its own given microstructural regime. Figure 11.12109,110,112–115 compares hardening in Fe/Fe3Al/FeAl during severe working, and shows how the 1/d dependence provides a better description of behaviour, with less data scatter, during the first stage of microstructure refinement, whilst the 1/√ d dependence is better for grain sizes smaller than approximately 100 nm. As a final comment, however, for grain sizes greater than about 50 nm, where a certain density of randomly arranged dislocation can be found (after deformation), and especially for grain sizes greater than about 100 nm, where dislocation cellular substructures are expected, the complete analysis of hardening must rely on equation 11.18, taking account of the density and misorientation of boundaries, as well as the presence of any loose dislocations.


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11.12 Analysis of hardening during cold working or milling of Fe/Fe3Al/ FeAl in terms of (a) reciprocal grain/cell size, or (b) reciprocal square root grain/cell size. Sources: Data taken from Valiev et al.;109 Fecht et al.;113 Todaka et al.;114 Zadra et al.;115 Morris et al.110,112

11.9 Conclusion and future trends There now appears to be good understanding of the reasons for strengthening by grain size refinement, and especially the evolution from Hall–Petch behaviour, dependent on local stress concentrations in one grain inducing strain in neighbouring regions, to individual dislocation nucleation and glide, and eventually partial dislocation operation. Grain boundaries can be seen as both obstacles for dislocations and as sources, but the role of grain boundary sliding or diffusion, as well as the ideas of some special structure or behaviour of the boundaries, seems to be discredited.



325

Studies today concentrate on materials produced by new fabrication methods, including those prepared by severe plastic deformation and the nano-pillar class of samples, and on improving ductility or toughness at the same time as strength. The role of alloying to complex crystal structures and mixed-phase microstructures, which will surely improve both nanostructure stability as well as overall mechanical behaviour, remains poorly understood and worthy of further attention. Specific references have been made throughout this chapter to important scientific publications. This is invaluable reading for a more profound understanding of this area. For the more general reader interested in a slightly deeper overview understanding of nanostructural strengthening than that presented here, the following reviews or general reports are recommended reading. Morris5 gives a simple, now somewhat outdated overview of fabrication and mechanical behaviour of nanocrystalline metals. Meyers et al.4 present a very complete analysis of strengthening in these materials. The importance of strain rate in analysing deformation is examined in some excellent publications by Asaro and Suresh,2 Wang et al.65 and Dao et al.3 Finally, information on severe plastic deformation and its materials is reviewed by Valiev et al.105 and Valiev and Langdon.106

11.10 References 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22

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12 Elastic and plastic deformation in nanocrystalline metals M.Y. GUTKIN, Russian Academy of Sciences, Russia Abstract: This chapter discusses theoretical models that describe structure, elastic strains and different mechanisms of strain relaxation and plastic deformation of nanocrystalline metals. Special attention is paid to structure, strained state and the pentagonal symmetry of nanoparticles, in which context the disclination models and channels of strain relaxation are reviewed. For nanocrystalline metals, various grain boundary stress sources and concentrators are examined with regard to their capacity to initiate the mechanisms of plastic deformation. Theoretical modeling of dislocation generation, deformation twinning, rotational and superplastic deformation, and athermal stress-induced grain growth is considered in detail. Key words: strained state in nanoparticles, mechanisms of plasticity in nanocrystalline metals, generation of dislocations and twins, rotational and superplastic deformation, athermal stress-induced grain growth.

12.1 Introduction Outstanding mechanical properties of nanocrystalline metals (NCMs) have attracted much attention since the end of the 1980s when first NCMs had been fabricated and studied. In particular, it became at once clear that the behavior of defects and mechanisms of plastic deformation in NCMs and conventional polycrystalline metals are rather different.1,2 However, the experimental study of defects in NCMs has met many difficulties, which determines the importance of theoretical modeling and computer simulations. This chapter reviews some analytical theoretical models that describe deformation phenomena in NCMs. Section 12.2 is devoted to elastic strains in as-fabricated NCMs. Our view is that understanding the initial strained state should be considered as the first and necessary step in modeling the deformation processes in NCMs. Moreover, the assumptions on the elastic-state characteristics of a representative NCM volume form the basis of the majority of theoretical models describing various mechanisms of plastic deformation and fracture in NCMs. That is why we pay much attention to elastic strains here. Starting from peculiarities of elastic-strain distribution and relaxation in isolated nanoparticles and their conglomerates, we then briefly consider grain boundary (GB) stress sources and concentrators in NCMs. In the stress fields of these GB sources and concentrators, various mechanisms of plastic deformation can start working, including dislocation emission from GBs, generation of deformation twins, GB migration, transformation and decay, etc. 329 © Woodhead Publishing Limited, 2011

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Theoretical models of these mechanisms are considered in Section 12.3. Then in the same section the interplay between translational and rotational modes of plastic deformation is discussed together with mechanisms that provide local changes in misorientation angles of GBs and can result in grain rotation. The theoretical models, which describe the effects of strengthening and softening of NCMs under superplastic deformation, are also reviewed there. It is demonstrated that most of the models under discussion can be analysed within a unified energy approach, where some critical values of parameters (for example, a critical value of the applied shear stress) are calculated to state the conditions necessary for the barrierless activation of the deformation mechanisms. When possible, theoretical estimates are compared with available experimental data that allows one to conclude that the model is either realistic or is not.

12.2 Elastic strains in nanocrystalline metals As-fabricated NCMs are always the subject of residual elastic strains. For example, Wunderlich et al.3 evaluated one of the first transmission electron microscopy (TEM) studies of a NCM (nc-Pd with the grain size of 4–9 nm, which was fabricated by high-pressure compaction of nanocrystallites condensed from the gas phase) and showed that many GBs have severely distorted nearboundary regions with smaller atomic density and higher level of elastic strains. In general, their sample contained about 25% of highly strained material. Similar conclusions followed from comparison of earlier experimental data from Mössbauer spectroscopy,4 positron lifetime spectroscopy,5,6 X-ray diffraction,7 EXAFS 8 and neutron diffraction.9 Later, in the middle of the 1990s, residual elastic strains were investigated in detail in NCMs obtained by severe plastic deformation.10 The general result was that the elastic strains were distributed inhomogeneously over the grains: they reached their maximum values in the vicinity of GBs and demonstrated an exponential slope at a distance of several nanometers from the GBs. To understand the origin of the residual elastic strains in NCMs, it is reasonable to start from the main features of NCM structure. Usually NCMs consist of crystalline grains (ranging from several to approximately one hundred nanometers in diameter), which are separated by GBs. The GBs meet each other at linear junctions that are called double if two GBs meet, triple if three GBs meet, etc. In their turn, the GB junctions meet each other at point nodes, which can be fourfold, fivefold, etc. Most GB junctions and their nodes are triple and fourfold, respectively. Their total volume fraction drastically increases with grain refinement and can reach up to 50% in fine-grained NCMs.1 As follows from these structural peculiarities of NCMs, there are two main reasons for their unique mechanical and physical properties: the first one is the nanoscopic grain size, and the second one is the unusually high density of GBs, GB junctions and junction nodes. Let us first consider the origin of residual elastic strains in isolated nanoparticles (or nanoclusters) and then in their conglomerates.



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12.2.1 Nanoparticles Residual elastic strains appear in isolated nanoparticles due to various reasons such as surface stress, pentagonal symmetry, presence of defects, phase transformations, etc. The physical origin of the surface stress is that the chemical bonding of atoms at the crystal surface is different from the bonding of atoms in the crystal bulk.11 Therefore, the equilibrium distance between the surface atoms differs from that between the bulk atoms, and the subsurface atomic layers occur in elastically strained state. For an isotropic spherical nanoparticle of radius R, there is a rough estimate of the average distortion of the interatomic distance a caused by surface tension that reads2,12:

[12.1]

where K is the volume compressibility coefficient and γ is the specific surface energy. For typical values of parameters K ~ 10–11 m3/J, γ ~ 1 J/m2 and R ~ 10 nm, this estimate gives approximately, 0.67·10–3, that is about one-tenth of a percent.2 It has also been noted that parameters entering equation [12.1] are size dependent.2 In particular, the surface energy of a nanoparticle depends on its radius R as13

[12.2]

where γ0 is the specific surface energy of a bulk crystal, α ≈ 1 and β ≈ α2 ≈ 1 are numerical coefficients. Thus, the surface energy γ decreases with decreasing nanoparticle radius R. It is worth noting that the surface energy of nanoparticles also decreases with increasing temperature (see, for example, Jia et al.14 and references therein). Nevertheless, equation [12.1] demonstrates the main contribution of radius R to the elastic strains caused by the surface stress in nanoparticles. The majority of isolated nanoparticles are synthesized in the single crystalline state;15 however, they also demonstrate a large variety of structures and shapes. ‘The next most common structure is probably simple twins, although there is rarely any publication of statistical data of particle populations. Of rather lower probability except for gold and silver is multiply twinned particles’ (Marks,15). Among the multiply twinned particles, fivefold-twinned nano- and microparticles have attracted much attention due to their pentagonal symmetry, which is impossible in bulk single crystalline solids (see, for example, the reviews2,15–22 and recent papers).23–26 Fivefold-twinned nanoparticles can have shapes close to regular decahedra, icosahedra or pentagonal prisms. De Wit27 and Galligan28 independently pointed out a direct relation between the structure of fivefold-twinned nanoparticles and disclinations (see also2,19,29). For illustration, de Wit27 suggested considering the undeformed body, which consists


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of five face-centered cubic (FCC) crystals oriented with the (1 ¯1 0) plane in the plane of the paper (Fig. 12.1 (a) ). Each crystal is in twin orientation with respect to the adjacent one, so that AC, AD, AE, and AF are twin boundaries. The angle between each pair of (1 1 1) and (¯1 ¯1 1) planes is 70°32' . Therefore the resulting polycrystal has a wedge BAB' with an apex angle of 7°20'. If the two sides of this wedge are brought together they will form a twin boundary, while at the same time a positive wedge disclination is created at A, where five twin boundaries terminate (Fig. 12.1 (b) ). Thus, the final configuration has no wedge-like cusp BAB' but contains a partial disclination of strength ω = 7°20', which creates inhomogeneous elastic strains and stresses in the polycrystal. In the case of decahedral nanoparticles (Fig. 12.2 (a) ) or pentagonal rods (Fig. 12.2 (b) ), there is only one such ‘star disclination’ whose line coincides with the pentagonal symmetry axis.27 In icosahedral nanoparticles, there are six such disclinations whose lines pass through twelve icosahedron vertices (Fig. 12.2 (c), see Ref. 19 for details). The idea to use the disclination concept has been very productive because it gives a straightforward way of modeling the elastic strains and stresses in fivefoldtwinned nanoparticles. For example, de Wit27 approximated the decahedral nanoparticle by a section of a cylinder containing a wedge disclination of strength ω along its axis. In this case the non-vanishing stress components (in cylindrical coordinates r, ϕ and z) read: [12.3]

12.1 De Wit’s schematics27 of partial disclination formation in the core of a fivefold twin in FCC crystals. (a) Initial undeformed state of a polycrystal consisting of five FCC crystals, each in twin orientation ¯ with respect to its neighbour; the plane of the paper is (1 1 0) and AC, AD, AE, and AF are twin boundaries. (b) A positive partial wedge disclination at A on which terminate the five twin boundaries AB, AC, AD, AE, and AF.



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12.2 Partial positive wedge disclinations of strength ω in (a) decahedral nanoparticle, (b) pentagonal rod, and (c) icosahedral nanoparticle.

where D = G/[2π(1–ν)], G is the shear modulus, ν is the Poisson ratio, and R is the cylinder radius. It is seen from equation [12.3] that the central region of the nanoparticle is compressed while its periphery is stretched. Indeed, the hydrostatic stress component σ = 1/3Trσij = 1/3 Dω (1+ν)[2ln(r/R)+1], is negative at r < 0.6R, zero at r ≈ 0.6R and positive at r > 0.6R. The stresses are singular at r = 0, which is a generic feature of solutions for defects (like cracks, dislocations, disclinations, etc.) within the classical theory of elasticity. Using an extended version of the elasticity theory (say, the strain-gradient,30,31 non-local32 or nonlinear33 theory of elasticity), one can dispense with such singularities. For example, in the framework of the strain-gradient elasticity, the hydrostatic stress component at the line of a positive wedge disclination, which is placed at the distance ~ 1 µm from a negative wedge disclination of the same strength, is estimated as30,31 σ ≈ –6Dω(1+ν), which gives σ ~ –D ~ –G/4 for ω = 7°20' ≈ 0.128 and ν = 0.3. Lazar34 has used the field theory of elastoplasticity to consider a wedge disclination in the center of a cylinder of radius R and obtained σ ≈ –1.14Dω(1+ν) at the dislocation line for R = 10/κ, where κ is the gradient coefficient, which can be estimated as ~ 10 nm–1. Then we get σ ~ –D/5 ~ –G/20 for R ~ 1 nm at the same values of ω and ν. Thus, the level of G/20 can be considered as the lower magnitude of σ in the finest nanoparticles, while G/4 as its upper magnitude in the coarse nanoparticles. Anyway, the compression in the nanoparticle center is very high. Moreover, it follows from equation [12.3] that the strain energy (per unit disclination length) is27 WDh = 1/8Dω2R2. Therefore, one can expect the activation of various mechanisms of stress relaxation when the nanoparticle radius will increase. The same results are valid for pentagonal rods, which can be modeled by long elastic cylinders containing positive wedge disclinations along their axes.2,19,29 Howie and Marks35 extended the disclination description to icosahedral nanoparticles (Fig. 12.2 (c) ). They considered:


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an elastic sphere having the same missing volume (about 12%), but spread uniformly throughout the sphere. This is equivalent to an angular average of the strains, and may be visualized as a multitude of thin radial cones, each subtending a very small solid angle dω at the centre, with small angular gaps between them in the unstrained state. The cones are now constrained by external forces to remain of the same length R while they are distorted sideways until they touch, are then ‘glued’ together. (Howie and Marks35)

This process, which replaces the discrete set of six wedge disclinations each of strength ω ≈ 7°21' by continuously distributed cone defects each of infinitely small strength dω, produces the distributed disclination which is now called Marks–Ioffe disclination.36 The Marks–Ioffe disclination is characterized by the eigenstrain εθθ * = εφφ * = 6ω/4π ≈ 0.0613 and creates the elastic stresses:35

[12.4]

where (r, θ, φ) is the spherical coordinate system with the origin in the center of the sphere. Again the central region of the nanoparticle is compressed while its periphery is stretched. The hydrostatic stress σ = 4/3Dω(1+ν)[3ln(r/R)+1] is negative at r < 0.7R, zero at r ≈ 0.7R and positive at r > 0.7R. The stress components [12.4] are singular at r = 0. The strain energy is35 WIc = 4/3Dω2(1+ν)R3. Since the strain energy of the fivefold-twinned nanoparticles drastically increases with their radii, the nanoparticle structure is unstable with respect to various transformations. This may concern the surface faceting37 and reconstruction,38 structural modification and transition to ‘normal’ single crystalline state,15,18–23 and formation of specific defect structures, which accommodate in part the initial strained state.2,15,18–25,36 In particular, Gryaznov et al.39 have theoretically considered the following relaxation channels of elastic stresses inside the pentagonal whiskers: 1) creating an edge dislocation inside the whisker, 2) opening a gap in the whisker, 3) creating a compensating negative partial wedge disclination near the whisker surface, 4) splitting the pentagonal axis (in terms of splitting the positive wedge disclination (Fig. 12.2 (a) ) into a pair of similar disclinations of the same total strength), 5) growing a single crystalline (non-pentagonal) region in the whisker center, and 6) displacing the pentagonal axis from the whisker center. The authors calculated and compared the energy changes, which are characteristic for the relaxation channels, and concluded that the principal channels are dislocation creation, displacement and splitting of the pentagonal axis. Recently Kolesnikova and Romanov have analysed the formation of a circular prismatic dislocation loop in the cross section of a pentagonal whisker40 and growth of a misfitting layer on the whisker surface41 as potential channels of stress relaxation. The latter stress relaxation channel has also been applied to icosahedral nanoparticles.36 For the case of an atomically heterogeneous pentagonal whisker, Panpurin and Gutkin42 have studied the nucleation of a



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precipitate in the shape of a finite-length cylinder coaxial to the whisker. In the approximation that the precipitate is subject of an axial positive eigenstrain ε*, they have demonstrated that nucleation and growth of the precipitate are energetically preferable if ε* is smaller than a critical value εc. If the eigenstrain is large (ε* τc (here τc = 1.53 GPa), the central dislocation moved far away from its initial position (see curve 6 in Fig. 12.7 (a)), and the GB decayed as a whole. The analysis of stability of low-angle GBs with different parameters showed that τc grows in a roughly linear way with rising θ (see curve 1 in Fig. 12.7 (b) ). On the other hand, the dependence of τc on the number N of dislocations, and thereby the GB length d (= Nh) at a constant value of θ, is very weak. This means that very short GBs in very small grains and comparatively long GBs in large grains decay at close values of the critical stress τc, if they have the same misorientation θ. The decay of a low-angle GB results in the formation of moving lattice dislocations that elastically interact with other lattice dislocations composing


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12.7 (a) Temporal dependence of the position x of the 8th dislocation in a low-angle GB with θ = 0.1 and N = 15, for τ = 0.5, 1.0, 1.4, 1.52, 1.53 and 1.54 GPa (curves 1, 2, 3, 4, 5 and 6, respectively). (b) Dependences τc(θ) for ωl = 0°, 1°, 3°, and 5° (curves 1, 2, 3, and 4, respectively).

neighbouring low-angle GBs. This interaction is able to stimulate decays of the neighbouring low-angle GBs and avalanche-like release of new mobile lattice dislocations.153,154 The main results are demonstrated in Fig. 12.7 (b), where the curves τc(θ) are plotted for different values of the strength ωl characterizing a disclination dipole that has been formed after the decay of a neighbouring lowangle GB. As was expected, the critical shear stress τc decreases with rising ωl. The phenomenon in question is able of causing plastic flow localization (carried by lattice dislocations released by low-angle GBs) in deformed NCMs containing high-density ensembles of low-angle GBs. As shown experimentally, high-angle GBs bow (become curved)84,159 and emit partial lattice dislocations47,159–164 that can provide deformation twinning in NCMs. To account for these experiments, Bobylev et al.153 extended the above model to the case of high-angle GBs containing GB dislocations. In general, high-angle GBs contain intrinsic dislocations with small Burgers vectors associated with misorientation of such GBs. They cannot glide easily in the grain interior, in contrast to the lattice dislocations. However, high-angle GBs bow and emit partial dislocations into adjacent grains in mechanically loaded NCMs (Fig. 12.8). Bobylev et al.153 first considered the GB bowing under a shear stress τ by means of 2D dislocation dynamics that account for the additional hampering force due to an increase of the GB length. Solution of the system of dynamics equations, adapted to this case, gives new equilibrium positions of the GB dislocations and, as a corollary, an equilibrium configuration of the high-angle GB in its curved state (Fig. 12.8 (b)). Now let one of the GB dislocations located at the curved GB split into an immobile GB dislocation and a mobile Shockley dislocation that moves in the adjacent grain interior under a stress τ (Fig. 12.8 (c) ). The authors



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calculated the energetics of the dislocation emission, which was considered as a transformation of the system from its initial state with the energy W1 (Fig. 12.8 (b) ) to the final state with the energy W2 (Fig. 12.8 (c)). The dislocation emission is energetically favourable, if the energy difference ∆W = W2 – W1 – A is negative. Here A is the work spent to transfer the Shockley dislocation under the stress τ. The energy difference ∆W was analysed for the exemplary case of pure nanocrystalline Cu, when the GB is characterized by the deviation ω of the GB tilt misorientation θ from that, θ0, of a low-energy (favourable) GB in the same material.63 The favourable GB Σ = 5/(210) with165 misorientation angle θ0 = 36.87° and specific energy γ = 0.9 J·m–2 was used. It was shown that an increase in τ enhances the splitting and emission processes (Fig. 12.9 (a) ). At the same time, the dislocation emission is energetically unfavourable at low τ and is hampered with rising ω (Fig. 12.9 (b) ).

12.8 Evolution of a high-angle GB with intrisic GB dislocations: (a) initial state, (b) bowing of GB, and (c) splitting of a GB dislocation and emission of a partial Shockley dislocation. The partial dislocation has Burgers vector with the edge (be) and screw (bs) components. Its glide causes a stacking fault. The immobile GB dislocation has the Burgers vector with the edge (bgb – be) and screw (–bs) components.

12.9 The energy change ∆W via the path lp of the 5th partial dislocation in the case of high-angle GB containing N = 20 GB dislocations, for (a) ω = 3° and τ = 0.4, 0.6, 0.8, and 1.0 GPa (curves 1, 2, 3 and 4, respectively); and (b) τ = 1 GPa and ω = 3°, 5°, 7°, and 9° (curves 1, 2, 3 and 4, respectively).


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Let us discuss now the emission of partial dislocation by a GB disclination. Following Gutkin et al.,166 consider a 2D model of a NCM with positive and negative wedge GB disclinations of a mean strength ω. Let such a disclination ensemble consist of disclination dipoles with a mean arm (grain size) d, which are distant by 2R from each other, and d < R (Fig. 12.10 (a) ). In this case, one can analyse a separate GB disclination dipole as a source for generation of lattice dislocations (Fig. 12.10 (b) ). Within an energy-based approach, we calculated some critical values of the external shear stress τ which correspond to the generation of a lattice dislocation, its localization in the bulk of the grain and its absorption by the opposite GB, depending on the principal parameters of the model: d, θ, and α (see Fig. 12.10 (b) ). For example, in Fig. 12.11,166 the curves τc(θ) are shown which were calculated for the case of pure nanocrystalline Al at ω = 0.1 (≈6°), α = 10° and d = 10, 20 and 30 nm. The curves τc(θ) determine (if exist) those regions at the (θ,τ) diagram, where three typical arrangements of partial dislocations must appear in a grain: I, when partial dislocations are localized near their GB sources; II, when they are spread inside the grain; and III, when they cross the grain and are absorbed by the opposite GBs. An increase in the grain size d is accompanied with an extension of the

12.10 (a) 2D model of a NCM with positive and negative wedge GB disclinations. (b) Emission of a partial Shockley dislocation from a moving GB disclination. The positive GB disclination moves by a distance l (l = b/[2sin(ω/2)] is the spacing between the intrisic GB dislocations with the Burgers vectors (b), thus emitting a lattice dislocation. This dislocation may be either partial, with the Burgers vector having the edge (b2) and screw (b3) components, or perfect, with the Burgers vector 2b2. At the place of generation, a difference GB dislocation forms, whose Burgers vector has either the edge (b1 = b – b2) and screw (–b3) components, or only the edge component (b – 2b2), respectively. The position of the negative GB disclination sets by the initial dipole arm L ≈ d and the azimuthal angle θ. The angle α determines the orientation of the dislocation gliding plane with respect to the GB.



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12.11 Critical stress τc via the azimuthal angle θ for different values of the grain size: (a) d = 10 nm, (b) d = 20 nm, and (c) d = 30 nm.

θ ranges, where the emission of partial dislocations must occur, and drastic changes in distribution of regions I, II and III (see Gutkin et al.166 for details). It is worth noting that these characteristic types of defect arrangements were observed in molecular dynamics simulations (for example, see156,157). As follows from calculations,166 there exist two characteristic grain sizes in nanocrystalline Al: dc1 (≈ 5 nm) and dc2 (≈ 30 nm). When d ≤ dc1, the generation of partial dislocations by GBs needs smaller values of τ than that of perfect dislocations, in the full range of possible values for θ and α. When d ≥ dc2, the generation of perfect dislocations becomes more energetically preferable for any of possible θ and α. In the grains of intermediate size, dc1 < d < dc2, the generation of either partial or perfect dislocations may dominate, depending on the values of the angles θ and α. Above we have considered some 2D models. However, the lattice dislocation slip, deformation twinning and GB sliding in real NCMs are 3D processes conducted by dislocation loops (DLs). In this context, a 3D description of the deformation mechanisms in terms of DLs seems to be important. As noted in Ref.167 the effective way of interaction between different modes of plastic deformation in NCMs is the generation of new DLs at the pre–existent DLs of other types. For example, pre-existent grain boundary DLs (GBDLs) can serve as sources for perfect or partial lattice DLs (Fig. 12.12 (a), 12.12 (b) ) or GBDLs (Fig. 12.12 (c) ). The pre-existent perfect or partial lattice DL can generate either a perfect or partial lattice DL into the neighbouring grain (Fig. 12.12 (d) ) or a GBDL (Fig. 12.12 (e) ). To summarize, there are 9 variants of the DL generation at the pre-existent DLs, depending on the types (GB, perfect lattice, partial lattice) of these DLs. These variants are called the modes for the DL generation at preexistent DLs. All these modes were analysed within a 3D energy-based approach for the exemplary case of nanocrystalline Al with the grain size d ranging from 10 to 100 nm.167 The basic results are briefly as follows: 1) loops of perfect lattice dislocations operate as effective sources for GB, partial and perfect lattice DLs (in order of preference); 2) loops of partial lattice dislocations serve as


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12.12 Different modes of generation of a new gliding DL at a segment of the initial gliding DL: (a,b) a lattice DL is emitted by a GBDL, (c) a GBDL is emitted by a GBDL, (d) a lattice DL is emitted by a lattice DL, (e) a GBDL is emitted by a lattice DL. In all the cases, a new DL is generated at a GB or at a triple junction of GBs.

effective sources for GB and partial lattice DLs (in order of preference), but are not effective to generate perfect lattice DLs; 3) loops of GB dislocations can be effective sources for GBDLs, while they are not so effective for generation of partial lattice DLs; GBDLs hardly can generate perfect lattice DLs. With these results, grains in NCMs can be divided into the three basic categories: relatively large (d ≈ 30 to 100 nm), intermediate (d ≈ 10 to 30 nm) and finest (d ≈ 3 to 10 nm) grains. The lattice dislocation slip effectively operates in large grains. The most effective sources of new DLs here are loops of perfect lattice dislocations, in which case the lattice slip enhances intense GB sliding. In intermediate grains, the conventional lattice dislocation slip is severely suppressed. The most effective sources of new DLs here are loops of partial (twinning) lattice dislocations, which enhance GB sliding. In the finest grains, GB sliding dominates over the lattice dislocation slip and deformation twinning. Here GBDLs serve as effective sources of new GBDLs that cause intense GB sliding. A further development of these 3D models was conducted by Bobylev et al.168,169 with the aim to explain anomalously wide stacking faults (SFs) between partial dislocations in nanocrystalline Al. The theory of DLs was used to calculate the system energy more accurately compared to some earlier models.105,170–173 By means of an original algorithm, the authors investigated both the generation of partial dislocation semi-loops and the dependence of the SF



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width on the grain size and applied stress level. They showed that anomalously wide SFs in nanocrystalline Al are caused by high stresses but not by small grain size as was derived in the earlier models. On the other hand, it was noted168 that ‘such high stresses are possible in nanocrystalline Al because the normal dislocation activity is suppressed by the small grain size. Therefore, although the small grain size is not directly connected with anomalously wide SFs in nanocrystalline Al, it represents the primary cause of this phenomenon.’

12.3.2 Generation of deformation twins As is well known, deformation twins (DTs) do not appear in coarse-grained metals with relatively high values of SF energy γ. A typical example is Al. The situation dramatically changes in the case of nanograins. DTs in nanocrystalline Al were observed in electron microscopy experiments.159–161 To explain this phenomenon, a number of theoretical models94,105,168–179 have recently been suggested that describe anomalously wide SFs whose overlapping would create DTs in nc-Al. However, some of these models105,168–174,179 deal with only one or two SF strips and cannot directly be used in a description of the generation of thick DT lamellae observed experimentally in nc-Al,160,161 Cu,47,180,181 Ni,84,182– 187 Pd188 and Ta.189 Following the experiment, the DT lamellae have typical thickness of several nanometers and occupy regions between opposite GBs in nanograins. Sometimes DT lamellae form V-, T- and X-shaped configurations studied in detail by Zhu et al.190 Let us briefly consider some models that describe the generation of thick DT lamella at GBs in NCMs. It seems rather evident that probability of DT nucleation increases in vicinity of stress sources and concentrators. Extrinsic GB dislocations can stimulate the emission of Shockley partials (see Section 12.3.1); however, their density is not so high and their stresses are not strong enough for initiation of thick DT lamella nucleation.176 Possible alternatives are GB disclinations176,177 and cracks,94 which create strong and long-range stress fields. In the model,176 a DT lamella is nucleated under the action of an applied stress and the stress field of a dipole of GB or junction wedge disclinations (Fig. 12.13 (a)). The model176 was used to consider pure nanocrystalline Al and Cu with d ≈ 30 nm. It was shown that, if the disclination strength ω and external shear stress τ are high enough (but still realistic for these NCMs), the DT generation is characterized by the absence of any energy barrier. The critical stress τc causing the emission of the first twinning dislocation is rather low (≈0.1 GPa and ≈0.3 GPa, for Cu and Al, respectively, at ω = 0.5). As the DT thickness (equal to δ (n –1), where δ is the distance between neighbouring {111} atomic planes and n is the number of emitted Shockley partials) increases, the critical stress τc (n) of the emission of new twinning dislocations first grows, then levels off, and again grows (Fig. 12.13 (b) ). Thus, there are two stages of local hardening and an


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12.13 (a) The twinning partial dislocations are emitted from a GB segment AB in nanocrystalline sample with GB disclinations of strength ±ω. The emission occurred in the region (bounded by dashed contour) where the shear stress of the disclination dipole reaches its highest level. The combined action of the external shear stress τ and the disclination stress field causes the emission and glide of partials along the adjacent slip planes. Most of the partials reach the opposite GB at its segment A‘B’. The overlapping stacking faults (generated behind the emitted partials) form the deformation twin lamella AA‘B’B. (b) Dependence of the critical external shear stress τc on the number n of emitted partials in nanocrystalline Cu (solid curves) and Al (dashed curves), for disclination strength ω = 0.5 (curves 1, 1‘), 0.4 (2, 2‘), and 0.3 (3, 3‘).



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intermediate stage of local flow of a NCM on a scale of one nanograin. In all stages, τc depends strongly on ω; indeed, a decrease in ω results in a sharp increase in τc. When studying the dependence of the equilibrium position peq of a twinning dislocation on its ordinal number n, we found the shape of the DT front (Fig. 12.14).177 Depending on the orientation of the disclination-dipole arm, the longitudinal section of DT lamella is close to a rectangle or a blunted wedge, which agrees well with the results of aforementioned experimental observations. The estimated DT thicknesses (5.6–7.0 nm for Al and 5–6 nm for Cu)177 are also consistent with the experimental data.47,160,161 The model of DT lamella nucleation at an extrinsic GB dislocation aside of a crack tip (Fig. 12.15 (a) ) has given similar results.94 It was shown that, if the external shear stress τ and the crack length L are sufficiently large, no energy barrier exists for the nucleation of a DT. Such values of τ and L fall in the ranges typical of the NCMs under study. For example, in nc-Al with d ≈ 30 nm the critical stress τc required for the nucleation of the first twinning dislocation at L = 20d = 600 nm is approximately 0.25 GPa (Fig. 12.15 (b) ). For a micro-crack with L = 200d = 6 µm, the critical stress decreases to approximately 15 MPa. With

12.14 Dependence of the equilibrium position peq of a twinning dislocation on its ordinal number n in nanocrystalline (a, c) Al and (b, d) Cu for the disclination-dipole strength ω equal to 0.3, 0.4, and 0.5. The dipole arm is oriented (a, b) along or (c, d) normal to the grain boundary.


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12.15 (a) Generation of a deformation-twin lamella at an extrinsic grain-boundary edge dislocation in the vicinity of a mixed I and II mode crack of length L. (b)–(c) The critical external shear stress τc and the equilibrium position peq of a twinning dislocation via its ordinal number n in nc–Al, for various values of the normalized crack length: L/d = 3, 10, 20 and 200.

raising the DT thickness, the critical stress of the emission of new twinning dislocations first grows, then saturates, and again grows, as is the case with DT generation in the disclination stress field.176,177 In all the stages, the critical stress τc strongly depends on the crack length L. A decrease in L results in an increase in τc. The curves peq(n), which determine the shape of the DT lamella, also depend on L (Fig. 12.15 (c) ). Depending on L, the longitudinal section of DT lamella is close to a rectangle or a trapezoid. The DT thickness was found to vary from 3.5 to 9.4 nm in nc-Al. The lower (higher) limit corresponds to the maximum (minimum) length L of the crack under discussion and the minimum (maximum) value of the applied critical stress τc. The main conclusion is that microcracks can stimulate the nucleation of thick DT lamellae far from the crack tip. Recently Fischer et al.178 have developed a similar micromechanical model and come to the same conclusion.



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12.3.3 Rotational deformation The principal structural features of NCMs, such as nanoscale grains, high volume fraction of grain boundaries and their triple junctions, and a high density of GB defects (see Section 12.2.2), provide many opportunities for development of rotational plastic deformation.78,132 Rotational modes of plasticity include stressand strain-driven formation of misorientation bands and new boundaries, change in GB misorientation angles and grain rotation, which are the processes of local reorientation of crystalline lattice.66,78,132,191 These processes are realized through the collective behavior of lattice and/or GB dislocations that is effectively described in terms of partial disclinations.27,29,64–67,78,102,132,191–193 Experimental evidence of rotational plasticity in deformed NCMs has been demonstrated in many works.194–205 Recent direct HRTEM observations of Murayama et al.195 have approved the existence of partial wedge disclinations in severely deformed nc-Fe. Ke et al.194 observed in situ GB sliding and grain rotation near the tips of opening cracks in nc-Au films. Shan et al.196–198 and Wang et al.203 reported on evident grain rotation in nc-Ni films deformed by in situ TEM tensile straining. Similar observations were made by Sergeeva et al.199–201 in nc-Ni3Al. The authors also noted that the mechanism of cooperative grain boundary sliding, which dominates in superplastic deformation of NCMs, is associated with sliding and rotation of entire grain groups. Yagi et al.202 studied the surface morphology and the crystallographic texture of nc-Au and nc-Cu after creep deformation and concluded that grain rotation takes place along the localized grain boundary sliding during creep deformation. Wang et al.203 observed that rotation of an individual grain is accompanied by rotation and further coalescence of neighbouring grains, which resulted in grain growth. Zizak et al.204,205 irradiated nc-Ti layers at room temperature with Au ions and studied the bombardmentinduced texture changes. They registered that ‘during off-normal irradiation, the nanocrystals undergo grain alignment and rotation up to ~90° at the highest ion fluence’.204 Recent computer simulations have also manifested the rotational plastic deformation in NCMs with finest grains (average grain size from 5 to 7 nm).157,206–210 Both the molecular dynamics206 and quasicontinuum (molecular statics)207–209 methods were used to simulate the evolution of atomic structure of NCMs in nc-Au206 and nc-Al207–209 under spherical nanoindenter. Among some other mechanisms of plasticity, the authors have observed the GB sliding accompanied by grain rotation and coalescence. Shimokawa et al.157 evaluated the molecular dynamics simulation of nc-Al under tensile loading and also the fixed relative rotation of some neighbouring grains. Monk and Farkas210 used the same method for studying the deformation behavior of nc-Ni nanowires under tension. They observed grain growth accompanied by grain rotation and measured the rotation angle of a sample grain in the center of the nanowire as a function of time for different strain rates. Their ‘data show that the grain rotation speed varies


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significantly with strain rate, indicating again that it is not a time controlled thermal process and is mostly driven by the strain itself’.210 Summarizing the results of experiments and computer simulations, one can conclude that stress- and strain-driven grain rotation is a typical mechanism of plastic deformation in NCMs with finest grains, which is accompanied by GB sliding and can lead to grain coalescence. To date there are a number of theoretical models which describe the gradual change in GB misorientation angles in the course of grain rotation. The earlier models211–213 were aimed at the analyses of energetics of splitting of GB disclinations into smaller-strength GB disclinations. It was shown that the split arrangements are always more energetically preferable than the initial disclinations. However these models did not include any mechanism of disclination motion along GBs. Later it was suggested that motion of GB disclinations could be realized through emission of lattice perfect (Fig. 12.16) and partial (Fig. 12.10 (b) ) dislocations into adjacent grains.149,150,166,214,215 This

12.16 Stress-driven displacement of the wedge disclination (black triangle) with the strength +ω from its initial position (dashed triangle) by the distance l is accompanied by the emission of two lattice dislocations with Burgers vectors b1 and b2. The +ω-disclination moves along the grain boundary plane towards another disclination (white triangle) with the strength –ω. See Gutkin et al.150 for details.



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mechanism seems to be more appropriate for NCMs, which may contain only few lattice dislocations inside the grains, than the earlier proposed mechanism66,216 of GB disclination motion through absorption of lattice dislocations from adjacent grains, which is appropriate for microcrystalline metals216,217 containing a high density of lattice dislocations. The scheme that illustrated the contribution of grain rotation, which is realized through motion of GB disclination dipoles, to plastic deformation of a NCM, was presented by Ovid’ko.218 The above-mentioned theoretical models manifest interplay between the translational (glide of lattice dislocations) and rotational (motion of GB disclinations) modes of plastic deformation in NCMs. For the case where the translational mode is mainly represented by GB sliding (smallest nanograins and/or superplastic deformation), another model (Fig. 12.17) was suggested.219 Its main idea is as follows. GB sliding occurs via the glide of GB dislocations with Burgers vectors, which are parallel to the GB planes along which these dislocations glide (Fig. 12.17 (b) ). Triple junctions of GBs serve as obstacles for the GB dislocation motion. GB dislocations stopped at a triple junction are capable of being split into climbing GB dislocations (Fig. 12.17 (c) ). When this process repeatedly occurs at a triple junction, it results in the formation of two walls of GB dislocations climbing along the GBs adjacent to the triple junction. The climbing GB dislocation walls cause the rotational deformation, in which case the repeatedly occurring splitting of gliding GB dislocations at the triple junction provides the crossover from the GB sliding to the rotational deformation mode (Fig. 12.17 (c), (d) ). This process can be spread over the grain, which has to rotate on an angle as a whole (Fig. 12.17 (e) ). Thus, the stopped GB sliding can stimulate plastic rotation of the neighbouring grain. Obviously this mechanism may only be effective under the condition of intensive GB diffusion of vacancies, which must be capable of providing the necessary velocity of GB dislocation climb. Analysing this model from a thermodynamic point of view, the authors219 concluded that the transition from GB sliding to rotational deformation becomes energetically favourable when the external shear stress achieves its critical value, and this depends on the elastic properties of the NCM, the structure of its GBs, its grain size and its shape. Smaller grains require smaller critical stress to rotate. Recent progress in theoretical modeling of rotational deformation in NCMs is mainly related with elaboration of dislocation–disclination models of grain refinement of polycrystalline metals under severe plastic deformation,220–222 interplay between GB sliding and grain rotation223–225 leading to the inverse Hall–Petch relationship in the range of smallest grain sizes,223,224 and GB migration95,96,226–230 and the formation of immobile disclinations whose strengths gradually increase during deformation as a result of grain boundary sliding and diffusion,231 as special mechanisms of rotational plasticity. Some of these models220–224 have been reviewed extensively by Romanov and Kolesnikova.29 The models226–230 are considered in more detail in Section 12.3.5.


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12.17 Combined action of grain boundary sliding and rotational deformation mode. (a) Nanocrystalline specimen in a non-deformed state. (b) Grain boundary sliding occurs via motion of gliding grain boundary dislocations under shear stress action. (c) Gliding dislocations split at triple junction O of grain boundaries into climbing dislocations. (d) The splitting of gliding grain boundary dislocations repeatedly occurs causing the formation of walls of grain boundary dislocations whose climb is accompanied by crystal lattice rotation in a grain. (e) Climbing dislocations reach triple junction O´ where they converge into gliding dislocations causing further grain boundary sliding.

Alternative approaches to theoretical modeling of grain rotation in NCMs have been represented by Kim et al.232 and Yang and Yang.233 These authors consider the kinetics and size effects of GB sliding and grain rotation driven by both GB energy and external stress. Ignoring the underlying structural mechanisms of GB



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sliding and grain rotation, they operate with continuum mechanics in terms of viscous GB gliding and GB diffusion as accommodation mechanisms. Due to its relative simplicity and high effectiveness, this approach looks rather attractive and fruitful although it does not allow one to visualize the structural mechanisms of grain rotation.

12.3.4 Mechanisms of strengthening and softening under superplasticity The superplasticity of NCMs has attracted much attention in the past decade (see original papers234–241 and reviews99,101,108,118,121,122,242). It has been found that the superplasticity in these materials is reached at lower temperatures and higher strain rates, offering strong possibilities for industrial application of this effect. Moreover, it has been discovered that the strength of a material increases significantly in the course of superplastic deformation. The yield stress and the hardening effect become especially great during deformation of NCMs, with an average grain size of about 50 nm. In this case, the stress–strain curves are bell-shaped, and demonstrate the presence of well-defined long hardening and softening stages. Among the main mechanisms of plasticity operating in NCMs (see Fig. 12.3), the GB sliding (in combination with accommodation mechanisms, such as GB migration and lattice sliding near GBs) is believed to be the dominant mechanism of superplastic deformation in NCMs.101,241 Therefore, the unusual effects of NCM hardening in the initial stage of superplastic deformation and subsequent softening, as well as very high values of the yield stress, can be due to the specific features of GB sliding. These features were described in theoretical models.243–245 First, we considered a situation near an isolated triple junction of GBs along which GB dislocations glide under an external shear stress τ (Fig. 12.18). Following the models,243,244 numerous acts of transfer of GB dislocations across the triple junction results in an increase in the Burgers vector of the difference sessile dislocation in the triple junction, which increases the critical stress τc necessary for dislocation transfer across the triple junction and hence leads to local strengthening. At the same time, the accompanying local migration of GBs leads to an increase in the angle a between the GB planes (adjacent to the triple junction), which decreases τc and hence leads to local softening. The competition between the strengthening and the softening effects is capable of crucially influencing the deformation behavior of NCMs exhibiting high strainrate superplasticity. In particular, superplastic deformation regime is realized if the strengthening dominates over the softening during the first extensive stage of deformation (characterized by a plastic strain of hundreds of percent). This strengthening prevents the necking and is responsible for an increase of the flow stress that drives the movement of GB dislocations. With rising plastic strain, local GB migration arranges GB planes to be tentatively parallel to each other in some local regions of a loaded sample. As a result, local softening becomes


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12.18 Numerous acts of transfer of GB dislocations across a triple junction and accompanying local migration of GBs leads to an increase in the angle a. (a) Initial (0th) state of defect configuration; two gliding GB dislocations move towards the triple junction. (b) Sessile dislocation with the Burgers vector b is formed; triple junction is displaced by the vector b2 from its initial position. (c) Generation of two new gliding GB dislocations that move towards the triple junction. (d) New sessile dislocation is formed; the triple junction is transferred by the vector 2b2 from its initial position. (e) The nth generation of two new gliding GB dislocations that move towards the triple junction. (f) The nth sessile dislocation is formed; the triple junction is transferred by the vector nb2 from its initial position.

substantial, which causes gradual macroscopic softening inherent in the second stage of superplastic deformation of NCMs. Secondly, we expanded these models by taking into account the effect of neighbouring triple junctions and the possible accommodation of the GB defect structure via emission of lattice dislocations (Fig. 12.19).245 In the model used, perfect lattice dislocations are emitted from triple junctions when Burgers vectors of sessile triple-junction dislocations reach critical values. After the first emission of a perfect lattice dislocation, the strength of the sessile dislocation again increases gradually. When its Burgers vector reaches a new critical value, a lattice dislocation is emitted again. A detailed examination of these processes allowed us to numerically calculate the strain–stress dependence shown by the solid curve in Fig. 12.20,245 for Al with the grain size of 100 nm. The dashed line represents experimental data.239 It can be seen that the theoretical and experimental values are close to each other. The theoretical curve is serrated due to the contribution from lattice sliding to the superplastic strain. Each elementary event of lattice sliding causes a drop in the critical stress, thereby leading to local softening.



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12.19 Emission of lattice dislocations with the Burgers vector be from a sessile dislocation with the Burgers vector Bm–1 in a triple junction on the mth transfer of GB dislocations across the triple junction.

12.20 External stress σ as a function of the total plastic strain ε.


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Further theoretical investigation of defect structure evolution near triple junctions of GBs during GB sliding has been evaluated recently by Ovid’ko and Sheinerman.246 The authors have taken into account the formation of disclination dipoles near triple junctions and the partial relief of disclination stresses due to GB diffusion. As the first process increases the strain hardening, while the second one decreases it, these factors could also be used in further theoretical models of superplasticity.

12.3.5 Athermal stress-induced grain growth In recent years, particular attention has been focused on the grain growth during plastic deformation of ultrafine-grained247–253 and nanocrystalline72,203,249–269 metals and alloys at room72,203,249–269 and cryogenic253–255 temperatures. Experimental studies on ultrafine-grained pure Al247,249–252 and Cu248,253 and Al-Mg alloys250,251 and on nanocrystalline pure Al,249–252,259–261,269 Cu,253–255,267 Ni,203,256–258,267,268 Pd72 and Co-P263,264 and Ni-Fe264–266 alloys have shown that the grain growth is possible during nano-249–252,257 and micro-indentation253–255 of thin films and torsion of them under high pressure,72,256 during compression of powder,247 micropillars258 and macroscopic samples,248,265 during cold-rolling,268 and, finally, during uniaxial tension of thin films203,259–262,269 and bulk planar samples.263,264,266 For an understanding of the physical nature of this phenomenon, the following experimental facts are of importance: (i) (ii)

(iii) (iv)

(v)

(vi)

At cryogenic temperatures, grains grow more rapidly than at room temperature.254 The grain growth is the most intensive in the regions of a sample where the elastic stress and its gradient are the largest (e.g. under a nanoindenter249–252,257 or in the immediate vicinity of a microindenter,253–255 near the tip of a slowly developing crack,259,262 in the surface layer of a sample in the vicinity of a neck forming under tension,266 or near specially prepared holes under tension269). The grain growth is completely suppressed250 or reduced261,263–266 in the presence of impurities. During grain growth, not only the grain size but also the character of the grain size distribution are changed; the distribution is broadened and sometimes becomes bimodal,254,259,264 with larger submicron grains occupying up to 15% of the volume254 and fine nanograins surrounding them. The grain growth occurs at relatively low nanoindentation rates257 and during microindentation in the creep mode,253–255 at relatively high compression rates (~10–3–10–1 s–1 258 and 10–3 s–1 265), and at widely ranged tension rates (~10–5 s–1,259–261 10–3 s–1,260,263 10–5–10–2 s–1,264 10–2 s–1 266). The grain growth somewhat decreases the ultimate strength, but it significantly increases the ultimate tensile strain (up to 25% in pure nc-Al259 and up to 7.2% in the nc-Ni-Fe alloy266), which is accompanied by noticeable hardening and the formation of dislocation structures in coarse grains. In micropillars of pure nc-Ni under uniaxial compression, ultrahigh plasticity © Woodhead Publishing Limited, 2011


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(up to 200% of the true strain) was observed at a flow stress of 2.0–2.4 GPa, which was accompanied by softening (due to equiaxial grain growth) followed by hardening caused by the elongation of grown grains and the accumulation of dislocations and twins in them.258 (vii) With increasing duration of holding of a sample under indenter, the lowangle GBs were observed to increase in number, especially at cryogenic temperatures.255 In submicron-sized grains grown during severe plastic deformation, subgrains were observed, which, in turn, were filled with dislocation cells.256 The authors72,203,249–269 believe that the above results unambiguously indicate the athermic character of grain growth, which occurs under elastic stresses forming at earlier stages of plastic flow. The process of grain growth is inhomogeneous over a cross-section of the sample; indeed, the grains that are located in places of concentrated stresses and, in addition, have a favourable orientation, increase in size. When the growing grains become a few hundred nanometers in size, the plasticity mechanisms typical of low-temperature deformation of coarse-grained metals begin to operate in them. For example, in copper, dislocation glide and the formation of dislocation pile-ups were observed at room temperature, and deformation twinning at a cryogenic temperature (77 K).255 Thus, the grain growth during plastic deformation increases the plasticity of NCMs, while the flow stress remains high at low temperatures and relatively high loading rates, which is very important for practical applications.252 Recent computer simulations157,207,208,210,270–274 have shown that lowtemperature stress-induced grain growth in NCMs is athermal. Its basic mechanisms are found to be stress-induced migration of GBs and their triple junctions, GB sliding, grain rotation and coalescence (see also Section 12.3.3). In particular, all of these mechanisms were observed to operate simultaneously in model samples of nc-Al208 and Ni210 with a mean grain size of 7 and 5 nm, respectively, when nanograins rotated through GB sliding under nanoindentation208 or uniaxial tension.210 The atomic mechanisms of motion of high-angle GBs have been considered in a number of recent works.275–281 Also, stress-induced GB migration and athermal grain growth have been described theoretically with the aid of dislocation-disclination models.95,96,152–154,226–230,282 For example, Bobylev et al.152–154 have studied the dynamics and decay of a low-angle tilt boundary under an applied shear stress τ (see Section 12.3.1). It was shown that, as the stress τ increases, the tilt boundary is first bent and then shifts to a new position corresponding to the applied stress. At a certain critical stress proportional to the misorientation angle θ of the boundary, it becomes unstable and glides irreversibly. The decay of one such boundary significantly decreases the critical stress for decay of neighbouring lowangle boundaries. As a result, the chain decay of the neighbouring boundaries occurs and the grains separated by them coalesce. The static model of the escape of dislocations from an infinite straight dislocation wall developed by Li282 also © Woodhead Publishing Limited, 2011

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permits one to estimate the critical stress for boundary decay, which is proportional to θ. The stress at which an intrinsic dislocation of a low-angle boundary (with θ = 0.1 (≈ 5.7°)) breaks away from it (estimated from this model to be about 2 GPa for Fe)282 is not far greater than that obtained from dynamic calculations (1.53 GPa).152–154 The model of Li282 also gives lower values of the critical stress for the decay of a boundary in the case where a few intrinsic or extrinsic dislocations break away simultaneously from it. However, the description of the boundary decay assuming that only single dislocations move while the positions of the other dislocations remain unchanged seems incorrect. Gutkin and Ovid’ko226 proposed a continuum disclination model for describing the migration of an arbitrary tilt GB. A migrating GB was approximated by a biaxial dipole of partial wedge disclinations capable of moving under an applied shear stress τ in the elastic field of a similar disclination dipole of opposite sign that forms when the GB breaks away from the neighbouring GBs (i.e. at the moment when triple GB junctions transform into double junctions) (Fig. 12.21). It was shown that there are two modes of GB migration. When the applied stress reaches the first critical value:

[12.7]

where D = G/[2π (1–ν)], G is the shear modulus, ν is the Poisson ratio, ω is the disclination strength equal to the misorientation angle of the migrating GB, 2a is the length of the GB and b is the interatomic distance, the GB begins to migrate in the stable mode in which its equilibrium position is determined by a stress level τ ≥ τc1. When the stress τ reaches the second critical value: ,

[12.8]

the GB migration becomes unstable; the equilibrium position of the GB disappears, and the GB migration no longer depends on τ. For pure nc-Al with grain size d ranging from 30 to 100 nm, the stress τc1 ranges from 7.6 to 23.5 MPa for ω = 5° and from 46.5 to 144 MPa for ω = 30°. The stress τc2 proves to be far greater, namely, 0.4 GPa for ω = 5° and 2.5 GPa for ω = 30°, irrespective of the grain size. We note that, in thin nc-Al films under tension, grains begin to grow intensively over the range of true tensile stresses from 130 MPa for d ≈ 90 nm to 190 MPa for d ≈ 40 nm,259,260 which correspond to the maximum values of τ from 65 to 95 MPa lying in the range τ1c < τ < τc2 for GBs with a misorientation angle ω = 5° and in a part of this range for GBs with ω = 30°. Computer simulations of nanoindentation of nc-Al films with a mean grain size of 7 nm showed208 that the migration of a low-angle tilt boundary with a misorientation angle of 13.5° becomes unstable under local shear stresses exceeding the estimated value 0.7 GPa obtained from equation [12.8]. Recently the model226 has been extended to the case of collective migration of the two opposite boundaries of a grain.227,228 We have considered the stress-induced



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12.21 Stress-induced migration of a low-angle (a,b) or high-angle (c,d) grain boundary (GB3) as a mechanism of rotational deformation realized through the glide of a wall of lattice dislocations (b) or motion of a dipole of wedge disclinations (d), respectively.

grain growth in a model nc-sample under a tensile stress σ (Fig. 12.22) and analysed in detail the situation with one pair of interacting GBs (Fig. 12.23). We have shown that two critical stresses, τc and τm, control the behavior of migrating GBs. When the external shear stress τ reaches τc, opposite GBs start to migrate to each other, their migration is stable, and their equilibrium positions are determined by τ ≥ τc. When τ ≥ τm >> τc, the GBs meet. Then the following regimes of cooperative migration are possible at τ > τm, depending on τ level and GB characteristics: 1) GBs annihilate in the very partial case where their misorientations are equal by magnitude and opposite in sign, 2) one GB captures another GB and makes it migrate together in one direction under a moderate τ, 3) GBs coalesce and stand at a local equilibrium position, 4) GBs can overcome their mutual attraction and migrate in opposite directions under a very high τ. In all cases, GB migration leads to unstable growth of a grain by annexing parts of its neighbours.


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12.22 Grain growth through collective GB migration in a model NCM under uniaxial tension: (a) the initial state of tilt boundaries with misorientation angles ω and Ω at a low tensile stress σ1; (b) at a stress σ2 > σ1, the boundaries begin to migrate into grains I–IV and partial wedge disclinations with strengths ±ω and ±Ω appear in the remaining double junctions and form dipole and quadrupole structures; (c) at a higher stress σ3 > σ2, some boundaries annihilate partially (grain I) or completely (grain II), while others pass through each other and stop only near the next boundaries (grains III, IV); (d) smoothing of the boundaries of the enlarged grains I–IV at a stress σ4 ≥ σ3.

The model226 has also been extended to the cases of GB migration and grain nucleation near cracks.95,96,229 It was shown that these processes result in moderate enhancement of fracture toughness96 and in an increase in the equilibrium lengths of the cracks, thus diminishing the probability of their development.229 On the other hand, the stress concentration provided by cracks leads to a decrease in the critical stresses τc1 and τc2.95 Bobylev and Ovid’ko230 have considered GB migration in hexagonal grains and found that, depending on the angle between the mobile and immobile GBs, © Woodhead Publishing Limited, 2011


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12.23 Collective migration of (a, b) low-angle and (c, d) high-angle tilt boundaries separating grains G1–G3 under applied shear stress τ: (a, d) geometrical models and (b, c) dislocation and disclination models, respectively.

GBs migrate more easily (at a lower stress level) compared to the previously examined situation226 with rectangular grains. The difference in the stress may reach a value of ~20 to 30%. The authors230 have concluded that ‘geometry of triple junctions crucially influences their mobility and thereby controls the stress level needed to drive migration of GBs and their triple junctions in deformed nanocrystalline materials’.

12.4 Conclusions and future trends We have considered some analytical theoretical models that describe elastic strains and plastic deformation phenomena in NCMs. Most of these models are © Woodhead Publishing Limited, 2011

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based on the theory of defects, a unified concept that allows one to describe the structure, the elastic fields and the mechanisms of plastic deformation from a unique physical viewpoint. Based on the results of such theoretical modeling, one can formulate the following general conclusions: (i) Due to their structural and scale features, NCMs always contain many elastic-strain sources and stress concentrators that are capable of initiating various mechanisms of plastic deformation under external loading. Most of the stress sources and concentrators are defects localized at/near GBs. At the same time, most of these defects can act as carriers of plastic deformation. As a result, GB-mediated mechanisms of plasticity dominate over other possible mechanisms in fine-grained NCMs. (ii) The GB mediated mechanisms of plasticity are emissions of partial and perfect lattice dislocations and twins from GBs; mass transfer along GBs and their triple junctions; GB sliding, decay and migration; grain rotation, growth and refinement. The present review demonstrates that most of these deformation mechanisms can be analysed theoretically within a unified energy approach. In doing so, one can calculate and analyse some critical values of the applied stress, which control the barrier-less activation of the deformation mechanisms and their transition from the stable regime of development to its unstable regime. Using these results, one can sometimes conclude which deformation mode is preferable in given conditions. When possible, the comparison of theoretical estimates with available experimental data and results of computer simulations shows rather good accordance. (iii) Due to the distribution in grain size, different mechanisms of plastic deformation can dominate in different grains; these mechanisms can also compete within the same grains. Interplay between different mechanisms of plasticity commonly occurs in NCMs. Theoretical modeling of this interplay seems to be a good and important challenge at present. This chapter has concentrated mainly on quasistatic theoretical models. Meanwhile, there are a number of models developed for ultrafine-grained and nanocrystalline materials within the evolutional dislocation kinetics78,120,283,284 and discrete dislocation dynamics.285,286 It seems that incorporating GB dislocation and disclination terms to these models may be a future trend in this field. One more future trend is the wider use of elastic fields of defects calculated in the framework of the strain-gradient elasticity,30,31,84 which allows one to avoid the classical singularities in elastic fields of defects and their interactions. Some examples of applying this theory to dislocation behavior in freestanding287 and in/near embedded nanowires288,289 have recently been demonstrated. Future theoretical models are also expected to describe in more details the interplay between dislocation–disclination and GB diffusion modes of plastic deformation, and between the mechanisms of plasticity and fracture as well.



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12.5 Sources of further information and advice Further information on the topics under discussion in this chapter can be taken from monographs,78,131–133 reviews1,2,10,17–22,29,59,97–130 and other references listed in Section 12.7. The most useful sources of current information are such materials science and physical journals as Acta Materialia, Applied Physics Letters, Journal of Materials Research, Journal of Materials Science, Materials Science and Engineering A, Nature Materials, Philosophical Magazine, Philosophical Magazine Letters, Physical Review B, Physical Review Letters, Physics of Solid State, Progress in Materials Science, Reviews on Advanced Materials Science, Science, Scripta Materialia, etc.

12.6 Acknowledgements The work was supported by the Russian Foundation of Basic Research (Grant No. 08–02–00304-a). I am deeply thankful to my friends and colleagues E.C. Aifantis, S.V. Bobylev, A.A. Fedorov, A.L. Kolesnikova, K.N. Mikaelyan, N.F. Morozov, I.A. Ovid’ko, C.S. Pande, A.E. Romanov, A.G. Sheinerman and N.V. Skiba for helpful discussions and collaboration.

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13 The mechanical properties of multi-scale metallic materials Y.H. ZHAO and E.J. LAVERNIA, University of California Davis, USA Abstract: Bulk nanostructured metallic materials with a multi-scale grain size distribution possess both high strength and good ductility, and therefore are expected to have important technological implications. This chapter introduces the basic concepts of bulk multi-scale, bimodal and multimodal metallic materials and discusses their development background and preparation methods, followed by a review of the experimental and numerical results of mechanical properties (primarily strength and ductility), and deformation and fracture mechanisms of bimodal and multimodal metallic materials, and ends with a final discussion on the potential technological impact and future work. Key words: bulk multi-scale metallic materials, bimodal and multimodal metallic materials, strength and ductility, deformation and fracture mechanisms.

13.1 Introduction In the case of polycrystalline materials, such as metals, alloys, ceramics and intermetallics, grain size (i.e. fraction of grain boundary volume) is one of the most important microstructural parameters that influence properties and deformation mechanisms. For instance, the mean grain size generally influences the low-temperature yield strength of polycrystals via the well-known Hall–Petch relationship. The grain size of conventional structural polycrystalline materials typically falls in what is widely described as the coarse-grained (CG) regime (>1 µm, see Fig. 13.1) which may include the fine-grained sub-regime (1–10 µm).1 Over the past couple of decades, nanocrystalline (or bulk nanostructured, 1.

[14.1]

The first term on the left-hand side of Hart’s criterion [14.1] describes the strainhardening, and m is the strain rate sensitivity (or strain rate hardening) defined as: . m = {∂ log σ /∂ ln ε}ε,T. [14.2] If Hart’s criterion [14.1] is valid, a solid under tensile load is stable relative to the necking. Commonly Hart’s criterion [14.1] in nanocrystalline metallic materials with intermediate grains is violated, and these materials are not stable against the necking.16,24 At the same time, there are several examples of enhanced tensile ductility of nanocrystalline metals,11–30 in particular, those with intermediate grains. In most nanocrystalline metallic materials with good ductility, the crucial suppression of plastic strain instability is due to strain hardening, while the role of strain rate hardening (characterized by m) is negligibly small. Thus, nanocrystalline metals are capable of exhibiting good tensile ductility when plastic strain, crack nucleation and propagation instabilities are suppressed in the metals. In order to understand the origin of these instabilities in nanocrystalline metallic materials, it is very important to identify the grain size effects on plastic flow and fracture mechanisms operating in these materials. Sections 14.3–14.5 briefly discuss the specific features of plastic flow and fracture mechanisms in nanocrystalline materials with a particular attention being paid to their sensitivity to the grain size.


Enhanced ductility and its mechanisms

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14.3 Plastic flow mechanisms in coarse-grained metallic polycrystals, ultrafine-grained metals and nanocrystalline metals with intermediate grains First, let us discuss the effects of grain size on plastic flow mechanisms operating in coarse-gained polycrystalline, ultrafine-grained and nanocrystalline metallic materials with intermediate grains. It is well known that the dominant deformation mechanism in conventional coarse-grained polycrystalline metals is lattice dislocation slip occurring in the large grain interiors.37 Its carriers are perfect lattice dislocations generated and stored in the form of dislocation cells/subgrains in the grain interiors during plastic deformation. Grain boundaries serve as obstacles for the movement of lattice dislocations, in which case they influence the level of the yield stress. This effect of grain boundaries in coarse-grained polycrystalline metals is described by the following classical Hall–Petch relationship between the yield stress τ and grain size d:38,39

τ = τ0 + kd –1/2,

[14.3]

with τ0 and k being constant parameters. However, in general, the mechanical behavior of coarse-grained polycrystalline metals is crucially affected by evolution of lattice dislocations in grain interiors, but not grain boundaries. For instance, the deformation-induced storage of lattice dislocations in grain interiors in coarsegrained polycrystalline metals is responsible for strain hardening. It means that the flow stress increases with rising plastic strain. This standard deformation behavior is exhibited by most coarse-grained polycrystalline metals with grain size d being larger than 300 nm. With grain refinement, the lattice dislocation slip shows deviations from its standard behavior due to both the nanoscale grain size and grain boundary effects. For illustration, let us consider ultrafine-grained metals (d ranges from 100 to 300 nm) and nanocrystalline metallic materials with intermediate grains (d ranges from dc to 100 nm). The lattice dislocation slip is still dominant in such materials. However, in contrast to the situation with conventional coarse-grained polycrystals, lattice dislocations are not intensively stored in grain interiors. In ultrafine-grained metals and nanocrystalline metallic materials with intermediate grains, the flow stress is crucially affected by the dislocation storage and annihilation at grain boundaries.16 The lattice dislocations are generated and move under the applied stress within the grain interiors. Then the lattice dislocations reach grain boundaries where they are transformed into grain boundary dislocations. This process leads to the dislocation storage at grain boundaries. The dislocation storage provides the strain hardening of a metallic material during plastic deformation. At the same time, grain boundary dislocations with opposite Burgers vectors tend to move towards each other and annihilate each other (when they meet). The dislocation annihilation at grain boundaries provides the strain softening (decrease in the flow stress with rising plastic strain) of a material during plastic deformation. Following


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Wang et al.,16 after some initial stage of deformation, the above opposing reaction rates reach an equilibrium by canceling each other. That is, such an equilibrium causes a steady state in which the dislocation generation rate is completely compensated by the dislocation annihilation rate. The steady state is characterized by an approximately constant flow stress, in which case strain hardening of the material during plastic deformation is practically absent. In this circumstance, the first term on the left-hand side of Hart’s criterion [14.1] is approximately 0. The conventional lattice dislocation slip typically results in the strain rate sensitivity m less then 0.1. Therefore, in nanocrystalline metallic materials with intermediate grains deformed by mostly the lattice dislocation slip, Hart’s criterion [14.1] is violated, and these materials under tensile load are unstable leading to the necking (Fig. 14.2). As shown in many experiments, this deformation behavior is typical for most ultrafine-grained materials and nanocrystalline materials with intermediate grains.16

14.4 Plastic flow mechanisms in nanocrystalline metals with the finest grains In nanocrystallin e metallic materials with finest grains (with grain size lower than dc = 10–30 nm), the lattice dislocation slip is very limited or even completely suppressed,1–10 because of the two factors. First, grain boundaries (of which there are many) stop gliding lattice dislocations in nanocrystalline materials. Second, the generation of dislocations by Frank–Read and other sources in nanoscale grains requires extremely high stress, which may initiate cracks.7 At the same time, alternative deformation modes such as grain boundary sliding, Coble creep, triple-junction diffusional creep, rotational deformation and nanoscale twin deformation effectively operate in nanocrystalline metals.1–10 Of primary importance to the ductility of nanocrystalline metallic materials with finest grains is the role of grain boundary sliding in plastic flow. This deformation mode means a relative shearing of neighboring grains, which is localized in the boundary between the grains. Since grain boundaries end at triple junctions, such junctions serve as natural geometric obstacles for grain boundary sliding. In this situation, the unfinished plastic shear (or, in terms of grain boundary dislocations, the dislocation Burgers vector) associated with grain boundary sliding is accumulated at triple junctions, which thereby serve as stress sources. There are several ways to accommodate of the unfinished plastic shear at the triple junctions in nanocrystalline materials: the emission of lattice dislocations from triple junctions (Fig. 14.4), diffusional accommodation, rotational deformation and void formation (Fig. 14.4 (c) ).40–46 The emission of lattice dislocations from triple junctions seems to be a rather widespread process in various nanocrystalline materials.45,46 Grain boundary sliding accommodated by such a dislocation emission process is characterized by creep strain rate:45,46


Enhanced ductility and its mechanisms . εis ≈ 9bDgb · d –3 [exp(2Mτb3/kBT) – 1],

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where b denotes the lattice parameter, τ the applied shear stress, M the stress concentration factor (at triple junction), kB Boltzmann’s constant, and T the absolute temperature. Following papers,45,46 equation [14.4] is valid in a wide temperature interval, including room and ambient temperatures. (At the

14.4 Grain boundary sliding and its accommodation through lattice dislocation emission from triple junctions. (a) Grain boundary sliding occurs through the movement of grain boundary dislocations along grain boundaries. Grain boundary dislocations are accumulated near triple junctions. (b) Grain boundary dislocations transform into lattice dislocations that are emited from triple junction B and glide within grain I. These processes are accompanied by formation of dipole of wedge disclinations (full and open triangles) A and B. (c) The lattice dislocations reach grain boundary CD where they transform into grain boundary dislocations that climb along this grain boundary. The distance between wedge disclinations A and B increases due to grain boundary sliding. (d) The distance between wedge disclinations A and B increases more due to grain boundary sliding. Nanocrack nucleates in the stress field of the dipole of wedge disclinations A and B.


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same time, there is a restriction concerning grain growth that may destroy the nanocrystalline structure. That is, the temperature should be lower than the temperature at which intensive grain growth starts to occur in a nanocrystalline metal.) According to estimates45,46 for nanocrystalline Ni, strain rate sensitivity m is typically lower than 0.05 (except for regimes with extra low strain rate . ε ≤ 10–8 s–1). Besides, grain boundary sliding produces dipoles of wedge disclinations – defects associated with crystal lattice orientation incompatibilities – at and near triple junctions (Fig. 14.4).47–49 (More precisely, a wedge disclination represents a rotational line defect located at either a grain boundary or a triple junction, and is characterized by the disclination strength or, in other words, the rotational misfit.50 For instance, a wedge disclination at a tilt grain boundary is the line dividing grain boundary fragments with different tilt misorientation angles, whose difference is the disclination strength. A wedge disclination exists at a triple junction of tilt boundaries if the sum of tilt misorientation angles of these boundaries is non-zero.50 The non-zero sum (angle gap) serves as the disclination strength). Figure 14.4 schematically shows formation of wedge disclination dipoles (two connected arrow signs in the figure) due to grain boundary sliding in a nanocrystalline specimen; for more details, see Ovid’ko and Sheinerman.47,49 Following,47,49 wedge disclination dipoles appearing in nanocrystalline metallic materials during grain boundary sliding create very pronounced strain hardening, and this factor can positively influence ductility of such materials (see Section 14.6). Now let us briefly discuss diffusional creep modes operating in nanocrystalline metallic materials with finest grains. The diffusion coefficient Dtj along triple junctions is much larger than the grain boundary diffusion coefficient Dgb,51 which, in its turn, is by several orders larger than the bulk diffusion coefficient Dbulk.52 Also, the volume fractions occupied by triple junctions and grain boundaries rapidly increase (at the expense of the volume fraction occupied by grain interiors) with decreasing the grain size d in nanocrystalline materials53 (Fig. 14.5). In these circumstances, the contributions of Coble creep and triple junction diffusional creep are enhanced with decreasing the grain size d54,55 more rapidly than that of the Nabarro–Herring creep (bulk diffusional creep). This tendency is . . reflected in various strain rates, Nabarro–Herring creep (ε bulk), Coble creep (εgb) . and triple junction diffusional creep (εtj), all of which are grain size dependent: . ε bulk ∝ Dbulk · d –2 σ, . εgb ∝ Dgb · d –3 σ, . εtj ∝ Dtj · d –4 σ, [14.5] where σ is the applied tensile stress. Since the diffusional mass transfer is enhanced with rising temperature, grain boundary and triple-junction diffusional



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14.5 Volume fractions of grain boundaries, triple junctions and interfaces (grain boundaries + triple junctions of grain boundaries + quadruple nodes of triple junctions) as a function of grain size d, for nanocrystalline metals with grain boundary thickness = 1 nm. Source: Reprinted from Scripta Materialia with permission from Elsevier.53

creep modes are capable of significantly contributing to plastic flow in nanocrystalline metallic materials with finest grains at intermediate and high temperatures (Tgbd < T < Tgg, where Tgbd ≈ 0.3 Tm is the minimum temperature at which intensive grain boundary diffusion occurs, Tgg ≈ (0.5–0.6) Tm is the minimum temperature at which intensive grain growth (destroying the nanocrystalline structure) occurs, and Tm is the melting temperature).54,55 Rotational deformation in coarse-grained and nanocrystalline solids is defined as plastic deformation accompanied by crystal lattice rotations within grains.50,56,57 Rotational deformation is commonly carried out by moving dipoles of grain boundary wedge disclinations.50,56,57 Disclination dipole movement in coarsegrained polycrystals occurs through rearrangement of lattice dislocations in grain interiors.50 In nanocrystalline metallic materials where the number of pre-existing lattice dislocations in grain interiors is very limited, rotational deformation occurs through 1) the emission of perfect lattice dislocations from grain boundaries and their absorption at opposite grain boundaries;57 2) stress-driven migration of grain boundaries;58 and 3) slip and climb of grain boundary dislocations.42,59 In the latter case, the rotational deformation can be effectively initiated by preceding grain boundary sliding and serve as its accommodating mechanism.42 The representations on rotational deformation are well supported by experimental observations of crystal lattice rotations within grains in deformed nanocrystalline metallic materials.40,60–64 Partial dislocations that carry partial dislocation slip and twin deformation have been experimentally observed in nanocrystalline metals with finest grains.65–72 In


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particular, pairs of partial dislocations emitted from grain boundaries and connected by wide stacking faults have been experimentally observed in nanocrystalline Al,69 whereas their formation in coarse-grained Al is commonly hampered due to high values of the specific stacking fault energy. The results of these experiments are indicative of the strong nanoscale and interface effects that enhance the partial dislocation slip. Also, twin deformation has been experimentally observed in nanocrystalline metals like Al, Cu, Ni and Ta.65–72 Twin deformation plays an important role, in particular, in nanocrystalline metals deformed at high strain rates and low temperatures, in which case grain boundary sliding and grain boundary diffusion are suppressed. Thus, grain boundary sliding, grain boundary diffusional creep, triple junction diffusional creep, partial dislocation slip, rotational and twin deformation modes effectively operate in nanocrystalline metallic materials with finest grains. These deformation mechanisms are characterized by very high values of the flow stress, which are much larger than those characterizing the lattice dislocation slip in conventional coarse-grained polycrystals and ultrafine-grained materials.1–10 At the same time, super-strong nanocrystalline metals with finest grains commonly show low tensile ductility, in particular, due to crack nucleation and propagation instabilities (Fig. 14.1). In doing so, the nanocrystalline structure is responsible for the action of specific crack nucleation and growth mechanisms operating in nanocrystalline metallic materials. This subject will be considered briefly in the next section.

14.5 Specific features of crack nucleation and growth processes in nanocrystalline metallic materials As it has been mentioned earlier, nanocrystalline metals can exhibit either ductile or brittle fracture behavior, depending on both their structural characteristics and the conditions of mechanical loading. In particular, there are several experimental reports on nanocrystalline metallic materials having an average grain size in the range of around 20 to 100 nm and showing slow ductile fracture with preceding neck formation and dimpled structures at fracture surfaces.18–23,40 The size of the dimples is commonly considerably larger than the grain size, and ductile fracture is believed to occur through the coalescence of microvoids. At the same time, there are nanocrystalline metallic materials showing the brittle fracture. For instance, nanocrystalline Ni-15%Fe alloy with an average grain size of around 9 nm under tensile test at room temperature18,19 and nanocrystalline Ni specimens with an average grain size of around 30 nm under fatigue test (tension–tension cyclic deformation) at room temperature73 exhibit intergranular brittle fracture. In these cases, the main brittle crack is believed to be formed through the multiple generations of intergranular nano/micro-scale cracks and their convergence.



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Brittle and ductile fracture processes in nanocrystalline metallic materials are crucially influenced by their structural features: nanoscale sizes of grains and large amounts of grain boundaries. In particular, grain boundaries serve as preferable places for nanocrack nucleation and growth because the atomic density is low, and interatomic bonds are weak at grain boundaries compared to the grain interior. In the case of ductile fracture carried by microvoid growth and coalescence in nanocrystalline metals, the microvoid growth by vacancy diffusion mechanism is enhanced in nanocrystalline metals due to the large amounts of grain boundaries characterized by high diffusivity. Besides, the extra energy of grain boundaries contributes to the driving force for intergranular fracture with cracks propagating along such boundaries and releasing the extra energy, compared to intragranular fracture with cracks propagating through grain interiors. At the same time, grain boundaries are short and curved at numerous triple junctions in nanocrystalline metallic materials. Therefore, if cracks tend to nucleate and grow along grain boundaries, crack propagation can be deflected from the axis of highest stress to less efficient orientations directed by curved grain boundary surfaces. This leads to increased fracture energy through increased fracture surface area and lower driving forces due to the reduced resolved normal stresses at the crack tip as a result of the deflection of the crack tip away from the most efficient (Mode I) loading orientation. As was noted in Section 14.4, plastic deformation in nanocrystalline metallic materials with finest grains occurs at very high stresses, and grain boundary sliding serves as one of its dominant deformation mechanisms. In the context discussed, one expects that crack nucleation and growth processes in nanocrystalline metals with finest grains are influenced by grain boundary sliding. This statement is confirmed by experiments, computer simulations and theoretical models. In particular, it was theoretically revealed that the enhanced generation of nanocracks in deforming nanocrystalline materials with finest grains can occur at triple junctions with defects produced by intergrain sliding, such as dislocations,43–46 disclination dipoles47,49 (Fig. 14.4 (c) ) and dislocation– disclination configurations48 serving as dangerous stress concentrators. Such nanocracks in the vicinities of triple junctions have been observed by Kumar et al. in in situ experiments using nanocrystalline Ni with an average grain size of around 30 nm.40 Also, molecular dynamics simulations74 show nanocracks being generated at triple junctions of grain boundaries near tips of pre-existing large cracks in nanocrystalline Ni with grain size ranging from 5 to 12 nm. With these experimental data, computer simulations and theoretical results, one expects that nanocracks at triple junctions of grain boundaries serve as typical elemental carriers (plate-like cracks of smallest size) of brittle fracture in nanocrystalline metallic materials with finest grains. Also, the unique structural features (nanoscale sizes of grains and large amounts of grain boundaries) of nanocrystalline metallic materials cause the specific features of crack growth in these materials. In most cases, super-strong


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nanocrystalline materials are characterized by low tensile ductility and low fracture toughness at room temperature.1–10 In particular, some nanocrystalline face-centred cubic (fcc) metals exhibit a ductile-to-brittle transition with decreasing grain size.18,19,23 In contrast, good ductility is typically inherent to coarse-grained fcc metals where the emission of lattice dislocations from cracks causes effective crack blunting and thus suppresses their growth. In the light of the discussed difference in the fracture behavior between nanocrystalline and coarse-grained fcc metals, of particular interest is the nature of the sensitivity of the crack-blunting process to nanocrystallinity. In paper,36 a theoretical model was suggested in describing the grain size effect on crack blunting through the emission of lattice dislocations from cracks in nanocrystalline metallic materials (Fig. 14.6 (a) and 14.6 (b) ). Within this model, grain boundaries serve as structural elements that hinder the movement of lattice dislocations emitted from cracks and thereby the blunting of cracks in nanocrystalline materials. In these circumstances, if the grain size of a polycrystalline solid is sufficiently large, the emitted dislocations move far enough from the crack tip and do not significantly hinder the motion of new dislocations until the number of the emitted dislocations becomes large enough (Fig. 14.6 (c) and 14.6 (d) ). As a result, the dislocation emission along one slip plane can induce significant blunting of the crack tip. Following,75,76 the significant blunting by lattice dislocations stops crack growth and makes the solid ductile. At the same time, in nanocrystalline materials with finest grains, the emission of even one dislocation and its immobility at the nearest grain boundary hinders the emission of the succeeding dislocations along the same plane due to dislocation repulsion (Fig. 14.6 (a) and 14.6 (b) ). In doing so, the dislocation emission does not induce significant crack blunting. As a corollary, the nanocrystalline solid tends to show low crack growth resistance. This conclusion is in good agreement with the experimental findings that most nanocrystalline materials with finest grains are brittle. On the other hand, the experiment77 showed enhancement of crack growth resistance of nanocrystalline Ni with grain size of around 20 nm, compared to that in coarse-grained Ni. These experimental data, as well as similar data78–81 on enhancement of crack growth resistance of nanocrystalline ceramics, are naturally explained within the theoretical concept82–86 that specific toughening micromechanisms can operate in nanocrystalline materials, which are not effective in coarse-grained polycrystals. Such micromechanisms are suggested to be nanoscale deformation twinning,82 Ashby–Verall creep carried by grain boundary sliding accommodated by grain boundary diffusion and grain rotations,83,84 stressdriven migration of grain boundaries85 and nucleation of nanoscale grains86 near crack tips. However, in most cases, as it has been previously noted, nanocrystalline materials with the finest grains exhibit brittle fracture.



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14.6 Grain size effect on crack blunting through emission of lattice dislocations from crack tips. (a) and (b) Emission of even one dislocation and its stop at the nearest grain boundary hinder the emission of subsequent dislocations along the same plane due to dislocation repulsion. As a result, the dislocation emission does not induce significant crack blunting in nanocrystalline specimen. (c) and (d) If the grain size of the solid is sufficiently large, the emitted dislocations move far enough from the crack tip and do not significantly hinder the motion of new dislocations until the number of the emitted dislocations becomes large enough. As a result, the dislocation emission along one slip plane can induce significant blunting of the crack tip in coarse-grained polycrystalline specimen.


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14.6 Enhanced ductility of artifact-free nanocrystalline metals with narrow grain size distributions Although most nanocrystalline metallic materials show disappointingly low tensile ductility at room temperature, several experimental examples have revealed substantial tensile ductility at room temperature.11–30 Of particular interest are experimental results20–22,27 that support the evidence of enhanced tensile ductility of single-phase nanocrystalline metallic materials with narrow grain size distributions and without artifacts, because these results are indicative of intrinsic ductility of the ‘pure’ nanocrystalline structures. (In such materials, ‘extrinsic’ factors like composite structures, bimodal/multimodal grain size distributions, pre-existent pores and contaminations do not operate.) In the experiments,20–22 artifact-free bulk nanocrystalline Cu and Al-5%Mg alloy with mean grain sizes of around 23 nm and 26 nm, respectively, were fabricated by in situ consolidation during mechanical alloying at liquid nitrogen temperature. These artifact-free nanocrystalline materials showed both ultrahigh strength and good tensile ductility20–22 (Fig. 14.7). (Similar good plastic properties were exhibited by the artifact-free nanocrystalline Cu specimens with narrow grain size distributions in the miniaturized disc bend test.87) They showed strainhardening and ductile fracture mechanism with ductile dimples at fracture surfaces.20–22 The lattice dislocation slip was reportedly active in artifact-free nanocrystalline Cu and Al-5%Mg alloys. With these data, Youseff et al.20–22 attributed the ductile behavior to both the strain hardening and thereby good

14.7 A typical tensile stress–strain curve for the bulk in situ consolidated nanocrystalline Cu sample in comparison with that of a coarse-grained polycrystalline Cu sample (an average grain size larger than 80 µm) and a nanocrystalline Cu sample prepared by an inert gas condensation and compaction technique (with a mean grain size of 26 nm). Source: Reprinted with permission from Applied Physics Letters.20



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ductility of the materials by lattice dislocation storage in grain interiors. However, this explanation did not take into account the microscopic mechanisms of generation and storage of lattice dislocations in interiors of fine grains. At the same time, this aspect of the dislocation behavior at the nanoscale level is of crucial importance because, in most cases, the lattice dislocation generation and storage in finest nanoscale grains are very limited or even completely suppressed. In particular, conventional lattice dislocation sources (like Frank–Read sources) do not operate in nanoscale grains.1–10 Besides, even if the lattice dislocations are generated in nanoscale grains, they tend to move toward grain boundaries (where these dislocations are absorbed) due to the image forces.88–91 The experimental data20–22 on simultaneously high strength and good tensile ductility of nanocrystalline metallic materials with narrow grain size distributions can be naturally explained within the approach49 focusing on the optimization of grain boundary sliding and diffusion processes. More precisely, grain boundary sliding in nanocrystalline materials results in the emission of lattice dislocations from triple junctions and produces wedge disclination dipoles at triple junctions of grain boundaries10,47,49 (Fig. 14.4). The wedge disclination dipoles create very pronounced strain hardening. The calculated strain hardening47,49 appeared to be so high that it leads to the experimental values of the ultimate stress (the peak stress at the experimental stress–strain curve) at very small values of plastic strain. For instance, the calculated stress reaches the value of 0.23 GPa (approximately equal to the experimental ultimate stress), at plastic strain = 0.01, for Cu, and the value of 0.61 GPa (approximately equal to the experimental ultimate stress) at plastic strain = 0.02, for Ni.49 Therefore, one can assume that such dramatic strain hardening (created by grain boundary sliding), although suppressing plastic strain instability to necking, commonly induces early fractures associated with intensive formation and growth of cracks. Nevertheless, experimentally detected examples of substantial tensile ductility20–22 of nanocrystalline metallic materials showing moderate strain hardening are naturally attributed to the strain hardening caused by grain boundary sliding, if it is relieved by some accommodation mechanisms. In particular, grain boundary diffusion can significantly reduce or even completely remove the disclination stresses and the associated strain hardening in nano crystalline materials. Following Ovid’ko and Sheinerman,49 diffusion processes are capable of suppressing crack nucleation and growth and thus result in good tensile ductility of nanocrystalline metallic materials at certain conditions that optimize grain boundary sliding and grain boundary diffusion process. The optimization in question means that, for a specified strain rate, the rate of diffusion should be high enough to decrease strain hardening and suppress nucleation of crack but, at the same time, small enough to suppress plastic strain instability. At the same time, for a specified strain, there exists an interval of strain rates and temperatures at which a nanocrystalline specimen is stable to necking and catastrophic fracture.49 With an increase of strain, this interval of strain rates and temperatures shrinks, and at some critical strain it disappears. Above this critical


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strain, a nanocrystalline specimen can no more be stabilized with respect to failure by either necking or fracture through the optimization of its deformation regime. Also, grain boundary sliding results in the emission of lattice dislocations from triple junctions (Fig. 14.4), and these dislocations cause the following two effects. First, lattice dislocations are absorbed by grain boundaries where they could glide and climb, enhance grain boundary sliding and produce grain boundary vacancies that enhance grain boundary diffusion, respectively.5,10 Second, lattice dislocations emitted from triple junctions can be stored in grain interiors due to Lomer–Cottrell locking92 and/or elastic interaction with other dislocations and grain boundary defects. For instance, intergrain sliding produces the wedge disclination dipoles of wedge disclinations which strongly interact with the lattice dislocations and prevent their movement toward grain boundaries; and thus are capable of enhancing the lattice dislocation storage in grain interiors. In this case, the experimentally observed lattice dislocations, as noted by Youseff and co-workers,20 can contribute to the strain hardening. However, it should be noted that, in the experiments,20 the lattice dislocation storage was observed near growing crack tips. At the same time, the conditions for lattice dislocation generation and storage in regions near crack tips (where extremely high local stresses operate, and the stress screening effects of crack free surfaces are pronounced) are much softer compared to those in nanoscale grain interiors located far from crack tips. Therefore, the lattice dislocation activity may be suppressed in the regions far from crack tips, and its contribution to the strain hardening of nanocrystalline metallic materials with narrow grain size distributions may be insignificant. Thus, the concept49 on the optimization of grain boundary sliding and diffusion process gives at least a semi-quantitative explanation of the experimentally observed20–22 good tensile ductility of artifact-free nanocrystalline metallic materials with narrow grain size distributions. Representations of this concept are also relevant to the description of experimentally observed superplasticity shown by nanocrystalline materials at higher strain rates and lower temperatures,31 compared to their coarse-grained counterparts. In the case of superplasticity, however, one should take into consideration several additional factors like grain growth, strain rate hardening, and formation of mesoscopic sliding surfaces.

14.7 Enhanced ductility of nanocrystalline metals due to twin deformation and growth twins There are experimental data indicating on the special role of twin deformation in an increase of strain-to-failure of nanocrystalline metals under tensile load. For instance, Karimpoor and co-workers14 experimentally revealed both high strength and enhanced tensile ductility of electroplated nanocrystalline Co (hexagonal close-packed) (containing 0.09 wt.% S and 0.07 wt.% C) with the mean grain size d = 12 nm at room temperature. These fully dense nanocrystalline Co specimens exhibited both moderate strain hardening approximately specified by the



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dependence σ = Kε n, where n = 0.4, and good tensile ductility characterized by strain-to-failure ranging from 0.06 to 0.09. Also, the nanocrystalline Co specimens are characterized by the yield and tensile strength, which are about 2–3 times higher than those of coarse-grained polycrystalline Co.14 In doing so, the yield and tensile strength increase as the plastic strain rate decreases from 2.5 10–3 s–1 down to 10–4 s–1. Since such a response is typical for a material in which the twin deformation mode is dominant,93 Karimpoor with co-workers14 postulated that enhanced tensile ductility of nanocrystalline Co occurs due to the dominant twin deformation that provides moderate strain hardening. Similar deformation behavior of electroplated nanocrystalline Co was reported in a paper.24 Further, a very high density of extremely thin twins was observed in the nanocrystalline Co specimens after tensile load. With these experimental data, the twin deformation mode associated with moderate strain hardening can serve as a micromechanism for enhancing tensile ductility in nanocrystalline Co and, probably, for other metals with low stacking fault energy. In recent years, particular attention has been paid to the unique combination of high strength and enhanced ductility of nanotwinned copper.17,28–30 Nanotwinned copper specimens have ultrafine-grained structure with a high density of nanoscale growth twins.17,28–30 Thus, the structure at the nanoscale level is composed of nanoscale elements – twins – divided by coherent twin boundaries serving as obstacles for moving lattice dislocations. Coherent twin boundaries have much lower energy (per unit area) and thereby are more stable against migration in nanotwinned materials, compared to high-angle grain boundaries in nanocrystalline materials with the same chemical composition.17,28–30 (The basic driving force for the migration of twin and grain boundaries is related to a decrease in the boundary energy. In this context, the boundaries with low energy (per unit area) are more stable against such a migration compared to those with large energy.) In the experiments,17,28–30 it is found that nanotwinned Cu specimens show high strength and good ductility. For instance, Lu and co-workers29 reported that nanotwinned copper (with the average twin lamella thickness of around 15 nm) exhibited good tensile ductility (strain-to-failure εf = 0.14), high values of the yield stress (900 MPa) and the ultimate tensile stress (1068 MPa). These strength values are at least one order of magnitude larger than those characterizing coarse-grained copper. Nanotwinned copper, with an average twin lamellar thickness of 4 nm, shows very good tensile ductility (strain-to-failure εf = 0.3), but at the expense of the ultimate tensile stress (around 700 MPa).29 Stress–strain curves of nanotwinned Cu specimens under tensile load are indicative of strain hardening.17,28–30 From the microstructural viewpoint, plastic deformation in nanotwinned metals occurs by lattice dislocation slip, which results in strain hardening due to accumulation and transformations of lattice dislocations in twin interiors and at twin boundaries.28–30 With decreasing of the average twin lamellar thickness, the hardening by the interaction between dislocations and twin boundaries increases and becomes dominant over the


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contribution from the hardening by the dislocation–dislocation interaction within twin interiors.29 In this context, of particular interest are the specific features of the dislocation behavior at twin boundaries in nanotwinned metals and its difference from the dislocation behavior at high-angle grain boundaries in nanocrystalline materials. When lattice dislocations reach coherent twin boundaries, they either keep their identity as lattice defects or transfer across twin boundaries into adjacent crystallites, in which case the residual dislocations are formed at coherent twin boundaries.28–30 As a result, the dislocations are accumulated at twin boundaries during plastic deformation and thus significantly contribute to the strain hardening. (This behavior is contrasted to that of lattice dislocations when they reach conventional high-angle grain boundaries in nanocrystalline materials under the action of the image forces and/or the external stress. The lattice dislocations are commonly absorbed by high-angle grain boundaries where they transform into grain boundary dislocations that intensively climb (due to enhanced diffusivity along high-angle grain boundaries), or glide and come into annihilation reactions or undergo other transformations reducing their density at grain boundaries.5,10 As a result, their accumulation is very limited or even completely suppressed at grain boundaries in nanocrystalline materials.) This activity of lattice dislocations within twin interiors and at coherent twin boundaries can serve as a micromechanism for enhancing the tensile ductility of nanotwinned copper and, probably, other metals with high densities of nanoscale growth twins.

14.8 Enhanced ductility of nanocrystalline metals due to strain rate hardening In papers,16,24 it was noted that enhanced tensile ductility of nanocrystalline and ultrafine-grained metallic materials can be achieved due to strain rate hardening, if it is characterized by large strain rate sensitivity (m = 0.5 or larger, as with conventional superplasticity of microcrystalline materials; e.g.94,95). This idea was indirectly illustrated by experimental data16 on simultaneously good ductility (strain-to-failure εf = 0.14) and high strength of ultrafine-grained Cu specimen under room temperature tensile tests at a low strain rate of 10–6 s–1. Also, Champion and co-workers13 fabricated nanocrystalline Cu that has large grains with size of around 200 nm divided into subgrains (with low-angle boundaries) whose typical sizes are between 50 and 80 nm. The Cu showed near-perfect elastic–plastic behavior with no strain hardening, absence of neck formation and strain-to-failure of 14% in a tensile test at a low strain rate of 10–6 s–1. However, in the experiment13 there are no direct experimental measurements of the strain rate sensitivity m, while Wang and Ma16 reported low values of the strain rate sensitivity (m = 0.025 or lower). In these circumstances, the enhancement of tensile ductility of nanocrystalline metallic materials through pronounced strain hardening rate needs further experimental and theoretical examinations.



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In general, strain hardening rate is high (m = 0.5–1) in nanocrystalline materials deformed by diffusional creep mode and grain boundary sliding. In particular, it is the case of creep in which grain boundary deformation processes can provide significant contribution to plastic flow. For instance, Coble creep (grain boundary diffusional creep) mode was recognized as the dominant deformation mechanism in tensile creep test of nanocrystalline Ni specimens (with grain size of around 30 nm) at room temperature.96 However, during the room temperature test, creep rates of these nanocrystalline Ni specimens very quickly diminish to very low . values (ε ≤ 10–9 s–1) under the applied stress close to the yield stress. Such low strain rates hardly allow one to reach reasonable degrees of plastic strain or, in other terms, good ductility at room temperature.

14.9 Enhanced ductility of single-phase nanocrystalline metals with bimodal structures One of the most effective strategies in achieving high strength in materials without loss of ductility is to fabricate single-phase metallic materials with bimodal structures composed of nanoscopic and comparatively large grains11,15 (Fig. 14.8). Such nanomaterials have two peaks in grain size distribution, one in the nanometer range, and the other in the submicrometer range. Although the micromechanisms responsible for combining high strength and good ductility of nanomaterials with bimodal structures in the course of their plastic deformation are still under discussion,11,15,97–99 the general assumption is that the presence of large grains suppresses crack formation and/or propagation (Fig. 14.8) and provides strain-hardening necessary for good ductility while the nanocrystalline matrix provides high strength and hardness. Apparently, the first experimental investigation of metallic nanomaterials with bimodal structures was performed by Tellcamp et al.,11 who fabricated a nanostructured Al alloy with an average grain size of 30 to 35 nm. The nanostructured alloy has been found to have a 30% increase in both yield strength and ultimate strength without the corresponding decrease in elongation. Such enhanced ductility has been attributed to the presence of larger Al grains in the bimodal grains. It is logical to assume that dislocation activity in these grains could blunt the propagating cracks and thereby enhance plasticity.11 In the experiment,15 crystallization of an initially amorphous metallic alloy – Fe-based metallic glass of the FINEMET type (Virtroperm) – was used as a method of obtaining a nanocrystalline material with a bimodal structure free from pores and contamination. Specimens with different grain size distributions were fabricated: 1) nanocrystalline specimens with a narrow grain size distribution (characterized by the mean grain size 15 nm), 2) specimens with a bimodal structure where distinct, large grains (with a grain size of around 200 nm) are randomly distributed in a nanocrystalline matrix (with a mean grain size of around 15–20 nm), and 3) specimens with a bimodal structure where large grains (with a


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14.8 Deformation and fracture processes in a specimen with bimodal structure. Large grains suppress crack propagation and provide strain hardening (related to lattice dislocation accumulation) necessary for good ductility while the presence of the nanocrystalline matrix results in high strength and hardness.

grain size of 100–200 nm) are arranged in groups randomly distributed in a nanocrystalline matrix (with a mean grain size of around 15 nm). These specimens showed different deformation behaviors under tensile tests at temperature T = 600°C and strain rate of 10–4 s–1. Nanocrystalline specimens with a narrow grain size distribution are characterized by high strength, low ductility, no strain hardening and strain rate sensitivity m = 0.5. Grain boundary sliding specified by m = 0.5 is supposed to dominate in these materials. Homogeneous nanocrystalline specimens show low tensile ductility when grain boundary sliding initiates nucleation of nanocracks at triple junctions that grow rapidly.15 Specimens with a bimodal structure containing distinctly separated large grains showed high strength (characterized by the ultimate tensile stress = 1.7 GPa), strain hardening and good tensile ductility (characterized by strain-to-failure εf = 0.15). The lattice dislocation activity seems to be responsible for strain accommodation, strain-



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hardening and good ductility, while the nanocrystalline matrix is responsible for the high strength.15 Specimens with a bimodal structure containing groups of large grains are characterized by comparatively low strength and intermediate ductility with poor resistance to plastic flow localization. The group of large grains most likely deforms by dislocation creep at low stresses. Plastic deformation by the lattice dislocation creep in large grains arranged in groups seems to control low strength and is responsible for neck formation in these materials.15 This approach – fabrication of materials with bimodal grain size distributions to obtain a combination of high strength and good ductility – has been extended to other alloys with bimodal structures consisting of large grains embedded into ultrafine-grained matrixes16,100–105 as well as the alloys with multimodal structures with several peaks in grain size distribution.106,107 For instance, Wang and co-workers16,100 fabricated copper specimens with a bimodal structure where large grains are embedded into an utrafine-grained matrix. To do so, they used equal-channel angular pressing followed by cryo rolling, i.e. cold rolling at a low temperature, and recrystallization at 200°C. The obtained bimodal structure showed both good plastic behavior, a high tensile strain-to-failure (about 65% in terms of engineering strain), and a high yield stress of more than 300 MPa, several times greater than the yield stress of coarse-grained Cu.

14.10 Enhanced ductility of nanocrystalline metallic composites with second-phase nanoparticles, dendrite-like inclusions and carbon nanotubes Another strategy in enhancing the ductility of high-strength nanocrystalline metallic materials is to fabricate a composite form of nanocrystalline materials. For instance, nanocrystalline Al alloys with second-phase nanoparticles are found to show high strength, strain hardening and enhanced tensile ductility.26 In the experiment,26 the 7075 Al alloy was solution-treated to obtain a coarse-grained polycrystalline solid solution. This coarse-grained specimen was cryogenically rolled into a nanocrystalline-structured sheet with a mean grain size of around 100 nm. Finally, the specimen was aged at a low temperature. This procedure produced a nanocrystalline structure with second-phase nanoparticles of a high density distributed within grain interiors.26 The mean interpacing between the nanoparticles was around 25 nm. The following three categories of nanoparticles were distinguished: 1) nanoscale spherical Guinier–Preston zones with coherent boundaries, 2) the same crystal lattice as the matrix and a Zn/Mg atomic ratio of about 1:1; plate-shaped nanoparticles of the metastable hexagonal η’ phase with semicoherent boundaries and a Zn/Mg atomic ratio of about 1.5:1; and 3) equiaxed nanoparticles of the stable hexagonal η phase with incoherent boundaries and a Zn/Mg atomic ratio of about 2:1. In tensile load test, the nanocrystalline Al alloy with second-phase nanoparticles exhibited high-yield strength, 615 Mpa, and functional tensile ductility


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characterized by the uniform elongation 7.4%.26 The yield stress value is larger than the yield stress values, 550 MPa and 145 MPa, characterizing nanocrystalline specimens without nanoparticles and coarse-grained specimens of the Al alloy under examination.26 The uniform elongation 7.4% of the nanocrystalline Al alloy with second-phase nanoparticles is larger than that (3.3%) of this alloy without nanoparticles. Such deformation behavior of the nanocrystalline Al alloy is crucially affected by second-phase nanoparticles. From a microstructural viewpoint, plastic deformation in the alloy occurs by lattice dislocation slip hampered by nanoparticles. After plastic deformation, a large number of lattice dislocations are located at nanoparticle boundaries and in their vicinity, whereas, before the tensile test, very few dislocations are found near nanoparticles.26 With this observation, Zhao and co-workers concluded that the composite structure is responsible for the experimentally documented difference in the deformation behavior between pure nanocrystalline Al alloy and the same alloy with nanoparticles. In particular, the presence of nanoparticles results in strain hardening (characterized by the dependence σ = Aε n, where n = 0.15) due to accumulation of lattice dislocations at and near nanoparticle boundaries.26 Also, enhanced ductility was shown by Ti-based nanocrystalline alloys with large dendrite-like inclusions of the second phase under compressive load. In these metallic nanocomposites, plastic flow is localized in shear bands propagating within the nanocrystalline matrix. Large dendrite-like inclusions of the second phase stop shear bands and cause the strain hardening that prevents dramatic localization of plastic flow. The discussed effect of the composite structure enhances compressive ductility up to strain-to-failure 14%.108,109 Very recently, the enhanced ductility of nanocrystalline Cu reinforced by multiwalled carbon nanotubes under compressive load has been reported.110 The nanocomposite consists of a nanocrystalline Cu matrix with the mean grain size d = 22 nm and 1% wt. carbon nanotubes which were located within grain interiors and at grain boundaries. In the experiment,110 the compression test of nanocomposite pillars showed good ductility (strain-to-failure εf = 0.28), strain hardening and the high yield stress (1125 MPa). Li and co-workers110 noted that the lattice dislocation slip is dominant in these nanomposites, while carbon nanotubes serve as the structural element hampering the dislocation motion. In this case, lattice dislocations tend to be accumulated at interfaces between the nanocrystalline Cu and carbon nanotubes, and this accumulation causes the strain hardening and, thereby, enhances compressive ductility.

14.11 Conclusions and future trends Thus, owing to the specific structural features of nanocrystalline metallic materials, the set of deformation mechanisms in these materials is richer than that in conventional coarse-grained polycrystals. In particular, such deformation mechanisms – grain boundary sliding, grain boundary diffusional creep, triple-



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junction diffusional creep, twin and rotational deformation modes – effectively operate in nanocrystalline metals with finest grains. Plastic deformation carried by grain boundary processes in nanocrystalline metallic materials with finest grains is characterized by very high values of the flow stress. Such plastic deformation very quickly leads to intensive nanocrack generation (at local stress sources and concentrators) and growth instabilities followed by macroscopic fractures (Fig. 14.1). The deformation behavior of nanocrystalline metallic materials with intermediate grains is controlled by grain boundaries operating as active sources and sinks of lattice dislocations. Plastic deformation carried by lattice dislocations in nanocrystalline materials with intermediate grains is characterized by the absence of strain hardening and low strain rate hardening, in which case it very quickly leads to plastic strain instability followed by fast ductile fractures (Fig. 14.3). The above factors – the absence of the strain hardening and low strain rate hardening in nanocrystalline materials with intermediate grains as well as very high flow stresses in nanocrystalline materials with finest grains – effectively explain numerous experimental data1–10 that are indicative of low tensile ductility exhibited by most nanocrystalline metallic materials at room temperature. At the same time, several experiments revealed substantial tensile ductility at room temperature.11–30 Of particular interest for understanding the fundamental micromechanisms of the intrinsic ductility of ‘pure’ nanocrystalline metals are experimental results20–22,27 giving evidence of enhanced tensile ductility of artifact-free nanocrystalline metallic materials with narrow grain size distributions. These results can be explained within the concept49 that is based on the optimization of grain boundary sliding and diffusion processes that cause moderate strain hardening and suppression of dangerous stress sources during extended plastic deformation of nanocrystalline materials. Also, enhanced tensile ductility comes into play in nanocrystalline metallic materials due to strain hardening provided by deformation-induced twins,14,24 pre-existent (growth) twins17,28–30 and secondphase nanoparticles.26 In addition, nanocrystalline metals with bimodal structures show good tensile ductility,11,15 because large grains embedded in nanocrystalline matrixes in these materials both provide strain hardening and stop crack growth due to crack tip blunting. Besides, dendrite-like inclusions and carbon nanotubes in nanocrystalline metallic composites serve as structural elements causing strain hardening effects that may enhance (at least, compressive) ductility of such nanocomposites.108–110 In general, a systematic attempt to obtain a combination of high strength and good tensile ductility in nanocrystalline metallic materials at widely ranged conditions (chemical compositions, structural parameters, conditions of mechanical load) represents a very important unresolved problem in nanomaterials science. This problem is of large significance for development of structural applications of nanocrystalline materials. In the context discussed, experimental identification, computer modeling and theoretical description of micromechanisms enhancing


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tensile ductility of super-strong nanocrystalline metals as well as determination of their structural characteristics and fabrication parameters that control/optimize ductility are the future critical directions of research in this area. In conclusion, let us outline the key points that are of particular interest for the future research of ductility of nanocrystalline metallic materials: (1) Development of methods for systematic fabrication of artifact-free metallic materials with narrow grain size distributions and various chemical compositions (in extension of the research efforts20–22,27). (2) Experimental identification and theoretical description of plastic flow, fracture and enhanced ductility micromechanisms operating in artifact-free metallic materials with narrow grain size distributions as those having “pure” nanocrystalline structures. (3) Experimental identification and theoretical description of new micromechanisms for suppression of plastic strain instability in nanocrystalline metallic materials with intermediate grains. (4) Experimental identification and theoretical description of new micromechanisms for suppression of crack nucleation and growth instabilities in nanocrystalline metallic materials. (5) Enhancement of ductility of nanocrystalline metallic materials with the aid of methods (e.g. fabrication of materials with multimodal grain size distributions,108,109 deformation at cryogenic temperatures111) found to be effective in ductilization of ultrafine-grained materials. (6) Experimental identification and theoretical description of the influence of stress-driven grain growth on tensile ductility of nanocrystalline metallic materials. (7) With results of (1)–(6) used as input, determination of structural characteristics and parameters of fabrication and processing that control and optimize strength and tensile ductility of nanocrystalline metallic materials with various structures and chemical compositions.

14.12 Sources of further information and advice Papers16,33,34 discuss the key factors – plastic strain instability as well as crack nucleation and growth instabilities – for suppressing tensile ductility of nanocrystalline metallic materials. Micromechanisms of plastic deformation and their sensitivity to the specific structural features of nanocrystalline metallic materials are considered in detail in reviews1–9 and Koch et al.10 An overview of experimental data, computer simulations and theoretical models concerning fracture processes in nanocrystalline materials, with the interface and grain size effects taken into account, is presented in Ovid’ko’s paper;32 see also Koch et al.10 Various strategies for enhancement of ductility in such materials are briefly reviewed in Ma’s paper.24 Experimental data on enhanced tensile ductility of



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artifact-free nanocrystalline metallic materials with narrow grain size distributions are presented in papers.20–22,27 Ductility enhancement in nanocrystalline metallic materials due to strain hardening is the subject of several papers focusing on the roles of deformation-induced twins,14,24 pre-existent (growth) twins,17,28–30 second-phase nanoparticles26 and bimodal grain size distributions.11,15 The effects of the composite structure on ductility of metallic nanocomposites are experimentally examined in papers.108–110

14.13 Acknowledgements This work was supported, in part, by the Russian Foundation of Basic Research (Grant 08–01–00225-a), Russian Academy of Sciences Program “Fundamental studies in nanotechnologies and nanomaterials”, and the Ministry of Education and Science of the Russian Federation.

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15 The mechanical behavior of nanostructured metals based on molecular dynamics computer simulations V.I. YAMAKOV, National Institute of Aerospace, USA Abstract: The major advances of the past two decades in the atomistic simulation of the fundamental deformation mechanisms in nanocystalline metals are presented in this chapter. The discussion focuses on an overview of work that has contributed to our understanding of the mechanical behavior of these important emerging materials while also noting several disputed and controversial issues that remain to be resolved. The chapter includes a discussion of the properties of grain boundaries, grain-boundary deformation mechanisms, dislocation processes, grain growth and structure evolution in nanocrystalline metals as seen from the perspective of molecular dynamics simulations. Key words: nanocrystalline metals, molecular dynamics simulation, nanocrystalline deformation.

15.1 Introduction More than 25 years since the first nanocrystalline (NC) materials were synthesized, there is still very little consensus on their characteristic mechanical properties (for recent reviews see References 1–4). Suggestions range from greatly enhanced ductility5–7 to dramatically increased strength and hardness.8,9 In this state of controversial findings, computer simulations performed at the atomistic level, such as molecular dynamics simulations, are able to provide key insights on the underlying deformation mechanisms in these materials. Though in many cases the outcome of these simulations is no less controversial than the experimental results, the ability to study a fully characterized model to the extent of knowing the microscopic state of each atom with machine precision is invaluable for better understanding of the deformation process. Among the various atomic-level simulation approaches developed during past decades, including lattice statics, lattice dynamics, Monte Carlo and molecular dynamics (MD), the latter has proven particularly useful for the investigation of plastic deformation. Based on the solution of Newton’s equations of motion for a system of atoms interacting through a prescribed interatomic potential function, MD simulations are capable of exposing the real-time behavior during deformation at atomic resolution. In addition to studying equilibrium configurations, MD simulations can explore the transient responses of the system as it probes and traverses complex, often unanticipated saddle-point configurations in the 459 © Woodhead Publishing Limited, 2011

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deformation path (for an overview, see Allen and Tildesley10). A particular feature of MD simulations is that the operating deformation mechanisms emerge from the interatomic forces, and are not a prescribed input of the simulation model (such as they are in mesoscale models11). This capability allows not only the study of the anticipated deformation processes, but also the observation of new ones as they appear during simulation. Like any simulation method, MD simulations have inherent limitations and constraints that should always be considered in the interpretation of their results. These limitations are well known. One such limitation is the modeling of systems of relatively small nanometer dimensions. The small system size may introduce substantial finite-size effects and an increased interference of the boundary conditions on the system behavior. Another limitation is the very short time period of a few nanoseconds over which the dynamics of the system can be probed. This short time duration is of particular consequence for the simulations of plastic deformation. As a result, such simulations usually involve extremely high strain rates (of typically >107/s, corresponding to 1% strain in 1 ns) that are many orders of magnitude higher than in conventional experiments. To make the deformation observable within such a short time window, very high stresses, exceeding substantially the experimentally known yield stress, have to be applied. The reliability of the interatomic potentials used is also of a major concern. The interatomic force descriptions used in most MD simulations are of empirical or semi-empirical origin.12 While the empirical force representation has the advantage of being computationally efficient, it is unable to fully capture the many-bodied nature of electron bonding, particularly the complex, self-consistent electron density variation as a function of local structure and chemistry in the vicinity of defects. As a consequence of these limitations, deducing the relationship between simulation predictions and experimental observations is not always straightforward, and has to be extrapolated on the basis of a rigorous theoretical analysis. In spite of their limitations, MD simulations have brought significant advances in understanding the peculiar mechanical properties of NC materials. In NC metals, MD simulations have revealed the intrinsic relationship between various deformation modes. Specifically, MD simulations have shown that the unique mechanical properties demonstrated by NC metals are a result of the competition between intergranular deformation modes, such as grain-boundary sliding13–15 and diffusion,16,17 and transgranular deformation modes, such as dislocation slip,18,19 deformation twinning,19–21 and in some cases, lattice diffusion.22 While this competition has long been suspected and suggested,23 it has been fully revealed in simulations,24–26 and experiments are still verifying most of the processes seen in the simulations.2–4 Often, simulations are becoming a guiding tool for experimentalists by helping them to identify and decouple the various deformation phenomena observed under the microscope. Examples include the studies of dislocation structures in nanograins;27,28 full dislocation emission versus partial


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dislocation emission29 leading to high concentration of stacking faults in the grain interior in face-centered cubic (fcc) NC metals; the unexpected role of deformation twinning in nanograins;30,31 grain-boundary diffusion as a plausible deformation mode and its connection to the observed grain-boundary sliding.32 The purpose of this chapter is to give a brief overview of the recent advances in MD simulations of NC metals. The material is presented in several sections summarizing focus areas of the MD simulations. In Section 15.2, a discussion on MD studies on the structure and properties of grain boundaries in view of their governing role in the overall mechanical behavior of NC metals is presented. In Section 15.3, the deformation mechanisms operating in nanosized grains are summarized. Section 15.4 is devoted to the microstructure evolution in NC metals, discussing grain growth and recrystallization, which are very active in these materials and strongly influence their mechanical behavior with time. Concluding discussions are presented in Section 15.5.

15.2 The structure and properties of grain boundaries in nanocrystalline (NC) metals by molecular dynamics (MD) simulation It is widely acknowledged that grain boundaries (GB) define to a great extent the mechanical properties of NC metals. Grain boundary-mediated processes, such as GB diffusion and sliding, are responsible for the observed inverse Hall–Petch behavior at grain sizes smaller than 20 nm. At grain sizes between 20 and 100 nm, GBs become active sources for dislocations and serve as nucleation sides for deformation twins, thus triggering intragranular deformation modes. Understanding of these processes begins with the structure and properties of GBs. Considering the existence of a vast amount of literature on GB structure and properties (see Mishin et al.33), this section will focus mainly on the specifics of the GBs in NC metals.

15.2.1 Grain boundary structural model for NC metals Two key questions related to the role of GBs in NC materials that have evolved from experimental studies and have become a focus of MD simulations are: (1) To what extent can the atomic structure of the GBs in NC materials be extrapolated from those of coarse-grained polycrystalline materials and bicrystals? (2) What is the structural and thermodynamic relationship between NC materials and amorphous solids? The significant body of atomic-level simulations suggests important similarities34,35 as well as some differences36,37 between the GBs in coarse-grained polycrystalline microstructures and NC microstructures. A series of studies by Swygenhoven et al.,


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based on a MD model of NC Ni of grain sizes from 5.2 to 15 nm,34 and 20 nm,35 showed that the GB structural types present in coarse-grained fcc metals are also found in NC metals, without major differences. However, this conclusion was based on a polycrystalline model prepared using Voronoi tessellation, which is known to result in a random, but non-equilibrated GB topology. Contrary to that conclusion, Phillpot et al.36,37 argued that the most important differences between GBs in NC and coarse-grained metals arise from the severe microstructural constraints present in NC materials. GBs in NC materials are strongly constrained by the grain morphology (shape, size and misorientation) of the surrounding nanograins. At nanometer dimensions, the discrete atomic structure starts to affect the grain morphology. For example, constraining the grain size to a whole number of interplanar lattice spacings leads to the appearance of so-called incompatibility strain inside the grains. Because of this constrained morphology, GBs in NC materials cannot achieve their minimum-free-energy thermodynamic state within a nanocrystal as in the coarse-grained materials or bicrystal interfaces, which at 0 K are of a crystalline structure. Grain boundaries in MD simulations36,37 where NC microstructures were synthesized by modeling a recrystallization process in a super-cooled Lennard– Jones melt, into which small crystalline seeds of random orientations had been inserted, showed the structural and dynamic characteristics of a frozen liquid, similar to the well known Rosenhain’s ‘amorphous-cement’ GB model.38 In Phillpot et al,36,37 GB energy was found to be uniform for all GBs and independent of the misorientation. Even when the grain seeds were oriented to form a coherent twin boundary, which is the interface between two twins in a fcc lattice and is expected to have a perfectly ordered crystalline atomic structure, the resulting GBs again showed a highly disordered structure of high excess energy. This disorder arises from the highly constrained NC microstructure, in which the rigidbody translations of the grains parallel to the GB plane cannot be fully optimized, by contrast with an unconstrained GB in a bicrystal interface. The extension of the work on fcc metals to silicon39 further elucidated the connection between the GBs present in NC and coarse-grained microstructures. The simulations of NC Si,39 involving grain sizes of up to about 7 nm, revealed the presence of highly disordered GBs of a uniform thickness. Similar simulations for NC Pd40 using a many-body embedded atom method (EAM) interatomic potential41 yielded qualitatively identical results. Therefore, while NC and coarse-grained polycrystalline microstructures appear to contain the same structural types of GBs (synthesis and processing dependent), the most important measure of their differences probably lies in their GB-energy distribution functions. Whereas coarse-grained materials usually exhibit a broad distribution of GB energies, the severe microstructural constraints present in NC microstructures seem to have the effect of significantly increasing the fraction of high-energy GBs at the expense of the low-energy boundaries: It appears that the more severe the microstructural constraints become (e.g. by decreasing the grain



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size or by the use of a highly non-equilibrium synthesis route), the larger is the fraction of the high-energy boundaries in the system. Grain-boundary structure changes with temperature. Many of the earlier simulations of high-temperature GB structure predicted ‘premelting’ at the GBs, i.e. GB disordering below the bulk melting point, Tm (for a critical review, see42). By contrast with thermodynamic melting, in which a liquid phase forms at T = Tm, the GB premelting takes place through the formation of a liquid-like GB layer at T < Tm. This liquefied layer is characterized by increased structural disorder and by enhanced diffusion within it. The width of the layer gradually diverges as T → Tm. A series of more recent simulations (reviewed in2) suggested that the highly disordered high-energy GBs in Si39 and Pd43 undergo a continuous reversible structural and dynamical transition at elevated temperatures. Upon heating from 0 K to melting, the high-energy GBs in the polycrystal undergo a transition from a low-temperature, semi-crystalline solid GB structure to a mixed vitrified solid with liquefied confined volumes of higher diffusivity at high temperature.43 Above a certain transition temperature, Tc (Tc  Tc GB diffusivity was found to be independent of the GB structure and becomes a universal property of the material.43 This universality has been widely exploited in follow-up MD simulation studies of GB diffusion creep as it allows the construction of a polycrystalline-microstructure model with GBs of uniform diffusivity.

15.2.3 Grain-boundary mobility Grain boundary mobility governs grain growth and microstructure evolution in NC materials at elevated temperatures. A large number of MD simulations on GB mobility46–49 have been performed using different types of microstructure models, exploring different types of GB-migration driving forces, such as elastic-driven or curvature-driven migration. A central point of all of these studies was to relate GB mobility to GB diffusion following the experimental knowledge that GB diffusion governs GB mobility. In the first of these studies, Schoenfelder et al.46 used elastic anisotropy to drive the migration of a flat, high-angle (001) φ = 43.60° (Σ 29) twist GB in an elastically strained Cu bicrystal. Later, this study was repeated and extended to cover the whole spectrum of (001) twist GBs.47 Both studies found a clear qualitative correlation between GB migration and diffusion that shows a similar transition from slow to fast migration/diffusion due to



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high-temperature premelting. Quantitatively though, the activation energy for migration was two to three times lower than that of diffusion. Similar results were reported for capillarity-driven migration of curved tilt boundaries in aluminum, first in two-dimensional,48 and later in three-dimensional49 simulation models. These simulation studies lead naturally to the conclusion that the mechanism of GB migration is not based on diffusion. In Schoenfelder et al.46 it was found that the estimated migration activation energy is close to the latent heat of fusion, supporting a GB migration mechanism proposed half a century earlier by Mott.50 According to Mott,50 GB migration involves local disordering, or ‘melting’, of small groups of atoms at the boundary, thereby enabling atoms belonging to one grain to reshuffle collectively while aligning themselves with the opposite grain. Compared to experimental results, the simulations of a family of (001) twist GBs in Cu47 reproduced the observed dependence of the GB mobility on GB misorientation, although the activation energies from the simulations were consistently much lower than the experimental ones. In situ experiments on elastic-strain-induced GB migration in Zn bicrystals51 revealed distinct activation energies of low-angle vs. high-angle and symmetric tilt GBs. While low-angle GBs exhibited values close to the activation energy of volume diffusion, high-angle GBs exhibited a value close to that of GB diffusion. A possible explanation for the role of diffusion in the experimental findings51 was that the impurities, always present in the experimental samples, cause a drag on the migrating GBs, thus increasing the activation energy to that for GB or volume diffusion, depending on the GB type. The finite mobility of GB vertices,52 which is diffusion governed, may also be a factor that connects GB diffusion to GB migration. In conclusion, while MD simulations have revealed many details of the structural properties of GBs, the full picture is far from complete. There is still no consensus on the difference between GBs in NC materials and their coarsegrained equivalents. The details of the atomistic mechanisms of GB diffusion and migration and their relation at elevated temperatures are not yet clear and require more studies. A thermodynamic picture of GB melting based on heterophase fluctuations in a constrained system has yet to emerge.

15.3 Deformation mechanisms in nanoscale grains Most of the deformation mechanisms known to operate in coarse-grained metals are also found in NC metals. What is notable though, is the striking difference in the regimes at which these mechanisms operate in a nanograin compared to a large micron-size grain, and in the intrinsic relation and competition between these mechanisms, which result in unique mechanical properties. The key to the mechanical behavior of NC metals lies in their specific microstructure consisting of small grains of crystalline matter embedded inside a dense GB network. Consequently, the intragranular processes such as dislocation slip or lattice


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diffusion are suppressed or have to compete with the enhanced GB-mediated mechanisms such as GB sliding and GB diffusion. Benefitting from the small grain size of NC metals, MD simulations proved to be very efficient in capturing the mechanical properties of these materials and in the study of their specific deformation mechanisms at atomic level.

15.3.1 Grain sliding Grain sliding is found in a large number of MD simulations of NC metals both at low temperatures (T < 0.3Tm)24,26,53 and at elevated temperatures (T > 0.5Tm).17 At present, there is a firm consensus among researchers that GB sliding is an important deformation mode in NC metals, but the debate continues regarding its nature and the underlying atomistic mechanism. Two opinions have been introduced: 1) GB sliding is a result of ‘atomic shuffling’ and ‘stress-assisted free-volume migration’,53 and 2) GB sliding is due to GB diffusion,17 which at low T involves individual movement of vacancies and interstitials or collective motion of small clusters of atoms.44 At high T, sliding is assisted by volume diffusion through the premelted GB layer.17 The difference between 1) and 2) is that while diffusion is a randomwalk process, the stress-assisted migration is a directed movement in response to the applied load. The latter is mostly reported in low- or room-temperature models where diffusion is too slow to accommodate deformation at the extremely high strain rates of 107 s–1 inherent in MD simulations.53 Sliding through GB diffusion (Fig. 15.2) has been unambiguously demonstrated in simulations performed at high temperatures as an accommodation mechanism for Coble creep.17 In coarse-grained metals, this type of GB sliding is known as Lifshitz sliding.54 The focus of debate is how reliably the diffusion-governed GB sliding at high temperatures can be extrapolated to low temperatures and low strain rate of the order of the typical experimental values of 10–1 to 102 s–1. It is still a challenge for MD simulations to probe low-temperature–low-strain-rate regimes and to give a definitive answer to this question.

15.3.2 Diffusion creep The role of diffusion creep as a possible deformation process in NC materials is currently under debate, with several conflicting reports arising from both the experimental and computer simulation communities. Gleiter,55 who first proposed this notion, rationalized that the abundance of GBs together with the absence of conventional dislocation activity would result in plasticity localized in the GB regions, namely diffusion and sliding, even at ambient temperatures. So far, MD simulation findings on diffusion creep in NC metals were reported only at temperatures that are close to the melting point of the material (T > 0.8 Tm).16,17 Simulations at lower temperatures24,26,53 report GB sliding as a dominant deformation mode.



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15.2 Atomic structure simulation snapshot of 8 nm size grains at 4% deformation during Coble creep at T = 1200 K in Pd. Strips of black lines, initially drawn in parallel at the beginning of the simulation, are used to monitor the deformation. The line offsets, seen at the GBs indicate GB sliding that has taken place to accommodate the diffusion creep. For clarity, only the GB and the strip atoms are visualized.

Molecular dynamics (MD) simulations of Si16 and fcc Pd17 on idealized threedimensional microstructures have clearly captured steady-state Coble creep. The microstructures for these simulations were carefully chosen to consist of grains with uniform size and shape thus eliminating the topological driving force for grain growth. The grains were randomly misoriented to form high-energy, structurally disordered GBs of uniform diffusivity as discussed in Section 15.2.2. During uniaxial loading, Coble creep was evidenced by several key signatures including: 1) equal activation energies for both the strain rate and GB diffusion, 2) the deformation was homogeneous over the entire simulation cell, and 3) observation of the accommodating Lifshitz-sliding mechanism54 (Fig. 15.2). The strain rate dependence on stress and grain size was also consistent with the Coble creep formulation56 after taking into account the finite width of the diffusive GB layer.17 Recent MD simulations22,57 in NC Mo (of body-centered cubic (bcc) structure) showed the unexpected result of creep via lattice diffusion (Nabarro–Herring


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creep58) and enhanced by GB-assisted vacancy nucleation. The observation of bulk self-diffusion facilitated by GB-nucleated vacancies opens up interesting possibilities for future atomistic studies of the role of vacancies and interstitials on the mechanical properties of materials that have traditionally been thought of as inaccessible by MD simulation.

15.3.3 Dislocation slips The role of dislocations in the deformation of NC metals has been a central focus of interest. This interest was mainly driven by the numerous, and in many cases controversial, reports on the break down of the Hall–Petch hardening effect at grain sizes below 20 nm, which is replaced by softening, known as an inverse Hall–Petch effect (as reviewed in3). It is believed that a modified dislocation–GB interaction mechanism in NC metals is responsible for reversing of the Hall–Petch effect. In MD simulations of fcc metals (Cu,13,14 Ni34) of very small grain sizes < 20 nm, dislocations were found in the form of Shockley partial dislocations emitted from the GBs and that produce faults behind, irreversibly destroying the crystal lattice. At this grain size, dislocations contribute less than 30% to the total deformation, which is dominated by GB sliding. MD simulations were used to study the structural changes in the GBs during dislocation emission and absorption and the atomistic mechanisms of dislocation nucleation from GBs. It was reported that the atomistic activity at the GB during emission of dislocations is similar to that during GB sliding.34 This finding suggests that dislocation emissions may be a possible mechanism for GB sliding, and that GB sliding can be accommodated by dislocation slip. Typical of all of the early simulations for NC fcc metals performed at grain sizes below 20 nm (such as13,14,34) is that dislocations were found only in the form of single partial dislocations. Since single partial dislocations are not common in coarse-grained fcc metals, which at low temperatures deform through slips of dissociated full dislocations, it is logical to expect a transition grain size, where the partial dislocation slip transforms into a full dislocation slip. The main difference between a full and a partial dislocation is that the Burgers vector of a partial dislocation is only a part of the lattice period. Thus, a partial dislocation produces a stacking fault in the crystal lattice that extends between the dislocation and its source of nucleation. This stacking fault carries an energy penalty – the stacking fault energy (SFE) per length – preventing the dislocation from traveling away from its source. The created stacking fault also presents an obstacle for other dislocations. By contrast, a full dislocation does not leave a stacking fault, but fully restores the crystal lattice after gliding away. This energetic and structural difference between a partial dislocation and a full dislocation can result in a substantial change in the mechanical behavior of the NC metals at the transition from a partial to a full dislocation slip. To find a regime of full dislocation nucleation in NC polycrystals, a special MD model has been constructed.18 Aluminum was selected as a material model



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because of its high SFE and small splitting distance, r (of 1–2 nm), between the two Shockley partials when joined in a full dislocation.59 The choice of aluminum proved to be crucial for the success of the simulation, as it was shown later60 that the ability to form full dislocations is strongly dependent on the generalized stacking fault energy curve, defined by the interatomic potential used in the MD models. An additional factor that restricts the formation of full dislocations is that the inherently high MD stress of deformation generally increases the splitting distance, which may become 10 to 20 times larger than its equilibrium value. To achieve a sufficiently large grain size to accommodate a full split dislocation under high stress a columnar model microstructure was chosen. This type of structure18 may be only a few nm thick in the columnar z-direction, allowing the simulation cell to be extended in the x-, and y-directions to simulate polycrystals of up to 100 nm grain size (achieved in Yamakov et al.21). The first results of these simulations in a system of four grains of up to 45 nm in size18 found full dislocation emission in grains of over 30 nm in size. As expected, the transition to full dislocation nucleation resulted in increased dislocation activity inside the grains due to the elimination of the stacking faults as obstacles for dislocation motion. This dramatically changed the deformation behavior of the material, triggering various types of intragranular dislocation– dislocation interaction processes19 such as cross-slip lock formations, stackingfault splitting, deformation twinning and formation of twin networks.20,21 The transition from partial to full dislocation nucleation in NC fcc metals introduces the splitting distance as an additional length scale in the deformation process. Since the splitting distance, r, depends on the local resolved shear stress acting on the dislocation, this length scale is a dynamic quantity and depends on both the SFE, ESF, and the applied stress, σ ; r = r(ESF, σ). Follow-up simulations on fully three-dimensional microstructures of varying d and ESF studied in more detail the role of this length scale on the deformation processes.25,61 The results are illustrated in four selected snapshots of intragranular deformation in nanograins shown in Fig. 15.3. Grains with d/r >> 1 are active in generating dislocations using GBs as nucleation sites (Fig. 15.3 (a)) and deformed mainly through dislocation slip. As the grain size approaches the size of the splitting stacking fault, d/r ≈ 1 (Fig. 15.3 (b)), the dislocation activity decreases. Grains with d/r 10 µm) and materials with relatively low SFE, such as Cu,63 these observations for NC Al were very unexpected. However, previous simulations for NC Cu had already shown the emission of extrinsic stacking faults from GBs early in the deformation process,64 but they did not show the development of deformation twinning during the later stages of the deformation because of the small grain size to which these simulations were limited. Deformation twinning in NC Al has been confirmed experimentally,30,31 and several additional twinning mechanisms in NC metals have been recently found.65 Similar findings have been reported for other fcc metals, such as Cu66 and Ni.67 Of particular interest is the report by Rösner et al.68 of similar deformationtwinning processes in another high-SFE fcc metal, Pd. A comparison between the Al30 and Pd68 experiments with the Al MD simulations19–21 showed similarities in the way that deformation twins formed. However, in contrast to the MD simulations, in both Pd and Al, twins were found to form on only one slip plane per grain; thus, the twins were always coplanar within each grain. As one slip plane is not enough to accommodate a general deformation, an additional deformation mechanism is required. Rösner et al. suggested that grain rotation would allow the grains to orient their active twin plane along the principal shear direction. By contrast, the MD simulations21 indicated the appearance of twin networks where two twin planes operate on an equal basis. A possible reason for this might be the much higher strain rates in the MD simulations compared to the experimental studies. The effect of twinning on the mechanical properties of NC metals can be twofold. During early deformation, when the grain interiors are practically free of dislocations, twinning can facilitate deformation by additional slip systems or by assisting the transfer between existing slip systems through dislocation–twin reactions. Once twins have formed, they can repel certain types of gliding dislocations and give rise to pile-ups with consequent strain hardening of the material.

15.3.5 The strongest size: competition between different deformation modes The well known and almost universal Hall–Petch relation, stating that the yield strength of a polycrystal is inversely proportional to the square root of the grain size, suggests that NC materials should acquire very high strength approaching the theoretical strength of a perfect crystal. Though in general, NC metals show much higher strength than their coarse-grained versions – more than an order of magnitude in some cases – theoretical strength is never attained. The reason is the breakdown of the Hall–Petch hardening effect observed below a certain grain size. The underlying reason for this breakdown is the increased role of the GB-mediated deformation processes. Ultimately, the overall strength is a result of


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a competition between intragranular deformation mechanisms that provide hardening, and intergranular mechanisms that provide softening of the material. This reasoning, formulated by S. Yip,23 leads to the conclusion of the existence of a characteristic length at which both softening and hardening mechanisms are equally strong. A polycrystal of that grain size, ‘the strongest size’,23 would have the highest practically achievable mechanical strength. Two MD simulation studies on fully 3D microstructures25,26 have been performed to capture the full range of grain sizes over which the crossover from dislocation to GB mediated deformation takes place and, thus, to elucidate the nature of the ‘strongest grain size’, dc, in NC fcc metals. The first of these studies,25 considered NC Al microstructures consisting of four grains in a periodically repeated simulation cell. This simple setup enabled exploration of a range of grain sizes from 7–32 nm, thus incorporating sizes below and above dc for Al, and allowing the transition from GB-dominated processes (for d < dc) to dislocation-dominated processes (for d > dc) to be probed. These simulations have demonstrated directly the coupling between the crossover in the deformation mechanism and the resulting mechanical behavior. In addition to yielding a value of dc ~ 18 nm for Al, these simulations showed unambiguously that the crossover in the mechanical behavior is, indeed, due to a transition in the dominant deformation process. These simulations, also, related dc to the splitting distance, r, as discussed in the previous section (15.3.4). In the second study, Schiotz and Jacobsen26 determined the flow stress of NC Cu with grain sizes ranging between 5 and 50 nm. These simulations revealed the expected crossover in the flow stress, from normal to inverse Hall–Petch behavior, at a value of dc ~14 nm for Cu. As in Yamakov et al.,25 this crossover in the mechanical behavior was accompanied by a change in the underlying mechanism from dislocation-mediated plasticity, dislocation slip and deformation twinning, to GB sliding.

15.4 Grain growth and microstructure evolution in NC metals Due to the extremely small grain size, NC metals are inherently unstable against grain growth (GG). In these materials, GG is not limited to high-temperature conditions but can occur even at relatively low temperature.69 Since the mechanical properties of NC metals are strongly dependent on the grain size, they are very sensitive to GG. For this reason, it is of significant practical importance to study GG and to determine the factors that have an influence on it. Experimental studies on NC GG are difficult to perform because of the substantial problems in fully characterizing NC microstructures and their evolution. For example, Malow and Koch70 have studied GG in NC Fe using X-ray diffraction to determine the grain size by the broadening of the diffraction peaks. To ensure that the internal lattice strain, which also causes peak broadening,



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does not affect the measurements, the estimated grain size had to be confirmed by TEM. Since thin metallic films make it easier to measure grain size, NC GG experiments are mostly performed on NC thin films.71,72 Theoretical studies of GG encounter considerable complexities in fully accounting for the dynamic topological features of evolving microstructures. These difficulties have led to extensive simulation studies on grain growth. The need to include large number of grains in statistically representative simulated systems required the use of mesoscale types of models (Potts models, front-tracking models, phase-field models, etc. reviewed in11), which consider the microstructure at the level of grains and GBs rather than at the level of atoms. While highly computationally efficient, these models require an input of prescribed parameters such as GB and vertex mobility, GB energy, etc. that may not be known a priori. The unaccounted effects of additional GG mechanisms or GG driving forces, not incorporated in the mesoscale models, may lead to qualitatively false predictions. The ability of atomistic simulations to generate GG driving forces through atomic interactions provides a fundamental understanding of the GG processes, which is not possible in the mesoscale models. The combined effect of a relatively small number of atoms per grain and a high driving force due to extremely small grain size, makes the observation of GG at MD time and length scales possible. At present, NC materials are the only systems where GG can be studied by MD simulations.

15.4.1 Grain growth due to grain-boundary migration As in coarse-grained metals, curvature-driven grain-boundary migration, i.e. the motion of GBs towards the center of their curvature,73,74 is also a dominant GG mechanism in NC metals. The driving force for such GG is proportional to the GB curvature, which for a given grain diameter, d, is of the order of 1/d. This makes GG very active in NC materials. In idealized, fully dense and impurityfree microstructures at temperatures close to the melting point where GB mobility is maximal, GG is fast enough to be observed and successfully studied by MD simulations on a timescale of 1 to 10 ns. This has been demonstrated in a series of papers by Haslam et al.75–78 in NC Pd. A system of 25 grains of average d = 15 nm75 has been simulated at T = 0.95 Tm for the period of 10 ns system evolution time. As a result of the GG, only 9 grains remained at the end of the simulation. The MD model has been reproduced by a mesoscale kinetic Monte Carlo GG simulation,76 where the GB mobility and GB energy parameters were extracted from the MD simulation. The good agreement between the two models in reproducing similar topological patterns in the microstructure evolution confirmed the GG mechanism through curvature-driven migration. This provides an example of a bottom-up multiscale approach where an atomistic simulation is used to provide parameters for a continuum-level model. In addition, the MD simulation revealed a series of processes taking place at the GBs and in the grain interiors


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during GG. Some of these processes, such as production of residual dislocations in the grains from GB disintegration, were a result of GG.77 Others, such as grain rotation and grain coalescence,75,76 present additional mechanisms of GG, which will be discussed in the next subsection. An important question to be addressed by MD simulations is ‘What is the activation energy of GG?’ The expected answer, based on experimental evidence that relates the activation energy of GG to that of GB or lattice diffusion, may not be trivial in view of the findings for the GB-migration activation energy in impurity-free MD simulations. As discussed in Section 15.2.3, the activation energy of GB migration was found to be substantially lower than that of GB diffusion, suggesting non-diffusion-related GB migration mechanisms.46,47 To address this issue and to evaluate the activation energy of curvature-driven GG, an idealized MD model of a polycrystal of bimodal grain size distribution was used.79 In this model, four-sided square grains were embedded between eight-sided octagonal grains. At high temperature, T > 0.8 Tm, all GBs were of uniform diffusivity and mobility, representing an isotropic system. As expected from the von Neumann–Mullins rule,80 the octagonal grains grow at the expense of the square grains. The activation energy of the grain growth process was found to be equal to the GB diffusion activation energy. This result suggested that while migration of a single GB may not involve diffusion, GG in a polycrystal is diffusion assisted. One possible role of diffusion is to accommodate the excess free volume generated during GG (because of the decreasing GB network, the density of the polycrystal increases). Alternatively, GB diffusion might be related to the vertex mobility, which can be the rate limiting mechanism for GG.52

15.4.2 Grain growth due to grain rotation and grain coalescence A novel mechanism for GG, specific for NC materials and shown by MD simulations, is grain coalescence due to grain rotation. In this mechanism, the driving force results from the dependence of the GB energy on the misorientation angle. This dependence creates a torque to rotate the grain to form less energetic GBs. When two grains assume the same orientation, they coalesce to form a single larger grain. This process is found in NC materials81,82 due to their extremely small grain size, resulting in relatively high grain mobility towards rotation.83 The mechanism of grain-rotation coalescence results in a power-law grain growth with time t, given as d ~ tν, with a universal scaling exponent, ν. A combined theoretical and simulation study84 demonstrated that the value of this exponent depends on the assumed mechanism by which the grain rotations are accommodated, being ν = 1/4, for GB diffusion, or ν = 1/3, for lattice diffusion accommodated grain rotation, respectively. For comparison, the growth exponent for isotropic curvature-driven GG is ν = 1/2.



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15.4.3 Deformation-driven grain growth Experimental studies on superplastic deformation of both metallic85,86 and ceramic87 materials have shown that high-temperature deformation of fine-grained polycrystals generally enhances the rate of GG compared to that at thermal annealing. This enhancement phenomenon is known as dynamic GG. As an extreme case of fine-grained materials, NC materials were also found to experience dynamic GG under various conditions including uniaxial tension88,89 and compression,90 high-pressure torsion91,92 and nanoindentation.93 A comprehensive MD simulation analysis of the relation between GG and deformation has been performed in two consecutive papers by Haslam et al.77,78 The first paper,77 described the effect of deformation on the enhancement of the GG in a 25 grain NC model of Pd as compared to GG in the same microstructure under thermal annealing.75,76 The second paper,78 considered the converse effect of GG on deformation, identified as Coble creep in this particular model. Based on the analysis, detailed in,77,78 mechanisms of deformation-accelerated GG were found to be: stress-enhanced GB migration, stress-induced grain rotation, dislocationassisted grain rotation, and dislocation emission due to grain coalescence. An example of the relationship between some of these mechanisms is presented in Fig. 15.4. The combined operation of GB-diffusion creep and GB-diffusion-assisted grain rotation resulted in splitting a grain in two parts, followed by a grain switching

15.4 Overall evolution of a MD-simulated Pd microstructure at σ = 0.6 GPa and T = 1200 K performed by Haslam et al.77,78 (unpublished figure). (a) Initial configuration. (b) Diffusion creep elongates grain B. (c) Stress-induced grain rotation separates grain B in two. (d) Neighborswitching event between grains A, B1, B2, and C is taking place according to the Ashby–Verrall mechanism.94


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event of Ashby–Verrall type.94 Independently, grain-rotation-driven dynamic GG has been found in MD simulations by Sansoz and Dupont,95 while stress-induced GB migration was reported by Farkas et al. in a similar simulation set-up.96 An interesting scenario for coupling between GG and deformation was found in.78 Monitoring the strain rate in these simulations showed that the deformation mechanism operating in this case, Coble creep, experienced enhancement in the first stages of GG before being slowed down by the increased grain size. This enhancement correlated with enhancement in the overall diffusion in the system, while the GB volume decreased. Further analysis showed that the diffusion was enhanced due to realignment of migrating high-energy GBs with respect to the deformation field. This realignment increased the diffusion flow through the GB network and maximized the work of deformation done by the external load. Another interesting example of a relation between deformation and GG was found as a coupling between GB sliding and GB migration of a tilt GB.78 This coupling has been investigated in detail by Cahn et al.97 for a symmetric tilt GB in Cu (MD simulation), and a theoretical model and criteria for the sliding/ migration relation have been derived. Experimental evidence for this mechanism has been reported recently.98,99

15.5 Conclusions The purpose of this by no means exhaustive review is to present the substantial advancement in understanding of the underlying deformation mechanisms in NC metals that has been achieved through MD simulations. As a result, in spite of the many seemingly controversial MD findings, an overall picture of the mechanical behavior of NC materials has emerged. Recognizing that GBs play a major role in these materials, MD researchers began with detailed investigations of the GB structural and dynamic properties. Researchers gained many valuable insights that would probably not otherwise have emerged given the difficulty in studying this field experimentally. Important among these insights are those regarding the nonequilibrium constrained GB structure present in NC materials, which have been seen to exhibit specific dynamic properties such as premelting and universal diffusivity at high temperature. In addition, a number of MD studies have revealed the role of GBs as dislocation sources during deformation, suggesting that GBs play a governing role in the dislocation dynamics of the nanograins. Understanding the competitive relation between GB-mediated and dislocation-governed deformation helped to uncover the mechanism of the crossover in the Hall–Petch effect, from hardening to softening, as the grain size decreases below 20–30 nm in the idealized fully dense simulated microstructures. The ‘strongest size’ has been explained as the smallest grain size at which the dislocation activity is suppressed, but at which the GB network is not yet dense enough for the GB deformation processes to take over. These simulation findings have triggered a wave of experimental research. As a result, many of the major MD results have met experimental supports, although



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in many cases, in regimes far different from the simulation models. Nevertheless, the experimental efforts have been inspired and directed by the simulation findings. Examples include: the role of GBs as dislocation sources in nanograins; deformation twinning as a viable deformation mode at nanoscale; suggestions for a possible contribution of GB-diffusion creep, in support of earlier speculations on its role in the deformation of NC materials; grain rotation as another deformation mode and grain-rotation-induced grain growth; coupling between deformation and grain growth, etc. There are still many unresolved issues in the global picture of NC material deformation. In many cases, MD simulations brought more questions than answers. The reported findings were sometimes counterintuitive or contradictive to the current experimental wisdom. For example, the finding in simulations of discrepancy between the activation energies for GB migration and GB diffusion is still an experimental puzzle. Another experimentally unexpected, but subsequently confirmed, result was the ability of fcc NC metals to deform through twinning. The controversial simulation findings whether GB mediated deformation is based on GB diffusion (Coble creep) or GB sliding still lacks a definitive experimental resolution. The fundamental question, whether there is a relation between NC materials and amorphous matter as a limiting state (when the grain size approaches zero), remains unanswered even after exhaustive efforts from MD researchers and the numerous theoretical models presenting NC materials as two-phase amorphouscrystalline systems. The thermodynamic state of such a system is unclear and escapes the ability of the MD models, limited in size and time scale, to probe it. The majority of MD simulations of NC metals to date have been focused on fcc metals. The reason for this is mostly due to the lack of reliable and computationally efficient interatomic potentials for bcc and hexagonal close-packed metals. As the skill in creating more accurate potential for atomistic simulations is constantly improving, MD studies are already broadening to other types of structures (for example, see Millett et al.22,57 for bcc NC Mo) thus giving a more complete picture on the deformation properties of NC metals. Definitely, there is a lot of room for further research and, as computing power continues to follow Moore’s law, many more exciting discoveries are awaited in the near future.

15.6 Acknowledgement V. Yamakov is sponsored through NASA cooperative agreement NCC-1-02043 with the National Institute of Aerospace.

15.7 References 1 Gleiter H. Acta mater 2000;48: 1. 2 Wolf D., Yamakov V., Phillpot S.R., Mukherjee A., Gleiter H. Acta mater 2005;53: 1, doi:10.1016/j.actamat.2004.08.045.


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16 The surface deformation and mechanical behavior of nanostructured alloys L.L. SHAW, University of Connecticut, USA Abstract: Many mechanical properties such as fatigue and wear resistance are highly sensitive to the surface condition and properties of the material. As such, processes based on surface deformation are important methods for improving mechanical properties. The latest development of surface severe plastic deformation (S2PD), namely a family of processes that entail repeated impacts against the workpiece surface by a stream of high-energy balls, has resulted in significant progress in this direction. In this chapter the fundamentals and mechanical properties derived from S2PD processing are reviewed. The topics discussed include development of deformation fields, formation of the nanocrystalline surface layer, evolution of the work-hardened surface region, profiles of macroscopic residual stresses, presence of the microstructure gradient, evolution of surface roughness, enhancements in mechanical properties (i.e., tensile properties, fatigue limits, and wear resistance), and mechanisms associated with the improved mechanical properties. The perspectives of future developments are also discussed. Key words: surface severe plastic deformation, surface mechanical attrition treatment, severe plastic deformation, surface nanocrystallization, nanostructured alloys.

16.1 Introduction Surface severe plastic deformation (S2PD) is a relatively new family of processes that have been developed with the aim to create a nanocrystalline (nc) surface layer.1–4 These processes, pioneered by K. Lu and J. Lu,5 rely on severe plastic deformation induced by impacts of high-energy balls, hammer peening, surface rolling, laser shock treatment, or machining to produce a nc surface layer. The common feature of these processes is S2PD. Among various methods, highenergy ball impact processes have received most of the attention because of their versatility in processing complex-shaped parts. Several different names have been used for this group of processes, including ultrasonic shot peening (USSP),6,7 high-energy shot peening (HESP),8 surface mechanical attrition treatment (SMAT),9–11 surface nanocrystallization and hardening (SNH),12–14 and particle impact processing (PIP).15,16 Differences among these processes stem mainly from the approach via which the high velocity of balls is generated. In USSP the movement of balls is generated through collision between balls and a vibrating chamber driven by an ultrasonic generator. For SMAT, HESP and SNH processes, the movement of balls is also generated through collision between balls and a vibrating chamber. However, the vibration of the chamber is driven by 481 © Woodhead Publishing Limited, 2011

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Table 16.1 Typical parameters of balls and shots used in SP and S2PD processes Process

Diameter of balls or Impact velocity (m/s) shots (mm)

Kinetic energy of balls or shots# (J)

SP USSP SMAT* SNH PIP

0.25–1.0 0.4–3.0 4.0–8.0 4.0–8.0 4

9.2 × 10–6–0.01 0.0001–0.02 100 µm.

the process parameters described. This would explain the random voids observed within the structure of the cold spray deposit. The best operating process parameters were selected based upon several primary factors, including maximum temperature, deposition efficiency, density and nozzle clogging. Helium was used as the accelerating gas at a temperature of approximately 400°C with a pressure of 400 psi. Figure 20.37 shows an as-polished cross-section


Processing nanostructured metal and metal-matrix coatings

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of the resultant deposit. Note the ‘splat’ or particle boundaries and the complete consolidation that was achieved using these process parameters. There were random voids observed within the structure that were later attributed to large agglomerates found in the original feedstock powder (Fig. 20.38). These agglomerates were in excess of 100 µm, and as such would not completely deform during impact, leaving

20.37 Optical microscope view of cold spray deposit of n-WERKZ nanostructured AA5083.

20.38 Original n-WERKZ nanostructured AA5083 feedstock with large agglomerates.


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behind these occasional defects. An attempt was made to sieve the feedstock powder using a 325-mesh sieve, which would remove any particle having a diameter greater than approximately 44 µm. The particle size analysis of the sieved powder shows new mean particle size of 33.9 µm, with no particles larger than 65 µm (Fig. 20.39). Additional spray trials were conducted and results indicated the elimination of these voids in the structure of the AA5083 cold spray deposit (Fig. 20.40).

20.39 Particle analysis of the sieved n-WERKZ AA5083 showing the average particle size as approximately 33.9 mm.

20.40 Optical microscope view of cold spray deposit of sieved n-WERKZ nanostructured AA5083.



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A typical bright-field TEM micrograph from cold-sprayed AA5083 is presented in Fig 20.41. Very little porosity and oxide inclusion were observed. Deformation of face-centered cubic (fcc) Al from high particle velocity deposition resulted in elongated grains with aspect ratio ranging from 2~3 to 1. Mean grain size was approximated at 100 ± 35 nm. Between nano-grains, excellent chemical bonding without deleterious voids or inclusions was observed as demonstrated by the high-resolution TEM micrograph in Fig. 20.42. However, inclusions and voids

20.41 Bright-field TEM micrograph of cold-sprayed AA5083.

20.42 High-resolution TEM micrograph of grain boundary in coldsprayed AA5083.


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were occasionally observed at splat (e.g. prior particle) boundaries as presented in Fig. 20.43. At the interface between AA5083 cold-sprayed coating and AA6061 substrate, excellent bonding was observed as presented in Fig. 20.44. Certainly, inclusions of oxides were observed but not as a continuous layer since they were

20.43 Bright-field TEM micrograph showing decohesion (white region) and inclusions (dark spots) observed at the splat boundary of cold-sprayed AA5083.

20.44 Bright-field TEM micrograph of coating-substrate interface.



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20.45 X-ray diffraction patterns from cold-sprayed AA5083 and uncoated bottom surface of AA6061 substrate.

broken apart due to the deformation of impinging particle associated with high velocity impact. Thus, a majority of the coating/substrate interface consisted of fcc-Al bonding between AA5083 and AA6061. Figure 20.45 presents X-ray diffraction patterns from cold-sprayed AA5083 and annealed AA6061 (e.g. uncoated bottom surface). While both patterns correspond to fcc-Al (i.e. also confirmed by electron diffraction from TEM), a noticeable compressive strain, estimated at 0.31% was observed for the cold-sprayed AA5083 coating.

20.12 Future trends The low temperature and high kinetic energy associated with the cold spray process allow for the retention of fine/nano-grain structure, absence of phase change, capability for thick deposits, and promotion of compressive residual coating stress. These capabilities make the cold spray process an ideal approach to depositing nanostructured metal-base coatings. In addition to the nanostructured metal-base coatings presented in this chapter, potential nanostructured coating applications may include: MCrAlY coatings for high temperatures; CuCr for oxidation protection; Al and Zn sacrificial cathodic protection coatings; Al- or Cu-base metals or their MMCs for thermal management; Al, Cu, and steel for electronics; Ti and Ta for bioengineering and corrosion protection; and CuNiIn for anti-fretting.


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In addition to applications revolving around nanostructured coatings, cold spray of nanostructured metal-base materials may also contribute to stronger near-net-shape spray nanostructured forms, and better repair of worn/damaged components.

20.13 Sources of further information and advice Additional sources of information pertaining to thermal-sprayed nanostructured metal-base coatings can be found in technical journals relating to thermal spray and/or materials science.

20.14 Acknowledgements We wish to thank Dr Lawrence T. Kabacoff (ONR), Ken Scandell (NAVSEA), and Linda K. Jensen (Juridica, Inc.) for their constructive contributions towards the preparation and the review of this manuscript. Special thanks should be given to Jimmy Walker and FW Gartner Thermal Spraying Co. for their contribution of industrial thermal spray processing photographs. As well, we would like to thank Professors Angela L. Moran (US Naval Academy) and Julie Schoenung (UC, Davis), as well as Dr Virgil Provenzano (NIST) for their technical contributions to portions of this chapter.

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8 Jordan E.H., Gell M. Nano Crystalline Ceramic and Ceramic Coatings Made by Conventional and Solution Plasma Spray. In Nanomaterials Technology for Military Vehicle Structural Applications, Meeting Proceedings RTO-MP-AVT-122, Paper 9. Neuilly-sur-Seine, France, 2005, pp. 9–19. 9 Wang D., Tian Z., Shen L., Liu Z., Huang Y. Preparation and characterization of nanostructured Al2O3-13wt.%TiO2 ceramic coatings by plasma spraying. Rare metals 2009, Vol. 28, no. 5, October, p. 465. 10 Marple B.R., Voyer J., Bisson J.F., Moreau C. Processing and Characterization of Nanostructured Cermet Coatings. Proceedings of the International Thermal Spray Conference (ITSC 2001), Singapore, May 28–30, 2001, p. 343. 11 Bernecki T. Surface Science. In Davis J.R., editor. Handbook of Thermal Spray Technology. ASM International, Materials Park, OH, USA, 2004, p. 14. 12 F.W. Gartner Thermal Spraying Co. 13 Qiao Y., Liu Y.R., Fischer T.E. Sliding and Abrasive Wear Resistance of ThermalSprayed WC-Co Coatings. Journal of Thermal Spray Technology, Vol. 10(1), March 2001, p. 118. 14 Guilemany J.M., Dosta S., Miguel J.R. Study of the Properties of WC-Co Nanostructured Coatings Sprayed by High-Velocity Oxyfuel. Journal of Thermal Spray Technology, Vol. 14(3), September 2005, p. 405. 15 He J., Ice M., Dallek S., Lavernia E.J. Synthesis of Nanostructured WC-12 Pct Co Coating Using Mechanical Milling and High-Velocity Oxygen Fuel Thermal Spraying. Metallurgical and Materials Transactions A, Vol. 31A, February 2000, p. 541. 16 Ibrahim A., Berndt C.C. Fatigue and Mechanical Properties of Nanostructured WC-Co Coatings. Proceedings of the International Thermal Spray Conference, May 10–12, 2004, Osaka, Japan, p. 878. 17 Morks M.F., Shoeib M.A., Ibrahim A. Comparative Study of Nanostructured and Conventional WC-Co Coatings. Proceedings of the International Thermal Spray Conference, May 10–12, 2004, Osaka, Japan, p. 857. 18 Zha B., Wang H., Su X., Nano Structured WC-12Co Coatings Sprayed by HVO/AF, Proceedings of the International Thermal Spray Conference, May 10–12, 2004, Osaka, Japan, pp. 881–881. 19 Liu S., Sun D., Fan Z., Yu H.Y., Meng H.M. The influence of HVAF powder feedstock characteristics on the sliding wear behaviour of WC-NiCr coatings. Surface & Coatings Technology 202 (2008), p. 4893. 20 Kim H.J., Lee C.H., Hwang S.Y. Superhard nano WC-12%Co coating by cold spray deposition. Materials Science and Engineering A 391 (2005), p. 243. 21 Smirnov N.I., Prozhega M.V., Smirnov N.N. Study of Tribological Properties of Detonation Nanostructured WC-Co-Based Coatings. Journal of Friction and Wear 2007, Vol. 28, No. 2, p. 200. 22 Zhu Y.C., Yukimura K., Ding C.X., Zhang P.Y. Tribological properties of nanostructured and conventional WC-Co coatings deposited by plasma spraying. Thin Solid Films 388 (2001), p. 277. 23 Jordan E.H., Gell M., Sohn Y.H., Goberman D., Shaw L., Jiang S., Wang M., Xiao T.D., Wang Y., Strutt P. Fabrication and Evaluation of Plasma Sprayed Nanostructured Alumina-Titania Coatings with Superior Properties, Mater Sci Eng, A301, 2001, p. 80. 24 Gell M., Jordan E.H., Sohn Y.H., Goberman D., Shaw L., Xiao T.D. Development and Implementation of Plasma Sprayed Nanostructured Ceramic Coatings, Surface and Coatings Technology,’ vol. 146–147, 2001, p. 48.


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25 Goberman D., Sohn Y.H., Shaw L., Jordan E.H., Gell M. Microstructure Development of Al2O3-13 wt%TiO2 Plasma Sprayed Coatings Derived from Nanocrystalline Powders. Acta Materialia, 50, 2002, p. 1141. 26 Papparado J. U.S. Navy Finding New Applications for Advances in Nanotechnology. National Defense Industrial Association’s Business & Technology Magazine. Available from: http://www.nationaldefensemagazine.org/issues/2004/oct/US_Navy_Finding. htm [accessed 14 December 2006]. 27 Williams J., Kim G.E., Walker J. Ball Valves with Nanostructured Titanium Oxide Coatings for High-Pressure Acid-Leach Service: Development to Application. Proceedings of Pressure Hydrometallurgy 2004, Banff, Alberta, Canada, October 23–27, 2004. 28 Kim G.E., Walker J. Successful Application of Nanostructured Titanium Dioxide Coating for High-Pressure Acid-Leach Application. Journal of Thermal Spray Technology, Volume 16(1), March 2007, p. 34. 29 Kim G.E. Thermal Sprayed Nanostructured Coatings: Applications and Developments. Chapter 3 of Nanostructured Materials Processing, Properties, and Applications – 2nd edn, Koch C.C, editor. William Andrew Publishing, 2007. 30 Kim G.E. Proven and Promising Applications of Thermal Sprayed Nanostructured Coatings. Proceedings of the International Thermal Spray Conference, Seattle, USA, May 15–18, 2006. 31 Schoenung J.M., Tang F., Ajdelsztajn L., Kim G.E., Provenzano V. Processing and Characterization of Thermal Barrier Coatings with Cryomilled Bond Coats. Materials Forum, Vol 29, pp. 414–419, 2005. 32 Ajdelsztajn L., Picas J.A., Kim G.E., Bastian F.L., Schoenung J.M., Provenzano V. Oxidation behavior of HVOF sprayed nanocrystalline NiCrAlY powder. Materials Science and Engineering, A338, 2002, p. 33. 33 Ajdelsztajn L., Tang F., Kim G.E., Provenzano V., Schoenung J.M. Synthesis and Oxidation Behavior of Nanocrystalline MCrAlY Bond Coatings. Journal of Thermal Spray Technology, Volume 14(1), March 2005, p. 23. 34 Klug H.P., Alexander L.E., X-Ray Diffraction Procedures: For Polycrystalline and Amorphous Materials, 2nd Edition, New York, NY: Wiley, 1974, p. 643. 35 Suryanarayana C., Mechanical Alloying and Milling, New York, NY: Marcel Dekker, 2004, p. 110. 36 Ur S.C., Choo H., Lee D.B., Nash P. Processing and Properties of Mechanically Alloyed Ni(Fe)Al-Al2O3-AlN. Metals and Materials, Vol. 6, No. 5 (2000), p. 435. 37 Dymek S., Dollar M., Hwang S.J., Nash P. Deformation mechanisms and ductility of mechanically alloyed NiAl. Materials Science and Engineering A152 (1992), p. 160. 38 Lee D.B., Kim G.Y., Park S.W., Ur S.C. High temperature oxidation of mechanically alloyed NiAl-Fe-AlN-Al2O3. Materials Science and Engineering A329–331 (2002), p. 718. 39 Dollar M., Dymek S., Hwang S.J., Nash P. The Role of Microstructure on Strength and Ductility of Hot-Extruded Mechanically Alloyed NiAl. Metallurgical Transaction A, Volume 24A, September 1993, p. 93. 40 Whittenberger J.D., Eduard A., Luton M.J. 1300 K compressive properties of a reaction milled NiAl-AlN composite. Journal of Materials Research, Volume 5, Issue 12, December 1990, p. 2819. 41 Evans A.G., Mumm D.R., Hutchinson J.W., Meier G.H., Pettit F.S. Mechanism controlling the durability of thermal barrier coatings. Progress in Materials Science, Volume 46, Issue 5, 2001, p. 505.



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42 Wright P.K., Evans A.G. Mechanisms governing the performance of thermal barrier coatings. Current Opinion in Solid State and Materials Science, Volume 4, Issue 3, June 1999, p. 255. 43 Wu Y.N., Qin M., Feng Z.C., Liang Y., Sun C., Wang F.H. Improved oxidation resistance of NiCrAlY coatings. Materials Letters 57 (2003), p. 2404. 44 Tang F., Ajdelsztajn L., Kim G.E., Provenzano V., Schoenung J.M. Effects of variations in coating materials and process conditions on the thermal cycle properties of NiCrAlY/ YSZ thermal barrier coatings. Mater Sci Eng A425 (2006), p. 94. 45 Mercier D., Kim G.E., Brochu M. Surface Oxide Selectivity of Nanostructured CoNiCrAlY and NiCoCrAlY Materials. Oral presentation at 2009 TMS Annual Meeting & Exhibition, February 15–19, 2009: San Francisco, CA. 46 Kaplin C., Mercier D., Brochu M. Nanostructured MCrAlY Coatings for High Temperature Oxidation in Petrochemical Applications. Oral presentation at Materials Science & Technology 2009, October 25–29, 2009: Pittsburgh, PA. 47 Papyrin A. Cold Spray Technology. Advanced Materials & Processes, September, 2001, p. 49. 48 Van Steenkiste T.H. Kinetic Spray Coatings. Surface and Coatings Technology, 1999, 111, p. 62. 49 Stoltenhoff T., Kreve H., Richter H. An Analysis of the Cold Spray Process and Its Coatings. Journal of Thermal Spray Technology, 2002, Vol. 11(4), p. 542. 50 Dykhuizen R., Smith M. Gas Dynamic Principles of Cold Spray. Journal of Thermal Spray Technology, 1998, 7(2), p. 205. 51 Kosarev V.F., Klinkov S.V., Alkhimov A.P., Papyrin A.N. On Some Aspects of Gas Dynamic Principles of Cold Spray Process. Journal of Thermal Spray Technology, 2003, Vol. 12(2), p. 265. 52 Grujicic M., Zhao C.L., Tong C., DeRosset W.S., Helfritch D. Analysis of the Impact Velocity of Powder Particles in the Cold-Gas Dynamic-Spray Process. Materials Science and Engineering A368, 2004, p. 222. 53 Dykhuizen R.C., Smith M.F., Gilmore D.L., Neiser R.A., Jiang X., Sampath S. Impact of High Velocity Cold Spray Particles. Journal of Thermal Spray Technology, 1999, Vol. 8(4), p. 559. 54 Grujicic M., Saylor J.R., Beasley D.E., Derosset W.S., Helfritch D. Computational Analysis of the Interfacial Bonding between Feed-Powder Particles and the Substrate in the Cold-Gas Dynamic-Spray Process. Applied Surface Science, Vol. 219, 2003, p. 211. 55 Helfritch DJ, Champagne VK. Optimal Particle Size for the Cold Spray Process. Presented at the International Thermal Spray Conference, May, 2006. 56 Champagne V., editor. The Cold Spray Materials Deposition Process: Fundamentals and Applications. Woodhead Publishing Limited, Abington Hall, Abington, Cambridge CB21 6AH, England, 2007, p.57. 57 Grujicic M., Saylor J.R., Beasley D.E., Derosset W.S., Helfritch D. Computational Analysis of the Interfacial Bonding between Feed-Powder Particles and the Substrate in the Cold-Gas Dynamic-Spray Process. Applied Surface Science, Vol. 219, 2003, p. 211. 58 Amateau M.F., Eden T.J. High Velocity Particle Technology. iMast Quarterly, 2000, p. 3. 59 McCune R.C., Donlon W.T., Popoola O.O., Cartwright E.L. Characterization of Copper Layers Produced by Cold Gas-Dynamic Spraying. Journal of Thermal Spray Technology, 2000, Vol. 9(1), p. 73. 60 Moriarty P. Nanostructured Materials. Reports on Progress of Physics, 64 (2001), p. 297.


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61 Shukla V., Elliott G.S., Kear B.H. Nanopowder deposition by supersonic rectangular jet impingement. Journal of Thermal Spray Technology, Vol. 9(3), 2000, p. 394. 62 Lima R.S., Karthikeyan J., Kay C.M., Lindemann J., Berndt C.C. Microstructural Characteristics of Cold-Sprayed Nanostructured WC-Co. Thin Solid Films, 416 (2002) p. 129. 63 Kim H.J., Lee C.H., Hwang S.Y. Superhard Nano WC-12%Co Coating by Cold Spray Deposition. Materials Science and Engineering A391 (2005), p. 243.


21 Nanocoatings for commercial and industrial applications J.L. McCREA, G. PALUMBO, I ntegran Technologies, Canada and U. ERB, University of Toronto, Canada Abstract: Recent advances in the development of bulk nanocrystalline materials have paved the way for a multitude of commercial and industrial applications whereby novel nanostructured coatings have either replaced conventional technologies or have enabled new technologies ultimately leading to new products. In this chapter, the unique functional and structural properties of various nanostructured materials are highlighted/reviewed along with several current and emerging commercial and industrial applications for nanostructured metal coatings. Key words: nanostructured materials, structure–property relationships, commercialization, chrome replacement, nanometal polymer hybrids, magnetic shielding, nanometal carbon fiber composite hybrids.

21.1 Introduction While the field of nanotechnology has developed rapidly over the last decade, the principle upon which it is based – nanoscale features resulting in unique properties – has existed in nature and engineered materials long before the term ‘Nanotechnology’ was defined.1 A good example of nature exploiting the distinct features of nanotechnology can be found in the moth’s eye. As a result of hexagonally arranged protrusions a few hundred nanometers tall and apart (smaller than the wavelength of light), the moth’s eye surface has a very low reflectance, thereby absorbing more light, which allow moths to see much better in the dark than humans.2 In the engineering world, nanometer size precipitates in age-hardened aluminium alloys have been responsible for significant increases in the alloy’s strength, long before the characterization equipment was available to positively identify these nanometer size structures.1,3 With the advent of sophisticated materials characterization techniques, such as high-resolution TEM, SEM, high-resolution SPM, etc., came the ability to effectively identify and characterize nanometer sized structures and features in materials. With these techniques, materials engineers now had the tools to study structural features of materials on the nanometer scale. With the revelation of the uniqueness of nanostructured materials4,5 and the development of various synthesis techniques to intentionally create these materials, engineers and scientists quickly worked to effectively characterize these structures, and establish direct correlations between the structure and the properties. 663 © Woodhead Publishing Limited, 2011

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As will be reviewed in Section 21.2, the outstanding structural and functional properties of nanostructured materials have resulted in the identification of numerous potential applications. However, as a result of multiple entry barriers for new materials in the commercial and industrial world, only a few of these applications have been successfully implemented in industry on a wide scale (i.e. commercialized). In Section 21.3, a quick overview of some of these barriers will be discussed and Section 21.4 will then highlight various applications of nanostructured coatings focusing on a few specific case studies where the market entry barriers have been overcome and new nanostructured materials were successfully introduced into the market.

21.2 Overview of nanostructured metals and alloys As already outlined in previous chapters (Chapter 5 in particular), the properties of a nanostructured material can differ significantly from those of a conventional material of equivalent composition. This is a direct result of the significant increase in the number of interfaces, or grain boundaries, in the material as the grain size decreases below 100 nm.6 It is the enhancement of many of these properties that make nanostructured materials very attractive for use in various commercial and industrial applications. Figure 21.1 shows a schematic diagram of a number of properties that are enhanced (or otherwise affected) by grain refinement to the nanometer scale along with a several potential applications that have been identified in the literature.7 The figure links each property to each application that it influences. With the large number of multiple correlations between properties and applications, the figure emphasizes the importance of the multifunctional nature of nanostructured materials, which is at the heart of the enabling proposition for many of the applications, which will be discussed in more detail later in this section. For simplicity, the material properties listed in Fig. 21.1 are separated into two broad categories: structural and functional. Structural properties include those that are critical for applications in which the nanostructured material will bear load, whereby the mechanical properties (for example: yield strength, elastic limit, ductility, thermal shock resistance) are critical. Functional properties are defined as those that bring additional function to the application and are unique to the nanostructured material, such as excellent wear resistance, lower friction, increased catalytic activity, excellent soft magnetic properties and high electrical resistivity, as well as many others. Rarely does one property alone dictate the use of a material for a specific application. With so many outstanding properties, nanostructured materials by definition are extremely multifunctional, wherein a combination of properties can create a synergistic effect, which essentially enables many applications. A good example of this multifunctional nature is in the fabrication of micro–electrical– mechanical (MEMS) devices. A process has recently been developed to make



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21.1 Enabling properties of nanostructured materials and the correlated applications.7

nanocrystalline nickel, nickel-iron and cobalt for microsystem component applications.8 The ultra-fine, equiaxed, grain structure of the nanocrystalline microcomponents results in outstanding isotropic mechanical properties that provide considerable enhancements of several performance indicators compared to conventional metals, including: higher elastic storage capacity (resilience) and thermal shock resistance. The high wear resistance and lower friction further increases the components’ functionality by significantly improving the tribological performance, and the enhanced electrical and soft magnetic properties, enable many electromagnetic applications for components operating at high frequency by lowering core loss and reducing eddy currents. Another good example of multiple properties coming together to enable an application is the structural reinforcement of polymer portable electronic component housings with excellent electromagnetic shielding performance.9,10,11


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For some applications, the properties of nanostructured materials are not always synergistic; in some cases they can be counter productive, in which case the evaluation and prioritization of the competing objectives must be considered. A good example of this is in the application of nanocrystalline metal coatings on copper wire to greatly enhance the strength-to-weight ratio of electrical conductors in wiring systems, in particular for aircraft applications.12 While a decrease in grain size significantly increases the tensile strength, it also increases the electrical resistivity, which is undesirable for electrical conductors. Potential compromises are therefore 1) to optimize the grain size to achieve an acceptable strength at an acceptable penalty to the overall conductivity, or 2) to design such that the nanocrystalline coating bears the majority of the mechanical load, while the copper core carries the majority of the electrical load. By following the latter approach, wires with ultimate tensile strengths of 1070 MPa were fabricated while retaining an overall conductivity of 57%IACS,12 thereby exceeding the strength-to-weight performance of the incumbent Cu-Be wires. The enhanced properties of nanostructured materials enable many applications where conventional materials would not work, however, it is critical that a comprehensive understanding of the full structure–property relationships exist, such that the synergies and/or trade-offs between them can be fully optimized. As will be shown in the next section, this understanding along with the ability to produce high-quality nanostructures (with predictable material properties), using low-cost production methods helps to minimize implementation risks and overcome the multiple entry barriers these new materials face during commercialization.

21.3 Commercialization of nanostructured materials Most early-stage research and development of new materials is performed in government research labs or universities.13 While the research pushes the boundaries of technology and is extremely innovative, fundamental science is typically the focus, and scaling the technology beyond lab-scale prototypes is usually of secondary importance. As a result, the technology transfer from research to product development can carry cumbersome process development costs that make it difficult for the technology to be commercially viable, regardless of how attractive the properties are. Returning to the moth’s eye as an example, multiple research groups are currently investigating recreating the nanostructured morphology found in the moth’s eyes in materials of various electronic devices (LEDs, lens) with very promising results. However, techniques that can scale beyond laboratory prototypes into cost-effective industrial processes have not yet been defined.14 By no means does this demean the importance, quality or value of the research, it is meant simply to emphasize one of the many hurdles new technology must overcome during commercialization: that of moving the technology out of the lab and into industry in a cost-effective manner. It is



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absolutely essential that the high introductory cost of new materials and processes be offset by compelling end-customer benefit. A common measure used by many of the world’s major companies and agencies (e.g. US DoD, NASA, etc.) to assess the maturity of evolving technologies is the Technology Readiness Level (TRL). Figure 21.2 shows a schematic of the TRL rating scale used by NASA.15 Basic research and technology development covers TRL levels 1 through 5. Before new technology can be effectively implemented in industry, the technology must pass through extensive technology demonstration and system level validation testing (TRL 6 through 8), which has been referred to as the ‘valley of death’.16 The term ‘valley of death’ alludes to the difficulty in maturing technologies through this demonstration and validation stage due to a number of barriers, which ultimately lead to a failure to transfer many new technologies to industry. Bringing new technology through the ‘valley of death’ is one of the most costly stages of development. Costs associated with extensive component level demonstration/validation testing, capital investment, redefinition of codes and standards, as well as others can be overwhelming and prohibitive. Aside from costs, another main barrier is risk aversion of the eventual end-user or of the party responsible for the development costs.

21.2 Technology Readiness Level (TRL): a rating scale commonly used by NASA and the United States Department of Defense to assess the maturity of evolving technologies [after Mankins15].


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There are many risks involved with the implementation of new materials, including: 1) market/product risk, 2) latent liability risk, 3) manufacturing risk, and 4) time to market risk.17 With new materials comes uncertainty, and as a result designers are reluctant to select a new material until it is extensively evaluated in service. However, this presents a chicken-and-egg scenario, as a new material cannot be evaluated in service until a designer selects it. This is a good example of risk adverseness with respect to market/product risk. There is no guarantee to investors/stakeholders that materials will find product acceptance and thus in order to minimize risk, ‘materials must find applications quickly or else lose user interest’.17 In general, the risk of the public’s reluctance to embrace innovative technology without real safety data or products is one of a few of the bottlenecks facing early-stage nanotechnology commercialization.18 The uncertainty factor comes into play again with respect to liability risk. Without the historical data to back long-term use, early adopters assume significant latent liability and warranty risk for the lifetime of the product. As previously mentioned, manufacturing risk (the risk that materials can be cost-effective in large-scale production) is also a significant barrier to the successful implementation of nanostructured materials. Another chicken-and-egg scenario exists here, in that the new materials do not gain market acceptance until their costs decrease (or cost-effectiveness is demonstrated on a large scale), but costs will not decrease until the material gains market acceptance and is produced on a large scale. Most materials advancements that occurred in the twentieth century required 20 years to move from research stage to full commercialization.17 Also known as the ‘20-year barrier’, this represents one of the biggest risks with regard to investing in new materials. The development time, however, can depend on the industry into which the material is being introduced (for example materials in aerospace and defense typically involve longer development times than in sporting goods or consumer electronics), as well as the manner in which it is being introduced. Table 21.1 shows typical development times for new materials in aerospace components depending on how it is being implemented.19 Only a handful of commercial companies exist today with the sole mandate to introduce new nanostructured materials into various industrial and commercial applications. Figure 21.3 shows a graph (the Lux Innovation Grid20), which compares different companies based on technical value and business execution. While the technical value of most companies is rated favorably, only a few of the companies are rated as mature with regards to business execution, thereby showing their relative infancy of the area of technology. As was shown in this section, nanostructured materials face many entry barriers and risks during development and commercialization. Through the use of costeffective production processes and risk mitigation, however, nanostructured materials have penetrated these barriers and have been effectively introduced into various applications across many industries, including: aerospace, defense, automotive, consumer electronics and sporting goods. In the following section,



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Table 21.1 Typical development times for new materials19 Development phase

Development time

Modification of an existing material for a non-critical component

2 to 3 years

Modification of an existing material for a critical structural component

Up to 4 years

New material within a system for which there is experience

Up to 10 years – includes time to define the material’s composition and processing parameters

New material class

Up to 20 years and more – includes time required to develop design practices that fully exploit the performance of the material and establish a viable industrial base

21.3 ‘Lux Innovation Grid’ comparing the technical value and business execution of various commercial nanomaterials companies.20

several current and emerging applications are reviewed and where possible the factors that led to market penetration in light of the aforementioned barriers will be highlighted.

21.4 Current and emerging applications Some of the earliest systematic studies on the use of electrodeposition to produce nanocrystalline materials occurred in the 1980s.21,22 The first large-scale structural


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application for nanostructured materials was introduced in 1993 (the Electrosleeve process for nuclear steam generator repair),23,24,25 which was followed shortly by some of the earliest issued US patents in the field of nanotechnology.26,27 Nearly 20 years have now passed since this first industrial application and patents were issued, and true to the ‘20-year barrier’, nanostructured materials are now starting to see widespread use in a variety of industrial and commercial applications. The following sections present some several case studies of current and emerging applications of nanostructured metal coatings, highlighting the value proposition and market entry in light of the risks described in the previous section.

21.4.1 Hard chrome replacement Commercial hard chrome plating from hexavalent chromium plating solutions has been around since the early part of the twentieth century.28 As a result of their intrinsic high hardness (600 to 1000 VHN) and low coefficient of friction (

Nanostructured metals and alloys - Processing, microstructure, mechanical properties and applications

Processing of Metals and Alloys

NANOSTRUCTURED MATERIALS Processing Properties and Potential Applications

Alloys: Preparation, Properties, Applications

Nanostructured Materials, Second Edition: Processing, Properties and Applications

Duplex Stainless Steels, Microstructure, properties and applications

Ceramic matrix composites. Microstructure, properties and applications

Engineering Properties and Applications of Lead Alloys

Plasticity of Metals and Alloys

Plasticity of Metals and Alloys

The Theory of the Properties of Metals and Alloys

Concrete: Microstructure, Properties, and Materials

Melting and Crystallization of Metals and Alloys

Mechanical Properties of Metals: Atomistic and Fractal Continuum Approaches

Geopolymers: Structures, Processing, Properties and Industrial Applications

Nanocrystalline metals and oxides: selected properties and applications

Fatigue Crack Propagation in Metals and Alloys

High Temperature Strain Of Metals And Alloys

Fundamentals of Creep in Metals and Alloys

Fundamentals of Creep in Metals and Alloys

High Temperature Strain of Metals and Alloys

Phase transformations in metals and alloys

Nanostructured materials: selected synthesis methods, properties, and applications

Maraging Steels: Modelling of Microstructure, Properties and Applications

Nanostructured materials. Selected Synthesis Methods, Properties and Applications

Plastics: Microstructure and engineering applications

Microstructure and Properties of High-Temperature SuperConductors

Steels: Microstructure and Properties, Third Edition

Aluminium Alloys, Theory and Applications

Structure and properties of engineering alloys

Structure and Properties of Nonferrous Alloys

Nanostructured metals and alloys - Processing, microstructure, mechanical properties and applications

Processing of Metals and Alloys

NANOSTRUCTURED MATERIALS Processing Properties and Potential Applications

Alloys: Preparation, Properties, Applications

Nanostructured Materials, Second Edition: Processing, Properties and Applications

Duplex Stainless Steels, Microstructure, properties and applications

Ceramic matrix composites. Microstructure, properties and applications

Engineering Properties and Applications of Lead Alloys

Plasticity of Metals and Alloys

Plasticity of Metals and Alloys

The Theory of the Properties of Metals and Alloys

Concrete: Microstructure, Properties, and Materials

Melting and Crystallization of Metals and Alloys

Mechanical Properties of Metals: Atomistic and Fractal Continuum Approaches

Geopolymers: Structures, Processing, Properties and Industrial Applications

Nanocrystalline metals and oxides: selected properties and applications

Fatigue Crack Propagation in Metals and Alloys

High Temperature Strain Of Metals And Alloys

Fundamentals of Creep in Metals and Alloys

Fundamentals of Creep in Metals and Alloys

High Temperature Strain of Metals and Alloys

Phase transformations in metals and alloys

Nanostructured materials: selected synthesis methods, properties, and applications

Maraging Steels: Modelling of Microstructure, Properties and Applications

Nanostructured materials. Selected Synthesis Methods, Properties and Applications

Plastics: Microstructure and engineering applications

Microstructure and Properties of High-Temperature SuperConductors

Steels: Microstructure and Properties, Third Edition

Aluminium Alloys, Theory and Applications

Structure and properties of engineering alloys

Structure and Properties of Nonferrous Alloys

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