Shape memory and superelastic alloys
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Shape memory and superelastic alloys Technologies and applications
Edited by K. Yamauchi, I. Ohkata, K. Tsuchiya and S. Miyazaki
Oxford
Cambridge
Philadelphia
New Delhi
© Woodhead Publishing Limited, 2011
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 978-1-84569-707-5 (print) ISBN 978-0-85709-262-5 (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 Toppan Best-set Premedia Limited, Hong Kong Printed by TJI Digital, Padstow, Cornwall, UK
© Woodhead Publishing Limited, 2011
Contents
Contributor contact details Preface
Part I Properties and processing 1
Mechanisms and properties of shape memory effect and superelasticity in alloys and other materials: a practical guide K. Tsuchiya, National Institute for Materials Science, Japan
xi xv
1
3
1.1 1.2 1.3 1.4 1.5 1.6
Introduction Properties of shape memory alloys (SMAs) Fundamentals of shape memory alloys (SMAs) Thermodynamics of martensitic transformation Conclusions References
3 4 5 12 13 14
2
Basic characteristics of titanium–nickel (Ti–Ni)based and titanium–niobium (Ti–Nb)-based alloys S. Miyazaki and H. Y. Kim, University of Tsukuba, Japan
15
2.1 2.2 2.3 2.4 2.5
Introduction Titanium–nickel (Ti–Ni)-based alloys Titanium–niobium (Ti–Nb)-based alloys Conclusions References
15 16 29 40 41
3
Development and commercialization of titanium–nickel (Ti–Ni) and copper (Cu)-based shape memory alloys (SMAs) K. Yamauchi, Tohuku University, Japan
3.1 3.2
Introduction Research on titanium–nickel (Ti–Ni)-based shape memory alloys (SMAs)
43 43 43 v
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Contents
3.3
Research on copper (Cu)-based shape memory alloys (SMAs) Conclusions References
3.4 3.5 4
Industrial processing of titanium–nickel (Ti–Ni) shape memory alloys (SMAs) to achieve key properties T. Nakahata, Sumitomo Metal Industries Ltd, Japan
48 49 52
53
4.1 4.2 4.3 4.4 4.5
Introduction Melting process Working process Forming and shape memory treatment References
53 54 58 60 62
5
Design of shape memory alloy (SMA) coil springs for actuator applications T. Ishii, Sogo Spring Mfg Co. Ltd, Japan
63
5.1 5.2 5.3 5.4 5.5
Introduction Design of shape memory alloy (SMA) springs Design of shape memory alloy (SMA) actuators Manufacturing of shape memory alloy (SMA) springs Reference
63 63 68 69 76
6
Overview of the development of shape memory and superelastic alloy applications S. Takaoka Furukawa Electric Co. Ltd, Japan
77
6.1 6.2 6.3 6.4
Introduction History of the applications of titanium–nickel (Ti–Ni)based shape memory and superelastic (SE) alloys Other shape memory alloys (SMAs) Examples of the main applications of titanium–nickel (Ti–Ni)-based alloys
Part II Application technologies for shape memory alloys (SMAs) 7
7.1
77 79 81 82
85
Applications of shape memory alloys (SMAs) in electrical appliances T. Habu, Furukawa Techno Material Co. Ltd, Japan
87
Introduction
87
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7.2 7.3 7.4 7.5
Automatic desiccators Products utilizing shape memory alloys (SMAs) Electric current actuator Reference
87 88 94 99
8
Applications of shape memory alloys (SMAs) in hot water supplies A. Suzuki, Daido Steel Co. Ltd, Japan
100
8.1 8.2 8.3
Shower faucet with water temperature regulator Gas flow shielding device Bathtub adaptors
100 103 103
9
The use of shape memory alloys (SMAs) in construction and housing M. Ozawa, NEC TOKIN Corporation, Japan, A. Suzuki, Daido Steel Co. Ltd, Japan and T. Inaba, Nishimatu Construction Co. Ltd, Japan
110
9.1 9.2 9.3 9.4 9.5
Introduction Underground ventilator Static rock breaker Easy-release screw Acknowledgements
110 111 112 116 119
10
The use of shape memory alloys (SMAs) in automobiles and trains T. Kato, Piolax Inc., Japan
120
10.1 10.2 10.3 10.4 10.5 10.6
Introduction Shape memory alloys (SMAs) in automobiles Oil controller in Shinkansen Steam trap Conclusions References
120 120 121 122 124 124
11
The use of shape memory alloys (SMAs) in aerospace engineering T. Ikeda, Nagoya University, Japan
125
11.1 11.2 11.3
Introduction Development and properties of CryoFit (Aerofit, Inc.) Development and properties of Frangibolt (TiNi Aerospace, Inc.)
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11.4
Development and properties of Pinpuller (TiNi Aerospace, Inc.) Development and properties of variable geometry chevrons (VGC) (The Boeing Company) Development and properties of hinge and deployment of lightweight flexible solar array (LFSA) on EO-1 (NASA and Lockheed Martin Astronautics) Development and properties of rotating arm for material adherence experiment (MAE) in Mars Pathfinder mission (NASA) References
11.5 11.6
11.7
11.8 12
12.1 12.2 12.3 12.4 12.5 12.6 12.7 12.8
Ferrous (Fe-based) shape memory alloys (SMAs): properties, processing and applications T. Maruyama, Awaji Materia Co. Ltd, Japan and H. Kubo, Kanto Polytechnic University, Japan Introduction Iron–manganese–silicon (Fe–Mn–Si) shape memory alloys (SMAs) Shape memory effect of iron–manganese–silicon (Fe–Mn–Si) alloy Mechanical properties of iron–manganese–silicon (Fe–Mn–Si) shape memory alloys (SMAs) Proper process for shape memory effect Applications of iron–manganese–silicon (Fe–Mn–Si) shape memory alloys (SMAs) Future trends References
Part III Application technologies for superelastic alloys 13
13.1 13.2
14
Applications of superelastic alloys in the telecommunications, industry T. Habu, Furukawa Techno Material Co. Ltd, Japan Introduction Products utilizing superelastic alloys in the telecommunications industry Applications of superelastic alloys in the clothing, sports and leisure industries T. Habu, Furukawa Techno Material Co. Ltd, Japan
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130 131
134
137 139
141
141 142 145 146 149 153 156 158
161
163 163 163
169
Contents 14.1 14.2
15
15.1 15.2 15.3 15.4 15.5 15.6. 15.7 15.8 15.9
Introduction Products utilizing superelastic alloys in the clothing, sports and leisure industries
ix 169 169
Medical applications of superelastic nickel–titanium (Ni–Ti) alloys I. Ohkata, Piolax Medical Devices Inc., Japan
176
Introduction Hallux valgus Orthodontic wire Guide wire Biliary stents Regional chemotherapy catheter Endoscopic guide wire Device for onychocryptosis correction References
176 176 178 179 183 187 191 195 196
Appendix: History of the Association of Shape Memory Alloys K. Shimizu, Osaka University, Japan
197
Index
201
© Woodhead Publishing Limited, 2011
Contributor contact details
(* = main contact)
Editors K. Yamauchi Innovation of New Biomaterial Engineering Center Tohoku University 1-1 Seiryo-machi, Aoba-ku Sendai Japan E-mail:
[email protected]. ac.jp I. Ohkata Piolax Medical Devices Inc. 179 Kariba-cho Hodogaya-ku Yokohama 240-0025 Japan
K. Tsuchiya Hybrid Materials Center National Institute for Materials Science Sengen 1-2-1 Tsukuba Ibaraki 305-0047 Japan E-mail:
[email protected] S. Miyazaki* Institute of Materials Science University of Tsukuba Tsukuba Ibaraki 305-8573 Japan E-mail:
[email protected] [email protected] E-mail:
[email protected] xi © Woodhead Publishing Limited, 2011
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Contributor contact details
Chapter 1
Chapter 4
K. Tsuchiya Hybrid Materials Center National Institute for Materials Science Sengen 1-2-1 Tsukuba Ibaraki 305-0047 Japan
T. Nakahata Sumitomo Metal Industries Ltd Shimaya 5-1-109, Konohana-ku Osaka 554-0024 Japan E-mail: nakahata-tkj@ sumitomometals.co.jp
E-mail:
[email protected] Chapter 5 Chapter 2 S. Miyazaki* and H. Y. Kim Institute of Materials Science University of Tsukuba Tsukuba Ibaraki 305-8573 Japan
T. Ishii Sogo Spring Mfg Co. Ltd 2-3-24, Yoshioka-Higashi Ayase-City Kanagawa 252-1125 Japan E-mail: takashi_ishii@sogospring. co.jp
E-mail:
[email protected] [email protected] Chapter 6 Chapter 3 K. Yamauchi Innovation of New Biomaterial Engineering Center Tohoku University 1-1 Seiryo-machi, Aoba-ku Sendai Japan
S. Takaoka Furukawa Electric Co. Ltd Special Metal Sales Div. Metal Company 5-1-8, Higashi-Yawata Hiratsuka-City Kanagawa 254-0016 Japan E-mail:
[email protected] E-mail:
[email protected]. ac.jp
© Woodhead Publishing Limited, 2011
Contributor contact details
Chapter 7, 13 and 14 T. Habu Furukawa Techno Material Co. Ltd Engineering & Development Section 5-1-8, Higashi-Yawata, Hiratsuka-City Kanagawa 254-0016 Japan E-mail:
[email protected] Chapter 8
xiii
A. Suzuki Daido Steel Co. Ltd. 2-30 Daido-cho Minami-ku Nagoya 457-8545 Japan E-mail:
[email protected] T. Inaba Nishimatu Construction Co. Ltd 2570 Shimotsuruma Yamato Kanagawa 242-8520 Japan E-mail: tsunomu_inaba@ nishimatsu.co.jp
A. Suzuki Daido Steel Co. Ltd 2-30 Daido-cho Minami-ku Nagoya 457-8545 Japan
Chapter 10
E-mail:
[email protected] Chapter 9 M. Ozawa* NEC TOKIN Corporation 7-1, Koriyama 6-Chome Taihaku-ku Sendai 982-8510 Japan E-mail:
[email protected] T. Kato Piolax Inc. 179 Kariba-cho Hodogaya-ku Yokohama 240-0025 Japan E-mail:
[email protected] Chapter 11 T. Ikeda Composite Engineering Research Center Graduate School of Engineering Nagoya University Furo-cho, Chikasa-ku Nagoya 464-8603 Japan E-mail:
[email protected] © Woodhead Publishing Limited, 2011
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Contributor contact details
Chapter 12
Chapter 15
T. Maruyama Awaji Materia Co. Ltd 2-3-13 Kanda-Ogawamachi Chiyoda-ku Tokyo 101-0052 Japan
I. Ohkata Piolax Medical Devices Inc. 179 Kariba-cho Hodogaya-ku Yokohama 240-0025 Japan
E-mail: t.maruyama@awaji-materia. co.jp
E-mail:
[email protected] H. Kubo Kanto Polytechnic University 612-1 Mitake Yokokura Oyama 323-0810 Japan
Appendix K. Shimizu Osaka University 1500-601, Ohitomi-chou Nishi-ku, Hamamatsu Shizuoka Japan E-mail:
[email protected] © Woodhead Publishing Limited, 2011
Preface
It has been a long time since shape memory alloys (SMAs) drew attention as functional materials possessing quite fascinating properties such as shape memory effect (SME) and superelasticity (SE), which are not possessed by ordinary metals. Nearly half a century has passed since the discovery of Ti–Ni SMA in 1963. After developing numerous applications of SMAs, some of them have grown up to be important world standard devices, though many of them ended up as just ideas or as transiently used applications disappearing from the market. This book has been written by members of the Association of Shape Memory Alloys (ASMA), who have worked on research and development of SMAs in addition to their practical use and industrialization. The book sums up the results of applications most of which have appeared on the market from the dawn of the research and development. In this book, we have tried to include as many examples as possible of applications with their key points of ideas, features and commercial performance. The book introduces not only successful applications but also unsuccessful ones which could not be commercialized simply because of bad timing. This book is naturally divided into three parts: research and development, fundamentals and production technologies (Part I), application technologies for SMAs (Part II) and application technologies for superelastic alloys (SEAs) (Part III). Part I covers mechanisms and properties of SME and SE for practical users (Chapter 1), basic characteristics of Ti–Ni based and Ti–Nb based SM/SE alloys (Chapter 2), development of alloy production technology (Chapter 3), industrial processing and device elements (Chapter 4), design of SMA actuators (Chapter 5) and an overview on the development of SM and SE applications (Chapter 6). Part II introduces SMA applications: SMAs in electrical applications (Chapter 7), SMAs in hotwater supply (Chapter 8), SMAs in construction and housing (Chapter 9), SMAs in automobiles and railways (Chapter 10), SMAs in aerospace engineering (Chapter 11) and Fe-based SMAs (Chapter 12). Part III focuses on xv © Woodhead Publishing Limited, 2011
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Preface
SEA applications: SEAs in telecommunications, and other areas (Chapter 13), SEAs in clothing, sports and leisure (Chapter 14) and SEAs in medical applications (Chapter 15). In the appendix, the history and activity of ASMA, which promotes the development and researches of SMAs, is briefly described. Throughout the book, many photographs of application products utilizing SMA or SEA are shown for the readers to grasp the images of the applications. Since many of the photographs are not published in any journals or books and were obtained through personal connections of each author, in many cases no specific references are cited. The authors are greatly appreciative of the generosity of the owners for allowing use of the photographs in this book. The editors hope this book will be useful for readers to access precious information on SM/SE alloys and their applications as well as applying SMAs and SEAs for readers’ application development. They also express their heartfelt thanks to the team of distinguished contributors who have been working on SMAs and SEAs in companies and universities for many years. Finally, they express special thanks to the staff at Woodhead Publishing Limited for their assistance. K. Yamauchi I. Ohkata K. Tsuchiya S. Miyazaki
© Woodhead Publishing Limited, 2011
Appendix: History of the Association of Shape Memory Alloys K. SHIMIZU, Osaka University, Japan
The Association of Shape Memory Alloys, the editorial committee responsible for this book, was established in 1993 in order to promote further research and development in the areas of fundamentals and applications of shape memory alloys (SMAs). In this appendix, the circumstances of the establishment, as well as the recent activities, of the association will be introduced in brief. As is well known, in 1963, Dr Buehler’s group at the US Naval Ordinance Laboratory recorded the appearance of a unique phenomenon of the shape memory effect (SME) in a familiar Ti–Ni alloy, although a similar phenomenon had already been observed in unfamiliar Au–Cd and In–Tl alloys in 1951 and 1954, respectively. Because of its remarkable uniqueness, the SME was immediately investigated to discover potential applications in the manufacture of the machine parts of industrial products and even in living essentials, mainly in the United States and the Netherlands. However, the results of this investigation could not be developed for practical use. After a while, in about 1970, the Raychem Corporation in the United States developed a Cryofit coupling and an electrical pin-and-socket contact made of the Ti–Ni SMA and offered them for sale in large quantities; the former coupling was typically applied in the production of the aircraft hydraulic tubing of the US F-14 fighter plane. On the other hand, at about the same time, the fundamental mechanism of the SME was investigated and clarified in relation to a thermoelastic martensitic transformation in ordered alloys. During the investigation, researchers discovered another unique phenomenon, super elasticity (SE), which was closely related to the SME. Since then, the SME and SE phenomena have been found not only in Ti–Ni alloys but also in many noble metal base and other alloys. In 1975, the first international symposium on SMAs was held at Toronto, Canada, and many academic and technological researchers participated from all over the world. By 1980, the US patented right for the processing and technological applications of Ti–Ni SMAs had lapsed, and extensive research had developed globally concerning the fundamentals and applications of Ti–Ni base, noble metal base and other SMAs. In the circumstances mentioned above, two organizations were established in Japan to promote the development research into the fundamentals 197 © Woodhead Publishing Limited, 2011
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and applications of SMAs; one (a semi-governmental organization) was a ‘Committee for Promotion of Applications of SMAs’ formed in Osaka Science and Technology Center in 1982, and the other (a private organization) was a ‘Research Cooperative Union for Processing of SMAs’ formed by six manufacturing companies of SMAs in 1983. The former organization, ‘Committee for Promotion of Applications of SMAs’, consisted of members from typical universities, governmental research institutes and manufacturing companies, and had conducted extensive investigations into the existing circumstances of the development research for the processing and applications of SMAs and of the test characterization methods for those SMAs. The organization had further examined the subjects and systems required to promote this research and development. As a result, the first work of the organization was the standardization of the terminology relating to SMAs used in academic and technological fields and of the methods of measuring martensitic transformation temperatures. After a little while, this organization was succeeded by a ‘Committee for SMAs’, which was a subdivision of the Committee for Investigations on Standardization of Test Characterization Methods on New Materials used as Electric Power Source instead of Petroleum, which was specially established in the Osaka Science and Technology Center with governmental support as one of the national projects intended to activate research into the various kinds of functional materials that were newly developed about that time. The investigation work carried out in the ‘Committee for SMAs’ effectively took over from that of the previous ‘Committee for Promotion of Applications of SMAs’. Thus, six items relating to the standardization of terminologies and test characterization methods of SMAs were established via careful discussion in the Japan Industrial Standards (JIS) Committee, which were JIS H7001, JIS 7101, JIS H7103, JIS H7104, JIS H7105 and JIS H7106; the first two were based on the investigations of the previous committee. After the establishment of the six JISs, the ‘Committee for SMAs’ was closed in 1992. The latter organization, the ‘Research Cooperative Union for Processing of SMAs’, was formed by six manufacturing companies and it was fortunately able to obtain a governmental grant-in-aid to carry out improvement work on processing technologies for SMAs under the national support system for the development of industrial technology research. Three of the six manufacturing companies were those which produced Ti–Ni SMAs. In alphabetical order, these were: Daido Special Steels, Furukawa Electric Industry and Tohoku Kinzoku (now NEC TOKIN). The other three companies were manufacturers of Cu–base SMAs: Dowa Mining, Mitsubishi Metals and Sumitomo Special Metals. All the companies had investigated individually and/or cooperatively with governmental
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support for various topics relating to SMAs, such as the minimization of inclusions, control of martensitic transformation temperatures, improvement of SMA and SE characteristics due to the addition of a third and/or forth element and due to thermomechanical treatments, and so on. Thus, those companies could be successful in producing various products (lines, pipes, plates, thin foils and coil springs) from SMAs with better SME and/ or SE characteristics, and the products were supplied for application in the manufacture of various industrial machine parts and medical interposition devices in the human body. The switch of a dry box, the sensor flap of an air conditioner, a medical stent and many others, as have been introduced in this book. This private organization had been acting in close cooperation with the former semi-governmental organization, contributing to the establishment of the above-mentioned six JISs for the SMAs. It was closed in 1993, having obtained the expected results to some extent although, with very few exceptions, noble metal-based SMAs could not be supplied for practical uses because of their being to some degree unsuitable for such applications. The above two organizations were closed as mentioned, but some members of those organizations had promptly advocated the establishment of another new organization. Ti–Ni SMAs had attracted an increasing amount of attention, not only among professional workers but also among ordinary people worldwide, and research and development into the fundamentals and applications of SMAs were required to promote them more extensively and strongly than before. Thus, the Association of Shape Memory Alloys (ASMA) was established in October 1993, as mentioned at the beginning. At the start, the ASMA was constituted of several individual members and of six supporting members from industrial companies. These were, in alphabetical order: Daido Special Steels, Furukawa Electric Industry, Kato Spring (now Piolax), Mitsubishi Material, NEC TOKIN and Sogo Spring. The ASMA has expanded little by little, and it now consists of 39 individual members and of nine supporting members from industrial companies. The individual members join the association voluntarily from universities and other research institutes, and the supporting members typically come from nine companies in the manufacturing industries, coil spring makers and those working with applications of Ti–Ni and ferrous SMAs. The ASMA is operated under a board of trustees and a general meeting, the former being constituted of one president, one secretary-general, eight trustees, one inspector and one counselor. The objective of the ASMA is to promote progress and development in the science and technology of SMAs and to contribute to the development of related industries. In order to achieve this objective, the following projects have been enforced:
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• • •
investigation and research on SMAs and their trusts; holding of lectures and research meetings on SMAs; publication of journals and other documents on the activities of the ASMA; • connection and cooperation with other related academic and technological organizations in domestic and foreign countries; • other necessary projects in order to achieve the objective of the ASMA. These projects, as well as the annual budget for them, are planned and implemented via discussion among the board of trustees and the general meeting. After its establishment in 1993, the ASMA has actively carried out various projects, such as the holding of short courses and symposiums on SMAs every year, the publication of a newsletter and of summary booklets of patent reports and new models for practical uses, financial support to several domestic and international meetings on SMAs, the holding of the Japan–China Bilateral Symposium on SMAs (1997), the organization of the International Conference on Shape Memory and Superelastic Technology (2007) and many others. The ASMA has also produced a standardization work on the Ti–Ni SMA wire itself, JIS H7107, in addition to some corrections and supplements to the other six JIS previously established. As has been mentioned above, the ASMA is now continuing its activity steadily, although some projects have been inevitably reduced due to the economic depression, and has greatly contributed to the progress and development of the science and technology of SMAs and to the development of SMAs industries in Japan and also throughout the world.
© Woodhead Publishing Limited, 2011
1 Mechanisms and properties of shape memory effect and superelasticity in alloys and other materials: a practical guide K. TSUCHIYA, National Institute For Materials Science, Japan
Abstract: This chapter describes fundamental knowledge about shape memory and superelastic alloys which may be useful to potential users of these alloys. Basic characteristics and properties of various shape memory/superelastic alloys are described in the first and second sections. The mechanisms of the shape memory effect and superelasticity are then explained, followed by a section on thermodynamics which is intended for more proficient readers. Key words: shape memory effect, superelasticity, stress–strain curve, martensitic transformation, martensite, austenite, R phase.
1.1
Introduction
As one of the most prominent functional metallic materials, shape memory alloys (SMAs) are widely used in a range of appliances, from coffee maker thermostats to glasses frames. They have also found an increasing number of applications in the rapidly progressing field of minimally invasive surgery, specifically in the production of medical devices such as stents, guide wires, and filtration devices (Morgan, 2004). It is the shape memory effect (SME) and superelasticity (SE), characteristics unique to SMAs, that make them suitable to these applications. SME and SE are illustrated in the form of stress–strain curves in Fig. 1.1. In SME, a previously deformed alloy can be made to recover its original shape simply by heating (Fig. 1.1(a)); while in SE, the alloy can be bent or stretched to a great extent, but returns to its original shape once the load is released (Fig. 1.1(b)). In the case of SME, shape recovery takes place at a particular temperature, and thus a single piece of material functions both as a sensor and as an actuator. This is the reason why SMAs are often referred to as smart or intelligent materials. Such materials are useful in the production of simple, compact and reliable actuator devices. SMA actuators will be discussed in greater detail in Chapter 5. SE is suited to applications which require the use of a material with large recoverable deformation. For example, in the case of TiNi wires, it is 3 © Woodhead Publishing Limited, 2011
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Shape memory and superelastic alloys
Stress
(b)
Stress
(a)
Loading
Loading
Unloading
Heating
Unloading
Strain
Strain
1.1 Stress–strain curves describing (a) shape memory effect and (b) superelasticity.
typically possible to recover approximately 8% strain, which is about 800 times larger than conventional elastic strain (Hooke’s law) in metals. Another important characteristic of superelasticity is its non-linear stress– strain response. This chapter describes the fundamental properties of SMAs in order to assist the reader in understanding the working principles of a wide variety of SMA applications (such as those described in Parts II and III) as well as to aid and motivate them towards researching and inventing novel applications for these materials.
1.2
Properties of shape memory alloys (SMAs)
Figure 1.2 consists of a series of tensile stress–strain curves for TiNi, obtained at different temperatures (Miyazaki et al., 1981). It is clear, at a glance, that the properties of SMAs are strongly temperature dependent. At low temperatures, the stress (or load) required to deform the sample is relatively low. Once the load has been removed, the deformation persists, just like a plastic deformation in conventional metals, such as steels or aluminum, but vanishes after the sample has been heated, as indicated by the broken arrows (SME). Above 232.5 K, the deformation stress starts to increase with temperature, and the deformation vanishes upon the removal of the load, even without heating (SE). At higher temperatures, the residual strain appears and the stress–strain curves are more or less similar to those of conventional metals. Stress–strain behavior is not the only property of SMAs to be affected by temperature. Various other properties, such as elastic modulus, electrical resistivity, and specific heats, are also strongly temperature dependent. The reason for such complex behavior is that the sample changes state as the temperature increases, and thus its deformation mechanism is different for various temperature ranges.
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A practical guide
5
(a) 77.0 K 300 (b) 153.0 K
(c) 164.1 K
200
(d) 171.2 K
100 0 200
0
(e) 182.7 K
0 (f) 193.3 K
100
0 (h) 213.5 K
(g) 203.0 K
0 0
0
0
Stress (MPa)
400
(l) 251.0 K (k) 241.0 K
300
(j) 232.5 K (i) 223.7 K
200 100 0
0
0
0 (o) 276.5 K
600
(n) 273.2 K (m) 263.4 K
400
(p) 283.7 K
200
Ms = 190 K At = 221 K 0
0
2
4
0
2
4
0
2
4
0
2
4
Strain (%)
1.2 Tensile stress–strain curves of Ti–50.6Ni obtained at different temperatures (Ms = martensitic transformation start temperature, Af = reverse transformation finish temperature, (Miyazaki et al., 1981).
1.3
Fundamentals of shape memory alloys (SMAs)
1.3.1 Martensitic transformation Both the SME and SE share a common origin, known as martensitic transformation. Martensitic transformation is a particular class of phase transformation. Most metallic materials and ceramics are crystalline materials in
© Woodhead Publishing Limited, 2011
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Shape memory and superelastic alloys
which the constituent atoms are regularly arranged in three dimensions, forming a particular crystal structure representing each phase. The structure of crystalline materials is often altered in response to a change in the external environment, such as a change in temperature, pressure, stress, etc. Phase transformation in crystalline materials can be classified into two categories; one is diffusional transformation and the other, diffusionless or displacive transformation. In the case of diffusional transformation, atoms leave one crystal structure to form another structure by diffusion. For this reason, a high temperature is generally necessary to ensure that the mobility of atoms is high, otherwise the transformation is too sluggish. Meanwhile, it is possible for the atoms to alter the crystal structure without leaving the original crystal by their coordinated displacive movements. This does not require long range diffusion of atoms and takes place in a relatively short time. Martensitic transformation belongs to this second category of diffusionless transformation and is characterized by well-coordinated shear dominant atomic displacement, as shown in Fig. 1.3. It can be seen that even though the displacement of each atom is much less than its interatomic distance, the process of transformation creates a large shear strain. Another important implication of shear dominant transformation is that the volume change during the transformation can be very small. Starting from the high temperature phase, which is typically a cubic phase such as a body centered cubic (bcc) or face centered cubic (fcc) structure, the crystal structure is cooled to below martensitic transformation temperatures and transforms into a product phase with lower crystallographic symmetry. The high temperature phase is called the parent phase or austenite, and the product of martensitic transformation is called the martensite phase or martensite. This phase transformation can be detected by various measurements, such as electrical resistivity measurements or calorimetric measurements. Figure
Cooling
Heating
Austenite
Martensite
1.3 Schematic illustration of change in unit cell shape on martensitic transformation.
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A practical guide
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1.4 contains an example of a differential scanning calorimetry (DSC) measurement for a Ti–50.2 mol% Ni. On cooling from a temperature at which the austenite is stable, the alloy transforms to a martensite phase via an exothermic reaction. Heating the sample again leads to a reverse transformation to austenite with an endothermic reaction. The martensitic transformation occurs within a certain temperature interval. In order to bracket these temperature ranges, it is practical to use four transformation temperatures, which consist of martensitic transformation start temperature (Ms), martensitic transformation finish temperature (Mf), reverse transformation start temperature (As) and reverse transformation finish temperature (Af). Peak temperatures of forward and reverse transformation peaks can be also useful. The corresponding changes in atomic structures during the transformation are illustrated in Fig. 1.5. A plate of martensite starts to form in austenite at Ms; the area of martensite increases on cooling and the whole sample becomes martensite at Mf. At the temperature range between Ms and Mf, the sample constitutes a mixture of martensite and austenite. It should be noted that in a fully martensitic state (below Af) the sample is composed of martensite crystals with two different orientations: opposite shear directions which are twin-related with each other. This morphology enables the martensite crystals to mutually cancel out the shear
Ti–50.2at%Ni 0.3 M* = 289.0 K 0.2
Heat flow, Q/W g–1
15.84 J/g 0.1
0.0
Mf = 277.4 K
Ms = 298.8 K
As = 313.3 K
Af = 338.6 K
–0.1 –16.79 J/g –0.2
–0.3 150
A* = 327.9 K 200
250
300
350
400
450
500
Temperature, T/K
1.4 Differential scanning calorimetry (DSC) measurement of martensitic transformation temperatures.
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Shape memory and superelastic alloys P Ms
MB
MB
Mf
MA
MA
P MB
MB Af
MA
As
MA
P Martensite (self-accommodated structure)
Austenite
1.5 Schematic illustration of atomic arrangements during martensitic transformation. P: parent phase, M: martensite phase, subscripts A and B stand for the martensite crystals with different shear directions.
deformation and thereby minimize the deformation of the sample, a process which is referred to as self-accommodation. Those martensite crystals that form from a single austenite but have a different orientation are called variant. There can be up to 24 different orientations when the martensite is monoclinic, as in the case of the B19′ phase in TiNi (Kudoh et al., 1985). When the sample is heated, the transformation from martensite to austenite occurs in reversed manner . It can also be seen from Fig. 1.4 that the transformation temperatures are different for forward and reverse transformation. This difference is called transformation hysteresis. The origin of hysteresis is related to the mobility of the austenite/martensite interface. Sometimes a martensite can be transformed into another martensite with a different crystallographic structure. Figure 1.6 shows the DSC curves for such multi-step martensitic transformation for Ti–50.6 mol% Ni. In this case, the austenite transforms first to the R phase and then to the B19′ phase on further cooling. It should be noted that on heating, the B19′ phase transforms to austenite without transforming into the R phase. This is due to the fact that there is a much larger transformation hysteresis in the B19′ to B2 (austenite) transformation than in the R to B2 transformation. The R phase has a much smaller transformation strain (∼1%) than that which occurs in B19′ (∼8%) (Stachowiak and McCormick, 1988) and often appears in a cold-worked sample or in a sample containing precipitates. A stress field, such as those produced by dislocation structures, tends to suppress the B19′ transformation and stabilizes The R phase. In this section, the martensitic transformation induced by temperature was described. However, the same transformation can be also induced by stress. This will be explained in Section 1.3.3.
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A practical guide
9
Endotherm.
Exotherm.
M* = 233 K R* = 302 K
A* = 308 K 150
200
250 300 350 400 Temperature, T/K
450
500
1.6 DSC curves showing multi-step martensitic transformation. Heating above Af
Austenite
Martensite
Deformation
1.7 Mechanism of the SME.
1.3.2 SME Figure 1.7 illustrates the mechanism of the SME. In this case, a piece of SMA (for example, a wire) is in martensite phase at room temperature and its martensitic transformation temperature is sufficiently above room temperature. The wire can be easily bent since the martensite phase can be easily deformed by twinning or detwinning. The deformation can be seen as a change in the fraction of the variants. If you heat the bent wire to a temperature above Af, the martensite transforms back to austenite and the sample regains its original straight shape. This is possible because all of the variants were originally formed from a single austenite crystal. On cooling
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Shape memory and superelastic alloys
to room temperature the wire re-transforms to martensite, but its shape does not change due to the self-accommodated structures. This is the mechanism of the SME. The strain recovered by the reverse transformation can be as great as ∼8 % whilst the recovery stress can be as large as several hundred MPa in the case of TiNi. This leads to an energy density as high as 107 J/m3 which is three orders of magnitude higher than those of other actuator materials, such as piezo-ceramics or magnetostrictive materials. It should be emphasized that the shape change caused by the SME occurs only upon heating, and this is referred to as the one-way SME. In order to obtain a shape change upon cooling, it is necessary to control the arrangement of the variants that form on cooling from Af to room temperature. This can be achieved, at least to some extent, with the introduction of a stress field, either through the fine precipitation Ti3Ni4 phase (Kainuma et al., 1986), which is semi-coherent to the austenite, or through the introduction of dislocation structures.
1.3.3 SE In the case of the SME, the SMA is deformed when it is in the martensite phase, which is deformation given at a temperature below Mf. In contrast, in the case of SE, the alloy is deformed at a temperature above Af. The mechanism of SE is illustrated schematically in Fig. 1.8. When the austenite phase is subjected to a stress , it transforms into martensite. In this case, the variant that forms upon the application of stress is that which gives the maximum strain in the given stress direction. Once the imposed stress is released the sample transforms back into the austenite and the strain also vanishes. The stress required to induce the transformation increases linearly with temperature, as illustrated in Fig. 1.9. The gradients of the lines are given by the Clausius–Clapeyron equation: dσ ΔH a / m =− dT εT0
1.1
where σ is transformation inducing stress, T0 is equilibrium temperature and ΔH is transformation enthalpy. For TiNi, the gradient is approximately 5.5 MPa/K for the B19′ phase and approximately 13 MPa/K for the R phase (Stachowiak and McCormick, 1988). This implies that the transformation temperature varies with load, an important factor to consider in the design of SMA actuators. It is apparent that the temperature at which superelasticity is obtained is limited to a certain range. If the temperature is below Af, the stress-induced martensite does not revert to austenite. Thus there remains some residual
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A practical guide s
p
11
q A B
s
r
0
e
0 →p, s →0
q →r
A, B P M-A P
M-A P
1.8 Mechanism of superelasticity. The upper part of the figure shows a typical superelastic stress (σ)-strain(ε) curve. The three lower figures schematically illustrate the atomic arrangements in the different states of the sample marked as p, q, r, s, A and B in the stress-strain curve. s s
Yield stress
T > Af sf ⎛ ds ⎛ DH ⎜ ⎜ =– ⎝ dT ⎝ eT
~150 MPa sr
Ms
~30 K
Af
Td
T
em
e
1.9 Temperature dependence of transformation stress.
strain which vanishes on heating above Af due to the SME. If the deformation temperature is too high, then the transformation stress exceeds the yield stress of the material and the alloy deforms plastically. Thus, in order to widen the window of a material’s superelastic temperature, one should
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Shape memory and superelastic alloys
increase the yield stress of the austenite, an effect which is usually achieved by work hardening and precipitation hardening.
1.4
Thermodynamics of martensitic transformation
This section describes the basic thermodynamic aspects of martensitic transformation. Those not familiar with thermodynamics may wish to consult an introductory textbook, such as Porter and Eastering (1981). Since many of the essential parameters, such as martensitic transformation temperatures and transformation stress, are determined by the difference in free energy between the martensite phase and the parent phase, we will consider the Gibbs free energy of the two phases. The molar Gibbs free energies of two phases, G, are given by: Ga = Ha − TSa
1.2
Gm = Hm − TSm
1.3
and
where H is enthalpy, S is entropy and T is temperature. Superscripts a and m stand for the austenite phase and the martensite phase, respectively. The enthalpy and entropy are strongly dependent upon the chemical composition of the alloy. At a certain temperature, the difference in free energy is given by: ΔGa/m = (Ha − Hm) − T(Sa − Sm) = ΔHa/m − TΔSa/m
1.4
The thermodynamic equilibrium temperature between the austenite and martensite, T0, is the temperature at which the free energy of the two phases is equal (ΔGa/m = 0) and is given by: T0 =
ΔH a / m ΔS a / m
1.5
In practice, the formation of the martensite requires some under-cooling, ΔT, since the process requires extra energy, Ge, due to the formation of the a/m interface and the elastic strain energy. Hence Ms is lower than T0 temperature, and is given by: Ms = T0 − ΔT =
ΔH a / m − Ge ΔS a / m
1.6
Similarly, in the case of reverse transformation on heating, Af, is given by: Af = T0 + ΔT =
ΔH a / m + Ge ΔS a / m
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1.7
A practical guide
13
Therefore, from the experimental values of Ms and Af, the equilibrium temperature can be determined as: T0 =
Ms + Af 2
1.8
In the case of stress-induced transformation (superelasticity), the effect of the applied uniaxial stress, s, and the strain, e, should be taken into account as an additional term in eq. 1.4: ΔGa/m = ΔHa/m − TΔSa/m − se
1.9
At an equilibrium state under a given temperature, equilibrium stress can be given by:
σ =−
ΔH a / m − TΔS a / m ε
1.10
The differentiation of eq. 1.10 with respect to T leads to the Clausius– Clapeyron equation (1.1). A more detailed analysis of the Clausius– Clapeyron equation can be found in Ahlers (1986).
1.5
Conclusions
In this chapter, the fundamental properties of the SME and SE were described. Although most of the currently used SMAs are TiNi, this particular alloy comes with some disadvantages. For example, its shape recovery temperature is limited to about 100 °C, although we might expect it to acquire more extensive applications if Af could be increased to above 150 °C. Some high-temperature SMAs have been developed, but most of them contain noble metal elements or rare earth elements, and therefore are not cost effective. Also the motion of SMA actuator elements is often sluggish, owing to the fact that it is limited by the thermal conductivity of the alloy. Ferromagnetic SMAs are able to operate at a much higher speed through the use of a magnetic field instead of temperature (Sozinov et al., 2002; Ullakko et al., 1997). However, all of the materials mentioned above are still at various stages of development. Those who want to obtain more detailed and precise knowledge about SMAs should consult Ahlers (1986), Nishiyama (1978), Otsuka and Wayman (1998) and Wayman (1992). The conference proceedings of the International Conferences on Martensitic Transformation (ICOMAT) (Ko, et al., 2006), the European Symposium on Martensitic Transformation (ESOMAT) (Eggeler and Kostorz, 2008) and Shape Memory and Superelastic Technology (SMST)
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Shape memory and superelastic alloys
(Miyazaki, 2008) are useful sources for those seeking the most up to date information on the research and applications of SMAs.
1.6
References
Ahlers, M., Martensite and equilibrium phases in Cu–Zn and Cu–Zn–Al alloys, Prog. Mater. Sci., 1986, 30, 135–186. Eggeler G. and Kostorz G. (eds), Proceedings of the 7th European Symposium on Martensitic Transformations (ESOMAT 2006), Mater. Sci. Eng., 2008, A481–482. Kainuma, R., Matsumoto, M., Honma, T., The mechanism of the all-round shape memory effect in a Ni-rich TiNi Alloy, in: ICOMAT-86, JIM, Nara, Japan, 1986, pp. 717–722. Ko T., Hsu Y. , Zhao L.C. and Kostorz G. (eds), Proceedings of the International Conference on Martensitic Transformations, Mater. Sci. Eng., 2006, A438–440. Kudoh, Y., Tokonami, M., Miyazaki, S., Otsuka, K., Crystal structure of the martensite in Ti-49.2 at.% Ni alloy analyzed by the single crystal X-ray diffraction method, Acta Metall., 1985, 33, 2049–2056. Miyazaki S. (ed.), Proceedings of the International Conference on Shape Memory and Superelastic Technologies (SMST-2007), ASM International, 2008. Miyazaki, S., Otsuka, K., Suzuki, Y., Transformation pseudoelasticity and deformation behavior in a Ti–50.6 at% alloy, Scrip. Metall., 1981, 15, 287–292. Morgan, N. B., Medical shape memory alloy application the market and its products, Mater. Sci. Eng., 2004, A378, 16–23. Nishiyama, Z., Martensitic Transformation, Academic Press, 1978. Otsuka, K., Wayman, C. M. (eds), Shape Memory Materials, Cambridge University Press, 1998. Porter, D. A., Eastering, K. E., Phase Transformations in Metals and Alloys, Van Nostrand Reinhold, 1981. Sozinov, A., Likhachev, A. A., Lanska, N., Ullakko, K., Giant Magnetic-field-induced strain in NiMnGa seven-layered martensite phase, Appl. Phys. Lett., 2002, 80, 1746–1748. Stachowiak, G. B., McCormick, P. G., Shape memory behaviour associated with the R and martensitic transformations in a NiTi alloy, Acta Metall., 1988, 36, 291–297. Ullakko, K., Huang, J. K., Kokorin, V. V., Handley, R. C. O., Magnetically controlled shape memory effect in Ni2MnGa intermetallics, Scripta Mater., 1997, 36, 1133–1138. Wayman, C. M., Shape memory and related phenomena. Prog. Mater. Sci., 1992, 36, 203–224.
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2 Basic characteristics of titanium–nickel (Ti–Ni)based and titanium–niobium (Ti–Nb)-based alloys S. MIYAZAKI and H. Y. KIM, University of Tsukuba, Japan
Abstract: Development of titanium–nickel (Ti–Ni)-based and titanium– niobium (Ti-Nb)-based shape-memory/superelastic alloys is surveyed. Their basic characteristics are reviewed: e.g., the crystal structures of the parent and martensite phases, the recoverable strain associated with the martensitic transformation, orientation dependence of deformation behavior and cyclic deformation behavior. Key words: shape memory alloy, superelastic alloy, titanium–nickel (Ti– Ni), nickel–titanium (Ni–Ti), Ti alloy, biomaterial, shape memory effect, superelasticity, martensitic transformation.
2.1
Introduction
Shape memory effect (SME) and superelasticity (SE) are associated with the crystallographically reversible nature of the martensitic transformation which appears in shape memory alloys (SMAs). Such crystallographically reversible martensitic transformation was especially named ‘thermoelastic martensitic transformation’. The martensitic transformation itself is not a new phenomenon, having first been found long ago in a steel which was heat-treated at a high temperature followed by rapid quenching: the martensitic transformation in most iron and steels is not thermoelastic, hence the SME does not appear. It has been found that many alloys including some special ferrous alloys show SME and SE (Miyazaki and Otsuka, 1989). Among them, the Ti–Ni alloys have been successfully developed as practical materials for many applications. The Ti–Ni alloys have been under investigation since the first report on SME in a Ti–Ni alloy in 1963 (Buehler et al., 1963). However, the Ti–Ni alloys had presented many difficult problems with many puzzling phenomena for about 20 years until 1982, when the basic understanding was established on the relationship between the microstructure and the corresponding deformation behavior such as SME and SE (Miyazaki et al., 1982; Miyazaki, 1990). Since then, many puzzling phenomena have been clarified: e.g., the microstructures which cause the rhombohedral phase (R-phase) transformation to appear (Miyazaki and Otsuka, 1984, 1986), the orientation dependence of shape memory and superelastic behavior observed in 15 © Woodhead Publishing Limited, 2011
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single crystals (Takei et al., 1983; Miyazaki et al., 1984; Miyazaki and Wayman, 1988; Miyazaki et al., 1988), the temperature dependence of deformation and fatigue behavior (Miyazaki and Otsuka, 1986; Miyazaki et al., 1986; Miyazaki, 1990), the shape memory mechanism (Miyazaki et al., 1989a, b), etc. The Ti–Ni alloys have been successfully applied as biomaterials in such devices as orthodontic arch wires, guide wires and stents in addition to many engineering applications as shown in the following chapters. Ti–Ni alloys are also considered among the most attractive candidates for orthopedic implants. However, it has been pointed out that pure Ni is a toxic element and causes Ni hypersensitivity. Although the Ti–Ni alloys are considered to be safe in the human body based on experience and scientific consideration, in order to solve the psychological problem of the risk of Ni hypersensitivity, Ni-free Ti-based shape memory and superelastic alloys have been recently developed, e.g., Ti–Nb–Sn (Takahashi et al., 2002), Ti–Nb–Al (Fukui et al., 2004), Ti–Nb–Ta (H. Y. Kim et al., 2006a, b), Ti–Nb–Zr (H.Y. Kim et al., 2005a; J.I. Kim et al.,2006), Ti–Nb–O (Kim et al., 2005b), Ti–Nb–Pt (Kim et al., 2007), Ti–Mo–Ga (Kim et al., 2004a), Ta–Mo–Sn (Maeshima and Nishida, 2004) and Ti–(8–10)Mo–4Nb–2V–3Al (mass%) (Zhou et al., 2004). It has been reported that Ti–Nb binary alloys exhibit SME and SE at room temperature, and their superelastic properties can be considerably improved by thermomechanical treatment (H. Y. Kim et al., 2004b, 2006c, d). It has been also reported that superelastic properties of Ti-Nb alloys can be improved by the addition of alloying elements such Zr, Ta, Pt and O (H. Y. Kim et al., 2006b, 2007; J. I. Kim et al., 2005a, b, 2006). The Ni-free Ti-based alloys have not been used for applications, but will be used for medical applications in the future. In this chapter, the basic characteristics such as the martensitic transformation and shape memory properties of both the Ti–Ni alloys and Ti–Nb alloys are to be reviewed based on the present authors’ works. The effects of alloying elements and thermomechanical treatment on shape memory properties are also to be mentioned. Much of Section 2.2 on Ti–Ni-based alloys is reprinted from Miyazaki et al. (2009), with permission of Cambridge University Press, which is greatly appreciated.
2.2
Titanium–nickel (Ti–Ni)-based alloys
2.2.1 Phase diagram An equilibrium phase diagram of the Ti–Ni system is shown in Fig. 2.1, which describes a middle composition region including an equiatomic composition Ti–Ni. Full information of the equilibrium phase diagram can be found in Murray (1987). In this chapter, Ti–Ni includes nearly equiatomic
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Basic characteristics of Ti–Ni and Ti–Nb-based alloys
17
2000
Temperature (K)
1800
L
1653 K
1583 K
1600
1391 K
1400 1257 K
Ti–Ni
1000
TiNi3
Ti2Ni
1200
903 K 30
40
50 60 Ni content (at.%)
70
80
2.1 An equilibrium phase diagram of the Ti–Ni system.
compositions and locates around the equiatomic composition region, while Ti2Ni and TiNi3 intermetallic compounds locate at 33.3 at.% Ni and 75 at.% Ni, respectively. These three alloys are equilibrium phases. There is another phase Ti3Ni4, which is not an equilibrium phase but is important since it affects both the transformation temperature and shape memory behavior (Miyazaki, 1990). The Ti–Ni single phase region terminates at 903 K as shown in Fig. 2.1; however, the region seems to extend to around room temperature in a narrow Ni-content width according to empirical information.
2.2.2 Crystallography of martensitic transformation The parent phase of the Ti–Ni has a CsCl-type B2 superlattice, while the martensite phase is three-dimensionally close packed (monoclinic or B19′) as shown in Fig. 2.2. The Ti–Ni alloy also shows another phase transformation prior to the martensitic transformation according to heat treatment and alloy composition. This transformation (rhombohedral phase or R-phase transformation) can be formed by elongating along any one of the directions of the B2 structure as shown in Fig. 2.3 and is characterized by a small lattice distortion when compared with that of the martensitic transformation. The R-phase transformation usually appears prior to the martensitic transformation when the martensitic transformation start temperature Ms is further lowered by some means other than the R-phase transformation start temperature TR. There are many factors effective to depress Ms as follows (Miyazaki and Otsuka, 1986):
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Shape memory and superelastic alloys b c′
a
c
c′
b′ b′ a′
a0 B2
β a′
Lattice correspondence
M-phase
2.2 Crystal structures of the parent (B2) and martensite (B19′) phases and the lattice correspondence between the two phases.
[110]B2 a¢ [100] R
–
[111]B2 c¢ [001] R c [001]B2
c [001]B2
a [100]B2 a [100]B2 b [010]B2
– –
[112]B2 b¢ [010] R
b [010]B2
(a) B2
(b) R-phase
2.3 Crystal structure of the R-phase which is formed by elongation along one of directions of B2 lattice.
• • • • •
increasing Ni-content; aging at intermediate temperatures; annealing at temperatures below the recrystallization temperature after cold working; thermal cycling; substitution of a third element.
Among these factors, all but the first are effective at revealing the R-phase transformation. The martensitic transformation occurs in such a way that the interface between the martensite variant and parent phase becomes an undistorted and unrotated plane (invariant plane or habit plane) in order to minimize the strain energy. In order to form such a martensite variant (habit-plane variant), it is necessary to introduce a lattice invariant shear such as twins,
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Basic characteristics of Ti–Ni and Ti–Nb-based alloys
19
dislocations or stacking faults. The lattice invariant shear is generally twinning, which is reversible, in the shape memory alloys. Crystallographic characteristics of martensitic transformations are now well understood by the phenomenological crystallographic theory (Wechsler et al., 1953; Bowles and Mackenzie, 1954; Lieberman et al., 1955). This theory describes that the transformation consists of the following three operational processes: (1) a lattice deformation B creating the martensite structure from the parent phase, (2) a lattice invariant shear P2 (twinning, slip, or faulting) and (3) a lattice rotation R. Thus, the total strain (or the shape strain) associated with the transformation is written in the following matrix form: P1 = RP2B
2.1
This theory requires that the shape strain produced by the martensitic transformation is described by an invariant plane strain, i.e., a plane of no distortion and no rotation, which is macroscopically homogeneous and consists of a shear strain parallel to the habit plane and a volume change (an expansion or contraction normal to the habit plane). Thus, the shape strain can also be represented in the following way: P1 = I + m1d1p′1
2.2
where I is the (3x3) identity matrix, m1 the magnitude of the shape strain, d1 a unit column vector in the direction of the shape strain, and p′1 a unit row vector in the direction normal to the invariant plane. If we know the lattice parameters of the parent and martensite phases, a lattice correspondence between the two phases and a lattice invariant shear, the matrix p′1 can be determined by solving Eq. (2.1) under invariant plane strain condition. Then, all crystallographic parameters such as P1, m1, d1 and orientation relationship are determined. The lattice invariant shear of the Ti–Ni is the M Type II twinning (Knowles and Smith, 1981; Matsumoto et al., 1987). There are generally 6, 12 or 24 martensite variants with each shape strain P1. Each variant requires formation of other variants to minimize the net strain of the groupe of the variants. This is called self-accommodation, hence the whole specimen shows no macroscopic shape change except surface relief corresponding to each variant by the martensitic transformation upon cooling.
2.2.3 Transformation strain The strain induced by the martensitic transformation shows strong orientation dependence in Ti–Ni alloys (Miyazaki et al., 1984, 1986; Miyazaki and Wayman, 1988). It is conventionally assumed that the most favorable martensite variant grows to induce the maximum recoverable transformation
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i strain e iM in each grain: e M can be calculated by using the lattice constants of the parent phase and martensite phase. The lattice constants of the parent and martensite phases of a Ti–Ni alloy are as follows: a0 = 0.3013 nm for the parent phase and a = 0.2889 nm, b = 0.4150 nm, c = 0.4619 nm and b = 96.923 degrees for the martensite phase, respectively. A calculation process for transformation strain follows. Using the lattice constants of the parent phase and martensite phase, the transformation strain produced by lattice distortion due to the martensitic transformation can be calculated. If it is assumed that the most favorable martensite variant grows to induce the maximum transformation strain in each grain, the lattice distortion matrix T′ is expressed in the coordinates of the martensite as follows using the lattice constants of the parent phase (a0) and those of the martensite phase (a, b, c, b):
⎡a ⎢a ⎢ 0 ⎢ T′ = ⎢ 0 ⎢ ⎢ ⎢0 ⎣
0 b 2a0 0
c′γ ⎤ ⎥ 2a0 ⎥ ⎥ 0 ⎥ ⎥ c′ ⎥ ⎥ 2a0 ⎦
2.3
where c′ = c sinb and g = 1/tanb. Then, the lattice distortion matrix T which is expressed in the coordinates of the parent phase can be obtained as follows: T = RT′Rt
2.4
where R is the coordinate transformation matrix from the martensite to the parent phase and Rt is the transpose of R. R corresponding to the most favorable martensite variant is expressed as follows: ⎡ −1 0 ⎢ ⎢ 1 R=⎢0 ⎢ 2 ⎢ ⎢0 − 1 ⎢⎣ 2
0 ⎤⎥ ⎥ 1 ⎥ − 2⎥ ⎥ 1 ⎥ 2 ⎥⎦
2.5
Since any vector x in the coordinates of the parent phase is transformed to x′ due to the martensite transformation using the following equation x′ = Tx
2.6
the maximum transformation strain e in each grain can be calculated as follows: i M
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Basic characteristics of Ti–Ni and Ti–Nb-based alloys
ε Mi =
x′ − x x
21 2.7
i Figure 2.4 shows the calculated result of the transformation strain e M expressed by contour lines for each direction in a [001] − [011] − [ 111] standard stereographic triangle. For example, the transformation strains along [001], [011], [ 111] and [ 311] are 3.0%, 8.4%, 9.9% and 10.7%, respectively. By applying the similar calculation for the R-phase transformation, the transformation strain e Ri at a temperature 35 K lower than TR is as shown in Fig. 2.5. The result indicates that the strain is the maximum along [ 111] and that along [001] is the minimum nearly equal to zero. The strain decreases with decreasing temperature from TR, because the rhombohedral angle of the R-phase lattice shows temperature dependence. i By averaging e M for representative 36 orientations which locate periodically in a stereographic standard triangle, the transformation strain for a polycrystal can be estimated as follows if there is no specific texture and the axis density distributes uniformly (Tan and Miyazaki, 1997):
⎛ i ⎞ ⎜⎝ ∑ ε M ⎟⎠ i =1 0 εM = 36 36
2.8
If there is texture, the axis density I i is not uniform in each inverse pole figure so that it is necessary to consider I i in the calculation of the transformation strain as follows (Miyazaki et al., 2000):
–
111 Calculated strain (%) 10.5
8.0 7.0 6.0 5.0 4.0 3.0 001
10.0 9.0 011
2.4 Orientation dependence of calculated strain induced by the martensitic transformation.
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Shape memory and superelastic alloys –
111 Calculated strain (%) 0.9
0.8 0.5
0.7
0.4 0.3 0.2 0.1
0.6
001
011 T = (TR–35) K
2.5 Orientation dependence of calculated strain induced by the R-phase transformation.
⎛ i i⎞ ⎜⎝ ∑ ε M I ⎟⎠ i =1 εM = 36 36
2.9
2.2.4 Transformation temperature The martensitic transformation start temperature Ms is shown in Fig. 2.6 as a function of Ni content. In the composition range of the Ti–Ni, Ms decreases with increasing Ni content above 49.7 at.% Ni, while they are constant below 49.7 at.% Ni. The reverse martensitic transformation temperature Af is above 30 K higher than Ms in all specimens in the composition region. The reason for the constant Ms in the Ni content region less than 49.7 at.% can be ascribed to the constant Ni content in the Ti–Ni phase, because the Ti2Ni appears in the Ni content region as shown in Fig. 2.6, keeping the Ni content of the Ti–Ni at 49.7 at.%.
2.2.5 Deformation behavior The deformation behavior of SMAs is strongly temperature sensitive, because the deformation is associated with the martensitic transformation: this is different from plastic deformation by slip which occurs in conventional metals and alloys. Schematic stress–strain curves of a Ti–Ni alloy obtained at various temperatures (T) are shown in Fig. 2.7. In the temperature range of T < Mf, the specimen is fully transformed before applying
© Woodhead Publishing Limited, 2011
Basic characteristics of Ti–Ni and Ti–Nb-based alloys
23
370 350
Temperature (K)
330 310 290 270 250 230 210 190
Ms
170 48.5
49.0
49.5 50.0 50.5 Ni content (at.%)
51.0
51.5
2.6 Ni content dependence of Ms temperature.
(a) T<Mf
(b) Mf
