Proceedings of the 1st World Congress on Integrated Computational Materials Engineering (ICME)

Proceedings of the

1st World Congress

on Integrated Computational Materials Engineering (ICME) Sponsored by TMS (The Minerals, Metals and Materials Society)

Co-sponsored by MetSoc (The Metallurgical Society of the Canadian Institute of Mining, Metallurgy and Petroleum) ABM (The Brazilian Metallurgy, Materials and Minerals Society) Materials Australia Japan Institute of Metals The Iron and Steel Institute of Japan Held July 10-14, 2011 at Seven Springs Mountain Resort, Seven Springs, PA Edited by John Allison, Peter Collins and George Spanos

A John Wiley & Sons, Inc., Publication

Copyright © 2011 by The Minerals, Metals, & Materials Society. All rights reserved. Published by John Wiley & Sons, Inc., Hoboken, New Jersey. Published simultaneously in Canada. No part of this publication may be reproduced, stored in a retrieval system, or transmitted in any form or by any means, electronic, mechanical, photocopying, recording, scanning, or otherwise, except as permitted under Section 107 or 108 of the 1976 United States Copyright Act, without either the prior written permission of The Minerals, Metals, & Materials Society, or authorization through payment of the appropriat e per-copy fee to the Copyright Clearance Center, Inc., 222 Rosewood Drive, Danvers, MA 01923, (978) 750-8400, fax (978) 750-4470, or on the web at www.copyright.com. Requests to the Publisher for permission should be addressed to the Permissions Department, John Wiley & Sons, Inc., I ll River Street, Hoboken, NJ 07030, (201) 748-6011, fax (201) 748-6008, or online at http:// www.wiley.com/go/permission. Limit of Liability/Disclaimer of Warranty : While the publisher and author have used their best efforts in preparing this book, they make no representation s or warranties with respect to the accuracy or completeness of the contents of this book and specifically disclaim any implied warranties of merchantability or fitness for a particular purpose. No warranty may be created or extended by sales representatives or written sales materials. The advice and strategies contained herein may not be suitable for your situation. You should consult with a professional where appropriate . Neither the publisher nor author shall be liable for any loss of profit or any other commercial damages, including but not limited to special, incidental, consequential, or other damages. Wiley also publishes books in a variety of electronic formats. Some content that appears in print may not be available in electronic formats. For more information about Wiley products, visit the web site at www.wiley.com. For general information on other Wiley products and services or for technical support, please contact the Wiley Customer Care Department within the United States at (800) 762-2974, outside the United States at (317) 572-3993 or fax (317) 572-4002. Library of Congress Cataloging-in-Publicatio n Data is available.

ISBN 978-0-47094-319-9 Printed in the United States of America. 10 9 8 7 6 5 4 3 2 1

A John Wiley & Sons, Inc., Publication

TABLE OF CONTENTS 1st World Congress on Integrated Computational Materials Engineering Preface Acknowledgements Conference Editors/Organizer s

ix xi xiii

Modeling Processing-Microstructure Relationships CorrelatedNucleation of Precipitates in Magnesium Alloy WE54 H. Liu, Y. Gao, Y. Wang, andJ. Nie

3

From Processing to Properties: Through-Process Modeling of Aluminum Sheet Fabrication 9 G. Gottstein, and V. Monies Advancement in Characterizatio n and Modeling of Boundary Migration during Recrystallization 19 D. Jensen, Y. Zhang, A. Godfrey, and N. Moelans Effect of Pulling Velocity on Dendrite Arm Spacing in Steady-State Directionally Solidified Transparen t Organic Alloy by Numerical Simulation Y. Shi, Q. Xu, B. Liu, and M. Gong More Efficient ICME through Materials Informatics and Process Modeling B. Gautham, R. Kumar, S. Bothra, G. Mohapatra, N. Kulkarni, and K. Padmanabhan

27 35

Multi-Attribut e Integrated Forming-Crush Simulation Optimization Using Internal State Variable Model A. Najafi, M. Rais-Rohani, and Y. Hammi

43

Multiscale Modeling of Polycrystalline Magnetostrictive Alloy Galfenol: Microstructura l Model V. Sundararaghavan

57

v

Numerical Evaluation of Energy Transfer during Surface Mechanical Attrition Treatment 63 X. Zhang, J. Lu, and S. Shi Phase-Field Simulation and Experimental Study of Precipitates in an Al-Si-Mg Alloy 69 Z. Gao, H Liao, K Dong, and Q. Wang Towards a Virtual Platform for Materials Processing G. Schmitz, and U. Prahl Integrated Modeling of Tundish and Continuous Caster to Meet Quality Requirementsof Cast Steels A. Kumar Singh, R. Pardeshi, and S. Goyal

75

81

Modeling Microstructure-Property Relationships Microstructure-base d Description of the Deformation of Metals: Theory and Application ...89 D. Helm, A. Butz, D. Raabe, and P. Gumbsch Large Scale Finite Element Computations Using Real Grain Microstructure s H. Proudhon

99

Modelling and Measurement of Plastic Deformation and Grain Rotation at the Grain-to-Grai n Level 107 D. Gonzalez, A. King, J. Quinta da Fonseca, P. Withers, and!. Simonovski Multi-Time Scaling Image Based Crystal Plasticity FE Models Dwell Fatigue Initiation in Polycrystalline Ti Alloys 113 S. Ghosh, andM. Callas Virtual Mechanical Testing of Composites: From Materials to Components J. LLorca, and C. Gonzalez

121

Design of Multifunctional Material Structures Using Topology Optimization with Feature Control 129 J. Guest, and S. Ha

VI

Development of Neural Networks for the Prediction of the Interrelationshi p between Microstructur e and Properties of Ti Alloys 135 P. Collins, S. Koduri, D. Huber, B. Welk, and H. Fraser Characterizin g Residual Stresses in Monolithic Silicon-Carbide through the Use of Finite Element Analysis 145 B. Munn, and K. Li Density Functional Theory Based Calculations of Site Occupancy in the Gamma Prime Ni3al Phase of Nickel Based Super Alloys 151 J. Du, M. Chaudhari, J. Tiley, and R. Banerjee Informatics for Mapping Engineering Data K. Rajan, and S. Broderick

159

Microstructura l Property Considerations in the Design of Stainless Steel Articles Case Hardened by Low-Temperatur e Carburizatio n 165 J. Rubinski, S. Collins, and P. Williams Deformation Twin Induced by Multi-strain in Nanocrystalline Copper: MolecularDynamic Simulation K. Chen, S. Shi, andJ. Lu

171

Nondestructive Evaluation Modeling as an Integrated Component oflCMSE J. Blackshire, R. Ko, and M. Chen

177

Numerical Simulation of Brake Discs of CRH3 High-Speed Trains Based on Ansys 183 L. Yu, Y. Jiang, S. Lu, K. Luo, and H. Ru Modeling and Simulation of Process-Structure-Propert y of Magnesium Alloy Casting 189 Z. Han, L. Huo, and B. Liu

The Role of ICME in Graduate and Undergraduate Education, Information Infrastructure, and Success Stories Teaching Transport Phenomena through Spreadsheet Programming and Numerical Methods J. McGuffin-Cawley vu

197

History of ICME in the European Aluminium Industry J. Hirsch, and K. Karhausen

203

ICME Success at Timken -The Virtual Fatigue Life Test P. Anderson, X. Ai, P. Glaws, andK. Sawamiphakdi

211

Advances in Computational Tools for Virtual Casting of Aluminum Components Q. Wang, P. Jones, Y. Wang, and D. Gerard

217

Modelling the Process Chain of Microalloyed Case Hardening Steel for Energy Efficient High Temperatur e Carburisin g 223 U. Prahl, S. Konovalov, T. Henke, S. Benke, M. Bambach, and G. Schmitz Cyberinfrastructur e Support for Integrated Computational Materials Engineering T. Haupt

229

Stability of Fe-C Martensite-Effect of Zener-Orderin g R. Naraghi, and M. Selleby

235

Unintended Consequences: How Qualification Constrains Innovation C Brice

241

What Barriers Prevent ICME from BecomingPart of the Designer's Toolbox? P. Ret

247

Author Index

253

Subject Index

255

viii

Preface This book represents a collection of papers presented at the 1st World Congress on Integrated Computational Materials Engineering, a specialty conference organized by the The Minerals, Metals, and Materials Society (TMS) and the three conference organizers, and held at Seven Springs Mountain Resort, PA, USA, on July 10- 14,2011. Integrated Computational Materials Engineering (ICME) is an emerging field with tremendous potential for developing advanced materials, manufacturin g processes, and engineering components more quickly and cost-effectively. The major goal of this conference was to help unlock that great potential by bringing together scientists and engineers working in ICME-related areas to share information, stimulate creative ideas and discussion, and identify opportunities for collaboration of computational and experimental efforts. To that end, more than 200 authors and attendees contributed to this conference, in the form of presentations, lively discussions, and the papers found in this volume. As emphasized in a 2008 National Academies study on ICME, successful ICME efforts typically involve nearly 50 percent experimental components for critical development, testing, validation, and enhancement of the computational models, so it was critical to bring together both experimentalists and modelers at this ICME World Congress. In that regard, the presentations included both computational- and experimentalbased research representing a wide range of programs relatedto ICME. The specific topic areas (sessions) of the conference were: Modeling ProcessingMicrostructur e Relationships - I & II, Modeling Microstructure-Propert y Relationships - I & II, The Role of ICME in Graduate and Undergraduat e Education, Information infrastructure , and ICME Success Stories. The conference included 10 Keynote talks from prominent international speakers working in ICME, 40 contributed podium talks, and an exceptional poster session (>140 posters) seamlessly embedded into the main conference hall. Internationa l representation was certainly a hallmark of this "World Congress", in that five materials societies outside of the US promoted the conference within their countries, and an international advisory committee representing 14 countries was active in advising and promoting this conference worldwide. This resulted in speakers from 11 different countries, and a third of the podium speakers were from outside of the US. The single session format and intimate setting were specifically planned to promote stimulating discussions and rich interactions amongst the attendees. The 35 papers in this proceedings are divided into three sections: (1) Modeling Processing-Microstructur e Relationships, (2) Modeling Microstructure-Propert y Relationships, and (3) The Role of ICME in Graduate and Undergraduat e Education, Information Infrastructure , and Success Stories; these articles

IX

represent a cross cut of presentations from this conference. It is our desire that this First World Congress on ICME, and these proceedings, will not only create opportunities to sustain, support, and enhance on-going ICME activities and evolving ICME strategies, but will additionally provide a greater awareness of ICME worldwide, and result in a recurrence of this ICME World Congress for many years to come.

x

Acknowledgements The organizers/editor s would like to acknowledge a number of people without whom this ICME World Congress, and the proceedings, would not have been possible. First, thanks to a number of people on the TMS staff who worked tirelessly to make this a first rate event and proceedings; these include (in alphabetical order): Becky Arnold, Michael Bazzy, Maria Boots, Maureen Byko, Adrianne Carolla, Margie Castello, Patricia Dobranski, Trudi Dunlap, Christina Raabe Eck, Beate Helsel, Warren Hunt, Colleen Leary, Robert Makowski, David Rasel, Jim Robinson, Lynne Robinson, Elizabeth Rossi, Marleen Schrader, Dan Steighner, Louise Wallach, and Chris Wood. Secondly we want to thank the international advisory committee of their input during planning and promotion of this conference world-wide. This committee included: John Agren, KTH - Royal Inst of Technology, Sweden; Dipankar Banerjee, Indian Institute of Technology, India; Yves Brechet, Institute National Polytechnic de, Grenoble, France; Dennis Dimiduk, USA F Research Lab, USA; Masato Enomto, Ibaraki University, Japan; Juergen Hirsch, Hydro Aluminum, Germany; Dorte Juul Jensen, Riso National Lab., Denmark; Nack Kim, Pohang University of Science and, Technology, Korea; Milo Krai, University of Canterbury, New Zealand; Peter Lee, Imperial College, UK; Baicheng Liu, Tsinghua University, China; Jianfeng Nie, Monash University, Australia; Tresa Pollock, UCSB, USA; Gary Purdy, McMaster University, Canada; Antonio J. Ramirez, Brazilian Synchrotron Light Lab., Brazil; K.K. Sankaran, Boeing Company, USA; Katsuyo Thornton, University of Michigan, USA; James Warren, NIST, USA; Deb Whitis, GE, USA. Finally, we would especially like to acknowledge the financial support of our US government sponsors: the Air Force Materials Laboratory , the Army Research Office, the National Institute of Standards and Technology, the National Science Foundation, and the Office of Naval Research. We likewise are grateful for the support of the congress' various corporate sponsors and exhibitors.

XI

Conference Editors/Organizers Professor John Allison is a Professor of Materials Science and Engineering at The University of Michigan. He joined the faculty in September 2010. Prior to that he was a Senior Technical Leader at Ford Research and Advanced Engineering, Ford Motor Company in Dearborn, Michigan, where he was for 27 years. At Ford he led teams developing Integrated Computational Materials Engineering (ICME) methods, advanced CAE tools and light metals technology for automotive applications. Dr. Allison was the 2002 President of TMS and served on the US National Materials Advisory Board from 2001-2007. He is a member of the National Academy of Engineering, Fellow of ASM and has received numerous awards including two Henry Ford Technology Awards. Dr. Allison received his PhD in Metallurgical Engineering and Materials Science from Carnegie-Mellon University, his MS in Metallurgical Engineering from The Ohio State University and his BS in Engineering Mechanics from the US Air Force Academy. Professor Peter Collins joined the faculty at the University of North Texas in September 2010. Prior to this, Collins has served as the Deputy Director Director of Technology for the Quad City Manufacturin g Lab (QCML), a notfor-profit manufacturin g laboratory and center of excellence in the production and manufacturin g of advanced materials, specifically titanium alloys for nonaerospace applications and as the Associate Director for the Center for the Accelerated Maturationof Materials (CAMM). His research has focused on the development of 2D and 3D characterizatio n techniques across length scales, the development of mechanistic understandin g of the role of microstructur e on tensile and fracturetoughness properties in Ti-based alloys, the development of combinatorial techniques to rapidly assess microstructure-propert y relationships, the use of advanced manufacturin g techniques for the production of novel materials, and the use of advanced transmission electron microscopic techniques (including aberration corrected scanning TEM) to probe the most fundamental aspects of a materials microstructure . Collins received his MS and PhD in Materials Science and Engineering from The Ohio State University and his BS in Metallurgical Engineering from The University of Missouri-Rolla.

Xlll

Dr. George Spanos is TMS Technical Director. He received his B.S., M.E., and Ph.D. degrees in Metallurgical Engineering and Materials Science from Carnegie Mellon University. In 1989 he joined the Naval Research Laboratory (NRL) as a staff scientist, in 1994 was promoted to Section Head at NRL, and in 2010 he joined TMS. Dr. Spanos is author/co-autho r of 92 technical publications in the fields of 3D materials analyses, phase transformations , processing-structure property relationships, and ICME. Some of his past and present professional affiliations include: member of the Board of Governors of Acta Materialia Inc., chairman and member of the Joint Commission for Metall and Materials Trans., Chairman and Key Reader of the Board of Review of Metall, and Mat. Trans. A, and member of a number of TMS technical committees. Some of his awards include: Fellow of ASM-International , the Marcus A. Grossman Award for best article in Metall, and Mat. Trans, in 2001 for authors under 40, two Technology Transfer Awards at NRL, and the NRL 2009 Commanding Officer's Award for Achievement in the Field of Equal Employment Opportunity .

xiv

1" World Congress on Integrated Computational Materials Engineering Edited by: John Allison, Peter Collins and George Spanos TMS (The Minerals, Metals & Materials Society), 2011

1st World Congress

on Integrated Computational Materials Engineering (ICME)

Modeling Microstructure-Property Relationships

1st World Congress on Integrated Computational Materials Engineering Edited by: John Allison, Peter Collins and George Spanos TMS (The Minerals, Metals & Materials Society), 2011

CORRELATED NUCLEATION OF PRECIPITATES IN MAGNESIUM ALLOY WE54 Hong Liu1, Yipeng Gao2, Yunzhi Wang1 '2 and Jian-Feng Nie1 1 2

Department of Materials Engineering, Monash University, Victoria 3800, Australia Department of Materials Science and Engineering, The Ohio State University, USA

Keywords: Magnesium alloys, Precipitation hardening, Microstructur e evolution, Interaction energy, Phase field approach. Abstract Magnesium alloy WE54 has been used commercially for fabricating components for aerospace and aircraft applications. Its useful mechanical properties are achieved via a precipitation process, ßi and ß' are the two strengthening precipitate phases when this alloy is peak-aged at 250°C. The ßi precipitate plates often form with ß' particles attached to their end facets. The aim of this study is to understand the correlated nucleation of the ßi and ß' phases. The equilibrium shapes of coherent ßi and ß' precipitates are simulated using the phase field method. The preferential nucleation site of a nucleating precipitate at the interface of preexisting particle/Mg matrix is analyzed through the calculation of the elastic interaction energy between the nucleating precipitate and the pre-existing particle. The evolution sequence of the ßi and ß' phases are also simulated in this work. Our results indicate that the coherency elastic strain energy can be reduced significantly if a ß' particle forms at an edge facet of a pre-existing ßi plate, and that the preferred nucleation sites of the ß' particles are at the two end-facets of the ßi plate. Under the assumption that the ßi phase nucleates first, the microstructur e evolution sequence is proposed in this work. Introduction The development of high strength, light-weight magnesium alloys for elevated temperatur e applications has experienced a rapid growth over the past 10 years [1-3]. One of the most successful magnesium alloys developed in this category is WE54 (5 wt% Y, 2 wt% Nd and 2 wt% heavy rare-eart h elements). The strength of this alloy is achieved by conventional agehardening treatments, i.e., a solution treatment for 8h at 525°C, followed by hot water quench and a subsequent ageing treatment of 16 h at 250°C [4]. The microstructrur e of such heat treated samples contains predominantl y two precipitate phases: plate-like ßi and globular ß', Fig. 1 [5]. The ßi is metastable and has an fee. structure with lattice parameter a = 0.74 nm. The orientation relationship between ßi and the Mg matrix is such that (112)pi//(l 100)a and [110]ßi//[0001]a [5]. There are six different orientation variants of ßi particles, which are shown in Fig. lb. The ßf phase is also metastable [6] and has an orthorhombi c structure (a =0.667 nm, b = 2.351 nm, c = 0.521 nm). The orientation relationship between ß' precipitates and the matrix phase has been determined as (100)p-//(1210)a and [001]p-//[0001]a. The ß' phase has three variants which are related to each other by 120° rotation about the [000 l] a axis [7]. Experimental results show that individual ßi plate always forms with ß' particles attached at its two ends [5] (Fig. la). This phenomenon is also observed in many other Mgrare-eart h based alloys. However, the reason behind this phenomenon is not clear. Apps et al. [8] claimed that the ß' globules formed first and therefore acted as heterogeneous nucleation sites for the nucleation of ßi phase. However, Nie and Muddle [5] suggested that ßi formed directly from magnesium lattice via an invariant plane strain transformation , then the ß' globules formed at the two end facets of individual ßi plate as a consequence of shear strain

3

accommodation. The aim of this project is focus on the explanation of the reason why individual ßi plate always forms with ß' particles attached at its two ends, and determine the formation mechanism of this structure by phase field simulation. Model Formulation Lattice Correspondence s and SFTS (Stress Free Transformatio n Strain) Tensor The lattice correspondences between the Mg matrix and ßi is [-1,-1,2,0]—♦[1,-1,1] , [1,1,0,0]—»[-1,1,3] and [0,0,0,1]—>[110], and lattice correspondences between the Mg matrix and the ß' is [-1,-1,2,0]—^[1,0,0], [l,-lA0]->[-l,l,3] and [0,0,0,1]^[0,0,1]. The number of orientation variants of precipitates is determined by the number of symmetry elements in the intersection group of parent and product phases for a given orientation relationship [13]. There are 6 different orientation variants of ßi,but according to Fig. lb, variant 1 and 6, 2 and 3, 4 and 5 have the same transformatio n strain and therefore there exists only three different types of SFTS. There are 3 different orientation variants of ß'. To ensure that the phase transformation s from Mg to ßi and ß' can be reflected into one coordinate system, in this work, the x direction corresponds to [l,-l,0,0]a//[-l,l,2]ßi//[l,0,0]ß-, the y direction corresponds to [-1,-1,2,0]a//[ 1,-1,1 ]ßi//[0,1,0]ß- and the z direction corresponds to [0001]a//[110]ßi//[0,0,l]ßfor simulation system. Thus the SFTS tensors of different variant of ßi and ß' are shown as follows:

With the particular form of the transformatio n strain given above, the microstructura l evolution during the Mg—»ßi/ß' transformatio n can be effectively modelled in two dimensions without losing any essential physics. Furthermore , on the basal plane of the hexagonal lattice, the elastic constants are indeed isotropic. Elastic Energy Calculation In the present study, a homogeneous modulus is assumed throughout the system and the elastic energy is calculated via Khachaturya n and Shatalov's microelasticity theory (KS theory) [9]. The modulus of the Mg matrix is selected as the reference, i.e. C;;=63.5GPa, C72=24.85GPa, CI3= 20.0GPa, Ci3=66GPa and CW=19.3GPa, which are obtained by ab initio calculations [10]. Assuming that the precipitate and the matrix phases are coherent and considering a zero strain Fig. 1. (a) Transmission electron micrograph showing a WE b o u n d a rv condition (i.e. a grain 54 alloy aged at 250°C 8 hours, showing six variants of ß2 embedded in a polycrystallme phase (arrowed) and the globular ß' phase, and (b) schematic aggregate), a close form of the representatio n of the six variants distinguishable in [0001]a coherency elastic strain energy r e a ds orientation [5]. P]:

4

where In Equation 1, to keep the stability of the programme, {P[r|p(r)]}gis the Fourier transform of n strain P function, i.e. P(r\) = r|3(10-15r|+6r|2), which is used to connect the transformatio between product phases and matrix, 8° is the STFS and o°=Cijkie° where Cyki is elastic constant, g is a vector in the reciprocal space and ni=g/g. The superscript asterisk indicates a complex conjugate. Bulk Chemical Free Energy Calculation In this study the WE54 alloy is simplified as Mg-5wt%Y-4wt%Nd . The Mg phase can be treated as a regular solid solution, and according to the CALPFLAD database [11], its chemical free energy density as a function of concentrations of Y and Nd can be expressed in the following dimensionless form and the energy normalised factor is 104J/mol: (3) where /o the length of one unit grid. Since both ßi and ß' are metastable phases, their free energy functions are not available from the CALPHAD database. In this work, the free energy of both ßi and ß' phases are approximated by parabolic functions of solute concentrations. A tangent surface is drawn from GMg at the equilibrium Mg matrix concentration, which should be tangential to the free energy curve of both ßi and ß' at their equilibrium compositions. Considering the effect of the curvature on the interfacial energy between the two phases, the following parabolic functions are used to describe the bulk chemical free energy densities (in reduced unit, i.e. //o3) of the ßi and ß' phases, respectively, and the energy normalised factor is 104J/mol: (4)

(S) P function, P(r\% is used to connect the free energy of the two phases. Thus the chemical free energy can be expressed as follows: (6) where K is the gradient energy coefficient. The numerical value (in reduced unit) used in the simulations in this project are K=0.4 to guarantee a diffused interface profile. Kinetic Equations The Cahn-Hilliard generalized diffusion equation [12] is used to describe the evolution of the concentration field c(r, t):

m 1

where M is the chemical mobility. M has its unit J^mo^m'V. In this study, due to the lack of data of inter-diffusion coefficient between Y and Mg, as well as Nd and Mg, the time step is used by reduced time step x. The numerical value of M used in this study is 1.0. £(r, t) is the Langevin noise term which describes thermal fluctuation. The time dependent Ginzburg-Landa u equation [14] is used to describe the time evolution of the structura l order parameter r/(r,t):

5

(8)

where L is the mobility of the order parameter , and the numerical value L used in this project is 5.0. Results and Discussion The system size used in the simulations is 256l0x256lo. The interfacial energy of a coherent interface between the Mg matrix and the precipitate phases is assumed to be 50mJ/m2 and possible anisotropy in the interfacial energy is ignored. The corresponding length scale is /O=0.98nm. Figs. 2a and b show the simulation results for a single particle of pi and ß' respectively. The simulation result shows the habit plane between plate shaped ßi particle and Mg matrix in the given orientation relationship is (1,-1, 0, 0)Mg, which corresponds to the experimental results [5-7]. indicates that this habit plane is an invariant plane. The reason why ßi particle has a plate shape is Fig. 2 2D Simulation results illustrate the growth and shape evolution process of one single (a) ßi particle, and because the elastic energy during (b) ß' particle in h.c.p Mg matrix for T=2000. Interfacial particle growth can be minimised to zero if these ßi precipitates energy is taken to be isotropic. growth along their invariant planes. The ß' particle in Fig. 3b is globular shape because all the value of transformatio n strains along the principle axes are positive, and the difference of elastic strain between different principle directions are not very large (2.17% in x direction and 3.6% in y direction). Figs. 3 a, b and c show the calculation results of the elastic interaction energy between a preexisting ßi particle (variant 1 in Fig. lb) and the three different variants of ß' particles respectively. The calculation results illustrate that the preferred nucleation site for ß' Fig. 3 (a, b and c) Interaction energy calculation results particles, under the influence of between a pre-existing ßi particle and three different stress field of the pre-existing ßi variants of ß' particles. The unit of interaction energy in this figure is 108 J/m3. (d) 2D Simulation result illustrates particle (variant 1, Fig. lb), is the the growth and shape evolution process of ß' particles upper right corner and the lower under the influence of stress field of the pre-existing ßi left corner of this ßi particle. This result agrees with the experimental particle in h.c.p Mg matrix. observations (Fig. 1). Also, the

6

values of the interaction energy between the pre-existing ßi and the different variants of ß' are different, which means that for ßi phase in each orientation relationship, it should has a preferred orientation relationship of ß\ However, this preferences haven't been examined in experiments because the difference of elastic interaction energy values between a ßi precipitate and different variants of ß' particles is very small. Figs. 4a, b and c shows microstructur e evolution by assuming that ßi particles form first, which then act as heterogeneous nucleation sites for ß' particles. Fig. Ab shows the simulation obtained right after the Langevin noise terms in Eqs. (7) and (8) are turn off. It is readily seen that, under the influence of the stress field of the pre-existing ßi particles, the preferred nucleation sites of ß' particles are the two ends of the pre-existing ßi particles. This is good agreement with the experimental observations. These ß' particles keep growing until the equilibrium volume fraction is reached. The microstructur e evolution by assuming that ß' particles form first, which then serve as heterogeneous nucleation sites for ßi, is shown in Figs. 4d, e and/ Fig. 4e corresponds to the moment when the Langevin noise terms are just turned off. As can be seen from this image, the preferred heterogeneous nucleation sites of ßi particles are at the interface between the pre-existing ß' particles and Mg matrix. It is interesting to note that the heterogeneously nucleated ßi particle shown in Fig. 4e has a tendency to grow towards a nearby ß' particle (Fig. 4j) due to their long-range elastic interactions. Fig. 4e, also shows a configuration that only one end of ßi has ß' particle attached (see the white circle). Comparing these simulation

Fig. 4 Nucleation sequence determination , (a, b, c) show the microstructura l evolution by assuming that ßi particles form first and then ß' particles nucleate under the influence of existing ßi particles and the associated stress and concentrationfields,while (d, e, f) show the microstructura l evolution by assuming that ß' particles form first and then ßi particles nucleate under the influence of existing ß'particles and the associated stress and concentration fields. Two different variants of ßi phase can be seen in (f). (a) and (d) show the pre-existing ßi and ß' particles, respectively, which are the initial condition for the two simulations. The interfacial energy is assumed to be isotropic.

7

results to experimental observations, we may conclude that ßi particles forms first during ageing followed by heterogeneous nucleation of ß'. Conclusion The existence of an invariant plane provides a tendency for ßi particles to grow along the invariant plane and form plate-shaped particles to minimise its elastic energy. The morphology of ß' particles is globular because all strains along principle directions are positive and the difference of elastic strain between different principle directions are not very large (2.17% in x direction and 3.6% in y direction). The interaction energy calculation results indicate that the coherency elastic strain energy can be reduced significantly if ß' particles forms at the two edge facets of ßi particles, and that in this case the preferred nucleation site of the ß' particles is at the end-facets of the pre-existing ßi particle. For microstrcutr e evolution sequences determination , if ß' phase forms first and then act as heterogeneous nucleation sites for ßi particles, only one ß' particle (the pre-existing one) can be observed attached at the end of the ßi particles thus formed, which is not in consistent with the experiment observations. Therefore, our modelling work indicates that the ßi phase may have formed first and then acted as heterogeneous nucleates sites for ß' particles. References [I] I. J. Polmear, "Magnesium Alloys and Applications," Mater. Sei. Tech., 10 (1994), 1-16. [2] A. Luo, and M. 0. Pekguleryuz, "Cast magnesium alloys for elevated temperatur e applications,"/. Mater. Sei., 29 (1994), 5259-5271. [3] L. Y. Wei, G. L. Dunlop, and H. Westengen, "Precipitatio n Hardening of Mg-Zn and Mg-Zn-RE alloys," Metall. Mater. Trans. A, 26 (1995), 1705-1716. [4] J. F. Nie, and B. C. Muddle, "Precipitatio n in Magnesium Alloy WE54 during Isothermal Aging at 250°C,"Scripta Mater., 27 (1997), 1089-1094. [5] J. F. Nie, and B. C. Muddle, "Characterisatio n of Strengthening Precipitate Phases in a Mg-Y-Nd Alloy" Acta Metall.,48 (2000), 1691-1703. [6] M. Nishijuma et al., "Characterizatio n of ß' Phase Precipitates in an Mg-5at%Gd Alloy Aged in a Peak Hardness Condition," Mater. Trans., 47 (2006), 2109-2112. [7] M. Nishijuma et al., "Characterizatio n of ß' Precipitate Phase in Mg-2atY% Alloy Aged to Peak Hardness Condition by High-Angle Detector Dark-Field Scanning Transmission Electron Microscopy (HAADF-STEM)," Mater. Trans., 48 (2007), 84-87. [8] P. J. Apps et al., "Precipitat e Reactions in Magnesium-Rear Earth," Scripta Mater. 48 (2003), 1023-1028. [9] A. G. Khachaturyan , Theory of Structural Transformations in Solids, (New York, John Wiley & Sons, 1983), 201-245. [10] S. Ganeshan et al., "Elastic Constants of Binary Mg Compounds from First-Principle s Calculation," Intermetallics, 17 (2009), 313-318. [II] F. G. Meng et al., "Experimenta l Investigation and Thermodynami c Calculation of Phase Relations in the Mg-Nd-Y Alloy" Mater. Sei. Eng. A, 454 (2007), 266-273. [12] J. W. Chan, and J. E. Hilliard, "Free Energy of a Nonuniform System. I. Interfacial Free Energy," J. Chem. Phys., 28 (1958), 258-267. [13] Y. H. Wen, Y. Wang, and L. Q. Chen, "Phase-Field Simulation of Domain Structure Evolution during a Coherent Hexagonal-to-Orthorhombi c Transformation, " Philos. Mag. A, 80 (2000), 1967-1982. [14] C. Shen, and Y. Wang, "Phase-field Microstructur e Modelling", ASM Handbook, 22 (2008), 1-22.

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1st World Congress on Integrated Computationa l Materials Engineering Edited by: John Allison, Peter Collins and George Spanos TMS (The Minerals, Metals & Materials Society), 2011

FROM PROCESSING TO PROPERTIES: THROUGH-PROCES S MODELING OF ALUMINUM SHEET FABRICATION G. Gottstein, V. Monies Institute of Physical Metallurgy and Metal Physics RWTH Aachen University, 52056 Aachen, Germany Keywords: Aluminum, Through-Process-Modeling , Deformation, Recrystallization, Texture Abstract The microstructur e of a material rather than the processing condition is the state parameter of material properties. We report on activities of microstructura l through-process modeling activities to predict the properties of a processed product from the knowledge of the processing conditions and the chemical composition of the material. The respective modeling tools are introduced. As an example we address aluminum sheet fabricationand material behavior during subsequent sheet metal forming. Using additionally atomistic modeling tools for the prediction of thermodynamic, kinetic and elastic data provides promising avenues for a comprehensive multi-scale modeling of materials processing. The Problem The control variables of a materials engineer for optimizing materials properties are overall chemistry and processing parameters. Therefore, it is desirable to derive processing-propert y relationships for cost-efficient production and property optimization. Such efforts have led in the past 20 years to the development of empirical models to predict properties of semi-finished products via closed form analytical functions, mostly power law relationships for monotonous dependencies. For a given material and processing route this is a very successful approach and the predictive power of such models is excellent so that many steel producers only computed final materials properties rather than measuring them. This modeling approach fails, however, if the processing window or the composition of the material is changed. In that case a complete reformulation of the used empirical function is necessary which involves a large number of measurements. To avoid these time consuming and costly efforts, attempts have been made to put physical metallurgy to work, i.e. to apply our scientific understandin g of the metallurgical phenomena for property predictions. Unfortunately, these concepts prove that the processing conditions are not the state variables of materials properties so that there is no such thing like a processing-propert y relation. Rather, the processing parameters determine the microstructura l development of a material and the microstructur e constitutes the state variables of materials properties (Fig. 1.)

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Fig. 1: While the properties of a part are measure on a macroscopic length scale, they are controlled by the microstructure , which is defined on a much smaller length scale. The Modeling Approach Hence, there are highly non-linear relationships between processing and properties, and at most, one can establish a processing-propert y correlation that can be used as a date base or for optimization procedures like neural networks. e has to be In order to describe metallurgical phenomena the development of microstructur known. We define microstructur e as the spatial distribution of elements and defects in a material, hence comprising thermodynami c constitution, crystal orientation, crystal defects etc. [1]. For through-proces s modeling (TPM), i.e. the prediction of properties along a process chain, microstructur e evolution through the entire process chain has to be modeled. The typical process chain for Al sheet production is given in Fig. 2.

Fig. 2: Processing chain of aluminum sheet production. Process and microstructur e are determined by different variables.

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It encompasses solidification, homogenization, hot rolling, cold rolling and annealing prior to sheet metal forming. Here, we want to restrict ourselves to solid state processing, starting with homogenization of a known (i.e. fully characterized) solidification microstructure . If we consider a specific volume element, it will undergo temperatur e changes T(x,y,z,t) and will suffer deformation e(x,y,z,t) during processing which can be computed by finite element modeling (FEM). Hence, a computation of the processing history will provide the path line for microstmcture development, i.e. the FEM model can serve as a process model. A given state of change of temperatur e or strain will cause microstructura l changes. At first glance, this is a simple problem since there are only three metallurgical phenomena that cause microstructura l changes, i.e. phase transformations , crystal plasticity, and recrystallization (including related processes like recovery and grain growth) [2]. The problem is the complexity of each of these metallurgical phenomena and their mutual interaction during processing. Therefore, in order to follow the microstructura l development in a volume element, the microstructura l changes caused by all phenomena have to be updated in a time increment, and the changed microstmcture will serve as input to the computation of microstmcture development in the next time step etc. Microstructura l processes like precipitation, dissolution, recrystallization, grain growth, plastic deformation have been extensively investigated in the past century and are most appropriatel y described on a microscopic scale. Accordingly, the metallurgical phenomena are adequately modeled by mesoscopic modeling tools, which utilize statistical information of a volume element, like solute content, precipitate size and volume fraction, dislocation density and arrangement or crystal orientation and grain boundary misorientation in conjunction with their change in space and time. Several TPM exercises have been successfully conducted in the past [3-7]. Since a comprehensive microstructura l characterizatio n requires the knowledge of a large number of parameters, it is recommendable to first define the target quantities of a TPM mn, in order to reduce the number of microstructura l parameters to the minimum necessary set of variables. Through-Process Modeling Modeling Tools In the following we will consider as an example a TPM exercise to predict the terminal strength and texture of a rolled sheet. The strength can be calculated with a dislocation based work hardening model if the nature and arrangement for dislocation motion is known, i.e. crystal structure, dislocation density, particle size and volume fraction, solute content, grain size and texture. The crystallographic texture is changed by plastic deformation and recrystallization, which in turn are affected by deformationand phase transformations . Hence, this is an intricate problem on top of the difficulty that the process of recrystallization itself proceeds by nucleation and growth of strain free grains in a deformed crystal, which are difficult to describe quantitatively and which are difficult to determine experimentally [8].

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Fig. 3: Used modeling tools for TPM and their connection The modeling tools used for this exercise are given in Fig. 3. They comprise a dislocation based work hardening model, a precipitation, coarsening and dislocation model and a recrystallization model that accounts for nucleation and nucleus growth. Of course, all effects can mutually influence each other. Example: Recrystallization To give a feeling for the complexity we specifically want to consider recrystallization. The growth of a viable nucleus can be reasonably numerically modeled by discretizing the microstructur e and tracking the location of the nucleus surface by solving the equation of motion for its grain boundaries under the given boundary conditions (dislocation density, particle distribution, misorientation etc.). This growth process can be successfully modeled with a variety of different approaches, like Monte-Carlo simulation, cellular automata or phase field methods. We will use cellular automata in the following [9]. The major problem for recrystallization modeling is to properly account for nucleation. Without quantitative information on the nucleation rate and nucleus orientation it is not possible to predict grain size, texture, and recrystallization kinetics. From a large body of experimental results on Al-alloys it is known that nucleation occurs preferentially at deformationinhomogeneities, grain boundaries and large particles (Fig. 4). To predict the microstructur e at these preferred locations, microstructur e development during deformation has to be simulated prior to recrystallization modeling to provide information on nucleation density, size and orientation. This can be accomplished by the code ReNuc [10].

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Fig.4: Nucleation of recrystallization ; at grain boundaries (left) and inhomogeneities (right) [1] More specifically, let us consider nucleation at large particles, i.e. particle stimulated nucleation (PSN). An FEM simulation of plane strain compression of a plate with a single particle reveals the strain distribution and the local texture (Fig. 5) [11]. In contrast to general belief it is found that the orientation distribution around a particle is not random although much weaker than the average texture. Moreover, the simulation renders the geometry of the deformation zone which extends infrontof the particle and contains the specific PSN orientations that are also found in the experimental recrystallization texture (Fig. 6).

Fig. 5: Deformation zone around particles; microstructur e (left) and computation (right) [11]

Fig. 6: Comparison of texture components in the deformation zone (DZ) and macroscopically [12]

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Besides, the dislocation density gradient in the deformation zone can be quantified. Application of a substructur e based nucleation probability model to this arrangement yields about 1 nucleation event per particle in agreement with measurements [12]. The information on nucleus orientation spectrum and nucleation frequency can be fed into a cellular automaton for modeling of nucleus growth in competition with nuclei from other nucleation mechanisms (Fig. 7). The output renders the recrystallization kinetics, the grain size distribution and the recrystallization texture [9]. Fig. 7: Discretization of grain arrangement in a polycrystal. The cells serve as cellular automata and contain all relevant microstructura l information

A particular complication arises if during nucleus growth other microstructura l changes impact the growth process [12]. An important example is concurrent precipitation, which changes the constitution of the alloy and the solute content. The latter impacts the grain boundary mobility, the former - the precipitates - reduce the effective driving force for grain boundary migration. Typically, in Al-alloys the driving force is also reduced by concurrent recovery processes, so that recrystallization, recovery, and precipitation have to be considered simultaneously. Since the three microstructura l processes have different kinetics, the heating schedule, in particular the heating rate is a powerful means to optimize microstructura l development. Case Study: TPM of AA5182 With these models, TPM exercises for different alloys and various degrees of complexity have been conducted [4-7]. An example is given for AA5182, an Al-Mg-alloy. The processing chain comprised 13 steps from multi-pass hot rolling, coiling to multiple cold-rolling and annealing sequences. The results in terms of texture components are given in Fig. 8. Note that the measurements were actually performed after the simulations; hence no optimization by fitting to target data was possible. The agreement between experiments and simulation is remarkably good.

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Volume Fractions Final Annealed Cold Band S=0.2

Fig. 8: Texture of a fabricated AA5128 sheet; experimental results (exp); simulation prior to measurement (SIM-1st); improved simulation tofitmeasurements (SIM-2nd) [4] The predicted texture data can be utilized for downstream sheet metal forming. The anisotropy of the yield stress in the sheet plane and the yield surface can be calculated to predict the earing behavior during deep drawing of a cup. Evidently, the location and height of the ears are well predicted (Fig. 9). Of course, more complex processing routes will require substantial refinements of the models and a sophistication of the approach.Nevertheless, the obtained results are promising.

Fig. 9: Deep drawing of a cup; FEM results (left) and earing profiles (right; top curve: simulation, other curves: measurements) [5]

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Outlook It is finally noted that the mesoscopic models have to make use of intrinsic material properties like elastic constants, mobilities, surface tension, activation energies etc. These data are difficult to measure, and it is virtually impossible to obtain a comprehensive database for multicomponent and heterogeneous alloys. It is expected, however, that such data can be provided by atomistic simulations like molecular dynamics or ab-initio simulations with electron density functional theory. Respective activities are reported for many relevant microstructura l mechanisms (Fig. 10). Hence, we trust that true multi-scale modeling of material processing is no longer a dream but will be reality soon.

Fig. 10: Molecular Dynamics simulation of grain boundary migration; atomistic arrangement (left) and Arrhenius plot of boundary mobility (right) [13] Conclusions Through-Process-Modelin g requires microstructura l modeling along the entire process chain. It is shown that such requirement can be met by mesoscopic models which reflect the physical metallurgy of the underlying microstructura l process. The modeling tools have been introduced, respective implications have been addressed, and a case study of aluminum sheet fabrication has been presented to predict the final texture and its effect on sheet metal forming. Acknowledgements The authors acknowledge financial support and provision of materials by Hydro Aluminium, RDB, M2i - the materials innovation institute, the Deutsche Forschungsgemeinschaf t (SFB 370 and TFB 63) and the German Research School for Simulation Sciences. The FEM simulations of the rolling process were performed with LARSTRAN/SHAPE by IBF (Institute for Metal Forming, RWTH Aachen University). We appreciate the contributions of M. Goerdeler, M. Crumbach, L. Neumann, V. Aretz, and C. Schäfer as doctoral students.

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References [I] G. Gottstein; Physical Foundations of Materials Science; Springer Verlag, Berlin, (2004) [2] G. Gottstein; Physical Metallurgy Fundamentals, in "Virtual Fabrication of Aluminium Alloys", J. Hirsch (ed.), Wiley-VCH, Weinheim (2005) [3] G. Gottstein (ed); IntegralMaterials Modeling: Towards Physics-Based Through-Process Models, Wiley-VCH, Weinheim (2007) [4] G. Gottstein, M. Crumbach, L. Neumann, R. Kopp; Through Process Texture Simulation for Aluminium Sheet Fabrication, Mat. Sei. Forum 519-521 (2006) 93 [5] M. Goerdeler, M. Crumbach, P.. Mukhopadhyay, G. Gottstein, L. Neumann, R. Kopp; Modelling the evolution of texture, micro structure and mechanical properties during hot rolling, cold rolling and annealing of VIR[*], Aluminium 80 (2004) 666 [6] L. Neumann, R. Kopp, H. Aretz, M. Crumbach, M. Goerdeler, G. Gottstein; Prediction of Texture-Induced Anisotropy by Through-Process Modelling, Mat. Sei. Forum 495-497 (2005)1657 [7] M. Crumbach, L. Neumann, M. Goerdeler, H. Aretz, G. Gottstein, R. Kopp, ThroughProcess Modelling of Texture and Anisotropy in AA5182, Mod. Sim. Mat. Sei. Eng. 14 (2006)835 [8] G. Gottstein, Review of Softening Models, in "Virtual Fabrication of Aluminium Alloys", J. Hirsch (ed.), Wiley-VCH, Weinheim (2005) [9] P. Mukhopadhyay, M. Loeck, G. Gottstein; A Cellular Operator Model for the Simulation of Static Recrystallization, Acta Mat. 55 (2006) 551 [10] M. Crumbach, M. Goerdeler, G. Gottstein, Modelling of Recrystallization Textures in Aluminium Alloys, I - Model Set-Up and Integration, II - Model Performance and Experimental Validation, Acta Mat. 54 (2006) 3275 and 3275 [II] C. Schäfer, J. Song, G. Gottstein; Modeling of Texture Evolution in the Deformation Zone of Second-Phase Particles, Acta Mat. 57 (2009) 1026 [12] C. Schäfer, Doctoral Dissertation, RWTH Aachen University (2011) [13] B. Schönfelder, G. Gottstein, L.S. Shvindlerman, Atomistic Simulations of Grain Boundary Migration in Copper, Met. Mat. Trans. A37 (2006) 1757

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1st World Congress on Integrated Computationa l Materials Engineering Edited by: John Allison, Peter Collins and George Spanos TMS (The Minerals, Metals & Materials Society), 2011

ADVANCEMENT IN CHARACTERIZATION AND MODELING OF BOUNDARY MIGRATION DURING RECRYSTALLIZATION Dorte Juul Jensen1, Yubin Zhang1, Andy Godfrey2, Nele Moelans3 Danish-Chinese Center for Nanometals, Materials Research Division, Riso National Laboratory for Sustainable Energy, Technical University of Denmark, DK-4000 Roskilde, Denmark laboratory of Advanced Materials, Department of Materials Science and Engineering, Tsinghua University, Beijing 100084, People's Reublic of China Department of Metallurgy and Materials Engineering, Katholieke Universiteit Leuven, Kasteelpark Arenberg 44, box 2450, B-3001 Leuven, Belgium Keywords: Recrystallization, boundary migration, protrusion and retrusion Abstract The boundary migration during recrystallization is characterized on the local scale using various experimental and modeling approaches. The modeling tools include atomic molecular dynamics simulations, numerical integration of the mesoscale equation of grain boundary motion and mesoscale phase-field simulations. The experiments cover in-situ 3D X-ray diffraction, 2D scanning electron microscopy (SEM), including in situ and ex situ annealing, as well as 3D SEM using focused ion beam sectioning, looking at Al, Ni and Cu deformed to medium, high and very high strains. It is discussed how the experiments and the modeling have been carried out hand in hand with the aim of advancing the understandin g of boundary migration during recrystallization. Introduction Many types of models exist within the fields of materials science and engineering, differentiated by the modeling approach, which can operate anywhere from the atomistic to component scale, and differentiated by the specific purpose of the model. Concerning the latter, two major groups of models are those that encompass: 1) Process (including synthesis) models. These can be models used, for example, for improving the processing conditions, for easy evaluation of the importance of various processing parameters, and/or for training purposes. 2) Physical models. These are generally used to achieve advances in the in-depth understandin g of a given phenomenon. Common to both groups of models is the need for experimental input and verification. The level of detail may vary between and within the groups depending on the specific purpose. As an example it can be mentioned that in a simulation study of the texture and grain size evolution during recrystallization it was found that 15 out of 59 very different nucleation and growth situations gave the same recrystallization texture and average grain size [1]. This may not be important if the purpose is to predict these two parameters, but more refinement is needed if, for example, the grain size distribution also has to be correctly predicted. Moreover, if the objective is to understand nucleation or growth, the focus of course has to be on finding the correct nucleation/growth model(s) for the given material.

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The present paper focuses on advancing the in-depth understandin g of boundary migration during recrystallization; i.e. Type 2 modeling as defined above. It is shown and discussed that experimental data are needed not only to verify the modeling but also to drive the formulation of new models. For example, advanced experimental characterizatio n has revealed local phenomena that are not included in recrystallization models because the models were derived based on experimental data that did not resolve specific local phenomena, and therefore the models were not detailed enough to predict these phenomena. As an example on the overall average scale the simple law v=M-F

(1)

where M is the boundary mobility and F the driving force, is known to work adequately for the description of the migration rate v of grain boundaries during recrystallization [e.g. 2-5]. However this is not the case on the local scale. The experimental results for the local scale boundary migration is resumed here and new modeling approaches which are developed to investigate these phenomena are described and discussed. Finally it is discussed how the two approaches - experimental characterizatio n and theoretical modeling have supplemented each other to give our knowledge and understandin g today of local boundary migration during recrystallization. Experimental Observations During recrystallization new almost strain-free nuclei develop at preferential sites in the deformed microstructur e and these nuclei grow by boundary migration, thereby consuming the deformed volumes of material. The present work is focused on the local boundary migration in the growth phase of recrystallization. The general concept of boundary migration during recrystallization is of a smooth continuous process during which a boundary moves at a given rate depending on e.g. deformation strain, grain boundary type and annealing temperature , until it impinges on another recrystallized grain thereby stopping further motion in that growth direction during recrystallization. Considering the many detailed studies of deformation microstructures , which reveal very inhomogeneous structures with many deformation induced high angle boundaries [e.g. 6-8], this assumption of a smooth continuous growth process may seem surprising, but only in-situ experiments can test its validity. In situ 2D scanning electron microscopy (SEM) investigations of growth during recrystallization reveal very complex boundary migration and velocities that deviate locally significantly from those predicted using equation (1) when average M and F values are used [e.g. 9]. Whether these observations are real or a consequence of the 2D character of the experiment cannot, however, be proven - for that 4D (3D (x, y, z) + time, t) experiments are required. The migration through a weakly deformed single crystal matrix of a boundary surrounding a single recrystallizing grain has been studied in situ by 3DXRD [10]. These measurements have also revealed a very complex boundary migration process and revealed several interesting observations including:

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1) Flat facets may form, i.e. extended flat boundary segments migrate forward at the same rate. 2) The non-faceted segments of the boundary do not migrate at a constant rate through the relatively homogeneous deformed matrix of the single crystal. On the contrary segments of the boundary move forward for a while then stop, move again etc. (stop-go motion) 3) Local protrusions and retrusions typically form on the migrating boundary The present paper focuses on the formation of protrusions and retrusions on migrating recrystallization boundaries. A picture from the 4D "movie" obtained by 3DXRD in which a protrusion is marked is shown in Fig. la, but actually many (most) published micrographs of partly recrystallized structures also clearly show pro/retrusion s (see e.g. Fig. lb-d).

Fig. 1 Some examples of micrographs showing protrusions on recrystallizing grains growing into deformed microstructures . Arrows are used to mark some of the protrusions. Protrusions are segments of the recrystallization boundary which have moved far further ahead than neighboring segments into the deformed matrix and appear as "peninsulas" . In contrast retrusions, segments left behind, are seen as "fjords" into the recrystallizing grain, a) 3DXRD snap shot of a recrystallizing grain in a 40% cold rolled aluminum alloy (AA1050) single crystal [10]; b) optical micrograph showing very large protrusions in weakly deformed super pure aluminum (courtesy R.A. Vandermeer); c) EBSP map of partially recrystallized 96% cold rolled pure (99.996%) nickel [11]; d) ECC map of partially recrystallized 50% cold rolled pure aluminum.

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One may speculate if the pro/retrusion s are related to effects of second phase particles/dispersoids . However owing to the fact that pro/retrusion s are veryfrequentlyobserved in super pure (e.g. zone refined Al), pure and less pure metals, the local interactions between the migration boundaries and the deformation microstructure s are believed to be the most important factor. Unfortunately, the spatial resolution of 3DXRD at present is not sufficient to characterize in any detail the deformed microstructur e in front of a moving boundary. To learn more about the formation and evolution of pro/retrusions , in-situ and ex-situ 2D SEM characterization s were therefore used to supplement the 3DXRD measurements [11, 12]. An example from the ex situ SEM investigations is shown in Fig. 2. The figure demonstrates that both protrusions and retrusions exist on the recrystallization boundaries and that they evolve during annealing. Some protrusions (3) and retrusions (2) are seen through all the annealing steps, while other protrusions (8 and 10) and retrusions (6 and 7) gradually disappear. A new protrusion (5) and retrusion (4) form at the second annealing step, remain for several annealing steps and disappear gradually. It is interesting to note that a protrusion can evolve into a retrusion (10), and vice versa (9). The merging of a protrusion (0) and retrusion (1) into a larger protrusion is also seen. In situ SEM investigations reveal similar results [13].

Fig. 2 ECC maps showing the microstructur e evolution during annealing at 250°C for: (a) 10 min; (b) 10 + 3 x 15 min; (c) 10 + 6 x 15 min; (d) location of the recrystallization boundaries during the entire annealing sequence, each annealing interval is 15min. Specific protrusions and retrusions are identified using numbers. [12] A further important result of the microscope investigations is that when a pro/retrusio n is formed on a recrystallization boundary it will provide an extra driving/draggin g force due to the local boundary curvature. In the example shown in Fig. 2, it is found that the maximum dragging forces Fmax from protrusions are in the range -0.005 to -0.2 MJm"3 whereas the driving forces

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Fmaxfromretrusions are much larger, in the range 0.2-1.0 MJm" [12]. The stored energy in this deformed microstructur e is 0.4-0.6 MJm"3. This implies that for many pro/retrusion s the magnitude of the local curvature based driving force (FG) is comparable to that of the stored energy within the deformed microstructur e (FD) i.e., the local migration rate may be expressed as: v=M-(FD+F0).

(2)

Many open questions remain from the present level of understandin g achieved by the experiments summarized above. Some of them are: 1) How do the formation and evolution of pro/retrusion s relate to the microstructura l inhomogeneities the deformed matrix (e.g. dislocation boundaries) in front of the recrystallization boundaries? 2) Are there relations between the type of dislocation boundary and its potential to form protrusions on a nearby recrystallization boundary? ? 3) How large variations in local stored energy are needed to form pro/retrusions 4) Do the pro/retrusion s affect the overall (non-local) average migration rate of the recrystallization boundary? These questions have been addressed by various modeling approaches. Modeling and Simulations MD simulations With the aim of addressing questions 1 and 2 above a molecular dynamics simulations tool was selected as it has the necessary spatial and temporal resolution to obtain atomic scale information on the interaction between various types of dislocation boundaries and a recrystallization boundary. In the work presented in [15] a 3D simulation cell is set up as shown in Fig. 3a. All "blocks" have a common direction parallel to the z-axis. The blue block represents a recrystallizing grain. The misorientation between the blue and the red block is 45° and the misorientation between the blue and the orange blocks is 35°. The orange-red boundary is chosen to represent a tilt dislocation boundary composed of edge dislocations with a misorientation of 10°. In the MD simulation [15] a Lennard-Jone s potential was used, but as shown in [16] an effective medium theory (EMT) interaction potential gave similar results. When heated, the simulations reveal that the recrystallization boundaries move towards the center of the simulation cell (y = 75; Fig. 3b). The process is not homogeneous and is believed to be due to the fact that the driving force in these simulations is localized in the dislocations (see Fig. 3b) rather than smeared out over the volume or the boundary. Two types of dislocation absorption are observed: either the dislocation remains stationary and the recrystallization boundary cusps out (see Fig. 3c) or the dislocation moves into the recrystallization boundary with no significant deformation or movement of the boundary. Often a mixture of the two is observed. The cusps on the recrystallization boundary (see Fig. 3c) resemble the protrusions observed experimentally except the scales are very different. The dislocation types within the dislocation boundaries seem to strongly affect the local migration of the recrystallization boundary. In [16] a MD simulation similar to those described above is reported with the difference that twist dislocation boundaries, composed of screw

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dislocations, were modeled as opposed to tilt dislocation boundaries In that case the migration of the recrystallization boundary is smoother and no cusps are observed, which makes sense as the recrystallization boundary now constantly "feels" the dislocations. For further details see [16].

Fig. 3 a) MD simulation cell containing ~ 9.3x104 atoms as set up. Colors indicate crystallographi c orientations of the crystal blocks; b-d) time sequence of simulation images showing a dislocation being absorbed during boundary migration; e-h) The atomistic details of one layer of atoms during the shoot-out. Adaptedfrom[15]. Mesoscale simulations Questions 3 and 4 above have been addressed using both numerical integration of the mesoscale equation of grain boundary motion (Eq. (2)) and mesoscale phase-field simulations. In both works [17, 18] a sinusoidal driving force is used to represent the inhomogeneous deformation microstructur e infrontof a recrystallization boundary. As expected the boundary moves forward following the shape of the driving force - i.e. develops both protrusions and retrusions, the magnitude of which depends on the amplitude andfrequencyof the driving force. As also observed experimentally the pro/retrusion s develop in such a way that they provide an additional driving force due to the local boundary curvature, which is comparable in size to the. driving force fromthe stored energy in the deformed microstructure . More surprising is that both types of simulations reveal that there is not a one to one correspondence between the sinusoidal driving force and the shape of the recrystallization boundary. The curvature related driving force

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from the retrusions can become significantly larger than the dragging force fromthe protrusions. The simulations thus suggest that when pro/retrusion s form on a recrystallization boundary they provide an extra positive driving force that leads to faster forward migration of such recrystallization boundaries. Discussion of Synergy between Experiments and Modeling Models predicting or focusing on the formation of protrusions and retrusions on migrating recrystallization boundaries were to the authors' knowledge not published before the 3DXRD insitu experimental characterizatio n of boundary migration in the bulk of a recrystallizing single crystal [10]. This is somewhat surprising as long before that it was already well documented that the deformation microstructure s driving the recrystallization typically are highly heterogeneous. An MD simulation (not discussed above) of the migration of a flat boundary driven by an artificial driving force distributed homogeneously over volumes of the sample has shown that in certain temperatur e intervals grain boundary roughening occurs [19]. The simulation is believed to refer more to grain growth than to recrystallization . It would, however, be interesting to study experimentally possible effects of annealing temperatur e on the formation of pro/retrusion s on migration of recrystallization boundaries. The models, discussed in this paper, do predict both atomic- and meso-scale protrusions. Experimentally, however, only micrometer scale pro/retrusion s are observed, because this is the resolution of the techniques applied so far. It would be interesting to go down in scale and see if cusps exist on the boundaries (and/or on the pro/retrusions) , and thus try to understand if the local interactions between the dislocation structures and the recrystallizing grain occur on the atomic scale or on a more macroscopic scale where larger volumes of material more simultaneously "transform " into the recrystallizing grain - i.e. really understand the boundary migration through a deformed microstructur e filled with dislocations and dislocation boundaries. Here both experiments and models are needed. Further work should also look at effects of recrystallization boundary type as well as dislocation boundary type. This will entail a large parametri c study where a good approach would be many model simulations and selected experiments. Concerning the latter, a dream experiment would be an in-situ 3DXRD technique with much better spatial resolution that the one reported in [10], so that the deformed microstructur e could be resolved and mapped in 3D. The models that are in present use for recrystallization are generic in nature, and as such do not directly mimic given experiments. This is considered an advantage, as the effects of isolated parameter s thus can be tested. However one to one comparisons of models to given experimental data are also of importance, both for model validation and to highlight areas where more efforts to develop more sophisticated model are needed. Acknowledgements The authors (DJJ, YBZ, AG) gratefully acknowledge supportfromthe Danish National Research Foundation and the National Natural Science Foundation of China (Grant No. 50911130230) for the Danish-Chinese Center for Nanometals, within this work was performed. NM is part-time postdoctoral fellow of the Research Foundation - Flanders (FWO - Vlaanderen) and also thanks

25

the foundation for an extra mobility grant V.4.280.10N - VC - 8217 to visit Tsinghua University, Beijing. References 1. D. Juul Jensen, "Simulation of recrystallization microstructure s and textures: Effects of preferential growth," Metal. Mater. Trans., 28A (1997) 15-25. 2. F. Haessner, Recrystallization of metallic materials. (Stuttgart: R. Riederer Verlag GmbH. 1978). 3. R.A. Vandermeer, D. Juul Jensen, E. Woldt, "Grain boundary mobility during recrystallization of copper," Me tal. Mater. Trans., 28A (1997) 749-754. 4. R.A. Vandermeer, "Dependence of grain boundary migration rates on driving force," Trans. TMS-AIME 233 (1965), 265-265. 5. E. Woldt, D. Juul Jensen, "Recrystallizatio n kinetics in copper - comparison between techniques," Metal. Mater. Trans., 26A (1995) 1717-1724. 6. N. Hansen, "Cold deformation microstructures, " Mater. Sei. Techn. 6 (1990), 1039-1047. 7. A. Godfrey, D. Juul Jensen, N. Hansen, "Slip pattern, microstructur e and local crystallography in an aluminium single crystal of brass orientation {112 }< 111 >," Ada Mater. 46 (1998), 835848. 8. A. Godfrey, D. Juul Jensen, N. Hansen, "Slip pattern, microstructur e and local crystallography in an aluminium single crystal of copper orientation {110} < 112 >," Ada Mater. 46 (1998), 823833. 9. E. Anselmino, Microstructural effects on grain boundary motion in Al-Mn alloys, (Ph.D thesis, Delft University Technology, 2007). 10. S. Schmidt et al., "Watching the growth of bulk grains during recrystallization of deformed metals." Science, 305 (2004), 229-232. 11. Y.B. Zhang, A. Godfrey, and D. Juul Jensen, "Measurement s of the Curvature of Protrusions/Retrusion s on Migrating Recrystallization Boundaries," Computers, Materials & Continua, 14 (2009), 197. 12. Y.B. Zhang, A. Godfrey, and D. Juul Jensen, "Local boundary migration during recrystallization in pure aluminium," Scripta Mater., 64 (2011), 331. 13. Y.B. Zhang, A. Godfrey, and D. Juul Jensen, "In situ observations of migration of recrystallization boundaries in pure aluminum," Proceedings of the 31st Risoe Symposium (2010), 497. 14. Q. Liu, D. Juul Jensen, and N. Hansen, "Effect of grain orientation on deformation structure in cold-rolled polycrystalline aluminum," Ada Mater., 46 (1998), 5819. 15. R.G. Godiksen et al. "Simulations of boundary migration during recrystallization using molecular dynamics," Ada Mater. 55 (2007), 6383. 16. R.B. Godiksen, S. Schmidt, and D. Juul Jensen, "Molecular dynamics simulations of grain boundary migration during recrystallization employing tilt and twist dislocation boundaries to provide the driving pressure," Modeling Simul Mater. Sei. Eng. 16 (2008), 065002. 17. M. A. Martorano, M. A. Fortes, and A.F. Padilha, "The growth of protrusions at the boundary of a recrystallized grain," Ada Mater., 54 (2006), 2769-2776. 18. N. Moelans et al, "Phase-field simulations of the formation of protrusions/retrusion s on recrystallization boundaries," in preparation , (2011). 19. E.A. Holm, S.M. Foiles, "How Grain Growth Stops: A Mechanism for Grain-Growth Stagnation in Pure Materials," Science 328 (2010), 1138.

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1st World Congress on Integrated Computational Materials Engineering Edited by: John Allison, Peter Collins and George Spanos TMS (The Minerals, Metals & Materials Society), 2011

EFFECT OF PULLING VELOCITY ON DENDRITE ARM SPACING IN STEADY-STATE DIRECTIONALLY SOLIDIFIED TRANSPARENT ORGANIC ALLOY BY NUMERICAL SIMULATION Yufeng SHI, Qingyan XU, Ming GONG, Baicheng LIU Key Laborator y for Advanced Materials Processing of Ministry of Education, Department of Mechanical Engineering, Tsinghua University, Beijing 100084, China Keywords: Dendrite arm spacing, Transparen t alloy, Pulling velocity, Simulation. Abstract A modified cellular automaton (MCA) model is proposed for columnar dendritic growth in directional solidification. Many factors including temperatur e gradient, pulling rate, constitutional undercooling, curvature undercooling are considered in the model. The model is helpful to understand the fundamentals of the formation of the cell-dendrite transition, the evolution mechanism of primary dendrite arm spacing change, which significantly impact the formation of microsegregation. and the mechanical properties of the castings. The MCA model illustrates that the simulated microstructur e parameter s (primary dendrite arm spacing X\, and secondary dendrite arm spacing À2) exhibited a power function of pulling velocity (V), which has c of good agreement with the theoretical models. NH4C1-H20 system has the characteristi transparency , cubic habit, liquidus line near room temperature , lower enthalpy of fusion, which allows the in situ observation of directionally solidified dendritic growth. A series of experiments were carried out under a range of pulling velocities, but a constant thermal gradient. Both branching and overgrowth mechanism of dendrite arm spacing were observed in the experiments. The terms X\ and À2, derived from the MCA model, agreed well with the experimental data. Introduction Dendrite arm spacing (DAS) is an important characteristi c of columnar dendrites which significantly impact the mechanical properties of the castings. Several theoretical models11,2], which describe primary DAS (X\) as a function of pulling velocity (V), thermal gradient (G) and solute concentration (Co), have been proposed. Hunt and Lu[3] also developed a numerical model to predict the cellular and dendritic spacings. They found that two adjustment regimes of primary DAS exist during directional solidification of transparen t succinonitrile acetone system. The primary DAS would be increased or decreased by overgrowth mechanism or growth of tertiary arm (branching), respectively. Zhang[4] et al investigated DAS and morphologies of directionally solidified DZ125 superalloy under high thermal gradient about 500 K/cm. Kaya[5]et al carried out directionally solidified Al-3wt.%Si alloy experiments under a range of thermal gradients and growth rates. The primary DAS of the experimental results had a good agreement with the t alloys at steady state growth theoretical models. Hansen[6] et al measured DAS of transparen conditions, and they found that the primary DAS of NH4CI-H2O was not compared well with the Hunt-Lu model. Numerical simulation was another way to predict the primary and secondary DAS in directional solidification. The cellular automaton (CA) method was one of the effective simulation methods, which could simulate the competitive growth the CET phenomenon, the coarsening and coalescence of secondary DAS, etc. Leef7] et al developed a combined cellular automaton-finit e difference (CA-FD) model to simulate solute diffusion controlled directional

27

solidification of binary alloys. The model illustrated that there was a range of possible stable spacing, and the final spacing was history dependent. The aim of the present work is to investigate the influence of solidification parameters (G and V) on microstructur e parameters (primary and secondary DAS) by numerical simulation. Therefore, a modified cellular automaton (MCA) method is performed for the directional solidification, which can simulate the adjustment mechanism of primary DAS under different solidification parameters. A NH4CI-H2O transparen t alloy is chosen to verify the MCA model, because it shows the cubic habit and low enthalpy of fusion as metals. A series of experiments were carried out under a range of pulling velocities, but at a constant thermal gradient. Experimental As Fig. la shown, the main part of the experimental system is a crystal-growth apparatus. The temperatur e gradient between hot and cold side is controlled by heating and cooling devices. The e is 288 initial solutal concentration (H2 0) of NH4C1-H20 is 74wt.%, and the liquidus temperatur K[8]. The solution at the bottom cold boundary is undercooled, where dendrites could nucleate and grow by moving from the hot side to the cold side. Both dendritic morphology and primary DAS measurement are conducted by an optical microscope as Fig. lb shown.

(a)

(b)

Fig. 1 Sketch map of experimental apparatus (a) and microstructur e (b) Description of mathematical models Mathematical models of directional solidification of NH4 Cl-74wt.%H2 0 solution includes heat transfer, solute diffusion and MCA equations. Heat transfer equation It is assumed that there is no convection during the directional solidification. The thermal diffusion efficiency is much higher than the solute diffusion efficiency. Therefore, the solution in the sample box will form a stable temperatur e gradient G very quickly in the directional solidification. Meanwhile the thickness H of the solution is much smaller than length L and width W, therefore the region can be reduced to two-dimensional simulation, while the left and right side of the sample box is adiabatic state. Above all, the two-dimensional temperatur e field is equivalent to the one-dimensional linear equation as follows T\x,y) = Tcold+Gy (1) Where T (x, y) is the temperatur e at (x, y), and Tœ\d is the temperatur e at cold side. Solute diffusion equation

28

Convective mass transfer is not considered and the solute field is mainly controlled by diffusive mass transfer. The governing equation for the solute redistribution in the liquid region is given by

^.»VK^VO+QO-*)^-

(2)

Where DL is the liquid solutal diffusion coefficient, and k is the partition coefficient. The last term on the right hand side of the Eq. (2) represents the amount of solute rejected to the solid/liquid interface. The diffusion equation in solid is given by ^

= V.(D,VC,)

(3)

Where Ds is the solid solutal diffusion coefficient. A hypothesis was proposed that there is no diffusion across the liquid/solid interface. MCA equations A local equilibrium condition is assumed at the solid/liquid interface^101 C[=C0 +[T* -TL +TKf{z(m2/s) -4.8 Liquidus slope mL (K/wt.%) Solute partition coefficient 0.30 ko Gibbs-Thomson Coefficient r (K-m) 5.0x10"8 0.019 Surface Energy Anisotropy y 257.75 Eutectic temperatur e re(K) Ce (wt.%H 80.3 Eutectic composition > . . _ 2_0) A two dimensional calculation domain of 2.4x3.6 mm was selected, and the cell size was set to 6 urn. Each cell had some properties, such as solute concentration, solid fraction, preferred growth direction and state of solid, liquid or interface. Before solidification, the domain was filled with undercooled liquid wrhich solute concentration was 74wt.%H2 0. Zero-flux boundary condition was used for the calculation domain. The bottom boundary cells were all nucleated with same preferred crystallographic growth direction, which is parallel to the heat flow. The domain had a constant temperatur e gradient G from the bottom to the top, but a changeable pulling velocity V. Adiabatic isolation was prescribed at the side faces.

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Fig. 2 Simulated dendritic arrays of NH4Cl-74wt.%H20 transparen t alloy comparing with experimental result under a constant temperatur e gradient lK/mm (a)~(c) pulling velocity is 5 um/s (Fig. 3b is part of 3a, and 3c is experimental result) (d)~(f) pulling velocity is 8 um/s (Fig. 3e is part of 3d, and 3 fis experimental result) (g)~(i) pulling velocity is 10 um/s (Fig. 3h is part of 3g, and 3i is experimental result) (j)~(l) pulling velocity is 15 um/s (Fig. 3k is part of 3j, and 31 is experimental result) NH4Cl-74wt.%H20 transparen t alloy was directionally solidified at a constant G and different V, and the simulated and experimental columnar dendrite morphologies were shown in Fig. 2. When the pulling velocity was 5 um/s, only a few dendrites grew ahead and the others were blocked by the formation of secondary dendrite arms. As V increased from 5 um/s to 15 um/s, the cooling rate increased, which could greatly suppress the growth of secondary DAS. Therefore,

31

more dendrites grew up and the dendritic microstructur e became refined and well developed, and the primary DAS decreased. From Fig. 2, it could be seen that dendrites of NH4Cl-74wt.%H20 transparen t alloy transited from sparse to dense with the increasing pulling velocity. Measured values of primary DAS k\ and secondary DAS k2 at different pulling velocities are shown in Fig 3. Both k\ and k2 decreased gradually.

Fig. 3 Experimental and simulated DAS and nonlinear regression equation of k\ and k2 vs. V (a) k\-V relation (b) k2-V relation Primary DAS k\ vs. V was shown in Fig. 3a. The simulated and experimental results are at constant thermal gradient G (1 K/mm). k\ decreases when F increases, and the simulated results gave good agreement with the experiments. In Fig.3a, The nonlinear regression of k\ with different pulling velocity V, which was Ai=1372.967xF°559 The Feurer-Wunderli n model model[15] gave the relationship between the secondary DAS A2and the cooling rate Rc as follows: k2=ARc~l 3, and RC=GV in the directional solidification. If G was constant, the function could be described as k2=B Vm, where V was pulling velocity during directional solidification and B was a constant. Fig. 3b indicated that the secondary dendrite arm t alloy decreased with increasing pulling velocity. The spacing of NH4 Cl-74wt.%H2 0 transparen relationship between the simulated and experimental k2 and the pulling velocity V was described by nonlinear regression analysis, and the regression equation was k2=\5%A9^V033, which compared well with the Feurer-Wunderli n model. Conclusions As simulated results show, increasing the directional solidification pulling velocity from 5 um/s to 15 um/s at a constant temperatur e gradient reduces both the primary and secondary DAS of NH4Cl-74wt.%H20 transparen t alloy, because increasing pulling velocity reduced the length of the solid-liquid mushy zone. In order to verify the MCA model, a series of experiments were carried out. It was found that k\ and k2 exhibited a power function of pulling velocity. The nonlinear regression equation of the simulated and experimental k\ versus Kwas 1372.967> 0. In JP PrFj) the constitutive equations (intended to characterize small elastic strains) to be defined below, the Green elastic strain measure É = \ (FeTFe — I) defined on the relaxed configuration (plastically deformed, unstressed configuration) is utilized. The conjugate stress measure is then defined as t = detFe(Fe)-1T(Fe)~T where T is the Cauchy stress for the crystal in the sample reference frame. The constitutive relation, for stress, is given by T — Ce \Ë \ where Ce is the fourthorder anisotropic elasticity tensor. It is assumed that deformation takes place through dislocation glide and the evolution of the plastic flow is given by Lp = Fp(Fp)-1

= ^2 0). Further, the resolved shear stress does not exceed sa on the inactive systems with 7 a = 0. The hardening law for the slip resistance sa is taken as, sa(t) = Y^ haßAfß, sa(0) = s%

(2)

ß

Single crystal model of magnetostriction When a magnetic field is applied to a Galfenol single crystal, the boundaries between the magnetic domains shift and rotate, both of which cause a change in the material's dimensions. Galfenol crystal has minimal energy in the < 111 > family of directions (easy direction of magnetization) and maximal magnetocrystalline energies in the < 100 > family (hard directions). Magnetostrictive strain is specified using two independent parameters, À100 and Am, that characterize the changes in normal strain along the < 111 > and < 100 > direction resulting from the rotation of a magnetization state into these directions. The magnetostrictive strain tensor for a crystal with magnetization direction given by the unit vector ra — (mx,my,mz) (in the crystal coordinate system) is then given by the following expression: Xioo(m2x-D \m{mxmy) \m(mxmz) Xin{mymx) Aioo(mJ - | ) Xni{mymz) (3) Xin(mzmx) \iu{mzmy) Xi0o(m2z - | )

58

A magnetic free energy is then defined that represents the amount of energy required to rotate a unit volume with a known magnetization to a given direction from a reference direction. We use the model from Armstrong [7] that represents the free energy as a sum of internal and external energy terms. The internal energy represents the energy released as the magnetization vector rotates away from a hard direction towards an easier direction of magnetization. The following form of internal energy is taken: Ej = A T i ( mX + mlml

+ rn2xml)

(4)

The simple form for Ej used here ensures that a domain in the crystal has minimal and maximal energies when oriented, respectively, along the < 111 > directions (easy direction) and the < 100 > family (hard directions). Application of an external magnetic field leads to an energy change in energy proportional to the intensity of the magnetic field, H, the magnetization of the domain, M, and the direction between them. The direction of the applied magnetic field is represented as n — (nx , ny , nz) in the crystal coordinate system. EH = -ß0MH(m

• n)

(5)

The energy contribution (per unit volume) associated with the interaction of externally applied stresses with magnetostrictive strains is given as: Ea = -a-\

(6)

In an ideal crystal without defects (at T = OK), the domain would align in the direction of minimal energy. However, domain magnetization is expected to follow a Boltzmann-like distribution at higher temperature s due to an increase in entropy. The probability, F, that the magnetization direction is equal to m is given as: r>( \ t Pi + EH + Ea) P{m) oc exp( '-) (7) The parameter Q, represents the spread of the magnetization direction from the ideal direction (of minimal energy). The magnetostriction strain tensor is obtained by averaging the strains over the probability density of magnetization in the crystal.

JP(m)Xdm fP(m)dm

{ }

The above integral is calculated by using a finite element representation of the surface of a unit sphere (with 320 quadrilatera l elements). Each point on the unit sphere represents a unit normal vector (magnetization direction). The free energy is computed over all the integration points for each element and the e is computed by summing up the element contributions. The actual magnetization is calculated by subtracting out the strains for an unstressed reference crystal of same orientation, but with zero applied magnetic field. Further, the strain are in the crystal coordinate system and are rotated back to the sample coordinates. The computed strains for each integration point in the FE mesh is then volume averaged to compute the overall magnetization strain in the material. A total Lagrangian FEM formulation is used to solve the microstructur e deformation problem. The unloading process is modeled as a non-linear (finite deformation) elasto-static boundary value problem. In this work, we assume that the residual elastic stresses after unloading contribute to the Ea term. In future work, the restriction will be relaxed by accounting for changes in residual stresses due to the effect of magnetostrictive strains.

59

Figure 1: (left) Comparison of textures (Euler angle space, 4>2 = 45°) predicted by our model (Fig. 1(b)) with experiments on BCC iron in Fig. 1(c) [9]. Experimental rolling textures of BCC Fe-16.83%Ga results (Fig 1(a) [8]) are also shown. The experiment indicates a {112} < 132 > texture in addition to the expected 7 texture, (right) Comparison of results of current model with published results in [8]. The plot shows tensile test curves of as-cast polycrystalline Galfenol at different temperatures . NUMERICAL EXAMPLES The slip system hardening model used in the examples is given as: haß = [q + (l-

q)öaß}hß (no sum on ß)

(9) aß

where hP is a single slip hardening rate, q is the latent-hardenin g ratio and ö is the Kronecker delta function. The parameter q is taken to be 1.0 for coplanar slip systems and 1.4 for non-coplanar slip systems. For the single-slip hardening rate, the following specific form is adopted: hß = h0(l - — ) a

(10)

where /i 0 , a, and ss are slip hardening parameters taken to be identical for all slip systems, with values h0 = 500 MPa, ss = 350 MPa and a = 2.25 for BCC Galfenol single crystals. The initial value of slip system resistance is calibrated as s0 = 180MPa. Values of elastic parameters for Galfenol crystal are taken as Cn = 213 GPa, Ci 2 = 174 GPa and C44 = 120 GPa. The initial texturing of the material is assumed to be random. Plastic deformation due to crystallographic slip is assumed to occur in the < 111 > direction, and the possible slip planes are of the {110} , {112} , and {123} type. The model adequately captures the macroscopic tensile mode stress-strain response at room temperatur e reported in [8] well as shown in Fig. 1 (right). To further validate the microscale model, we compared the results with textures seen in BCC iron rolling processes and textures predicted by our model. The model results from Fig. 1(b) captures both a and 7 texture seen from experiments (in Fig. 1(c) [9]). Results were also compared with experimental rolling textures of BCC Fe-16.83%Ga results (Fig 1(a) [8]). However, the experiment indicates a {112} < 132 > texture in addition to the expected 7 texture pointing to the possible presence of additional deformation mechanisms in Galfenol that needs future study. The magnetostrictive performance of single crystal Galfenol was first studied using model parameters of K\ = 3.6e4, À100 = 170ppm, À m = —4.67ppm, M = 1.83//i0 and Q = 625 calibrated in [3]. These parameters lead to a magnetostrictive X — H (magnetostrictive strain - magnetic field) response shown in Fig. 2(a) for various compressive pre-stress values of 0,

60

(a)

(b)

Figure 2: (a) Magnetostrictive X — H response for various compressive pre-stress values of 0, 5, 20 and 40 MPa along [100] crystallographic direction, (b) Final microstructur e after rolling to 1% strain and unloading. The mis-orientation distribution over grains that depicts the change in Neo-Eulerian angle from the initial configuration (t=0). 5, 20 and 40 MPa along [001] crystallographic direction. Note that the magnetic field is also along the [001] crystallographic direction. The effect of a rolling process on polycrystalline Galfenol was subsequently studied. A microstructur e with 31 grains was generated using a standard Voronoi tessellation based on our previous work [4]. Texture was randomly assigned and the microstructur e was discretized into 690 quadrilatera l elements. A rolling process (with plane strain compression along yaxis) was studied with a strain rate of 10~ 3 for a time of 10 seconds. The microstructur e was subsequently unloaded to study the effect of the rolling process. After unloading from a strain of 1%, a spring back of 0.065% was observed in the y-direction. The misorientation development was computed using the change in neo-eulerian angle of rotation f (t) at time t from the values of £(£ = 0) of the initial texture, f is obtained from the Rodrigues parametrizatio n given by r = n t a n ( |) where n denotes the axis of rotation. The change in the neo-eulerian angle from the initially assigned orientation of grains shown in Fig. 2(b) clearly shows the formation of disoriented regions within grains at this moderate deformation. Using the magnetostriction model, the final magnetostrictive state was computed over each element. Here, a 20000 A/turn (= 251.33 Oe) magnetic field was applied along the y-direction. The magnetostrictive strains along the x- and y- directions, respectively, are plotted in Fig. 3. It is seen that grains with high x- strains are associated with low y- strains and vice versa. Significant changes in magnetostriction strains are seen even within a single grain due to the effect of misorientations and residual stresses. CONCLUSION This preliminary study shows that internal inhomogeneous strains introduced by microstructural changes play an important role in determining the final magnetostriction in Galfenol. The microstructura l model of Galfenol developed in this paper will be used in the future to design processes that would lead to optimal meso-scale features (such as texture, misorientation distribution). Such new processing routes can be used to produce polycrystalline galfenol with good magnetostrictive strains for a variety of sensing applications.

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Figure 3: Magnetostrictive strain distribution in the as-rolled microstructur e (to l % strain) under a y-direction magnetic field of 251.33 Oe. (a) Magnetostrictive strains along x-direction and (b) strains along the y- direction. References [1] R.A. Kellogg, A.M. Russell, T.A. Lograsso, A.B. Flatau, A.E. Clark and M. WunFogle, Tensile properties of magnetostrictive irongallium alloys Acta Mater. 52 (2004) pp. 5043-5050 . [2] L.M. Cheng, A.E. Nolting, B. Voyzelle and C. Galvani, Deformation behavior of polycrystalline Galfenol at elevated temperatures , in Behavior and Mechanics of Multifunctional and Composite Materials, Edited by Dapino, Marcelo J.. Proceedings of the SPIE, Volume 6526 (2007) pp. 65262N. [3] J. Atulasimha, A.B. Flatau and E. Summers, Characterizatio n and energy-based model of the magnetomechanical behavior of polycrystalline irongallium alloys Smart Mater. Struct. 16 (2007) pp. 1265-1276. [4] V. Sundararaghava n and N. Zabaras, Design of microstructure-sensitiv e properties in elasto-viscoplastic polycrystals using multi-scale homogenization, Internationa l Journal of Plasticity, 22 (2006) pp. 1799-1824. [5] N. Srisukhumboworncha i and S. Guruswamy, Crystallographi c Textures in Cold-Rolled and Annealed Fe-Ga And Fe-Al Alloys, Metallurgical Materials Transactions A, 35A (2004) pp. 2963-2970. [6] L. Anand and M. Kothari, A computational procedure for rate-independen t crystal plasticity, Journal of the Mechanics and Physics of Solids, 44(4) (1996) pp. 525-558. [7] W.D. Armstrong, Nonlinear behavior of magnetostrictive particle actuated composite materials, Journal of applied physics, 87(6) (2000) pp. 3027-3031. [8] J.H. Li, X.X. Gao, J. Zhu, X.Q. Bao, T. Xia and M.C. Zhang, Ductility, texture and large magnetostriction of FeGa-based sheets Script a Materialia 63 (2010) pp. 246-249. [9] P. S. Bate, and J. Quinta da Fonseca, Texture development in the cold rolling of IF steel, Materials Science and Engineering A, 380(1-2), (2004), pp. 365-377.

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1st World Congress on Integrated Computationa l Materials Engineering Edited by: John Allison, Peter Collins and George Spanos TMS (The Minerals, Metals & Materials Society), 2011

NUMERICAL EVALUATION OF ENERGY TRANSFER DURING SURFACE MECHANICAL ATTRITION TREATMENT Xiaochun ZHANG1, Jian LU2, San-Qiang SHI1 department of Mechanical Engineering, The Hong Kong Polytechnic University, Hong Kong 2 College of Science and Engineering, City University of Hong Kong, Hong Kong Keywords: Surface Mechanical Attrition Treatment, random impact, dissipated energy, stored energy Abstract Experiments showed that Surface Mechanical Attrition Treatment (SMAT) is one of the most effective ways to optimize the surface structure of metals and alloys, and therefore to enhance the global behaviors of a material and its service lifetime. However, there is still a lack of clear relationships between desired surface structures/propertie s and controlling parameters in SMAT process. The relationship between impact ball parameters and the indent coverage on a sample surface has been obtained from the previous work by coupling a global random impact model and a local impact frequency model. In this work, a more realistic SMAT model is built according to the previous investigation. The cyclic deformation process during SMAT always leads to change in the temperatur e of deformed material. Thus, the thermodynamic frameworkof the mechanical constitutive model allows the partition of the plastic work into the dissipated energy (usually, dissipated as heat) and the energy stored in the material due to increasing the grain boundary area (grain refinement) and introducing dislocations. The computational model of random flying balls with three different ranges of oblique angle is defined and the components of impinging and rebounding velocity during SMAT are monitored in this study. The stored energy and the fraction of plastic work converted into heat (ß) are numerically evaluated. Introduction In the current economic environment, engineers and scientists must constantly improve their capacity to design and make things more efficient. In the past decade, nanocrystalline mateials, which possess novel properties and performance over their coarse-grained polycrystalline counterpart [1], has drawn significant attention. Various methods have been proposed to achieve surface nanocrystallization , among them the technique of surface mechanical attrition treatment (SMAT) [2] has been extensively studied by Jian Lu and his co-workers on various metallic materials [3-5]. The experimental set-up of SMAT is illustrated in Figure 1. It is a mechanical deformation process. The spherical balls are placed in a reflecting chamber (including an ultrasonic concentrator) vibrated by an ultrasonic generator. Because of the high frequency of the system (20kHz), an extremely high sound pressure will be produced close to the sonotrode (horn) surface, which will be the main driving force to propel the balls to the desired velocity. Once the balls are resonated, the entire surface of an engineering component to be treated is blasted with a stream of balls over a controlled period of time.

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Figure 1 Schematic illustration of the ultrasonic-assisted SMAT set-up The cyclic deformation process during SMAT always leads to change in the temperatur e of deformed material. Thus, in the numerical simulation, the thermodynamic framework of the mechanical constitutive model allows the partition of the plastic work into the dissipated energy (usually, dissipated as heat) and the energy stored in the material as the internal elastic energy of defects such as vacancies, interstitials, dislocations, or/and twins. The temperatur e change in a deforming sample may be measured using thermometers. A review of such experimental studies was given by Bever et al. (1973)[7]. It reported that, in general, no more than 5% of the work done is stored in metals as the elastic energy of defects. For moderate strain rates, most of the plastic energy put into metals is converted to heat. Theory analysis During SMAT process, each impact will induce plastic deformationwith a high strain rate in the surface layer of the sample. An estimated value of strain rate is about 10 - l O V 1 in the top surface of the Fe sample [4]. Thus, strain-rate dependent plasticity theory must be employed in numerical analysis of the mechanical response under SMAT. In recently years, numerous empirical and semi-empirical temperatur e and strain-rate dependent models have been developed, among them the Johnson-Cook (JC) [8] model is the most widely used as it requires fewer material constants and also few experiments to evaluate these constants. JC model for the flow stress oy is given by T-T

1 + Cln

T -T , m rJ

(i)

where e p\s the equivalent plastic strain, ep is the plastic strain rate and sp is the reference plastic strain rate of the quasi-static test used to determine the yield and hardening parameters A, e and Tm is the melting B and n. C is the strain rate coefficient. Tr is a reference temperatur temperature . Previous studies have proved that JC model can provide a good prediction and an excellent description of the mechanical response of the target material AISI 316L stainless steel under high strain rate deformation induced by SMAT. Our early work on modeling of SMAT process focused on the influence of ball parameters [6]. Determination of energy partition during SMAT

64

is our prime concern in this work. During a ball impact, mechanical work (energy) is injected in the structure. The mechanical energy, Wext, can be decomposed into an elastic part, We, and a plastic part, Wp, Wext=We+Wp (2) The thermodynami c framework of the mechanical constitutive models allows the partition of the plastic work into the energy dissipated as heat Wd, and a sum of internal energy Ws stored in the material due to strain hardening by increasing dislocation density and grain boundary area during grain refinement. Wp=Wd+Ws (3) In the case of an isotropic and/or kinematical model the intrinsic dissipation can be written: Wd=\\\\{cr:èp-X:à-Rp)dVdt (4) V

t

where Fis the geometrical domain occupied by the sample, a is Cauchy's stress tensor, ^ t he plastic strain rate, (X,â) and (R,p) the couples (thermo-dynamica l force, state variable) respectively associated with the kinematical and isotropical hardening. When the elastic domain is defined by Von Mises's criterion, the dissipation can be rewritten as

(5)

^=ïiliffyépdVdt V

t

The dissipated energy is to generate heat. Here, the thermo-mechanica l coupling is treated as locally adiabatic heating and the temperatur e is regard as an inner variable. Thus, the total heat Q generated is, Q = f'pCpdT

= Wd

(6)

where T0 and Tf represent the initial and final temperatur e states, respectively. For constant density p and specific heat capacity Cp, pCp(Tf-TQ) = Wd (7) The fraction iß) of plastic work converted into heat is define as ß = ^iWp

(8)

Numerical simulation and results The material investigated in this study is AISI 316L austenite stainless steel with medium stacking fault energy. Figure 2 shows a typical impact event of aflyingball. The upper panel in Figure 2(a) indicates the displacement, //, as a function of time, t. The velocity, v, which is monitored during impact process, is plotted in the lower portion. The points in the upper panel demonstrate the vertical displacement of the impact point from the sample surface, while the curve is integrated fromthe v-t data. The point of initial contact is identified by the onset of ball deceleration, and is assigned as /z=0, the impinging velocity at contact is denoted Vimp. When the depth of the indentation reaches to a maximum value hmax, the ball velocity decreases to 0 and the ball begins to springback, leaving a permanent indentation on the sample surface. The rebound velocity of the ball is denoted as vreb- Figure 2(b) shows the temperatur e profile along depthfromthe impact surface after one impact.

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Figure 2. (a) Representative data from the initial impact event on a AISI 316L specimen; (b) Temperatur e distribution along depth The energy injected (work done) on the structure by the ball impact is of two types: reversible and irreversible. The reversible energy (elastic) provides the driving force for the sample surface recovery and "pull" back the contacting ball to obtain the rebound velocity. Thus, the change in kinetic energy of a flying ball (kinetic energy lost) can be defined as the total work done by the external forces in irreversible deformation (the plastic work Wp).

^=z^=s^[kl+k^+(va)-kJ+kJ+(v;j)]

(9)

Here, / denotes the /th flying ball, N is the total number of balls, m, is the mass of the /th ball and x,y,z are the directions of velocity components as shown in Figure 3(b).

Figure 3 Full coverage multi-impingement s model The schematic model used in this study is shown in Figure 3(a). A full coverage random impact model is employed. Each small circle stands for an indent produced by one impact, (j) and 6 in Figure 3(b) are the angles between the impact direction of the flying ball and the vertical and horizontal axis, respectively. For random impact, 0° < < 90° and 0° < 6 < 360°. In order to investigate the influence of the impingement direction on the fraction of energy storage, three different ranges of oblique angle are defined as listed in Table 1, while the magnitude velocity of the flying balls are the same, i.e., |v|=10.0m/s according to the experiment study [9]. Thus, vx =|v|-sin^cos#, v^ =|v|-cos^, vz =|v|-sin^sin# (10) The impinging and rebound velocity components during these three SMAT cases are monitored for the defined frictionless impacts. Figure 4(a)-(c) plot the results in case III. It is clearly shown that only the vertical velocity is significantly decreased due to the elastoplastic deformation of the sample. The average vertical and horizontal velocity components of the impinging balls are ~8.79m/s and ~2.46m/s, respectively. The results in this case agree with the experiment observation (Figure 4(d)) very well.

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Figure 4 Distribution of velocity components in case III (a) simulated vx, (b) simulated vz, (c) simulated vy, (d) experiment average impinging v^and impinging |vx| [9]

Further analysis shows that the flying ball with high oblique angle will obtain low vertical rebound velocity. When the vertical velocity of an impinging ball varies between 1 and 1 lm/s, the rebound vertical velocity remains at a velocity of about 2~4m/s as shown in Figure 5. Thus the work done on the sample during SMAT is directly related to the incident angle of the flying balls (j> according to Eq.(9) and Eq.(lO). Table 1. Different SMAT Cases easel 50°a(X)*a,(tf,T) = 5> a (X) £ AlNi + NiAi ) and Schottky-type (0 -> 3VaNi + VÜAI) account for total defects. Table I lists the calculated formation energies for all defects in both the supercells. A good agreement has been established with the existing results of DFT calculations [3,7,8,9], experimental studies [3,4,17] and to those calculated from EAM potentials [10,11]. The elemental chemical potentials of Ni, Al and Cr were found out to be -5.748, -3.733 and -9.594 eV/atom respectively. The total energies are calculated for two alloy structures by substituting one Cr atom at the Ni or the Al-sites. In order to characterize site preference of Cr in M3AI, three different formalisms including standard defect formalism [3], antisite based formalism [7] and vacancy based formalism are used. Although the former two have been utilized widely in the literature to determine site preferences, the vacancy based mechanism has not been not commonly used.

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Table I. Intrinsic defect formation energies. Defect type

Designation

Defect formation energy 2x2x2 3x3x3

Other Studies

VaAi

Al vacancy

3.647

3.570

3.09[7],2.65[8]

VaNl

Ni vacancy

1.559

2.064

1.15[7], 1.87[8], 1.60[9],1.80[17]

NiAi AlNi

Ni antisite

2.096

1.957

0.986[3], 2.04[7]

Al antisite

-1.058

-0.838

0 -> AlNi + NiAi

Exchange

1.038

1.118

0 -> 3VaNl + VaAi

Schottky

8.323

9.764

0.742[3], -0.92[7] 1.729[3], 1.12[7], 1.44[8], 1.02[9], 1.15[10], 1.67[11] 6.54[7], 8.26[8], 6.50[9], 6.33[10], 6.73[111

[17] - Experimental study; [3,16] - ab initio DFT method [8,9] - First principles method; [10,11] - EAM potential method 2) Extrinsic defects: In the widely used standard defect formalism [3], the formation energies are calculated as per the definition below: E

CrM = l t e - „ 0 K

^CrAl

+

^ ) - t e ,

= P ^ x (^/(r_i)Cr) + PAI ) ~ \pNixAlY

+Mcr)\ +

Mcr ) \

The one with lower formation energy is the preferred sublattice for Cr. However, in this formalism, the choice of chemical potential of the elements can play an important role in the final results. The common practice is to use the cohesive energy of the elements as the chemical potential, which might not realistically reflect the real alloy condition. In both 32-atom and 108atom supercell, the calculated energies indicate that Cr prefers the Ni-sublattice in agreement with Jiang [16] and in disagreement with Seidman [3]. Various systems [1,7,16] have been studied by Ruban [1] and Jiang [7] using anti-site based substitutional formalism [7]. The mediator for the site substitution is anti-sites in this formalism. The parameter E^Al is defined as the energy required in moving Cr atomfromone sublattice to the other sublattice via a reaction such that the absolute value of the parameter is totally independent of the elemental reference states or its chemical activities. Ni(X_X}AlYCr + NixAlY -» NixAl^Y_^Cr + Ni^x_^AlYAl - E(Ni{x_l}AlYCr) - E(NixAlY) Em->Ai = E(NixAl{T_l)Cr) + EiNi^^A^Al) The formation energy of an exchange antisite defect in the M3AI structure i.e. Ni AI + Alm was calculated to be 1.038 and 1.118 for 2x2x2 and 3x3x3 supercells respectively. If the calculated value of E^~*Alis less than zero, then the reaction prefers going forward i.e. Cr prefers to go to the Al site, whereas if the value is greater than the exchange antisite energy, then the Cr prefers to go to the Ni site. If the value is in between the two, then the Cr atom has a compositionally dependent site preference.

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Our calculations suggested that Cr strongly prefers to go to the Al site in both the cases of 2x2x2 and 3x3x3 supercells. This confirms with the study of Jiang [16] that showed a discrepancy with the numbers back-calculated from data in ref [3]. Similarly, the mediation of vacancies is called vacancy based substitutional formalism. The parameterE ^ A l , as calculated below, is defined similar to the way it is defined in the antisite based formalism so that the absolute value of the parameter is totally independent of the elemental reference states or its chemical activities. In our case, we have studied the energy required in transferrin g Cr atom from Ni sublattice site to Al sublattice site. Ni(x_^AlYCr + NixALY_ù —» NixALY_J2r Al

E™-> = NixAl{Y_xfr

+ Ni,x_x\AlY

+ Ni{x_x)AlY - Ni{x_x)AlYCr -

NixAl{Y_x)

The formation energy of a schottky defect in the Ni3Al structure i.e. VaAi + 3Vam was calculated to be 8.323 and 9.764 for 2x2x2 and 3x3x3 supercells respectively. If the value of E^Alis less than zero, then the reaction obviously prefers going forward i.e. Cr prefers to go to the Al site, whereas if the value is greater than the schottky defect energy, then the Cr prefers to go to the Ni site. Else if the value is in between the two, then the Cr atom has a compositionally dependent site preference. Our calculations suggest that Cr shows a very strongly prefers to go to Al site. Discussion Calculations show inconsistency in the standard defect formation formalism. This discrepancy may be attributed to two reasons: insufficient definition of formation energy of the defect or unfair direct comparison of the calculated formation energy of different structures. The size of the supercell can't be compared directly with the choice of the reference state and the elemental chemical activity alone. Because of the different total number and types of atoms in both structures, the comparison becomes unusual. Same number of atoms on each side is a necessity in order to compare the formation energies. Table II. Site preference energies calculated from the standard defect formalism, antisite and vacancy mechanism with different super cell sizes. Our Calculations Other Studies Standard defect formation formalism 2x2x2 3x3x3 Seidman[3] Jiang[16]

Et El ..

Antisite based formalism z?Ni-*Al

1.193

1.363

0.565

1.33

0.946

1.212

0.648

1.29

Our Calculations 2x2x2 3x3x3 -0.917

-0.810

Other Studies Seidman[3] Jiang[16] 0.695

Our Calculations 2x2x2 3x3x3

Vacancy based formalism TrNi-+Al

-1.580

155

-1.585

-0.50

Negative formation energies in Table II indicates that both vacancy and anti-site based formalisms prefer Cr to go to the Al sublattice in y'-NisAl. Calculations suggest that the substitution process will be dominated by vacancy based substitution due to its larger negative value, -1.58 eV as compared to around -0.85 eV for antisite based mechanism. We also need to consider the concentration or the availability of the defects in order to determine the total reaction rate. From Table II, the exchange type defect formation energy is lower than the schottky formation energies, which indicate that antisite will have a much higher concentration than vacancy defects. As a result, Cr will be incorporated in Al sublattice through both vacancy and antisite based substitutionalmechanisms. The interaction between two Cr atoms in M3AI has been investigated. A 3x3x3 supercell was used in our calculations. The total energies of two Cr atoms were calculated as a function of distance of separation and the site occupied i.e. Ni-Ni, Al-Al and Ni-Al. Table III provides the calculated total energies versus the distance of separation between the Cr atoms. The decrease of the total energy as a function of the distance between the chromium atoms, in all three sites combinations indicates that chromium atoms prefer to be close to each other irrespective of the sublattices that they are sitting on. Table HI. Interaction energy as a function of Cr-Cr distance in different sublattices.

Sites of Substitution Ni-Ni site

Al-Al site

Ni-Al site

Formula Ni79Al27Cr2

Ni8iAl25Cr2

Ni8oAl26Cr2

NearsNeighbors No.

NN Distance

Energy (eV/atom)

3 rd

5.050À

2nd

3.571Â

-618.8253 -618.8822

1st

2.525Â

-619.5511

ord

6.185Â

-622.2315

^nd

5.050Â

-622.4081

JS.

3.571Â

-622.4581

ord

5.646Â

-620.7318

^nd

4.373Â

-620.9229

lSt

2.525Â

-620.9927

Conclusions To summarize, ab initio based computational approach shows that Cr atom has a strong preference for Al sublattice. Inconsistency in results indicated by the standard defect formation formalism is because of the incomplete definition and the choice of reference states. A strong preference for the Cr towards the Al site has been shown by both vacancy and antisite based formalisms with the prior being a dominant substitutional process. The interaction between two Cr atoms shows that the two Cr atoms will tend to be as close as possible to each other. Acknowledgement y We would like to acknowledgefinancialsupportfromthe Air Force Research Laborator (AFRL) and the Institute for Science and Engineering Simulation.

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References I. A. V. Ruban and H.L. Skriver, "Calculated site substitution in ternary y'-Ni3Al: temperatur e and composition effects," Physical Review B, 55 (1997), 856-74. 2. M. Donachie & S. Donachie, "Superalloys: A technical Guide," 2 nd edition, ASM international. 3. C. Booth-Morrison et al., "Chromium and tantalum site substitution patterns in M3AI (Ll2 ) y' precipitates," Applied Physics Letters, 93 (2008), 033103:1-3. 4. D. Shindo et al., "Site determination of Fe, Co and Cr atoms added in Ni3Al by electron channelling enhanced microanalysis," Transactions of the Japan Institute of Metals, 29 (1988), 956-961. 5. K. Hono et al., "Determinatio n of site occupation probability of Cu in N13AI by atomprobe field ion microscopy," Ada metallurgica et materialia, 40 (1992), 419-425. 6. M.K. Miller and J.A. Horton, "Site occupation determinations by APFIM for Hf, Fe, and Co in N13AI,"Scripta metallurgica, 20 (1986), 1125-1130. 7. C. Jiang, D. J. Sordelet, and B. Gleeson, "Site preference of ternary alloying elements in N13AI: A first-principlesstudy," Ada Materialia, 54 (2006), 1147-1154. 8. C.L. Fu and G.S. Painter, "Point defects and the binding energies of boron near defect sites in Ni3Al: a first-principlesinvestigation," Acta Materialia, 45 (1997), 481-488. 9. H. Schweiger et al., "Energetics of point defect formation in Ni3Al," Scripta Materialia, 46 (2002), 37-41. 10. Sun J and Lin D. L., "Theoretical and positron annihilation study of point defects in intermetallic compound Ni3Al," Acta materilia et Materialia, 42 (1994), 195-200. II. Mishin Y., "Atomistic modeling of the y and y'-phases of the Ni-Al system," Acta Materialia, 52 (2004), 1451-1467. 12. G. Kresse and J. Furthmuller , "Efficiency of ab-initio total energy calculations for metals and semiconductors using a plane-wave basis set," Computational Materials Science, 6 (1996), 15-50. 13. G. Kresse and J. Furthmuller , "Efficient iterative schemes for ab initio total-energy calculations using a plane-wave basis set," Physical Review B, 54 (1996), 11169-86. 14. J. P. Perdew, K. Burke, and M. Ernzerhof, "Generalized gradient approximation made simple," Physical Review Letters, 11 (1996), 3865-3868 15. Y. Amouyal et al., "On the interplay between tungsten and tantalum atoms in Ni-based superalloys: An atom-probe tomographic and first-principles study," Applied Physics Letters, 94 (2009), 041917:1-3. 16. C. Jiang and B. Gleeson, "Site preference of transition metal elements in Ni3Al," Scripta Materialia, 55 (2006), 433-436. 17. K. Badura and H. E. Schaefer, "Thermal formation of atomic vacancies in Ni3Al," Physical Review B, 56 (1997), 3032-3037. 18. M. H. F. Sluiter and Y. Kawazoe, "Site preference of ternary additions in Ni3Al," Physical Review B, 51 (1995), 4062-4073. 19. Y. H. Wen, J. V. Hill, S. L. Chen, J. P. Simmons, "A ternary phase-field model incorporating commercial CALPHAD software and its application to precipitation in superalloys", Acta Materialia, 58 (2010), 875-885.

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Informatics for M a p p i n g Engineering Data

Scott R. Broderick and Krishna Raj an Institute for Combinatorial Discovery & Department of Materials Science and Engineering, Iowa State University, 2220 Hoover Hall, Ames, IA 50011 Keywords: Informatics, Ashby Maps, Materials Design Abstract Since their inception nearly forty years ago, Ashby maps have demonstrated their value in providing guidelines for materials selection. Through the mapping of structure and property data through the use of dimensional analysis tied to phenomenological relationships, these maps have been shown to be a useful tool for classifying materials behavior. In this paper, we demonstrate how computational tools based on data mining and informatics methods can provide a new dimension to such maps by permitting the prediction of new materials and expected properties. The value of such methods rest in the fact that it can effectively fill in new information that is at present is missing in Ashby maps. It is proposed that informatics based methods provides the critical link to integrate data and information for computation and experiment in materials engineering.

Introduction A seminal development in materials discovery is the development of the so-called Ashby map [1]. Ashby maps present an empirical mapping of data, showing trends between and within classes of materials for a pair of properties. While Ashby maps do provide empirical trends, they are not predictive, in as much as the prediction of new materials. The primary benefit for Ashby maps is identifying the relationship between classes of materials, where clear trends are apparent when multiple engineering properties are plotted. An example is in Young's modulus versus density, as shown in Figure 1, with the polymer class which is the focus of this work highlighted. In this plot, foams, metals and composites have linear change in the logarithmic Young's modulus versus logarithmic density, while non-foam polymers form a different trajectory. This plot can be used to select the class of material, and whether the desire is primarily high strength (Young's modulus) or low weight (low density). While this map is good for selecting the appropriat e material class, it is of limited use for discovering new materials. That is, this map provides an empirical plotting only. The question we are asking here is if we can use informatics with the information plotted in the Ashby map to develop some design guidelines. To address this question, we use informatics to relate the basic descriptions of the materials to the properties and to assess the obvious correlation between Young's modulus and density. The focus in this paper is polymers, and specifically to relate

159

chemistry and molecular structure to Young's modulus and density. We present a new mapping of molecular structure descriptors, which can be coupled to the Ashby map to begin making it more predictive. We have previously identified structure-propert y relationships in polymer systems via experiment [2] and via computation [3]. Here we use informatics to identify structure-propert y relationships, with the added challenge of identifying descriptors which impact two highly correlated properties in different ways.

Figure 1. Ashby map for Young 's modulus versus density. Clear correlation between the two properties is shown. The different classes of materials are shown, in terms of their relative strength versus weight. The circled region (polymers) is the area of our focus in this paper. Figure adaptedfrom Reference [1]. A clear relationship between molecular structure descriptors and properties, including density, have been demonstrated [4,5]. This topological approach works through calculating properties or morphology of a polymer based on the structure, with calculations based on either additive group contributions or through graph theory where coefficients are calculated based on bonding configuration and electronic structure. We have gone even further and demonstrated that with the use of informatics, drug release kinetics of biopolymers can be modeled as a function of kinetic energy [6]. In this paper, we demonstrate a mapping of molecular structure descriptors, which can be used to screen for chemistries, and has implications for future modeling.

160

Informatics Description The informatics approach employed in this work is principal component analysis (PCA) [7,8]. PCA operates by performing an eigenvector decomposition of the data. As such, the principal components (PCs) capturing the most information are associated with the largest eigenvalues of the covariance matrix and their corresponding eigenvectors. The original data is decomposed into two matrices of interest for this paper: the scores (t) and loadings (/?). The scores matrix classifies the samples, in this case different polymer chemistries. The loadings matrix contains information on how the different descriptors (here molecular structure descriptors and properties) differentiate the samples. The PCA equation is summarized by the following equation, where E is the residual matrix and X is the input data matrix. X = t - pT + E

(1)

The typical approach for a data mining analysis is to construct the database so that different conditions constitute the rows of the database (X) while the responses compose the rows. However, this organization results in a limited understandin g of the underlying chemistry/physics and does not provide much guidance in a design sense due to the complexity of the polymer chemistries. By effectively considering the conditions as properties, we are able to begin to fully assess the role of molecular structure descriptors for a specific property criterion. The logic for determining the role of specific molecular structure descriptors on multiple properties with PCA is presented in Figure 2, where each point represents a descriptor in the loadings plot

Figure 2. A schematic of the interpretation of inter-correlations between descriptors plotted within PC-space.

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The descriptors analyzed in this work (comprising the columns of input data matrix X include: • • • • •

Chemistry, defined by percentage of each atom (C, N, O, H, S) Backbone structure, defined by percentage of backbone atoms/groups (C, N, O, S, amine ring, benzene ring) Side groups (CH3, O, benzene,....) Description of each bond as percentage of total number of bonds (C bonded to C, O and N; O double bonded to C, ) Property values (density and Young's modulus)

Each row of the matrix then represents a unique polymer chemistry / structure.

Results The result of the PCA analysis is shown in Figure 3. In Figure 3(a), we find that in PCI and PC2 (the two axes capturing the maximum amount of information on the system), density and Young's modulus have the same loadings values. That is, any change in the descriptors will impact density and Young's modulus the same. However, when we take PC3 into account (Figure 3(b)), we find that there is some difference between density and Young's modulus. The challenge becomes to extract these differences in the form of molecular structure descriptors which will impact one property but not the other property.

Figure 3. PC A loadings plot of molecular structure descriptors, density, and Young's modulus. In PC1-PC2, we find a very high correlation between density and Young's modulus so that no independent design guidelines can be discovered. However, in PC1-PC3, we find some difference between density and Young's modulus. Utilizing the logic presented in Figure 2, we define a direction within the PC space with a property which is correlated to Young's modulus, but is uncorrelated to density (Figure 4). We define this direction by first noting that the line connecting density and the origin represents very

162

high correlation to density. The line which is orthogonal to this line has then no correlation to density. However, points which fall on this line are still related to Young's modulus, as seen by the acute angle formed between the circled descriptors-origin-Young' s modulus. These descriptors (N bonded to two C and one H atom, composition of O atoms, and number of nonbackbone N atoms) should be much more correlated to Young's modulus than to density. Therefore, a new polymer designed to increase these descriptors should have higher Young's modulus relative to the change in density. A similar interpretatio n can be carry out on all points, and also for lowering density independent of Young's modulus and taken into account the interrelationships between the molecular structure descriptors.

Figure 4. Using the PC A result of Figure 3 to define descriptors which are related to Young's modulus, while being uncorrelated with density. The direction of maximum correlation with density is labeled "strong correlation with density, " while, following the logic of Figure 2, any points on the orthogonal line are uncorrelated with density, yet have some correlation with Young's modulus. While the PC1-PC3 plot does not utilize all of the information of the system, it does provide some basic design guidelines and can be used to suggest new chemistries for modeling. Additionally, it provides a clear mapping of the relationship between descriptors, which is necessary due to the complexity of the system, where changing one descriptor impacts all of the descriptors. Therefore, we propose that the integration of this mapping approach with the Ashby maps can lead to a more powerful design tool.

163

Summary We have developed a new approach to identify molecular structure descriptors which can be used to tailor a polymer property independent of correlated properties. Several descriptors were identified which are proposed to improve Young's modulus without impacting the highly correlated density. This mapping serves to integrate data of different length scales and to assess highly complex chemistry-structure-propert y relationships in polymer systems.

Acknowledgements The authors acknowledge support from the National Science Foundation: NSF-CDI Type II program: grant no. PHY 09-41576 and NSF-AF grant no. CCF09-17202, and Army Research Office grant no. W911NF-10-0397. KR would also like to acknowledge support from Iowa State University through the Wilkinson Professorship in Interdisciplinar y Engineering.

References [1] M.F. Ashby, Material Selection in Mechanical Design (Oxford, UK: Elsevier, 1992) [2] S.R. Broderick, J.R. Nowers, B. Narasimhan, K. Rajan, Journal of Combinatorial Chemistry. 12 (2010), 270-277. [3] K. Wang, M. E. Glicksman, K. Rajan, Macromolecular Rapid Communications. 25 (2004), 377. [4] J. Bicerano, Prediction of Polymer Properties (New York, NY: Marcel Dekker, 2002) [5] W.V. Krevelen, Properties of Polymers (Oxford, UK: Elsevier, 2009) [6] X. Li, L. Petersen, S. Broderick, B. Narasimhan, K. Rajan, ACS Combinatorial Science. 13 (2011), 50-58. [7] P.V. Balachandran , S.R. Broderick, K. Rajan, Proceedings of the Royal Society A. (In Press) [8] S.R. Broderick, H. Aourag, K. Rajan, Statistical Analysis and Data Mining. 6 (2009), 353360.

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1st World Congress on Integrated Computational Materials Engineering Edited by: John Allison, Peter Collins and George Spanos TMS (The Minerals, Metals & Materials Society), 2011

Microstructural Property Considerations in the Design of Stainless Steel Articles Case Hardened by Low-Temperature Carburization Jeffrey M. Rubinski1, Sunniva R. Collins1, Peter C. Williams1 Swagelok Company; 318 Bishop Rd.; Highland Heights, OH 44134, USA Keywords: austenitic stainless steel, low-temperatur e colossal supersaturatio n (LTCSS), carburization , mechanical design,finiteelement analysis, tube fitting Abstract Low-temperatur e carburizatio n is a patented, diffusional surface hardening process applied to austenitic stainless steels and other alloys. Swagelok has used this technology for the back ferrule design of its advanced geometry tube fitting since 1999. In this process, the formation of carbides is kinetically suppressed, enabling extremely high or colossal carbon supersaturation . Surface carbon concentrations in excess of 12 atomic percent are routinely achieved. Treated stainless steel articles show a uniform and conformai hardened surface gradient at least 25 microns thick, with a near surface hardness of -1200 HV (over 70 HRC). This treatment increases the surface hardness by a factor of four tofive,improving resistance to wear, corrosion, and fatigue, with significant retained ductility. An interesting design consideration is that a carburized surface can strengthen the elastic-plastic behavior of an article. A designer must draw from this knowledge when optimizing the profile or topology of an article to achieve a desired mechanical response. A combination of tensile coupon tests and inverse finite element methods are seen as key elements of the design process. This paper will describe the finite element approach used to determine an effective stress-strain response for the hardened surface layer in a 316 S S material and how low-temperatur e carburizatio n aided the successful development of the patented hinging-colleting action of the advanced geometry Swagelok® tubefittingback ferrule. Introduction The inverse finite element approach for determining the constitutive behavior of materials has , the technique is very useful for been used morefrequentlyover the past decade. In particular characterizin g the true stress versus true strain relationship for ductile materialsfromthe onset of necking to fracture[1]. Methods for characterizin g the behavior of a carburized surface layer have been published that include using electric resistance strain gauges on 4-point bend test with X-ray diffraction techniques [2] and the blending of nanoindentatio n methods with inverse finite element analysis (FEA) [3]. The main difficulties associated with these approaches are their high cost and sophisticated experimental setups. Therefore, we looked for a simpler approach to obtain the stress-strain behavior of the carburized surface layer using a standard round bar tensile test, commonly performed in industry, and inverse FEA, to predict effectively the mechanical response of a surface treated Swagelok tube fitting back ferrule whose application requires plastic deformation of the core material.

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Preparation of Tensile Specimens [4] Studies of the bulk mechanical properties of low-temperatur e carburized stainless steel were performed using standard ASTM E8 geometry involving circular bars with a 31.75-mm long gauge section of 6.35-mm diameter. The wrought rods were carburized in the cold worked condition. The process was performed at temperature s low enough to avoid the formation of carbides, but for a sufficient time to allow carbon diffusion to occur. This process results in a hardened conformai case on the treated parts, approximately 20 to 30 microns thick, without distortion or change to dimension. Illustrated in Figure 1(b), carbon concentration profiles using X-ray diffraction (XRD) patterns and applying the Nelson-Riley(cos#cot#) correction show carbon levels in excess of 10 atomic percent in treated 316 stainless steel. These carbon levels were also confirmed by glow discharge optical emission spectroscopy (GDOES). A microhardnes s profile, as a function of depth, was obtained and showed hardness values reaching 1200 HV (70 HRC) at the surface, dropping to the value of the base material (300 HV or 23 HRC) at 25 microns. A residual stress profile, shown in Figure 1(b), was generated fromXRD measurements of the expanded austenite lattice and a relation between stress, a11, Vickers hardness, H, and the strain hardening exponent, n, in Eq. 1 [4, 5].

^n=f(o.ir

(a)

(1)

(b)

Figure 1. Microstructura l evaluation of low-temperatur e carburized 316 stainless steel. [4] (a) X-ray diffraction (XRD) of different depths within the case, obtained by serial removal of the surface via electropolishing. Note the peak shift to the left fromuntreated specimen to carburized surface, indicating lattice expansion. No peaks associated with carbides are evident in the case. (b) Microhardnes s profile as a function of depth. Measurements were takenfrommultiple componentsfroma single process run. Superimposed curves of carbon concentration (Xc, at. %) and residual compressive stress (a11, GPa) are obtainedfromthe XRD spectra shown in Figure 1(a).

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Results of Experimental Tensile Tests [4] The tensile test results reported the 0.2 % tensile yield stresses for the nontreated and carburized specimens to be 552 and 593 MPa, respectively. No significant embrittlement was observed in the hardened surface layer, but a mild decrease in ductility was caused by the carburization treatment, as shown in Figure 3(a). Michal et al. [4] confirmed through additional experiments that the hardened surface layer does not contribute to a higher 0.2 % yield stress. In fact, the 465°C paraequilibriu m heat treatment, without the use of carburizing gases, was responsible for the change of approximately 4 % in the 0.2 % yield stress; increasing from 648 MPa in the nontreated state to 675 MPa in the heat-treated but not carburized state. The results indicate a tempering effect caused by the paraequilibriu m process that redistributed the initial carbon content (0.23 atom %) in the nontreated core that delayed the onset of microplasticity. Finite Element Model A two-dimensional, half-symmetry, axisymmetric model of the round bar tensile specimen was built and simulations were carried out using ABAQUS/Standard v6.9-l. One thousand six hundred four-noded, two-dimensional axisymmetric reduced integration (CAX4R) elements were used to represent the core material, i.e. cold-worked 316 stainless steel. One-dimensional shell elements with 5 integration points through the thickness (25 microns) were used for the carburized surface layer, and were placed on the outer perimeter of the geometry as a skin reinforcement, as shown in Figure 2. Unique elastic-plastic material properties were assigned to the core and carburized regions of the model using Mises yield surface (J2 plasticity) with isotropic hardening [6]. A displacement boundary condition was applied along the larger diameter shank of the specimen geometry, while a symmetry boundary condition was placed at the right side of the geometry to prevent rigid body motion and to allow necking to occur. By a trial-and-erro r method, the finite element model was used to determine the individual stressstrain relationship for the carburized surface layer."

Figure 2. Finite element model of tensile specimen, (a) Undeformed state, (b) Deformed state

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Inverse Finite Element Approach for Determining Effective Stress-Strain Curve of Carburized Surface Layer To implement the inverse finite element approach easily, the Ludwik equation, Eq. 2 [7], was used to generalize the mechanical response of the core material and hardened surface layer: a = G0+Ksnp

(2)

where a is true stress, a0 is initial stress, K is the strength coefficient, sp is true plastic strain, and n is the strain hardening coefficient. Tabular * Plastic data was generated fromEq. 2 and an iterative process of running multiplefiniteelement simulations, with various combinations of aD, K, and n, was performed until good agreement was achieved between the experimental stressstrain curves and the analytical stress-strain response predicted by the model. The process started with establishing baseline behavior of the nontreated 316 stainless steel material. Before initiating a search for the material constants of the carburized surface layer, the strengthening effects of the paraequilibriu m heat treatment, without carburizing gases, of the core material, were accounted for by increasing the initial stress, a0 , by 4 %. Next, the core material constants were held fixed while the appropriat e values for the carburized layer were determined through modeling to match experimental results. As depicted in Figure 3(a), finite element analysis suggests that the carburized layer possesses appreciable strain hardening characteristic s to achieve good correlation with experimental results within the range of 5 to 20 % engineering strain. To improve the finite element prediction of ductility beyond 25 % engineering strain for the carburized tensile specimen, perfect plasticity beyond 20 % true plastic strain for the low-temperatur e carburized surface layer is necessary, portrayed in Figure 3(b). Scanning electron microscopy of the surface within the neck region of the failed tensile specimens show profuse slip traces, (Figure 4)[4], with no decohesion of the treated layer, and provides physical justification for applying perfect plasticity behavior to the material model of the carburized surface layer. Thefinalmaterial constants are displayed in Table I.

(a)

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(b) Figure 3. Experimental and FEA-determined stress-strain curves. (a) Comparison between experimental and inverse FEA-determined engineering stress-strain tensile responses. (b) Comparison of true stress-strain responses for nontreated 316 SS, paraequilibriu m heat treated 316 SS, and low-temperatur e carburized surface layer of 316 S S determined by inverse FEA.

Figure 4. Scanning electron micrograph of plastically deformed carburized surface. [4] Profuse slip traces of a low-temperatur e carburized 316 S S tensile specimen. The treated material retains its austenitic structure, as well as its ductile deformation characteristics. Table I. Material Constants Determine d by Inverse Finite Element Method n K (MPa) 316 SS Material Condition a 0 (MPa) 635 Nontreated Strain-Hardene d 865 0.8 662 0.8 Paraequilbriu m heat treatment only 865 0 3800 0.45 Low-temperatur e carburized surface layer

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Case Study: Optimization of Swagelok Tube Fitting with Finite Element Analysis Using Effective Stress-Strain Properties for Carburized Surface Layer During the early stages of the design process, when the complete surface hardening was initially applied to a traditional back ferrule design, it presented several drawbacks. First, installation torque increased because the surface-hardened , traditional back ferrule design was less able to flex or bow into position. As a result, the standard 1 1/4 turns assembly of the development prototypes required more effort and demonstrated reduced tube grip performance. Therefore, finite element modeling enabled the rapid development of a back ferrule geometry that leveraged the improved surface hardening process. After several iterations of the finite element model, the final profile of the ultimately commercialized back ferrule was achieved which resulted in a patented hinging-colleting design and improved performance margins in gas seal/leak integrity, vibration resistance, and tube grip. Figure 5 shows the finite element model of the back ferrule and tube connection after the nut is assembled to the required 11/4 turns. A cross section verified the accuracy of the model.

Figure 5. Swagelok Tube Fitting Finite Element Simulation Comparison between the FEA-predicted elastic-plastic response of Swagelok tube fitting back ferrule and the mounted micrograph of cross-sectioned Swagelok tube fitting properly assembled at 1 1/4 turns. References 1. Y. Bao, "Prediction of Ductile Crack Formation in Uncracked Bodies" (Ph.D thesis, Massachusetts Institute of Technology, 2003), 84-89. 2. A.C. Batista and A.M. Dias, "Characterizatio n of Mechanical Properties in Surface-Treated Materials," Journal of Testing and Evaluation, 28 (3) (2000), 217-223. 3. N.A. Branch, et al., "Determinatio n of constitutive response of plastically graded materials," Int. J. Plasticity (2010), doi:10.1016/i.iiplas.2010.09.001 4. G.M. Michal et al., "Carbon supersaturatio n due to paraequilibriu m carburization : Stainless steels with greatly improved mechanical properties," Ada Materialia, 54 (2006), 1597-1606. 5. J.R. Cahoon, W.H. Broughton, and A. R. Kutzak, "The Determination of Yield Strength From Hardness Measurements," Metallurgical Transactions, 2 (1971), 1979-1983. 6. Dassault Systèmes ABAQUS Theory Manual v6.9-l. 7. Y. Berström, "A Dislocation Model for the Plastic Deformation of Single-phase Alpha-iron" (Paper 1 ,www.plastic-deformation.com , 2010).

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1st World Congress on Integrated Computational Materials Engineering Edited by: John Allison, Peter Collins and George Spanos TMS (The Minerals, Metals & Materials Society), 2011

Deformation twin induced by multi-strain in nanocrystalline copper: Molecular Dynamic Simulation Kaiguo Chen1, S Q Shi1, J Lu2 department of Mechanical Engineering, Hong Kong Polytechnic University; Hung hung, Kowloon, Hong Kong, China 2

College of Science and Engineering, City University of Hong Kong, Hong Kong, China Keywords: Multi strain, Nanocrystalline copper, Deformation twinning. Abstract

A multi-strain deformation model is introduced to MD simulation. Abundant nanosized deformation twin (DT) lamellas are developed during shearing after compression to the elastic limit. DTs are nucleated through two different mechanisms facilitated by Shockley partial slips. A process for DT nucleation and its reaction with Shockley pärtials are observed in this simulation. Introduction Continuous efforts have been made for centuries to try to simultaneously improve both strength and ductility of structura l materials made from metals and alloys. It is widely accepted that the generations of, and the interactions among internal defects control materials mechanical properties. Such defects include atomic vacancies and interstitials, dislocations, grain and interface boundaries, stack faults, voids etc.. Recently nanoscale twin boundary has attracted scientists' interests after K Lu's work [1, 2] on pulsed electro-deposited nanotwinned copper. Nanotwinned copper, with nano twin boundaries (twin spacing is less than lOOnm) in ultrafine or nanocrystalline copper, shows a significant higher strength with good ductility [2-5] than its ultrafine counterpart . The deformation mechanism of nanocrystalline metals with preset nanotwins has been investigated by molecular dynamic simulations [6-8]. These simulations showed that the impediment to dislocation slip by twin boundaries results in an enhancement of strength, while the accommodation of dislocation slip along twin boundaries gives an interpretatio n of the considerable ductility. As nanotwin provides a feasible way to produce materials with a combination of high strength and considerable ductility, scientists are keeping seeking more methods for producing nanotwinned ultrafine and nanocrystalline metals besides electro-deposition method. Severe Plastic Deformation (SPD) at high strain rate and very low temperatur e has been recently investigated and is confirmed to be able to produce bulk materials with nanoscale twin [9, 10]. A classic model [11] suggests that low temperature , high strain rate, and low stacking fault energy (SFE) help DTs' nucleation during plastic deformation and could explain the experimental results [9, 10]. This model also gives an inverse relationship between DT nucleation stress and grain size, which suggests that DT

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nucleation stress will be very high when the grain size is less than lOOnm. For FCC metals with medium and high SFE, it was generally believed that the nucleation of DT is impossible when the grain size is smaller than 1 micrometer. However, through the development of nanocrystalline metals synthesis technology in recent years, DT was found to be a possible plastic deformation mechanism in nanocrystalline metals after a MD prediction of DT nucleation in nanocrystalline aluminum [12] with very high stacking fault energy (SFE). Recently, nano twin was developed in the nano crystalline structure of a metal surface treated by Surface Mechanical Attrition Treatment (unpublished). MD simulation has been widely implemented in investigating deformation mechanisms of nanocrystalline metals. In a MD simulation, whether the deformation mechanism is dominated by partial/full dislocation travelling through grains or through the generation of DT may be understood on the basis of generalized planar fault energy curve (GPFE) [14]. For aluminum, with a very high SFE but a low ratio of unstable twin fault energy barrier (UTF) to SFE, DT is always observed in MD simulation. However for copper, with a much lower SFE but a much higher unstable twin fault energy barrier (higher ratio of UTF/SFE) due to the atomic potentials used, DT was not expected and rarely observed in MD simulation. Only through carefully designing the orientation of grains in nanocrystalline (NC) copper sample, can high enough shear stress along the slip direction overcome the unstable barrier for DT nucleation [13]. In our work, a multistrain deformation model is firstly introduced to MD simulation to generate DTs in NC copper. Our results predict that shearing an appropriatel y pre-deformed bulk NC sample could generate abundant nano twins. Model A 3D NC copper sample was generated by a modified voronoi method developed by Chen [15]. The sample has 8 grains in a 20nmx20nm> is the angular frequency, k is the wave number, E is the elastic modulus, p is the density, and c is the sound velocity. In materials which are highly attenuating, the particle velocity and particle displacement can be out of phase, causing the elastic modulus and density

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of the material to be complex and dispersive in nature (i.e. frequency dependent). For many materials, the attenuation coefficient is fairly small (i.e. a«co/c), which permits the simplification in Equation 1 to be made. In general, the speed of sound is proportiona l to the square root of the elastic modulus divided by the density of the material. In practice, the ultrasonic velocity of a material can be determined by measuring the ultrasonic wavelength at a known frequency (c = Xf) or the time t taken by the wave to travel a known distance d (c = d/t). Ultrasonic Attenuation Ultrasonic attenuation occurs when energy is lost in an ultrasonic wave as it travels through a material. It is primarily caused by absorption, scattering, diffraction, and to a lesser degree by thermodynami c relaxation. Ultrasonic scattering is often the dominant factor for attenuation in heterogeneous materials, where the ultrasonic wave is scattered by discontinuities in directions other than that of the incident wave. Measurements of ultrasonic absorption/scatterin g can provide information about particle concentrations, viscosity, and microstructure . The contribution of ultrasonic scattering is also determined by the volume fraction of dispersed particles/scatterers , and can result in dispersion and phase variations in the ultrasonic velocity. The attenuation coefficient (a) of a material is a measure of the decrease in amplitude of an ultrasonic wave as it travels through a distance x, and can be expressed (in nepers per meter) as: A = A0- exp(-a • JC) .

(2)

Reflection at a Boundary, Acoustic Impedance, and Ultrasonic Scattering When an ultrasonic wave impinges normally on a boundary between two different materials, it is partially reflected and partially transmitted . The ratio of the amplitude of the reflected wave (Ar) to that of the incident wave (Ai) is called the reflection coefficient (R), which can be written as: R=

^~{zl

+ z2)'

(3)

where the subscripts 1 and 2 refer to the material the wave travels in and reflects from, respectively, and where Z is the acoustic impedance of the materials, where Zi = pjcj. If the materials have very different impedances, most of the ultrasound is reflected. Like the ultrasonic velocity and attenuation coefficient, the acoustic impedance is a fundamental physical property of the material, influenced by the composition and microstructur e of the material concerned. The scattering of ultrasound can have a significant effect on the elastic and ultrasonic properties of a material, making the velocity, attenuation, and impedance dependent on particle sizes, microstructure , and concentration levels. On a macroscopic scale, the ultrasonic response of a heterogeneous, scattering material can be described in a statistical sense, where the attenuation or phase velocity is based on a mean ultrasonic field. Classical, first-ordertheories predict three different scattering regimes based on the ratio between the size of the scatterer and the ultrasonic wavelength [6]. These include the Rayleigh regime where xo«l, the stochastic regime where l<xo99%, (i5o=l.5 urn). Since the SiC network ceramic is a very promising material for high temperatur e structura l applications and reinforcement in the SiC/Fe-2Crl3 composite materials, the composite has the excellent mechanical properties and thefrictionbehavior, and can be used as

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the brake disc material. The microstructur e of SiC/Fe-2Crl3 composites is shown in Fig. 1. The bright phase is the Fe-2Crl3 matrix, and the dark phase is the SiC network. The analysis is carried out for models of the SiC/Fe-2Crl3 composites shaft brake disc shown in Fig. 2. The disc is screwed on the hub, which is set upon the axle of the train wagon. During the analysis only one part of the working cycle is considered, and the process of heating and cooling is discussed. The paper is focused on the stress analysis of a brake disc considering centrifugal and thermal load. 2 Numerical Models 2.1 Modeling and preparing the 3D model In this analysis two models of the disc are considered (a) the brake disc without wear; (b) the brake disc with a 5 mm wear on each side. 2.2 Determination of the load The load is applied when braking down from the maximum speed of 380 km/h to a standstill shown in Fig.3. The initial temperatur e of the brake disc and the surrounding is 50 °C. The goal is to find out the distribution of the temperatur e in the brake disc. The deceleration factor is 0.77 m/s2. The part of the braking energy that transfers on the surrounding air is not considered. The main reason for this is the high braking power which causes the dominant effect of the heat flux. An assumption is made that the heat flux uses the convection with a heat transfer coefficient of 10 W/m2 K [3]. Additionally, the effect of the humidity in the air and the heat transfer with radiation are not considered. 2.3 Determination of the physical model Braking on the flat track derives from the physical model for determination of the heat transfer in dependency from the braking time. Besides that, the weight distribution of the vehicle is considered. The weight arrangement is 60/40 [4] in the favor of the front part of the carriage. This means that the front part of the carriage takes 60% of the whole load. In our case only 10% of the whole brake force is applied to one disc from the front part of the carriage. Because of the mentioned weight distribution, only the front part of the carriage is analyzed. Every carriage consists four axles with three brake discs attached to each axle. The kinetic energy [3] for one wheel considering constant deceleration is:

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Fig.3 Stop braking load

0,1 • 1 • M • vl = £ P{t)dt = 2 • F ^ £ vt dl(0 500°C to strip thicknesses of 3 to 7 mm [5]. The coarse grain structure is compressed and usually begins to recrystallize. Particularly brittle constituent particles break up into small pieces affecting formability, also of the final product. A fine grain size, particle distribution and specific (cube) texture is achieved in multi-stand tandem hot-rolling mills, including "self annealing" to a fully recrystallized state. The process can now be simulated in great detail and applied to develop and improve process technology (e.g. [4,5]) and product quality (besides flatness, profile and surface). Annealins: Annealing is applied in-between or after forming steps to reduce strain hardening in non-age hardening alloys. Here recovery and recrystallization softens the material and may generate a new grain structure and texture. The mechanisms involved strongly depend on the

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previous process history and can be simulated in high accuracy. Age hardening alloys, as often used in extrusion, require an ageing treatment of the super-saturate d quenched microstructur e to generate the most efficient nano-particles for increased strength. The optimum ageing anneal leading to a peak hardness depends on the alloy and the preprocessing as well as on a dedicated furnace practice and is simulated accordingly. Industry and academic cooperation in the VIR* Projects In the VIR* projects the scientific challenge was to link existing (or develop new / better) quantitative models that describe the microstructur e evolution and related material properties. The technological challenge was to establish a framework for integrated microstructur e models that applies them to industrial processes. This required major communication efforts between plant and R&D engineers of different, highly competitive companies, in the individual processes involved, and their counterpart s in the academic consortium in scientifically competitive areas of process simulation and physical modelling. The VIR* consortium managed to meet these challenges, forming a strong community with fruitful and most efficient co-operations /2-4/. Several long term co-operation's existed before between some industrial partners and academic partners. Their specific expertise helped to integrate the different views on the problems encountered and define the corresponding activities. However, the differences in R&D focus of the industrial and academic partners required major efforts in start-up communication, co-ordination of expertise, goal setting and work package co-operation, in the first project period, as well as in its final exploitation. Table 1) The VIR* industry and academic partnerships and their main activities Industrial R&D • * * • * *

Corus Mean Pechiney SAPA Hydro VAW

«

Raytek

■:::>

- ■

:.-.-> =}

:::>

- ■

main activities

Academic partner

PSC, lab/plant rolling (TPM) /* Charakterization / FEM simulation /* Characterization (particles) /* Characterization (recrystallization) Simulation, experiments (extrusion) /* Simulation, experiments (TPM) 1*

o o o o o o o c>

Temperature sensor (prototype)

=>

/* Material supply

NIMR IMMPETUS EMSE SIMR NTNU IMM IBF (Uni Brandenburg

main activities ■ = >

Microchemistry (TEP)

= WP#5

FEM simulation = WP#6 =>particle break-up = WP#5 ::.-> Characterization -^AlFlow /AlSoft (TPM) == WW PP ## 33 :::,TPM: 3IVM, GIA, StaRT = W P # 4 ^ > r> FEM simulation,interface= WP#1,6

) ^

new temperature sensor = W P # 7

= WP#2

Table 1 lists industry and academic partnership s within the VIRFAB project. Industry contributed mainly in problem definition 151 (parti), material supply, plant and lab trials and material characterisation . For process integrated simulations several modelling approaches and material characterisatio n methods were evaluated and benchmarked before the suitable ones were further developed, adapted to the aluminium specific aspects and then linked and applied in the verification experiments of the "Through-Process-Model " 151 (part3). Industrial application of "TPM" Through Process Modelling The models established were tested on an industrial scale for the process chain of aluminium sheet production of sheet rolling and extrusion in several "TPM" trials :

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• • •

AA3103 : material produced within VIRCAST by Hydro / rolling trials on the equipment of a reversing hot rolling line of Corns / Koblenz / Germany) AA5182 (material from Elkem / rolling trial on the 4-stand hot tandem rolling mill of Alcan/Hydro at AluNorffGermany) . 6060, 6082 profiles processed by Hydro/NTNU/Trondhei m & Sunndalsoera/Norwa y

The applied blind simulations of the TPM exercise produced data on microstructur e (dislocations, particles, crystallographi c texture) and properties (strength, formability, anisotropy). The alloys and processes give a broad spectrum of properties - from soft to hard, in combination with formability and specific microstructures . The results showed that besides the chemical composition - the integration of material properties to control the parameter s of the thermo-mechanica l processes involved is essential. An effective TPM-tool requires clear communication between various sub-models. These have to run numerically stable and converge in acceptable computing times to make necessary adjustments upstream in the processing chain The models used are no longer an empirical (intelligent) curve fitting of data obtained under laboratory conditions and translated to plant conditions, but of a more fundamental level and require the input of specific - physically based - parameters . These had been obtained also from lab experiments, but evaluated accordingly, based on physical principles, so they yield generally valid results, capable for extrapolation to other process or alloy constitutions. The accuracy of these models depends on the depth of physical details (variables). Here a compromise is usually made between the accuracy needed and the applicability of models. Nevertheless, some conventional empirical predictions limited to pre-defined conditions have now been replaced by physically based models, as e.g. the classical flow stress simulation. It now can be based on dislocation models (3/4IVM, AlFlow, -Soft /13/), including aspects of alloy variations, inter-stand and subsequent softening effects. This allows to couple deformation, annealing and sheet forming processes. Also deformation (and recrystallization ) texture evolution (GIA, StaRT /14/) and their effect on rolling force can now be considered, where it has significant influence, besides classical (anisotropy) property predictions /15,16/.

Figure 3. The VIRFAB - TPM simulation tool box is composed of empirical and physically based models [17].

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The full integration of the models into a network of industrial process simulations (Fig.3) is now realized individually by the different industries with their different processes (reversing or tandem hot rolling, fast or slow cold rolling, extrusion, coil or batch annealing, e.t.a.). They now are able to link the complete production chain and predict material properties in any process step and the elements developed are now successfully applied and prove their value. This is the major success of the VIR* projects to initiate and support the transition from the traditional "plant guided (R&)D " (i.e. on-site development of processes and products on plant equipment) and conventional "laboratory guided R&D" (i.e. off-site investigations and laboratory experiments on down-scale equipment) to the new methods of "computer guided R&D" (i.e. on/off-site PC based process simulation with integrated material models, deduced from plant and lab data) /17/. This new method is the result of the VIRFAB project that provides the new (prototype) tools for quantitative simulation of material properties within process models and process and prototype production by computer simulation [18]. Using defined state variables and their evolution throughout the process chain, it is possible to derive the resulting properties of a material in intermediate stages or in the final condition. Since specified properties have to be delivered to customers their prediction is the main motivation of through process modelling [19]. It allows the variation of alloy- and production conditions to adjust these properties or to develop more efficient production chains. Table 2: Key requirements on alloys treated in VIR[*] ref/19/

In VIR[*] a range of alloys for specific products have been defined with their key performance requirement s listed in table 2. These data can now be linked to a model that gives a quantitative description based on physical parameter s and relates properties with

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specific microstructure s for a range of alloy variants. For some cases specific features can be further evaluated (like earing simulation in can-body sheet [16]) but the general application of models to a general applicable quantitative description of the main features is main benefit of a full through process model linked to the casting and forming project. 6.

Summary and outlook

The "Virtual" fabrication projects l\ AI are an excellent example for successful ICME. Within this project, the connection of material related simulation tools to the mechanically related processing tools was established. Since then, the couplings have further been developed by companies individually and implemented to optimize their specific processes with suitable integrated (empirical and/or physical) models to predict related properties. They now support applied research and help to improve industrial production processes and resulting product quality, to design most efficient fabrication and processing routes and reduce significantly the number of expensive test runs in productive plants, thus reducing cost and time to market of new products and processes. They can easily adapt new "physically based" material models, formulated in suitable quantitative form, to be integrated into advanced process simulations. These new methods are now being implemented and will affect future scientific research and application and influence the Aluminium producing industries, e.g. in their research and development strategies, time and efficiency, know-how development and exploitation, inhouse education and training, manufacturin g flexibility, equipment design and process and quality control. The main VIR* project achievements and industrial benefits are : o o o o o o o o o o o o o o o

Through process modelling capabilities Predict resulting material properties in any step Test / verify new alloys and new processes conditions Illustration of complex process interactions Clarify effects at inaccessible processing steps Make production processes more flexible and efficient Design and assess of new process equipment Monitor process parameter s and product quality Assess special process conditions and alloys Introduce and test new (quantitative) scientific results Document and conserve technical know-how Teach scientific know-how (fundamental and application) Train engineers off-line (university and plant based) Establish and improve industry - academic interaction Standardisatio n of microstructur e characterisatio n

The VIR* project results provided a better understandin g of the conventional economically most relevant wrought aluminium alloys and products, the material characteristic s and the development of quantitative physically based models of microstructure s and property evolution during production processes, customer applications and forming operations. "Virtual" fabrication defines a new tool developed that is able to describe the relevant processes with integrated microstructur e evolution. They can be adapted to the specific parameter s of many fabrication or processing route and applied to many purposes, such as: > Improvement of industrialproduction processes and product quality > Improvement of R&D quality for process and product optimisation > Design of microstructura l states and resulting specific material properties

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> > > > >

Design most effective and efficient fabrication and processing routes Significantly reduce the number of expensive test runs in productive plants Reduce cost and time to market new products and processes Standardize aluminium alloys for application and to enhance recyclability Support customer application by material data from the production line

The new methods has changed the European Aluminium producing industries in issues like know-how development, manufacturin g flexibility, equipment design and quality control, in-house education and training, research and development. A cknowledgements Thanks to all EAA companies and R&D colleagues that contributed to the success of the VIR* projects.The VIR[*] projects were carried out under the EU 5th FP : VIR[CAST] (Contract No. G5RDCT-2000-00153), VIR[FAB] (Contract No. G5RD-CT-1999-00132), VIR[FORM] (Contract No. G5RD-CT-1999-00155). References : [I] [2] [3] [4] [5] [6] [7] [8] [9] [10] [II] [12] [13] [14] [15] [16] [17] [18] [19]

The VIR[*] projects ; EU 5th FP Contracts : VIR[CAST] (G5RD-CT-2000-00153), VIR[FAB] (G5RD-CT-1999-00132), VIR[FORM] (G5RD-CT- 1999-00155). Zeitschrift Aluminium,Vol.78/10 2002 (special VIR* mid term-conference edition) p.816-937 Zeitschrift Aluminium,Vol.80/6 2004 (special VIR* end -conference edition) p.550-752 "Virtual Fabrication of Aluminium Products", edt. by J.Hirsch, (2006) Wiley-VCH Verlag, Weinheim, ISBN: 352731363X, SKU: 352731363X J.Hirsch, Kai F. Karhausen, Olaf Engler in "Continuum Scale Simulation of Engineering Materials, Fundamentals-Microstructures-Proces s Applications" edt. by D.Raabe, F.Roters, F.Barlat, Chen, Long-Qing 2004, ISBN 3-527-30760-5 - Wiley-VCH, Weinheim, p.705 M.Rapaz, in ref. [7] p.559 and Q. Du, A. Jacot ibid p.634, and A. Jacot in ref. [3] Y.J.Li, A.Johansen, S.Benum, C.J.Simensen, A.L. Dons, A.Hakonsen, L.Arnberg in ref. [3] p.578 and same authors, ibid p.583 M.Serriere, CH.A.gandin, M.Dehmas, E.Gautier, P.Archambault ; in ref. [3] p.592 L.Löchte, M.Schneider, G.Gottstein; in ref. [3] p.685 A.L.Dos, K.pedersen, O.Lohne, T.Petersen, A.Bigot in ref. [4], p.640 A. Miroux, Z.J. Lok, E. Anselmino, A.Fleming,A.Bigot, E.Janot, J.Hagstrom, C.Liu, J.H.Driver, H.Klöcker, A.L.Dons, L.Loechte, S. van der Zwaag; in ref [4], p.654 T. Pettersen, T.Furu in ref. [4] ], p.65 B.Holmedal, E.Nes and K.Marthinsen in ref. [5], pl29 P.v.Houtte, S.Li, O.Engler in ref. [5], pl77 O.Engler, J.Hirsch, S,Kalz in ref. [5], pl89 O.Engler, K.Karhausen , J.Hirsch, ASM Handbook, Volume 22A (2010), edt. D.U.Furrer, S.L.Semiatin et.al. Materials Park, Ohio ISBN-10: 1-61503-001-8, pp.510-521 J.Hirsch, K.F.Karhausen , L.Löchte, proc. ICAA8 Cambridge/UK ; Materials Science Forum Vol. 396-402 Transtec Publications, Switzerland, (2002), pl721 J.Hirsch in "Fundamental s of aluminium metallurgy: Production, processing and applications" Edt. by R Lumley; Woodhead Publ. Ltd, UK, (2010) ISBN: 978184569 654 2, p 721 K.F.Karhausen , J.Hirsch, in ref. [5], p315

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1st World Congress on Integrated Computationa l Materials Engineering Edited by: John Allison, Peter Collins and George Spanos TMS (The Minerals, Metals & Materials Society), 2011

ICME Success at Timken - The Virtual Fatigue Life Test Patrick I. Anderson1, Xiaolan Ai1, Peter C. Glaws1, Krich Sawamiphakdi1 !

The Timken Company, P.O. Box 6930, Canton, OH, 44706, USA Keywords: Steel, Fatigue, Inclusions Abstract

Many strategic decisions on issues important to the Timken Company rely on information relating steel cleanness to the performance of a mechanical component. Currently, these decisions are based on information experimentally obtained either through costly custom life testing or ultrasonic steel cleanness measurement along with the application of an older UT-Life algorithm. There is a clear need for a means of delivering useful, technical information in a timely fashion in order to facilitate the decision making process. A computer simulation tool - the Virtual Fatigue Life Test model - designed to predict life has been developed. Its ultimate goal is to deliver a computational tool providing predictive capabilities for inclusion-controlled fatigue performance of stressed components based on their non-metallic inclusion content. The model is based on application of constant Hertzian contact load to an elastic material containing a population of non-metallic inclusions. Numerous computational experiments were run to generate a transfer function relating inclusion properties to a normalized fatigue index. This computationally efficient algorithm can be applied to each inclusion in the stressed volume of the virtual component to establish the normalized fatigue index for that component. Despite adopting numerous simplifying assumptions, validation runs have been conducted and found to be in reasonable accord with existing fatigue life test data. Additionally, parametric studies have been performed on a few defining properties of inclusions and inclusion populations. Introduction Many strategic decisions on issues important to the Timken Company rely on information relating steel cleanness to the performance of a mechanical component. The goal of this project was the development and delivery of a computer simulation tool that will provide predictive capabilities for fatigue performance of steel components based on the non-metallic inclusion content of the steel. As with any well developed model, the final package should furnish: results of sufficient accuracy and precision, computation efficiency (speed) and model robustness. Beyond providing information in support of decisions on particular quality issues, this simulation model may also be employed in fundamental parametric studies relating specific inclusion and inclusion population properties with the performance of a steel component. The development and evolution of the Virtual Fatigue Life Test (VFLT) model has been accomplished through a collaborative effort between a cross-functional team of engineers from Timken and several external universities.

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Model Structure Initially, the intention was to start with a very simple model involving a limited number of inclusion and steel matrix parameters by employing many reasonable assumptions. Once the framework- a working version of the simple model - is assembled and vetted, future work could be directed toward iterative improvements in the model. With the ongoing sophistication of the model, many of the initial assumptions would gradually be relaxed. The primary assumptions in the current model include simplifications related to properties of the non-metallic inclusion distribution, properties of the steel matrix, inclusion/matrix interfacial properties, loading conditions and fatigue damage criteria. Steel Cleanness The particular focus of the current simulation model has been on the impact of non-metallic inclusion populations on contact fatigue performance. Experience has shown that inclusion related fatigue damage during rolling contact fatigue has been ascribed to large oxide stringer inclusions, hereafter referred to as macroinclusions (the cause of fatigue damage in some other types of components may be related to significantly smaller non-metallic inclusions, microinclusions, as opposed to macroinclusions). These same macroinclusions are detectable by the standard Timken ultrasonic test. Thus, the basis for the relatively good correlation between contact fatigue life and ultrasonically measured macroinclusion content of the steel is apparent as shown in Figure 1. In accordance with this, the input values used to define the non-metallic inclusion distributions simulated by the current model have been derived from data on the macroinclusion population. The use of macroinclusion distribution data in the model permits direct comparison between cleanness measurements and model predictions of relative component fatigue life indexes. While the current model employs steel cleanness parameters based on the macroinclusion population, the fundamental design of the model permits, with the appropriat e input values, simulations of microinclusion populations in steel as well. However, due to the significant increase in the number of microinclusions (several orders of magnitude greater than the number of macroinclusions), the actual operation of the current simulation model with such a population would increase the computation time proportionally. Component Loading The model validation of loading characteristics and loading routine was conducted using the commercial finite element package, ABAQUS. The stress contour and magnitude compared well with the known analytical results. The loading analysis was conducted for several inclusion variations, documenting key input variables and the associated results for each simulation run.

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1000 CO

£

100 H

10 H

0.0001

0.001

0.01

0.1

1

Inclusion Density (in/in3) Figure 1. Plot showing life dependency on steel cleanness, as represented by inclusion density. Different data symbols represent different steel making practices [1]. Calculation of Fatigue Life Index Initial versions of a relative life predicting model were based on a fatigue life index. The fatigue life index assesses the average fatigue risk integral over a stressed material volume that contains inclusions and then normalizes it by the fatigue risk integral over the same volume. Correlations were established between the fatigue life index and the inclusion characteristics through a virtual design of experiments (VDOE). An approximate relationship, Equation (1), can be obtained between the fatigue life reduction factor and the fatigue index.

LRF =

1 l +c

(1)

where LRF = life reduction factor T = fatigue index ß - Weibull slope p = inclusion density c = constant Results Validation results were generated for a number of steel components of varying geometry. The example discussed below is a steel component machined directly from a seamless tube. Therefore, the inclusion distribution was fairly straight forward to model. The VDOE for the test component was carried out using a standard loading condition intended to induce inclusion initiated damage. The actual fatigue test data from the test component was normalized to provide a relative life value for direct comparison with the model simulation output. The actual life of the test

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component produced from vacuum induction melted - vacuum arc re-melted (VIM VAR) steel was employed as the maximum attainable life, i.e., assigned a relative life value of unity. All other actual fatigue life test data was referenced to the value achieved with the VIM VAR material. The relative life values of the test component using different steel cleanness levels were evaluated and the results were in good accord with the normalized actual fatigue life test data as shown in Figure 2.

D •

• Actual DVFLT Model

D •

-

D

□ •

1

1

1 1 1 Mill

1— 1 1 1 M i l l

»

1 1 1 Mill

1

1

10 100 1000 10000 Increasing Inclusion Content-►

Figure 2. Plot showing the relative life results, as a function of steel cleanness, for the VFLT model compared to the normalized actual fatigue test data for the test component. Discussion The design and development of the concept, framework and detailed structure of the initial version of a computer simulation tool that provides predictive capabilities for inclusion controlled fatigue performance based on steel cleanness has been completed. Despite adopting numerous simplifying assumptions, validation runs on the current model have been conducted and found to be in reasonable accord with existing life test data. Additionally, parametric studies have been performed on defining properties of inclusions and inclusion populations. The model developed in this program has already been successfully employed to provide guidance on selection of appropriat e steel cleanness levels for specific applications. Development continues in order to increase the capability, complexity, accuracy and computational efficiency of the model.

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Acknowledgements The authors gratefully acknowledge the helpful discussions with, and the assistance of, Purdue University, Georgia Tech University and Northwestern University as well as the dedicated effort and significant contributions of internal supporters E. Buddy Damm, Jim Gnagy, Luc Houpert, Praveen Pauskar and Matt Wilmer. References 1. J.D. Stover, R.V. Kolarik II, D.M. Keaner, "The Detection of Aluminum Oxide Stringers in Steel Using an Ultrasonic Measuring Method," 31st Mechanical Working and Steel Processing Conference, Chicago, IL, USA, 22-25 Oct. 1989, Iron and Steel Society, 1990, 431-440.

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1st World Congress on Integrated Computationa l Materials Engineering Edited by: John Allison, Peter Collins and George Spanos TMS (The Minerals, Metals & Materials Society), 2011

ADVANCES IN COMPUTATIONAL TOOLS FOR VIRTUAL CASTING OF ALUMINUM COMPONENTS Qigui Wang, Peggy Jones, Yucong Wang, and Dale Gerard Global Powertrain Engineering, General Motors Company Pontiac, MI 48340-2920, USA Keywords: Computational Tools, Virtual Casting, Aluminum Abstract The increasing use of cast aluminum components in critical structures has required improved quality, with more reliable and quantifiable performance. Aluminum shape casting processing is very complex and often involves many competing mechanisms, multi-physics phenomena, and potentially large uncertainties. The only effective way to optimize the processes and achieve the desirable mechanical properties is through the development and exploitation of robust and accurate computational models. Numerous modeling and simulation techniques have been developed and applied in practice for aluminum casting and subsequent processing that enable both casting designers and process engineers to better design and develop sound shape cast components with minimum lead time and cost. This paper reviews the latest development and applications of computational tools at GM for aluminum shape casting processing from casting design through microstructur e control to mechanical properties. Introduction Many critical structural applications, such as engines, transmissions, suspension systems, etc., have utilized cast components. Casting processes are often the most cost effective method to produce geometrically complex components and offer near net-shape capability. With the development of computational methodologies and, in particular, the rapid advance of microcomputers over the past three decades, mathematical modeling and numerical simulation of various metallurgical casting processes has become increasingly popular in the metal casting industry. Today software to predict and visualize the heat transfer and fluid flow events is integral to casting process design. The Virtual Cast Component Development (VCCD) program was initiated at GM in 1999. The vision of the program was to integrate manufacturin g processes with component design to produce reliable and high quality cast structural components with minimum lead time and cost. In the past decade, the VCCD program at GM has achieved its objectives and demonstrated the benefits of its use in both product design and manufacturin g process optimization. The application of the VCCD at GM Powertrain and its suppliers has become increasingly widespread, and the methods are being adapted to other alloy systems and processes. VCCD is a comprehensive virtual process of rapid development of manufacturable , durable and cost effective cast components. It includes alloy design/selection, process optimization, multiscale defects and microstructur e simulation, and comprehensive analyses and predictions of component mechanical properties and performance. The VCCD process is realized through the integration of computational tools with advanced materials models linking multiple length scale physics and metallurgical phenomena. The VCCD is based on the principle which is also called

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ICME (Integrated Computationa l Materials Engineering). This paper reviews the latest development and applications of the VCCD program at GM Powertrain for aluminum shape casting processing. Overview of the VCCD The GM VCCD system consists of four key modules shown as the circles in Fig. 1. They are: a) casting design module, b) process selection and optimization module, c) casting defect and microstructur e prediction module, and d) structura l performance evaluation module. The casting design module creates an optimized geometry of the casting and gating/riser system based on the machined product geometry, structure characteristics , and performance requirements . The process selection and optimization module provides optimal manufacturin g procedures for casting, heat treatment, and machining to ensure quality product with minimum casting defects, residual stress and distortion, as well as manufacturin g cost. The casting defect and microstructur e prediction module delivers accurate estimates of casting defects and microstructur e constituent distributions in the cast components based on the casting design and process inputs. The structure performance evaluation module conducts a variety of reliability and durability analyses of the cast component based on probabilistic micromechanics models. The modules can execute individually or collaboratively. The VCCD modules interface with commercial software such as MagmSoft™, Flow-3D, ABAQUS, FE-safe, Pandat, iSIGHT, and UGNX.

Fig. 1. A schematic illustration of virtual cast component development (VCCD) system.1 In virtual development of a cast component, Fig. 1, an initial product geometry is provided to the system for casting design, process optimization, and performance durability evaluation. Based on the product geometry and property requirements , the casting design module selects the most

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economical alloy and casting processes for the product and recommends feasible casting and gating/riser system designs. The casting process modeling tools (such as mold filling and solidification simulations) are used to further optimize the casting and gating/riser system designs and casting process parameters . The process optimization module also selects and optimizes the heat treatment and machining processes to minimize residual stresses, distortion, and manufacturin g cost. For a given casting design and manufacturin g process, the multi-scale defect and microstructur e module simulates and predicts populations of defects and microstructur e constituents in every node of the interested product. The predicted multi-scale defect and microstructur e distributions are exported to the structura l performance module to predict nodal-based mechanical properties as well as durability of the product. If the predicted properties and durability meet the requirements , the optimal product casting is developed. Otherwise, the initial product geometry may need to be modified and the manufacturin g processes such as casting, heat treatment and machining need to be re-optimized. Optimal Casting and Gating System Design The optimal casting and gating system design is performed in a VCCD sub-module called CDOS (Casting Design Optimization System).2 The CDOS is comprised of a knowledge database, a graphical user interface, a geometry analyzer, an inference engine, a process simulation module, and an optimization module. The knowledge database contains casting design data and rules. The graphical user interface accepts as input a product design that is to be manufacture d by a casting process. The geometry analyzer analyzes the input product design and generates the geometry characteristic s of the product to be cast. The inference engine is adapted to generate casting designs by searching the knowledge database, performing pattern-matchin g operations, and implementing logical processes. The proposed casting designsfromthe inference engine are exported to the process simulation and optimization module (dark blue in Figure 1). Fig. 2 shows an example of the gating system designed using CDOS for an engine block casting. Compared with the baseline design, the casting yield is improved by 15%while the predicted casting defects (oxides and porosity) are reduced by more than 25%. Most importantly, the development cycle (time to get the optimal solution) is significantly reducedfrommore than two months to about a week by using CDOS.

(a)

(b)

Fig. 2. An example of the gating system designed with CDOS for an engine block casting, (a) Baseline gating system design, and (b) the optimized gating system design.

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Process Modeling and Optimization Based on the input of the casting model and gating/riser designsfromthe casting design module, the process modeling and optimization module provides recommendation s for optimal and robust manufacturin g processes to produce high quality casting products with minimum manufacturin g cost. The process modeling and optimization module consists of a casting evaluation tool, a residual stress evaluation tool, and a machining evaluation tool. The casting evaluation tool evaluates a virtual casting defined by the casting design module and cast through a simulated casting process. The virtual casting is evaluated for formation of casting defects to determine feasibility of the casting design. The residual stress evaluation tool simulates the heat treatment process recommended for the virtual casting to predict residual stress levels and potential cracks. The machining evaluation tool models the machining processes applied to the virtual casting to assess dimensional accuracy and potential cracking of thefinishmachined product. Fig. 3 shows an example of the heat treatment process simulation module used in prediction of residual stresses near the chain guard area in a cylinder head quenched in water after solution treatment. The predictions of the residual stresses are in very good agreement with the experimental measurements. The module has been used by product design and manufacturin g engineers to resolve several casting geometry and heat treatment issues.

Fig. 3. Comparison of the predicted residual stresses near chain guard area in a cylinder head with experimental measurements.3

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Modeling of Multi-Scale Casting Defects and Microstructures The multi-scale casting defect and microstructur e module (gray in Fig. 1) provides detailed predictions of defect populations and microstructur e distributions for the given casting and gating design and process conditions. The casting defects that can be predicted in VCCD include macro and micro porosity, oxides and inclusions, core gas, cold shuts, entrained air, and hot tearing. The microstructur e constituents that are simulated in VCCD include dendritic grains, dendrite cells, and second phase particles in both micro and nano scales. As an example, the microporosity, due to hydrogen, oxide and shrinkage, in aluminum casting is predicted with the integrated interdendriti c flow and pore growth model.4 The theoretical basis for the pore growth model is that pore growth is governed by the rate at which hydrogen diffuses to the pore/liquid interface. A diffusion equation (eqn 1) is solved for a specified volume of material surroundin g a spherical pore of a specified initial radius. Hydrogen rejected to the liquid phase during solidification is represented by the source term SH-, given in equation 2. d

-££jL = ot

V(DHVCH)+SH

^ p d(„o ( l - ( l - ^ )K, ./s)j

(1)

(2)

where CH is the hydrogen concentration in the liquid at the pore interface. Experimental validation, Fig. 4, proved that the maximum pore sizes and distribution can be well predicted using the developed integrated interdendriti c flow and pore growth model. Together with other casting defects and multi-scale microstructur e constituents, the predicted maximum pore sizes are used for product performance analysis and product quality improvement.

(a)

(b)

Fig. 4. a) Predicted microporosity distribution in the cross section of a cast Al end-chill casting, and b) comparison of the predicted pore sizes with X-ray CT measurements. Prediction of Local Mechanical Properties and Structural Performance Mechanical properties, and in particular the fatigue resistance, of aluminum castings strongly depend upon the size and spatial distribution of casting defects and characteristic s of

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microstructura l constituents. The presence of casting defects significantly reduces fatigue crack initiation life. However, in the absence of casting defects or when the defect size is smaller than a critical size, crack initiation occurs at the fatigue-sensitive microstructura l constituents. Cracking and debonding of large silicon (Si) and Fe-rich intermetallic particles and crystallographic shearing that forms persistent slip bands in the aluminum matrix play an important role in crack initiation. With the quantitative prediction of multi-scale defects and microstructures , local mechanical properties of the casting component and its performance under a testing or service load can be predicted using multi-scale fatigue models,5 Fig. 5.

Fig. 5. The VCCD process flow from the casting design through process and microstructur e simulation to nodal property and structure performance prediction. Life predictions were well within an order of magnitude of actual block and head component fatigue and dynamometer test data for both low and high cycle fatigue conditions. Conclusion Virtual cast component development has been demonstrated successfully at GM in aluminum shape casting and is being extended to magnesium castings. The VCCD approach and methodology is applicable to other metal and plastic forming processes. References 1. 2. 3. 4. 5.

Q. Wang, P. Jones, Y. Wang, D. Gerard, GM Patent Application, GMP012157. Q. Wang, P. Jones, M. Osborne, W. Yang, US Patent 7761263B2. Q. Wang, C.C. Chang, G. Zhang, D. Paluch, SAE 2011-01-0539. G. Backer, Q. Wang, Metall. Mater. Trans. B (2007), pp. 533-540. Q. Wang, P. Jones, US Patent U.S. Patent 7623973 Bl.

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1st World Congress on Integrated Computational Materials Engineering Edited by: John Allison, Peter Collins and George Spanos TMS (The Minerals, Metals & Materials Society), 2011

Modelling the process chain of microalloyed case hardening steel for energy efficient high temperature carburising Sergey Konovalov1, Thomas Henke2, Stefan Benke3, Georg J. Schmitz3, Markus Bambach2 and Ulrich Prahl1 department of Ferrous Metallurgy, RWTH Aachen University, Intzestr. 1, D-52072 Aachen, Germany department of Metal Forming, RWTH Aachen University, Intzestr. 10, D-52072 Aachen, Germany 3

ACCESS e.V. at the RWTH Aachen University, Intzestr. 5, D-52072 Aachen, Germany

Keywords: high temperatur e case hardening, precipitation evolution modeling, phase-field modeling, fine grain stability, process chain variation Abstract Case hardening steels with selective additions of microalloying elements are used for carburizing at temperature s of 1050 °C and more. The addition of elements like niobium, titanium or/and aluminium together with the nitrogen content allows grain growth control in these steels. During the carburizing process the grain size of austenite depends on the particle state as well as on the kinetics of its formation from the previous structure during the heating. All previous process steps such as heat treating and plastic deformation may influence the grain stabilization effect. Phase transformation , particle formation and evolution happen during the thermal or thermomechanical conditioning. For a knowledge-driven design of materials and processes it is necessary to consider the entire process chain in order to reach optimal fine grain sizes in microalloyed steels. To model all the relevant steps along the process chain, various simulation programs acting on different scales have to be linked. The virtual platform concept AixViPMaP® is used to couple different simulation programs in order to model almost arbitrar y process chains in materials processing. The data exchange is realized using a standardized , universal data format which is able to represent all factors influencing the mechanical behavior of a component in an integrative, multiscale simulation approach. Using the simulation platform, a particular process chain has been modelled and compared with experimental results. Introduction and problem Current production of transmission components aims at increasing the efficiency of the production processes as well as at improving the quality in application. These objectives are of major importance for an increased competitiveness. An up-to-date development is the idea of rising the carburizing temperatur e in order to shorten the carburizing time. However, to some extent such a temperatur e increase is limited by furnace capabilities, but - more importantly - by a suitable control of the grain size at high temperatures . As the final grain size has a major influence on the life time of hardened components [1][2], the grain size stability during high temperatur e case hardening is a critical issue which can be improved by adding micro alloying

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elements like Ti, Nb and V. The efficiency of these microalloying elements in terms of grain boundary pinning depends on the entire manufacturin g route and the respective process parameters . The alloying concept and the production process chain thus have to be developed and optimized accordingly [3][4]. As illustrated in fig 1, a typical process chain for the manufacturin g of gear components comprises a combination of several heating, forming and cooling steps. The precipitation state and the microstructur e undergo a complex evolution along the process chain, which is very sensitive to various process parameters . Moreover, distortions after case hardening may cause substantial costs due to additional finishing operations or unacceptable scrap rates. Such distortions are mostly caused by a combination of inhomogeneities stemming from segregation effects, inhomogeneous grain size distributions or an inhomogeneous temperatur e distribution in the component [5] [6]. Process chain for the production of gear components In fig. 1, a typical process chain is shown for the production of transmission components together with the relevant metallurgical processes taking place during processing on the micro scale. These micro-scale phase transformation s and grain growth processes are correlated to the evolution of precipitates like aluminum nitrides (A1N) and titanium-niobium-carbonitride s (Ti,Nb)-(C,N) that take place on the nano scale [7].

Figure 1: Upper row: Typical process chain for transmission components. Middle row: Examples of simulation results for a simplified shape of a transmission component on the macro scale along the process chain. Lower row: Simulation of the phase transformatio n on the micro scale. The process parameter s for both simulation and experimental verification in this test case were chosen close to industrial parameters . The investigated material 25MoCr4+Nb is a typical microalloyed case hardening steel for high temperatur e case hardening.

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The process chain starts with a hot rolling process, during which the cast slab is shaped into a long bar. The near-net shape of the component is created by closed-die forging. The final shape is produced by machining. This machining process requires a pearlitic-ferriti c microstructur e in order to enhance machinability, which typically is reached by a special FP-("Ferrite-Pearlite" ) annealing between the forging and the machining step. Afterwards, the case hardening process, which is a combination of a carburizing and a quenching process, increases the hardness and wear resistance of the component's surface while maintaining a ductile core. In the simulation of the process chain, the machining process is not simulated because its influence on the microstructur e and the precipitation evolution is assumed to be negligible. Thus, the final grain size stability is investigated as a consequence of all former hot forging and annealing steps. The simulation platform concept which has been used in the current work allows for modeling of the entire process chain. However, up to now the initial microstructur e of the rolled bar is not calculated from the as-cast microstructur e but assumed to be homogeneous. The consideration of macro segregations originating from the continuous casting process and the formation of banded structures influencing distortions of the final gear wheel will be tackled in the future. Integrative simulation of the process chain Scopes of the integrative simulation approach are (i) the design of a combined process and alloy concept with respect to an improved grain size control during high temperatur e case hardening including the identification of all process parameter s (ii) the minimization of the experimental effort to develop this new concept and (iii) the optimization of the process chain in terms of cycle times, energy and costs. For these integrative simulation tasks the AixViPMaP® platform is used which is currently being developed at RWTH Aachen University [8]. The simulation takes place on three scales: (i) on the level of the component (macro level), (ii) on the microstructur e level and (iii) on the scale of precipitations (nano level). For each process step, finite element (FE) codes are used on the macro level taking into account metallurgical phenomena based on mean field formulas of the Leblond type [9]. The time-strain-temperatur e at specific locations in the component are calculated and passed to the micro and the nano scale as boundary conditions. On the nano scale the precipitation evolution is simulated following the concept of Kampmann-Wagne r [10]. On the micro scale the phase transformation s and the grain growth kinetics are calculated using the multi-component multi-phase field method [11]. The precipitation results are incorporated into the phase field calculations using the Zener pinning force as a scalar variable which controls the grain boundary movement [12]. After definition of the initial state and calculation of the initial conditions, the simulation of the first hot forming process steps is carried out. On the macro level of FE calculations, the hot forming simulations of rolling and forging processes are split into three steps: heating, deformation, and cooling. Here, two different simulation tools are linked together for the calculation of these process steps. For the calculation of the heating and cooling steps including all phase transformation s the FE code CASTS® is used [13], while the forming simulations of the austenite phase at high temperature s are performed using the FE code LARSTRAN/shape® which uses the StrucSim microstructur e simulation module [14] to take into account the microstructur e evolution including dynamic and static recrystallization kinetics . The results (e.g. grain size, recrystallized volume fraction, dislocation density) of this calculation can be transferre d to the micro and nano scale and to subsequent process steps. The temperatur e distribution and phase transformation s during heat treatments like FP-annealing and high temperatur e case hardening can be calculated on the component scale by means of CASTS® using empirical approaches [7]. On the micro scale, the temperatur e history at specific

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integration points of the FE grid is used as boundary condition for the commercial phase field program MICRESS® for calculating the phase transformatio n and microstructur e development on the basis of physical models [15],fig.2.

Figure 2: Comparison of the simulations with experimental (LOM: light optical microscopy) and dilatometer results for austenite formation from aferritic-pearliti c structure (top) and comparison of simulated and experimental austenitic microstructur e at carburizatio n temperatur e (bottom)

Figure 3: Precipitation simulation of an exemplarily process chain for a gear component consisting of two forging passes, FP annealing and high temperatur e carburizing. Left: time temperatur e schedule; right: evolution of mean precipitation size for Nb-carbides and Al-nitrides, comparison of experimental (squares, triangles) and MatCalc® simulation results (line)

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The evolution of the precipitate distribution during the different heat treatments is calculated on the micro scale using MatCalc® [16] (see fig. 3) and then used to calculate an effective Zener force. This effective Zener force enters into the MICRESS® simulations, where it reduces the grain boundary mobility and accordingly affects grain growth [18]. Phenomena like abnormal grain growth can be tackled this way [19]. A schematic description of this integrative approach over all three length scales is demonstrated in fig. 4. Here, the areas of no grain growth, abnormal grain growth and normal grain growth are shown as a function of austenite grain size and Zener force at the beginning of the carburizatio n step. Using this scheme, process parameter s can be identified which ensure fine grain stability. As the simulation spans all three scales along the process chain, the identification of an optimal process chain and optimal process parameter s will be realized in future.

Figure 4: Precipitation management and process parameter identification for a microalloyed case hardening steel for high temperatur e carburizing; prediction of precipitation evolution during processing and calculation of the Zener force during carburizing in order to predict the grain growth behavior of 20MnCr5B+Nb after carburizing at 1050 °C for 90 min; the grain growth behavior can be calculated as a function of Zener (Pinning) force (precipitation state and size distribution) and austenite grain size. Summary and outlook In this paper a concept for an integrative simulation of microalloying concepts and process chains for the processing of carburizing steels which are able to undergo time and energy efficient high temperatur e carburizing processes at 1050 °C and more is shown. The integrative simulation was made possible by linking several commercial and in-house software codes using the AixViPMaP® approach, which is designed as a network based platform for ICME. Future work will focus on extending the simulation capabilities of the ICME platform in various ways, e.g. by incorporatin g simulation tools for the prediction of fatigue life. Acknowledgements: The present article is part of the on-going project AixViPMaP® performed by a consortium of the following institutes at the RWTH Aachen University: Foundry Institute (GI), Institute for Ferrous Metallurgy (IEHK), Welding and Joining Institute (ISF), Surface Engineering Institute (IOT), Institute for Metal Forming (IBF), Institute for Plastics Processing (IKV), Institute for Scientific Computing (SC), Department of Information Management in Mechanical Engineering (ZLW/TMA), Institute for Textile Technology (ITA), Fraunhofer Institute for Lasertechnology (ILT/NLD) and ACCESS. Funding of the depicted research by the German Research

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Foundation (DFG) in the frame of the Cluster of Excellence "Integrativ e Production in High Wage Countries" is gratefully acknowledged [19].

References 1. J. Grosch, D. Liedtke, K. Kallhardt, D. Tacke, R. Hoffmann, C. H. Luiten, F.W. Eysell: „Gasaufkohlen bei Temperature n oberhalb 950 °C in konventionellen Öfen und in Vakuumöfen" , HTM Härterei-Techn . Mitt. 36 (1981) 5, pp. 262 2. J. L. Pacheco, G. Krauss: „Geflige und Biegewechselfestigkeit einsatzgehärtete r Stähle", HTM Härterei-Techn . Mitt. 45 (1990) 2, pp. 77 3. F. Hippenstiel, W. Bleck, B. Clausen, F. Hoffmann, R. Kohlmann: „Innovative Einsatzstähle als maßgeschneidert e Werkstofflösung zur Hochtemperaturaufkohlun g von Getriebekomponenten" , HTM Härterei-Techn . Mitt. 27 (2002) 4, p. 290-298 4. K. Klenke, R. Kohlmann: „Einsatzstähle in ihrer Feinkornbeständigkeit , heute und morgen"; HTM Z. Werkst. Wärmebehand . Fertigung 60 (2005) 5, pp. 260 5. J.P. Wise, D.K. Matlock: "Bending Fatigue of Carburized Steels: A Statistical Analysis of Process and Microstructura l Parameters" , SAE 2000 World Congr., March 2000, Detroit 6. C. Prinz, B. Clausen, F. Hoffmann, R. Kohlmann, H.-W. Zoch: "Metallurgica l influence on distortion of the case-hardening steel 20MnCr5", Materialwissenschaf t und Werkstofftechnik , 37 (2006) 1, pp. 29 7. J. Rudnizki, B. Zeislmair, U. Prahl, W. Bleck: "Thermodynamica l simulation of carbon profiles and precipitation evolution during high temperatur e case hardening" , Steel Res. Int. 81 (2010) 6, pp. 472. 8. G.J. Schmitz, U. Prahl: Toward a Virtual Platform for Materials Processing; JOM 61 5 (2009)26 2009 9. J.B. Leblond et al., Acta Metall, 32, (1984), 137 10. R. Kampmann,R. Wagner: „Kinetics of precipitation in metastable binary alloys - theory and application to Cu-1.9 at% Ti and Ni-14 at% Al", Acta Script Metall (1984), pp. 91103 11.1. Steinbach, F. Pezzolla, B. Nestler, M. Seeßelberg, R. Prieler, G.J. Schmitz, J.L.L Rezende: „A phase field concept for multiphase systems", Physica D. 94 (1996) 3, pp. 135-147 12. T. Gladman: "Grain Size Control", OSP Science (2004). 13. S. Benke, G. Laschet: "On the interplay between the solid deformation and fluid flow during solidification of a metallic alloy", Comp. Mat. Science 43 (2008) 1, pp. 92 14. R. Kopp, C. Horst: "Modelling of elastic effects in forming processes, particularl y the rolling process". AIP Conf. Proc. - June 10, 712 (2004), pp. 375-381 15. MICRESS®: The MICRostructur e Evolution Simulation Software: www.micress.de 16. E. Kozeschnik, J. Svoboda, F.D. Fischer, P. Fratzl: "Modelling of kinetics in multicomponent multi-phase systems with spherical precipitates: II: Numerical solution and application" , Mater. Sei. Eng. A, 385 (2004) (1-2), pp. 157 17. M. Apel, B. Bottger, J. Rudnizki, P. Schaffhit, I. Steinbach: "Grain growth simulations including particle pinning using the multiphase-field concept", ISIJ 49 (2009) 7, pp. 10241029 18. J. Rudnizki, B. Zeislmair, U. Prahl, W. Bleck: "Prediction of abnormal grain growth during high temperatur e treatment" , Comp. Mat. Sei. 49 (2010) 2, pp. 209 19. www.production-research.d e

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1st World Congress on Integrated Computationa l Materials Engineering Edited by: John Allison, Peter Collins and George Spanos TMS (The Minerals, Metals & Materials Society), 2011

Cyberinfrastructure support for Integrated Computational Materials Engineering Tomasz Haupt Mississippi State University, Starkville, MS 39762, USA Keywords: Cyberinfrastructure , Data Repository, Multiscale Modeling Abstract The objective of this effort is to develop an Engineering Virtual Organization which provides a cyberinfrastructur e platform that exploits the recent transformativ e research in material science involving multiscale physics-based predictive modeling, multiscale experiments, and design. The Virtual Organization is open to its participants through a "community of practice" interactive Web site with the primary goal of accumulating and protecting the intellectual property generated by the participants of the organization. The intellectual property includes experimental data, material models and constants, computational tools and software artifacts, and the knowledge pertaining to multiscale physics-based models for selected properties and processes. To this end, our research and development activities have focused on the development of the necessary IT infrastructure . Whenever possible, we have adopted available Open Source components (such as Java-based Web servers, a Wiki server, an Enterprise Service Bus, a Subversion revision control system, and others), augmented by custom modules (such as a secure data repository integrated with the online model calibration tools). Introduction The goal of this effort is to create an environment for the accumulation, development, integration, and dissemination of material models and their use for the material and product design by exploiting both the recent transformativ e research in materials science involving multiscale physics-based predictive modeling, multiscale experiments and design, and transformativ e progress in the information technologies. More specifically, the creation of this cyberinfrastructur e system has resulted in the creation of the Engineering Virtual Organization for Cyber Design (EVOCD) focusing on the accumulation of "intellectual capital" pertaining to Integrated Computational Materials Engineering (ICME). EVOCD is accessible to the general public through a "community of practice" Web portal (http://ccg.hpc.msstate.edu ). The portal provides means for the accumulation of the community knowledge (Wiki) and, in addition, it provides access to repositories of experimental data, material models and computational tools at different length scales, exploiting the integrative nature of ICME. The implementation of the portal demonstrates the use of modern information infrastructur e based on rich user interfaces implemented using Asynchronous JavaScript and XML (AJAX) [1] technology, Service Oriented Architecture (SOA), Web Services and Grid computing. It streamlines the process of gathering experimental results, and deriving the material properties (using online model calibration tools) for multiscale materials models for selected properties and processes. The development of the Portal leverages tools, technologies, and software approaches developed by other large-scale scientific cyberinfrastructur e projects supporting researchers and engineers in

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domains such as astronomy, medicine, biology, geophysics, earthquake engineering, and many more. Vision of the MSU Cyberinfrastructure System for ICME In a long-tem vision (Figure 1), the Mississippi State University (MSU) cyberinfrastructur e system for ICME would support performing multi-objective metamodel-based design optimizations involving multiscale simulations. From the end-user perspective, the system would be necessarily comprised of many independent components (services) such as data and metadata services, compute services, and workflow management services. The data services would provide access to community-wide repositories of

I

Figure 1: Long-term vision for the MSU Cyberinfrastructur e e x p e r i m e n t a l data, m a t e r i a l Constants, a n d system for Integrated Computational Materials Engineering. p r o d u c t g e o m e t r i e s . T h e Compute S e r v i c e s

would allow performing operations on these data, such as model calibration (i.e., deriving the material constants for particular material models) or performing FEA analysis using the calibrated material models. Moreover, to fulfill the promise of computational material engineering, in the future, the system will provide the runtime environment for running complex, evolving, data-driven workflows that involve running hierarchical multiscale simulations on distributed and heterogeneous high-performanc e platforms. The technical challenges of running these workflows are intimidating for a material scientist and therefore the complexity must be hidden behind a user-friendly intuitive interface that interacts with an autonomie, that is, self-protecting, self-healing, self-configuring, and self-optimizing system. New Web technologies, such as AJAX, and new software engineering approaches, such as REST[2] and Service Oriented Architectures make these objectives possible. This is the long-term vision of the system. At this early stage of the project, the focus is on the development of mechanisms for the accumulation of knowledge. This includes the repositories of experimental data and material constants integrated with the online model calibration tools (upper-left quadrant of the chart in Figure 1) as well as the repositories of material models and other computational tools. Independently, we are also coordinating this system with a broader cyberinfrastructur e effort organized by The Minerals, Metals, & Materials society (TMS), in order to integrate it with other cyberinfrastructur e efforts such as the Nano-Hub[3], MatDL[4], the Materials Atlas[5], and others. The architecture of the EVOCD portal The architecture of the EVOCD portal is shown in Figure 1. It is comprised of five major components: knowledge management (implemented as a Wiki), repositories (databases) of experimental data and material constants integrated with the online model calibration tools (henceforth referred to as the ICME repository), a repository of codes (material models and other

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software artifacts), and a runtime environment for autonomie execution of the dynamic, multiscale computational workflow and multistep optimization.

Figure 2: Components of the EMOCD Cyberinfrastructur e system for ICME

Knowledge management: Wiki Knowledge management has been achieved by applying "architectur e of participation" advocated and implemented by Web 2.0 concepts and technologies. The most important aspect of Web 2.0 is a focus on usergenerated content, as opposed to centrally managed information. Tools like Wiki, in conjunction with content ratings, lead to creation of a collective (read: peer-reviewed) knowledge that is always up-to-date and has a spontaneously evolving structure reflecting the current state of the art. Commercial and community-based implementation of this concept, including Wikipedia, Amazon.com, and Facebook.com prove that this approach is very effective, and the process of knowledge accumulation is proven to be convergent. Therefore, we have chosen Wiki as the mechanism for community-driven knowledge management. The Wiki (http://ccg.hpc.msstate.edu ) has become the façade for the EVOCD Portal. The main purpose of it is to accumulate the knowledge pertaining to ICME. As shown in Figure 3, the Wiki captures the knowledge about different classes of materials (Metals, Ceramics, Polymers, and others), material models at various length scales, and design issues, from process and performance models, to optimization under uncertainty, to bioinspired design. Many researchers contribute to these Wiki pages, and the contents of the pages grow and improve daily. In addition, the Wiki provides direct access to resources, such as data and code repositories (described below). In the near future it will also provide access to an autonomie runtime environment for composing and executing multiscale workflows directly from the Web Browser. Finally, the Wiki provides documentation and tutorials on how to contribute and format the contents. The EVOCD Wiki is implemented using Open Source MediaWiki software, Figure 3: Knowledge m e same that is used by the popular Wikipedia. It is open to the general mto\Tïn^ntofl public, however, only (self) registered users, identified by a valid email screen shot of the address, are allowed to provide or edit the contents. This allows us to actual page - the monitor the evolution of the contents and give credit (or blame) to the navigation panel)

contributors.

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The ICME Repository The ICME Repository integrates two independent web applications: the repository of experimental data and material constants (online database), and online model calibration tools (web applications). Although the data repository and model calibration tools can be used independently, the advantage of the ICME Repository is that Figure 4: The ICME repository it integrates all three application into one (cf. Figure 4), thus allowing the complete cycle of analysis: upload of experimental data, apply the calibration tools to extract the material constants, save the constants to the database, and retrieve them in a form suitable to perform numerical simulations. Currently, the repository supports force-displacement, stress-strain, and strain-life (fatigue) data, and images of the microstructure . The model calibration is the process of deriving the material constants from the experimental data, usually by performing a fit of a model-specific function(s) to the experimental data. EVOCD currently provides three model calibration tools that are integrated with the Portal: Damage Model, Image Analyzer, and Multistep Fatigue Fit.

Figure 5: Example screen shot of the ICME repository of experimental data.

Damage Model: The Mississippi State University internal state variable (ISV) plasticity-damage model (DMG) production version 1.0 is based on the ISV plasticity formulation of Bammann [6]

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with the addition of porosity [7] and the void nucleation, growth, and coalescence rate equations that admit heterogeneous microstructure s [8]. The model is implemented as an ABAQUS user material subroutine (UMAT). The model calibration routine DMGfit [9] updates the original BFIT routine by Lathrop [10] . The calibrated model constants can be directly merged into the "USER MATERIAL, CONSTANTS" section of an existing ABAQUS input deck. Image Analyzer: ImageAnalyzer is a utility for calculating some model constants from an optical image of a material. Groups of pixels in the image that satisfy user-specified criteria are interpreted to be objects of interest (particles, grains, voids, etc.). Associated with each object are the following quantities: area, centroid, first nearest neighbor distance, major axis length, minor axis length, and orientation. The material constants derived using the Image Analyzer tool are used for creation of both Damage and Fatigue models. Multistage Fatigue Fit: MMF is a high fidelity multistage fatigue (MSF) model to predict the amount of fatigue cycling required to cause the appearance of a measurable crack, the crack size as a function of loading cycles. The model incorporates microstructura l features of the fatigue life predictions for incubation, microstructurall y small crack growth, and long crack growth stages in both high cycle and low cycle regimes. Repository of codes

Figure 6: Partial list of codes documented in the Wiki (screen shot)

The repository has been initially populated with sixteen open-source codes. Each code comes with documentation (installation instruction, user manual, theoretical background, and examples). In addition to the Open-Source material models, the repository provides tutorials and examples for popular commercial or otherwise proprietar y codes (such as ABAQUS and LAMMPS, cf. Fig 6).

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Summary This paper reports on the concept, design, and preliminary implementation of a cyberinfrastructur e system for Integrated Computational Material Engineering developed at Mississippi State University (MSU). The repository of experimental data, material models, and computational tools at different length scales is available online and is being tested by a selected group of users. The most prominent feature of this system is a tight integration (mashup) of separate services providing an integrative environment for research and development of multiscale physics-based materials models for selected properties and processes. The next phases of this project involve the development of the runtime environment for executing complex, dynamic, workflows for multiscale modeling and multistep optimization. The site is operational for the last 18 months, supporting the research communities involved in the DOE-sponsored Southern Regional Center for the Innovative Lightweight Design, and the Three Nations (Canada, China, and the U.S.) Magnesium Front-End Pilot Project (MFERD). We are also recently collaborating with the Minerals, Metals, and Material Society (TMS) to integrate the site developed under this funding with a broader TMS cyberinfrastructureeffort on Integrated Computational Materials Engineering. The MSU site is also being extensively used to support the training of engineering graduate students at Mississippi State University. The EVOCD is a web application, which provides access to a number of remote services. However, by applying AJAX technology that enables Rich User Interface and services mash-ups, this distributed system has a look and feel of a stateful desktop application. The complexity of the interfaces of the underlying services is hidden by adopting the REST architectura l style. Acknowledgment

This work has been supported by the U.S. Department of Energy, under contract DE-FC2606NT42755. References 1. For an introduction to AJAX (Asynchronous JavaScript and XML) see the Wikipedia article: http://en.wikipedia.org/wiki/Ajax_(programming ) (2011) 2. For and introduction to REST (Representationa l State Transfer) architectura l style see the Wikipedia article http://en.wikipedia.org/wiki/Representational_State_Transfe r (2011) 3. Nano-Hub, home page: http://nanohub.org / (2011) 4. MatDL, home page http://matdl.org/(2011 ) 5. 3D Material Atlas, home page https://cosmicweb.mse.iastate.edu/wiki/display/home / Materials+Atlas+Hom e (2011) 6. Bammann, D. J., "Modeling Temperatur e and Strain Rate Dependent Large of Metals," Applied Mechanics Reviews, Vol. 43, No. 5, Part 2 (1990) 7. Bammann, D. J., Chiesa, M. L., Horstemeyer, M. F., Weingarten, L. I., "Failure in Ductile Materials Using Finite Element Methods," Structural Crashworthines s and Failure, eds. T. Wierzbicki and N. Jones, Elsevier Applied Science, The Universities Press (Belfast) Ltd, (1993) 8. Horstemeyer, M.F., Lathrop, J., Gokhale, A.M., and Dighe, M., "Modeling Stress State Dependent Damage Evolution in a Cast Al-Si-Mg Aluminum Alloy", Theoretical and Applied Fracture Mechanics, Vol. 33, pp. 31-47 (2000). 9. Carino, R., Horstemeyer, M., & Burton, C, Re-engineering DMGFIT" Fitting Material Constants to Internal State Variable Models. MSU.CAVS.CMD.2007-R0040 (2007) 10. Lathrop, J.F., (Dec 1996). BFIT, A Program to Analyze and Fit the BCJ Model Parameters to Experimental Data Tutorial and User's Guide. SANDIA REPORT SAND97-8218. UC-405, Unlimited Release (1996)

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1st World Congress on Integrated Computationa l Materials Engineering Edited by: John Allison, Peter Collins and George Spanos TMS (The Minerals, Metals & Materials Society), 2011

STABILITY OF FE-C MARTENSITE - EFFECT OF ZENER-ORDERING Reza Naraghi, Malin Selleby Department of Materials Science and Engineering, KTH (Royal Institute of Technology), Stockholm 100 44, Sweden Keywords: Thermodynamic modeling, Zener Ordering, Fe-C Martensite Abstract A model has been developed to describe thermodynamic properties of body centered tetragonal (bet) martensite and body centered cubic (bec) states of iron-carbon interstitial solid solutions by applying (Fe\ (C, Va\ (C, Va\ (C, Va\. The order-disorder transition in dilute solid solutions is described using experimental data, and the effect of so called Zener ordering on the stability of martensite is evaluated. From the proposed thermodynamic model it is evident that the selection of model parameters of the bec phase has an important physical meaning related to the redistribution of carbon atoms prior to carbide precipitation (spinodal decomposition in Fe-C martensite during early stages of aging). Introduction Early X-ray measurements have shown that the lattice of freshly formed martensite is tetragonaly distorted which differs from the equiaxed bec structure of ferrite [1]. Bain pointed out that upon a uniform difrusionless transformation , only one third of the interstitial positions in the bec lattice correspond to interstitial positions in the original fee lattice and the preferred distribution of carbon atoms leads to the tetragonality of martensite [2]. Zener suggested that the observed tetragonality is not merely an effect of the difrusionless transformatio n and the elastic (strain induced) interactions in Fe-C martensite may cause ordering [3]. According to Zener, at each carbon concentration a critical temperatur e exists below which the ordered distribution is thermodynamicall y more advantageous than the disordered one. Kurdjumov and Khachaturya n later used a more fundamental approach to describe the order-disorder transition using the static concentration waves method [4] and microscopic elasticity theory (MET) [4-7]. In this paper a revision of the modeling based on the compound energy formalism (CEF) [8] is presented. A four-sublattice model is developed to describe the thermodynamic properties of bet martensite and bec ferrite with a single Gibbs energy expression and taking all experimental and theoretical data into account. Using the proposed model the thermodynamic properties of bec, the transition between the disordered (bec) and ordered (bet) structures and the co-existence of ordering and spinodal decomposition in martensite is consistently described. Thermodynamic Models All models used are based on the compound energy formalism [8]. The thermodynamic properties of pure iron and pure carbon have recently been analyzed by [9] and [10]. Their descriptions of iron and carbon were accepted and used in this paper. The re-evaluation of the binary Fe-C phase diagram and experimental data will be published in a parallel paper and will not be discussed further here.

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The ordering on the bet lattice can be modeled with the four-sublattice model, (Fe)x(C,Va)x(C,Va\(C,Va\, where each interstitial sublattice corresponds to one of the octahedral sites in the bec lattice. In order to favor the stability of the ordered state in certain temperature or composition ranges, it is necessary to impose some constraints on the coefficients of the Gibbs energy applied to this phase. The following relations for the coefficients of the Gibbs energy expression of the bet phase can be derived mathematically when limiting the model to regular interaction terms [11]: °(~ibct U UT FeVaVaVa "= l °f~