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 <111> 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 <100> 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

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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 <100> 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

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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{
(4) (5)

Cl=k0C[

, mL is where Co is the initial concentration of the alloy, TL is the equilibrium liquidus temperature the liquidus slope, T is the Gibbs-Thomson coefficient, K is the mean curvature of the S/L interface, f[ç,y/) is the surface energy anisotropy, ko is the partition coefficient, Q* and c / are the interface liquid and solid solute concentration of the S/L interface, respectively. The interface curvature of a solidifying cell is related to its neighbors, which can be calculated by a discrete method from the following equation1111

K = [\-2(fs+Y,fi)/(N

+ l)]/L

(6)

Where L is the size of CA cells, N is the numbers of the neighbors, which equals to 24 in the two-dimensional condition. The NH4CI-H2O transparen t alloy has the typical fourfold-branchin g dendritic feature. In order to describe the 4-fold anisotropy of the surface energy of NH4C1-H20 solution, the surface energy anisotropy J[ç,if/) at the S/L interface can be calculated as follows1121 f( - y/)] (7) ^ = arccos dfs / dx[{dfs làxf+{dfs

I dyf\yi

(8)

Where y is the anisotropy coeflicient; y/ is the preferred crystallographic growth direction, and the calculating method is in reference [13]. During the dendritic growing process, growth velocity at the S/L interface can be exhibited as[13] vnC[(\-k) = -DLVCL+DsVCs (9) In two dimensional condition, vn^(vA, vv), so the interface velocities in the x- and y-directions can be expanded as [12] VxC'L0-k)

= -DL^

+

29

Ds^-

(10)

vAO-k) = -DLf

+D s

^

(11)

When/s equals 1 or 0, the cell is solid or liquid, respectively. When Q
(13)

Where Ax and Ay are the cell size in the x- and y-directions, n and n+\ means the time step of current step and next time step, respectively. When/v at an interface cell equals 1, the cell change to solid state, and capturing the neighboring liquid cells. Simulation and experimental validation Numerical simulation was carried out in the directional solidification of NH4CL-74 wt%H2C) system to study the influence of different pulling velocities on the primary dendrite arm spacing of the columnar dendrites. The thermophysical properties of NH4CI-74 wt.%Ii20 solution was shown in table 1. Table I. ThermoPhysical properties of NH4Cl-74 wt.%H2Q solution [6'14] Variable Value Variable name 4.8xl0 _y Solute diffusion coefficient in liquid £>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,

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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>
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References l [ 1 ] J.D. Hunt, "Cellular and primary dendrite spacings", [in] Proceedings of Internationa Conference on Solidification and Casting of Metal, London, 1979, 3. [2] W. Kurz and D.J. Fisher, "Dendrite growth at the limit of stability: tip radius and spacing," Ada Metallurgies 29(1981), 11-20. [3] J.D. Hunt and S.-Z. Lu, "Numerical Modeling of Cellular/Dendriti c Array Spacing and Structure Predictions Growth," Metallurgical and Materials Transactions A, 27(1996), 611-623. [4]W.G. Zhang, L. Liu and X.B. Zhao,, "Effect of cooling rates on dendrite spacings of directionally solidified DZ125 alloy under high thermal gradient," Rare metals, 28(2009), 633638. [5] H. Kaya, E. Çadirli and M. Gündüz, "Dendritic Growth in an Aluminum-Silicon Alloy," Journal of Materials Engineering and Performance, 16(2007), 12-21. [6] G. Hansen, S. Liu, S.-Z. Lu and A. Hellawell, "Dendritic array growth in the systems NH4CIH2 0 and [CH2 CN]2 -H2 0: steady state measurements and analysis," Journal of Crystal Growth, 234 (2002), 731-739. [7] W. Wang, P.D. Lee and M. McLean, "A model of solidification microstructure s in nickelbased superalloys: predicting primary dendrite spacing selection,"^eta Materialia, 51(2003), 2971-2987. [8] YH. Feng, H. Nie and X.X. Zhang, "Coupled macro-micro transports with double diffusive flow during directional solidification, " Journal of Engineering Thermophsics, 29(2008), 301305. [9] Y Liu, Q. Y Xu and B.C. Liu, "A Modified Cellular Automaton Method for the Modeling of the Dendritic Morphology of Binary Alloys," Tsinghua Science and Technology, 11(2006), 495500. [10] J.Yu, Q.Y Xu and B.C. Liu, "Numerical simulation of microstructur e evolution based on a modified CA method," Acta Metallurgica Sinica, 43(2007), 731-738. [11] B. Li, Q.Y. Xu, D. Pan, B.C. Liu, YC. Xiong, YJ. Zhou and R.Z. Hong, "Study on Microstructur e Simulation of ZL114A Alloy during Low Pressure Die Casting Process," Acta Metallurgica Sinica, 44(2008), 243-248. [12] L. Nastac, "Numerical modeling of solidification morphologies and segregation patterns in cast dendritic alloys,"Acta Metallurgica, 47(1999), 4253-4262. [13] L. Beltran-Sanchez and D.M. Stefanescu, "A quantitative dendrite growth model and analysis of stability concepts," Metallurgical and Materials Transactions A, 35(2004), 24712485. [14] W.D. Bennon and F.P. Incropera, "The evolution of macrosegregation in statically cast binary ingots," Metallurgical Transactions B, 18(1987), 611-616. [15] U. Feurer and R. Wunderlin, Fundamentals of Solidification, Trans. Tech. Publications Ltd., Aedermannsdorf , Switzerland, 1986, Appendix 8, 214.

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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

MORE EFFICIENT ICME THROUGH MATERIALS INFORMATICS AND PROCESS MODELING 1 3 B. P. Gautham1, R. Kumar1, S. Bothra2, G. Mohapatra , N. Kulkarni1, K. A. Padmanabhan

*Tata Research Development and Design Centre, A division of Tata Consultancy Services; 54-B Hadapsar Industrial Estate; Pune, Maharashtra , 411013, India department of Mechanical Engineering, Indian Institute of Technology Bombay; Powai, Mumbai, Maharashtra , 400076, India 3 School of Engineering Sciences & Technology and Centre for Nanotechnology, University of Hyderabad;Hyderabad,Andhra Pradesh, 500046, India Keywords: Material Informatics, Data Mining, Fatigue Life, Steel, Modeling Abstract The handling of information that is vital to materials engineers and process/component designers needs a paradigm shift for achieving superior designs. For this, the ability to predict the mechanical properties of manufacture d components is essential. This is a complex step because of the interactions among material composition, processing and design. Currently,this is addressed through a combination of materials property databases, experience of engineers, and modeling and simulation tools. But, it is possible to derive more useful information from the databases, in combination with physics-based modeling. Fatigue properties of steels subjected to different treatments vary considerably. Here the first set of results of an attempt to link the fatigue properties available in NIMS database through a combination of materials informatics and physics-based modeling to derive relations that can predict the fatigue properties as a function of different variables, made by us, is reported. The study gave useful information on composition-processing-performanc e relationships. The database consisted of -20 grades of steels including carbon, low alloy, carburizing and spring steels and -450 datum points. The model predicted the experimental fatigue life of-98% of the steels within ±10%error. Introduction It is a matter of great concern that materials engineering has not been able to keep pace with the product design and development cycle and that insertion of new materials has become more infrequent [1]. The conventional ways of experimentation and simulation for search of new or alternative materials have been a slow and arduous task and most often result in unexpected discoveries. Even with advances in computational materials science, there are severe limits on prediction of structure-propert y relationships in new materials. In the process of development of materials, a number of experiments and simulations are carried s are stored in databases. However, these out and the outcomes of these experiments/simulation databases are viewed as static documents/look-up tables and used just for retrieval of the information/ property required. Recently, a paradigm shift has been observed in the way the above mentioned problems are dealt with. Researchers have started to utilize various data mining techniques on the huge materials property databases to seek meaningful knowledge out of it [24]. This field of research is given a new name and is known as "Materia l Informatics (MI)"[5].

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Informatics is an approach which utilizes ideas from statistics and machine learning to extract knowledge in the form of classifications and predictions from massive databases. The experimental and computational resources that are needed to enable material informatics are: data generation, data warehousing, dimensionality reduction, clustering analysis, predictive modeling techniques, visualization techniques and cyber infrastructure . Although informatics is well developed infieldslike biology, drug discovery etc., materials informatics is still emerging. There exist only a few studies which deal with the application of an informatics approach in materials science. Fatigue strength is the most important and basic data required for design and failure analysis of mechanical components. It is reported that fatigue accounts for over 90% of all mechanical failures of structura l components. Hence, fatigue life prediction is of utmost importance to both the materials science and mechanical engineering communities. In the present work, we have applied the informatics approach on NIMS fatigue database to link fatigue life of steels to upstream parameter s such as chemical composition, processing parameter s and structure. Investigation of these kinds of relationships has always been an important area of research. Such correlations are highly desirable, considering the amount of time and effort that could possibly be saved by using them. However, the complicated nature of these relations, non-linear in most cases, has made it difficult to model the relationships between constituents, processing and final properties. Also, there is the absence of a single multiscale theory which can capture such information. It is important to mention here that development of such empirical relationships will provide industry and academia a fast and reliable method of predicting mechanical properties of new grades of materials and also understandin g the relations between the desired properties and control parameters . Methodology Data on chemical composition (%C, %Si, %Mn, %Cr, %Ni etc.), processing parameter s (normalizing temperature , time, cooling rate etc.) and mechanical properties (YS, UTS, fatigue limit etc.) were collected from NIMS (National Institute for Materials Science, Japan) fatigue database [6]. The database comprises carbon and low-alloy steels, carburizing steels and spring steels. Fatigue life data, which pertain to rotating bending fatigue tests at room temperatur e conditions, was the key property for the current study. Principal component analysis (PCA) was carried out on the collected data to understand the patterns and interrelationship s hidden in the database. PCA is one of the widely used techniques for dimensionality reduction and finding property correlations with widespread applications in life sciences, pharmacology, economics etc [7, 8]. The fact behind dimensionality reduction is that most of the descriptors are interrelated and these correlations in some instances are high. PCA creates a new series of uncorrelated (orthogonal) variables called principal components (PCs), which are projected in the direction of decreasing variance. PCs with variances above a critical level are retained to describe the whole dataset. In PCA the initial data matrix is represented as score matrix and loading matrix. The property of score plot is that if we plot a score vector against another score vector, materials with similar properties will cluster [9]. The loading plot gives insight on the relationships between the variables/characteristics . In the loading plot, if the PC values are very close together, a high degree of correlation is suggested

36

and if the values are diagonally located in different quadrants , an inverse correlation is indicated [10]. After carrying out PCA, partial least square regression (PLSR) was carried out on different clusters identified by PCA. With the help of PLSR, models were built to predict various response variables including fatigue life based on the control variables such as chemical composition and processing conditions. Results and Discussion PCA was first carried out on a dataset consisting of a 437x35 matrix, which included all control and response variables. Figure 1 plots the eigenvalues of each principal component and cumulative confidence levels obtained from PCA. It can be seen from Figure 1 that for 95% confidence level, i.e. to capture 95% of the variance in the original dataset, PCA reduces the dimensionality of the datasetfrom35 to 14.

Figure 1. Eigenvalue explained by each component and cumulative confidence levels obtained from PCA. The score plots, PCI vs. PC2 and PCI vs. PC3 are shown by Figures 2 (a) and 2 (b). It can be observed from Figures 2 (a) and (b) that the whole dataset gets divided into 3 clusters. By analyzing the clusters, it was discovered that different clusters belong to different types of steels. Clusters 1, 2 and 3 in Figures 2 (a) and (b) represent carbon and low alloy steels, spring steels and carburized steels, respectively. This is an important outcome of the PCA analysis as it helps in identifying different types of steels without taking any scientific inputs fromthe user. It must also be noted that PCI and PC2 cover -59% of the variance while PCI and PC3 cover only 54% of the variance. Hence, plot of only two principal components is not enough to visualize any possible patterns. One needs to consider higher dimension visualization tools to get patterns out of the PCA scores. We used clustering algorithm in higher dimensions corresponding to 95% confidence level to get the actual clusters.

37

Figure 2: Score Plots (a) PC2 vs. PCI (b) PC3 vs. PCI Figure 3 shows a loading plot for all 35 parameters . The loading plot gives information on degree of correlation between different parameters . The degree of correlation is quantified in terms of the angle (cosine) between the lines joining the two points of interest to the origin [4]. If the angle made by the two variables at the origin is 6, then 0=Oo signifies highly positive correlation between variables, 0=180o signifies highly inverse correlation between variables, and 0=9Oo signifies no correlation between variables. An expected inverse correlation is highlighted in Figure 3 by the two filled diamonds connected by a line and open boxes. The parameter s are the percentage elongation in quadrant2 and fatigue strength in quadrant4.

Figure 3: Loading plot from PCA with 35 parameters, which includes fatigue strength and shows thefirsttwo PCs Figure 4 shows the plot of cosine of angle (0) that various parameter s make at origin with respect to fatigue strength in the loading plot. As it was mentioned earlier, two PCs are not enough to visualize any pattern or to draw any conclusion; the angles were calculated by considering the number of PCs required for 95% confidence level, which amounted to 14-dimensional-space of

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principal components. It can be observed from Figure 4 that HvCase (case hardness), HvCore (core hardness), UTS, YS, Tt (tempering time), case depth, oR (residual stress) and Ct (carburizatio n time) are highly positively correlated with fatigue strength. In contrast, % elongation, % reduction in area, TT (tempering temperature ) and TCr (cooling rate from tempering temperature ) and charpy impact strength, are highly inversely correlated with fatigue strength. Here, it may seem at firstthat these relationships are already known and also that most of these variables are response variables and not control variables. But, this study, exclusively statistical, by truly predicting the correlations, which are already known, gives confidence that the informatics approach works well and that it can also result in the creation of new knowledge, which is not yet discovered.

Figure 4: Plot of degree of correlation of various variables w.r.t. fatigue strength The interpreted results from the loading plot were validated with the existing knowledge on relations between fatigue strength and the other parameters . Rossele et al. [11] examined correlations among the various monotonie and fatigue properties of steels commonly used for ground vehicle industry. They concluded that there is strong correlation between transition fatigue life and hardness of steels. Genel [12] developed a simple analytical method to predict bending fatigue limits of case hardened steels. His analysis resulted in a correlation between fatigue strength, core hardness, effective case depth and residual stress at surface. Hence, the results obtained in the present study guided by statistics were in close agreement with the experimental findings. Besides this, the well-known fact of UTS being highly correlated to fatigue life was also observed. After finding patterns and correlations in the database, PLSR was applied on different clusters to build correlations between control variables and response variables including fatigue strength. Figure 5 shows the predicted against experimental values of fatigue strength. Large R2 values in the range of 0.88-0.94 were obtained for different clusters, indicating a high level of confidence for these predictions. It was also observed that -81% of the predictions were within ±5%error margin and -98% of the predictions lay in the ±10%error margin.

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Figure 5: Predicted vs. experimental fatigue strength values The application of PLSR on different clusters resulted in the building of models, which could predict the fatigue strength/life of a material (limited to carbon and low-alloyed steels, spring steels and carburized steels) by taking inputs as chemistry and processing conditions. Although these models result in correlations among chemistry, processing and properties, the structure part (microstructura l features) is still missing. The NIMS fatigue database does not give information on the structural parameters such as phase fraction, grain size, precipitate fraction etc. We believe that building correlations among chemistry, processing, structure and properties would be of great interest to the industrial community for accelerating the design process, which in turn will result in the accelerated insertion of new materials. Currently, we are working on integrated physics-based modeling of heat treatment operations (such as carburizing, through hardening, tempering etc.) of steels to bring the structural parameters into the materials informatics approach. We believe that the informatics approach in combination with physics-based modeling will help the materials engineering community and also designers in accelerating the materials development, including the prediction of new materials with superior properties, and design processes. Conclusion The current state of materials development process is very time consuming and expensive and there are problems associated with chemistry-processing-structure-performanc e correlation prediction. In this regard, the informatics approach seems to be promising for understandin g such correlations. Therefore, such an approach could lead to accelerated materials development. In the present study the correlation between chemistry, processing and fatigue strength of different types of steels was predicted, with a confidence level of more than 90%, totally based on informatics/statistica l approach. The study also resulted in understandin g the influence of various parameters such as fraction of alloying elements, % reduction and processing conditions on the

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fatigue strength of steels, which could guide materials engineers on the shop floor to design new grades of steels with tailored performance , once a physics-based approach to bring in the microstructura l aspects is also incorporated . Appendix Abbreviation C Si Mn P S Ni Cr Cu Mo NT THT THt THQCr CT Ct DT Dt QmT TT Tt TCr RedRatio dA dB dC Ncase YS UTS El (%) RA (%) Charpylmp HvCore HvCase CaseDep oR Fatigue

Details % Carbon % Silicon % Manganese % Phosphorus % Sulphur % Nickel % Chromium % Copper % Molybdenum Normalizing Temperatur e Through Hardening Temperatur e Through Hardening Time Cooling Rate for Through Hardening Carburizatio n Temperatur e Carburizatio n Time Diffusion Temperatur e Diffusion time Quenching Media Temperatur e (for Carburization ) Tempering Temperatur e Tempering Time Cooling Rate for Tempering Reduction Ratio (Ingot to Bar) Area Proportion of Inclusions Deformed by Plastic Work Area Proportion of Inclusions Occurring in Discontinuous Array Area Proportion of Isolated Inclusions Austenite Grain Size Number Yield Strength Ultimate Tensile Strength % Elongation % Reduction in Area Charpy Impact Strength Core Hardness Case Hardness Case Depth (For Carburization ) Residual Stress Rotating Bending Fatigue Strength (10A7 Cycles)

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References [I] Committee on Integrated Computational Materials Engineering, "Integrate d Computational Materials Engineering: A Transformationa l Discipline for Improved Competitiveness and National Security," National Research Council, 2008. [2] S. Gadzuric et al., "Extractin g Information from the Molten Salt Database", Metallurgical and Materials Transactions A, 37 (2006), 3414-3414. [3] L. George et al., "Principal component analysis on properties of binary and ternary hydrides and a comparison of metal versus metal hydride properties" , Journal of Alloys and Compounds, 478 (2009), 731-735. [4] C. Suh and K. Raj an, "Informatic s for Chemical Crystallography" , JOM Journal of the Minerals, Metals and Materials, January (2009), 48-53. [5] K. Rajan, "Materials Informatics" , Materials Today, 8 (10) (2005), 38-45. T6I http://tsuge.nims.go.ip/top/fatigue.htm l [7] S. Wold, K. Esbensen, and P. Geladi, "Principal Component Analysis", Chemom. Intell. Lab. Syst., 2 (1987), 37-52 [8] M. R. Euerby and P. Petersson, "Chromatographi e Classification and Comparison of Commercially Available Reversed-Phase Liquid Chromatographi e Columns Using Principal Component Analysis, J. Chromatogr. A, 994 (2003), 13-36. [9] J. Bajorath, "Selected Concepts and Investigations in Compound Classification, Molecular Descriptor Analysis, and Virtual Screening", J. Chem. Inf. Comput. Sei., 41 (2) (2001) 233-245. [10] C. Suh, A. Rajagopalan, X. Li and K. Rajan, "The Application of Principal Component Analysis to Materials Science Data", Data Sei. J., 1 (1) (2002), 19-26. [II] M. L. Roessle and A. Fatemi, "Strain-Controlle d Fatigue Properties of Steels and Some Simple Approximations" , International Journal of Fatigue, 22 (2000), 495-511. [12] K. Genel, "Estimation Method for the Fatigue Limit of Case Hardened Steels", Surface & Coatings Technology, 194 (2005), 9 1 - 95.

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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

Multi-Attribute Integrated Forming-Crush Simulation Optimization Using Internal State Variable Model "Ali Najafil, Masoud Rais-Rohani2, Youssef Hammil" "1 Center for Advanced Vehicular systems, Mississippi State University;" "Mississippi State, MS 39762, USA" "2 Department of Aerosapce Engineering; Mississippi State University;" Mississippi State, MS, 39762, USA Keywords: "Process-Produc t Simulation, Process-Product optimization, InternalState Variable model." Abstract As metal alloys go through different stages of a manufacturin g (e.g., sheet forming) process, their microstructur e and engineering properties tend to change. Consequently, when optimizing a structural component (e.g., rail) for performance (e.g., energy absorption), it is important to account for the evolution of material state variables. Material behavior of sheet metal components used in vehicle body will be significantly changed due to the forming process. The work hardening effects along with the residual stresses and other state variables can change the material behavior which can be resulted into different energy absorption behavior. This also can open up a new opportunity to assign process parameters based on not only the process acceptance level but based on the product performance. In this paper, an internal state variable theory is used for integrated process-product simulation optimization. State variables are initialized due to history of the material in forming and springback process so that the performance response is going to be affected by the history of the material represented as state variables. This methodology is used to design optimize of proper energy absorbing components. The optimization is performed on the metamodels that are developed based on a table of design of experiment to train an analytical function representing deep drawing, spring back and crush. Introduction It is important to account for the evolution of material and structure state to be able to evaluate a component as built rather than as designed. Coupling of the material, process and performance scenarios is an important factor to capture the actual physical behavior of material and structures. This coupling facilitates the idea of integrated material-process-performanc e design [1-2]. Both material (micro-level) and structure (macro-level) will be affected due to the history of loading in the structures. In micro-level, the material state including microstructure , defect and internal stresses evolve subject to different loading paths. In macro-level, the geometry permanently deforms to form a desired shape. The history effects usually emerge from plastic deformation and failure and fracture. Plastic deformation occurred in metallic materials is resulted from slip or twins associated with a complex deformation mechanisms, such as thermally activated dislocation motion and generation, dislocation annihilation, dislocation drag, texture effects, void nucleation, growth and coalescence, small deviatoric elastic stretching, potentially large volumetric elastic stretching and large rotations [3]. Ideally, all the aforementioned effects should be considered as history variables known as state variables in the material. The residual stresses and geometric distortion can also be accounted as history variables. It is worth noting that there is no reaction or material change is considered here and all the aforementioned

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mechanisms are emerged as consequences of deformation. As the loading environment becomes more severe, the influence of history effects becomes much more important. Although the intent of material modeling is to include all the features and state variables into account, most of the models are limited to specific applications because of ignoring the gradient of state variables. Another difficulty is coming from the numerical implementation of material models. As our understandin g of material and modeling expands the importance of coupled simulation to consider the history effects becomes more feasible and interesting. Ultimately, the aim is to reduce the material characterizatio n experiments to the early stage of manufacturin g processes (e.g. testing a blank sheet before forming process) and then carry out the history of microstructur e as well as geometry changes through coupled simulation. It has been shown that accounting for the load history provides a more realistic simulation that results into more reliable predictions [4-7]. In recent years, there has been some research to integrate the history effects on the performance simulations [8]. Most of these researches are incorporating classical plasticity models and consider equivalent plastic strain as the major driver to introduce the history effects on the performance [9]. Their main focus was on forming simulations to capture the history used in crush simulation. It has been identified that the considering the kinematic hardening as state variables can improve the correlation between numerical and experimental results. It is identified that the kinematic hardening is also a major player to capture a proper spring back because of the more accurate predictions of stress distribution in the components [4]. It is worth noting that computational tools may also limit us in order to include the history effects of processing in performance simulation. In general, most of finite element codes have restart options which can be used once the whole procedure of coupled process-product simulation is done in identical framework. One major limitation for coupled simulation is the code limitation on transferrin g the state variables from one simulation to other. This research tries to incorporate the history effects from forming into crush simulation. Previously developed internal state variable model that accounts for combined isotropic and kinematic hardening as well as damage nucleation, growth and coalescence is considered. The material integration is modified for plane stress problems which are more popular for these types of simulation because of the better behavior in combined membrane-bendin g deformation as well as its computational efficiencies for complicated models. This draft paper addresses the finite element modeling strategy related to process-performanc e simulation, sensitivity analysis of the major players from manufacturin g and geometric point of view, while using ISV pure plasticity model as well as coupled damage-plasticity models. Coupled Process-Performance Simulation In order to perform mathematical optimization to include manufacturin g process effects in energy absorption behavior (performance), integrated forming-spring back-crush simulation is performed in ABAQUS. For forming and crush simulations, ABAQUS/Explicit [10] and for springback analysis ABAQUS/STANDARD [11] is used under isothermal condition. A double hat tube which is modeled by joining two single hat c-channel tubes is taken into account. In this study, both c-channels are assumed to be identical is assumed to be identical. In order to perform the forming simulation, two sets of blank/holder/die sets are defined in FE model. Figure. 1 shows the FE model of a single hat blank/holder/die sets. The same die set is mirrored with respect to a parallel plane to the blank plane considering the offset of the half blank thickness. The forming simulations for each single hat are performed so that the punch and holder forces are applied in opposite directions to produce the actual cross-section of closed section double hat assembly.

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The presented forming simulation contains two basic steps in explicit finite element. The steps are distinguished based on the boundary and loading conditions: Gripping the blank between die and holder: The holder forces are increased linearly to reach the actual holder force specified as one of the manufacturin g process parameters . In this step, punch and dies are kept fixed in their positions. By increasing the holder force, the contact between the holders and dies with blank is increased. In this stage, the kinematic contact formulation is used because of the computational efficiency of the formulation. The simplicity of the geometry enabled us to define the surfaces through standard analytical rigid surfaces. Therefore, in this stage as well as the next stage (the deep drawing stage), punch, dies and holders are defined by analytical rigid surfaces. Contact surfaces are defined on both sides of the blank surfaces by considering the surface offset due to the blank thickness. Penalty formulation is used in tangential contact and a friction coefficient is defined as manufacturin g process parameter s representing both surface roughness and draw beads. Drawing simulation: After fixing the blank between holders and dies, the deep drawing stage is modeled by applying constant velocity to punch that has the final geometry of the product. So the result of previous step is directly transformed to this step. In this step, the boundary conditions on the fixed punch are removed in the direction normal to the blank surface and a constant velocity is applied to the punch to forms the c-channel cross-section of the single hat section. The amount of punch displacement which is going to represent the height of the single hat section is extractedfromthe termination time and the velocity of the punch. In this study, the velocity of the punch is assumed to be constant that result into linear displacement. It should be noted that this will not guarantee that rate will not be constant throughout the simulation for the entire elements and the rate sensitivity of the material should also be taken into account. In this step, dies are remained clamped and the holders are fixed in all degrees offreedomexcept the direction perpendicular to the blank surface. In this direction, the final holder force that is constantly applied in order to preserve the constant gripping force throughout the drawing process as well.

Figure 1. Finite element model for forming of each single hat section

In order to evaluate the amount of spring back in the model, the state variable and geometric information from the deep drawing simulation is transferre d and treated as the initial state in the model. Spring back process is considered to be a quasi-static problem considering the stress distribution captured fromdeep drowning, dynamic effects and contact conditions. Additionally, all the rigid surfaces including punch, dies and holders are removed from the FE model which makes model to be more suited for implicit finite element analysis considering the quasi-static nature of the spring back phenomenon and absence of highly nonlinear factors in the model. The springback deformation is resulted fromthe initial state resulting fromdeep drawing simulation. In order to guarantee the convergence and the stability of the non-linear implicit FE analysis,

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boundary conditions are defined such that the two edges of the hat sections are fixed perpendicular to the actual normal surface. As shown in figure 2, the equilibrium condition is achieved by constraining the model in all the transverse directions. The boundary condition defined in this stage is designed such that the effect of the force required to assemble a non-fitted double hat section is considered and the resulting stress distribution is affected by the final assembly. In this stage residual stresses and geometric attributes are updated during quasi-static analysis while other computational state variables such as plastic strain are remained unchanged. It is worth mentioning that similar to deep drawing simulation, the spring back analysis is performed on two single hat sections simultaneously. The two double hat sections are simulated separately and there is no interaction between the two pieces in both deep drawing and spring back simulations. Two double hat sections will be assembled in the next stage to produce a double hat crush tube.

Figure 2. Boundary condition defined in spring back analysis

Crush simulation is performed using the resulting geometry, residual stresses and state variables based on the material model used in the simulation resulted from deep drawing and spring back analysis in explicit finite element solver because of the high nonlinearity associated with crushing process. The two double hat sections resulted from the spring back simulation trimmed by removing the elements and then the resulting shapes are assembled on two edges of the hat sections as shown in figure 3. Tubes are connected through the highlighted edges shown in figure 3 using tie contact formulation. Tie contact is constrained the surfaces of the master and slave surfaces similar to multiple constraint points when once the clearance between two surfaces are below the tolerance defined as an input variable. If the surfaces are out of prescribed tolerance, the interaction becomes a contact formulation. Study showed that the switching the master and slave surfaces will not affect the crushing behavior of the tube. Once the distance between two surfaces becomes more than the clearance tolerance the contact formulation is activated similar to the conventional contact definition. Owing to the geometry of double hat and presence of the initial condition imported from previous steps, selecting a proper contact formulation to perform the crush simulation is critical. Six contact interaction sets between elements are defined in the crush simulation including interactions between lower single hat and rigid wall, upper single hat and rigid plate, interaction between upper and lower single hat sections, tie contact between the assembly edge of upper and lower surfaces, and self contact interaction for upper and lower hat separately. For all of the aforementioned contact interaction sets penalty function formulation is used. Despite of computational cost, using penalty function provides a proper flexibility for the explicit code to find the stable time step affected by severity of the contacts. Moreover, maximum ratio of thickness to element length is used to overcome the difficulty of the fine mesh density that results to have relatively thick shell elements. This option is used to enhance the effect of contact thickness and consequently to reduce the mesh distortion and ultimately unsuccessful simulation.

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Figure 3. Trimming and Joining of single hat tubes after springback simulation

Crush simulation is done by fixing the tube in one end and applying load through a rigid wall defined with prescribed displacement in the other end. The rigid wall is defined to move with constant velocity to simulate constant loading rate as shown infigure4. The material model used in this section is piece-wise linear isotropic hardening material model. In this material model, stresses and deformation will be transferre d between simulations and the computational state variable considered is the equivalent plastic strain. Considering the equivalent plastic strain captured from deep drawing simulation in crush represented by the modification of the yield surface for crush analysis. In this study, a magnesium AZ31 sheet material data at room temperatur e is used for all the simulations.

Figure 4. Description boundary conditions and loading for crush

Constitutive Model In order to predict structura l responses and performance in the virtual design optimization methodology, it is essential to link external loads (like force and displacement) to the structura l internal material responses, such as stress and strain. The relationship between external stimuli and material internal responses are termed as constitutive equations of the material. They are essentially set of mathematical or phenomenological equations. The phenomenological equations are established based on the physical behavior observed in dislocation plasticity in lower length scales such that the continuum model can also link to the material microstructure . In the present study, the plastic behavior is represented through isotropic and kinematic hardening to model the post yield behavior as well as static and dynamic recovery that can model the saturation of stressstrain responses. The model has 21 plasticity constants as well as physical properties such as density, elastic modulus, Poisson ratio, heat coefficient and ambient temperatur e [12-14]. The model is implemented as VUMAT in ABAQUS/EXPLICIT by considering total strain, plastic strain, kinematic hardening and back stress tensors and plastic equivalent strain, volumetric inelastic strain, isotropic hardening as the computational state variables [15]. In this model, the coupling between damage and plasticity is ignored and it is assumed that the material will not experience any deterioration due to damage. The model is implemented for both 3D-continuum and plane stress elements. The numerical solution of the differential equations representing the

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constitutive relations requires starting with initial guess. Initial values are usually assumed to be zero in the simulations since there is no information about the material state from experimental characterizations . In the calibration process offittingconstants the initial value is assumed zero. Therefore, all the constants are calibrated based on the fact that the material initial state is pristine and state variables are zero. In this paper, it is assumed that all the constants are calibrated before stamping process. Thus the initial state of the stamping process is zero. But as the material state evolves during the deformation imposed by deep drawing, the values of these state variables accumulates and are not zero anymore. These values are directly sent to crush simulation to initiate the plasticity model used in the energy absorption simulations. In this study, magnesium AZ 31 is used for simulation the constants are listed in table 1. Tablel. Material constants for AZ 31 magnesium alloys

Sensitivity Analysis To facilitate the optimization process and find a proper range to vary the parameter s mentioned above, the sensitivity of the variables to responses is considered. The average point of all the design variables are considered as base line model and each design variable is perturbed by ±15% at a time while keeping the rest of design variable constants. Table .2 listed the range defined for each design variable and the table is used for the sensitivity analysis. Figure 5 and 6 show the result of the sensitivity study. Effect of varying each design variable is normalized and shown in eachfigureseparately. Bar chart is divided into two groups and each color represents a response related to deep drawing, spring back and crush simulations. The left side illustrates the responses that are deviated as a result of -15% deviation of design variable and rightrepresents the responses derived as a result of+15% deviation of design variable. As it is clearly shown the spring back is very sensitive to the design variables. It can be also shown that the manufacturin g process variables such as holder force or punch velocity can affect the performance the crush tube which are defined as maximum and mean crush forces.

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Table 2. The value assigned in each FE simulation for sensitivity Corner Height Width Thickness Radios Sensitivity (mm) (mm) (mm) (mm) 55 27.5 1.75 Friction Coefficient 55 27.5 1.75 ±15% 55 27.5 1.75 55 27.5 1.75 55 27.5 1.75 Punch Velocity ±15% 55 27.5 1.75 55 27.5 1.75 55 Holder Force ±15% 27.5 1.75 55 27.5 1.75 55 27.5 1.75 Thickness ±15% 55 27.5 1.3125 55 27.5 2.0125 55 27.5 5 1.75 Comer Radios ±15% 55 27.5 3.75 1.75 27.5 5.75 55 1.75 55 5 1.75 27.5 55 Height ±15% 1.75 20.625 5 55 31.625 5 1.75 55 27.5 1.75 Width ±15% 27.5 41.25 1.75 27.5 63.25 1.75 70 40

study and the actual range of variables Holder Punch Friction Velocity Force Coefficient (m/s) (KN) 30 0.225 30 0.16875 30 0.25875 30 6 0.225 30 4.5 0.225 30 6.9 0.225 30 0.225 22.5 0.225 34.5 0.225 30 0.225 30 0.225 30 0.225 30 0.225 30 0.225 30 0.225 30 0.225 30 0.225 30 0.225 30 0.225 30 0.225 30 0.225 0.35 0.1

Figure 5. Sensitivity of the stamping process parameter s on the manufacturin g and performance responses

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Figure 6. Sensitivity of the forming tools and blank on the manufacturin g and performance responses

In order to find the most affected response by varying design variables aforementioned plots are presented in figure 7 to 11. Friction coefficient and punch velocity are shown to be more effective in rupture response calculations. Thinning and springback is highly affected by punch velocity as shown in figure 8,9. Figure 8,9 also show a nonlinear relationship between design variables and response such that the amount of increase and decrease of the design variables do not have the same impact on the thinning.

Figure 7. The influence of design variables on the rupture response from stamping process

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Figure 8. The influence of design variables on the thinning response from stamping process

Figure 9. The influence of design variables on the springback response from stamping process

The effect of design variable on the crush response in terms of maximum crush force and mean crush force are illustrated in figures 10 and 11. It has been shown that the geometric attributes have more impact on the crush behavior with the expense of mass increase. It is shown that the deviation fromthe base line model will result into the increase in the responses seen in the crush simulations. Friction coefficient has the least effect on the maximum force where as holder force is considered to have the least effect on the mean crush force.

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Figure 10. The influence of design variables on the maximum force response from crush simulation

Figure 11. The influence of design variables on the mean crush force response from crush simulation

In order to reduce the computational cost during design optimization, a reduced order models such as metamodelling can be used. Different metamodelling technique including response surface approximation (RSA), radial basis function (RBF), support vector regression (SVR), Gaussian process regression (GPR), Kriging model and ensemble of metamodels is taken into consideration. In order to train the metamodels a set of training points are required. The presented training points are captured through Latin hypercube sampling in MATLAB. Fifty points are generated for seven variables including four geometric attributes and three process parameter s as described in previous sections. Table.2 is listed out the training points used for the present study.

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Table 2. Design of experiment points based on Latin hypercube sampling (LHS) method

Table 3. Results of simulation related to the DOE points using integrated process-product simulation

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The training points are used as different set of parameter s to perform integrated process-product simulation using ABAQUS. After running each simulation user defined results generator is ran to extract the responses defined in the previous sections. Table 3 provides the response information related to each DOE point. Training points and the responses are used to build up different metamodels based on the different formulations. Our study showed that RSA formulation can capture the rupture behavior of material during manufacturin g process. Thinning is captured through Kriging formulation and rupture spring back and weight is represented via GPR. The multi-objective optimization is formulated to minimize rupture,thinning, springback, maximum crush force and weight and minimize the mean crush force subject to the side constraint mentioned in table 2. The solution to the multi-objective problem provides a set of optimum points that can minimize the combination of the aforementioned objective functions. The set of optimum points representing Pareto frontier are extracted showing different combinations of weight factor as shown infigure12. Table 4. Optimum points considering different weight factors for the objective functions

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Figure 12. Paterto frontier for the multi-objective

Conclusion In this paper, the influence of manufacturin g process affected response on the energy absorption behavior of thin-walled tube is investigated. The history effects from manufacturin g process is carried out to the crush simulation through the state variables defined in the constitutive model developed based on internal state variable theory. A sensitivity analysis on design variables including manufacturin g process parameters as well as blank geometric attributes is performed to identify the impact of each design variable on the responses. In order to accelerate the optimization process, metamodels are developed to use to explore the design space. Multi-objective optimization based on genetic algorithm is utilized to find the best optimum points located in the Pareto frontier. Acknowledgments This material is based on the work supported by the US Department of Energy under Award Number DE-EE0002323. References [1] McDowell, D.L., Choi, H.-J., Panchal, J., Austin, R., Allen, J.K. and Mistree, E, "Plasticity -Related Microstructure-Propert y Relations for Materials Design," Key Engineering Materials Vols. 340-341, 2007, pp. 21-30. [2] cDowell, D.L., "Simulation-Assisted Materials Design for the Concurrent Design of Materials and Products," JOM, Vol. 59, No. 9, 2007, pp. 21-25.

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[3] Regueiro R.A ,Bammann D. J., Marin E. B., Garikiapati K., A Nonlocal Phenomenological Anisotropie Finite Deformation Plasticity Model Accounting for Dislocation Defects, Journal of Engineering Materials and Technology, July 2002, Volume 124, Issue 3, 380 [4] Williams, B.W., Simha, C.H.M., Abedrabbo, N., Worswick, M.J., Mayer, R., Effect of Anisotropy, Kinematic Hardening, and Strain Rate Sensitivity on the Predicted Axial Crush Response of Hydroformed Aluminum Alloy Tubes, Internationa l Journal of Impact Engineering, 37, 652-661, 2010. [5] Ryou H., Chung K., Yoon J., Han C, Incorporation of Sheet-Forming Effects in Crash Simulations Using Ideal Forming Theory and Hybrid Membrane and Shell Method Journal of Manufacturin g Science and Engineering, Vol. 127, No. 1, pp. 182-192, February 2005 [6] Lee Y., Han C, Chung K., Youn J., Kang T. J., Influence of back stresses in parts forming on crashworthiness, Journal of Materials Processing Technology, Volume 168, Issue 1, 15 September 2005, Pages 49-55 [7] Gadekar G.B., Raj P., Kshirsagar S., Anilkumar C, Inclusion of Forming Effects in Crash simulations Using One Step Forming Simulations, Altair CAE User's Conference Innovation Through Simulation August 3-5, 2006, Banglore, I [8] Oliveira, D.A., Grantab, R., Worswick, M.J., Williams, B.W., Mayer, R., Relationship Between Forming and Subsequent Crashworthines s of Aluminum Alloy Tubejnternationa l Journal of Impact Engineering, 32 (5), pp. 826-846, May, 2006. [9] Najafi, A. & Rais-Rohani, "Sequential Multi-Attribut e Process-Performanc e Simulation and Optimization of Thin-Walled Components", 16th Design for Manufacturin g and the Life Cycle Conference (DFMLC), August 28-31, 2011, Washington, DC. (under review) [10] ABAQUS/Explicit version 6.10, user's manual.," 2010, Hibbit, Karlsson and Sorensen Inc., Rhode Island, USA [11] "ABAQUS/Standar d version 6.10, user's manual.," 2010, Hibbit, Karlsson and Sorensen Inc., Rhode Island, USA [12] Bammann, D. J., "Modeling Temperatur e and Strain Rate Dependent in Large Deformation of Metals," Applied Mechanics Reviews, Vol. 43, No.5, Part 2, May, 1990. [13] 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 andN. Jones, Elsevier Applied Science, The Universities Press (Belfast) Ltd, 1993. [14] 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. [15] Hammi Y, Horstemeyer M.F., A physically motivated anisotropic tensorial representation of damage with separate functions for void nucleation, growth, and coalescence, Internationa l Journal of Plasticity, Volume 23, Issues 10-11, October-November 2007, Pages 1641-1678. Disclaimer: This report was prepared as an account of work sponsored by an agency of the United States Government. Neither the United States Government nor any agency thereof, nor any of their employees, makes any warranty, express or implied, or assumes any legal liability or responsibility for the accuracy, completeness, or usefulness of any information, apparatus, product, or process disclosed, or represents that its use would not infringe privately owned rights. Reference herein to any specific commercial product, process, or service by trade name, trademark , manufacturer , or otherwise does not necessarily constitute or imply its endorsement, recommendation, or favoring by the United States Government or any agency thereof. The views and opinions of authors expressed herein do not necessarily state or reflect those of the United States Government or any agency thereof.

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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

Multiscale modeling of polycrystalline magnetostrictive alloy Galfenol: Microstructura l model 1 Veera Sundararaghavan

department of Aerospace Engineering University of Michigan; Ann Arbor, MI 48109 USA Keywords: Magnetostriction, Crystal plasticity, Galfenol, Texture. Abstract A recently discovered alloy, Galfenol, has been shown to exhibit magnetostrictive strains up to 400 fi in single crystal form (more than 10 times that of a—Fe). This letter presents preliminary computational investigation of microstructura l changes during deformation that affects the final magnetostrictive performance. We have developed a microstructur e evolution model that captures crystallographic texture evolution and evolution of magnetization orientation using crystal plasticity simulations. Both loading and unloading processes were simulated and a finite strain homogenization algorithm was developed to investigate final microstructura l response under coupled magnetic and stress fields. Introduction When a magnetic field is applied to Galfenol single crystal, the boundaries between the magnetic domains shift and rotate, both of which cause a change in the material's dimensions. This behavior, termed magnetostriction, has been successfully to transduce magnetic field to mechanical force in micro-scale (MEMS) sensors and actuators. While single crystals of Galfenol provide large magnetostriction, their preparation is expensive. It is well known that thermomechanica l processes (such as rolling and extrusion) may provide means to develop polycrystalline Galfenol with properties comparable to expensive single crystals [1]. However, it has proved difficult to predict (and thus, control) the large changes in properties such as magnetostriction and yield strength that occur during thermomechanica l processing. For example, warm rolled and annealed specimens retain high magnetostriction but are quite brittle; whereas, cold rolled specimens have high yield strength but lose their magnetostriction [2, 3]. Consequently, it is critical to develop predictive models that can be used to optimize thermomechanica l processes and control properties in the final product. Properties of Galfenol can be tailored by controlling the evolution of features of underlying polycrystalline microstructur e through controlled plastic deformation. Simulation of microstructur e evolution in polycrystals has been well studied in the past. The success of such approaches has allowed efficient computation of the effect of macroscopic parameters (such as forging rates) on the microstructura l response. Microstructure-sensitiv e design methods can then employ these techniques to address inverse/optimization problems such as computation of optimal crystal orientation distributions that lead to desired elasto-plastic properties [4]. In order to control properties during processing, it is important to study the effect of mesoscale features (such as texture, misorientation distribution) on the response of these alloys. For example, experimental studies suggest that internal inhomogeneous strains introduced by microstructura l changes play an important role in determining the final magnetostriction in Galfenol [5]. In this paper, we have calibrated a rate-independen t elasto-plastic model of

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BCC Galfenol single crystal for studying the effect of forming processes on the microstructure response. Both loading and unloading processes have been simulated and a finite strain homogenization algorithm has been developed to investigate final microstructura l response under coupled magnetic and stress fields. Microstructur e Evolution Direct Problem A rate-independen t single-crystal plasticity model developed in Kothari and Anand [6] is used to compute the effect of macroscopic strain on the polycrystal. For a material with a = 1 , . . . , TV slip systems defined by ortho-normal vector pairs (ma,na) denoting the slip direction and slip plane normal respectively, the constitutive equations relate the following basic fields: the deformation gradient F which can be decomposed into elastic and plastic 1 parts as F = FeFp , the Cauchy stress T (= and the slip resistances sa > 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
(1)

a

where S% = ma 0 na is the Schmid tensor and j a is the plastic shearing rate on the ath slip system. The resolved stress on the ath slip system is given by ra = T • S%. The resolved shear stress ra attains a critical value sa on the systems where slip occurs (7° > 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 - | )

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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.

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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,

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(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

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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°<<90° (High oblique angle) case II 0°<< 90° (Whole range) caselll 0 ° < ^ < 5 0° (Low oblique angle)

Figure 5 Comparison of the vertical impingement and rebounding velocities in different SMAT cases

The results of the numerical evaluation of the stored energy as a function of plastic deformation in different cases are presented in Figure 6. It has been shown that the total stored energy increase monotonically with deformation. The ratio (ß) of total heat generated to total plastic work provides an approximation of the average fraction of plastic work converted into heat. The calculated ratio fromEq.(5)-(6) and Eq.(9) is plotted in Figure 7. It increases with the amount of energy injected in the material. As strain increases, the ability to stored energy is reduced. When the material is SMATed, about 90% to 95% of the deformation energy is converted to heat. The SMAT process in case I stored a relatively large amount of energy in defects as compared with other two cases. Due to the random impact process, some regions of the sample surface may have received impacts by the flying balls for many times while some other locations may have received much less impacts. Thus, locally, the temperatur e distribution is not uniform even in the same layer. Here the center location of the sample is chosen and the temperatur e distribution

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along depth from the surface layer is plotted in Figure 8. It can be seen that the temperatur e increase at the sample surface layer due to impacts is about 30~80°C. This is in agreement with the experimental measurement [3].

Figure 6 The total stored energy as a function of plastic work

Figure 7 Fraction of plastic work convert into heat

Figure 8 Temperatur e rise profile

Conclusions SMAT is a promising method to optimize the material surface structure. Various experiments have been carried out to study the properties of SMATed material. In this paper, the energy partition during SMAT process is studied by employing a local full coverage random impact model. When AISI 316L stainless steel is SMATed, most of the deformation energy (about 90% to 95%) is converted to heat and the remainder of the energy is stored in the lattice as strain energy. The energy injected in the material by the flying balls is directly related to the impact angle. Impact directions with high oblique angle will store large amount of strain energy in defects. As the strain increases, the ability to store strain energy is reduced. Our simulation results confirm that the mechanical multi-directiona l impingements under high strain rate during SMAT process of AISI 316L stainless steel can create a considerable amount of stored energy in the surface layer. This amount of stored energy represents a significant driving force for the grain . This work was supported by a research grantfromAREVA NP. refinement at low temperatures Reference 1. 2. 3. 4. 5. 6. 7. 8. 9.

H.Gleiter, "Materials with ultrafine microstructures : retrospectives and perspectives," Nanostruct Mater 1(1992),1-19. K.Lu, J.Lu, "Surface Nanocrystallization (SNC) of Metallic Materials Presentation of the Concept behind a New Approach," J.Mater.Sci.TechnoL, 15(3)(1999), 193-197. K.Lu, J.Lu, "Nanostructure d surface layer on metallic materials induced by surface mechanical attrition treatment," Materials Science and Engineering A, 375-377(2004), 38-45. N.R. Tao, Z.B. Wang, W.P. Tong, M.L. Sui, J. Lu, K. Lu, "An investigation of surface nanocrystallization mechanism in Fe induced by surface mechanical attrition treatment," Acta Materialia, 50 (2002), 4603. H.W.Zhang, Z.K.Hei, G.Liu, J.Lu, K.Lu, "Formation of Nanostructure d Surface Layer on AISI 304 Stainless Steel by Means of Surface Mechanical Attrition Treatment," A eta Materialia, 51 (2003), 1871. X.C.Zhang, J.Lu, S.Q.Shi, "A computational study of plastic deformation in AISI304 induced by surface mechanical attrition treatment," ISCMIIAND EPMESCXII, PTS J AND 2. 1233 (2010), 328-333. M.B.Bever, D.L.Holt, A.L.Titchener, "The stored energy of cold work," Prog. Mat.Sci., 17 (1973), 1. G.R.Johnson, W.H.Cook, "A constitutive model and data for metals subjected to large strains, high strain rates and high temperature, " Proceedings of the 7th International Symposium on Ballistics: (1983),541. H.L.Chan, H.H.Ruan, A.Y.Chen, J.Lu, "Optimization of the strain rate to achieve exceptional mechanical properties of 304 stainless steel using high speed ultrasonic surface mechanical attrition treatment," Acta Materalia 58(2010), 5086-5096.

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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

Phase-Field Simulation and Experimental Study of Precipitates in an Al-SiMg Alloy Zhiqiang Gao1, Hengcheng Liao1, Ke Dong1, Qigui Wang2 2

Southeast University, SiPaiLou #2, Nanjing, 210096, China Advanced Materials Engineering, GM Powertrain,483-710-251,895 Joslyn Ave. Pontiac, MI 48340

Keywords: phase-field simulation, Al-Si-Mg Alloy Abstract To better understand the physics that govern the precipitation of meta-stable phases in aluminum alloy, including precipitation kinetics, crystal structure,morphological evolution and particle size distribution of precipitates, the coarsening kinetics of ß" precipitates in a ternary Al-Si-Mg alloy was studied using phase-field simulations. The bulk thermodynami c information and atomic diffusion mobility was obtained from the first principle calculation, CALPHAD, as well as experiments, while the experimental values for the interfacial and elastic energy are directly employed in the phase-field model. The morphological evolution and average precipitate size are predicted as a function of time for a given temperatur e and composition. Comparison of the phase-field simulation results with experiments shows good quantitative agreement in both time and length scales. 1 Introduction Phase field modeling has emerged as one of the most powerful methods for modeling of many types of microstructur e evolution processes in recent years. Phase field applications cover solidification, solid-state phase transformation , coarsening and grain growth [Chen, 2002] [Chen et al., 2001]. Zhu et al. studied the coarsening kinetics of/'precipitates in binary Ni-Al alloy using 3D phase-field simulations [Zhu et al., 2004]. Long et al. developed a phase-field model for multi-component alloys based on binary phase-field model [Long et al., 2006]. ACCESS conducts a research in phase field modeling and has developed software MICRESS1, which is based on the phase-field method and is capable of simulating solidification and solid state phase transformation s in multiple-phase alloys. FiPyframeworkincludes terms for transient diffusion, convection and standard sources. Currently implemented models include phase field treatments of polycrystalline and dendritic phase transformations , etc2 . The goal of the Mesoscale Microstructur e Simulation Project (MMSP) is to provide a simple, consistent, and extensible programmin g interface for all grid and mesh based microstructur e evolution methods. It provides Monte Carlo methods, cellular automata methods, as well as phasefieldmethods3. The purpose of this paper is to report our quantitative predictions of the coarsening kinetics of /?" precipitates in Al-Si-Mg alloys using 2D phase-field simulations, which is based on the publically available software package FiPy. Simulation results are compared with experimental observations and measurements. It is shown that 2D phase-field simulations on coarsening kinetics of /?"precipitates are in quantitative agreement with experimental measurements in both real time and spatial scales. 1 2 3

http://web.access.rwth-aachen.de/MICRESS / http://www.ctcms.nist.gov/fipy / http ://www. matforge.org/cmu/wiki/mms p

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2 Model Description According to the documents of FiPy, we consider a free energy density f(,C0,...,CN,T)that is a function of phase (j) . The interstitial components are C0,...,CM , and the substitutional components areCA/+1,...,C# _ 1 . A solvent C^that is constrained by the concentrations of the other substitutional species, such thatC^ = 1 ~ X =M^J • * n m e

case

°f Al-Si-Mg alloys the interstitial

component is C0 , and the substitutional components are C, = CSi , C2 = CMg . The solvent is C3 = CAl, and it is constrained by C3 = 1-C, - C 2 , i.e. C

1 - CSi - CMg . The simulation

temperatur e is 7 = 150°C, 160°C, 170°C, respectively. 2.1 Phase Equation The free energy density of such a system can be written as A
= j^CJ\u^J) L

7=0

+

(1)

RT\n^\ P \

where R = 8.314JI{mol K) is the gas constant. u^,T)

= p^)u;^,T)

+

(\-p^))uf(T)

+

W -^g^)

(2)

is constructed with the free energies of the pure components in each phase, given the tilting function / ^ ) = ^ ( 6 ^ - 1 5^ + 10)

(3)

and the double well function g W = ^2 (l-«>) 2

(4)

We consider a simplified model that has partial molar volumes V0=... = VM = 0 for the interstitials and VM+l =...= VN =lfor the substitutionals. This approximation has been used in a number of models where density effects are ignored. Under these constraints

Z-tcZ-tc r u°UJ)RT\n-t-

P

w ,CjJ)

~\

(5) (6)

for T=0...M and uU,T)RT)n^-

>,T)RT\n^ (7) --[uJV9CJ9T)-uNU,CIf9T)] P P . wyis the classical chemical potential of fory' = M + l . . j V - l, whereu°jaß"(T) = u0"(T)-u°f"(T). dC,

component j for the binary species, and p = 1 + ^ ._ Cy is the total molar density. We "cook" the standard potentials to give the desired a and ß " concentrations, with a a phase rich in interstitials and the solvent and aß"phase rich in the two substitutional species. We create the phase equation

70

w

LÄ.v.«,-f ,

C M, dt y=o with a simi-implicit source. Where

+ 0(l-)m(,AT)

(8)

(9) m ( ^ A r) = ^ - - - ^ a r c t a n ( ^2 A r) 2 n represents a source of anisotropy. The coefficient D is an anisotropic diffusion tensor in two dimensions

l + cß D = a\l + cß)-cdJdy/

-c dy/ X + cß

(10)

1_(D2 (N \ , and TV is the where/? = —■—, 2 0 = tan — ¥ , ¥ = # +arctan—-——, 0 is the orientation l+O (,2 ) didx symmetry. 2.2 Composition Equation We could construct the diffusion equations one-by-one. For the interstitial diffusion equations, we arrange in canonical form: dC, 2 — L = DS/2Ci + D,VD dt

J

J

'

C J -

W,

1 + S î l o C J^

uorVp() + ^r

-Zvc,

The canonical form of the substitutional diffusion equations is dC,. , C, — ^ = £> .V2C, + D,VQ ^ & J J J 1 + 5£C -**/ 4 PF —PF

I Or.

(12)

AT

Eve I J

i=M+l

(a) t=30 min

(b) t=60 min

71

(11)

'=0

(c)t=90min (d)t=150min Figure 1 Phase-field distribution of /?"precipitates growing parallel to [001] direction of matrix atl60°C after 3 hours 3 Results and Analysis 3.1 Simulation Results Grid size is dx = 0.025 ,dy = 0.025 .Grid number is wc = 200, ny=200 . The fixed time step is<# = 5xlO-\£V=2.25, a = 0.015, c = 0.02, N = 6, 0 = - , r = 3xl0 - 4 , *:, = 0.9, A:, =20. 8

T

»

1

»

2

One simulation is shown in Figure 1, in which we show the coarsening process of /?"phase growing parallel to the [001] direction of matrix at different times. The experimental result is shown in Figure 2, and comparison of the phase-field simulation results with experiments shows good quantitative agreement in both time and length scales.

Figure 2 TEM micrographs of 160°C peak-aged L2 alloy, taken in Jan, 2009

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3.2 Experimental Results The composition of two A356 alloys was measured by a spectrometer, shown in Table 1. All samples were solutized in an Quenching Furnace. The temperatur e inside the furnace was fixed at 535 °C± 2°C. When the furnace was heated up to 535 °C, the samples were put rapidly into it. After 6h solutization, the samples were quenched in water within a 15s of delivering time. One experimental result is given in Figure 2. It could be found that the simulated morphology of/?"precipitate s coincide well with the experimental ones. Table 1 Composition of experimental Al-Si-Mg alloy

L

Si

Mg

Zn

Mn

Fe

Ti

Sr

Al

7.078

0.195

O.010

O.010

0.067

0.114

0.012

bal

5 Conclusions We have applied a 2D phase-field model to simulate the coarsening kinetics of /?" needles in AlSi-Mg alloys with real length and time scales. While keeping the interfacial energy constant, we are able to simulate micro-structura l evolution in physical systems with length and time scales comparable to experimental results. The simulated morphological pattern agrees well with experimental observations in terms of morphology and spatial correlations. The model developed is promising for quantitatively modeling and predicting micro-structura l evolution in commercial Al-Si-Mg alloys. References [Chen, 2002] L. Q. Chen: Phase-Field Models for Microstructur e Evolution, Annual Review of Material Research 32, pp 113-140. 2002 [Chen et al., 2001] L. Q. Chen et al.: Modeling Solid-State Phase Transformation s and Microstructur e Evolution, MRS Bulletin 26 (3), pp 197-202. 2001 [Guyer et al., 2009] J. E. Guyer, D. Wheeler, J. A. Warren: FiPy: Partial Differential Equations with Python, Computing in Science & Engineering 11(3) pp6-15. 2009 [Long et al, 2006] W. Y. Long, Q. Z. Cai, B. K. Wei, L. Q. Chen: Simulation of Dendritic Growth of Multicomponent Alloys Using Phase-field Method. ACTA PHYSICA SINICA, 55(3), pp 1341-1345. 2006 [Zhu et al., 2004] J. Z. Zhu, T. Wang, A. J. Ardell, S. H. Zhou, Z. K. Liu, L. Q. Chen: Threedimensional Phase-field Simulations of Coarsening Kinetics of y ' Particles in Binary Ni-Al Alloys. Acta Materialia, 52(9). pp2837-2845. 2004

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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

Towards a virtual platform for materials processing Georg J. Schmitz1 and Ulrich Prahl2 ACCESS e.V. at the RWTH Aachen University, Intzestr. 5, D-52072 Aachen, Germany department of Ferrous Metallurgy, RWTH Aachen University, Intzestr. 1, D-52072 Aachen, Germany Keywords: ICME, phase-field modeling, simulation platform, microstructure , effective properties, standardization , vtk visualization toolkit Abstract This article outlines ongoing activities at the RWTH Aachen University aiming at establishing a platform for ICME comprising a virtual, integrative numerical description of processes and of microstructur e evolution along the entire production chain and even extending further towards microstructur e and properties evolution under operational conditions. Based on a standardized interfacing between microstructur e evolution simulations and macroscopic process simulations, the efforts aim at predicting effective material properties from calculated microstructure s and at the extraction of relevant data adapted to the requirement s of higher level simulation codes. Following a short description of the platform concept, some details of the standardizatio n concept are highlighted and the web-based operation of the platform is shortly addressed. Results on first simulations of partial process chains for simple parts indicating the benefits of an ICME approach using the platform concept conclude the article. Introduction Permanently increasing complexity of products and their manufacturin g processes combined with the demand on high quality products with tight dimensional and material quality tolerances require the use of integrative simulation techniques in product and process design. This situation leads to a dilemma, where more and more effort has to be spent in planning in order to meet the challenges of producing a high value product. Strategies to reduce the dilemmas of production are addressed within the Cluster of Excellence "Integrativ e Production Technologies for High Wage Countries" [1] Simulations form an essential part of the planning activities for production processes. To decrease the dilemma between the efforts spent for planning and the product value eventually being generated, a reduction of planning efforts and/or an increased value of the resulting product are possible approaches, fig 1.

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Figure 1 : Planning efforts can be strongly reduced with respect to time and costs (i) if the performance of individual simulation processes is improved, (ii) if only those models relevant to mimic the desired effect in sufficient detail are used and especially (iii) if the information exchange between individual models is improved by standardized interfaces. Simulating the entire production chain also leads to an increased value of the products e.g. by a future prediction of their life-cycle. Concept of a platform for ICME Describing or even predicting the properties of a component is a key objective of ICME, which has been identified as a strategic approach for future competitiveness [2]. These properties are essentially determined by the microstructur e of the component. Tracking the local microstructur e evolution - besides a number of other data - requires boundary conditions for all processes affecting the microstructur e during the life cycle of the component. These boundary conditions can be provided by a variety of different FEM simulations on the component scale being daisychained to cover the entire production sequence and extending even to the subsequent operational conditions. A structura l framework for ICME comprising a variety of academic and/or commercial simulation tools operating on different scales and being modular interconnected by a standardized data exchange thus will allow integrating different disciplines along the production chain, which by now have only scarcely interacted. This will substantially improve the understandin g of individual processes by integrating the component history originating from preceding steps as initial condition for the actual process. Eventually this will lead to optimized process and production scenarios and will allow effective tailoring of specific materials properties. Efforts to standardize and generalize data formats for the exchange of simulation results thus represent a major step towards successful future applications of ICME. A suitable data standard easily links e.g. the successful FEM models used in mechanical engineering and computational fluid dynamics amongst each other and especially with microstructur e models like the phasefield method, which actually seems to become the "FEM for metallurgists" . This eventually will allow for monitoring the evolution of the microstructur e - and thus the properties of the component - starting from the sound initial condition of a homogeneous, isotropic and stress free melt and eventually ending in the prediction of failure under operational conditions. Furthermor e effects of transformation s in the microstructur e on the properties of the component can be tackled by extracting local effective properties from the microstructur e information and feeding them back into the simulation tools on the component level.

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Based on previous work on integrative materials modeling [3], the simulation platform concept AixViPMaP® has been defined [4]. The basic philosophy of the AixViPMaP® is to provide an open, modular, standardized , extendable and comprehensive platform for any type of simulation related to materials processing and production. In the long term this platform may even be extended to and applied for logistics and factory layout. The nucleus of the AixViPMaP® platform is based on several software codes and models for materials processing available at the RWTH Aachen University, which have been adapted to a common standard based on the vtk format [5] [6] by using semantic approaches [7] and by drawing back on the university's IT infrastructure . The platform in future is meant to be extendable and open to any interested user and to any provider of simulation models. This platform presently allows for an efficient information exchange between the process simulation tools along the process chains and also across several length and time scales, fig. 2. It already has been applied to several test-scenarios.

Figure 2: Modular concept of the AixViPMaP simulation platform. Individual simulation tools being considered as black-boxes can be combined for different processes along the entire production chain on different length scales. The scales being addressed by the platform by now are limited to continuum models in 2D and 3D. The methods being used comprise CAx, FEM, FDM X-FEM at the component scale and - at the scales of the microstructur e and in the sub-micron range - multi-phase-field-models , cellular automata, CALPHAD type thermodynamic s and kinetics and CP-FEM (i.e. Crystal plasticityFEM). Bridging between the scales is realized by boundary conditions for small scale simulations being locally extracted from larger scale simulations. Properties being determined at a small length scale are homogenized resp. averaged by means of virtual testing and/or mathematical homogenization and fed back to the higher level codes. The precision of simulations at the component level is significantly improved by consideration of locally varying, anisotropic materials properties. The platform is embedded between the smaller length scales of atomistic and ab-initio simulations and the larger length scales of production machinery and factory layout/ logistics, to which interfacing will be increasingly provided.

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Figure 3: Scheme of the information flow between two different modules of the AixViPMaP simulation platform. Individual simulation tools are daisy chained along the different processes . along the entire production chain in a bus-bar type architecture The standardizatio n concept of information flow, fig. 3, on the one hand refers to a standardized exchange of data comprising information about the geometry of the simulated components/processes, their boundaries and field values within the simulation domain: scalar fields like temperature , concentration of alloy elements; vector fields like e.g. flow velocities or higher order tensors like stresses/strains. All these data - along with some additional information on units/scales being applied and others - are stored in an enriched .vtk format [5][6]. Physical properties of individual phases, which do not depend on process history or actual load conditions, are stored in material data files in an Abaqus type ASCII format. The content of these files may be generated from other software codes like Thermo-Calc [8], JMatPro [9], FactSage [10] or similar, from ab-initio simulations on the atomistic level or from experimental observations. Similar to commercial FE-codes like ABAQUS, Ansys, FEAP, MARC, STAR-CD and others material data depending on actual conditions or comprising a history are calculated on the basis of Fortran subroutines, which will - at least for elastic materials properties - be made available as a library in the future [11]. Calls for materials laws are similar to USERMATHT (thermal materials law), USERMAT (mechanical materials laws) USEREXPAN (mechanical materials laws including thermal expansion) USERPTRAN (phase transitions and solidification) or USEREL (FE-integration ) calls in ABAQUS. The definitions for standardized calls will be published soon elsewhere [11]. The boundary conditions are either taken fromprocess parameters provided by the user or - in case of microstructur e simulations - taken fromlarger scale process simulations. The results of a simulation are forwarded to an enrichment/reduction/data-integration module, which may serve as a parser/sequence r for data conversion if necessary, but especially monitors meta-information about the overall history of the simulated process chain (e.g. absolute position/orientatio n of the component in a global coordinate system, total process time elapsed, integrated energy consumption for a process chain and others) and integrates this information as meta-data for further evaluation by the user. Once a simulation chain has been set up, the user essentially will only modify process parameters in the frameof parameter variations. The control files comprise information e.g. for numerical stability and other data relevant for numerics. These files in general have to be composed by users skilled in the specific software tool.

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Web-based operations of the platform To that point the standardizatio n is already most useful to exchange simulation results and to use simulation results of a preceding process as an initial condition for a simulation of the subsequent process step. Efforts for data conversion by now representing a major part of work when performing coupled simulations can thus be omitted or at least be strongly reduced. In a next step the number of different simulation tools may become part of a computational network. Presently, workflow sheets for process chains can be easily edited and simulations for some cases can be performed on a GRID using a suitable middleware like a Condor system [12],fig4.

Figure 4: Scheme of a simulation chain running on a computer grid. The input file being created with a work flow editor is submitted to the middleware, which checks for the software tools being required and identifies computers being capable to run these tools. The middleware further controls the timing between different simulations, provides conversion routines from/to the platform standard and eventually collects the results and meta information. ICME results for test scenarios First integrative simulations for dedicated testcase scenarios reveal that specific properties resp. phenomena can only be understood in the frameof a holistic approach covering several process steps on both the process scale and the scale of the microstructure . Result highlights comprise the description of flow-curves for ferritic-pearliti c line-pipe steels [11,13], the reduction of the experimental effort for the determination offlow-curves,the optimization of the production of case-hardened components with respect to reduced carburizatio n times while maintaining grain size stability [11,13,14], determination of the influence of inner properties on mechanical properties in thermoplastic materials by simulation of spherolitic microstructure s comprising anisotropy of the molecules [11,15], calculation of the effective, anisotropic modulus of textile reinforced components [11], identification of a combination of segregations originating from solidification and mechanical stresses resulting from heat-treatmen t and machining as origin of a martensitic transformatio n leading to failure of the component [11,13,16]. Future perspectives This paper has described a concept for a platform for ICME, its present status and first results. ICME is a field where - due to its broad, complex and interrelated topics - hierarchical research structures will probably fail. In order to promote a "self-assembly" of the ICME community a common language based on a standardized information exchange seems to be a major pre-

79

requisite. The authors would be happy, if the proposed platform concept [11] would be picked up and further developed by the ICME community in the future. Acknowledgements: The present article is based on on-going work of 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/IMA), Institute for Textile Technology (ITA), Fraunhofer Institute for Lasertechnology (ILT/NLD) and ACCESS. Funding of the depicted research by the German Research Foundation (DFG) in the frame of the Cluster of Excellence "Integrativ e Production in High Wage Countries" is gratefully acknowledged.

References 1. www.production-research . de 2. National Research Council: Integrated Computationa l Materials Engineering: A Transformationa l Discipline for Improved Competitiveness and National Security; National Academic Press, Washington, D. C. (2008), ISBN: 0-309-12000-4. 3. G. Gottstein (eds.): Integral Materials Modelling: Towards Physics Based ThroughProcess Models, Wiley - VCH Verlag, Weinheim (2007), ISBN 978-3-527-31711-0. 4. G.J. Schmitz, U. Prahl: Toward a Virtual Platform for Materials Processing JOM 61 5 (2009)26 2009 5. W. Schroeder, K. Martin, B. Lorensen: The Visualization Toolkit - An Object-Oriente d Approach To 3D Graphics, 4th Edition, Kitware, Inc. (2006), www.vtk.org. 6. S. Benke et al.: "Definition of a standardized data format for the exchange of simulation data", available online at: www.aixvipmap.de 7. D. Schilberg, A. Gramatke, K. Henning: Semantic interconnection of distributed numerical simulations via SOA. Proc. of: World Congress on Engineering and Computer science, San Francisco, USA,2008, S. 894-897, ISBN 978-988-98671-0-2 8. Thermo-Calc : Thermo-Calc Software AB, Stockholm, www.thermocalc.se 9. JMatPro: Sente Software, Surrey, UK, www.sentesoftware.co.uk 10. FactSage: GTT Technologies, Aachen, Germany, www.factsage.com 11. G.J. Schmitz and U. Prahl (eds): "Integrativ e Computationa l Materials Engineeringconcept and applications of a modular simulation platform" , book currently under preparation : Wiley - VCH Verlag, Weinheim (2011) ISBN 978-3-527-33081-2 12. P. Cerfontaine et al.: "Towards a Flexible and Distributed Simulation Platform" , Computationa l Science and its Applications - ICCSA 2008, Springer Lecture Notes in Computer Science LNCS 5072 Parti 13. G.J. Schmitz et al.: "Towards Integrative Computationa l Materials Engineering of Steel Components" , accepted for publication: Prod. Eng. Res. Devel. (2011) 14. U. Prahl et al.: "Modelling the process chain of microalloyed case hardening steel for energy efficient high temperatur e carburizing" paper presented at this conference 15. W. Michaeli et al.: "Integrativ e materials modeling of molecular orientation in amorphous thermoplastic parts" to appear: Proc. of the 27th Annual Meeting of the Polymer Processing Society, Marrakesh , Marocco, May 2011 16. S. Benke et al.: "Through process simulation of manufacturin g and service life of highprecision cast parts made from austenitic stainless steel" accepted for publication: The Internationa l Journal of Multiphysics (2011)

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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

Integrated Modeling of Tundish and Continuous Caster to Meet Quality Requirements of Cast Steels Amarendra K Singh*, Ravindra Pardeshi, and Sharad Goyal TRDDC-TCS Innovation Labs, TCS Ltd., 54 B, Hadapsar Industrial Estate, Pune, India *amarendra.sinqh(5)tcs.com Keywords: ICME, Integrated Modeling, Steelmaking, Tundish, Continuous Caster

its limitations since not every parameter of interest can be measured, and even if it is possible to measure these, it may not be economical or feasible to conduct measurements on a regular basis. It is well known that mathematical models play a major role in not only filling up this gap, but also enabling better understandin g of the process, the effect of various parameter s (including their interactions) on the performance of the process, and also, assisting in process control.

Abstract Mathematical modeling has been used extensively by the steel industry to optimize individual unit operations such as tundish and caster to address productivity and quality related issues of the plant. This approach has worked well for various plants to some extent. However, there are major limitations to this 'Silo' based approach. The operation of continuous casting is interlinked with the transient nature of tundish operation which gives rise to the need to develop an integrated modeling framework to provide optimum solutions for productivity and quality related issues to meet the requirement s of down stream processes. Some of the highlights of this integrated modeling approach are presented in this paper. A new methodology of providing optimum casting speed is also discussed

1. Introduction

The general name, steel, comprises hundreds of different steel grades which have broad range of various physical and chemical properties. Besides iron and carbon, steel usually consists of manganese, silicon, micro-alloying elements (such as Cr, Ti, V, Nb, Mo, B, etc.) and impurities like sulphur and phosphorous. Steel is produced by melting iron ores and/or scrap and figure 1 shows typical process flow line for steelmaking process. In the second step the molten steel is purified and several chemical elements are added to it to create the desired steel composition. Once it has gone through this process the molten steel is nowadays often cast by continuous casting, where the steel solidifies. After casting, the steel is rolled into the desired dimensions and heat-treated . Besides the chemical composition of steel, all these processes affect the steel properties and quality. Because steel is formed of several chemical elements, its solidification is characterized by a temperatur e range, unlike pure metals which solidify in specific temperature s (e.g. iron).

Figure 1 : Secondary steelmaking - process flow line

The steel industry has been introducing new alloys for automotive applications to improve the product performance and to meet the challenges posed by other materials. Introduction of new and improved alloys such as AHSS requires enabling technologies to reduce the costs and lead times of the development. The performance of a formed sheet component in an automobile is influenced by the entire life cycle the material has gone through its production. Starting from the chemistry and cleanliness of the molten steel, casting, rolling, heat treatment, forming and other processes influence its properties and performance. Tracking the evolution of the properties as well as determining the cause of a particular property is a challenging task, especially when diverse manufacturin g processes influence them.

With increasing emphasis on the production of consistent quality slabs at higher casting speeds, it has become mandatory to focus on making improvements at every stage of the casting process. Slab quality is directly affected by various intermediate operations, viz., ladle operations, tundish operations, transfer operations and finally, mold and caster operations. Tundish and continuous casting operations, subject of the present study, greatly affect steel quality. In this direction, it is necessary to quantify the effect of various operating parameter s on the performance of the process. One way to do this is by direct measurement through process sensors. However, this method has

1.1 Problem Definition

The mechanical properties of the final cast product are defined by the final macro/microstructur e and defect levels in the cast product. As seen in figure 2 (adapted from ref [1]), the macrostructur e showing the three zones (1) columnar grains (2) equiaxed grains and (3) chill zone at the border. From quality control point of view, the equiaxed grains give better mechanical

81

properties and reduced defect levels (eg. segregation). The control of micro/macro structure and defects of the cast product depend upon the temperatur e coming inside the continuous caster. The schematic of tundish and continuous caster is shown in figure 3. In steel plants, there is thrust towards strict control of liquid metal temperatur e coming out from tundish to inlet to continuous caster (CC). The temperatur e above the liquidus temperatur e of metal is called 'superheat' , and controlling superheat at CC inlet has been a major challenge in the steel plants for controlling the quality of cast product. As the steel plants operate under several transient processing conditions, it becomes difficult to control superheat at CC inlet. In practical conditions, the plant operates under varying superheat conditions leading to varying quality along the slab length which in turn can lead to problems during down stream processing or in the field application. It is important to understand the quality problems occurring during transient varying superheat conditions at CC inlet. Also, it will be very useful to find the possible solution to overcome the quality issues arising due to superheat variations at CC inlet.

Figure 3 : Tundish and continuous caster

2. Model-Based Approach A. Through-Proces s Modeling

Mathematical models describing individual and combined processing operations are used widespread throughout the materials processing industry. In the past, separate models were developed to describe the process for each operation but recently, the need to describe the interactions of these physical phenomena based model has led to integrated computational materials engineering (ICME) approach.[2-6] The modeling of tundish and continuous caster (CC) process has been useful tools in understandin g the process and solving issues related to processes. In almost all previous works, the model based on 'silo' approach - where an individual model has been used to study the tundish or caster separately without considering the effects of upstream / down stream processing conditions considered. They have been used to study several problems such as the formation of dead zone in tundish or crack formation in caster through thermo-mechanica l analysis under steady state conditions. But, in the present problem such approach will not work as the tundish processing conditions will give input temperatur e to CC and CC processing conditions and will decide the final quality of cast product at the caster exit. The schematic of modeling framework is shown in figure 4.

Figure 2 : Macrostructur e of cast product [1] The superheat variations at the caster inlet have a direct impact on mechanical properties and defects generated in the cast product. During continuous casting, there are transient variations of superheat due to dynamic variations of processing conditions (casting speed, caster cooling conditions, tundish weight, etc.) which cause variations in properties along the slab length. In the present work, an integrated modeling approach is used that will consider the transient processing conditions. The model will identify several possible solutions towards reducing property variations at caster outlet.

Figure 4 : Modeling approach

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variation, casting speed variation are shown in the figure 7. The plant data shows variations in tundish weight variation with time for five ladle heat sequence where it shows there is variation in tundish height based on transient plant operations.

2.1 Brief Description of Individual Models 2.1.1 Tundish Model

The variation of tundish temperatur e under the influence of various operating parameter s is numerically simulated using a mathematical model. A two-dimensional mathematical model, based on coupled fluid flow and heat transfer, is developed to simulate tundish operation. The model accounts for turbulent fluid flow and dynamic level changes in tundish. The model is validated with data published in literature as well as with data obtained during plant campaign. Simulation of tundish operation demonstrates the capability of the model in capturing process dynamics correctly. The typical flow pattern inside tundish is shown in figure 5.

Figure 7 : Measured tundish weight variations [7] Based on the superheat measured at the tundish exit after interval of approximately 15 min, the casting speed is varied based on measured temperatur e value. Also, during changeover of ladle the casting speed is reduced to maintain metal level at tundish. Based on the transient operating conditions, the plant measured casting speed variation for five heats are shown in figure 8.

Figure 5 : Metal flow inside the tundish [7]

2.1.2 Continuous Caster Model

A quasi-3D finite-element based thermo-mechanica l model of continuous caster has been developed that predicts temperatur e and stress/strain developed during different cooling conditions. The materials model used in FEM simulations are based on laboratory data obtained using Gleeble® data. The model has been calibrated using in shop-floor data. The model can accurately predict thermal and stress field during continuous casting operations. The typical stress and temperatur e field predicted by model is shown in figure 6.

Figure 8 : Measured casting speed variations [7]

3.2 Simulation Results

The simulations were carried out using plant data described in previous section. Figure 9 shows model predicted tundish outlet temperature . As seen from figure 9, there can be caster superheat variation of ~ 25 °C during casting of one ladle pouring operations. Also, during changeover there can be large variations of caster superheat.

Figure 6 : Thermo-mechanica l conditions at caster Figure 9 : Model predicted tundish outlet temperatur e [7]

3. Plant Condition and Simulations 3.1 Plant Data used for Simulations

Using this caster superheat variation at the inlet of caster, the thermo-mechanica l model for caster was used to simulate thermal and stress/strain conditions at the cast product. Based on multislice simulation of thermo-mechanica l model, the model predicted shell thickness variation with time, shown in the figure 10.

Simulations were done using actual plant data collected during our previous work with Tata Steel Ltd. from their LF and CC sections [7]. The typical plant data on tundish weight

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3.3 Microstructure and Defects Predictions

The model parameter s of cooling rate and caster superheat are used to predict the secondary dendrite arm space and columnar-to-equiaxe d transition point (CET) at various locations. These two are important parameter s as secondary dendrite arm space gives estimate of microstructur e grain size and CET gives morphology of final microstructur e of cast product. Figure 13 shows variations of secondary arm space with time at three locations from centre to surface of the slab.

Figure 10 : Model predicted shell thickness of cast product The model predicted temperatur e at four locations on the cast slab surface is shown in figure 11. For different times, the variation of slab surface temperatur e depends upon caster superheat variations and change in cooling conditions based on caster superheat variations. It can be seen that the existing cooling strategy is not able to compensate for caster superheat variations.

Figure 13 : Variation of secondary dendrite arm space

Figure 11 : Model predicted surface temperatur e

Figure 14 : Variation of equiaxed zone

Figure 12 : Model predicted plastic strain

Figure 14 shows percentage of equiaxed zone in cast product versus time as predicted by the model using correlations from the literature.

Based on model simulations, the plastic strain variation with time is shown in figure 12. As seen from the figure, there have been large variations in the plastic strain based on dynamic cooling conditions and caster superheat variations.

During continuous casting, the cooling conditions can lead to thermal and stress conditions which can lead to possibility of crack formation. As seen in figure 15, at time 40 mins, there is a condition when the stresses are high, mold exit shell thickness is low and surface temperatur e is high. This scenario can lead to crack formation.

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Figure 16 : Different cooling segments of CC

Figure 15 : Crack prediction Hence, as seen from the simulation results there are variations of cast microstructur e and defect variations due to transient operating conditions in the tundish and continuous caster.

4. Solution to the Problem Modified Cooling Strategy The current plant practice is to measure caster superheat after 15 mins. (approximately) and the casting speed is changed based on the value of the caster superheat. Based on casting speed the controller changes the water flow rates (or cooling conditions) at all sections of primary and secondary cooling zones. The problem in this approach is that the material in downstream segments (see figure 16) might have come with different superheat and it is cooled with superheat conditions at current superheat at caster inlet. In order to overcome this issue, we have modified the cooling conditions based on spray water flow rate of different sections that will be based on the caster superheat the material has experienced. To explain it further, the model will track the material in different cooling sections and have water flow rates for that material based on caster superheat of material. The model was used to simulate casting conditions based on modified cooling practice and it shows improvement in cooling which is shown in figure 17.

Secondary dendrite arm spacing (A2)

Figure 17 : Effect of modified cooling condition on SDAS

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[3] John Allison, Dan Backman and Leo Christodoulou, "Integrate d computational materials engineering: A new paradigm for the global materials profession", JOM, Volume 58, Number 11, 25-27, 2008.

5. Conclusions

In the present work, the operation of continuous casting is interlinked with the transient nature of tundish operation and an integrated modeling framework is used to address issues of property and defect variations in cast product. Due to plant operation practice during secondary steelmaking, there are large variations of caster inlet temperatur e which cause variations in properties and defects. Using actual plant data, the simulation results showed variations in the grain size and cracks during CC in present plant practice. In order to address this issue, two solution methodologies are proposed. Based on simulations of solution methodologies, we see potential for quality and productivity improvement in steel plants.

[4] Krishna Raj an, "Informatic s and integrated computational materials engineering: Part II", JOM, Volume 61, Number 1, 47, 2008. [5] L. M. Bartolo, S. C. Glotzer, C. S. Lowe, A. C. Powell, D. R. Sadoway, J. A. Warren, V. K. Tewary, M. J. M. Krane and K. Raj an, "Materials informatics: Facilitating the integration of data-driven materials research with education", Volume 60, Number 3, 51-52,2008. [6] Committee on Integrated Computationa l Materials Engineering, National Research Council, Integrated Computationa l Materials Engineering: A Transformationa l Discipline for Improved Competitiveness and National Security, National Academies Press, 2008

6. Acknowledgments

Encouragement and support from CTO, Mr. K Ananth Krishnan, and Dr. Pradip are gratefully acknowledged.

7. References

[1] A. Ghosh, "Secondary applications", CRC Press

steelmaking:

principles

[7] R. Pardeshi, R., S. Basak, A.K. Singh, B. Basu, V. Mahashabde, S.K. Roy, and S. Kumar, "Mathematica l modeling of the tundish of a single-strand slab caster," ISIJ International , 44(9): p. 1534-1540, 2004.

and

[8] S. K. Choudhary and S. Ganguly, "Morphology and Segregation in Continuously Cast High Carbon Steel Billets", ISIJ International , vol. 47, no. 12, pp. 1759-1766, 2007.

[2] Diran Apelian, "Integrate d Computationa l Materials Engineering (ICME): A model for the future?", JOM, vol. 60, no. 7, pp. 9-10, 2008.

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

MICROSTRUCTURE-BASED DESCRIPTION OF THE DEFORMATION OF METALS: THEORY AND APPLICATION Dirk Helm 1, Alexander Butz 1, Dierk Raabe2, Peter Gumbsch 1,3 1 Fraunhofer Institute for Mechanics of Materials IWM, 79108 Freiburg, Germany 2 Max-Planck-Institut e for Iron Research, 40237 Düsseldorf, Germany 3 Institute for Applied Materials IAM, Karlsruhe Institute of Technology KIT, 76131 Karlsruhe, Germany Keywords: crystal plasticity, process chain, sheet metal forming, homogenization This article is a shortened version of JOM Journal of the Minerals, Metals & Materials Society, 63 (2011), 26-33. [1] Abstract Aiming for an integrated approach to computational materials engineering in an industrial context poses big challenges on the development of suitable materials descriptions for the different steps along the processing chain. The first key component is to correctly describe the microstructura l changes during the thermal and mechanical processing of the base material into a semi-finished product. Explicit representation s of the microstructur e are most suitable there. The final processing steps and particularly component assessment then has to describe the entire component which requires homogenized continuum mechanical representations . One of the main challenges is the step in between, the determination of the (macroscopic) materials descriptions from microscopic structures, which can be seen as a virtual testing laboratory. In the first part this manuscript gives a short overview of the different methods to include microstructur e into descriptions of the deformation of metals. In the second part it demonstrates the central steps of the simulation along the processing chain of an automotive component manufactured from a dual phase steel. The simulation of the cold rolling of the steel sheet provides the morphology, texture and deformation history of the individual grains in a representative microstructure , which is then evolved in a virtual thermal treatment into the dual phase ferritic-martensiti c structure from which the anisotropic yield surface of the sheet can be calculated. The simulations are compared to dedicated experiments performed at each step. The results demonstrate the enormous potential of such a systematic computational approach. 1 Introduction Industrial success in materials related technologies relies on the possibility to specifically engineer materials and products with improved performance. The key success factor is the ability to make these material-relate d developments timely and at relatively low cost. This demands not only the rapid development of new or improved processing techniques but also better understandin g and control of material structure, performance, and durability. Such control of materials involves multiple length and time scales and multiple processing stages or the coupling of processing and performance assessment. To achieve this, the materials descriptions and the flow of information necessarily have to be based on materials microstructur e characteristics.

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Such inclusion of materials specifics in engineering simulation still is one of the major challenges for the development of improved materials modeling and simulation (cf. [2], [3]). The linkage between materials microstructur e and materials properties is at the heart of materials modeling in general but very specifically so for the description of materials deformation. Multiscale approaches (cf. Figure 1) are required to make the link fromthe discrete dislocations, grain and phase boundaries which constitute the materials microstructure , to the continuum plasticity descriptions appropriat e at larger scales. While it may certainly be appropriat e to investigate micro-components like micro-pillars [4] or micro-bending bars [5] directly at the level of discrete dislocations, large scale components mandate the final treatment of the component in a continuum mechanicalframework[6]. Although there have been many attempts to include the discrete dislocation behavior rigorously in continuum mechanical materials modeling (see e.g. [7]), the mathematical frame for such inclusion has only recently been developed (see [8], [9]) and is still farfrombeing applicable. Consequently the materials models are either effective materials descriptions or have come to be physically based to at least include some direct microstructura l information. Similarly it is neither desirable nor intended to include the grain or phase morphology of a material explicitly in the materials modeling at large scale. One therefore either uses effective representation s of texture or homogenization techniques to arrive at continuum mechanical models.

Figure 1. Scheme of a continuum mechanical framework for poly crystal-polyphase mechanics with various ingredients describing the material behavior at different degrees of microstructur e coarse graining and homogenization. The applicability of modern microstructure-base d modeling in industrial forming simulations is assessed in [10]. The drive towards microstructure-base d models comes on the one hand from process simulation and the optimization of individual processing steps or the entire processing chain during manufacturin g and on the other hand from the requirement of higher precision in the simulation of component manufacturin g and component assessment. Figure 3 pictorially displays such a processing chain and thefinalcomponent assessment.

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Today, microstructure-base d simulations are used for example in the process simulation of semifinished parts in the aluminum industry [11]. This aids process optimization and the specific adjustment of materials properties of the sheet material. For aluminum, alloy development and the individual processes determining the microstructur e are reasonably well understood and modeling is developed to a relatively high level [12]. Other materials and particularl y the steels are less well understood and detailed microstructura l modeling is still rare. This is in part due to the many complex phase transformatio n phenomena and kinetic pathways involved [13]. In the overall component design which involves an assessment of the crash worthiness of automotive components, or even the shape, springback or property predictions of components out of the deep drawing and stretching steps, microstructura l modeling is basically not yet employed. However, the perspectives for microstructure-base d modeling in this field are great. It can for example correctly represent the anisotropic yield surface and its non-uniform evolution during deep drawing and thereby not only enable much more precise prediction of the local properties of a component but also allow for integrated product optimization through the entire process chain. As an application example of such integral materials modeling we report here simulations of the final steps in the processing chain of a dual phase carbon manganese steel sheet, which is intended for use in automotive components. 2 Crystal Plasticity in the Framework of Continuum Mechanics During the last decades, the evolved knowledge about deformation mechanisms in metals has stimulated the development of appropriat e constitutive theories in the framework of continuum mechanics. The continuum mechanical representatio n has clear restrictions but is at the same time the best way to represent certain parts of a complex process chain. An important ingredient when aiming at through-proces s models is the use of internal variable constitutive formulations that are capable of tracking history dependent behavior. Typical internal variables are dislocation density, grain size, and second phase dispersion. The use of external variables (such as strain) cannot describe inheritance of microstructure s through a sequence of processes. While most constitutive modeling has hitherto focused on the modeling of single crystalline materials or homogeneous materials, modern developments increasingly focus on materials microstructure . Poly crystalline and also multiphase metallic materials are of particular interest in technical applications. The inhomogeneity in the microstructur e due to texture, precipitations, different phases, etc. requires suitable homogenization schemes for the transition from single crystals to polycrystals. 2.1 Mean-field Methods A reasonable way to obtain the effective properties of a material is given by homogenization schemes on the basis of simplified assumptions about the material behaviour and the morphology . In such mean-field approaches the microstructur e can be considered as a of the microstructure system of an inclusion that is embedded in a matrix. The most basic assumptions would be either uniform stress or uniform deformation gradient among all phases or respectively grains present in the microstructure . These cases were suggested by Reuss [14] and Voigt [15] for elasticity. The fully constrained Taylor [16] model for plasticity or the extension of Lin [17] for elastoplasticity correspond to the uniform strain assumption. Both assumptions ignore the shape and specific local neighbourhood of the inclusions and generally violate strain compatibility and stress equilibrium, respectively. More sophisticated mean-field assumptions make use of the Eshelby-solution [18] of an elastic ellipsoidal inclusion in an infinite elastic matrix. Out of those, the most frequently employed are the self-consistent approach originally suggested by Kröner [19], and the scheme introduced by Mori and Tanaka [20]. In the former method, each inclusion

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is treated as isolated within a matrix having the unknown integral stiffness of the compound. The latter approach embeds each inclusion into the original matrix but considers the average matrix strain to act as far-field strain on the overall composite. Extension of such homogenization schemes from the linear to the non-linear case faces difficulties, because the stiffness, i.e. strain(rate)-sensitivit y of stress, is typically inhomogeneous for a given phase due to its heterogeneous strain. The stiffnesses are usually homogenized by using the average strain per phase as a reference input into the respective constitutive law. To establish a link between stress and strain per phase, secant (connecting total stress to total strain) and tangent (connecting stress increments to strain increments) formulations for the moduli are employed (cf. [49]). As an example, the viscoplastic self-consistent mean-field approach (VPSC) has been successfully applied to represent the texture evolution in different types of polycrystalline metals: e.g. zirconium alloys [21], TWIP-steels [22], and tungsten [23]. Recent developments incorporate elasticity in the model [24] enabling a more accurate description of the material behavior. An alternative set of mean-field polycrystal approaches are the grain-cluster models. They represent an intermediate approach between the mean-field schemes and full-field solutions. They reduce the high computational cost of the latter by restricting the degrees of freedom to a small number of regions with (typically) homogeneous strain inside each region. Those areas are grains or phase, thus extending the mean-field approaches by taking into account direct neighbor-neighbor interactions among the constituents of a polycrystalline and potentially also multiphase aggregate. The introduction of grain aggregates allows relaxation of the assumption of homogeneous strain in each constituent (Taylor)—which generally led to an overestimation of the polycrystalline strength and rate of texture evolution—by enforcing compatibility only in an average sense for the aggregate as a whole. Typical examples of such models were suggested by Van Houtte (cf. [25], [26]), Gottstein (cf. [27]), and Eisenlohr [28] (cf. Figure 2). The reasonable numerical effort for solving mean-field problems enables the coupling of the homogenization schemes in finite element algorithm (cf. [6], [28], [29], [30], [31]) for solving more complex initial boundary value problems like the deep drawing of a cup (see Figure 3) or study the texture evolution during rolling (cf. [30]).

Figure 2. Right: Example of a grain-cluster approximation (RGC [28]) Constraints are placed on the corners of the aggregate while internal relaxations are admitted; Left: two simulation runs using two different homogenization models (courtesy of D. Tjahjanto) 2.2 Full-field methods Full-field models of crystal mechanics pursue strategies for solving initial boundary value problems of polycrystalline unit cells. In contrast to the mean-field methods, full-field methods provide a more realistic representation of the stress and strain state in each grain and also the

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accompanied gradients, along with an accurate description of the grain morphology, an improved quantitative description of the texture, and a reasonable representation of the interaction between the considered constituents, i.e. grains, phases, etc. Most of the current numerical treatments of the fiill-field homogenization schemes are based on the finite element method. Examples of this approach were given by [32], [33], [34], and [35] for simple deformation paths and by [36] and [37] for applications (simplified) bulk metal forming processes like rolling and wire drawing. However, without appropriat e strategies (cf. Section 3.2), such full-field approximations are usually too time consuming for applications in through-process modeling. In comparison to the high computational demand of FE based methods, fast Fourier transform (FFT) based full-field solutions [38] require much less computer times [39]. 3 Application of Multiscale Models for Solving Engineering Problems 3.1 Virtual Laboratory In the industrial practice of simulating complex forming operations, the prediction of exact shapes, material flow, thinning, wrinkling, earing, and springback effects is a challenge, particularly when materials with complex textures and microstructure s are involved. In the simulation packages that are currently in commercial use, for instance, in the automotive industry, only empirical constitutive laws are available. As these formulations provide only limited empirical access to the material anisotropy and heterogeneity they do not properly take into account the effects of microstructur e and texture and their evolution during deformation. The crystal plasticity finite element method (CPFEM) bridges the gap between the polycrystalline texture and macroscopic mechanical properties and opens the path to a more profound consideration of metal anisotropy in commercial forming and process simulations. The example presented in this section is an application of the CPFE method for the concept of virtual material testing (virtual laboratory) using a representative volume element (RVE) approach. By using such numerical test protocols it becomes possible to determine the actual shape of the yield locus as well as corresponding anisotropy coefficients (i.e. Lankford parameters, r-values) directly through CPFE simulations, and to use this information to calibrate empirical constitutive models used, for example, in the automotive industry. Along with standard uniaxial tensile tests, other strain paths can be simulated, such as biaxial tensile, compressive or shear tests. The analysis of loading condition which can not be realized experimentally (like biaxial compression of sheet metal) is also of interest to extend the experimental available data. For practical application, the homogenized results obtained from the virtual lab can be processed in the same manner as conventional experimental results. In the present example the use of the CPFE method for virtual testing is demonstrated for a dual-phase C-Mn steel grade where the parameters of an empirical yield surface function were calibrated by the full-field crystal plasticity predictions (cf. Figure 7). 3.2 Representation of Process Chains While simulation solutions for single process steps are applied successfully to virtually study the ability to process or service parts, a unified approach that reuses knowledge and results from previous steps along the production chain is still an exception. Especially the gap between numerical steel design and corresponding simulation techniques in sheet metal forming and crash simulation is a challenging topic for industrial applications. In this example (cf. [40]), a process chain simulation is presented that covers the consecutive stages of production of a dual phase steel DP800 material. It starts with the hot rolled strip which is followed by cold rolling, heat treatment, deep drawing and finally the analysis of the crashworthiness of the deep drawn component. An important aspect to take into account is the

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microstructur e evolution during the different process steps for an appropriat e modeling of the material behavior. Depending on the process step, different simulation strategies on different length scales are applied (see Figure 3).

Figure 3. Modeling strategy for representing the process chain for sheet metal production The first process step to be simulated is cold rolling. Here, a full field simulation approach (RVE) in combination with a CPFE model is used. Different experimental analysis procedures were carried out to account for the initial state of the hot rolled sheet material. Micrographs were used to analyze the ferritic-pearliti c microstructure . To obtain a realistic distribution of the pearlite phase within the ferrite matrix, a statistical reconstruction scheme based on [41] was applied. EBSD data are used to consider a realistic initial texture. Finally, the parameters of the single crystal plasticity material model are calibrated using macroscopic tensile and compression tests (Figure 4).

Figure 4. Tensile test on the hot rolled sheet. Figure 5. Tensile tests on the (hard, as rolled) Comparison between experimental data and cold rolled sheet (hard as rolled) for different the calibrated microstructur e model. degrees of rolling. The initial thickness of the hot rolled sheet is 3.5 mm. A prescribed deformation was applied on the RVE-model to simulate the cold rolling process. Three different degrees of rolling were considered with final sheet thicknesses of 2.20, 1.75 and 1.45 mm. According to real tensile test on the as rolled material, similar virtual tests were performed on the rolled RVE-models. Figure 5 shows the very good agreement between the tensile test and the prediction of the model. The hardening behavior can be predicted independently from the applied deformation. During the subsequent thermal treatment the final dual phase steel microstructur e composed of ferrite and martensite is obtained. The corresponding simulation aim at describing the

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microstructur e change (phase transition, recrystallization and recovery) due to the annealing procedure. The simulation of the thermal treatment is carried out by a cellular automaton [42]. Figure 6 displays the evolution of the volumefractureof the different phases. The morphology of the cold rolled RVE-model is mapped onto a regular grid. Data concerning the grain orientation and the accumulated plastic strain were provided fromthe rolling simulation to define the initial state for the annealing simulation. The accumulated plastic strain is used to estimate the dislocation density which acts as a driving force within the annealing simulation.

Figure 6. Simulation of the microstructur e evolution during the annealing procedure. For practical application of deep drawing simulations, models which directly consider the microstructur e are not appropriat e due to the high numerical cost and the complexity of the material description. Usually, deep drawing simulations are continuum-based which describe the yielding and hardening behavior with phenomenological models. For this reason,the obtained data from the annealing simulation were homogenized using the virtual lab as described in Section 3.1. The obtained macroscopic uniaxial stress-strain curves are used - similar to experimental data - to adjust the parameter of the phenomenological plasticity models. Here, the Barlat89 [43] yield function is applied to describe the initial yielding of the dual phase steel. In Figure 7 this procedure is illustrated. The yield points obtained from the virtual lab and the Barlat89 yield locus which is calculated from experimental data do agree well. After the determination of the material behavior by means of the virtual laboratory, the resulting material parameter s are used to calibrate macroscopic models for complex deep drawing simulation. Finally, the crashworthines s of the deep drawn component is virtually analysed. To obtain accurate failure predictions, the load history from the previous deep drawing process is considered. Therefore, the local thinning of the sheet and the actual hardening of the material at the end of the deep drawing simulation is mapped to the crash simulation (cf. [44]). 4 Conclusions We have demonstrated here how to build up a simulation set-up along the central steps of the processing chain of an automotive component manufacture d from a dual phase steel. This requires dedicated experimentation along with the development of the models, which involves not only mechanical testing at intermediate stages but also detailed determination of microstructure , grain morphology and texture before and after the individual processing steps.

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From an initial microstructure , the cold rolling of the initial ferritic-perliti c microstructur e of a C-Mn steel sheet was evolved in a CPFE simulation to give the texture changes and a grainspecific deformation. This information was sufficient to feed the simulation of the recrystallization processes during heat treatment. With the dual phase microstructur e after recrystallization , virtual testing of the deformation behavior was performed. This required two simple calibration experiments but then nicely predicted multiaxial deformation behavior. In the subsequent deep drawing and crash simulations one then has access to local changes in the mechanical properties of a component, which goes far beyond classical component analysis. On the basis of appropriat e numerical treatments,the discussed constitutive theories are capable to represent the microstructur e evolution and the resulting effective properties of complex polycrystalline and also multiphase metallic materials. This results in a deeper insight into the process and the interactions between the process steps. This knowledge will help to optimize individual process steps and also to improve the complete process chain. Once established, the modeling along the processing chain allows for both virtual process development and component assessment in unprecedented detail and with unprecedented precision. 5 Acknowledgements Financial support fromthe German Ministry for Education and Research (BMBF 03X0501) and support by the Fraunhofer and Max Planck Societies is gratefully acknowledged.

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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

Large Scale Finite Element Computations Using Real Grain Microstructure s H. Proudhon1 ^ I N ES ParisTech, Centre des matériaux, CNRS UMR 7633, BP 87, F-91003 Evry Cedex, France Keywords: Finite Element, Crystal Plasticity, Experimental Microstructur e abstract Large scale finite element simulations of the elastoviscoplastic behavior of polycrystalline aggregates have become a standard technique to study the stress-strain heterogeneities that develop in grains during deformation and is therefore of primary interest for an Integrated Computational Materials Engineering approach. Comparison between continuum crystal plasticity and experimental field measurements have long been confined to surface observations but recent 3D experimental techniques are now opening new validation perspectives for computational crystal plasticity and homogenization models. In this work, crystal plasticity simulations are conducted on samples imaged by Diffraction Contrast Tomography, which allows to resolve the 3D shape and orientation of each grain within the specimen. Average strain tensors in each grain are compared with the experimental values extracted from the diffraction data, which provide first class validation data for continuum models. A more complicated example of application deals with short fatigue crack propagation in polycrystals. One fundamental problem caused by short fatigue cracks is that so far no reliable prediction of the crack propagation rates, comparable to the well-known Paris law in the long crack regime, could be established. The short crack behavior is commonly attributed to factors like their complex three dimensional shapes and the influence of the local crystallographic environment affecting their propagation. The first steps of a fatigue crack growth within a known 3D grain network are computed and compared with real propagation rates obtained in situ via X-ray micro-tomography . Numerical difficulties related to the crack singularity and complex shape are discussed. Introduction Continuum crystal plasticity has proved to be a powerful tool to interpret experimental results obtained in the deformation of metal polycrystals [1]. Large scale simulations on polycrystalline volume elements can now be performed with sufficient local discretization to predict the transgranula r plastic strain fields. They are necessary for comparison with results of sophisticated 2D and 3D full field measurements providing total strain fields based on grid methods and/or image correlation techniques, lattice rotation fields by means of EBSD and, more recently elastic strain fields using for instance micro-diffraction techniques. In the first part, computational crystal plasticity is applied to polycrystalline films under thermal loading. The heterogeneous displacement field is then used as input to predict coherent diffraction patterns which may be confronted to experimental measurements. Effects such as the grain shape and the strain level on the diffraction pattern are investigated. The second part deals with a more classical approch to simulate strain fields but using a numerical microstructur e as close as possible as the experimental one. Crystal plasticity is

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thus coupled to real 3D microstructure s obtained by diffraction contrast tomography. The prospect of simulating the presence of sharp interface such as cracks within the real grain network is demonstrated. Simulation of Coherent X-ray Imaging X-ray coherent diffraction has recently been recognized as a promising tool to experimentally characterize complex elastic strain fields in single crystals or grains in a polycrystal, up to very small length scales [2, 3]. Such measurements can be performed on thin films, especially in polycrystalline films with columnar grains but the interpretatio n of experimental data has for now remained difficult and very limited. While most attempts to analyse 3D coherent diffraction patterns turn to the inversion problem to retrieve the missing phase from the diffracted intensity, finite element simulations of the behaviour of polycrystalline aggregates have not been used to interpret diffraction patterns yet. The objective of the present section is to show that the detailed intragranula r displacement field predicted by 3-dimensional FE computations can be exploited to delineate the respective effects of grain shape, orientation and strain on the evolution of complex diffraction patterns. Theoretical aspects Within the framework of the kinematic theory of diffraction*, the 3D intensity produced by a coherent beam diffracted by a small crystal is expressed as the sum of the complex amplitude scattered by each atom: I I2 I

(sû(x \Y2fn(q)expiqXri\

(i)

with Xn being the atomic position at n and fn its scattering factor. For a deformed crystal, we define u(2L) as the displacement vector field which is the difference between the current and initial atom positions. The displacement field can be easily introduced and Eq. 1 which can be rewritten using a Fourier transform, within Takagi approximation [4] and with q — G_: 1(g)

oc \TF{P(2L)-^P(IG.U{2L))}\

(2)

The diffracted intensity I(q) can therefore be evaluated using the displacement field computed by large scale finite element analysis of a polycrystal sample. Numerical simulation of a 3D coherent diffraction pattern To compute the strain heterogeneities within a polycrystalline sample, a suitable mesh of the grains must be obtained. A standard way to mesh a polycrystal is to use Voronoi tessellations in two or three dimensions, but real grain geometry can also be used favourably if available [5]. In this work, thanks to their columnar nature, the precise shape of the grains can be extracted from a SEM image in back scattered electron mode (which provides some crystalline contrast), as shown on Fig. 1. The resulting 2D microstructur e is then extended in the Z direction to obtain the 3D mesh with 133 grains. The mesh closely matches the. gold *this assumption is valid because of the small reflected intensity compared to incident beam (large rocking curve (~ 0.3°))

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(a) SEM image of isolated polycrystal

(b) Grain topology extracted from the SEM image

Fig. 1: Extraction of the surface grain topology. sample size o f l 0 x l 0 x 0 . 2 urn. As the exact orientations of the grains were not available at the time of the computations, a fiber texture with (111) parallel to the surface and random in-plane orientation, is applied. To match as closely as possible the experimental orientation set, small deviations of the (111) direction are taken into account. These deviations are applied randomly within the experimental scatter, as measured on the laboratory X-ray diffractometer. FEM calculations were performed using Z-SeT software suite^ using linear elasticity behaviour with cubic anisotropy to represent the gold crystal network. The following elastic constants Qj have been used [6]: Cu = 192 340 MPa, CX2 = 163140 MPa and with C44 = 41950 MPa. For FCC crystals, the Bragg vector is Ghkt = ^[h,k,l] a = 0.4078 nm the atomic spacing. The effect of temperature on these parameters is neglected. The different steps chained to obtain the 3D diffraction pattern on a selected grain are shown on Fig. 2. Starting with the 3D mesh and the grain orientation set (Fig. 2a), boundary conditions are applied (sample fixed on the lower face to simulate a rigid glass substrate and a temperature change of AT = 100K applied linearly over time. FEM calculation is carried out to retrieve the heterogeneous stress and strain fields (Fig. 2b). The displacement field u(2L) is then transferred onto a regular mesh (typically 200 x 200 x 5 elements, Fig. 2c). Finally Eq. 2 is computed with a complex FFT on a 2003 array filled with zero outside the grain and with {cos(2ir / a(hux + kuy + luz)),sin(27c/a(hux + kuy + luz))} inside the selected grain. The amplitude of the complex output is stored into a 3D data set which can then be visualised in the reciprocal space (qx,QyiQz) and further analysed (Fig. 2d). By simulating the heterogeneous displacement field in a polycrystal, one can easily change a variety of parameters like grain shape and/or orientation, level of strain, boundary conditions. .. Tying those computations with FFT can provide a very useful tool to understand the complexity of the real 3D coherent diffraction pattern observed experimentally. t available from www.nwnumerics.com

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(a) 3d polycrystal mesh subjected to thermal loading

(b) heterogeneous von Mises stress field

(c) displacement field transfered on regular mesh

(d) 3d diffraction pattern for selected grain

Fig. 2: Illustration of the methodology used to compute the 3d diffraction pattern on a selected grain within a poly crystalline microstructure . FEM Calculations based on D C T experiments DCT is a monochromatic beam rotation technique, combining the principles of 3D X-ray diffraction microscopy [7] and X-ray micro tomography. During a 360 degree continuous rotation of the sample, each grain runs through a series of diffraction alignments, giving rise to diffracted beams. Part of these diffraction spots are captured on the high resolution imaging detector system, positioned closely behind the sample. Like in conventional micro tomography, one can determine the three-dimensional distribution of the X-ray attenuation coefficient from the attenuation in the transmitted beam. The analysis of the diffracted beams provides access to the crystalline microstructure . The processing route is briefly summarized here. After segmentation, Friedel pairs of diffraction spots (hkl and -h-k-1 reflection from the same grain) are automatically identified ( "pair matching" ). A polycrystal indexing algorithm based on the analysis of such pairs of diffraction spots [8] classifies the diffraction spots according to their grain of origin and determines the average orientation and elastic strain state of the grains. The 3D shape and the position of the grains in the sample volume are determined with the help of algebraic reconstruction techniques, using the 2D diffraction spots as parallel projections of the unknown 3D grain volume. Thanks to those recent advances with X-ray microtomography , the complete set of grain shapes and orientations in a polycrystalline microstructur e can now be obtained [9]. From

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(a) Grains from DCT experiment (grains have been made half transparent)

(b) Grain boundaries meshed with shell elements (only half of the sample is shown)

(c) Full 3D mesh ready for FEM computation

Fig. 3: Generation of a 3d mesh from a reconstructed sample imaged with DCT. there, it becomes possible to recreate a numerical avatar of the specimen for computational purposes. This can be done by first meshing all the grain boundaries with shell elements. This interface mesh can then be used as input for a generalised 3D mesher (eg. tetgen/GHS3D software package) to obtain a full 3D mesh suitable for FEM computations. This process is demonstrated in Fig. 3 using a dataset reconstructed from a cylindrical sample of 600 urn diameter made of large grain ß titanium alloy. Having both the microstructur e enabled mesh and the crystal plasticity model described in [10, 11], it is then possible to use the simulation as close as possible from the experiments incorporating microstructura l effects. Such comparisons remains rare in 3D. Here we have simulated an experimental tension test on a ß stabilized titanium sample from which the grain structure and orientations are known (see Fig. 4). The specimen pole figure seen on Fig. 4a shows no particular texture. The elastoplastic calculation was carried using the mesh shown on Fig. 3c which uses 65000 nodes and 368000 linear tetrahedra . Fig. 4b depicts the von Mises stress as computed for a 150 N load (the average axial stress in 500 MPa) and 3c shows the average axial stress/strain curve in each grain. A good agreement was found comparing the average stress distribution in each grain with the one measure during the diffraction experiment. Inserting a 3D mesh of a crack imaged by microtomograph y into a grain network is still a challenge, but the study of short fatigue cracks is a domain where 3D in situ microtomograph y can bring a lot of new insight, especially if experiments and simulations can be carried out in synergy. Here experiments are still far ahead computations since based on previous work using attenuation and phase contrast [12] and new possibilities offered by diffraction contrast, it may now be possible to follow a small crack within a set of grains during its growth. One problem with computation accounting at the same time for a grain network and a sharp discontinuity can be stated as producing an appropriat e spatial discretization of such a problem with a reasonable number of elements. Fortunately, solutions to this

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(a) Pole figure of the 130 grains constituting the specimen

(b) Computed von Mises stress (<7 = 500 MPa)

(c) Average behavior of each grain compared to the polycrystal

Fig. 4: 3D calculation of a polycrystalline sample of /3-titanium alloy images by diffraction contrast tomography; in the experimental test, the specimen was loaded with 150 N. problem are becoming more and more available: one may benefit at the same time of (i) the general increase in computational power, (ii) using of parallel computing and (iii) using more powerful remeshing and topological simplification algorithms. It is important to highlight that this particular cracking problem is made far more complex by segmentation errors which may produce holes and/or unwanted features in the crack geometry. Such computations are expected in a near future. Conclusions and prospects This paper first showed how large scale finite element simulations of polycrystalline aggregates have become a standard way to study the heterogeneous deformation of materials. Crystal plasticity computations are now ready to simulate complete specimens based on the real grain geometries and shapes. A numerical avatar of the sample can be quite easily obtained for thin films with a columnar grain geometry but can also be retrieved for the general 3D case thanks to recent advances using diffraction contrast tomography. Closing the gap between 3D experimental techniques able to probe strains at the grain level and below and computational mechanics is the key to extensively test the many micro-mechanical models available in the literature. This may lead to significant advances in closely related problems such as the propagation of microstructurall y short cracks in a grain network. References [1] C. Teodosiu. Large plastic deformation of crystalline aggregates. CISM Courses and Lectures No. 376, Udine, Springer Verlag, Berlin, 1997. [2] Mark A. Pfeifer, Garth J. Williams, Ivan A. Vartanyants, Ross Harder, and Ian K. Robinson. Three-dimensional mapping of a deformation field inside a nanocrystal. Nature, 442(7098):63-66, July 2006.

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[3] N Vaxelaire, H Proudhon, S Labat, C Kirchlechner, J Keckes, V Jacques, S Ravy, S Forest, and O Thomas. Methodology for studying strain inhomogeneities in polycrystalline thin films during in situ thermal loading using coherent x-ray diffraction. New Journal of Physics, 12(3):035018, 2010. [4] Satio Takagi. A dynamical theory of diffraction for a distorted crystal. Journal of the Physical Society of Japan, 26(5):1239-1253, 1969. [5] R. Parisot, S. Forest, A.F. Gourgues, A. Pineau, and D. Mareuse. Modeling the mechanical behavior of a multicrystalline zinc coating on a hot-dip galvanized steel sheet. Computational Materials Science, 19:189-204, 2001. [6] J. R. Neighbours and G. A. Alers. Elastic constants of silver and gold. Phys. Rev., 111(3):707-712, August 1958. [7] H. F. Poulsen. Three-Dimensional X-ray Diffraction Microscopy- Mapping Polycrystals and Their Dynamics, volume 205 of Springer Tracts in Modern Physics. Springer, Berlin, 2004. [8] W. Ludwig, P. Reischig, A. King, M. Herbig, E.M. Lauridsen, G. Johnson, T.J. Marrow, and BufRère J.Y. Three-dimensional grain mapping by x-ray diffraction contrast tomography and the use of friedel pairs in diffraction data analysis. Review of Scientific Instruments, 80(3), 2009. [9] W. Ludwig, A. King, P. Reischig, M. Herbig, E.M. Lauridsen, S. Schmidt, H. Proudhon, S. Forest, P. Cloetens, S. Rolland du Roscoat, J.Y. Bufîière, T.J. Marrow, and H.F. Poulsen. New opportunities for 3d materials science of polycrystalline materials at the micrometre lengthscale by combined use of x-ray diffraction and x-ray imaging. Materials Science and Engineering: A, 524(1-2) :69-76, 2009. Special Topic Section: Probing strains and Dislocation Gradients with diffraction. [10] L. Meric and G. Cailletaud. Single crystal modeling for structural calculations: Part 2—finite element implementation. Journal of Engineering Materials and Technology, 113(1):171-182, 1991. [11] L. Meric, P. Poubanne, and G. Cailletaud. Single crystal modeling for structural calculations: Part 1—model presentation. Journal of Engineering Materials and Technology, 113(1):162-170, 1991. [12] E. Ferrie, J.-Y. BufRère, W. Ludwig, A. Gravouil, and L. Edwards. Fatigue crack propagation: In situ visualization using X-ray microtomograph y and 3D simulation using the extended finite element method. Ada Materialia, 54(4): 1111—1122, 2006.

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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

MODELLING AND MEASUREMENT OF PLASTIC DEFORMATION AND GRAIN ROTATION IN 3D AT THE GRAIN-TO-GRAIN LEVEL David Gonzalez1, Andrew King2, Igor Simonovski3, Joäo Quinta da Fonseca1, Philip J. Withers1 School of Materials, University of Manchester, Grosvenor St., Manchester, Ml 7HS, UK. ESRF, Polygone Scientifique Louis Néel, 6 rue Jules Horowitz, Grenoble, 38000, France. institute for Energy, P.O. Box 2, Petten, NL-1755 ZG, The Netherlands

2

Keywords: Image-based model, Texture, Plastic deformation, Aluminium Abstract The deformation of a polycrystalline sample of aluminium at the microstructura l scale was studied by a combination of computational modelling and synchrotron X-ray diffraction contrast tomography (DCT). DCT was used to map the 3D grain arrangement in a poly crystal. This was the basis of a microstructurall y faithful mesh for crystal plasticity finite element modelling (CPFEM). The sample was then monitored by DCT during incremental uniaxial compression. Changes in the diffracted spots during deformation were interpreted in terms of crystal reorientation and orientation spread within grains. Reorientation within grains of ~ ± 1 ° has been observed after 1.2% compressive strain and alongside considerable grain-to-grain variation in reorientation relative to that expected according to simple crystal plasticity models, The CPFEM results showed similar grain-to-grain variations, indicating that the local geometry is important in determining the level of heterogeneity in deformation at this scale. However, on a grain-to-grain basis, agreement is relatively poor. Possible reasons for the observed differences are discussed. Introduction Plastic deformation in polycrystalline materials is heterogeneous at the microstructura l scale. It has been suggested that strain localisation at this scale is important in determining the fundamental processes responsible for failure in fatigue [1] and environmental assisted cracking [2]. In some cases large local strains can help relax local stresses (e.g. favourable slip near grain boundaries) preventing damage, whereas in other cases heterogeneous deformation can lead to stress concentrations and even damage nucleation [3]. There is therefore a need to understand and model the deformation of metals at the microstructura l scale. When deformed in isolation, the mechanical behaviour of a grain is simply related to its orientation, but in a polycrystal the deformation is further influenced by its shape, size, and the constraint of neighboring grains. As a consequence, it is not possible to compare the results from deformation models to results from experiments without a complete description of the microstructure. Consequently, while surface techniques such as electron back scattered diffraction (EBSD) can provide spatially resolved measurements of lattice rotation during straining [2], they cannot be directly compared to results from polycrystalline deformation models such as Crystal Plasticity Finite Element Models (CPFEM) [4] because there is no information regarding subsurface grains before deformation. The only way to obtain this information is by destructive sectioning [5], which of course precludes further deformation. Synchrotron X-ray diffraction makes it possible to study individual grains in the bulk [6]. Diffraction Contrast Tomography (DCT) has recently become established as a technique for map-

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ping poly crystalline microstructure s in 3D [7, 8]. Since DCT is non-destructive, diffraction measurements during deformation are possible. We have used DCT to fully map the grain geometries and orientations of an aluminium sample as a function of deformation. This has enabled us to build a microstructurally-faithfu l crystal plasticity model and to compare its deformation directly with experimental 3D observations. To the best of our knowledge, this is the first sideby-side experiment vs model comparison for a real 3D microstructur e that includes a full description of the local neighbourhoods. Material & Experimental Methods Material: We have studied a high purity aluminium (0.1% Mg) sample because of its low elastic anisotropy, almost perfect plasticity and high stacking fault energy (SFE). Traditionally, texture has been poorly captured by CPFEMs for low SFE FCC metals [9], in part due to the occurrence of twinning which is difficult to account for. Moreover, in high SFE metals obstacles to dislocations can be readily by-passed, in line with the idealised behaviour assumed by CPFEM. Diffraction Contrast Tomography: The experimental arrangement is similar to that used for absorption contrast tomography. The sample is illuminated by a parallel, monochromatic x-ray beam. A high resolution 2D detector placed close behind the sample records simultaneously radiographs (projections) of the sample and diffraction spots arising from grains oriented for Bragg diffraction. During rotation of the sample through 360°, many diffraction spots are observed from each grain. Diffraction spots are assigned to grains according to a range of geometrical criteria and the grain orientations reconstructed from the diffraction events. Grain shapes are reconstructed from the diffraction spots using a 3D ART algorithm [10]. More details about the DCT technique can be found elsewhere [11, 12]. A material comprising perfect grains would give diffraction spots that are spread over only 1-2 projections. However, distortion of the crystal lattice means diffraction spots arising from a grain smear out over many successive projections (scanning angle, Q). We refer to these 3D objects as "diffraction blobs". Their spread in Q can be used to give a measure of the misorientation spread within a grain [6]. Each blob can be summed in the two detector directions resulting in a profile of intensity as a function of Q. The profile can then be fit using a Gaussian function. The observations are corrected for the Lorentz factor (blobs with a scattering vector that is close to the rotation axis spread over more images). After this correction, the average angular blob spread gives a scalar measure of the grain mosaicity [6]. Each grain comprises many diffraction blobs. To get a single value representative of the grain, we have averaged the blob values of the middle 50%. This discards outliers, reducing the effect of bad data points. Since the grains for the undeformed sample showed distortion (probably due to residual strain during grain growth), the blob values have been normalized by their initial value. During deformation the intensity within a blob does not spread out uniformly, but instead sub-structure s are often observed within a blob. We have used an algorithm that estimates the misorientation as a function of position within a grain based on the observed diffraction blobs [13]. The algorithm can consider both the full elastic strain tensor and the rotation at each point. In this measurement, because of the low yield stress the elastic strain was neglected, and only the three components of rotation determined. DCT scans of the (0 1 mmx 1.5 mm) cylindrical sample in its undeformed state revealed the grain size to be around 160 urn (Fig.l). As shown in Figure 2, the sample has a significant <100> texture. Grain distortion may mean that the DCT algorithms may fail to identify certain grains in later deformation steps. In this work, only grains whose orientations are available in all loading steps have been considered. Unfortunately it was not possible to measure the precise compres-

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sive strains at which DCT was carried out. Consequently, we have averaged the known angle of the average grain rotations for the two loaded steps (0.43° and 1.30°). We then calculated from the model the strains at which these average grain rotations are achieved (1.2% and 4.4%) which accord well with the loads applied. CPFEM Model: The sample reconstructed by DCT had 284 x 284 x 176 voxels. This volume was imported into Amira™ to reconstruct the grain boundaries. The number of these surfaces was 2,067,409. Since this would require too many elements for CPFEM computation, the surface geometry was simplified to 9,994 surfaces. These faces were used to create the grains in ABAQUS software (using 3D10M elements) via a Python script [14]. Each grain was linked to its neighbours by merging the nodes. The total number of grains, elements, nodes and Gauss points of the model were 117; 31,490; 93,699 and 125,960 respectively (Figure 1).

Figure 1. Mesh built from 3D grains measured by DCT on 1mm diameter sample.

The base of the sample was constrained only in the loading direction and a compressive displacement applied to nodes on the opposite face. A UMAT subroutine [15] has been implemented in ABAQUS to simulate the behaviour of each grain. This subroutine assumes elasto visco-plasticity where plasticity is treated uniquely via slip [16], [17]. We assume that flow on one slip system causes the same hardening on all slip systems. The UMAT parameter s used in Table 1 were used to adjust the macroscopic stress-strain curve of the model to that of the experiment. Cn(GPa)

Ci2(GPa)

ÏÔS2

62.16

Table 1. UMAT parameters used in the present work

C44(GPa)

n

à

/*0(MPa)

xs(MPa)

To(MPa)

283

55

ÖÖÖl

26Ö

18

9Ü

Average grain rotations were calculated using quaternion algebra [18]. We have used the Grain Orientation Spread (GOS) to quantify the average misorientation within a grain, enabling comparison with experimental results.GOS is defined as the arithmetic mean of the minimum misorientation angles of local points when the reference is taken as the average orientation of the grain [19]. Finally, we have used quaternions to compute local misorientation angles from the grain average orientation about each axis [20] for direct comparison with experiment. Results and discussion Grain Rotations: The crystal directions parallel to the compression axis for the CPFEM model and experiment are presented in Figure 2. In aluminium it is well known that a <110>fibretexture develops following compression [21]. Further, rotation of the crystal directions away from <100> and <111> poles is usually reported while rotations near <114> are hindered. These

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trends, marked by arrows in Fig 2, are weakly evident in the DCT data. Both model and measurements show grain-to-grain deviations from the Taylor model predictions, which assume homogenous plastic deformation due to grain-to-grain interactions. Although the predicted rotations have the correct magnitude, the grain trajectories only agree for some grains being marginally better near the <100> pole than elsewhere. The overall lack of correlation grain-for-grai n may be attributabl e to microstructura l features that are neglected by the model. For example, deformation bands [23] and dislocation boundaries aligned with one of the {111} planes [24] have been reported in lightly deformed aluminum crystals.

Figure 2. The crystal directions parallel to the compression axis after 0,1.2% and 4.4% strain; a) measured by DCT, b) modelled by CPFEM. The circles represent 4.4% strain. Surface contacting grains (red) and bulk grains (blue). Only those grains where data is available for all three loading steps are shown.

Orientation spread: GOS results for each grainfromCPFEM correlate with the average equivalent plastic strain and the accumulated slip (not shown here). The GOS and the experimental blob spread, quantified as the normalized FWHM of the Gaussian fit are weakly correlated. That reasonable correlation is seen when they are normalized by the volume of the grain (Figure 3) suggests that spread increases with grain size for both model and measurement. In this respect mosaicity has been reported elsewhere to strongly correlate with the grain area in 2D measurements [18, 22]. Further this correlation of mosiacity with grain volume has also been observed in steels heated above the austenite transition temperature , which might be expected to be in an undeformed state [20]. Unsurprisingly spread increases with plastic strain. For both loading steps bulk grains show a higher spread (GOS and normalized FWHM), probably due to the higher constraints imposed by their neighbors.

Figure 3. Normalized diffraction blob spread (FWHM of the Gaussian fit) measured by DCT versus Grain Orientation Spread (GOS) by CPFEM as loaded in compression to; a) 1.2% strain, b) 4.4% strain

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Local Rotations: The intragranula r rotations mapped over a cross-section through the sample at about 1/3 of the cylinder height for the experiment and model are presented in Figure 4. These results represent the intermediate loading step (1.2% strain), since the less deformed diffracted spots are easier to process. Again, some intragranula r rotations were measured prior to loading. In Figure 4, we have subtracted thesefromthefinalrotations.

Figure 4. Intragranula r rotations (°) about X, Y and Z axes; above) based on the observed diffraction spots, below) calculated from CPFEM after 1.2% strain

The experimental results show substantial grain-to-grain variation in both the magnitudes of the local rotations and in the local, intragranula r gradients of deformation. The spreads of the local lattice rotations predicted by the model agrees well with those observed, but the predicted intragranular variations are smoother and lower in magnitude. Since the model is micro structurall y faithful, one might expect to see good agreement on a grain-to-grain basis. By contrast, we find poor relatively poor agreement. Interestingly, the patterns of lattice rotation often match well with those observed but are either the wrong sign or magnitude. There are several possible reasons for this lack of agreement. The analysis of the experimental diffraction data ignores elastic distortions, which might be a significant source of error, since elastic strains can also cause changes in contrast. Although the alloy is extremely soft, the low elastic stiffness of aluminium means that elastic strains will be large even if stresses are low. The procedure is now being extended to include elastic distortion effects. The material model used is also very simple and it is likely that it cannot capture well the results of multiple slip and the associated recovery that is known to occur in aluminium [19, 20]. It is also not clear whether the mesh density is sufficiently high to capture local variations faithfully. A sensitivity study on mesh density will shed some light on this issue. Furthermore , the boundary conditions employed in the model are likely to be somewhat different to those in the experiment. It is indeed very difficult to deform such a small sample in an idealised manner. Conclusions DCT has been used both to map the 3D arrangemen t in a poly crystal and to study the evolution of crystal re-orientation and orientation spread within grains with compressive deformation. A CPFE model has been constructed with the same initial polycrystal arrangement . In both cases reorientation of the grains by ~± 1 ° has been observed after 1.2% strain. In both cases, consider-

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able grain-to-grain variation in reorientation under compressive deformation has been observed relative to the overall expected reorientation (Fig.2). This is presumably due in part to the effect of local neighbours. Some grains show good agreement between model and experiments, others much less so. This may be due to intragranula r heterogeneities in deformationnot accounted for in the model, or to oversimplifications in the analysis of the diffracted data. Nevertheless, this work shows that DCT can provide unique data for comparison with crystal plasticity deformation models. Although these initial results allow only limited insight into the effectiveness of the models, it is clear that the methodology has significant promise and we believe it will play an important role in the validation and development of future crystal plasticity models. Acknowledgem ents The authors thank Alexei Bytchkov (instrument scientist in ID11, ESRF) for his support. [I] [2]

[3] [4] [5] [6] [7] [8] [9] [10] [II] [12] [13] [14] [15] [16] [17] [18] [19] [20] [21] [22] [23] [24]

References Z. Zhang, Z. Wang, Prog. Mater. Sei., 53, (7) (2008) 1027-1099. T. Couvant et al., "Development of understandin g of the interaction between localized deformation and SCC of austenitic stainless steels exposed to primary PWR environment," , in 14 th International Conference on Environmental Degradation of Materials in Nuclear Power System, Virginia Beach, Virginia, USA, 2009. T. R. Bieler et al., Int. J. of Pias., 25, (9) (2009) 1655-1683. J. Q. da Fonseca et al., Materials Science and Engineering: A, 437, (1) (2006) 26-32. A. Musienko et al., Ada Mater., 55, (12) (2007) 4121-4136. H. F. Poulsen et al., Acta Mater., 51, (13) (2003) 3821-3830. A. King et al., Science, 321, (5887) (2008) 382-385. M. Herbig et al., Acta Mater., 59, (2) (2011) 590 - 601. P. Van Houtte, Acta Metal, 26, (4) (1978) 591 - 604. R. Gordon, R. Bender, G. T. Herman, J. Theoretical Biology, 29, (3) (1970) 471-481. G. Johnson et al., J. of App. Crystall, 41, (2) (2008) 310-318. W. Ludwig et al., Review of Scientific Instruments, 80, (3) (2009).033905 A. King et al., "Grain mapping by diffraction contrast tomography: extending the technique to sub-grain information" , in Proc. of the 31st Riso Int. Symp. on Materials Science, Technical University of Denmark, 2010. I. Simonovski, L. Cizelj, Computational Materials Science, 50, (5) (2011) 1606-1618. Y. Huang, A user-material subroutine incorporating single crystal plasticity in the ABAQUS finite element program, Mech Report 178,. Division of Engineering and Applied Sciences, Harvard University, Cambridge, Massachusetts, 1991. R. Hill, J. R. Rice, J. of the Mech. andPhy. of Solids, 20, (6) (1972) 401-413. D. Peirce, R. J. Asaro, A. Needleman, Acta Metall, 31, (12) (1983) 1951-1976. W. He, W. Ma, W. Pantleon, Materials Science and Engineering A, 494, (1) (2008) 21-27. A. J. Schwartz, M. Kumar, Electron Backscatter Diffraction in Materials Science, Springer, 2009. W. Pantleon, Scr. Mater., 58, (11) (2008) 994-997. F. J. Humphreys and M. Hatherly, Re crystallization and related annealing phenomena, Elsevier, 2004. M. Kamaya, A. J. Wilkinson, and J. M. Titchmarsh, Nuclear Engineering and Design, 235, (6) (2005) 713 - 725. R. W. K. Honeycombe, The Plastic Deformation of Metals,. 1984. W. Pantleon et al., Materials Science and Engineering A, 387 (2004) 339-342.

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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

MULTI-TIME SCALING IMAGE BASED CRYSTAL PLASTICTY FE MODELS DWELL FATIGUE INITIATION IN POLYCRYSTALLINE TI ALLOYS Somnath Ghosh, Michael G. Callas Professor Johns Hopkins University, MD, USA, E-mail: [email protected] Abstract Microstructur e based mechanistic calculations, coupled with physically motivated crack initiation criterion, can provide effective means to predict fatigue cracking in polycrystalline materials. However the accommodation of large number of cycles to failure is computationally exhaustive to simulate using conventional single time scale finite element analysis. To meet this challenging requirement , a novel wavelet transformatio n based multi-time scaling algorithm is proposed for accelerated crystal plasticity finite element simulations. The wavelet decomposition naturally retains the high frequency response through the wavelet basis functions and transforms the low frequency material response into a "cycle scale" problem with monotonie evolution. Introduction Metals and alloys, such as titanium alloys and Ni-base superalloys are often exposed to cyclic loading in service conditions due to start up and shut down processes or load reversals. In many cases, this results in their fatigue or time delayed fracture. Ghosh et. al. [2, 3] have developed crystal plasticity models for deformation and creep in titanium alloys, e.g. TÏ-6AL and Ti6242, along with associated crack nucleation under cyclic loading in [4, 1]. Typically fatigue life in metallic materials is of the order of thousands of cycles, depending on the material and loading conditions. A major shortcoming of the crystal plasticity finite element simulations for fatigue life prediction is modeling the large number of cycles to failure or nucleation. In single time-scale finite element solutions using conventional time integration algorithms, each cycle is resolved into a number of time steps over which integration is performed. In crystal plasticity calculations, a high resolution in time steps is required for each cycle throughout the loading process, leading to exorbitant computational requirements . It is desirable to conduct simulations for a large number of cycles to reach local states of crack nucleation and growth. This paper introduces a novel wavelet transformatio n based multi-time scaling (WATMUS) algorithm for accelerated crystal plasticity FE simulations to overcome the above deficiencies [5]. The wavelet decomposition naturally retains the high frequency response through the wavelet basis functions and transforms the low frequency material response into a cycle scale problem with monotonie evolution. No assumption of scale separation is needed with this method. Adaptive methods improve the algorithm accuracy and efficiency. Crystal Plasticity Constitutive Relations The material studied is a polycrystalline titanium alloy Ti-6A1 with a hexagonal close packed or hep structure. For elasticity, a transversely isotropic response with five independent elastic constants is used [2]. Plastic deformation occurs by crystallographi c slip on the different

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slip systems. The deformation behavior of the hep material is modeled using a rate dependent, isothermal, elastic-viscoplastic, finite strain, crystal plasticity formulation. The stressstrain relation is written in terms of the second Piola-Kirchoff stress S and the work conjugate Lagrange-Gree n strain tensor E as S = C:Ee ,

where Ee = ^ (V eTFe - 1 )

(1)

e

Here C is a fourth order anisotropic elasticity tensor and F is the elastic component of the deformation gradient which is obtained by multiplicative decomposition F = FeF^,

det(F*)>0

(2)

where F is the deformation gradient tensor and F^ is its plastic component. The flow rule governing plastic deformation is expressed in terms of the plastic velocity gradient as: nslip LP =

F PF P - I=

£fs« a

(3)

where the Schmid tensor associated with a-th slip system s a is expressed in terms of the slip direction m^ and the slip plane normal n" in the reference configuration as sa = m^ ® ng\ For a plastic slip rate f* on the slip system a, a power law dependence on the resolved shear stress Ta and the slip system deformation resistance g" is used as: ff = f l ^ r ^ li s i g n ( T a - ^ a ) ,

Ta = (F*TFe S):sa

(4)

Here m is the material rate sensitivity parameter , y is the reference plastic shearing rate and xa is the back-stress that accounts for kinematic hardening in cyclic deformation. Slip System Deformation Resistance: The evolution of the slip system deformation resistance is assumed to be of the form:

g« = £^Vl

(5)

Za = ckr-dixa\itt\

(6)

ß The moduli haP =qa^h^ (no sum on ß) corresponds to strain hardening rate due to self and latent hardening on the a-th slip system due to slip on the j3-th slip system. Here, 1$ corresponds to the self-hardening and qa$ is a matrix describing the latent hardening. Back Stress Evolution: For modeling cyclic deformation it is important to include kinematic hardening including a backstress in the power law equation (4). The resolved effective stress Xa, which is the driving force for the dislocation motion on slip system a is defined as: Ck and dk are the direct hardening and dynamic recovery coefficients, respectively. Size Effect: To account for size effects in crystal plasticity formulation, a Hall-Petch type relationship that relates the slip system deformation resistance to a characteristi c length scale has been incorporated [3]. The dependence is expressed as:

ga=ë + a

Ka

" 7m

(7)

g" and K are size effect related slip system constants that refer to the interior slip system deformation resistance and slope respectively and Da is the characteristi c length scale.

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Wavelet Transformation based Multi-time Scaling Methodology for Cyclic Plasticity Simulating a large number of cycles for crystal plasticity simulations is computationally prohibitive using conventional FEM with a single time scale integration. In these conventional methods of numerical time integration using semi-discretization, each cycle is discretized into a number of time steps for time integration. A high time step resolution may be required for each cycle, depending on the evolution pattern of the response variables throughout the loading process. In addition, it is often necessary to conduct simulations for a significantly high number of cycles to reach local states of damage initiation and growth. This presents a significant challenge due to the presence of two distinct time scales, viz.: (i) The fine time scale T of each cycle, dictated by the frequency of loading (ii) The coarse time scale / of material evolution, characterized by the material relaxation time To overcome this challenge, a wavelet transformatio n based multi-time scaling (WATMUS) methodology has been proposed in [5] for accelerated time integration in crystal plasticity finite element analyses. Shown in figure 1(a) is the evolution of a rate dependent crystal plasticity state variable (y), solved by the finite element method. Clearly, the material response can be resolved into two time scales, viz. (i) a rapidly oscillating response within each cycle corresponding to a fine time scale T as shown in figures 1(b), and (//) a slowly varying monotonic response over the entire loading time span as shown in figures 1(c), corresponding to a coarse time scale t. The coarse time scale in this methodology can be identified with the cycle scale N, and hence projects a monotonie behavior. Correspondingly , the value of any given state variable y0 at the beginning of a given cycle can be thought of as a coarse time scale variable. This state variable will not vary in the T-scale within each cycle and hence, it can be considered to be purely a function of the cycle number N, i.e. -f = y°(N). The objective then is to obtain a coarse time scale (cycle scale) evolution equation of the form: ^=f(y°(N),ek(N))

(8)

where ek(N) are the wavelet decomposed strain coefficients over the cycle TV that is resolved with respect to wavelet basis functions y/fc(T) in the T-scale. Note that without the wavelet components £k(N), it is not possible to obtain the right hand side in equation (8) and a globallocal approach would have to be used along with its limitations. Thus, any variable, e.g. the strain can be resolved in a wavelet basis as: e(*,0 = e(*,tf,T) = £**(*>

tf)Vfr(T)

(9)

k

The coefficients ek(x,N) depends only on the cycle number N and the location x in the material microstructure . It is important to note that the T-scale basis functions V^M do not change with cycles N. For any material variable, the coarse scale behavior is associated with the cycle number N and thefinescale behavior with the time scale T e [0, T], T being the loading period. Equations (8) and (9) can then be used to delineate the coarse and fine scale behavior of the constitutive equations. A single integration step of equation (8) can traverse many cycles AN, resulting in significant computational efficiency of the algorithm. The value of AN is expected to increase with response stabilization. The WATMUS methodology requires appropriat e basis functions for temporally resolving the displacement vector, and the corresponding strain or

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deformation gradient fields as in equation (9). An ideally chosen set of basis functions should satisfy the following conditions: • The functions should be orthogonal, i.e. form a linearly independent set. • The basis functions should be able to represent all possible waveforms in the response variables to a pre-determine d resolution. • The number of coefficients, corresponding to the number of basis functions must be optimally small.

(b)

(a)

(c)

Figure 1 : Decoupling fine and coarse scale responses for a viscoplastic problem under cyclic loading: (a) fine scale solution, (b) zoomed in fine scale solution, (c) coarse scale solution. Coarse (Cycle) Scale Crystal Plasticity Finite Element Equations The wavelet transform based multi-time scale (WATMUS) algorithm is applied to the crystal plasticity constitutive models. The evolving microstructura l variables in the crystal plasticity constitutive relations (l)-(6) are: ¥p, ga, %a. The coarse scale evolution equations for these variables can be expressed, e.g. as:

dFf?

dgao -Ga(F*(N),F%°,g<*o,xao) (10) dN " J ' '* ' ' dN ao ao Here Ff? is the initial value of plastic deformation gradient, g and % are the initial values of hardness and back stress respectively for slip system a for the cycle N. The right hand side in equation (10) is calculated as: = JlJX

0 ao a fij(F^N)^ lJX l ö ,g a

^=[w,w=ferMW*

(ID

The integral in the numerator of the RHS is evaluated numerically using the backward Euler method. Once the values of coarse scale variables are known, the increments of the Cauchy stress AO(N,T) and other state variables can be computed over the cycle N. The finite element formulation for the coarse scale equations introduces wavelet coefficients of nodal displacements as the primary solution variable, as opposed to nodal displacement components in conventional FEM. The element displacement field and the associated generalized nodal displacements of each element are expressed in terms of the wavelet basis expansion as:

tt,(X,tf,T) = 5>a(X)*a,(tf,T) = 5> a (X) £ <4WV*M

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(12)

where Na(X) is the shape functions corresponding to the node a, qai is the nodal displacement component / for the a - th node in an element, and qkai(N);k = 1 • ~Nwav are the corresponding wavelet coefficients. The wavelet coefficients are functions of N and not of T, i.e. they evolve in the cycle scale alone. The corresponding wavelet coefficients of the deformation gradient field is derived as:

f*(X,JV) = £(S,j + 1 | ) VtWrfT = 6,j j *

Vk(r)dt + Ç ïl^lfaN)

(13)

The accuracy and efficiency of the wavelet transformatio n based multi-time scaling (WATMUS) methodology depends on two specific parameters , viz. (/) the number (Nwav) of wavelet bases or displacement coefficients qkai(N) selected in (12) and (//) the step size AN or the number of cycles traversed in each increment of the numerical integration scheme. Optimally, Nwav should be low and AN as high as possible, while keeping the net errors due to waveform representatio n and series truncation respectively to under pre-determine d bounds. Numerical Examples Solved with the WATMUS Algorithm The WATMUS methodology is used in this example to simulate cyclic deformation of the Ti-6A1 alloy using the 3D crystal plasticity finite element (CPFE) model. A model problem of a poly crystalline microstructur e is developed, consisting of 27 cubic grains with different crystallographi c orientations. Each grain is subdivided into 27 brick elements resulting in a total of 729 elements for the CPFE model. Euler angles, corresponding to the crystallographi c orientation distribution for the model are depicted in figure 2(a). The model is subjected to cyclic loading with a mean stress of 500 MPa, together with a superposed oscillatory portion with a peak of 350 MPa and time period of T — Is. The starting value of cycle jump is taken as NNjUmp = 2, while the subsequent cycle steps with loading is obtained from a criterion. The Daubechies-4 wavelet basis is used to decompose the nodal displacement components in each cycle according to equation (12). This criterion selects coefficients from regions having rapid fluctuations in values of the response functions and those that are most likely to change as the problem progresses leading to a total of 116521 coefficients with an average of 39 coefficients per degree of freedom for the present problem. The simulation is run for only 1000 cycles, so that results can be compared with results from computationally exhaustive single (fine scale) simulations. Figure 3(a) shows a comparison of the cycle-scale plastic deformation gradient Fpo by coarse and fine time-scale simulations at a typical material point in a grain as a function of the number of cycles. The results of the two methods are indistinguishable for the range considered. The state of stress ozz in the microstructur e along the loading direction at the 1000//* cycle is shown in figures 2(b,c) and 3(b) for both coarse and fine time scale simulations. As is observed, the coarse time scale and fine time-scale results are in excellent agreement with each other. Once the coarse scale variables for a given cycle are known, the fine scale response over that cycle can be reconstructed. A computational time advantage of approximately 7 times is observed for the current problem. The predicted cycle jump ANjUmp is expected to increase as the problem progresses due to stabilization of the response, resulting in even higher computational savings.

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(b)

(a)

(c)

Figure 2: Stress ((a) Euler angle distribution for the 729 element crystal plasticity FE model; Ö33) contour by: (b) multi time-scale simulations and (c) fine time-scale simulations

^

500 Cycle (N)

0.5

1000

(a)

1 1.5 Distance (|l m)

(b)

Figure 3: (a) Coarse scale evolution of plastic deformation gradient ¥po as a function of cycle number TV; (b) Variation of stress along the diagonal of the model cube (729 element case) Conclusions This paper develops a novel wavelet transformatio n based multi-time scaling (WATMUS) method for crystal plasticityfiniteelement simulations of cyclic deformation in poly crystalline materials leading to fatigue failure. Multi-time scaling is motivated by the large number of cycles that may be required to initiate a fatigue crack in a poly crystalline sample. Simulating such large number of cycles remains intractable to conventional single time scale finite element analysis. The unique aspect of the WATMUS method is that the algorithm does not require inherent scale separation as with other conventional methods that assume averaging, periodicity or near periodicity. References [1] M. Anahid, P. Chakraborty , D.S. Joseph and S. Ghosh, Wavelet decomposed dual-time scale crystal plasticity FE model for analyzing cyclic deformation induced crack nucleation in polycrystals, Model. Simul. Mater. Sei. Engng. 17 (2009) 064009.

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[2] D. Deka, D.S. Joseph, S. Ghosh and M.J. Mills, Crystal plasticity modeling of deformation and creep in polycrystalline Ti-6242, Metall. Trans. A. 17A(5) (2006) 1371-1388. [3] G. Venkataramani , S. Ghosh and M.J. Mills, A size dependent crystal plasticity finite element model for creep and load-shedding in polycrystalline Titanium alloys, Acta Mater. 55(2007)3971-3986. [4] K. Kirane and S. Ghosh, A cold dwell fatigue crack nucleation criterion for polycrystalline Ti-6242 using grain-level crystal plasticity FE model, Int. J. Fatigue 30 (2008) 2127-2139. [5] D. S. Joseph, P. Chakrabort y and S. Ghosh, Wavelet transformatio n based multi-time scaling method for crystal plasticity FE simulations under cyclic loading, Comp. Meth. Appl. Mech. Engng. 199 (2010) 2177-2194.

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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

VIRTUAL M E C H A N I C AL T E S T I NG OF C O M P O S I T E S: F R OM MATERIALS TO C O M P O N E N TS Javier LLorca1,2 and Carlos Gonzalez1'2 Madrid Institute for Advanced Studies of Materials (IMDEA Materials Institute) C/Professor Aranguren s/n, 28040 - Madrid, Spain. 2 Department of Materials Science, Polytechnic University of Madrid E. T. S. de Ingenieros de Caminos. 2804 - Madrid, Spain. Keywords: composite materials; virtual testing; multiscale modeling. Abstract A bottom-up, multiscale modeling strategy has been developed to carry out high fidelity virtual mechanical tests of composite materials and structures. The whole strategy is based on finite element simulations performed at different length scales (lamina, laminate and component) and the main features each simulation strategy as well as the information transferred between length scales are briefly described. Future lines of development are finally indicated. Introduction Polymer-matrix composites are nowadays extensively used in applications where outstanding mechanical properties are necessary in combination with weight savings. Good examples can be found in the A380, the last civil Airbus aircraft containing up to 25% in weight of composite materials (used for wings, fuselage sections and tail surfaces) while the Boeing 787 Dreamliner claims to be the first airliner with a fully composite fuselage manufactured with advanced technologies. However, despite all existing information and current knowledge about these materials, their complex mechanical behavior (highly non-linear, anisotropic and with different and novel failure mechanisms not found in traditional structural materials) requires greater research efforts to optimize their performance and take advantage of their full potential. In addition, due to the difficulties in accurately predicting the failure stress of composite materials, the burden of testing is immense so as to prove safety in composite structures upon whose integrity human lives depend. For instance, certification of an airframe structures requires « 104 tests of material specimens along with tests of components and structures up to entire tails, wing boxes, and fuselages [1]. Recent developments in multiscale simulations, together with increased computational power and improvements in modeling tools, are rapidly changing this scenario. Nowadays it is possible to accurately predict the behavior until failure of composite coupon specimens and simple components through the application of bottom-up approaches. The main features of this novel approach to carrying out high-fidelity simulations of the mechanical behavior of composite materials and structures are presented below. Bottom-up multiscale modeling strategy for structural composites The need for refined simulations to predict the mechanical behavior of composite structures is well-known in the structural engineering community. The standard strategy to tackle this problem starts from a numerical analysis of the whole structure (normally using the finite element method) in a global-to-local approach. This initial evaluation identifies "hot spots"

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in which damage is likely to occur, and these regions are subjected to further refined analyses. Non-linear constitutive models (as well as damage) are taken into account in these cases using phenomenological models for the material behavior. These models contain a number of parameters whose values are chosen to reproduce the actual material behavior as a result of experience and costly testing campaigns [2]. Although this strategy has been in place for many years, it has two obvious limitations. Firstly, materials innovations in critical regions are limited because of the lack of reliable data to assess the onset and propagation of damage upon loading. Secondly, extrapolation of current knowledge to different loading/environmenta l conditions is problematic due to the phenomenological nature of the models. As opposed to this strategy, a new hierarchical, bottom-up approach has recently been developed to carry out virtual tests of composite materials and structures. The overall multiscale simulation scheme is depicted in Fig. 1 and takes advantage of the fact that composite structures are made up of laminates which in turn are obtained by stacking individual plies with different fiber orientation. This leads to three different entities (lamina, laminate and component) whose mechanical behavior is characterized by three different length scales, namely fiber diameter, lamina and laminate thickness, respectively. Fiber diameters are of the order of 5-10 /im, while lamina thicknesses are in the range 100-300 /xm and standard laminates are several mm in thickness and above. This clear separation of length scales is very useful to carry out multiscale modeling by computing the properties of one entity (e.g. lamina) at the relevant length scale, homogenizing the results into a constitutive model, and passing this information to the simulations at the next length scale to determine the mechanical behavior of the larger entity (e.g. laminate). Thus, multiscale modeling is carried out through the transfer of information between different length scales rather than by coupling different simulation techniques. Virtual testing of composites up to the component level is thus carried out in three successive step within the framework of finite element method (FEM). In the first one, computational micromechanics is used to predict the lamina properties from the thermomechanical properties of the constituents (fiber, matrix and interfaces), together with the volume fraction and spatial distribution of the fibers within an individual lamina. Starting from the homogenized lamina properties and information about the interply behavior, computational mesomechanics is then used to determine the homogenized behavior of laminates. These results are finally used within the framework of computational mechanics to obtain the response until fracture of structural components. The main features of the simulation techniques at each step of the simulation ladder, as well as the information transferred between length scales, are detailed in the following sections. Computational Micromechanics Homogenization theory is an efficient and accurate methodology to compute the elastic properties of composites from the properties and spatial distribution of the different phases in the material. Extension to the non-linear regime and particularly to situations involving strain localization and fracture is more complex and has to be carried out by means of computational micromechanics [3]. In this context, the mechanical behavior of a composite lamina is determined by numerically solving the boundary value problem for a representative volume element of the composite which is much larger than the heterogeneities (fibers) in the microstructure . Fiber and matrix properties can be obtained from experiments on isolated fibers and matrix coupons while interface strength and toughness can be measured by means

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Figure 1: Schematic of the multiscale modeling strategy for virtual testing of composites of push-in tests on lamina cross-sections [4]. This modeling strategy allows the inclusion of complex nonlinear behaviors (geometrical and material), stress states (multiaxial) as well as the nucleation and growth of damage. This is shown in Fig. 2a, which shows the localization of damage due to interface decohesion and matrix plasticity in a unidirectional C/epoxy lamina subjected to transversal compression. The numerical simulations provide the "averaged" stress-strain behavior of the lamina and, in particular, the strength of the lamina and the evolution of damage. Simulations under multiaxial stress states (i.e. transverse compression and shear) can be carried out to develop a failure surface for the lamina behavior which explicitly takes into account the physical failure micromechanisms controlling the lamina behavior (Fig. 2b). This failure surface (and the evolution of damage along each loading path) is the critical information passed on to the next set of simulations. Computational Mesomechanics The main elements of the computational mesomechanics simulations are the individual lamina. The virtual composite laminate is built by stacking lamina with different fiber orientation and the finite element model explicitly includes each ply, while the interfaces between plies are modeled with cohesive elements (Fig. 3a). The constitutive equation for each lamina takes into account the elastic anisotropy induced by fiber orientation as well as the effect of the different failure mechanisms on the lamina strength and post-peak behavior. They are introduced through the formalism of continuum damage mechanics [8] where the failure surface and the evolution of damage along each direction is the information provided by computational micromechanics. In addition, the mesomechanical model needs information

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Figure 2: (a) Contour plot of the accumulated plastic strain in the matrix showing the localization of failure in a shear band during transverse compression [5]. (b) Determination of the failure locus of an unidirectional C/PEEK lamina subjected to transverse compression and in-plane shear [6]. Experimental data from [7]. about the mechanical properties (strength and toughness) of the interfaces between plies, which are normally obtained from standard fracture tests. The main advantages of computational mesomechanics are its ability to deal with full three-dimensional stress states and to take into account explicitly intraply and interply damage, together with the complex interaction between both. The main limitation of this approach lies in the computational power required to carry out these simulations, which limit their application to coupons or structural details. Current examples can be found in the analyses of laminates subjected to impact, where excellent correlation with experimental data has been achieved [9]. The multiscale simulation strategy continues by developing the corresponding failure surface for a given laminate. This is achieved by carrying out simulations of the laminate behavior until failure under different loading conditions (tension and compression in perpendicular directions, shear as well as multiaxial loading). The results of the analysis provide a detailed picture of the dominant deformation and damage mechanisms under each circumstance and the corresponding stress-strain curves until failure. The failure surface of the laminate in the stress space can be built from this data, which can also provide quantitative parameters (in terms of the reduction of stiffness along different directions) to assess the evolution of the damage during deformation. This information is again passed on to the simulations at the next level.

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Figure 3: (a) Schematic of computational mesomechanics approach, (b) Simulation of highvelocity impact on a C/ epoxy laminate. Damage by decohesion between plies is clearly visible. In addition, contour plot indicates the level of damage by matrix cracking — from intact (0) to fully damaged (1) — within the individual plies. Computational Mechanics The analysis of composite structural components by the finite element method is normally carried out using shell elements within the framework of computational mechanics. This approach is limited to bidimensional stress states but it is very efficient from the numerical viewpoint and ideal to analyze large structures. The shell elements contain as many integration points through the thickness as the number of plies in the laminate in each region of the component but different plies are not modeled independently. Thus, interply decohesion cannot be included explicitly and this hinders the accuracy of the simulations as the actual interaction between intraply and interply damage is not accounted for. Nevertheless, this limitation is overcome within the current multiscale modeling approach owing to the failure surface and the evolution of damage provided by computational mesomechanics for the whole laminate. This information (which contains the actual interaction between the different failure mechanisms) is used as input for a continuum damage model of the laminate which is able to reproduce the deformation and damage until failure at the macroscopic level. This approach can be then used to accurately reproduce the mechanical behavior until failure of structural components by means of shell elements (Fig. 4b). Concluding Remarks A bottom-up, multiscale modeling strategy has been developed to carry out high-fidelity virtual mechanical testing of composite materials and structures. The whole strategy is based on finite element simulations performed at different length scales to take into account the relevant microstructura l and structural features relevant to the mechanical behavior. Instead of directly coupling simulations at different length scales, multiscale modeling is introduced by successive homogenization of the mechanical behavior, so information about the deformation and damage is introduced in a constitutive model and passed on to the simulations at the next scale. Future developments will proceed in different directions. Besides refining the current strategy, it should be noted that it is built up from the experimental values of fiber, matrix and interfaces. While this is feasible from the industrial viewpoint, a more academic approach would aim to compute these properties from first principles, so new composite materials can be designed and validated in silico, well before they are actually manufactured and tested.

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Figure 4: (a) Schematic of computational mechanics approach, (b) Simulation of highvelocity bird impact on a composite leading edge. Contour plot of damage by fiber fracture is shown in the figure. In addition, incorporation of other physical properties to the simulation ladder (thermal and electrical conductivity, permeability, moisture absorption, etc.) will pave the way to designing and characterizing multifunctional composites. Finally, Computational Materials Engineering of composites will require coupling this virtual testing strategy with similar models devoted to virtual processing. Acknowledgements This investigation was supported by the Ministerio de Ciencia e Innovacion de Espana through the grant MAT 2009-14396, by the Comunidad de Madrid through the program ESTRUMAT (S2009/MAT-1585), by the research project DEFCOM (Era-Net MATERA, EU, 6th FP) and by the European Communitys Seventh Framework Programme FP7/20072013 under grant agreement 213371 (MAAXIMUS, www.maaximus.eu). In addition, the authors want to acknowledge the support of Airbus, Gamesa, Astrium Espana and Airbus Military through various industrial projects. References [1] B. Cox, Q. Yang, In quest of virtual tests for structural composites, Science 314 (2006) 1102-1107. [2] Department of Defense Handbook, MIL-HDBK-17-1F, Composite Materials Handbook, Vol. 1. Polymer matrix composites, Guidelines for characterizatio n of structural materials, 2002. [3] J. Segurado, C. Gonzalez, J. LLorca, A numerical investigation of the effect of particle clustering on the mechanical properties of composites, Acta Materialia 51 (2003) 23552369. [4] J. M. Molina-Aldareguia, M. Rodriguez, C. Gonzalez, J. LLorca, An experimental and numerical study of the influence of local effects on the application of the fibre push-in test, Philosophical Magazine (2011) in press.

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[5] C. Gonzalez, J. LLorca, Mechanical behavior of unidirectional fiber-reinforced polymers under transverse compression: microscopic mechanisms and modeling, Composites Science and Technology 67 (2007) 2795-2806. [6] E. Totry, C. Gonzalez, J. LLorca, Prediction of the failure locus of C/PEEK composites under transverse compression and longitudinal shear through computational micromechanics, Composites Science and Technology 68 (2008) 3128-3136. [7] T. J. Vogler, S. Kyriakides, Inelastic behavior of an AS4/PEEK compoiste under combined transverse compression and shear. Part I: experiments, Internationa l Journal of Plasticity 15 (1999) 783-806. [8] P. Maimi, P. P. Camanho, J. A. Mayugo, C. G. Dâvila, A continuum damage model for composite laminates: Part I constitutive model, Mechanics of Materials 39 (2007) 897-908. [9] E. Arévalo, C. Gonzalez, F. Gâlvez, J. LLorca, Modelling low velocity impact in C/epoxy laminates, in: 23rd Internationa l Symposium on Ballistics, 2007, pp. 1123-1132.

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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

DESIGN OF MULTIFUNCTIONAL MATERIAL STRUCTURES USING TOPOLOGY OPTIMIZATION WITH FEATURE CONTROL James K Guest and Seung-Hyun Ha Johns Hopkins University; Civil Engineering Department; Baltimore, MD 21218, USA Keywords: Topology Optimization, Architectural Optimization, Inverse Homogenization Abstract The design of materials with targeted performance properties may be viewed as an inverse homogenization problem. The goal is to identify material structures that yield prescribed effective properties and symmetries at the macro-scale. This paper will review a systematic, computational (FE-based) approach known as topology optimization that offers an efficient means for solving such design problems. Topology optimization is a free-form design methodology for optimizing material distributions across design domains, which for periodic materials is the characteristic unit cell. Candidate material phases may be placed at any point within the domain, thus enabling generation of new design ideas. The cost of this design freedom is that topology optimized solutions may in fact be suboptimal when subjected to realworld fabrication conditions and operating environments. This work will discuss recent advances in topology optimization for considering manufacturin g constraints and flaws, with the goal of designing realizable and reliable multifunctional material structures. Competing performance properties are assigned levels of importance, or relative weights, so that the material may be tailored according to its future application. The developed techniques utilize the Heaviside Projection Method (HPM) to topology optimization, a physics independent approach that provides the designer with physically meaningful control over phase feature length scales and geometries. The discussion focuses on elastic properties, but the methodology may be applied to properties governed by other physics, including (for example) thermal conductivity and fluid permeability. Introduction Topology optimization is a systematic design tool capable of identifying optimal phase distributions across a design domain. Although its development is rooted in structural applications, several researchers have used topology optimization to design the underlying structure, or architecture, of periodic materials. In such cases, the unit cell serves as design domain and is defined at the micro, or 'small', length scale, while performance properties to be optimized are measured at the macro, or Targe', length scale. Microstructura l topology and behavior is linked to macroscopic properties through homogenization theory, which provides a means for computing the effective (average) properties of a material via analysis of the representative unit cell. The design of material structures is therefore an inverse homogenization problem: find the unit cell design that yields optimized effective properties. Topology optimization has proven very effective at solving inverse homogenization problems to design material structures with optimized or exotic properties. These include minimum weight truss and frame micro structures with prescribed elastic stiffness properties, including negative Poisson's ratio [1]; three-phase continuum materials with optimized elastic stiffness and thermal

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expansion properties [2]; two-phase continuum materials with maximal fluid permeability [3]; optimized piezocomposites [4]; and optimized multifunctional materials governed by multiple physics, including elastic stiffness and thermal conductivity [5,6] and elastic stiffiiess and fluid permeability [7]. Figure 1 illustrates the latter, displaying a porous material with 50% volume fraction optimized for mechanical stiffness (bulk modulus) and fluid flow permeability, with each property weighted equally. As suggested in Figure 1, the great power of topology optimization is that it is a free-form design tool capable of discovering new design ideas. Given a suite of candidate material phases that can be used in the design of the material structure, the topology optimization algorithm is used to identify which phase should be located at each point in space within the unit cell. The example in Figure 1 uses two-phases: a void (or fluid) phase and a solid (material) phase. The key requirement is that the properties of these phases, or at least statistics of the properties, must be known. While powerful, the free-form nature of topology optimization algorithms make them susceptible to numerical instabilities and means realized solutions may be suboptimal when subjected to real-world fabrication conditions and operating environments. This paper reviews the inverse homogenization formulation and discusses solution strategies for incorporating manufacturin g constraints and uncertainties in topology optimization problems.

Figure 1. Inverse homogenization of porous material optimized for mechanical stiffness and fluid flow. Unit cell initial guess (left), optimized unit cell topology with streamlines (center), and resulting periodic material shown with eight unit cells (right). The solid phase is shown in red and the streamlines represent the fluid phase. Inverse Homogenization via Topology Optimization The inverse homogenization problem is formulated such that the designer may tailor the microstructur e according to the material's future application. This is achieved by assigning a level of importance, or weighting factor (w;), to each property /. The problem is stated in general as: Maximize: Design variable: Constraints :

I w, * (effective performance property)} phase distribution function p(y) bounds on effective performance properties prescribed constitutive symmetries governing physics and homogenization equations resource (phase) availability manufacturing constraints

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where the distribution function p( y) to be optimized indicates the phase occupying location y within the unit cell. The weights w,- may be selected based on the application, or be varied to build a Pareto optimal front. The reader is referred to [7] for a detailed discussion. Elastic Homogenization Equations The technique is demonstrated herein on optimization for elastic properties, where we look to tailor the effective stiffness tensor CH of a material that relates macroscale stresses ( a ) and strains ( e ) as follows: a = CHs

(1)

Using asymptotic expansion [8,9], the effective stiffness tensor of a periodic material is calculated as

^ = ^ /r C M , ( C , - < , ^ ) ) ( < ( ", - < s ^ ' ) )^

(2)

where Cyu is the elastic tensor of the base material at location y, e°p^j) are the unit test strain tensors, e*pq(xlJ) are the fluctuation strain tensors due to the inhomogeneous unit cell topology. Also, the displacement fields xlJ are calculated from the unit cell problem as

L

lJpq

dyqdy

L

upqpq

av,.

'

V v e

^

(3)

V = {v : v is Y - periodic} The homogenization problem is typically solved numerically using finite elements. The unit cell is discretized and the material phase distribution is considered constant over the elemental domain and subsequently denoted as pe . Integration of Eq. (2) yields the following expression for the effective elastic stiffness tensor [10]:

c

ä -n2K & ' ) - d ^ ) r ke (p e )K H) - d ' (tf) ) I I eEY

e

(4>

e

where k (p ) is the element stiffness matrix as a function of the element composition pe. Also, deoUj) and deW are the nodal displacement vectors for element e related to the unit test strain e°m and the fluctuation strain s*(xu), respectively. Elastic Properties The objective function and/or performance constraints for the optimization problem are typically some combination of effective engineering properties such as bulk, Young's, or shear modulus, or Poisson's ratio. Effective elastic symmetries, such as isotropy, may also be prescribed. Regardless of the combination selected by the designer, the important point here is that all of these properties are functions of the effective elasticity tensor CH, and consequently the distribution pe. These elastic properties are thus readily computed for a given unit cell topology.

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Solution Algorithm Detailed discussion of the numerical topology optimization algorithm is outside the scope of this paper. In short, a gradient-based optimizer is used to guide the design process, with sensitivities computed using the adjoint method. The inverse homogenization logic may be applied to any structures with periodicity. In continuum topology optimization, the design domain is discretized with finite elements such as four-node quadrilaterals , and, in the design of porous materials, the goal is to determine whether each element contains material or is void. For material structures composed of fiber or frame type elements, topology optimization with a frame ground structure may be more appropriat e (Figure 2a), where the goal is to determine the optimal connectivity of the frame elements. The popular SIMP Method [11] is used to interpolate the discrete space and facilitate calculation of gradient information. For continuum structures, the Heaviside Projection Method (HPM) is used to eliminate well-known numerical instabilities of mesh dependence and checkerboard patterns [12]. Manufacturabilit y 7 Algorithmic consideration of manufacturability is ultimately dependent on the type of structure elements used. In frame topology optimization, it is typically assumed that the initial ground structure is manufacturable , and thus optimized solutions are likely to be manufacturable . Figure 2, for example, shows frame-like material structures optimized for bulk modulus under the condition of square elastic symmetries. For comparison, this figure also contains the continuum solution. Although the continuum structure offers higher performance due to the increased design freedom, it may be more difficult to manufacture compared to the largely orthogonal frame networks. Such orthogonal networks, however, are not capable of generating isotropic solutions, which require either discontinuous frame networks or continuum structures (Figure 3). Controlling the manufacturabilit y of optimized continuum structures, on the other hand, is more challenging as features are defined by the union of elements of like phase. HPM can prove an effective tool in this regard, as it implicitly controls the minimum length scale of designed features, including the minimum size and maximum curvature of load carrying and/or void features. The phase to be constrained is a function of the process used to fabricate the periodic material [12]. For example, materials created through a phase removal process may require constraining the length scale of the etching tool, while materials created using deposition processes may require constraining the length scale of the solid phase. One may also constrain the maximum length scale of designed features [13].

(a) (b) (c) (d) Figure 2. Maximum bulk modulus unit cells with square symmetry, (a) Dense frame ground structure used as initial guess and optimized solutions using (b) orthogonal elements only, (c) orthogonal plus diagonal elements, and (d) continuum elements.

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Figure 3. Maximum bulk modulus unit cells with isotropic elastic symmetry found using frame (left) and continuum (right) domains. Material structures designed using traditional continuum topology optimization approaches are monolithic such as those seen in Figure 1. That is, the connectivity of like-phase element forms a continuous feature. Recent algorithmic advances based on HPM, however, now allow for the design of material structures containing discrete objects, such as fibers and particles, which maybe used to enhance strength or multifunctionality of the material. Figure 4, for example, shows a fiber-based composite optimized for bulk modulus using a fixed fiber radius, a prescribed minimum fiber spacing (for bonding), and maximum fiber volume fraction of 10% [14].

Figure 4. Maximum bulk modulus material structure with isotropic symmetry found using discrete feature HPM: unit cell (left) and periodic material (right). Conclusions Topology optimization is an effective tool for the systematic design of periodic materials with optimized properties. Recent algorithmic advances based on the projection methodology HPM now also provide designers with a means for influencing manufacturabilit y of the optimized materials, including design of materials containing discrete objects, such as fibers and/or particles, which may be used to enhance material multifunctionality. Fabrication flaws, in the form of material properties or geometry uncertainties, may also be included in the topology optimization formulation (e.g., [15,16]). Extending these ideas to the design of material structures is the subject of ongoing work by the authors. References 1. O. Sigmund, "Materials with prescribed constitutive parameters: an inverse homogenization problem," International Journal ofSolids and Structures, 31 (1994), 2313-2329. 2. O. Sigmund and S. Torquato, "Design of materials with extreme thermal expansion using a three-phase topology optimization method," Journal of Mechanics and Physics of Solids, 45 (1997), 1037-1067.

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3. J.K. Guest and J.H. Prévost, "Design of maximum permeability material structures," Computer Methods in Applied Mechanics and Engineering, 196 (2007), 1006-1017. 4. O. Sigmund, S. Torquato, and I.A. Aksay, "On the design of 1-3 piezocomposites using topology optimization," Journal of Materials Research, 13 (1998), 1038-1048. 5. V.J. Challis, A.P. Roberts, and A.H. Wilkins, "Design of three dimensional isotropic microstructure s for maximized stiffness and conductivity," International Journal of Solids and Structures, 45 (2008), 4130-4146. 6. N. de Kruijf, S. Zhou, Q. Li, and Y.W. Mai, "Topological design of structures and composite materials with multiobjectives," International Journal of Solids and Structures 44 (2007), 7092-7109. 7. J.K. Guest and J.H. Prévost, "Optimizing multifunctional materials: design of microstructure s for maximized stiffiiess and fluid permeability," International Journal of Solids and Structures, 43 (2006), 7028-7047. 8. A. Bensoussan, J.L. Lions, and G. Papanicolaou, Asymptotic Analysis for Periodic Structures, North-Holland, Amsterdam, (1978). 9. E. Sanchez-Palencia, "Non-homogeneous Media and Vibration Theory," Lecture Notes in Physics 127 (1980). 10. J.M. Guedes and N. Kikuchi, "Preprocessin g and postprocessing for materials based on the homogenization method with adaptive finite element methods," Computer Methods in Applied Mechanics and Engineering 83 (1990) 143-198. 11. M.P. Bendsoe, "Optimal shape design as a material distribution problem," Structural Optimization, 1 (1989), 193-202. 12. J.K. Guest, "Topology optimization with multiple phase projection," Computer Methods in Applied Mechanics and Engineering, 199 (2009) 123-135. 13. J.K. Guest, "Imposing maximum length scale in topology optimization," Structural and Multidisciplinary Optimization, 2>1 (2009) 463-473. 14. J.K. Guest, "Optimizing Discrete Feature Layouts in Structures and Materials: A ProjectionBased Topology Optimization Approach," Computer Methods in Applied Mechanics and Engineering, in review. 15. J.K. Guest and T. Igusa, "Structura l optimization under uncertain loads and nodal locations," Computer Methods in Applied Mechanics and Engineering, 198 (2008), 116-124. 16. A. Asadpoure, M. Tootkaboni, and J.K. Guest, "Robust Topology Optimization of Structures with Uncertainties in Stiffiiess - Application to Truss Structures," Computers and Structures, in press, doi: 10.1016/j.compstruc.2010.11.004.

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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

Development of Neural Networks for the Prediction of the Interrelationship between Microstructure and Properties of Ti Alloys S. Koduri1, P.C. Collins2, D. Huber, B. Welk, H.L. Fraser Center for the Accelerated Maturation of Materials, Dept. of Materials Science and Engineering, The Ohio State University, Columbus, OH, ^ntel Corporation, Hillsboro, OR, 2Dept. of Materials Science and Engineering, University of North Texas, Denton, TX Abstract Ti alloys possess a rich set of microstructura l features that exist over a wide range of size scales. Their interdependent nature has prevented controlled experiments from being undertaken with the aim of identifying the functional dependences of microstructur e on properties, and hence there exist no phenomenological relationships to permit the assessment of microstructure property relationships. Therefore, in the present study, an approach involving Bayesian neural networks has been adopted. Suitable databases relating microstructure , composition and properties, here including tensile and fracturetoughness, have been produced for both beta heattreated and alpha/beta processed versions of the alloys. These databases have been divided into two parts, one being used to train the neural networks and the other to test the quality of the network outputs. The optimized networks have been used to predict, within the ranges of the databases, the interrelationship s between microstructur e and tensile properties and fracture toughness, generally providing accuracies 3%. In addition to providing an interpolative prediction (i.e., with input parameters whose values lie within the ranges of the database used to develop the given neural network) of microstructure/propert y relationships, importantly these networks have been used to conduct virtual experiments to reveal functional dependencies between properties and the input parameters. In this way, mechanistic information may be obtained which may be subsequently used in the development of more sophisticated and physically-based predictive models. For example, in the case of tensile properties of Ti-6A1-4V, virtual experiments indicate that the most significant strengthening mechanism in this alloy is solid solution hardening. Introduction The attractive combination of properties present in many titanium alloys has resulted in their application across a wide range of industries (e.g., aerospace, automotive, biomédical) [1-3]. Many of these structural alloys, including the commonly used cc/ß alloys such as Ti-6A1-4V, exhibit a rather extended range of mechanical properties (e.g., 725-930MPa). Researchers have claimed that, for a specific titanium alloy, the mechanical properties are dependent upon the microstructure s [4-6]. However, until recently the microstructure-propert y correlations have been at best qualitative [4-12]. It is highly desirable that predictive models be developed in which an important design property, such as tensile properties or toughness, may be predicted based upon awareness of the composition and microstructur e of the material. While it may be desirable that such predictive models be based upon operating mechanisms, such models have long development cycles and are still in their infancy. Therefore, the current paper focuses on the development of a predictive model based on a short-term approach, namely the application of rules-based approaches, such as neural networks [13-16]. For this research, a microstructure based models of tensile and toughness properties of a+ß processed Ti-6A1-4V was developed

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using a probabilistic Bayesian neural network architecture with three-layers and a feed-forwardtype network. The number of hidden nodes and the initial values for the weight vectors were inferred through training and comparison with model quality from with the corresponding databases. The successful application of such neural networks has been described elsewhere by researchers who have developed predictive models to describe quantitatively the dependencies of properties upon microstructur e [17,18]. While these models have proven to be the most accurate tools developed for the prediction of mechanical properties, each has been developed for one specific alloy composition (e.g., Ti-6.4Al-4V-0.16Fe-0.18O - the composition from a single melt of a typical Ti-6-4 alloy). Thus, there exists a significant risk in the application of such models to alloys that do not fall within a small region of the compositional and microstructura l space. In addition, as they do not allow for any variation in composition, there is no direct or indirect inclusion of non-microstructura l feature based strengthening mechanisms, such as solid solution strengthening, in the models. Therefore, there are three principle aims of the research that is presented in this paper. The first is to develop a well-populated database for an ot-ß processed Ti-based alloy with significant variations in both composition and microstructure . Such variations have been affected using standard industrial practices. The composition space is the Ti-Al-V system, nominally around the alloy Ti-6-4, with explicitly designed variations in not only the Al (4.76 to 6.55 wt%) and V (3.30 to 4.45 wt%), but also the O (0.07 to 0.20 wt%) and Fe (0.11 to 0.41 wt%) interstitial contents. The second is to use the database to develop Bayesian neural network models for the prediction of properties given a specific composition and microstructure . The third is for a first approximation of functional dependencies of the two types of variables (composition and microstructure ) on properties. This research has several important aspects that differ from previous work. The most important difference is the standard, industrially accepted way in which the alloys were prepared and processed, and the subsequent thermomechanica l processing that was performed. The other differences include the size and degree of sophistication of the resulting database (e.g., this study has more samples from a smaller region of compositional space), and the fact that the alloys of interest are a/ß processed rather than ß processed. In this fashion, it is in keeping with the very premise of the ICME approach, where advances in computational modeling approaches must be based upon and provide data that is not only of the highest quality, but relevant to industrially complex engineering materials. Experimental Procedures A total of nine different titanium alloys (based around Ti-6A1-4V) were produced with deliberate variations in the relative amounts of the individual alloying elements, including the trace substitutional Fe and interstitial O contents. The alloy variations were tailored to maximize the impact of these studies. The compositions, as measured by Timet using inductively coupled plasma (ICP) mass spectrometry and close to their target levels, include the: (1) aluminum content that extended beyond standard Ti-6A1-4V (on the low-side, to avoid the development of embrittling ot2 domains); (2) vanadium content that was slightly extended beyond Ti-6A1-4V; (3) oxygen content with a slightly extended range and included extra low interstitial (ELI) grade products; and (4) iron with a significantly extended range. For each of the nine alloy compositions, fourteen samples were exposed to different thermomechanica l processing histories (including 7 equivalent to ß-processing and 7 equivalent to a+ß-processing), producing a total of 56 ß-processed samples and 56 a+ß-processed samples. It should be noted that in the preparation

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of these samples, all were taken from the same radius of a round billet, minimizing the differences in strain during deformation and a resulting difference in texture. The samples were subjected to room temperatur e mechanical tests to assess the tensile and toughness properties. Following testing, undeformed sections of the grip fromeach sample was sectioned for metallographic preparation . Following traditional metallographic techniques, the samples were characterized using a FEI/Philips Sirion scanning electron microscope (SEM) operating in backscattered electron (BSE) imaging mode at 15 kV with a resolution of approximately 3.0 nm. Each image had a resolution of 3872 x 2904 pixels and a depth of 8 bit. The resolution afforded using the SEM, especially when compared with other available techniques (e.g., optical micrographs),is of paramount importance to provide the highest fidelity quantified microstructura l data to the neural networks. The specimens were imaged at four random locations avoiding overlap and edge effects. Microstructura l features present in the four micrographs were quantified using the stereological techniques which have been developed by the authors and are described in previous work [19]. These features include the equiaxed alpha size (equiaxed-ot size, urn), the volume fractionof equiaxed alpha (pveciuiaxed-alPha)5 the volume fraction of total alpha (Fvtotal-alpha), and the width of the alpha laths in the transformed ß regions using Gundersen' s derivation (a-lath width, urn) [20,21]. The experimentally determined data regarding alloy composition, microstructure , and tensile or toughness properties was included in a database for additional analysis. A training dataset, comprising 40 samples, was used to develop the optimum neural network model based upon a Bayesian architecture . A testing dataset, containing 16 samples, was used to test the model and determine the associated errors. Following training and testing, the neural network model was used to conduct a series of virtual experiments, where all but one of the inputs was held at a value (e.g., their average) while the single input was allowed to vary across its range, and its effect on the property determined. These experiments are typically impossible to conduct in the laboratory, owing to the interdependenc y among various compositional and microstructura l inputs. Therefore, these virtual experiments can provide dependencies between a single input parameter and a property that can not otherwise be determined. Results and Discussion a+ßprocessed Ti-6Al-4V Tensile Model-Database An example of the motivation to use advanced analytical tools to help isolate the individual influences of the compositional and microstructura l inputs is shown in fig. 1 (a-d). The four different samples whose microstructur e and composition are shown in this figure result in roughly an equivalent yield strength (within ± 7.5 MPa, or -lksi). It is clear that there is a competing and often offsetting Fig. 1 : Four different Ti alloys around TÏ-6A1-4V whose compositional effect of compositional and and microstructura l parameter s offset the effects, and result in a nearly identifical property.

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microstructura l parameters on the mechanical properties. These four samples have been selected from the database to illustrate the challenges faced in determining the influence of composition and/or microstructur e on the properties of Ti-bsed alloys. The average property reflects on property in a wide range of properties for the alloy Ti-6A1-4V. The range for this dataset was, as expected, rather large (i.e., -683 MPa to 955 MPa). Clearly, it is necessary to use additional tools to isolate the effects. These models include both variations in both composition and descriptors of the microstructura l features. The optimum models result in predictions of both the training and testing datasets that are within ± 2.5%. In addition to this figure, which is a qualitative analysis of the models, it is possible to determine the figures of merit for the accuracy of the model. Such figures of merit include the comparison of the average and maximum deviations between the experimentally measured and predicted properties using the both the training and testing datasets (ÔAvg and ômax), the average and maximum uncertainty (i.e., error) predicted by the Bayesian model (Eavg. and Emax), and the number of cases where the experimentally measured and predicted properties are statistically equivalent, given the predicted uncertainty of the datapoint. The deviations (ô) and errors (E) are normalized with respect to the experimental and predicted values, respectively, and expressed as a percentage. These are (for yield strength): 8aVg = 0.72%, ômax = 2.14%, Eavg = 0.48%, Emax= 0.95%. Based upon previous experience, these numbers represent a model that is well developed and provides accurate predictions of the properties.

Fig. 2: The effect of different microstructura l variables on ayS;0.2%m Ti-6A1-4V a+ß processed material (model includes a basketweave factor).

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a+ßprocessed Ti-6Al-4V Tensile Model-Functional Dependencies The models have been exercised in a virtual fashion in order to discover the functional dependencies of the yield strength on a given input parameter . The dependencies of the yield strength on the 4 microstructura l (equiaxed-a size, Fvequiaxed-alpha, Fvtota,"alpha, and a-lath width) and compositional (Al, V, Fe, O) parameter s are shown in figures 2 and 3 respectively. Prior work on optimization of these model also lead the authors to discover the importance of and consequently include as an input the basketweave microstructur e that occurs in the transformed ßBased upon these results (seefigs.2(a-d)), it is clear that the microstructura l feature that has the greatest impact on the mechanical properties is the volume fraction equiaxed alpha, while both the size of the equiaxed alpha and the thickness of the a-laths has a slight effect. It is interesting to note that the influence of the a-laths appears has to have less of an influence in these a+ß processed structures (~40MPa/um) than in previously analyzed ß-processed datasets (~100MPa/um). This is likely due to the fact that the equiaxed alpha particles have an average slip length that is much larger than that in the equiaxed alpha particles. It is expected that these particles will accommodate a large fraction of the deformation prior to failure. While these microstructura l features do influence the mechanical properties of the material, the composition has a far greater influence. Most notably, oxygen has the most pronounced effect (-940 MPa/wt%), an observation that is consistent with the legacy qualitative knowledge of the influence of oxygen on titanium alloys. While the influence of aluminum and iron on the yield strength are of the same order of magnitude (-50 and -75 MPa/wt%, respectively), it is worth

Fig. 3: The effect of the four elemental species on the yield strength in Ti-6A1-4V a+ß processed material.

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noting that the Al partitions primarily to the a-phase (90% of the microstructure ) while Fe partitions primarily to the ß-phase (10%of the microstructure) . Vanadium has very little direct effect on the yield strength of Ti-6A1-4V. It is worth noting that these effects do not have an immediate correlation to classical solid solution strengthening models, as neither the modulus nor concentration can be immediately correlated. a+ßprocessed Ti-6Al-4VFracture Toughness Model-Database The three backscattered scanning electron micrographs shown in fig. 4 (a-c) clearly illustrate the difficulty often faced by researchers when attempting to isolate the interdependent , and their combined effect upon tensile properties, effects of alloy composition, microstructure crack-tip opening/stress state, and the resulting property - fracture toughness. These three micrographs correspond to three different samples of the alloy Ti-6A1-4V, with intentional variations in alloy composition and thermomechanica l processing, resulting in notably different microstructura l feature sizes and spatial distributions. However, these three samples have nominally identical toughness properties (KQ ~ 83 MPaVm). Three models have been developed, one that includes only the continuum effect, one that includes only microstructur e and composition, and one that includes both continuum inputs as well as microstructur e and composition. Based upon these three models, it was clear that the poorest model (8 max = 19.5%and ôavg = 3.5%) relies upon only the continuum variables. The models excluding continuum inputs are better (8 max = 7.9% and ôavg = 1.8%), and the models e and composition are the best (8 max = 5.6% including both continuum inputs and microstructur and ôavg = 1.1%). These results help to illustrate the not only the importance of considering both continuum and micromechanistic input variables but also the risk associated with the traditional approach when developing tools to predict toughness that are based solely upon the yield strength of a material. A complication associated with the prediction of toughness arises due to the fact that there are both a continuum effect (e.g., yield strength) that is itself affected by the composition and microstructur e and a micromechanistic effect. Therefore, it is challenging to determine which features affect the fracture toughness singularly through influencing the continuum parameters, and which features also effect the micromechanisms of fracture.

Fig. 4: Three backscattered electron micrographs which exhibit nominally the same KQ (-83.5 MPaVm) (a) Ti4.76Al-4.27V-0.39Fe-0.07O; ays,0.2% = 725 MPa (b) Ti-5.64Al-3.83V-0.25Fe-0.14O; ays,0.2%= 832 MPa (c) Ti6.51Al-4.29V-0.11Fe-0.08O; ays'0.2%= 790 MPa.

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Therefore, the functional dependencies of toughness on the microstructura l features were determined excluding (figs. 5(a-c)) and including (figs. 6(a-c)) continuum effects. Using this strategy, one may interpret that the volume fraction equiaxed alpha and a-lath thickness do not directly effect the micromechanisms of fracture, as these two microstructura l parameter s have effects on toughness excluding yield strength but do not have an effect on toughness including yield strength. However, it is clear that the size of the equiaxed alpha particles does continue to influence the fracture toughness through micromechanistic details. In-depth microstructura l characterizatio n of the regions near the fracture surface have corroborate d these results. A series of voids and microcracks have been observed within the plastic zone. These microcracks are largely associated with boundaries that occur within equiaxed alpha particle clusters (see figs. 7(a-b)). Interestingly, the microcracks are most often associated with a special type of basal twist boundary, where the basal planes of adjacent grains are parallel, and the twist between grains about the c-axis are between 15 and 30°. Importantly , the trace of the boundary must also lie within a few degrees of the basal plane. Of the microcracks observed and analyzed, -70% of microcracks occur on this special type of boundary. Interestingly, this boundary only occupies -2% of all boundaries between adjacent equiaxed alpha particles within particle clusters. TEM analysis of these particles show highly deformed particles with significant dislocation activity localized the basal planes, with some pyramidal slip and some cross-slip. The active dislocations are both c+a and a-type dislocations. The model and experimental data can be linked and explained in the following fashion. Consider that Griffith's original postulation for energy balances during fracture included a work

Fig. 5: The influence of the microstructura l variables (a) Fv equiaxed alpha (b) equiaxed alpha size, and (c) a-lath thickness on fracturetoughness excluding the influence of yield strength

Fig. 6: (a-c): The influence of the microstructura l variables (a) Fv equiaxed alpha (b) equiaxed alpha size, and (c) alath thickness on fracturetoughness including yield strength.

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term associated with the creation of surfaces of a particular energy, ys. In order for a crack to grow, the energy for the entire system, including the balance of work required to create the new surfaces and the work released by the destruction of the existing surfaces, must decrease. Therefore, it is likely that this formation of new surfaces which can often be easily accomplished at the interfaces which already have an associated interfacial energy component. When the interfaces present in the material, the equiaxed alpha particle interfaces can exhibit a range of values (depending upon the misorientation between adjacent particles), including some that can be high. Conversely, the energy associated with interfaces between the ct-laths in the transformed ß is low, and the energy associated with the colony boundaries higher, but likely less than the energy associated with some boundaries within the equiaxed alpha particle clusters. Effectively, this boundary represents a region of ABC stacking which is rarely (if ever) observed in titanium. It has bee postulated that this is a very high energy stacking fault - or grain boundary. The high strains present within both grains, as well as the material constraint, results in these very high energy interfaces 'popping', adding new cracks (and stress concentrators ) ahead of the crack tip. Interestingly, when considering the influence of the size of the equiaxed alpha particles, as the particle size decreases (for a fixed volume fractionequiaxed alpha), the effective surface area goes up, corresponding to the observed functional dependency. Conclusions Neural networks based upon Bayesian statistics has been used to predict both the tensile and toughness properties of a+ß-processed Ti-6A1-4V. The accuracy of these models is <3% for the tensile properties and <6% for the fracturetoughness. Virtual experiments have been conducted to assess the role of composition and microstructur e on the properties. Based upon these experiments, it has been observed that the composition of the alloy has the dominant affect on the yield strength, while the microstructur e has less of an effect. Specifically, O has the greatest effect, followed by Al and Fe, with V having very little direct effect on the tensile properties. This points to solid-solution strengthening as the dominant strengthening mechanism, although the classical models do not seem to fit the data. For fracturetoughness, the two

Fig. 7: Electron backscattered diffraction (EBSD) micrograph showing cracks within particle clusters using (a) OIM (alpha inverse pole figure coloring with an image quality map overlaid) and (b) Image Quality micrograph

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dominant influences are the tensile strength and the size of the equiaxed alpha particles. While the tensile properties of the material are an important continuum parameter, there is only one microstructura l feature that affects both the continuum and micromechanistic details of fracture. Evidence points to a critical feature that has not been previously identified - very high energy interface between adjacent equiaxed alpha particles (within a cluster) where the c-axis is common, the basal planes are parallel to the interface, and with a twist about the c-axis - as the key microstructura l feature governing the fracturetoughness of these microstructures . References 1. J.C. Williams, M.J. Blackburn: Transactions Quarterly, 1967. vol. 60(3): pp. 373-383. 2. J.C. Williams and E.A. Starke: The Role of Thermomechanical Processing in Tailoring the Properties of Aluminum and Titanium Alloys, in ASM. Metals/ Materials Technology Series, 1982. 3. E.W. Collings: The Physical Metallurgy of Titanium Alloys. ASM Series in Metal Processing, H.L. Gegel, ed., Metals Park, OH, American Society for Metals, 1984. 4. G. Lütjering: Proceedings, 9th World Titanium Conference, China, 1998, pp. 1-19. 5. R.Boyer, G. Welsch, E.W. Collings: Materials Properties Handbook: Titanium Alloys, ASM International , Materials Park, OH, 1994. 6. P. A. Blenkinshop, W.J. Evans, H. M. Flower, eds.: Titanium '95: Science and Technology, Proceedings of the 8th World Conference on Titanium, The Institute of Materials, London, UK, 1996. 7. G. Lütjering: Materials Science & Engineering A, vol. 243, 1998, pp. 32-45. 8. G. Lütjering: Materials Science and Engineering A, 1999, vol. 263, pp. 117-126. 9. G. Lütjering, J. Albrecht, and O.M. Ivasishin. Titanium '95: Science and Technology, Proc. of the 8th World Conf on Titanium. The Institute of Materials, London, UK, 1996. 10. O.M. Ivasishin, P.E. Markovsky: JOM, July 1996, pp. 48-52. 11.R.R. Boyer, D.R. Wallem: Microstructure/ Property Relationships of Titanium alloys, 1994, pp. 125-132. 12. CG. Rhodes, J.C. Chesnutt and J.A. Wert: Microstructure, Fracture Toughness and Fatigue Crack Growth Rate in Titanium Alloys, A.K. Chakrabart i and J.C. Chesnutt, eds., TMS, Warrendale, PA, 1987, pp. 39-54. 13. D.J.C. MacKay: PhD Thesis, 1992, California Inst. Of Tech., Pasadena, CA. 14. http://www.inference.phy.cam.ac.uk/mackay / 15. R.J. Grylls: Materials Science and Engineering A, vol. 234, 1997, pp 267-270.S. 16. D.J.C. Mackay: Neural Computation, vol. 4(3), 1992, pp 448-472. 17. Kar, T. Searles, E. Lee, G.B. Viswanathan, J. Tiley, R. Banerjee, and H.L. Fraser: Metallurgical and Materials Transactions A, vol. 37A (3), 2006, pp 559-566. 18. Tiley, J.S., Modeling of microstructure property relationships in Ti-6Al-4V, in Dept. of Materials Science and Engineering. 2002, The Ohio State University: Columbus, OH. 19. Welk, B, Searles, T, Collins, P, Tiley, J, Russ, JC, and Fraser, HL, "Quantificatio n of microstructura l features in a+ß processed a/ß titanium alloys", Materials Science and Engineering A, 508, pp 174-182, 2009. 20. J. Russ, R. Dehoff, Practical Stereology, Kluwar Academic Publishers/Plenum Publishers, Dordrecht/New York, 2000. 21. HJG Gundersen, EB Jenson, R Osterby, "Distribution of membrane thickness determined by lineal analysis", J Microscopy, 1978, 113:27.

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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

CHARACTERIZING RESIDUAL STRESSES IN MONOLITHIC SILICON-CARBIDE THROUGH THE USE OF FINITE ELEMENT ANALYSIS

Brian Munn and Keyu Li Oakland University; Department of Mechanical Engineering; Rochester, Michigan, 48309, USA Keywords: Silicon-Carbide, Residual Stresses, Finite Element Analysis, Temperatur e Gradients Abstract Recent studies have documented the existence of residual stresses in numerous types of ceramic components. Residual stresses can be created by secondary machining operations which are becoming more prevalent in ceramics today or through the firing/sinteringcycle used to produce most net-shaped ceramic components. Monolithic silicon-carbide (SiC) in the form of tiles and plates had recently been documented as having positive (tensile) residual stresses. SiC is brittle by nature and any positive (tensile) residual stresses could be detrimental to component performance in service. In this investigation, a finite element program (FEA), Abacus was used to create a detailed model of the tile configuration having positive residual stresses. Subsequent simulations focused on the cooling stage of the firing/sinteringcycle. The cooling stage is the final phase in the sintering cycle that takes the component from a holding temperatur e to room temperature . The finite element results revealed varying temperatur e fields that were dependent upon the tile thickness. These temperatur e fields gave rise to thermal strains and ultimately surface residual stresses. The severity of the cooling rate was used to calculate the type (tensile) and magnitude of the surface residual stresses. Introduction Until recently, residual stresses were not considered significant in components made from monolithic ceramic materials. This conclusion was based on two simple assumptions: 1. The lack of secondary manufacturin g processes for ceramic components such as shot peening and grinding. 2. Most ceramics have a very high elastic modulus rendering any residual stresses relatively insignificant. However, recent studies have shown that residual stresses can be induced through mechanical means such as grinding and lapping. These machined induced residual stresses were found to be tensile in nature with magnitudes large enough to impact component performance in service [1]. Another means of inducing residual stresses in engineered ceramics is through the development of thermal strains. Thermal strains arise as a result of thermal expansion anisotropy and crystallographic misorientation across the grain boundaries during the cooling stage of the sintering operation [2]. There are several analytical techniques for measuring residual stresses in engineered components. For metals, there is an extensive amount of published data on each analytical technique. Unfortunately, for ceramic structural components the published data are limited. Pfeiffer and Hollstein [3, 4] were the first to publish residual stress data on surfaced machined

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silicon-nitride (Si3N4) using X-ray diffraction (XRD). Their results showed that the hard contact created by grinding and lapping created positive residual stresses at the surface of Si3N4 components. Pfeiffer followed up his initial findings by applying XRD to measure surface residual stresses in a Si3N4 substrate that had been subjected to a shot peening process [5]. There is a lack of published research on the characterizatio n of residual stresses in monolithic silicon-carbide (SiC). Munn (et al.) [6] were the first to publish findings on residual stresses found in SiC tiles of varying thicknesses. Through a strain gage-hole drilling method the type and magnitude of surface residual stresses were determined in four separate tile configurations. This paper extends the initial work done by Munn (et al.) by taking a more detailed look at how the residual stresses were created in the monolithic SiC tiles. In particular, simulating the cooling stage of the sintering process to determine how residual stresses were created in tiles where no secondary machining operations had been performed. Sintering Cycle Due to the proprietar y nature of this work, very little information was provided on how the tiles were manufactured . However, the tiles provided were produced through a pressureless sintering process. In other words, no pressure was applied at any time during the sintering cycle. Only temperatur e was used to fuse the green specimen into the final tile configuration. In high temperatur e diffusion bonding processes, residual stresses can be created during the cooling down of the material from its holding temperatur e to room temperature . Upon cooling, thermal mismatches are created that induce thermal strains into the material. Most materials have thermal expansion characteristics that are temperatur e dependent. Thermal expansion is how a solid expands when heated and contracts when cooled. The thermal expansion coefficient, a is used to describe this dependency. The other key material parameter that depends upon temperatur e is the thermal conductivity of material. Thermal conductivity is the ability of the material to either absorb or dissipate thermal energy. In most materials, heat conductivity varies with temperature . For SiC, thermal conductivity performance with respect to temperatur e is shown in Table 1. Table 1 : Thermal Conductivity Values Description

Conductivity (W/m K) *

RM

RM-200

125.6

200

200-400

102.6

400

>400

77.5

A typical sintering cycle consists of three different temperatur e zones [7]. In the first zone, the green specimen (compacted powders) is heated to a desired steady state or holding temperature . The heating rate is typically in the range of 8 °C/min from room temperatur e up to around 1500 °C. From this temperatur e up to the desired holding temperature , the heating rate can be increased to 2x or 3x the original heating rate. In the second temperatur e zone the green specimen is held at a constant temperatur e for an extended period of time. For SiC the holding

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temperatur e is usually in the range of 1800 °C to 2200 °C. In the third temperatur e zone, the specimen is cooled from the holding temperatur e to room temperature . Cooling is accomplished by circulating Argon gas through the furnace. The cooling rate is controlled by the circulation rate of the Argon gas. The cooling rate can range from 1°C/min up to approximately 15 °C/min. A typical time vs temperatur e cycle for the sintering of SiC specimens is shown in Figure 1. Of particular interest, was how the SiC tiles cooled from the holding temperatur e to room temperature .

Figure 1 : Typical sintering cycle for SiC Finite Element Analysis Throughout this analysis, the SiC is assumed to be a single-phase homogeneous material. The single-phase was also considered to be elastic with any stress redistribution due to high temperatur e creep considered negligible. Another simplification was to assume a homogenous or steady-state was attained during the time spent at the holding temperature . Cooling was assumed to be slow enough that the temperatur e remained uniform around the body at all times. As can be seen in Figure 1, the two (2) key cooling parameters are time and temperature . Since this was a pressureless sintering process, pressure was not an input requirement into to the software program for analysis. This simplified both the boundary and input requirements into the FEA model. The software package used to perform the FEA analysis was a commercial code Abacus. All FEA analysis was conducted on a PC computer with a 1.7 GHz processor, and 2 GB of RAM. For this study two (2) different square tile configurations were modeled for analysis in Abacus. The only geometric difference between the two (2) models was the through thickness. The through thickness was also assumed to be uniform in both model configurations. All other physical dimensions remained the same. A standard C3D8R (8-node linear brick, reduced integration, hourglass control) mesh was applied to each of the tile models. A uniform transfer of heat from all free surfaces was employed with each tile having isotropic thermal characteristics. The material property and process parameter inputs used to produce the results discussed in the next section are summarized in Tables 2.

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Table 2: Material properties and process parameters for thermal analysis Young's modulus, E (GPa) 1 Poisson ratio, õ I Thermal Expansion/Contractio n Coefficient, a (xlQ-6mm/mmK) Thermal Conductivity, k (W/mK) Density, p (kg/m3) Mean Specific Heat, Cp (J/kgK) Holding Temperatur e (°C) End Temperatur e (°C) 1 Constant Cooling Rate (°C /min.)

410 0.14 ±4.02 See Table 1 3100 670 2050 1 Room Temp. 1 15 ~|

FEA Results and Discussion To study the thermal-mechanica l behavior of the tiles a temperatur e field was first generated from the parameters shown in Table 2. The temperatur e field gives rise to the thermal stresses of interest. The temperatur e field of a thick and thin tile at thirty (30) minutes into its cooling phase from aholding temperatur e of 2050 °C to room temperatur e is shown in Figure 2. As can be seen in Figure 2, the edges cool quickest (blue) while the core remains at the highest temperatur e (red) for the longest period of time in both plate configurations.

Figure 2: Temperatur e field in thick and thin plates A furnace was programed to maintain a constant rate of heating and cooling as described in Figure 1. When a furnace is heated or cooled at a constant rate, the effective value of the heat transfer coefficient, h changes with temperature . In the case of cooling with a constant surface temperatur e change, both temperatur e gradients and stress become dependent on the cooling characteristics of the tile.

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In this study, a single element on the surface of each tile was chosen for thermal analysis to determine the cooling characteristics of each tile configuration under a constant rate of cooling. This element was chosen since this is the location where actual residual stresses have been measured. From the temperatur e fields shown in Figure 2, a cooling curve for each tile was determined and, then plotted from aholding temperatur e of 2050 °C to room temperatur e as shown in Figure 3.

Figure 3: Cooling curves for both a thick and thin tile The cooling rate, § calculated from each curve is listed in Table 3. The cooling rates were determined by finding the slope of each curve as constructed in Figure 3. As can be seen in Table 3, there is a significant difference in cooling characteristics with the thick tile cooling at a rate, approximately 18% slower, than the thin tile. Table 3: Tile cooling rates Cooling rate (cj>)

Ar At

73

89

For a constant rate of heating or cooling, the stress at the surface can be calculated by applying the following thermo-elastic relationship [8, 9]; _ Ea 4>r2 °surf —

(1)

where the thermal diffusivity, D = k/pCp, having units of m /sec. In the case of a plate or tile cooling (Tsurf < Tint), the interior will constrain the surface from contracting setting up a tensile stress at the surface. From Equation 1, the surface stresses were calculated and are given in Table 4. The calculated residual stresses are also compared to some actual, experimental measurements taken by Munn et al. for tiles of similar thickness.

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Table 4: Calculated versus experimental surface residual stresses Experimental Calculated Surface Residual Stresses Residual Stress (MPa) (MPa) 132 Thick 140 149 Thin 161

Percent (%) Difference 6% 8%

Conclusions A finite element analysis was performed to help determine the cause of tensile residual stresses experimentally measured at the surface of a thick and thin SiC tile. The finite element analysis was used to simulate the cooling stage of the sintering process. The FEA simulation helped define a difference in the cooling characteristics between a thick and thin tile at a constant rate of cooling. The cooling rates were then used in a general thermo-elastic equation to estimate the surface residual stresses in each tile. There was good correlation between calculated stresses and actual measured experimental results. Correlation results show the thick plate with only a 6% difference and the thin plate having an 8% difference respectively. References 1. Jahanmir, S., Ramulu, M, Koshy, P., 1999, Machining of ceramics and composites, CRC Publishing, 704 p. 2. Pan M, Green, D. J., and Hellmann, J., R., 1997, "Influence of Crystal Anisotropy on Residual Stresses in Ceramic Composites", Scripta Mateaialia, Vol. 36, No. 10, 1095-1 100 p. 3. Pfeiffer, W., Hollstein, T., 1996, "Characterizatio n and Assessment of Machined Ceramic Surfaces", T International Conference on Machining Advanced Materials (MAM), VDI-Verlag, Düsseldorf, Germany, VDI Bulletin #1276, 587-602 p. 4. Pfeiffer, W., Hollstein, T., and Sommer, E., 1995, "Strength Properties of Surface-Machined Components of Structural Ceramics", Fracture Mechanics, Vol. 25, 19-30 p. 5. Pfeiffer, W. and Rombach, M., 1997, "Residual Stresses and Damage in Ceramics due to Contact Loading", Proceedings of the ICRS5, Linkopping, Sweden. 6. Munn, B. S., Li, K., Zheng, J. and Masters, K., "Characterizatio n of Residual Stresses in SIC Based Ceramic Plates", 35th International Conference and Exposition on Advanced Ceramics and Composites, January 23-28, 2011, Daytona Beach, Florida, USA. 7. Sanjay, A., and Venkateswara R., 2008, "Experimenta l Investigation of Surface/Subsurfac e Damage Formation and Material Removal Mechanisms in SiC Grinding", International Journal of Machine Tools & Manufacture, Vol. 48, 698-710 p. 8. www://sgrgroup.materials.ox.ac.uk/lecture/ceramics_handout_3.pd f 9. Kingery, W. D., "Factors Affecting Thermal Stress Resistance of Ceramic Materials", Ceramics Division, Department of Metallurgy, MIT, Cambridge, MA.

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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

DENSITY FUNCTIONAL THEORY BASED CALCULATIONS OF SITE OCCUPANCY IN THE GAMMA PRIME Ni3Al PHASE OF NICKEL BASED SUPER ALLOYS 1 Mrunalkuma r Chaudhari , Jincheng Du1*, Jaimie Tiley2, and Rajarshi Banerjee1 1

Department of Materials Science and Engineering, University of North Texas, Denton, TX 2 Air Force Research Laboratory , Wright Patterson Air Force Base, OH

Abstract Nickel based super alloys are used in turbine engines for aerospace and land based applications. These alloys have unique combinations of high temperatur e tensile strength, creep and oxidation resistance. The precipitation of Ll2 structured Ni3Al gamma prime phase in the gamma matrix is one of the major strengthening mechanism of these alloys. Various studies have shown that the high temperatur e creep and oxidation resistance of the nickel based alloys can be improved by the addition of substitutional elements. The distribution of these elements in the gamma and gamma prime phases and their site occupancy behavior in gamma prime precipitate (Ni3Al) are especially important to the high temperatur e properties. In this paper, we investigated site occupancy of a common substitutional element, chromium in the y'-Ni3Al using periodic Density Functional Theory (DFT) based first principles calculations. Comparisons are made between the site occupancy behavior using formalism namely vacancy based, anti-site based and standard defect formation based formalism. The impact of the simulation size (2x2x2 and 3x3x3) has also been studied in order to gain more understandin g of the simulation size effect on the occupancy behavior. In addition, this paper also investigated the interaction energy between two substituted atoms as a function of separation distance has also been studied. Various comparisons are made between our results, existing theoretical and experimental studies in the literature. Introduction Ni based superalloys are used in disk applications for hot sections of jet engine and industrial gas turbines used in the aerospace and power industries. The efficiency of these engines can be improved by increasing the Turbine Inlet Temperatur e (TIT), which directly depends on the working temperatur e and high temperatur e mechanical properties of the Ni base superalloys. Precipitation strengthened nickel-base superalloys consists of the gamma (y) matrix with the intermetallic y' precipitates. The y-phase is a solid solution with a face-centered crystal lattice and randomly distributed different species of atoms. Ni3(Al,Ti), also called gamma prime (y'), acts as the primary strengthening phase with an ordered Lh crystal structure. The y'-NißAl compound has also a significant technological importance due to the positive temperature e oxidation resistance which dependence of its yield strength as well as its good high temperatur makes Ni base superalloys ideal for high temperatur e applications.

* Correspondin g author. Email: i incheng. [email protected], phone: 940-369-8184

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Similar to the case of pure metals, the mechanical properties of pure compounds must be improved by substitutional alloying which affects the physical properties at the atomic level [1]. Ab initio calculations can provide us with the understandin g of the site substituting behavior of any foreign element on the atomic scale. Alloying elements can make a significant impact on solid solution strengthening, oxidation resistance and promoting precipitation of the y1 phase [2]. The misfit between the matrix and y1 impacts the mechanical properties of the alloys, and specific elements are often added to modify the resulting strains and affect the physical properties at the atomic level [1,2]. In fact, various studies using both experimental and computational methods have investigated to understand the partitioning of transition metal elements (such as Cr, Co, W, Ta) between y and y\ Several researchers have concluded that Cr occupies the Al sublattice in y'-NisAl by using atom-probe tomography (APT) [3], scanning electron microscopy (SEM) [3], atom location by channeling enhanced microanalysis (ALCHEMI) technique [4]. Site preference of y partitioning atoms like Co has been studied by atom probe field ion microscopy (APFIM) by several researchers [5,6]. Site preference for different elements in Ni3Al has been calculated by a variety of computational techniques including ab initio based [3,7], first principles method [8,9], EAM potential based [10,11] and cluster variation methods [18]. Majority of literature focuses on standard defect formation formalism [3] and anti-site based substitution formalism [7] to study of site substitution behavior of different elements on y'N13AI. In this paper, we present our results based on a methodical comparison between the site preference behavior using the aforementioned formalisms and a vacancy based formalism for Cr in Ni3Al. This element was chosen because of its reported concentration build-up at the interface of y' and its suspected impact on y' growth mechanisms [19]. In addition, investigation is done to evaluate the effect of two Cr atoms in the Ni-Ni, Al-Al and Ni-Al sublattice as a function of separation distance. Simulation details The Vienna ab initio Simulation Package (VASP) [12,13] was used to carry out the DFT based calculations. In the electronic structure calculations, a plane wave basis set with a kinetic energy cutoff of 400 eV with Projected Augmented Wave (PAW) pseudopotentials were used in the simulations. The generalized gradient approximation (GGA) with the PBE [14] form was used for the exchange and correlation functions and all the calculations performed were spin polarized. The initial structures were fully relaxed until the forces acting on each of the atoms were less than 0.01 eV/Â. The microcanonical ensemble (NVE) was utilized for the direct dynamics simulations. In the microcanonical, or NVE ensemble, the system is isolated from changes in moles (N), volume (V) and energy (E) which corresponds to an adiabatic process with no heat exchange. A microcanonical molecular dynamics trajectory may be seen as an exchange of potential and kinetic energy, with total energy being conserved. We have adopted three sizes of y' supercells from 4 atoms l x l x l supercell, 32 atoms 2x2x2 supercell and 108 atoms 3x3x3 supercell. The lattice parameter was calculated to be 3.567Â which is in good agreement with previous reports [3]. Because these calculations were computationally time intensive and expensive, a new approach was adopted that used multiple files to relax the structure efficiently. Instead of using specific input parameters and k-points to relax the structure, we relax the structure through four different sets of configurations involving

152

different parameters and different k-points from lower k-points and basic parameters to higher kpoints and stringent parameters in order to relax the structure in the most effective manner. Computationally, the calculations require less computational resources as compared to direct relaxation and hence, reducing the computational cost of the calculations. The new approach lowered the computational cost of the calculations by reducing the number of average computational runs in half. In order to get consistent results with the varying supercell size, kpoints were optimized to allow comparison with published results. The energy values without entropy are plotted in Figure 1 against k-points for different supercell. The data shows the optimum k-points for each of the supercells, which were used in the later calculations. Figure 1. Optimizing k-points for different size of supercells: 15x15x15 for l x l x l unit cell, 9x9x9 for 2x2x2 supercell and 4x4x4 for 3x3x3 supercell.

Results 1) Intrinsic defects Point defects accommodate any off-stoichiometry and mediate atomic diffusion in intermetallic compounds [11]. At T = 0 K, the point defect structure is solely governed by enthalpy and the point defects at this temperatur e are known as the intrinsic defects. The standard defect formation formalism [3] is used to calculate the formation energy of intrinsic defects in NisAl. Defects in the nickel and aluminum sites like vacancies i.e., VaNi and VaAi, and anti-sites i.e., NÏAI and AINI are included. Thermal defect complexes such as exchangetype (0 -> 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.

153

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.

154

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

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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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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

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

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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.

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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

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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.

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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><20nm cube filled with 690,000 atoms. Average grain size is lOnm and all the orientations of grains are random with no texture. In order to eliminate high internal stress and energy of sample, initial nonequilibrium sample was relaxed thermally to a minimum energy state with nearly no internal stress. LAMMPS was chosen as the simulation tool. The interaction between copper atoms was described by Mishin's embedded atom potential [16] which gives a SFE of 45mJ/m2. Periodic boundary condition is applied and the time step is set to lfs during whole simulation. Before applying multi-strain deformation, compression tests were carried out along x, y and z directions respectively. From these compression tests, the highest Von Mises stress all occurred at a strain of 8=4.3% which may be considered as the elastic limit of our sample. Then the sample was compressed for 50ps along x, y and z directions respectively and for each direction 3 different compression strains (e =2.5%; 8 =4.285%; 8 =5.0%) were simulated. Finally a shearing deformation of 8 =30% was applied to the compressed sample along a direction orthogonal to the compression direction for another 50ps. All deformations in our simulation were conducted under NVE instead of NVT ensembles and temperatur e increment was observed in our simulation. The microstructur e of NC copper was analyzed by the common neighbor analysis method [17], which can distinguish fee, hep and bec structures. Two adjacent

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hep planes in a fee crystal represent a partial dislocation while one single hep plane represent a twin boundary. Results and Discussion Fig. 1(a) describes the atomic structure of a cross-section of the deformed sample at z=T5nm. The sample was compressed within the elastic region with a strain of sy= 2.5% and then sheared for 20ps along xz direction up to e^ = 12%. This figure shows only partial dislocations but no DT in the interior of grain. A detail review in the whole process on atomic structures of samples which were respectively elastic compressed along different directions and then sheared along orthogonal directions at the same strain rate confirmed that no DT was nucleated under the multi-strain deformation. Partial dislocations were emitted from and annihilated at grain boundaries (GB), and GB sliding was the dominant deformation mechanism here, similar to the observations in simple tension simulation reported in previous literatures. Fig. 1(b) shows a part of the crosssection of a deformed sample at z=15nm, which was compressed to plastic region with a strain of ey = 5.0% along y-direction and then sheared for 3 Ops along xz direction up to Sxz = 15%. This figure indicates that a twin lamella was formed as marked in sample. Detail examinations revealed that only 3 twin lamellas were developed in 2 different grains in the whole process. In this case, the sample deformed through partial dislocation, GB sliding and DT generation. However, DT was not observed in sample which was compressed along x or z direction followed by shear. This indicates that DT isn't the primary deformation mechanism when NC copper experienced a plastic compression plus an orthogonal shear. Fig. 1(c) illustrates that abundant DTs were nucleated in a sample which was compressed to the elastic limit with a strain of ex= 4.285% and then sheared along yz direction. Dense DTs were found in most grains. The same phenomena were also found in samples with multi-strain deformation in different orientations up to the elastic limit plus an orthogonal shear. The higher quantity of DTs than that of partials suggests that DT was the primary deformation mechanism. Since the samples were not prepared with a texture and crystallograph y orientations of each grain were random, DT nucleation in Fig. 1(c) should not depend on crystallograph y orientation according to Schmid factor of different grains. For comparison, pure compression or pure shears along different directions were also simulated on the same sample and no DT was observed in each simulation as predicted by GPFE model. For Fig. 1(c), multi-strain deformation is the only reason which can account for DT nucleation. As a summary, appropriat e multistrain deformation was able to alter microstructur e deformation mechanisms and to generate DTs in NC copper.

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FIG. 1. Cross section views of atomic structure after multi-strain deformation, yellow ball represent HCP atom and red ball represent FCC atom: a. shearing after elastic compression; b. shearing after plastic compression; c. shearing after a pre-compression up to the elastic limit. Our simulation results agree well with HRTEM images of SMAT treated copper surface which shows that DT were formed in the nano crystalline surface layer. The multi-strain model introduced here is similar with the strain fields of SMAT treated copper surface according to X C Zhang's FEM simulations (unpublished result). During SMAT, a surface element may experience both compression strain and shear strain, often not at the same time. There is an argument about ensemble used in our MD simulation. Thermal equilibrium is always conducted for NVT ensemble, which induces heat exchange with environment and keeps system's temperatur e as a constant. However, for a short time duration in the dynamic process such as SMAT, the strain rate is high (~10000/s), and heat transfer to environment is relatively small. Temperatur e of the samples under SMAT can rise about 100K both in Zhang's FEM simulation and in experiments. Our MD simulation was conducted at OK under NVE ensemble and got a similar temperatur e increase of around 120K. It indicates that for dynamic process, NVE ensemble may be more suitable than NVT ensemble. The comparison among our simulation, FEM simulation and experiments indicates that compression followed by large shear could be the reason for DT generation in the nanocry stall ine surface layer of copper under SMAT. DTs are usually formed in NC fee metal via mechanisms different from those proposed for their coarse grain counterpart . Single twins with two coherent boundaries as marked in Fig. 1(c) are observed frequently in HRTEM images and MD simulations. Several mechanisms have been proposed for the nucleation of twin lamellas, including RAP mechanism [18], the dislocation rebound mechanism [20], self-partial multiplication mechanism [19]. In our simulations, DTs in the form of twin lamella are also formed via partial emissions from GB. Two different partial-mediate d mechanisms were observed in our simulation. Fig. 2 describes microstructur e evolution of a single grain in Fig. 1(b) and depicts a mechanism via 3 partial slips. The 3-slip mechanism was only observed in the deformed sample under shearing after compression into plastic region but not under shearing after compression to the elastic limit. For the latter case, DTs were nucleated by the glide of 2 partials with the same Burgers vector away from the same GB on two adjacent (111) planes. This mechanism needs only 2 partial slips and was proposed before. Our simulation not only generated DTs in NC copper, but also revealed the interaction between DT and partials. Dislocation-twin boundary (TB) interaction may generate mobile or sessile dislocations either in neighboring domains or at TBs and account for the enhancement of strength of nano twinned materials without significant loss of ductility. Such interaction was also observed in our simulation. Twin lamella as marked in Fig. 2 was found to expand through the interaction with a partial B as observed in experiment [21] and other MD simulation [8] of pre-twinned copper.

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FIG. 2. 3-step mechanism of nucleation of twins via partial emissions Conclusion MD simulations confirmed that appropriat e multi-strain deformation can generate high density of nano twins in nanocrystalline copper. Shearing after a compression to the elastic limit is the best formation condition for DT nucleation. DTs were observed to nucleate through two different mechanisms. One needs two Shockley partial glide on neighboring (111) planes and another needs three slips. The whole process from DT nucleation to DT reaction with Shockley partials was observed in our simulation. This work was supported by a grant from Research Grant Council of Hong Kong (PolyU7/CRF/08) and by the postgraduat e scholarship of the Hong Kong Polytechnic University. Reference 1. Lu K, Lu L and Suresh S, Science, 5925,349-352(2009). 2. Lu L et al., Science, 5914, 607-610(2009). 3. Dao M et al., Ada Materialia, 20, 5421-5432(2006). 4. Shen Y.F et al., Scripta Materialia, 10,989-994(2005). 5. Chen, X. H., Lu L and Lu, K., Scripta Materialia, 4,311-314(2010). 6. Wu, Z. X. and Zhang, Y. W. and Srolovitz, D. J.,Acta Materialia,15,4508-4518(2009). 7. Shabib. I, Miller .R. E., Modelling and Simulation in Materials Science and Engineering, 17, 5- (2009). 8. Li et al., Nature, 7290, 877-880(2010). 9. Hong et al., Scripta Materialia^,289-292(2009). 10. Zhao W S et al., Scripta Materialia, 6,745-749(2005).

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11. Meyers, M. A., Vohringer O. and Lubarda V A., Acta Materialia, 19, 4025-4039(2001). 12. Yamakov V et al., Acta Materialia, 20, 5005-5020(2002). 13. Wang J. and Huang H. C, APPLIED PHYSICS LETTERS, 24, 5983-5985(2004). 13. H. VAN SWYGENHOVEN, P. M. DERLET and A. G. FR0SETH, Nat. Mat, 399(2004). 15. Chen Da, Computational Materials Science, 3, 327-333(1995). 16. Mishin Y et al., Physical Review B, 22, 16(2001). 17. Clarke Andrew S. and J'osson Hannes, Physical Review E, 6, 3975(1993). 18. X. L. Wu et al., Physical Review Letters, 095701(2008). 19. Y. T. Zhu et al., APPLIED PHYSICS LETTERS, 031909(2009). 20. Zhu, Y. T et al., Acta Materialia, 13, 3763-3770(2009). 21. Wang Y. B., Sui M. L. and Ma, E., Philosophical Magazine Letters, 12, 935-942(2007).

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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

NONDESTRUCTIVE EVALUATION MODELING AS AN INTEGRATED COMPONENT OF ICMSE James L. Blackshire1, Ray T. Ko2, and Ming-Yung Chen3 !

Air Force Research Lab (AFRL/RXLP), Wright-Patterso n AFB, Ohio 45433, USA 2 University of Dayton Research Institute, Dayton, Ohio 45469, USA 3 Air Force Research Lab (AFRL/RXBC), Wright-Patterso n AFB, Ohio 45433, USA Keywords: Nondestructive Evaluation, Finite Element Modeling, Ultrasound Abstract The development of advanced material systems has become increasingly complex with regard to performance requirements, tailorable material options, and recent innovations in manufacturin g technologies. A key area of intense research involves the use of integrated computational materials and manufacturin g science and engineering (ICMSE) approaches which can assist in the development, enhancement, and validation of these complex material systems. At its core, ICMSE involves material-centri c models which synergistically integrate computational tools related to materials development, processing, manufacturing , and property/performanc e assessment. In addition to material-centri c models, the use of nondestructive evaluation (NDE) sensing models may provide an additional capability for understandin g and assessing the critical properties of an advanced engineering material system. The use of ultrasonic finite element analysis models, for example, can provide important insight into the elastic properties and internal structure of a virtual material system. In the present effort, ultrasonic nondestructive evaluation models are used to develop inverse methods capable of extracting key material properties related to porosity, microstructur e sizes, and foam infiltration fill-factor. As an integrated component of ICMSE, NDE modeling can be utilized for in-situ process monitoring applications, material prototype evaluations, and usage monitoring applications, where important connections between NDE signals and material properties can be made in a virtual environment. Introduction A recent World Technology Evaluation Center (WTEC) report has suggested that we are at a "tipping point" in computer simulation capabilities for engineering and science, where computer simulations are becoming more pervasive, and are having more of an impact, than at any other time in human history [1]. To a large degree this is being made possible by next generation hardware and algorithms, where the study of very complex multi-scale, multi-physics, and multidiscipline phenomena are beginning to be studied. Combined with a strong theoretical foundation and experimental validation of model predictions, numerical simulations are poised to provide new, unprecedented opportunities for simulation-based discovery and innovation, enabling the development of many critical technologies that cannot be understood, developed, or utilized without simulation efforts. A key technical discipline that is benefiting significantly from advanced computational tools involves material science and engineering. As described by Cummings [1], integrated computational materials science and engineering, or ICMSE, is changing how new materials are being discovered, developed, and applied. Moving away from trial-and-erro r processes, which

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have historically been time consuming and costly, materials engineers are currently embracing ICMSE to enhance and accelerate new material development [2], to better understand material performance and degradation issues [3], and to provide opportunities for linking material processing, properties, performance, and products with modeling at multiple length scales [4]. As pointed out recently by Rosenberger [5], the detailed and quantitative characterizatio n of material properties at multiple lengths scales during the processing, manufacturing , and usage stages of a material system remain a significant challenge for ICMSE. As a result, nondestructive evaluation (NDE) methods are being considered for characterizatio n of material properties with an increasing emphasis on quantifying material properties at multiple length scales, at spatially resolved locations, and while changes are actively occurring in the material system (e.g. phase transformation s occurring during a processing step). With recent advances being made in computational NDE, the possibility of synergistically connecting physics-based NDE sensing models with other ICMSE models is currently a possibility, providing an additional capability for understandin g material properties and material performance in a virtual environment. This paper explores the use of three ultrasonic NDE models for extracting material properties related to microporosity state in a polymer, grain size estimation in a graded microstructur e nickel superalloy, and polymer fill-state in aluminum foams. The models represent NDE interactions with complex microstructur e and multi-material systems, which are of significant interest for ICMSE. Similar to other computational methods, the NDE model results provide an opportunity for studying a wide variety of variables in a virtual environment, which would have been time consuming or impossible to accomplish experimentally. Preliminary model results show promise for quantifying the microporosity states in a polymer using backscatter signals, estimating polymer fill state in aluminum foams using time-of-flight reflected signals, and estimating grain sizes using phase and amplitude signal levels. The remainder of the paper provides a brief overview of elastic wave propagation and scattering in heterogeneous materials, followed by a description of the finite element modeling studies and key results. Ultrasonic Characterization of Material Properties The evaluation of a material using ultrasound relies on some characteristic of a measured signal response, which can be related to its physical/chemical properties. The two parameters most frequently measured in ultrasound NDE are the ultrasonic velocity and attenuation coefficient. In addition, some measurements are related to the acoustic impedance or scattering properties of the material. These parameters are characteristic of each material and can be related to physical properties such as elastic constants, density, composition, and microstructure . Ultrasonic Velocity The ultrasonic velocity in a material is determined primarily by the elasticity and density of the medium. The measurable ultrasonic properties of a material can be related to its properties by: (^] \K)

=19

P

2

c

(fora«(o/c),

=-

(1)

P

where a> 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<xo
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dependence exists in the stochastic regime, and an inversely proportional size dependence exists in the geometric regime [6]. With respect to ultrasonic phase velocity, the three scattering regimes also determine basic signal response characteristics including quasistatic conditions in the Rayleigh regime, a statistical unweighted average response in the stochastic regime, and a weighted average response with directional effects in the geometric regime [6]. In general, Equation 1 can be used in the Rayleigh regime to describe the velocity in a scattering medium. For the stochastic regime, however, random phase theory predicts macroscopic phase delays to occur based on microscopic variations in the degree of inhomogeneity [6], where dispersive phase velocity changes on the order of 1% can be expected. For large scatterers relative to ultrasonic wavelength (geometric regime) significant variations in phase velocity can also occur as ultrasonic wavefronts distort due to reflection and refraction at boundaries (Equation 3). Finite Element Model Studies A series of 2D-finite element models were used to study the behavior of longitudinal wave interactions with simulated coarse/fine grain microstructure s in a nickel superalloy material. The models were developed in the commercially available finite element package PZFlex, which is designed and optimized for elastic wave propagation analysis. The model geometries were based on the microstructur e image in Figure la, which was imported directly into the finite element model. Material properties were assigned to individual grains based on thresholded 8-bit graylevel values (Figure lb). The material properties of nickel were approximated in the model based on a density of 8800 kg/m3, a longitudinal velocity of 5900 m/s, and a shear velocity of 3000 m/s. In order to simulate crystallographic heterogeneity in the models, the values of the Cn and C22 stiffness matrix elements were arbitraril y increased by 10% for each of 4 grain designations: Matl = 3.29ell pa, Mat2 = 3.61ell pa, Mat3 = 3.94ell pa, and Mat4 = 4.27ell pa. The remaining stiffness matrix elements were left unchanged for each grain type. The goal was to approximate in the model heterogeneous grain properties due to varying crystallographic features such as orientation. The dimensions of the model was 1.9 mm x 1.9 mm. Idealized longitudinal waves were initiated along the entire left side of the model geometry, propagating towards the right with absorbing boundary conditions applied to the top, bottom, and right surfaces. Discretization of the domain was set to greater than 20 elements per wavelength, which provided adequate stability and convergence of the model, and an accurate representation of the scattering features. A typical model included 640x640 elements, corresponding to grid resolution of 2.97 microns, permitting accurate representation of microstructur e features in the model. A series of 2D-finite element models (Figure 2) were also developed to study the behavior of longitudinal wave interactions with distributed, lOOum diameter, spherical bubbles in a polymer matrix. The material properties of the polymer were approximated in the model based on a density of 1150 kg/m , a longitudinal velocity of 2700 m/s, and a shear velocity of 1100 m/s, while the air bubbles used a density of 1.24 kg/m3, a longitudinal velocity of 344 m/s, and a shear velocity of 17.4 m/s. The model dimensions were 10 mm x 10 mm, with 1000x1000 grid elements, corresponding to a grid resolution of 10 urn. Wave propagation and absorbing boundary conditions were the same as the Nickel microstructur e studies. A final series of 2D-finite element models (Figure 3 and 4) were developed to study the infiltration of a polymer into an aluminum-air foam material. The model parameters were the same as those used in the polymer bubble models. The material properties of the aluminum foam were approximated in the model based on a density of 2700 kg/m3, a longitudinal velocity of 6419 m/s, and a shear velocity of 3039 m/s. A realistic foam image was imported into the model.

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Results and Discussion The results of the nickel graded microstructur e modeling study are depicted in Figure 1, where distinct phase and amplitude fluctuations can be observed in the upper portion of the ultrasonic wave due to interactions and scattering effects with the coarse grain features (stochastic regime).

Figure 1. Modeling results for coarse/fine grain nickel superalloy material. The results of the polymer bubble modeling study are depicted in Figure 2, where backscatter signals were collected in a pulse-echo simulated measurement process. The scattering effects from increasing bubble densities are present in both of the plots showing a systematic increase from 1 to 100 bubbles.

Figure 2. Polymer bubble study: a) model output, b) backscatter signals, and c) peak amplitudes.

Figure 3. Ultrasonic pulse-echo model for studying polymer infusion into foam material. m foam infusion modeling study are depicted in Figures 3 The results of the polymer-aluminu and 4, where backscatter signals were collected in a pulse-echo simulated measurement process.

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Although scattering effects from the foam are present, a distinct reflection from the polymer-air interface was present in the measurement providing evidence of its location based on signal amplitude levels and signal arrival times as depicted in the Figure 4 plots. The results are consistent with reflection and attenuation/scatterin g predictions from Equations 2 and 3.

Figure 4. Ultrasonic pulse-echo model results for increasing fill-factor of polymer into aluminum-air foam: a) pulse-echo signals, and b) arrival time and peak amplitude trends. Conclusions Three ultrasonic NDE models were developed and used to study material property variations related to microporosity state in a polymer, grain size estimation in a graded microstructur e nickel superalloy, and polymer fill-state in aluminum foams. The models represent NDE interactions with complex microstructur e and multi-material systems, which are of significant interest for ICMSE. In addition to material-centri c ICMSE models, the use of nondestructive evaluation (NDE) sensing models may provide an additional capability for understandin g and assessing the critical properties of an advanced engineering material system. References 1. S.C. Glotzer, S. Kim, P.T. Cummings, A. Deshmukh, M. Head-Gordon, G. Karniadakis, L. Petzold, C. Sagui, and M Shinozuka, "Internationa l Assessment of Research and Development in Simulation-Based Engineering and Science," WTEC Technical Report, 2009. 2. R. LeSar, "Materials informatics: An emerging technology for materials development," Statistical Analysis and Data Mining, 1, 6, 372-374, 2009. 3. J.M. Larsen, M.J. Caton, A.H. Rosenberger, R. John, J.R. Jira, P.J. Golden, S.K. Jha, and D.J. Buchanan, "Understandin g Materials Uncertainty for Prognosis of Advanced Turbine Engine Materials," AFRL-RX-WP-TP-2010-4139, 2010. 4. G. Olson, "Designing a New Material Word," Science, Vol. 288, 993-998, 2000. 5. A. Rosenberger, "Emerging Methods for Matching Simulation and Experimental Scales," in Computational Methods for Microstructure-Propert v Relationships. Springer, NY, 2011. 6. F.E. Stanke and G.S. Kino, J. Acoust. Soc. Am., 75(3), 665-681, 1984.

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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

Numerical simulation of brake discs of CRH3 high-speed trains based on Ansys Liang Yu1, YanLi Jiang1, Senkai Lu2, Kun Luo1, and HongQiang Ru3 !

Key laboratory of new processing technology for nonferrous metals & Materials, Ministry of Education, Guilin University of Technology, Guilin, 541004, China department of Physics and Information Technology, Guilin Normal College, Guilin, 541004, China 3 Key laboratory for anisotropy and texture of materials (MOE), School of materials and metallurgy, Northeastern University, Shenyang, 110004, China

Keywords: Finite Element Method (FEM); CRH3; Disc Brake; temperatur efield;thermal stress Abstract The shaft disc prepared with three-dimension SiC/Fe composite of the CRH3 high speed train with a speed at 380 km/h was chosen as the research object. ANSYS was applied to simulate the course of emergency brake. Based the three dimension model, the way of applying loads were discussed, and the temperatur e field and thermal stressfieldwere obtained. The result shows that the highest temperatur e is 467 °C, which appears at about 75 s after braking. The high temperatur e region exists always in the friction ring. The biggest stress can reach 185 MPa, appearing at 61 s after braking. The stress regions mainly distribute at the surface corresponding with the radiating ribs, and close to the inner diameter side. The hoop stress is larger than other directions. It is found that the kind of structure and material can meet the requirement of the shaft disc of the high speed train with a speed at 380 km/h 1 Introduction The main problem of braking and stopping a high-speed train, such as CRH3 (China Railway High-speed 3) system, is the great input of heat flux into the disc in very short time. Because of high temperatur e gradient the material is exposed to high stress, which will induce a heat shock. In fact, the problem can be solved by applying a non stationary and numerical calculation [1, 2]. In our previous work, the co-continuous metal-ceramic (SiC/Fe2Crl3) composites consist of two interpenetratin g continuous networks; one of Fe-2Crl3 and one of a SiC phase were prepared. They was obtained by infiltration of a molten Fe-2Crl3 alloy (14.00 wt. % Cr/1.00 wt.% Si/ 0.003 wt.% S/ 0.035 wt.% P/1.00 e of SiC/Fe-2Crl3 wt.% Mn/ 0.25wt.% C) into SiC network ceramic by FlS- l Microstructur vacuum-pressur e casting process. The SiC network composite of the disk structures ceramic preforms were prepared by the porous polyurethane coated with large amounts of an aqueous reactant containing finely divided sinterable a-SiC power (purity>99%, (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<#

(1)

The change of energy is equal to the heat flux on the surface of the disc. This ratio is used to calculate the thermal load on the brake disc. Other data used for the analysis are listed in table 1. Tab. 1 Data for calculating the heat flux Mass of the vehicle - M [kg] Start velocity - v0 [m/s] Deceleration- a [m/s2] Braking time - th [s] Effective radius of the braking disc - rd [m] Radius of the wheel - rw [m] Incline of the track - 5 \%o] Friction coefficient disc/pad - n [/] Surface of the braking pad Ac - [mm2] Forces which work on the brake disc [3]: ^

1 w

..2

(2)

= 8963.7 [N]

F** = ' •^•Oo-'z

55000 105 0.77 138 0.254 0.430 11 0.32 20000

•a-t/)

Instant heats flux entering one side of the braking disc [3]: 0 ( 0 = F*sk • vdisk ( 0 = Fdlsk ■ ^- • (v 0 - a ■ t) = 556000 - 40761 [W]

(3)

2.5 Determination of boundary conditions, mesh properties and loads The calculated heat flux is considered for both sides of the disc. Because the stress is also analyzed, the disc needs to be properly fixed. The disc is put together rigid where the disc is screwed onto the hub (Fig. 4). The forming of the volume mesh is automatic. The mesh consists 96178 tetrahedra l elements. To perform the analysis, the material properties from the table 2 are used.

Fig.4 The brake disc section with the load and fixing spot

Tab.2. SiC/Fe-2Crl3 composite, the material of disk properties Heat conductivity - X [W/m-K] 44.8 5500 Density - p [kg/m ] 515 Specific heat - cp [J/kg-K] Module of elasticity - E [MPa] 254000 0.15 Poisson number - v [/] 3 The Analysis of the Results 3.1 Thermal analysis The first results show the case of a flat track and a new disc (the initial temperatur e of the disc and the surrounding is 50 °C). Considering that the disc during braking phases does not cool down to 50 °C, a presumption is made that the new temperatur e of the disc is 150 °C. The temperatur e of the surrounding is still 50 °C. In case of braking on the flat track the highest temperatur e reaches up to 467 °C, for the new disc, and the highest temperatur e region is always in the friction ring, shown in Fig. 5(a). This temperatur e is reached after a time period of 75 s.

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Because the heat flux is decreasing, the temperatur e falls after 103 s down to 267 °C. The cooling ribs and the place where the disc is bolted to the hub are almost unaffected by the changing temperatures .

Fig. 5 Temperatur e fields for the different disc braking on a flat track (a) the new disc; (b) the worn out disc For the worn out disc with the same load, the maximum temperature s of 523 °C, are achieved after 78 s, shown in Fig. 5 (b). They appear on areas where the wreath of the disk and the cooling ribs are not connected. In this case the ribs are more severely exposed to the heat flux because the disc wreaths are thinner. The temperature s are from 50 ~ 60 °C, higher. After a time period of 105 s, the temperatur e of the disc reaches 497 °C. 3.2 Analysis of the stress Thermal stresses in the disc appear because the temperature s rise. Beside the thermal stress, the centrifugal load and the holding force of the brake caliper is also considered. The goal of this analysis is to determine the influence of the centrifugal load in comparison with the thermal load. The comparison stress is given on von Mises. In the case of a flat track and considering the centrifugal load, the regions distribute at the surface corresponding with the radiating ribs, and near the inner diameter. The stresses are 153 MPa, shown in Fig. 6 (a). On spots where the thermal stresses are the highest, the value is 185 MPa, shown in Fig. 6 (b).

Fig.6 Stress field for the different discs braking on a flat track (a) the new disc; (b) the worn out disc For the worn out disc with the same load, the maximum values stress is 202 MPa, which appear on the passage of the holding teeth, shown in Fig. 7. The values on areas where the wreath of the disk and the cooling ribs are not connected are 178 MPa, which are lower than that of the holding teeth. In this case the ribs are more severely exposed to the heat flux because the disc wreaths are thinner, which can lead to the high stress of the disk. For the pad with the same load,

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the maximum values of stress are 289 MPa, which appear near the screw, shown in Fig. 7.

Fig.7 Stress field for the worn out disc braking on a flat track

Fig.8 Stress field for the pad on a flat track

4 Discussions Of The Results Of the cases, the highest temperature s arise from the worn out disc on a flat track. In 78 s the temperature s rise to 523 °C. The actual braking time is shorter and amounts to 125 s. The highest allowed temperatur e of the disc is 600 °C, (long-term). From the results we can see that centrifugal loads contribute 10 -20 MPa of stress, depending on the model of the disc and the load. The highest comparison stress on von Mises is 185 MPa - that value is still smaller than the permitted value of 314 MPa, which considers a safety factor of 1.7 (table 3). Numerical Flat track

Tab.3 The results of numerical analyze analyze T [°C] ather [MPa] New disk 166 153 Worn out disk 202 145

Other cent

185 174

[MPa]

5 Conclusions This paper shows a thermal and stress analysis of a brake disc for railway vehicles using the finite element method (FEM). The performed analysis deals with the case of braking to a standstill. Temperature s and stress in discs under different loads are very high. Although they are fulfilling the buyer's requirements for safety, we did not considered shearing forces, residual stress and the cyclic loads during brake discs lifespan. The results need to be compared with experimental results, which is also our suggestion for future work. 6 Acknowledgment This work was supported by the Natural Science Foundation of Liaoning, China (No. 20072026), the Basic Research Fund for the Northeastern University (N090302005), the China Postdoctoral Science Foundation (No. 20090451271), the National Natural Science Foundation of China (No. 50902018, No. 50872018,) and the Program for Chang Jiang Scholars and Innovative Research Team in University (IRT0713). Province science and technology in the Guangxi offends pass item (1099043). 7 References [1] Mackin, T.J.: Thermal cracking in disc brakes. Engineering Failure Analysis (2002), no. 9, str. PP.63-76. [2] Reibenschuh, M.: Stress analysis of a brake disc under centrifugal and thermal load. Maribor: Faculty of Mechanical Engineering, 2008. [3]Oder,G.; Reibenschuh,M.; Lerher,T.; Sraml,M.; Samec,B.; Potrc,I. Thermal And Stress Analysis Of Brake Discs In Railway Vehicles.Advanced Engineering 3(2009)1,ISSN 18465900.PP.95-102.

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[4]Oder, G.: Determination of non stationary thermal and stress fields in brake discs. Maribor: Faculty of Mechanical Engineering, 2008.

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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

MODELING AND SIMULATON OF PROCESS-STRUCTURE-PROPERTY OF MAGNESIUM ALLOY CASTING Zhiqiang HAN1, Liang HUO1 , Baicheng LIU1'2 1

Key Laboratory for Advanced Materials Processing Technology, Ministry of Education Department of Mechanical Engineering, Tsinghua University, Beijing 100084, China 2 State Key Laboratory of Automotive Safety and Energy, Tsinghua University, Beijing 100084, China

Key words: Microstructure , Mechanical Property, Dendrite Morphology, Numerical Simulation, Magnesium Alloy Abstract The increasing needs from industry for efficient and economic manufacturin g lead to the emergence and rapid development of integrated computational materials engineering (ICME) that integrates manufacturin g simulation, advanced materials models and component performance analysis into a whole comprehensive framework, which can be used to optimize the manufacturin g process, materials selection and product design. Modeling and simulation of process-structure-propert y is one of the primary themes of ICME. The present paper presents some latest research and development of modeling and simulation of magnesium (Mg) alloy castings at different length scales for predicting the microstructur e and mechanical properties of the casting components, where macro-scale simulation of mold filling and solidification, microscale model of microstructur e evolution during solidification, and mechanical property model based on structure information are demonstrated. The macro-scale simulation of the casting process took the process parameters as initial inputs and provided thermal history of the whole casting for micro-scale modeling. In the micro-scale modeling, the dendritic structure of primary phase was simulated in both two dimensions (2D) and three dimensions (3D) using a modified cellular automaton (MCA) model that takes heterogeneous nucleation, solute diffusion, interface curvature, and growth anisotropy into account. In the mechanical property modeling, main strengthening mechanisms of Mg-Al series cast Mg alloy were considered. Using the current model the yield strength distribution of Mg alloy wheel casting for automobile was predicted. Material property tests were carried out and the capability of the model was evaluated. Introduction Integrated computational materials engineering (ICME) has emerged as a promising way for efficient, economic, and environmental friendly manufacturin g by an integrated framework composed of manufacturin g simulation, advanced materials models and component performance analysis, which can be used to optimize the manufacturin g process, materials selection and product design[1]. In the ICME framework, modeling and simulation on process-structure property relationship is one of the most concerned fields. The present paper presents modeling and simulation of process-structure-propert y for Mg alloy castings under the ICME framework. The current modeling considers the physical phenomena occurred during the production of Mg alloy casting at different length scales for predicting the microstructur e and mechanical properties, in which macro-scale simulation of mold filling and

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solidification process, micro-scale model of microstructur e evolution, and mechanical property model based on structure information are integrated. The macro-scale simulation consisted of the mold filling and solidification simulations. It took the casting process parameters as initial inputs and provided thermal history of the whole casting as output which was also the input for micro-scale modeling of solidification microstructure . In the micro-scale modeling, MCA model was established to simulate the microstructur e evolution considering dendrite morphology of primary or-phase of Mg alloy in both 2D and 3D. To reflect the texture of Mg alloy dendrites[2], CA calculation was performed with a hexagonal mesh in 2D and a mesh defined by the HCP crystal lattice in 3D. By employing such meshes the artificial growth kinetics introduced by square and cubic meshes[3] was avoided. In the mechanical property model, yield strength of Mg-Al series cast magnesium alloy in as-cast, solution treated (T4) and aging (T6) conditions was predicted based on main strengthening mechanisms and microstructur e information. The strengthening mechanisms considered were solid solution strengthening <JSS, grain boundary strengthening ags, Orowan looping hardening oor and deformation incompatible effect <rp. Using the present process-structure-propert y modeling, the evolution of dendrite morphology of primary ör-phase during solidification were simulated both in 2D and 3D, and the yield strength distribution of commercial AZ91D Mg alloy wheel casting for automobile with 500 mm in diameter and 264 mm in height was predicted. Tensile property tests were also performed in ascast, T4 and T6 conditions for validation. Micro-scale Modeling of Solidification Microstructure In the micro-scale modeling, MCA model was used to simulate the solidification microstructur e of cast Mg alloy in 2D and 3D concerning the dendrite morphology of primary ophase. Some key features of the model is described very briefly below, and the details of the model can be found elsewhere[4'5l The challenge encountered when simulating dendrite morphology of Mg alloy by CA method is the artificial anisotropy of growth kinetics caused by the square and cubic meshes[3]. To get rid of the artificial growth kinetics and to reflect the texture of Mg alloy dendrites, a hexagonal mesh is used in 2D to perform CA calculations, as is illustrated in Fig. 1 (a). Each hexagon represents a CA cell and has six closest neighbors. The cell would capture its six closest neighbors once its solid fraction equals one. The cell configuration and state transition rule for the CA cell in 3D are illustrated in Fig.2 (a). In 3D case a cell has twelve closest neighbors and it would capture these neighbor cells once it is fully solidified. If degenerate the 3D model in Fig.2 (a) to 2D at the basal plane, it can be found that the degenerate model is identical to the 2D model in Fig.l (a). In the current model, the growth kinetics of dendrite tip is determined by the difference between local equilibrium composition and local actual composition obtained by solving the solute transport equation, which means that the growth of dendrite is controlled by the solute balance at S-L interface. Using such method the solid fraction increment of CA cell can be directly obtained by the solute field at S-L interface instead of calculating the resolved interface velocity. Mechanical Property Model of Mg Alloy Casting

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Various hardening mechanisms contribute to the strength of Mg-Al series Mg alloy, which arise from interactions between the characteristi c of material microstructur e and deformation induced defects, of which the most important is dislocation. In single phase ploy-crystal alloy the strengthening mainly comes from the interaction between the lattice and the dislocations, the solid solution strengthening arising fromthe solute atom, and the grain boundary hardening. For alloys containing dispersion of second phase precipitates additional strengthening contribution arisesfromthe interaction between the particles and defects. In the mechanical property model, yield strength of Mg-Al series cast magnesium alloy in as-cast, solution treated (T4) and aging (T6) conditions is formulated based on main strengthening mechanisms and the microstructur e information. The strengthening contributions considered are the solid solution strengthening <JSS, the grain boundary strengthening
(a)

(b)

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(c)

Fig.l. (a) CA cell configuration and capture rule in 2D. (b) Simulated equiaxed dendrite morphology of AZ91D Mg alloy in 2-D. (c) Metallographic photo obtained under light optical microscopy showing the texture of Mg alloy dendrites.

(a) (b) (c) (d) Fig.2. (a) CA cell configuration and capture rule in 3D. (b) Early development stage of 3D equiaxed dendrite of AZ91D Mg alloy, (c) Equiaxed dendrite with well-developed secondary and higher order arms, (d) The 2D solute field of (c) where the plane is perpendicular to the caxis and passing through the nuclei. Simulated and experimental results of yield strength distribution Simulated results of solid fraction evolution during casting process of the AZ91D Mg alloy wheel for automobile is shown in Fig.3, and the predicted distribution of yield strength of the casting is shown in Fig.4 in as-cast and T6 treated conditions. It can be observed that at the spoke of the wheel, the yield strength is much higher resulted from faster cooling rates and smaller grain size. By comparison, the cooling rate at the rim of the wheel is relatively slower, which leads to coarser grains and lower strength. The results show that the local cooling condition plays a key role in determining the distribution of yield strength of Mg alloy wheel castings, which is also proved by experimental measurements show in Fig.5. By the comparison between the simulated and testing mechanical properties as shown in Fig.5 it can be seen that the current modeling can be used to predict the yield strength distribution of Mg-Al series alloy castings with acceptable accuracy.

Fig. 3. Illustration of the solid fraction evolution during casting of the automobile wheel. (a)~(d) show the time elapsed from the start of pouring.

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(a) (b) (c) Fig.4. Geometry model and predicted yield strength of Mg alloy wheel casting for automobile, (a) Geometry model of the final part, (b) Yield strength distribution of the casting in as-cast and (c) T6 treated condition.

Fig. 5. Comparison of experimental measured and predicted yield strength at the rim,flangeand spoke of the wheel casting in as-cast, T4 and T6 treated conditions. Conclusions y model was developed for Mg-Al series Mg alloy casting, which (1) A process-structure-propert integrated the macro-scale modeling of casting process, micro-scale modeling of microstructure , and mechanical property model for whole casting. (2) In micro-scale modeling, 2D and 3D MCA model was developed concerning the dendrite morphology evolution of Mg alloy. The model used a hexagonal mesh in 2D and a mesh that is defined by the HCP lattice in 3D to reflect the texture of Mg alloy dendrites. (3) In the mechanical property model, main strengthening mechanism was taken into account for predicting the yield strength of Mg-Al series Mg alloy casting. For different heat treatment conditions the yield strength was formulated by moderate combination of strengthening contributions. (4) Using the current process-structure-propert y model, dendrite morphology evolution of Mg alloy in 2D and 3D were simulated and distribution of yield strength of Mg alloy wheel castings for automobile was predicted in as-cast, solution treated and aging conditions.

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Mechanical property tests were performed and comparison between simulated and experimental results was made. Acknowledgments This research is funded by The National Basic Research Program of China (2005CB724105 and 2006CB605208) and the National Natural Science Foundation of China (50875143). References 1. J. Allison, B.C Liu, K. Boyle, et al, "Integrate d Computational Materials Engineering (ICME) for Magnesium: An Internationa l Pilot Project ", Magnesium Technology 2010, The 139th TMS Annual Meeting and Exhibition, Feb. 14-18, 2010. 2. A.K. Dahle, et al., "Development of the As-cast Microstructur e in Magnesium - Aluminum Alloys," Journal of Light Metals. 1 (2001), 61-72. 3. L. Beltran-sanchez, D.M. Stefanescu, "Growth of Solutal Dendrites: a Cellular Automaton Model and Its Quantitative Capabilities," Metall. Mater. Trans., 34A (2003), 367-382. 4. L. Huo, Z.Q Han, B.C. Liu, "Two- and Three-dimensional Cellular Automaton Models for Simulating Dendrite Morphology Evolution of Cast Magnesium Alloys", Magnesium Technology 2010, The 139th TMS Annual Meeting and Exhibition, Feb. 14-18, 2010. 5. L. Huo, Z.Q Han, B.C. Liu, "Modeling and Simulation of Microstructur e Evolution of Cast Magnesium Alloys", Materials Science Forum, 2010, Vols.638-642, 1562-1568. 6. L. Huo, Z.Q Han, B.C. Liu, et al, "Modelling and Simulation of Mechanical Properties of Magnesium Alloy Wheel Casting for Automobile", The 140th TMS Annual Meeting and Exhibition, Feb.27 - March 3, 2011.

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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)

The Role of ICME in Graduate and Undergraduate Education, Information Infrastructure, and Success Stories

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

Teaching Transport Phenomena Through Spreadsheet Programming and Numerical Methods James D. McGuffin-Cawley Department of Materials Science and Engineering Case Western Reserve University 10900 Euclid Avenue Cleveland OH 44106-7204 Abstract Available textbooks on transportphenomena in materials processing are few, and typically are based on analytic rather than numerical approaches to solving problems. I have found that a set of numerical approaches based on the use of straightforwar d explicitfinitedifference methods applied to the appropriat e partial differential equations offers significant advantages in teaching this subject. After experimenting with a variety of programmin g environments, I have settled on one of the universally available spreadsheet programs. Experience has revealed that spreadsheet programs are often a more accessible format for students, and easier to debug. Other advantages include straightforwar d modification of boundary conditions and geometry without having to introduce new class of functional forms or problem solving strategies. Introduction This effort to teach transport phenomena applied to materials engineering grew out of a combined interest in demonstratin g the combination of power and the simplicity of numerical methods and through the connection of fluid, mass, and heat flow to materials processing. The pioneering textbook in this subject is that of Poirier and Geiger, originally published in 1973 [1]. It was massively revised and rewritten for a second edition twenty years later [2] around the time two other books on the subject appeared [3,4]. The approach taken by all these books appears strongly inspired by the classic chemical engineering textbook of Bird, Stewart, and Lightfoot [5]. (This book was originally published in 1960, with the second edition arriving over forty years later in 2002 [6].) The great value of Poirier and Geiger is in the translation to problems and situations encountered in the processing of materials. Thus, the approach was largely formed prior to the arrival of low-cost accessible highpower computing, and certainly before the advent of electronic spreadsheets [7,8]. My own tendency to employ spreadsheets as a platform arosefromthe experience of teaching computere curriculum in the based problem solving in the context of a ceramic engineering undergraduat heyday of ceramics, that is the late 1980s (the "new stone age"). Myfirstexperience involved taking a relatively small set of well-defined problems of relevance to ceramic processing (batch reformulation , glass tempering, rational analysis, etc.) and forcing the students to solve them three ways - first analytically or iteratively by hand, second using a standard programmin g language (at the time fortran) and lastly using a spreadsheet. Over time it became evident that the students succeeded most quickly in the context of the spreadsheet as by this time the user interface had become relatively intuitive (in the commercial programs of Lotus 123 and then Excel). In contrast, there was appreciable overhead infirstlearning a programmin g language and after that in properly setting up the program. Manual solution provided intellectual rewards

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for individual students, but was most generally regarded as unnecessarily tedious. Further, my experience is consistent with that described in [8], "[i]n hindsight it seems obvious, but probably one of the most profound, clear benefits of using spreadsheets that emerges from this study is just that of saving time. The time gained can then be spent on investigating properties of the mathematical objects created in the spreadsheet environment: the so-called what-if scenarios." The absence of frustrationin setting up and solving problems allowed more attention to be devoted to the purpose of the problem and significance of the results. It is in this sense that the approach seems aligned with the goals of integrated computational engineering (ICME) [9]. As it became my responsibility to teach transport phenomena, I initially reproduced the strategy in the text(s). However, over time I modified the approach to one based largely on numerical methods and referred to the textbook solutions. It is my contention that though this approach admittedly sacrifices some experience with application of traditional methods of solving partial differential equations, it offers advantages that more than compensate. The books of the 1990's all include a description of numerical methods. However, in none of them is it integrated into the text - it is usually introduced in the context of heat transfer carrying the implication that it is less general than is true. One of the chief advantages are the ability of one simple program, based on explicit finite differences, to provide solutions to a wide set of problems that, if done analytically, require a range of problem solving strategies and produce functional forms that are not simply related to each other. The second is that the formalism offers the opportunity to develop physical insights. A number of books have come out that describe manifold applications of spreadsheets for scientists and engineering [10-13]. In particular, however, the early text by Dobson and Wolff [13] provides a very clear set of descriptions for spreadsheets programming of transport problems (amongst others). Another notable advantage of Dobson and Wolff is that the book does not presume a particular spreadsheet. I adopted the frameworkof their book and do not use features particular to any spreadsheet. (Although Excel has become the overwhelming spreadsheet in use [14], in any given class someone will have a preference for a different one.) First Spreadsheet Problem The explicit finite difference method involves iteration. To introduce this to the students to this before introducing the formalism of transport, I make recourse the so-called Babylonian square root method. This is familiar to those above a certain age, but generally not to today's college students. Online descriptions of the method are, of course, readily available [16]. It is entirely straightforwar d and this allows the focus to be on the structure of the program. The method for finding the square root of any positive number, S, begin with an arbitrar y positive starting value x0 (this introduces the idea of initializing a program - one convenient choice is to use S/2). Sequential approximations for -\[S, denoted xn+i are obtained by calculating the average of xn and S/xn. This is repeated until the desired accuracy is achieved (determined by comparing two sequential values). Typically, when programmed in a spreadsheet, a large series of rows is used and each row makes reference to that immediately above it [e.g., as presented in 16], see Fig. la. However, I present an alternate format that takes advantage of a particular property of the spreadsheet and iteration. In a spreadsheet the "equals sign" actually means "replace the value of this cell with the results of the expression that follows." This is the key to doing recursion in a spreadsheet as it

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permits iteration using so-called circular references in which a cell is populated with a computation that involves the prior value of the cell. The program in Fig. lb has two cells that require input. In addition to the target number, Cell B2, whose square root is to be calculated, Cell Bl is set to zero until it is desired to begin iteration at that point a value of one is entered. Under "preferences " for the spreadsheet the flag to allow "iteration" must be set so that the spreadsheet does notflagthe intentional circular references in the program as errors. a) 1 2 3 4 5 6 7 8 9 10

n 0 1 2 3 4 5 6 7

A number S xfn) =Bl/2 =(D5+E5V2 =(D6+E6)/2 =(D7+E7)/2 =(D8+E8)/2 =(D9+E9)/2 =(D10+E10)/2 =(D11+E11V2

B input number here = B$1/A3 = B$1/A4 = B$1/A5 = B$1/A6 = B$1/A7 = B$1/A8 = B$1/A9 = B$1/A10

b) 1 2 3 4 5 6 7 8 9 10

A reset (zero) S

B input either 0, or 1 to start iteration input number here

n = # iterations

= B1*(B4+1)

x ( n + l ) = 0.5*(x(n)+S/x(n)) xfn)

= 0.5*(B7+B2/B7) = Bl*B6+(l-Bl)*(B2/2)

Fig. 1. a) Row-by-row spreadsheet program to compute square roots using the Babylonian algorithm. A fixed set of rows must be defined ahead of time. This can lead to either insufficient convergence or over calulation. b) An iterative program that performs the equivalent calculation. After a value of 1 is entered in cell Bl each time the spreadsheet recalculates corresponds to one iteration.

1-D Transport To make clear that a single program can be used for manyfluid,heat, and mass flow problems, I introduce the 1-D expressions for together and stress the analogy in functional form. Although all of the texts begin withfluidflow,I choose heat transfer as it is generally the aspect of transportphenomena with which students have familiarity. I choose the stress that Fourier's law of heat conduction is the definition of thermal conductivity, i.e.,

* - - <

' '/(-I

can be rewritten as * . % ^ AL )/ \dx) and diffusion coefficient is defined by Fick's First Law, and that viscosity by Newton's law of viscosity, i.e., respectively, can 'be rewritte J . . - D A* - n as D- = ''• dx \ and, dvv Fv = ~fJA—~ c a n be rewritten as n = dx \Alj where all the symbols have their usual meaning. I further choose to introduce the convective flux densities collectively at the beginning of the class to again stress the analogies. That is, for heat flow Qx = pCpTA±vx, for momentum flow Fx = pvxA±vx, and for mass flow Jx = cA±vx.

imm t

Finite Differences in a Spreadsheet Program The best problem to initially program is a heatflowin a plane sheet with convection at the surfaces. The sheet is assumed initially isothermal and in equilibrium with the colder fluid.

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Provision is made for different heat transfer coefficients at the two surfaces. This is a 1dimensional problem that has many interesting and useful limiting forms. In the continuum it can be written: PDE

d2T — T2 dx

~dt'

dT d2T or — = athth —=with ath th =. dt dx2 \pCp)

IC

r(o < x < 0) - o

BC1

hl(T^-T(x=0))

BC2

k—] =

Defining a 1-dimensional grid as illustrated in Fig. 2, allows the equivalent finite difference problem to be specified. For grid points 1-9, the following standard finite difference expression developed by conservation of energy, a At

T[i,m +1] = ^th

dT = k-— h2(T(x=ô)-Tx2)

J

Fluid-l at Txl with h,

+0| + l | +2 +3J +4J +5J +6J +7 +8Î +9J +10 "^ I I

fc! I I Ax

i

Ar

at T

°°,2 with h2

i

Fig. 2 Definition of the grid used for heat transport in a plane sheet.

. «,AA?

!(T[/ + l,m] + 7ti-l,m])+l-2^|7t,>],

where i is the grid point index, m is the time step, and Ax & A? are the magnitudes of the grid spacing in units of length and time step, respectively. Two things to note for the students is that the coefficient (athAt/Ax2} is dimensionless and corresponds to a local "Fourier number" (although it is sometimes defined as the square root of this coefficient and/or its reciprocal) and that the temperatur e at interior point after a unit of time has elapsed is entirely determined by a weighted average of the beginning temperatur e at that point and the beginning temperature s at its immediate neighbors. (My experience is the latter point is particularly helpful to students understanding. ) Conservation of energy is also applied to the two half-size cells that hold the boundary points yielding, respectively, ( athAt\( hlAx\ T[i,m + l] T^+2 ~k Axz and h2Ax\ a At y K Ax athAt a. At) T[i,m +1] = 2| th z r[/,m]. |z;;2 + 2^r[/-i,.] 2 + J i-2 k f'* \ Axz ) L """ \~ \\ Ax A*z){A k ) \ Axz Ax With reference to the diagram in Fig. 2, the upper expression correponds to i=0 and the lower to i=10, the index i left in the expressions to reinforce the relative positions of the grid points involved on the right hand side of the expressions. At this point the local Biot number, (hAx/k), can be pointed out to students.

(^♦-M-^X^H^K 0

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The resultant program is shown in Fig. 3 and a typical result, representing cooling of window glass with a forced convection on one side and free convection on the other, in Fig. 4. Fig. 3. Spreadsheet program to calculate temperatur e distribution a plane sheet with convection boundary conditions as described in the text. Absolute references are preceded by dollar signs in Excel to allow ease of "fill right" and fill down" commands when generating the program.

Fig. 3. Spreadsheet program to calculate temperatur e distribution a plane sheet with convection boundary conditions as described in the text. Absolute references are preceded by dollar signs in Excel to allow ease of "fill right"and fill down" commands when generating the program. The graphic utput is "hot linked" and updates after each iteration. Advantages of this form of programmin g is that the entire program is visible on the screen making debugging easy and allowing users to see how all the values change with each time step.

This single simple program can be used to generate solutions to a wide family of problems including: diffusion problems in finite media, infinite media (by using lots of cells), no flux boundary conditions, thin film sources, thick film sources, extended distributions, no-flux boundary conditions, etc. (essentially all of the solutions in chaps. 2-4 of ref. 17 can be obtained); it also can be used to obtain solutions to the wide range viscous tranport problems and heat transport problems from refs. 2-4. Such comparison allows students to develop confidence in the values calculated by the program. Furthermore , it allows the physical significance of less familiar functional forms (such as an infinite series of the error function) to be more accessible. Students are able to reproduce the Heisler charts (pg. 293-299 in ref. 2) and develop an understandin g of scaling relationships, etc. The next step is to alter the program to include convective flow terms. Additionally, one great advantage of numerical approaches is the ability to incorporate variable properties including temperatur e and/or time dependencies of values in the boundary conditions or in

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transport conditions. With incremental modification, the spreadsheet program outlined herein readily accomodates these and permits hot linked output graphically depicting their instanteous values as well as how they change throughout the history of the situation being modelled. Examples include, viscosity as a function of shear rate, temperatur e dependent heat transfer coefficients, multi-step quenching, concentration dependent diffusion coefficents, etc. Learning Outcomes In general, students with experience in programmin g find their strategies for program construction are readily adapted to spreadsheet programmin g and students with little programmin g experience find spreadsheet programmin g easy to learn. Particularl y gratifying have been the stories that come back such as a graduate who wrote a diffusion-problem spreadsheet program in his first week on the job and solving what had been a six-month old puzzles to the engineers there, and the student who became such an accomplished spreadsheet programmer that he authored a text on the subject [18]. In summary, the spreadsheet format is highly-accessible, but also sufficently powerful that it respresents an appropriat e modality for many aspects of ICME. References 1. G. H. Geiger and D. R. Poirier, Transport Phenomena in Metallurgy., Addison-Wesley Pub. Co., Reading, MA, 1973. 2. D.R. Poirier et G.H. Geiger, Transport Phenomena in Materials Processing. TMS, Warrendale , PA, USA, 1994, pp. 327-329. 3. D.R. Gaskell, An Introduction to Transport Phenomena in Materials Engineering. Macmillan Publishing Company, New York, USA, 1992, pp.401-416. 4. S. Kou, Transport Phenomena and Materials Processing. New York : John Wiley & Sons, 1996. 5. R. Byron Bird, W. E. Stewart, E. N. Lightfoot, Transport Phenomena. John Wiley & Sons, 1960. 6. R. Byron Bird, W. E. Stewart, E. N. Lightfoot, Transport Phenomena 2nd edition. John Wiley & Sons, 2002, and revised 2nd edition, 2007. 7. Power, Daniel J. "A History of Microcomputer Spreadsheets," Communications of the Association for Information Systems: Vol. 4, Article 9, 2000. s in Education -The First 25 Years," Spreadsheets in Education 8. J. Baker and S. J. Sugden, "Spreadsheet (eJSiE) Vol. 1, Issue 1. Article 2,2007 9. Committee on Integrated Computationa l Materials Engineering, National Research Council, Integrated Computationa l Materials Engineering: A Transformationa l Discipline for Improved Competitiveness and National Security. National Academies Press, 2008. 10. E. J. Billo, Excel for Scientists and Engineers, J. Wiley & Sons, New York, 2007 11. D. M. Bourg, Excel Scientific and Engineering Cookbook, O'Reilly Media, Sebastopol CA, 2006. 12. S. C. Bloch, Excel for Engineers and Scientists, 2nd Ed., J. Wiley & Sons, New York, 2003. 13. W. G. Dobson and A. K. Wolff, Engineering Problem Solving with Spreadsheet Programs. American Society for Metals, Metals Park, OH 1984 14. http://en.wikipedia.org/wiki/Spreadsheet , last accessed March 1,2011. 15. R. Ghez, Primer on Diffusion Problems. John Wiley & Sons, New York, 1988. 16. pg. 134 in K. Krieth and G. D. Chakerian, Interactive Algebra and Dynamic Modeling: A curriculum for the third millennium. Springer-Verlag , New York, 1999. 17. J. S. Crank, Mathematics of Diffusion 2" ed.. Oxford University Press, London, 1975. 18. E. Bendoly, Excel Basics to Blackbelt: An Accelerated Guide to Decision Support Designs. Cambridge University Press, New York, 2008.

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History of ICME in the European Aluminium Industry Jürgen Hirsch , Kai F. Karhausen Hydro Aluminium Rolled Products GmbH , R&D / Bonn Germany Abstract : The history of material and process models and the achievements of the EU funded VIR* projects VIRCAST, VIRFAB and VIRFORM are presented, which resulted in the ICME (at this time termed Through Process Modelling: TPM) application of integrated simulation of conventional fabrication of Aluminium semi-finished products for sheet and extrusions. In Europe the development was triggered in the year 2000 by the R&D initiative of the European aluminium industry and its academic partners. The objectives were to apply advanced modelling tools and to develop new methods of "virtual fabrication" suitable for industrial application. For the first time they included fundamental physical processes and modelling approaches for casting, forming and annealing processes and the corresponding microstructur e evolution and integrated them in industrial process models, applicable now for "through process simulations" of plant production. Introduction Due to Aluminum relative young age, fundamental and applied research and development are still quite intensive also for conventional alloys and products and related fabrication issues. The properties of aluminium wrought alloys and their products strongly depend on the process conditions imposed during almost each fabrication step (i.e. casting, homogenisation, hot and cold rolling or extrusion). It is very specific for aluminium as compared to other materials, that already very early process stages may take effect on the final properties. Therefore the control and optimisation of properties requires sound knowledge of the underlying mechanisms and the sometimes complex interactions between metallurgical and processing parameters. These are well developed in plant experience, but often based on trial and error. The implementation of a new alloy and processing routes involve extensive testing, which are very costly and time consuming in-plant. Therefore the main European aluminium producers - represented by the European Aluminium Association (EAA) - started, in 2000, three coordinated EU funded VIR* projects: "VIRCAST", "VIRFAB" & "VIRFORM" /1-4/. These projects developed and applied new simulation tools and methods to integrate fundamental and physically based models to the main wrought aluminium alloys and their fabrication routes, covering DC-casting, extrusion, hot / cold rolling and annealing processes. The result was a through process modelling "TPM" exercise that proved the validity of the different material and microstructur e models applied, integrated into process models of industrial practices. Aluminium fabrication processes and microstructur e evolution The typical conventional processing route to produce Al-alloy sheet, as described in [4] and [5] is depicted in Fig 1 (a) together with the main process parameter s that affect the metallurgical processes involved and thus determine the corresponding microstructur e evolution, i.e. size and form of the deformed and/or recrystallized grain structure (b), size, shape and (local) distribution of 2nd phase particles (constituents and dispersoids) (c) and preferred grain textures developed (d). A basis of most through process models is the tracing of a typical material volume element through the processing chain. This element undergoes a sequence of thermo-mechanica l process steps that need to

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be modelled to predict its microstructur e evolution, which in turn determines its intermediate and final properties relevant to specific customer specifications [4] :

Figure 1: Processing steps of the conventional production route of Aluminium sheet and the main process parameters (a) that determine the corresponding microstructure evolution, i.e. grain structure (b), constituent and dispersoid particles (c) and textures (d). (Examples given for Al-Mg-Mn [5]). Casting and Homosenisim: Aluminium is conventionally DC cast into long round billets of various diameters for hot extrusion of profiles or into large rolling ingots for strip/sheet production. A coarse grain structure with a dendritic cell structure is formed with alloy elements in solid solution and/or as coarse (eutectic) precipitations distributed inhomogeneously. To eliminate micro segregation, re-dissolve some precipitated (soluble) particles and precipitate supersaturate d elements the ingots are "homogenised" at high temperatures . The resulting microstructur e is the foundation for most of the following microstructur e evolution effects occurring during further processing (rolling, extrusion), thus affecting properties of the final product. Solidification models have been developed based on effects of solute diffusion, interfacial surface energy, atom attachment kinetics, solute trapping and anisotropy of surface energy [6]. They predict solidification microstructures : dendritic grain structures, solid state concentration profiles, micro- and macro segregation, volume fraction and size of constituent particles and textures. This is input for the subsequent simulation of microstructur e evolution during ingot homogenisation [7-9] that precedes any subsequent (hot) forming operation. Here dissolution, precipitation and phase transformatio n occurs, based on the material's microchemistry in terms of solid solution levels, size and volume fraction of constituents and dispersoids. They affect recrystallization and particle break-up during subsequent deformation in the break-down hot rolling line or the (hot) extrusion press [10,11].

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Extrusion: Extrusion of Al alloys is a widely used way to fabricate semi-finished products, such as profiles and tubes, in sometimes quite complex shapes. Heat-treatabl e alloys (i.e. medium Al-Mg-Si or high-strength Al-Zn-Cu-Mg alloys) can easily be used due to the hot deformation and quenching effect implied in the extrusion process [12]. The hardening precipitates are dissolved during preheating and retained in solid solution by quenching the material directly after the (hot) extrusion process. Therefore the as-cast precipitates must be fine and uniformly dispersed which can be achieved by appropriat e casting and homogenisation practices (incl. rapid reheating to the extrusion temperature) . The different sub-models cover all process and microstructur e aspects of the process chain [4] and allow to predict local deformation and recrystallization structures and textures that determine forming properties of the extruded products.

Figure 2. TPM simulation of extrusion processes incl. microstructure parameters for the submodels covering the process chain from casting untilforming of extruded products [12]. Rollins: In hot rolling the slab thickness of 300-600 mm is reduced in several passes > 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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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.

212

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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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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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~
(1)

u

(2)

1 2 ~ UFe:Va.C:C '= -u, +—u, 3 l 3 2 2 1 °s~,bct _ °/~
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alloy. While the material has not changed, the fabrication process has; based on current methodology this requires requalification of the material. Given the overall magnitude of the F35 program and the corresponding total accumulated cost savings for a relatively high production run platform, the expense of A/B-Basis re-qualification can be justified. This is not the case for the vast majority of other candidate vehicles. The data generated under the qualification program effectively "fixes" the materials and procedures in-place and requires the process to become static. While this is desirable and necessary for a standardized and repeatable process, it also limits the ability to seek improvements in the process (and in the materials generated by the process). The additive manufacturin g approach allows for more degrees of freedom in the fabrication process. Multiple process paths can yield the acceptable end product, both microstructurall y and mechanically. Furthermore , the conditions and/or material chosen in the qualification study may turn out to not be the ideal path as the process evolves and matures. Unfortunately, any excursion from the standard deposition process, as established in the specification procedures, will not be allowed under the current methodology. The challenge for the additive manufacturin g community is that the process segment of the process-microstructure-propert y relationship is not necessarily uniform or static. This implies the need for an outcome-based approach for material qualification. Currently, design minimum values are linked to a specific product form and often times further segmented based on section thickness. All of this is directly related to the microstructur e (and indirectly to the resultant properties) though microstructur e is not a governing criterion in the specification itself. Put another way, if two wildly different processing routes for the same material produce identical microstructures , the current methodology treats them as two different materials. The focus clearly needs to be on the outcome of the process, not the process itself. The complication lies in the fact that it will no doubt be contentious proving two microstructure s are "identical". This is where computational methods can help by filling in the "continuum" in the processmicrostructure-propert y relationship where data does not exist to predict subtle variations in the outcome of the process. Sharing the Qualification Burden Historically, the qualification burden for a new material has been the responsibility of the primary producer. For aerospace metallic materials, the majority of these producers are large semi-integrated operations that have the financial resources to undertake an expensive qualification program for a promising new material. Much like the case for additive manufacturin g on F-35, the magnitude of the qualification effort requires large companies that can allocate the financial resources. The continued advancement of additive manufacturin g will require a more nimble, less cost-intensive approach. For with these new methods, the responsibility for final melting will now lie with much smaller companies that can not afford a large qualification campaign. An effective way for these small producers to work together towards qualification is necessary. A novel approach taken by the fiber composite community is to pool resources and share data through a non-competitive organization. This method was established through the Advanced General Aviation Technology Experiments (AGATE) Consortium and managed through the

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National Institute for Aviation Research at Wichita State University [8]. There are a number of advantages to a centralized non-proprietar y repository of certified test data. First, an equivalency method for qualification can be utilized through comparison of select new data to the existing master database. This limits the need to recreate a large dataset for any change (however major or minor) to the process or raw material condition. A second benefit, related to the first, is that the cost barrier for a new supplier is greatly reduced. Equivalency testing allows smaller material producers to qualify their product relatively quickly and affordably and thus enables a larger supply chain. A similar approach to data handling will be required if additive manufacturin g is to advance and mature into widespread use. Likewise, computationally driven material design in the aerospace market will not realize its full potential without a more adaptable approach to qualification testing and data handling. Unconstrained Potential Computationally driven materials design has already claimed some significant, well known successes in other market segments. The virtual aluminum casting program at Ford Motor Company is one such success [9]. The high-fidelity model neatly tying together the processmicrostructure-propert y relationship in aluminum engine block castings demonstrates the fundamental goal of the computational approach. This approach is well suited for processes such as additive manufacturing . In additive manufacturing , the controllable mass addition and thermal path offer the prospect of customizable structures with variable microstructures , chemistries, and properties. Predictive modeling can improve and accelerate advances already being made resulting in advances in alloy performance and the development of new classes of alloys. Demonstrations of gradient compositions, gas-phase in-situ alloying, functional density gradients, and other novel constructs have already been demonstrated by additive manufacturin g techniques [10, 11, 12]. It is likely that the pace of adoption and integration of these new materials will be severely constrained in the aerospace market by the inability to fund a largescale data allowables program. Likewise, incorporating processing advancements brought on through advanced thermal modeling techniques will also be limited due to the constraining nature of the qualification procedures. Improved thermal management strategies resulting in less distortion/residua l stress are very desirable for optimizing the net shape capability of the process. Control of phase transformation s in order to control microstructura l morphology and scale are also very desirable. These and other advancements will be made available through the use of computational methods applied toward additive processes. The community of users, however, must be ready to accept these changes and find a better, more adaptable way of validating their outcomes. Otherwise, each new improvement becomes a new "process" requiring another expensive requalification of the material. Finally, machine-to-machine variability can also add constraints to the overall maturation of the process. A dataset generated on a certain platform requires consistency not only from part-topart but also from machine-to-machine. This challenge is compounded by the equipment manufacturer s constantly evolving hardware configurations. As the process models mature and begin to dictate the optimized operating conditions, the hardware will be required to adapt to these changes. This can only happen through a reformed data allowables procedure, one focused on the outcome of the process and not on the process itself.

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Conclusions Aerospace structural metallic materials require a rigorous, expensive, and time consuming qualification procedure prior to their implementation onto an air vehicle system. This requirement creates a buffer that limits how quickly (if at all) promising new materials get introduced and fully adopted. The changing landscape of metallic material manufacturin g creates a strong need for a fresh approach to qualification. The users with a vested interest must be willing to share precompetitive data in order to advance the broad industry. This is absolutely necessary for additive manufacturin g to gain traction and expand beyond the few players fortunate enough to find a program willing to subsidize the huge cost of qualification. Similarly, the computational materials engineering community also needs a better approach to data qualification. The promise of robust, validated modeling as a means to move away from the empirically dominated current approach will never come true without significant qualification reform. The shift away from a process-specified approach towards an outcome-based approach will be necessary in order to take full advantage of benefits new manufacturin g methods have to offer. The combination of additive manufacturin g with computationally driven materials design holds tremendous promise to create revolutionary new materials. Consideration for how these new materials get into the marketplace must become a priority. Acknowledgements I would like to thank my former colleagues at Lockheed Martin Aeronautic Company for their many years of insightful knowledge and guidance into the complicated world of air vehicle manufacturing . I would also like to thank my current colleagues at the NASA Langley Research Center for their support and insightful contributions to this paper. References 1. J. Jackson, "Definition of Design Allowables for Aerospace Metallic Materials", (Paper presented at 2007 AeroMat Conference and Exposition, Baltimore, MD, 2007. 2. W.E. Frazier, D. Polakovics, and W. Koegel, "Qualifying of Metallic Materials and Structures for Aerospace Applications", JOM, 53, 3 (2001), 16-18. 3. Metallic Materials Properties Development and Standardizatio n (MMPDS-01), U.S. Department of Transportation , 2003. 4. J.T. Staley and W.H. Hunt, Jr., "Needs of the Aircraft Industry for Aluminum Products", (Paper presented at the 12th Annual National Center for Manufacturin g Sciences Technology Conference and Exposition, Orlando, FL, 1998). 5. "Accelerating Technology Transition: Bridging the Valley of Death for Materials and Processes in Defense Systems", National Research Council, National Academies Press, Washington, D.C., 2004.

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6. Defense Advanced Research Projects Agency, Accelerated Insertion of Materials website: http://www.darpa.mil/dso/archives/aim/index.ht m 7. C.A. Brice, S.D. Needier, and B.T. Rosenberger, "Direct Manufacturin g at Lockheed Martin Aeronautics Company", (Paper presented at 2010 AeroMat Conference and Exposition, Bellevue,WA,2010). 8. J.S. Tomblin, J.D. Tauriello, and S.P. Doyle, "A Composite Material Qualification Method that Results in Cost, Time, and Risk Reduction", Proceedings of the 32nd Internationa l SAMPE Technical Conference, Boston, MA, 2000. 9. J. Allison, M. Li, C. Wolverton, and X. Su, "Virtual Aluminum Castings: An Industrial Application of ICME", JOM, 58, 11, (2006) 28-35. 10. R. Banerjee, P.C. Collins, D. Bhattacharyya , S. Banerjee, and H.L. Fraser, "Microstructura l Evolution in Laser Deposited Compositionally Graded a/b Titanium-Vanadiu m Alloys", Acta Materialia, 51, 11, (2003) 3277-3292. 11. C.A. Brice, "Nitride Strengthened Titanium via Deposition Processing", Proceedings of the 11th World Conference on Titanium, Kyoto, Japan, 2007. 12. B. Carcel, A.C. Carcel, I. Perez, E. Fernandez, A. Barreda, J. Sampedro, and J.A. Ramos, "Manufactur e of Metal Foam Layers by Laser Metal Deposition", Proceedings of XVII Internationa l Symposium on Gas Flow, Chemical Lasers, and High-Power Lasers, Lisbon, Portugal, 2008.

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WHAT BARRIERS PREVENT ICME FROM BECOMING PART OF THE DESIGNER'S TOOLBOX? P. L. Ret1 ^ ir Force Research Laboratory, Materials and Manufacturin g Directorate, Wright-Patterso n Air Force Base, OH Keywords: Validation, Design, Model, Accuracy, Precision, Culture Abstract Integrated computational materials engineering methodologies promise a revolutionary step forward in the qualification, certification, and sustainment of Air Force systems via reduction of the historically slow and costly materials data development footprint [1,2,3]. The establishment of scientifically-based, statistically-robust processes by which computational materials models can be quantitatively graded, accepted and utilized by the aerospace structures design, manufacture, and sustainment communities for cost and time savings presents a major hurdle towards the realization of the potential of ICME. To allow for the change to the materials qualification paradigm offered by ICME, several barriers (economic, cultural, and technical) must be overcome. Via identification and discussion of these issues, this article challenges the ICME community to position itself for success via integration with the industrial structural design community. Introduction The development of a fully integrated computational materials engineering (ICME) based structural materials technical field is within reach and its impact upon the aerospace engineering & manufacturin g practice and the United States Air Force promises to be profound. Both the aerospace community and the Department of Defense have invested heavily in and developed technically and legally robust structural design, certification, and sustainment processes [4,5,6,7]. Historically, to be integrated into aerospace structural design and life analysis systems, materials were required to undergo millions of dollars (and multiple years) of standardized mechanical testing. The intent of this testing was to develop statistically significant representation s of the materials' behavior to independent, but complimentary, combinations of material, manufacturing , and load spectrum combinations. Clearly, ICME presents the opportunity to replace a large degree of historically required mechanical testing providing for faster, less costly design and materials integration cycles. Furthermore , ICME methodologies will enable "transparent " materials and processes substitutions/improvement s without the required regeneration of exhaustive materials datasets. To achieve this goal, the materials scientist and engineer community must be cognizant of barriers facing the implementation of ICME in structural design. Economic, cultural, and technical barriers exist. It is the materials community's responsibility to ensure that these barriers are overcome by working to address them in its research, development, and transition activities. Discussion Economic Barriers: The cost and time invested in the development of current aerospace design practices and the generation of the supporting materials datasets present a significant barrier to the acceptance of ICME. The economic justification to pull industry toward ICME and invest in new design practices must be cultivated. It is widely recognized [1] that

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significant investment must be undertaken to facilitate integration of ICME tools into structural aerospace design. The likely quickest path to overcome this barrier is by the demonstration of point successes (cost and time savings) that can be delivered by ICME. By this mode, examples of ICME acceptance/applicatio n in design and manufacture are becoming more frequent [8,9]. The majority of these recent efforts, however, are noted to have been necessitated by time and cost constraints in component development or production driven by unexpected difficulties that did not allow traditional approaches to be utilized. As an emergency stopgap, ICME has been successfully applied in such instances and has been observed to have developed preliminary footholds in specific companies. As a whole, however, confidence must still be established with the structural design community to the extent that the replacement of existing culture and organizational/proces s infrastructur e can be economically justified. Cultural Barriers: Cultural barriers also present themselves with the integration of ICME into design. Design currently optimizes shape based upon functional requirement (rotating turbine disk, wing spar, e t c . ), anticipated load spectrum, and materials properties linked to a fixed composition and a correspondingly fixed manufacturin g path. Materials are treated as an oversimplified fixed variable in the design optimization process with "shape" being the principal outlet of designer creativity and innovation. ICME presents designers with the opportunity to treat materials as true variables where such concepts as tailoring to achieve location specific properties presents the opportunity for extended creativity where material property can vary with 3-D location in a component. Unfortunately, the addition of materials as an independent variable is a radical departure from current work practice. Such flexibility will push designers into areas where they have neither formalized training, nor corresponding materials backgrounds. It will fall on the materials community to support this re-education of the design community. The path toward ICME implementation in industry will necessarily require a merging of mechanical engineering and materials science and engineering disciplines at this hand-off point. Technical Barriers: While the economic and cultural barriers faced by ICME are not insignificant, they may not be within the power of all materials researchers to influence. There are, however, multiple global technical barriers that must be addressed to garner the confidence and acceptance of the design community. These barriers include: • The 'goodness' of current industry practice is accepted, but is not well statistically quantified with respect to materials. • The accuracy, precision, and error in integrated modeled system predictions are generally not statistically quantified making model predictions difficult to globally accept. • The ranges over which model predictions are "accurate" are usually not defined, let alone addressed in integrated systems of models. • "Research" model maturity issues hinder the credibility of computational modeling as a developed technology in the eyes of the structural design community. The following discussion of these global technical issues is presented to generate thought for researchers developing ICME tools. Without keeping these barriers in mind when developing computational models and presenting their results, materials researchers will not see the transition of their activities to the serve the very needs their research sets out to address. The complexity of the development of computational models, the verification that such models accurately represent the underlying mathematics models, and confirmation that such

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models reflect the reality of actual behavior is immense and has been well addressed elsewhere [10].

Figure 1. Verification and validation computational model cycle [11]. This discussion will focus specifically on the validation of computational models and the integrated modeling suites (process-microstructure-behavior ) to support the aerospace design community (Fig 1.). Validation is defined [12] as, "the process of determining the degree to which a model is an accurate representation of the real world from the perspective of the intended uses of the model.'" Underlined are the key subjective words in this definition. The design community's perspective and needs are those that materials researchers must ensure are able addressable as their models are presented for validation. Globally, ICME model validation strategies have not been pervasively established [13]. To enhance the acceptance of ICME by the design community and support the development of validation methodologies, the materials community must begin to look at ICME from the designer's perspective and be prepared to address some of the following questions: What Is "Goodness " In A Designers Eyes? US Air Force design is focused on driving the probability of catastrophic field failure to less than one in ten million (0.00001%) [14]. Such failure rates and the current design infrastructur e have been validated by field experience. Unfortunately, while the conservative failure goals are well defined statistically, the assumed materials contribution is not probabilistically defensible. To meet probabilistic system failure rate goals, materials are assumed to have normal behavior distributions and their -3a properties are typically utilized from these distributions as 'safe' design values [15] for critical components. It is therefore this probability of failure (0.15%) that is rolled into the structural design calculation as the materials contribution. This approach appears sound at first review, but implicit to this approach is the fundamental assumption that the property data collected is, in fact, the "worst case" distribution of properties, exercising the limits of specification chemistry, manufacturin g process control, and mechanical test variability. Furthermore , the assumption that all behaviors (even those structurally driven) act as normal distributions is clearly not a universal truth. Current, US Air Force airframe structural integrity practice also adds an additional layer of conservatism (an assumed initial flaw) to account for "unexpected" manufacturin g anomalies not captured in the development of design data as a response to historical aircraft mishaps [16]. This approach has served the US Air Force well, however,

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the direct application of this somewhat flawed approach toward acceptance of ICME generated probabilistic results presents real problems for the materials community. An ICME prediction of mean behavior alone is insufficient for use in probabilistic design. A useable computational prediction of material behavior must address the shape and tails of behavior distribution curves. An ICME framework with validated ability to model chemistry, manufacturin g processes, resulting microstructure , and predicted behavior presents a double edged sword of opportunity for the design community. In its best case, a well modeled material may show a distribution with -3a behavior higher than the traditional dataset. If accompanying high confidence manufacturin g process modeling could convince designers to remove the assumed initial flaw assumption, substantial weight savings, or load capacity could be recovered. In its worst case, however, accurate modeling of extreme behavioral outcomes from the material and processing path may show the historical design data based assumptions to be unconservative. Clearly, this result could drive increased inspections of fielded aircraft or fleet groundings if applied to legacy systems, unpopular outcomes to say the least. The materials community must seek to address the technical issue of delivering results that can be incorporated into probabilistic design, but at the same time be cognizant of the implications that may result and designer hesitancy to move forward too quickly. How Should Model Accuracy and Precision be Addressed? Qualitative comparison of model prediction to experimental data has become typical for research model validation. Modeled curves of similar shape, slope and data overlap are clearly indicative of "goodness", but are often not quantified. To a designer, such subjective analysis is unusable. The issue at hand becomes comparison of experimental behavior mean curve (with distributions at each point) with model predicted mean curves and distributions in a statistically robust manner. Until such methodologies for model evaluation for accuracy and precision are developed and promoted by the materials community, the design community cannot be expected to establish acceptance criteria for model performance. Implicit to any statistical analysis of model prediction to actual experimental behavior is detailed knowledge of the exact materials pedigree (chemistry, process history, resulting microstructure , etc..) as well as experimental conditioning. Unfortunately, details of much of the required pedigree information do not exist for historical datasets. Historical mechanical behavior dataset development required only knowledge that the material tested was produced to appropriat e specifications and did not capture the specifics that models will eventually be able to address in detail. The true evaluation of model quality must include experimental results from materials whose exact pedigrees (including such things as chemistry, processing strains, strain rates, temperature , etc..) can be linked to the predictive models exercised. In addition to statistical "fit" analysis, further quantification of a model's accuracy and precision can developed by the modeling of similar and degeneratively simplified problems [10]. Demonstration of successful, high quality prediction of behavior of simplified devolved (subset) problems will add credibility to any result. Likewise, the systematic use of sensitivity [17] tests to evaluate model response to small changes in inputs and assumptions will give insight into model stability and even identify limitation issues.

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Complicating the model accuracy barrier even further are the instances where models attempt to predict phenomenon that there are no trusted (or high quality) experimental techniques. In these instances, the role up of these models into larger scale models where validation can occur is the most sensible approach. The tracking of error roles into that of the larger scale model and must be accounted. What is the Range Of Accuracy of the Models (and can they be Extrapolated?)? Once a methodology is established to compare model prediction with experiment and designers can quantify and specify required accuracy, boundary value testing can be applied to track model "sweet spots" and bound ranges of accuracy. Models should strive to demonstrate one and only one period of experimental convergence with model prediction as an accuracy range. Multiple, complex regions of accuracy will induce doubt in the eyes of the design community. Similarly, when rolling multiple models into a complex integrated predictive suite, tracking and appropriatel y managing these ranges of accuracy will be critical and will require materials community driven methodologies to be developed. Of significant interest to the structural designer are material behavior regimes beyond historical precedent. This exploration is indeed the promised fruit of ICMSE. Such exploration will require extrapolation or use of models beyond where their established range of accuracy. Such extrapolation should only be considered/supporte d by the materials community in instances where the applied models have sufficient physical basis (nonphenomenological) and have not incorporated any type of calibration. Model calibration (even to physics based models) exhibits lack of confidence in the model by the materials scientist/engineer. It is viewed similarly by the designer! Calibration to achieve agreement in a regime of interest fundamentally corrupts the model's ability to be applied/extrapolate d elsewhere with confidence. Finally, a robust means of holistically evaluating model quality and applicability can be accomplished via the use of benchmarking [18]. By using design of experiments methodologies to produce materials that capture and extend beyond current industrial practice norms (i.e. forged shapes that include both nominal and abnormal plastic deformation, rates, & temperatures ) data can be generated to exercise and evaluate model quality outside of normal ranges. During such manufacture, critical 3D microstructura l information (chemistry, geometry, texture, and residual stress) could be extracted (as computational models input). Following manufacture, multi-scale mechanical testing can be used to generate statistically robust experimental datasets. Such a benchmark would enable studies of individual models as well as integrated modeling suites for purposes of validation. Are the Presented Models Sufficiently Developed? Computational materials model creation and development is thankfully on the rise. A "cottage industry" is developing in both the academic and commercial sector towards this end. It is the author's observation that the combination of funding direction and targeted application is, however, resulting in the development of such models stopping at relatively immature states. When either the problem the model was developed for has been "solved" or the model is subjectively "validated," development often ceases. At this point, significant work has gone into the mathematical model development, code development, and verification that the code represents the mathematical model. Many models, have no documentation on neither their basis nor use and can be generally best be characterized as user unfriendly (if available for use at all). While there are economic and competitive drivers

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for keeping close hold on certain models, the end effect is often a lack of transition of this work to the community at large. A cursory review of any major university materials department dissertation library will show record of model development and some degree of validation success. The real challenge then becomes obtaining (or gaining access) to the exact model that generated those results. Lack of documentation, revision control and availability of that model then all quickly become significant issues that impede subsequent successful application. The design community will require any supporting model to be developed to such an extent that revision control, underlying assumptions, required inputs, and operation are knowns. The materials community must come to grips with the fact that until models reach this point of development, they will largely not be useable by the design community. Conclusion The materials scientist and engineer community must keep in mind the perspective of the design community (their ultimate customer) as they continue to create and develop ICME technologies. The materials community will have to take an active role in the development of methodologies to quantify accuracy, precision, track error propagation, and envelope of model relevance. The materials community must also strive to provide models that are developed sufficiently to transition into integrated computational suites. Only by satisfying the design community's concerns and establishing confidence in the utilization of ICME tools to replace a robust historical paradigm, will a future home for computational materials science technologies be ensured. References "National Research Council (NRC), National Materials Advisory Board, Integrated Computational Materials Engineering: A Transformational Discipline for Improved Competitiveness and National Security, Washington, D.C., National Academies Press, 2008 2 National Research Council (NRC), Materials Research to Meet 21s' Century Defense Needs, Washington D.C., National Academies Press, 2003 3 National Science and Technology Council, Fast Track Action Committee on Computational Modeling and Simulation Committee on Technology, Simulation-Based Engineering and Science for Discovery and Innovation, Released for Comment, May 2010 4 Department of Defense Handbook, Aircraft Structural Integrity Program General Guidelines For, MIL-HDBK-1530C, 1 Nov, 2005. 5 Department of Defense Handbook, Engine Structural Integrity Program, MIL-HDBK-1783B, 15 Feb, 2002. 6 Department of Defense Joint Service Specification Guide, Aircraft Structures, JSSG-2006, 30 Oct 1998. 7 Department of Defense Joint Service Specification Guide, Engines, Aircraft, Turbine, JSSG-2007A, 29 Jan 2004. 8 J. Allison, L. Mei, C. Wolverton, S. Xuming, Virtual Aluminum Castings: An Industrial Application of ICME, JOM, Vol. 58, No. 11, pp. 28-35. 9 Materials Modeling and Simulation—A Game Changing Technology for Propulsion Materials Development D. D. Whitis\ R. Schafrik2, (1)GE Aviation, Evendale, OH, (2)GE Aircraft Engines, Cincinnati, OH, Aeromat, 2007. 10 C. Kuehmann, H.J. Jou, "Model Quality Management," ASM Handbood, V22A, Fundamentals of Modeling for Metals Processing, ASM International , 2009. 11 S. Schlesinger, "Terminology for Model Credibility," Simulation, Vol. 32, No. 3, 1979, pp. 103-104. 12 ASME Validation and Verification Guide, 10-2006, 2006. 13 Personal communications with US Air Force supplier base , Air Force Research Laboratory, Materials and Manufacturin g Directorate, Closed Verification and Validation Workshop, Feb, 2011. 14 J.P. Gallagher, C.A. Babish, J.C. Malas, "Damage Tolerant Risk Analysis Techniques for Evaluating the Structural Integrity of Aircraft Structures, " Proceedings, 11 th Internationa l Conference on Fracture, ISBN 978-88-903188-0-1, March 2005. 15 DOT-FAA-AR-MMPDS-01, Metallic Materials Properties Development And Standardizatio n (MMPDS), 31 JAN 2003. 16 Gebman, J. R., "Challenges and Issues with the Further Aging of US Aircraft - Policy Options for Effective Life-Cycle Management of Resources, ISBN 978-0-8330-4518-8, UG1243.G429.2009. 17 A.V. Fiacco, "Sensitivity and Stability in NLP: Approximation," ENCYCLOPEDIA OF OPTIMIZATIO N 2009, Part 19, 3454-3467, DOI: 10.1007/978-0-387-74759-0_594 18 F. Stern, R. Wilson, J. Shao, "Quantitativ e V&V Of Cfd Simulations And Certification Of Cfd Codes With Examples," Proceedings of CHT04,ICHMT Internationa l Symposium on Advances in Computational Heat Transfer, April 2004.

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

AUTHOR INDEX 1st World Congress on Integrated Computational Materials Engineering A

Ai, X Anderson, P

B

Bambach, M Banerjee, R Benke, S Blackshire,J Bothra, S Brice,C Broderick, S Butz,A

C

Callas, M Chaudhari, M Chen,K Chen, M Collins, P Collins, S

D

Dong,K Du,J

F

Fraser, H

G

Gao,Y Gao,Z Gautham,B Gerard, D Ghosh, S Glaws,P Godfrey, A Gong, M Gonzalez, C Gonzalez, D Gottstein, G Goyal, S

Guest, J Gumbsch,P 211 211

H

Ha, S Hammi,Y Han,Z Haupt, T Helm,D Henke,T Hirsch, J Huber,D Huo,L

223 151 223 177 35 241 159 89

J

Jensen, D Jiang, Y Jones, P

113 151 171 177 135 165

K

Karhausen, K King, A Ko,R Koduri, S Konovalov, S Kulkarni,N Kumar Singh, R

69 151

L

135

Li,K Liao,H Liu, B Liu,H LLorca, J Lu,J Lu, S Luo,K

3 69 35 217 113 211 19 27 121 107 9 81

M

McGuffin-Cawley, J Moelans, N Mohapatra ,G Mohles,V

253

129 89

129 43 189 229 89 223 203 135 189

19 183 217

203 107 177 135 223 35 35

145 69 27, 189 3 121 63,171 183 183

197 19 35 9

Munn,B

145

X

Xu,Q

N

Najafi, A Naraghi, R Nie,J

P

Padmanabhan ,K Pardeshi,R Prahl, U Proudhon, H

Q

Quinta da Fonseca, J

R

Raabe, D Rais-Rohani, M Rajan, K Ret, P Ru,H Rubinski, J

S

Sawamiphakdi,K Schmitz, G Selleby,M Shi, S Shi, Y Simonovski, 1 Sundararaghavan ,V

T

Tiley,J

w

Wang,Q Wang, Y Welk,B Williams, P Withers, P

Y

43 235 3

Yu, L

z

Zhang, X Zhang, Y

35 81 75,223 99

107

89 43 159 247 183 165

211 75, 223 235 63,171 27 107 57

151

69,217 3,217 135 165 107

254

27

183

63 19

1" World Congress on Integrated Computational Materials Engineering

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

A

Accuracy Additive Manufacturin g Al-Si-Mg Alloy Aluminium Aluminum Architectural Optimization AshbyMaps Austenitic Stainless Steel

B

Boundary Migration

C

Carburizatio n Chromium Composite Materials Computational Tools Continuous Caster CRH3 Crystal Plasticity Culture Cyberinfrastructur e

D

Data Mining Data Repository Deformation Deformation Twinning Dendrite Arm Spacing Dendrite Morphology Density Functional Theory (DFT) Design Diffusion Disc Brake Dissipated Energy

E

Effective Properties Experimental Microstructur e

F

Fatigue Fatigue Life

Fe-C Martensite Fine Grain Stability Finite Element Finite Element Analysis Finite Element Method (FEM) Finite Element Modeling

247 241 69 107 9, 217 129 159 165

G

Galfenol Gamma Prime Phase

H

19

High Temperatur e Case Hardening Homogenization 165 151 121 217 81 183 57, 89, 99 247 229

I

ICME Image-based Model Inclusions Informatics Integrated Modeling Interaction Energy Internal State Variable Model Inverse Homogenization

35 229 9 171 27 189 151 247 197 183 63

235 223 99 145, 165 183 177

57 151

223 89

75,81 107 211 159 81 3 43 129

L

Low-temperatur e Colossal Supersaturatio n (LTCSS)

M

Magnesium Alloy Magnesium Alloys Magnetostriction Material Informatics Materials Design Mechanical Design Mechanical Property Microstructur e Microstructur e Evolution Model Modeling Multi Strain Multiscale Modeling

75 99

211 35

255

165

189 3 57 35 159 165 189 75, 189 3 247 35,241 171 121, 229

N

Nanocrystalline Copper Ni3Al Nickel Based Super Alloy Nondestructive Evaluation Numerical Simulation

P

Phase Field Approach Phase-field Modeling Phase-Field Simulation Plastic Deformation Precipitation Evolution Modeling Precipitation Hardening Precision Process Chain Process Chain Variation Process-Product Optimization Process-Product Simulation Programming Protrusion Pulling Velocity

Q

Qualification

T

Temperatur e Field Temperatur e Gradients Texture Thermal Stress Thermodynamic Modeling Through-Process-Modelin g Topology Optimization Transparen t Alloy Transport Tube Fitting Tundish

171 151 151 177 189

3 75,223 69 107 223 3 247 89 223 43 43 197 19 27

U

Ultrasound

V

Validation Virtual Casting Virtual Testing Visualization Toolkit VTK

Z

241

Zener Ordering

R

Random Impact Recrystallization Residual Stresses Retrusion

63 9, 19 145 19

S

Sheet Metal Forming 89 Silicon-Carbide 145 Simulation 27 Simulation Platform 75 Site Occupancy 151 Spreadsheet 197 Standardizatio n 75 Steel 35,211 Steelmaking 81 Stored Energy 63 Surface Mechanical Attrition Treatment 63

256

183 145 9,57,107 183 235 9 129 27 197 165 81

177

247 217 121 75 75

235