materials processing and texture · in ti added high purity ferritic stainless steel sheets 223 ....

Materials Processing and Texture

Ceramic Transactions, Volume 200

A Collection of Papers Presented at the 15th International Conference on Textures of

Materials (ICOTOM 15) June 1-6, 2008

Pittsburgh, Pennsylvania

Edited by

A. D. Rollett

The American Ceramic À Society A

WILEY

A John Wiley & Sons, Inc., Publication

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Ceramic Transactions, Volume 200

A Collection of Papers Presented at the 15th International Conference on Textures of

Materials (ICOTOM 15) June 1-6, 2008

Pittsburgh, Pennsylvania

Edited by

A. D. Rollett

The American Ceramic À Society A

WILEY

A John Wiley & Sons, Inc., Publication

Copyright © 2009 by The American Ceramic Society. All rights reserved.

Published by John Wiley & Sons, Inc., Hoboken, New Jersey.

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Contents

Preface xv

Acknowledgments XVII

FRICTION STIR WELDING AND PROCESSING

Texture Evolution during Friction Stir Welding of Stainless Steel 3 Jaehyung C h o

Texture Development in Aluminum Friction Stir Welds Richard W . Fonda , Keith E. Knipling, John F. Bingert, Anthony P. Reynolds,

We i T a n g , Kevin J . Col l igan, a n d John A. Wer t

17

Microstructural Studies of a Friction-Stir-Welded AA5052 29 N. T. Kumbhar , Santosh . K. Sahoo , R. Tewar i , G. K. Dey, I. Samajdar , and

K. Bhanumurthy

Effect of Microstructure on Mechanical Properties of Friction-Welded Joints between Aluminum Alloys (6061, 5052) and 304 Stainless Steel 35

Ν. T. Kumbhar , A. Laik, G. K. Dey, Κ. Bhanumurthy , J . Krishnan, D. J . Derose,

R. L. Suthar, S. K. Sahoo , and I. Samajdar

Effect of Texture on Fracture Limit Strain in Friction Stir Processed AZ31F3Mg Alloy 43

Y u t a k a S . Sa to , Akihiro Sug imoto , Hiroyuki K o k a w a , and C h a n g - W o o Lee

Microstructure and Texture Analysis of Friction Stir Welds of Copper 53 T. Saukkonen . , K. Savola inen, J . M o n o n e n , and H. Hänninen

TEXTURE AND ANISOTROPY IN STEELS

The Effects of Texture on the Corrosion Resistance of SS304 Stainless Steel 63

M . Azzi and J . A. Szpunar

ν

Microstructural Characterization of Dual Phase Steels by Means of Electron Microscopy 71

Liesbeth Barbé and Kim Verbeken

Grain Size Effect on the Tensile Behavior of a FeMnC TWIP Steel in Relation with the Microstructure and Texture Evolutions 79

David Barbier, Nathal ie Gey , Alain Sébast ien , and Michel Humber t

Combination of Two X-Ray Diffraction Settings for Determining the Texture of Small Sheared Samples 87

D. Barbier, Β. Bolle, J . J . Fundenberger , C . Laruelle, and A. Tidu

Texture of Non-Oriented Rolled Steels by X-Ray and Electron Diffraction 95

Martin Öernik, Mi los Predmersky , Andrej Lesko, and Erik Hilinski

Effect of Coating Texture on Powdering Behavior of Industrially Produced Galvannealed Coating on IF, IFHS and HSQ Grade Steels 103

A. Chakrabor ty , R.K. Ray, a n d D. Bhattacharjee

Including Elastical Anisotropy Due to Texture in a Finite Element Model for the Prediction of Residual Stresses in Welds 115

Koen Decroos , Carsten O h m s , and Yvan Houbaer t

Texture and Microstructure Evolution in a Fe-Si CGO Sheet during the Processing Route before Secondary Recrystallization 123

Francisco Cruz-Gandar i l la , Richard Penelle, Thierry Baudin, Hector M e n d o z a

Leon, and J . G. C a b a n a s - M o r e n o

TEM Study of the Inhibition Layer of Commercial Hot-Dip Galvanized Steels 131

Jack Elia, Ε. Petit , J - S L e c o m t e , B. Gay , and V. Pitchon

Measurement of the Texture Sharpness in Grain-Oriented Electrical Steels 143

M . Frommert , C. Zobrist , D. R a a b e , S. Zaefferer, and L. Lahn, Α. Böttcher

Effects of Composition and Coiling Temperature on Precipitation and Texture Formation in a Few Interstitial Free High Strength Steels 151

P a m p a Ghosh a n d R Κ Ray

Microstructure and Texture Development in Warm Rolled High Strength IF Steels Containing Cu, Ρ and Β 161

Arunansu Haldar and Ch i radeep Ghosh

Effect of Tin on the Texture of Nonoriented Electrical Steels 173 C h u n - K a n Hou , T o n g - H a n Lee, and Chun-Ch ih Liao

vi · Mater ials Processing and Texture

Effect of Cold Rolled Reduction on the Texture and Plastic Strain Ratio of 2205 Duplex Stainless Steel 183

C h u n - K a n Hou and C h a n g - C h i a Liu

Importance of Dislocation Substructures in Texture Control of Low Carbon Steel 193

Hirosuke Inagaki

Texture Control in Manufacturing Current and Future Grades of Low-Carbon Steel Sheet 207

Leo A. I . Kestens and R o u m e n Petrov

Relative Preference for Strain Localizations in Ultra Low Carbon Steel 217

R. Khatirkar, L.A.I. Kestens, R. Petrov, and I. S a m a j d a r

Influence of Texture on Surface-Roughening during Press Forming in Ti Added High Purity Ferritic Stainless Steel Sheets 223

Ken Kimura, M a s a h a r u Hatano , and Akihiko Takahashi

Effect of Tin on the Recrystallization Behavior and Texture of Grain Oriented Electrical Steels 231

Chun-Ch ih Liao, C h u n - K a n H o u

EBSD Investigation of Phase Transformation in Low Carbon Steels 243 Sophie Lubin, Anne-Françoise Gourgues-Lorenzon , Hé lène Regle, Frank

Monthei l let , and Brigitte Bacroix

A Monte-Carlo Algorithm for the Zener Drag Effect in the Fe-3%Si Magnetic Alloys 251

N. M a a z i , R. Penelle, A. L. Etter, and T. Baudin

Effect of Strain and Strain Path on Deformation Twinning and Strain Induced Martensite in AISI 316L and 304L Austenitic Stainless Steel 257

S. K. Mishra, P. Pant , K. Naras imhan and I. S a m a j d a r

Analysis of the Formation and Growth of Recrystallizing Grains in IF Steels by In-Situ EBSP 265

H. Nakamich i and F. J . Humphreys

Stability of Secondary Recrystallization in Grain-Oriented Silicon Steel 275

Eiichi N a m b a , Satoshi Arai, Ho taka H o m m a , and Yoshiyuki Ushigami

A Practical Investigation into Identifying and Differentiating Phases in Steel using Electron Backscatter Diffraction 285

M a t t h e w M. Nowel l , Stuart I. Wright , and John O. Carpenter

Materials Processing and Texture vii

Influence of Precipitate Distribution on Normal Grain Growth Simulation at the Beginning of the Secondary Recrystallization Annealing in a Fe-3%Si Electrical Steel HiB - Role of the MnS and AIN Precipitates 293

C. Sekkak , N. Rouag , and R. Penel le

Microstructure and Texture Development during Cold Ring Rolling of 100Cr6 301

K. Ryttberg, M. Knutson W e d e l , L. Nyborg , and P. Dah lman

Development of Texture, Microstructure and Grain Boundary Character Distribution after Heavy Cold Rolling and Annealing in a Boron Added Interstitial Free (IF) Steel 311

Rajib S a n a and R. K. Ray

Texture of Nb-Containing Ferritic Stainless Steel after Secondary Recrystallization 317

Rodrigo P. Siqueira, H u g o R. Z . S a n d i m , and Tarcisio R. Oliveira

Quantitative Prediction of Transformation Texture in Hot-Rolled Steel Sheets by Multiple KS Relation 325

Toshiro T o m i d a , Masayuk i Wak i ta , Mitsuru Yoshida, and Norio Imai

Crystallographic Characterization of a Phosphorus Added TRIP Steel 333

Kim Verbeken , Liesbeth Barbé , and Dierk R a a b e

Microstructural and Textural Evolutions in a Cold Rolled High Mn TWIP Steel 341

Kim V e r b e k e n , Lieven Bracke, Leo Kestens, and Jan Penning

Stored Energy Evolution in a Cold-Rolled IF Steel 349 A. Wauthier , B. Bacroix, T. C h a u v e a u , O. Caste lnau, and H. Réglé

A Comparison of Texture Measurements Via EBSD and X-RAY 357 Stuart I. Wright and M a t t h e w M . Nowel l

The Measurement Approach of X-Ray Residual Stress in Fe-Ni Alloy with Different Textures 365

Qiulin W u , Xiaojun H u , Zuming Fu, Haiyan Z h a o , Bing Z h a n g , Y o n g W a n g ,

We i Fang , and Limin Li

Influence of Grain Orientation on Magnetic Aging Behavior of a Non-Oriented Silicon Steel Sheet 371

L. Xu, W . M a o , P. Y a n g , a n d H. Feng

viii · Mater ials Processing and Texture

EFFECTS OF MAGNETIC FIELDS

Eutectoid Point Shift and Orientation Relationships between Ferrite and Cementite in Pearlite in a High Magnetic Field 381

Y. D. Z h a n g , C . Esling, H. Klein, X. Z h a o , and L. Z u o

Characteristics of Recrystallization Texture of Cold-Rolled IF Steel Sheet Annealed with a Magnetic Field in the Transverse Direction 389

Y a n W u , C h a n g s h u He , Y u d o n g Z h a n g , Xiang Z h a o , Liang Z u o , and

C l a u d e Esling

Crystallographic Features during Martensitic Transformation in Ni-Mn-Ga Ferromagnetic Shape Memory Alloys 397

D. Y. C o n g , Y. D. Z h a n g , C. Esling, Y. D. W a n g , X. Z h a o , and L. Zuo

Grain Boundary Misorientation and CSL in Magnetically Annealed Fe-0.75%Si 405

C . M . B . Bacal tchuk, G.A. Caste l lo -Branco, and H. Garmestani

The Effect of Ultra-High Magnetic Fields on Grain Growth and Recrystallization in Metals 413

A . D . Sheikh-Ali and H. Garmestani

New Approach to Texturing and Grain Boundary Engineering by Magnetic Field Application 421

T a d a o W a t a n a b e , Sadahi ro T su r ekawa , Y u d o n g Z h a n g , Xiang Z h a o , Liang

Z u o , and C laude Esling

Effects of Magnetic Field Direction on Texture Evolution in a Cold-Rolled IF Steel Sheet during High Magnetic Field Annealing 435

Y a n W u , C h a n g s h u He , Xiang Z h a o , and Liang Z u o

HEXAGONAL METALS Electrochemical Behavior of (001), (100) and (110) Ti Single Crystals under Simulated Body Fluid Condition 443

M . Azzi , S . Faghihi, M . Tabr iz ian, and J . A. Szpunar

Identification and Rationalization of Secondary Twin Variants in a Magnesium Alloy 451

M . R. Barnett a n d P. Cizek

Textures in HCP Titanium and Zirconium: Influence of Twinning 461 Nathal ie Bozzolo and Francis W a g n e r

Texture and Microstructure Evolution during Asymmetric Rolling of Mg Alloys 473

Jaehyung C h o , H y u n g - W u k Kim, and S u k - B o n g Kang

Mater ia ls Processing and Texture • ix

Prediction of Anisotropic Properties in Mg Alloy Sheets Using the Crystal Plasticity Finite Element Method 483

S . - H . Choi , J.K. Choi , H.W. Lee, and D .H . Kim

Strain Hardening Behaviour of an Initially Textured TI6AL4V Titanium Alloy as a Function of Strain Rate and Compression Direction 491

Frederik C o g h e , Luc Rabet , and Paul V a n Hout te

Texture Evolution during the Static Recrystallization of Three Binary Mg-Y Alloys 501

R. C o t t a m , J . R o b s o n , G. Lorimer, and B. Davis

Grain Size and Orientation Distribution Function of High Purity α-Titanium 509

Bradley S. F r o m m , Brent L. A d a m s , S a d e g h A h m a d i , and M a r k o Knezevic

Textures in Titanium Alloys - An Industrial Perspective on Deformation, Transformation and Properties 521

David Rugg , David Furrer, and Nigel Brewitt

Annealing Related Microstructural Developments in a Two-Phase ZR-2.5 Nb Alloy 533

V . D . Hiwarkar, S.K. Sahoo , I. Samajdar , K. Naras imhan, Κ. V. Mani krishna,

G.K. Dey, D. Srivastav, R. Tiwari , a n d S . Banarjee

Texture Aspects of Delayed Hydride Cracking in Products from Zr-Based Alloys 539

Margar i ta Isaenkova a n d Yuriy Perlovich

Effect of Twinning on the Strain Hardening Behaviors of Two Mg Alloys Deformed Along Four Different Strain Paths 547

L. Jiang and J .J . Jonas

EBSD Study of Annealing Rolled Zirconium 555 L. J iang, M.T. P é r e z - P r a d , O.A. Ruan , and M.E. Kassner

Texture Evolution during Multi-Pass Equal Channel Angular Extrusion of Beryllium 563

Saiyi Li, David J . Alexander , Irene J . Beyerlein, and Donald W . Brown

A Mechanism of Determining the Formability of AZ31 near Room Temperature 571

Hualong Li, Emilie Hsu , and Jerzy Szpunar

An EBSD Study of the Misorientations Related to Dynamic Recrystallization in Mg AM30 Deformed At High Temperatures 577

Etienne Mart in , S t é p h a n e G o d e t , Lan J iang, Abde lbaset Elwazri , Pascal J .

Jacques , and John J . Jonas

χ · Mater ials Processing a n d Texture

Texture Evolution in Boron Modified Ti-6AI-4V Alloy 585 Shibayan Roy, Nilesh Gurao , S a t y a m S u w a s , S. Tamir isakandala , R. Srinivasan,

a n d D.B. Miracle

Heterogeneous Deformation in Single-Phase Zircaloy 2 593 S. Κ. S a h o o , V. D. Hiwarkar, I. Samajdar , P. Pant, D. Srivastav, R. Tewar i ,

G. K. Dey and S. Banerjee

Texture of Magnesium Alloy Sheets Heavily Rolled by High Speed Warm Rolling 601

Tetsuo Saka i , Satoshi Minamiguchi , Hiroaki Koh, and Hiroshi Utsunomiya

Microstructure and Texture Gradient in Titanium Severely Strained by Friction Roll Processing and Subsequent Annealing 609

Meiqin Shi , Tomohi ro U m e t s u , Yosh imasa T a k a y a m a , Ha j ime Kato, and

H ideo W a t a n a b e

Evolution of Transformation Texture in a Metastable ß-Titanium Alloy 617

S a t y a m S u w a s , Nilesh P. Gurao , Ashkar Ali

Dislocations in Textured Mg-4.5%AI-1 %Zn Alloy: TEM and Statistical Studies 629

V . N . T imofeev, V . N . Serebryany, and Yu A. Zal iznyak

Microstructure and Micro-Texture Evolution of Compression Twins in Magnesium 637

P. Y a n g , L. M e n g , Χ. Li, W . M a o , and L. C h e n

TEXTURE IN MATERIALS DESIGN

Accessing the Texture Hull and Properties Closure by Rotation and Lamination: Results in the Primitive Basis of Dilation Functions 647

Brent L. A d a m s and David T. Ful lwood

Correlation Relationship between Yield Strength and the Elastic Compliance for the Polycrystalline Nickel 201 657

S a d e g h A h m a d i , Brent L. A d a m s , David T. Ful lwood, and Bradley S. F romm

Modeling Rolling Texture of Twinned Cu Single Crystals 665 Khaled Al -Fadhalah , A r m a n d Beaudoin , and M a r e k N iewczas

Multiscale Modeling of Equal Channel Angular Extruded Aluminum with Strain Gradient Crystal Plasticity and Phenomenological Models 671

L. Duchêne , M . G . D . Geers , W . A . M . Brekelmans, E. C h e n , B. Verl inden, and

A . M . Habraken

Mater ials Processing and Texture · xi

Effect of Deformation Constraints on the Texture Formation in Al-5mass%Mg Solid Solution at High Temperatures 679

Kazuto O k a y a s u , Masayuk i Sakak ibara , and Hiroshi Fukutomi

Spectral Methods in the Statistical Description and Design of Microstructure 687

D.T. Ful lwood, B.L. A d a m s , K.A. S tevens , S.R. N iezgoda , and S.R. Kalidindi

A Comparison of Deformation Textures and Mechanical Properties Predicted by Different Crystal Plasticity Codes 701

Craig S. Hart ley, Paul R. D a w s o n , Donald E. Boyce , Surya R. Kalidindi, M a r k o

Knezevic, Carlos T o m é , Ricardo Lebensohn, S . Lee Semiat in , T o d d J . Turner,

and A y m a n A. S a l e m

Simulation of Texture Development in Pure Aluminum Deformed by Equal Channel Angular Pressing 713

Majid Hoseini , M a h m o o d Merat ian , Hualong Li, and Jerzy Szpunar

Plastic Heterogeneity Due to Grain Boundaries and Its Influence on Global Deformation Textures 721

Anand Κ Kanjarla, Paul Van Hout te , and Laurent Delannay

On the Correlation of Surface Texture and Strain Induced Surface Roughness in AA6XXX Aluminum Sheet 731

S. Küsters, M . Seefeldt , and P. V a n Hout te

The Variation Range for the Results of FCC Texture Simulations Based on {111 } Slip 743

Torben Letters

Development of Low Magnetism and Strongly Cube-Textured Composite Ni-7%W/Ni-10%W Substrate for Coated Superconductor 751

Dan-min Liu, Fei H a o , Jiu-xing Z h a n g , Y a n - c a o H u , Mei- l ing Z h o u , a n d

W e i - p e n g Liu

Two-Point Orientation Coherence Functions: An Orthonormal Series Solution 759

Peter R. Morris

The Influence of Shear Bands on Microtexture Evolution in Polycrystalline Copper 765

H. Paul and J . H . Driver

Influence of Dislocation Stress on the Corrosion Behavior of (111) and (123) Surface Plane of Aluminum Single Crystal 775

Dashi Pei , We imin M a o , and Huiping Feng

xii · Mater ials Processing and Texture

Texture Randomization by Intense Shearing in Layered AI and AI (0.3%Sc) ARB-Processed Sheet 783

M.Z. Quadir , O. A l - B u h a m a d , L. B a s s m a n , a n d M . Ferry

Texture Development of Molybdenum Sheets during Last Step of Heat Treatment 791

C . - G . Oerrel , I. Hünsche , W . Skrotzki , A. Lorich, and W . Knabl

Solute, Superplasticity and Texture Change in Aluminium Alloys 801 K. S o t o u d e h , P.S. Bate , and F.J. H u m p h r e y s

Texture-Based Plastic Potentials in Stress Space 809 Albert Van Bael , S a m p a t h K. Yerra, Paul Van Hout te , and Albert Van Bael

Hierarchical Multi-Level Modelling of Plastic Anisotropy using Convex Plastic Potentials 817

Paul V a n Hout te , S a m p a t h K. Yerra, and Albert Van Bael

Author Index 827

Materials Processing and Texture xiii

Preface

It has been a pleasure, of a rather hard working type, to edit the proceedings for the

15th International Conference on Textures of Materials (ICOTOM 15). First and

foremost I acknowledge the hard work and time that the symposium organizers

have devoted to this task. This represents truly a community effort to sustain the de-

velopment of this field o f materials research.

Texture, or crystallographic orientation, plays an important role in many differ-

ent areas of materials research and development. It grew out of metallurgical pro-

cessing but now is significant to geology, welding, thin films, electronic devices,

fuel cells, biomaterials and other applications too numerous to list. I am pleased that

this meeting brings together such a broad range of interests. The papers included in

this Ceramic Transactions volume (as well as its companion volume—Ceramic

Transactions Volume 201 , Applications of Texture Analysis) illustrate this broad

range of applicability o f the tools. Friction Stir Welding has undergone extensive

development in recent years so it is appropriate that this volume has an entire sec-

tion on the topic. Texture development and its effect on properties in steels remains

of great interest to the community. Hexagonal metals such as titanium have greatly

increased their range o f applications so it is not surprising that texture is an essential

aspect o f these complex alloy systems. Magnetic fields have a strong effect on

many materials and their influence on processing and resulting textures has attract-

ed substantial interest. Lastly, materials design is being placed on a much firmer

theoretical and computational foundation, as is evident in the work reported here. I

have no doubt that the community will find these proceedings as essential in their

work as they have for all the previous ICOTOM conferences.

I would like to thank the many colleagues who helped in organizing the confer-

ence and especially Dr. Carlos Tomé of Los Alamos who put together the work-

shops that are such a distinctive feature of this conference. Many of these individu-

als also made substantial contributions to the review process o f the proceedings.

Their names are listed on the Acknowledgments page.

I also thank the National Science Foundation, the Air Force Office of Scientific

Research and the Alcoa Technical Center for their support of the conference. Their

XV

sponsorship made it possible for the many young scientists and engineers to attend

the conference. The staff of The American Ceramic Society (ACerS) were unfail-

ingly supportive and professional in their management of the conference. The Min-

erals, Metals and Materials Society (TMS) also played an important role in devel-

oping the workshops. I thank the many students and staff who contributed to the

smoothing running and organization of the meeting.

A . D . TONY ROLLETT

Carnegie Mellon University

xvi · Mater ials Processing and Texture

Acknowledgments

Conference proceedings co-editors

Brent Adams, Brigham Young University, U S A

Katayun Barmak, Carnegie Mellon University, U S A

Thomas Bieler, Michigan State University, USA

Keith Bowman, Purdue University, USA

Paul Dawson, Cornell University, U S A

Roger Doherty, Drexel University, U S A

OlafEngler, Hydro Aluminium Deutschland GmbH and R&D Center, Germany

Hamid Garmestani, Georgia Institute of Technology, U S A

Amit Goyal, Oak Ridge National Laboratory, USA

Erik Hilinski, US Steel, U S A

Roland Loge, The Centre for Materials Forming, France

S. Lee Semiatin, Air Force Research Laboratory, U S A

Robert Suter, Carnegie Mellon University, U S A

Carlos Tomé, Los Alamos National Laboratory, U S A

Sven Vogel, Los Alamos National Laboratory, U S A

Hasso Weiland, Alcoa Technical Center, U S A

Stuart Wright, EDAX-TSL, U S A

xvii

Friction Stir Welding and Processing

TEXTURE EVOLUTION DÜRING FRICTION STIR WELDING OF STAINLESS STEEL

Jaehyung Cho Korea Institute of Materials Science, 66 Sangnam-dong, Changwon-city, Kyungnam, South Korea 641-010 Email: jhcho@ kims.re.kr

ABSTRACT Texture evolution during ruction stir welding (FSW) of stainless steel was investigated using

both experimental measurements and model predictions based on a polycrystal plasticity. Material undergoes heating and deformation sufficient to alter its microstructural state during FSW. Texture evolution is quite complex in FSW, owing in particular to its dynamics under the induced stirring motion. Modeling approaches help to better understand how the stirring can both strengthen and weaken textures, which is an essential element in a complete description of texturing during FSW. In a two-dimensional way, texture stability is addressed from the computed velocity gradients along streamlines of the flow field. The texture is assumed to be uniform initially and shows monoclinic sample symmetry after deformation. Upstream and downstream of the tool, the deformation is nearly monotonie, causing little change of the texture. Around the tool pin, the texture strengthens, weakens, and restrengthens. The mixture of pure and simple shear textures was found. The effects of frictional conditions with the tool pin and shoulder on the complicated flow and texture evolution in the through thickness were examined with a three-dimensional approach. Trends in regard to strengthening and weakening of the texture were discussed in terms of the relative magnitudes of the deformation rate and spin. The computed textures were compared to EBSD measurements and were discussed with respect to distributions along orientation fibers and the dominant texture component along the fibers.

1. INTRODUCTION

Material undergoes severe heating and deformation during friction stir welding (FSW) and its microstructural features, such as texture, grain size and shape changed. Material in the weld zone experiences strains large enough to drive the texture toward a few dominant components. Dynamic recrystallization is found, particularly in aluminum alloys because of the elevated temperatures present around the tool. Materials flow is so complicated and texture evolution is also dynamic and complex.

A number of studies characterizing the texture alterations and variations of the mechanical responses have been reported [1]. From electron backscatter diffraction (EBSD) measurements of various aluminum alloys, it has been shown that severe texture gradients exist through the thickness direction and across the width of parts joined by FSW. Shear-type texture components, which are rotated from the ideal shear components [2], often are observed. From a microtexture analysis after postweld heat treatment, dynamic recrystallization during FSW generates the recrystallized grains at the weld center instead of static recrystallization [3]. Using a stop-action method, the initial stages of texture evolution ahead of the pin in Al-Li 2195 alloys have been examined [4, 5] . The primary mechanism of grain refinement appeared to be grain subdivision induced by deformation, although the initial grain refinement seemed to be followed by continuous dynamic recrystallization and recovery [4]. The fine subgrains ahead of the tool display a typical fee shear texture after suitable rotation. In addition to grain subdivision, geometric dynamic recrystallization was suggested to contribute the ultrafined grain structure with shear orientations in the nugget [5]. The recrystallization phenomenon during FSW of 304L stainless steel was examined in Ref. [6]. The dynamically recrystallized grains have two types of orientation distributions, i.e., textures with one dominant component and distributions along the adjacent fiber.

Texture evolution can be computed by coupling the finite element solution for the material

3

Texture Evolution during Friction Stir We ld ing of Stainless Steel

motion with crystal plasticity for texture analysis. Crystal flow over orientation space is driven by a reorientation velocity field that smoothly varies. Some orientations are stable under a monotonie deformation. While, there are no stable components for torsion textures even though the deformation remains monotonie to large strains. The relationship between the derivatives of the reorientation velocity at ideal orientations and the local flows around the orientations was explored in [7], The dynamical behavior of crystal flows was analyzed for idealized planar crystals in [8]. Consideration of flow dynamics also has been reported in the case of a flow field that does not exhibit equilibria. The continuous flow associated with simple shear (torsion) in terms of the structure of the reorientation velocity field was investigated in [9, 10]. An analysis of the stability of texture components in fee systems under simple and pure shear modes of deformation was also presented in [11].

The focus of this paper is on modeling texture evolution in 304L stainless steel as it is altered by the FSW process and on comparing the computed textures to ones measured using EBSD. The material response during FSW was modeled using an isotropic, strain hardening, viscoplastic constitutive equation in a strongly coupled thermomechanica! formulation. The model equations were solved in an Eulerian reference frame for both two-dimensional and two-dimensional geometries using a finite element method [12, 13]. Temperature and strength distributions from the simulations were compared with experimental results. Based on the material response in two-dimensional model, studies on the cry stallographic texture evolution focused on an examination of the dynamics of the texture evolution. It was found that some combinations of the symmetric and skew parts of the velocity gradient induced constantly changing texture patterns, while others promoted monotonie texturing. The effect of friction between the tool and the workpiece on the three dimensionality of the flow was investigated and its consequences regarding texture evolution was discussed. It is considered how the material rotation impacts the strength of the texture and the occurrence of fiber textures and strong texture components. Finally, predicted textures were compared with ones measured by EBSD over a cross section of the welded plate. A three-dimensional schematic diagram illustrating the FSW process is shown in Fig. 1.

Figure 1. A schematic diagram of the friction stir welding process.

2. MODEL GEOMETRY AND BOUNDARY CONDITIONS The complete FSW process includes the plunge, dwelling, main welding, and pull-out operations.

For simplicity, a stress was placed on the main welding process during successful steady-state welding. During the welding, the effects of the tool pin and shoulder produce complex material motions. More details on two- and three-dimensional modeling are found in references [12, 13].

4 Mater ia ls Processing and Tex ture

Texture Evolution during Friction Stir W e l d i n g of Stainless Steel

Figs. 2(a) and 2(b) display two- and three-dimensional discretized meshes of FSW. The three-dimensional model (Fig. 2b) has both the tool shoulder (surface 6) and tool pin (surface 5), while in the two-dimensional model (Fig. 2a) only the tool pin is considered. Elements are concentrated near the tool surface where gradients of the velocity and temperature are greatest. The tool pin is located in the center of the region and material moves from left to right. The tool spins clockwise with an angular velocity, Ω, of 5rad/s. Therefore, the lower part of the region corresponds to the advancing side and the upper part to the retreating side. Boundary conditions and model geometries are listed in Table 1.

Friction boundary conditions were used to represent the contact condition between the workpiece and the tool pin and shoulder. On the shoulder, the friction coefficients were allowed to linearly decrease with radial distance. On the tool pin, the friction coefficients were constant, but an axial component of traction was added to simulate the pin thread effect. The ratio of the axial component to the tangential component determines the thread angle. It is known that the tool shoulder generates more heat than the tool pin. Even with the lower friction coefficient in these simulations, the tool shoulder effect remains dominant in deformation and heating.

Table I. Boundary conditions for FSW models

Type Translation

iT, [mmIs] Rotation

Ω [radis] Pin angle

[Deg] Shoulder On/off

Geometry Pm radius[mm]

Geometry Shoulder radius [mm]

2D 1.7 5 N/A N/A to N/A 3D 1.0 5 5 on 3 12

Note: us is the welding speed; Ω is the angular velocity of the tool pin. Friction coefficients for the shoulder

(ßühmiidcr) linearly decrease with distance from the tool pin, from 150x10* to 150x10° [N-s/m 3 ]. Friction

coefficients for the pin(ßmn) have constant values of 150x109 [N-s/m 3 ] .

(a) (b)

Figure 2. Finite element meshes and overall descriptions of the surface boundary conditions for FSW models. In Fig. 2(a) (2D): Inlet; .Ou t l e t ; _ Top and Bottom (adiabatic); _ Tool pin. In Fig. 2(b) (3D):

Inlet; and Top and Bottom (adiabatic); Outlet; Tool pin; Tool shoulder; Plate to be welded (adiabatic).

Mater ia ls Processing a n d Texture · 5

Texture Evolution during Friction Stir We ld ing of Stainless Stee l

3. MODELING TEXTURE EVOLUTION The FSW tool usually consists of two parts, the shoulder and pin. Both pin and shoulder

contribute to complex, three-dimensional material flow patterns. Visualization techniques have been employed to study the complicated material flow experimentally, as reported in [14, 15]. Simulation of the process also offers the opportunity to better understand the effects of these aspects of the tool geometry on resulting flow and the resulting evolution of microstructure. The simulations presented here utilize a methodology that decouples the computations for the velocity and temperature fields from the integration of the texture evolution equations. The procedure consists of three basic steps. The first step is to compute the velocity and temperature fields over the control volume. This is followed by a step to extract thermomechanical histories along streamlines leading to target positions at the outlet. The final step is to integrate evolution equations for texture along the streamlines using the thermomechanical data. In using this decoupled procedure, it is assumed that the plastic anisotropy present in the yield surface due to crystallographic texture has little influence on the overall flow field. Isotropic strain hardening or softening was allowd, so the overall magnitude of the flow stress does change as material is deformed and heated. Full coupling is possible for other applications, but would require considerably greater execution times for the same spatial resolution [16 ,17] . In this study, greater spatial resolution over full coupling was preferred.

3.1 COMPUTING THE EVOLUTION OF CRYSTALLOGRAPHIC TEXTURE Texture evolution is computed using a framework based on polycrystal plasticity [18] together

with a methodology of integrating the texture along the streamlines. The macroscopic velocity of a representative volume of material at a specified spatial position χ in an Eulerian flow field is n. The velocity gradient L is obtained by taking the spatial gradient of the velocity field L = 3 u / 3 x . This motion at the macroscopic scale is linked to the crystal scale by adopting the extended Taylor hypothesis such that all the crystals comprising the representative volume experience the macroscopic velocity gradient [19]. In the case of the high symmetry crystals and large strains considered here, this is a reasonable approximation. As our attention is focused on regions that experience large deformations, elastic effects are neglected and crystals are assumed to deform solely by crystallographic slip. In this situation, the crystal velocity gradient L c can be decomposed into a shearing along slip systems and a rigid lattice rotation

L = LC = SI+ ΣγαΎ" (1) a

where Ω is the lattice spin, γ° is the shear rate on slip system a, and Τ is the Schmidt tensor. Here, Τ = b ® η , with b , the slip direction, and n, the slip normal for slip system. In this paper, modeling F S W of stainless steel, which has a face-centered cubic (FCC) structure was investigated. For this material, slip is assumed to occur on the {111} planes and in the directions. As b and η are tied to the crystal lattice, Τ is a function of the crystal orientation, defined here using an angle-axis representation r . The skew part of crystal velocity gradient in Eq. (1) yields an expression for the lattice spin

«=w - x r < r (2) where W is the macroscopic spin and Q=skew T . From Ω , the rate of reorientation of the crystal lattice can be written as

r = — ω + (ω • r ) r + c o x r (3)

6 · Mater ia ls Processing a n d Texture


where ω = vect( f t ) . Equation (2) is the evolution equation for the lattice orientation of a specific crystal.

It is integrated for every crystal in a representative volume, or aggregate, over the deformation history

that the aggregate experiences as it flows through the Eulerian domain. The collective responses of all

the crystals within an aggregate define the texture evolution.

The reorientation velocity for a particular crystal at any time depends on the current values of its

slip system shearing rates, γ". A viscoplastic constitutive relation is used to relate the shear rate

on a slip system to the resolved shear stress

τ where τ " = Ρ" • a' (4)

where m is the rate sensitivity, τ is the slip system hardness (assumed identical for all slip systems), γ0 is a reference strain rate, and τα is the resolved shear stress on slip system obtained as the projection of

the crystal stress onto the slip system. P=sym Τ and ac is the deviatoric crystal stress. The rate

sensitivity strongly influences the relative activity of the slip systems with the net effect that under

monotonie loading, weaker textures result from higher rate sensitivity. For the results shown, a value is

given with rate insensitive behavior (TH=0.05). A variable value, ranging from 0.05 at 273 Κ to 0.11 at

1100 Κ was also used to incorporate the effect of greater rate sensitivity with elevation of the

temperature. Qualitatively, the textures were similar, but those computed using variable rate sensitivity

were weaker, as expected. An expression for the crystal stress follows by combining the symmetric part

of crystal velocity gradient equation (1) with Eq. (4):

e r = [ C , ; ] D ' ' (5)

where the stiffness C c depends on the lattice orientation r and is defined as

(6)

and D r is the crystal deviatoric deformation rate. Equation (5) is solved for the crystal stress knowing the current values of the lattice orientation and the crystal deformation rate which under the extended Taylor hypothesis is the same as the macroscopic deformation rate. The slip system shearing rates are subsequently evaluated from Eq. (4) and used in Eq. (2) to compute the lattice spin.

3.2 IDEAL PURE A N D SIMPLE SHEAR TEXTURES During FSW, the basic deformation modes are shearing. Therefore, it is useful to look through

textures computed using the extended Taylor assumption that evolve as a consequence of monotonie straining over two ideal deformation modes: simple shear and pure shear. These deformation modes differ in the amount of spin imposed, which is apparent by decomposing the velocity gradient into symmetric and skew parts to give the deformation rate D and the spin W as

L = D + W (7)

The 111 pole figure in Fig. 3(a) shows the pure shear texture. Note that the pure shear texture possesses symmetries about the lines x=y and x=~y, coinciding with the principal axes of the deformation rate. The 111 pole figure in Fig. 3(b) shows the simple shear texture. The texture is rotated



about the ζ axis from the pure shear texture and the symmetries apparent for pure shear breakdown due to

the effect of the superimposed spin. Shear textures and their associated ideal orientations have been

studied in several experiments [20, 21] and modeling [22, 23 , 24, 25, 26] on cubic polycrystals. Pure

shear possesses a number of stable equilibria, as computed using a linearized stability analysis, in the

reorientation velocity field. The stable equilibria are listed in Table 2 and are displayed in Fig. 3(c) on a

111 pole figure. Only the stable equilibria, meaning that the divergence of the reorientation velocity field

is negative, are shown. Under monotonie loading, the texture will continue to increase in strength at

these points, as can be seen by comparison of Fig. 3(a) with Fig. 3(c). The addition of spin to pure shear

alters the structure of the reorientation velocity field. For simple shear, the spin is sufficient to destroy

the equilibria. Nevertheless, the texture does strengthen under simple shear in the vicinities of the ideal

orientations. The ideal components are listed in Table 3 and shown in Fig. 3(d), along with two ideal

fibers, referred to as the A and Β fibers, {111} and{AW/, respectively. However, as none of the ideal orientations are stable equilibria, the texture will not increase monotonically, but instead will

eventually diminish under continued straining. Thus, although the texture may temporarily increase in

strength under a simple shear deformation, the strengthening will not persist indefinitely, as discussed in

more detail in [25]. As will be shown later, along segments of a streamline, the motion often is

reasonably described by this reduced form of the velocity gradient with differing levels of the spin. The

strengthening and weakening of the textures can be understood in part by comparison to the ideal

shearing textures and by analysis of the flow in terms of level of spin superimposed on shearing

deformations. Such textures might be expected in the FSW process, except that the principal directions

of the deformation rate are constantly changing as the material is swept around the tool pin.

Figure 3. For face-centered cubic crystals, 111 pole figures under (a) pure and (b) simple shear modes of

deformation and the locations of the (c) stable and (d) ideal texture components for pure shear and simple

shear, respectively. Repeated numbers indicate equivalent poles. See Tables 1 and 2 for identification of

the poles.

8 · Mater ia ls Processing a n d Texture

Texture Evolution during Friction Stir We ld ing of Stainless Steel

Table II. Coordinates of stable equilibria for pure shear of FCC. Given as Miller indices, Euler angles, and Rodrigues vector.

Component Nairn; (hkl)[mm] {*,.*. Φ J {rx. rr i-J

1 C (0 I Γ)[7 5 5 ] {45.0. 135.(1. 0 } {04142. 0.1716. 0.4142} •> Bi (1 1 l ) [ l l 4 15] {75.0. 125.2. 45.0 } (-0.3657. 0.3657. 0.0000} V D: (f 1 T ) [ l ! 15 4] {15.0. 125.2. 315.0} {0.3657. -0.3657. 0.0WW} 3 £, (1 1 0)[2i 2~1 95] {72.4. 90.0. 45 .0} {0.4142, -0.0642. -0.1551} y E2 (1 1 0)[67 67 30] {17.6. 90 0 . 4 5 . 0 } {0.0642.-0.4142. 0.1551}

3.3 SIMPLIFIED CIRCULAR STREAMLINE MODEL (2D) There are dynamic variations of velocity gradients around the tool pin. The simplified circular

streamline model provides information on how the symmetric deformation rate and the skew spin affect each other. A simplified circular model is described by a flow along a circular path around the tool pin (small window in the upper-left of Fig. 5a). Consider a local coordinate system with base

Table III. Coordinates of ideal orientations for simple shear of FCC. Given as Miller indices, Euler angles, and Rodrigues vector.

Component Name ( Λ Η Η > · Η · ] { * , . φ . Φυ { ' , . V r.)

1 -»1 (1 I ί)[Ι ί ο ] {Ο. 35.26. 45 } {0.3178 -0.1316 0.4142}

ι ί Γ ΐ ) [ ί ι ο] {IW, 35.26. 45 } {-0.3178 0 1316 0.4142}

3 (I I ί)[2 f 1] {35 26. 45. Ο } {04142 0 1316 0 317»}

4 (I Γ ! ) [ ϊ Γ I ] . {144 74. 45. 0 } {-0.4142 11.1316-CI.3I7X}

5 ß , (I I 2")[1 Î 0 ] {(). 54 74. 45 } {-0.317)1 0.4142 -0.1316}

6 β. (f ί2 ) [Γ 1 0] {ΙΚΟ. 54.74. 45 } {0 3178 -0.4142 -0.1316} 1 C I l 0 01(0 1 I] {90. 45. 0 } {0.(ΚΧΚ> -11.4142 0.Ο0ΟΟ}

vectors that are tangent and normal to the circle. The model velocity gradient is constant in this frame. In the global frame, the velocity gradient is found by a change of basis transformation:

L = R L R T (8)

where L is a local velocity gradient and R is a rotation tensor relating the local and global coordinate systems. The components of symmetric deformation rate in the global reference frame, Du and Dxy,

exhibit distributions of trigonometric functions.

A range of crystal flows developed under arbitrary deformations is generated using different

values of the ratio of the macroscopic spin, Wxy, to the effective deformation rate, DrJf, or JFF^ / .

The condition \WS) I De(l | > | / ? r > / | corresponds to cases in which the reorientation velocity field has

no stable orientations. The pure and simple shear cases are given in Fig. 4. The texture of pure shear (Fig.

4a) results in a monotonie increase in the intensity of several stable orientations. In this case,

\Wtf I Dtl] I < \DV I Dell I . In contrast, the texture of simple shear repeatedly strengthens and weakens. The



distance along the streamline is normalized by the length of the streamline, so that the starting and ending points assume normalized distances of 0 to 1, respectively. Texture indices for both pure and simple shear are shown in Fig. 4(c) and 4(d). The texture index measures the sharpness of ODF (orientation distribution function). The texture index of pure shear increases monotonically toward a saturation value. That of simple shear shows regular oscillation between high and low values.

3.4 TEXTURE PREDICTION USING CRYSTAL PLASTICITY (2D) The velocity gradients used in the circular streamline model maintain a constant ratio between

the magnitudes of the skew and symmetric parts. This results in a regular variation in the texture indices. Unlike the simple circular model, the velocity gradients along the streamlines in FSW modeling vary greatly. In Figure 5(a). the longest streamline, which closely surrounds the tool pin (2D case), can be divided roughly into 12 blocks from LI to L6 and R l to R6. Six of them are located upstream of the tool pin center (from LI to L6) and six are located downstream of the tool pin center (from R6 to R l ) . Each block corresponds to a region of strengthening texture. The small window in the upper right side of Fig. 5(a) is the enlarged figure around the tool pin. It can be seen that the principal directions of the deformation rate are rotating in a similar manner to those in the simplified circular streamline model. This suggests that the dominant shear plane and shear direction are approximately tangent and normal to the tool pin, respectively. The stagnation point and transition region between blocks also are selected to illustrate the texture evolution. The strengthening of texture around the tool pin is displayed in Fig. 5(b) for each of the 12 blocks in Fig. 5(a).

Figure 4. Velocity gradient distributions [ s 1 ] and texture indices around the circle. Local velocity gradients of pure shear and simple shear are shown in (a) and (b), respectively. The corresponding texture indices are shown in (c) and (d).

A global reference frame is given by the x-y-z directions, and the center of pole figures corresponds to the global ζ direction. The local frame around the tool pin is given by another set of axes: one axis

10 Mater ia ls Processing a n d Tex ture

materials processing and texture · in ti added high purity ferritic stainless steel sheets 223 ....

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