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Crystal Plasticity Model with Back Stress Evolution. Wei Huang Louisiana State University and Agricultural & Mechanical College

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Crystal Plasticity Model with Back Stress Evolution. Wei Huang Louisiana State University and Agricultural & Mechanical College Louisiana State University LSU Digital Commons LSU Historical Dissertations and Theses Graduate School 1996 Crystal Plasticity Model With Back Stress Evolution. Wei Huang Louisiana State University and Agricultural & Mechanical College Follow this and additional works at: https://digitalcommons.lsu.edu/gradschool_disstheses Recommended Citation Huang, Wei, "Crystal Plasticity Model With Back Stress Evolution." (1996). LSU Historical Dissertations and Theses. 6154. https://digitalcommons.lsu.edu/gradschool_disstheses/6154 This Dissertation is brought to you for free and open access by the Graduate School at LSU Digital Commons. It has been accepted for inclusion in LSU Historical Dissertations and Theses by an authorized administrator of LSU Digital Commons. For more information, please contact [email protected]. INFORMATION TO USERS This manuscript has been reproduced from the microfilm master. UMI films the text directly from the original or copy submitted. Thus, some thesis and dissertation copies are in typewriter face, while others may be from any type o f computer printer. The quality of this reproduction is dependent upon the quality of the copy submitted. Broken or indistinct print, colored or poor quality illustrations and photographs, print bleedthrough, substandard margins, and improper alignment can adversely affect reproduction. In the unlikely event that the author did not send UMI a complete manuscript and there are missing pages, these will be noted. Also, if unauthorized copyright material had to be removed, a note will indicate the deletion. Oversize materials (e.g., maps, drawings, charts) are reproduced by sectioning the original, beginning at the upper left-hand comer and continuing from left to right in equal sections with small overlaps. Each original is also photographed in one exposure and is included in reduced form at the back of the book. Photographs included in the original manuscript have been reproduced xerographically in this copy. Higher quality 6” x 9” black and white photographic prints are available for any photographs or illustrations appearing in this copy for an additional charge. Contact UMI directly to order. UMI A Bell & Howell Information Company 300 North Zeeb Road, Ann Arbor MI 48106-1346 USA 313/761-4700 800/521-0600 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. CRYSTAL PLASTICITY MODEL WITH BACK STRESS EVOLUTION A Dissertation Submitted to the Graduate Faculty of the Louisiana State University and Agricultural and Mechanical College in partial fulfillment of the requirements for the degree of Doctor of Philosophy in The Interdepartmental Program in Engineering Science by Wei Huang B.S., Shanghai Jiao Tong University, 1982 M.S., Shanghai Jiao Tong University, 1985 M.S., Louisiana State University, 1991 May 1996 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. UMI Number: 9628308 UMI Microform 9628308 Copyright 1996, by UMI Company. All rights reserved. This microform edition is protected against unauthorized copying under Title 17, United States Code. UMI 300 North Zeeb Road Ann Arbor, MI 48103 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. ACKNOWLEDGMENTS I would like to express my thanks to my beloved advisor Professor George Z. Voyiadjis, who not only guided, supported and encouraged me during my doctoral study, but also made a tremendous effort to make this dissertation become possible. I would also like to thank him for the financial aid that he provided me during this study. I would like to thank other members of my doctoral advisory committee, Professor M. Sabbaghian, Dr. S. S. Peng, Professor J. R. Dorroh and Professor R. Gambrell for reviewing the dissertation and serving in the committee. I wish to thank my colleagues at LSU, Dr. A. R. Venson, Dr. P. U. Kurup, Dr. P. I. Kattan, Mr. R. Echle, Mr. G. Thiagarajan, and Dr. T. Park for many useful discussions and numerous help in the aspect of numerical computation. They also made my stay at LSU a pleasant one. My beloved wife, Yuxian, with whom I have been married for ten years and have two wonderful daughters, Linda and Jennifer, deserves special worlds of thanks. My wife helped and supported me during this study in so many ways that cannot be listed. My parents have been the key roles in my career in pouring me with love and emphasized the importance of education in my life. My father, now a retired electrical engineer, was the first one in my early childhood to introduce many wonderful fields of science and engineering. In recent years, my mother made two trips to the U.S., helping me and my wife take care of our children ii Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. while we were working and studying. It has been a dream for her that I complete this study. I would like to dedicate this dissertation to her. iii Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. TABLE OF CONTENTS ACKNOWLEDGMENTS ....................................................................................... ii LIST OF TABLES ................................................................................................... vi LIST OF FIGURES................................................................................................... vii ABSTRACT ................................................................................................................... ix CHAPTER 1 INTRODUCTION............................................................................. 1 2 THEORETICAL BACKGROUND................................................ 5 2.1 Phenomenological Approach ................................................ 5 2.1.1 Isotropic Strain Hardening ...................................... 6 2.1.2 Kinematic Hardening ............................................... 6 2.1.3 Anisotropic Hardening ............................................ 7 2.2 Crystal Plasticity Approach ................................................ 8 2.2.1 Single Crystal Plasticity ......................................... 8 2.2.2 Concepts of Dislocation and Backstress................................................................... 10 2.2.3 Polycrystal Plasticity ............................................... 16 2.2.4 Current Crystal Plasticity Approaches by Asaro and Needleman and Rashid and Nemat-Nasser ..................................................... 17 2.3 Objectives and Method of Approach .................................. 21 3 THEORETICAL FORMULATION OF CONSTITUTIVE EQUATION ..................................................... 22 3.1 Fundamentals ........................................................................... 22 3.2 The Hardening Rule and the Evolution of the Backstress X ............................................ 25 4 NUMERICAL IMPLEMENTATION ........................................... 32 4.1 Application to the Simple Shear ........................................... 32 4.2 Numerical Results.................................................................. 35 4.2.1 Comparison Between the Two Models .................. 36 4.2.2 Effect of Initial Orientation ................................... 40 4.2.3 Evaluation of Coefficients A, B, C for Model 2 ..................................................... 43 4.2.4 Evaluation of the Interacting Factors qj ................................................................ 49 iv Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 5 DISCUSSION OF RESULTS ......................................................... 52 6 CONTINUUM PLASTICITY THEORY FOR POLYCRYSTALS WITH MICROSTRUCTURAL CHARACTERIZATION................................................................. 56 6.1 Introduction ............................................................................. 56 6.2 Continuum Mechanics and Dislocation T h eo ry ..................................................................................... 56 6.3 Macroscopic Mechanical Behavior of Polycrystalline Materials ............................................... 59 7 PROPOSED FUTURE WORK FOR THE THREE- DIMENSIONAL CASE ................................................................. 65 7.1 "Pan-Cake" Type Polycrystal .............................................. 66 7.2 "Hexagonal Column" Type Polycrystal ............................ 68 8 SUMMARY AND CONCLUSION ................................................. 72 REFERENCES............................................................................................................. 74 A PPEN D IX .................................................................................................................. 79 VITA ............................................................................................................................. 100 v Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. LIST OF TABLES Table 2.1 Designation of slip systems in FCC crystal ................................. 9 Table 4.1 List of different numerical problems conducted ............................ 37 vi Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. LIST OF FIGURES Figure 2.1 A schematic illustration
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