Meso-Scale Modeling of Polycrystal Deformation DISSERTATION

....................................................................................................................... ii DEDICATION................................................................................................................... iv ACKNOWLEDGEMENTS................................................................................................ v VITA.................................................................................................................................. vi PUBLICATIONS............................................................................................................... vi FIELDS OF STUDY......................................................................................................... vii TABLE OF CONTENTS.................................................................................................viii LIST OF TABLES............................................................................................................. xi LIST OF FIGURES ......................................................................................................... xiii 1. INTRODUCTORY NOTE.......................................................................................... 1 2. BACKGROUND......................................................................................................... 3 2.1 Polycrystal Plasticity Models ............................................................................... 4 2.2 Theories on Evolution of Dislocation Densities in Plasticity Models ................. 7 2.3 HallPetch Law.................................................................................................. 11 3. SINGLE CRYSTAL CONSTITUTIVE EQUATIONS............................................ 22 3.1 Abstract .............................................................................................................. 22 ix 3.2 Introduction ........................................................................................................ 23 3.3 Crystal Plasticity based on Single Crystal Constitutive Equations .................... 29 3.3.1 Common Elements of SCCE-T and SCCE-D............................................. 30 3.3.2 Single-Crystal Constitutive Equations developed for Texture models (SCCE-T)................................................................................................................... 31 3.3.3 Single-Crystal Constitutive Equations based on the Dislocation density model (SCCE-D) ....................................................................................................... 32 3.4 CP-FEM Implementation ................................................................................... 36 3.5 Prediction of Single Crystal Stress-strain Response .......................................... 37 3.6 Prediction of stress-strain response and texture evolution in polycrystals......... 53 3.7 Role of qlat/qself in SCCE-T ................................................................................ 59 3.8 Conclusions ........................................................................................................ 60 4. TWO-SCALE MODEL............................................................................................. 62 4.1 Abstract .............................................................................................................. 62 4.2 Introduction ........................................................................................................ 63 4.3 Simulation Procedures........................................................................................ 66 4.3.1 Grain-Scale Simulation (GSS).................................................................... 69 4.3.2 Meso-Scale Simulation (MSS) ................................................................... 72 4.3.3 1D stressed pileup....................................................................................... 80