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The-Generation-Of-Internal-Stresses-In THE GENERATION OF INTERNAL STRESSES IN SINGLE AND TWO PHASE MATERIALS A thesis submitted to the University of Manchester for the degree of Doctor of Philosophy in the Faculty of Science and Engineering September 2002 By Edward Charles Oliver Manchester Materials Science Centre Contents Abstract 6 Declaration 7 Copyright 8 Publications 9 Acknowledgements 10 Notation and Nomenclature 11 1 Introduction 14 2 Internal Stress Development in Single and Two Phase Materials 16 2.1 Definitions and Origins of Internal Stress and Residual Stress . 16 2.1.1 Thermal Misfit . 18 2.1.2 Heterogeneous Plastic Flow . 18 2.1.3 Phase transformations . 18 2.2 The Concept of Eigenstrain . 20 2.3 The Eshelby Theory . 20 2.3.1 The Homogeneous Ellipsoidal Inclusion . 20 2.3.2 The Equivalent Inclusion Method . 21 2.4 Elastic Properties of Heterogeneous Solids . 22 2.4.1 Single Crystal Elastic Anisotropy . 24 2.4.2 Voigt and Reuss Elastic Averages . 25 2.4.3 Eshelby-Based Approximations . 25 2.5 Plastic Deformation of Single Crystals . 28 2.5.1 Slip in Single Crystals . 29 2.5.2 Deformation Twinning . 32 2.5.3 Martensitic Transformation . 34 2.6 Plastic Properties of Polycrystals . 35 2.6.1 Sachs model . 35 2.6.2 Taylor model . 35 2.6.3 Bishop and Hill Analysis . 37 2.6.4 Elastoplastic Self-Consistent Model . 37 2.6.5 Crystal Plasticity Finite Element Method . 40 2.7 Plastic Properties of Composites . 42 2.7.1 Forward and Reverse Yield Stress . 43 2.7.2 Plastic Relaxation . 43 2.7.3 Finite Element Method . 44 2.8 Martensitic Transformation . 45 2 2.8.1 Experimental Observations of Martensitic Transformation . 45 2.8.2 Crystallographic Theories of Martensitic Transformation . 46 3 Measurement of Internal Stress by Neutron Diffraction 50 3.1 Bragg Diffraction as a Strain Gauge . 50 3.1.1 The Bragg Condition . 50 3.1.2 Fixed Wavelength Diffractometry . 51 3.1.3 Time-of-Flight Diffractometry . 51 3.2 Determination of Elastic Strains from Diffraction Spectra . 52 3.2.1 Elastic Grain Family Strains via Single Peak Fitting . 52 3.2.2 Elastic Phase Strains via Rietveld Refinement . 53 3.3 The ENGIN Instrument . 54 3.3.1 Flight Path . 55 3.3.2 Collimation . 55 3.3.3 Detector Banks . 55 3.3.4 Loading Rig . 56 3.3.5 Cooling Grips . 56 3.4 Review of Type II Internal Stress Measurements Using Neutron Diffraction . 57 3.4.1 Intergranular Stress . 57 3.4.2 Interphase Stress . 61 3.4.3 Stress-Induced Martensitic Transformation . 63 4 Interphase and Intergranular Stress In Carbon Steels 66 4.1 Materials Review . 67 4.2 Materials . 68 4.3 Neutron Diffraction Method . 69 4.4 Macroscopic Response . 70 4.5 Interphase Strains . 72 4.5.1 Strains Under Applied Loading . 73 4.5.2 Residual Strains . 76 4.5.3 Unrelaxed Model . 78 4.6 Intergranular Strains . 80 4.6.1 Strains Under Applied Loading . 80 4.6.2 Residual Strains . 84 4.7 Reproducibility of Data and Influence of Crystallographic Texture . 86 4.7.1 Reproducibility of Data . 88 4.7.2 Influence of Crystallographic Texture . 90 4.8 Rationalisation of Transverse Intergranular Strains in Ferrite . 90 4.9 Investigation into Intergranular Stress in Ferrite using the Elastoplastic Self- Consistent Method . 95 4.9.1 Model Specification . 96 4.9.2 Comparison of EPSC Predictions With Experimental Data . 97 4.9.3 Influence of Elastic Anisotropy . 100 4.9.4 Summary of Findings from the EPSC Model . 101 4.10 Note on Linear Elastic Response of Transverse Grain Families . 102 4.11 Finite Element Model of Interphase Stress in High Carbon Steel . 106 4.11.1 FE Model Design . 106 4.11.2 Constituent Properties . 106 4.11.3 Extent of Constraint . 107 4.11.4 Comparison of FE Model Predictions With Experimental Data . 108 4.11.5 Summary of Findings from FE Model of Interphase Stress . 111 4.12 Combined Model of High Carbon Steel . 111 4.12.1 Combined Modelling Strategy . 112 3 4.12.2 Combined Model Results . 112 4.12.3 Comparison of Combined Model Approach With Two Phase EPSC Model 114 4.13 Summary of Chapter . 120 5 Stress-Induced Martensitic Transformation in TRIP Steel 122 5.1 Review of Transformation-Induced Plasticity (TRIP) . 122 5.1.1 Overview . 122 5.1.2 Observed Features of the TRIP Phenomenon . 123 5.1.3 Models of Stress-Induced Transformation in TRIP Steels . 126 5.2 Materials . 128 5.3 Characterisation of Microstructure and Mechanical Behaviour . 129 5.3.1 As-Received Microstructure . 129 5.3.2 Ms Temperature . 129 5.3.3 Mechanical Behaviour . 129 5.3.4 Martensite Volume Fraction . 132 5.3.5 Influence of Hot Swaging . 133 5.4 Evolution of Crystallographic Texture . 138 5.5 Neutron Diffraction Method . 138 5.6 Macroscopic Response During Neutron Diffraction Tests . 139 5.7 Evolution of Diffraction Spectra and Observation of Preferential Transformation 140 5.7.1 Texture Prior to Testing . 140 5.7.2 Development of Martensite . 142 5.7.3 Changes in Austenite Texture . 144 5.7.4 Summary . 146 5.8 Orientation Dependence of Transformation . 147 5.9 Rietveld Refinement . 150 5.10 Martensite Volume Fraction . 151 5.11 Elastic Phase Strains . 152 5.11.1 Elastic Strain in Austenite . 153 5.11.2 Elastic Strain in Martensite . 156 5.11.3 Discussion and Comparison with High Carbon Steel . 157 5.12 Intergranular Strain in Austenite . 160 5.13 Elastoplastic Self-Consistent Simulation of Deformation in Austenite . 163 5.13.1 Simulation of Unswaged Material . 163 5.13.2 Simulation of Hot Swaged Material . 165 5.14 Summary of Chapter . 168 6 Conclusions and Suggestions for Further Work 170 6.1 Summary and Conclusions . 170 6.2 Suggestions for Further Work . 172 4 Abstract The subject of this dissertation is the generation of internal stresses arising from mechanical deformation in single and two phase engineering materials. The method of neutron diffraction is employed to study the evolution of both intergranular and interphase stresses in low and high carbon ferritic steels and in an austenitic steel which exhibits stress-induced martensitic transformation. In low carbon steel, intergranular stresses develop.
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