Applied RVE Reconstruction and Homogenization of Heterogeneous Materials
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Preface ix
Introduction xiii
Chapter 1 Literature Survey 1
1.1 Random heterogeneous material 1
1.2 Two-point probability functions 2
1.3 Two-point cluster functions 4
1.4 Lineal-path function 4
1.5 Reconstruction 4
1.5.1 X-ray computed tomography (experimental) 4
1.5.2 X-ray computed tomography (applications to nanocomposites) 6
1.5.3 FIB/SEM (experimental) 6
1.5.4 Reconstruction using statistical descriptor (numerical) 10
1.6 Homogenization methods for effective properties 11
1.7 Assumption of statistical continuum mechanics 12
1.8 Representative volume element 13
Chapter 2 Calculation of Two-Point Correlation Functions 15
2.1 Introduction 15
2.2 Monte Carlo calculation of TPCF 17
2.3 Two-point correlation functions of eigen microstructure 19
2.4 Calculation of two-point correlation functions using SAXS or SANS data 21
2.4.1 Case study for structural characterization using SAXS data 24
2.5 Necessary conditions for two-point correlation functions 28
2.6 Approximation of two-point correlation functions 30
2.6.1 Examination of the necessary conditions for the proposed estimation 34
2.6.2 Case study for the approximation of a TPCF 39
2.7 Conclusion 42
Chapter 3 Approximate Solution for N-Point Correlation Functions for Heterogeneous Materials 43
3.1 Introduction 43
3.2 Approximation of three-point correlation functions 45
3.2.1 Decomposition of higher order statistics 45
3.2.2 Decomposition of two-point correlation functions 46
3.2.3 Decomposition of three-point correlation functions 47
3.3 Approximation of four-point correlation functions 51
3.4 Approximation of N-point correlation functions 56
3.5 Results 60
3.5.1 Computational verification 60
3.5.2 Experimental validation 62
3.6 Conclusions 66
Chapter 4 Reconstruction of Heterogeneous Materials Using Two-Point Correlation Functions 67
4.1 Introduction 67
4.2 Monte Carlo reconstruction methodology 69
4.2.1 3D cell generation 72
4.2.2 Cell distribution 75
4.2.3 Cell growth 77
4.2.4 Optimization of the statistical correlation functions 79
4.2.5 Percolation 79
4.2.6 Three-phase solid oxide fuel cell anode microstructure 81
4.2.7 Reconstruction of multiphase heterogeneous materials 82
4.3 Reconstruction procedure using the simulated annealing (SA) algorithm 86
4.4 Phase recovery algorithm 91
4.5 3D reconstruction of non-eigen microstructure using correlation functions 96
4.5.1 Microstructure reconstruction using Monte Carlo methodology 96
4.5.2 Sample production 97
4.5.3 Monte Carlo calculation of a two-point correlation function 98
4.5.4 Microstructure optimization 99
4.5.5 Results and discussion 99
4.6 Conclusion 101
Chapter 5 Homogenization of Mechanical and Thermal Behavior of Nanocomposites Using Statistical Correlation Functions: Application to Nanoclay-based Polymer Nanocomposites 103
5.1 Introduction 103
5.2 Modified strong-contrast approach for anisotropic stiffness tensor of multiphase heterogeneous materials 104
5.3 Strong-contrast approach to effective thermal conductivity of multiphase heterogeneous materials 112
5.4 Simulation and experimental verification 117
5.4.1 Computer-generated model 118
5.4.2 Thermal conductivity 120
5.4.3 Mechanical model 122
5.4.4 Experimental part 125
5.5 Results and discussion 127
5.5.1 Thermal conductivity 127
5.5.2 Thermo-mechanical properties 128
5.6 Conclusion 130
Chapter 6 Homogenization of Reconstructed RVE 133
6.1 Introduction 133
6.2 Finite element homogenization of the reconstructed RVEs 134
6.2.1 Reconstruction of FIB-SEM RVEs 134
6.2.2 Finite element analysis of RVEs 138
6.3 Finite element homogenization of the statistical reconstructed RVEs 141
6.3.1 FEM analysis of reconstruction RVE using statistical correlation functions 141
6.3.2 Finite element analysis of RVEs 143
6.4 FEM analysis of debonding-induced damage model for polymer composites 149
6.4.1 Representative volume element (RVE) 150
6.4.2 Cohesive zone model 152
6.4.3 Material behavior and FE simulation 157
6.4.4 The effect of the GNP's volume fraction and aspect ratio in perfectly bonded nanocomposite 158
6.4.5 Comparing the effect of the GNP's volume fraction and aspect ratio in perfectly bonded and cohesively bonded nanocomposites 160
6.4.6 The effect of the GNP's aspect ratio and volume fraction in weakly bonded nanocomposite 163
6.5 Conclusion and future work 166
Appendices 169
Appendix A 171
Appendix B 175
Bibliography 179
Index 185
