Micro-Macro-Interactions (eBook)

Title Page 2
Preface 5
Contents 7
Part I Inelastic Material Behaviour of Polycrystals 10
Normal Grain Growth: Monte Carlo Potts Model Simulation and Mean-Field Theory 11
Introduction 11
Monte Carlo Potts Model Simulation 12
Monte Carlo Simulation Results 15
Coarsening Process: Growth Law, Scaling Regime and Grain Size Distribution 15
Topology: Number of Faces vs. Grain Size 17
Volumetric Rate of Change 18
Mean-Field Theory 20
Comparison of Simulation with Experimental Measurements and Analytical Theory 21
Conclusions 23
References 24
Microstructural Influences on Tensile Properties of hpdc AZ91 Mg Alloy 27
Introduction 27
Experimental Procedures 28
Results and Discussion 29
Macro Properties 29
Microstructure 31
Fracture Behaviour 34
Micro-Macro Interactions 34
Summary and Conclusions 37
References 38
On Different Strategies for Micro-Macro Simulations of Metal Forming 40
Introduction 40
The Isotropic Background Model (IB) 42
The Continuous Taylor Model (CT) 42
The Two Scale Model (TS) 44
Conclusions 45
References 45
Simulation of Texture Development in a Deep Drawing Process 47
Introduction 47
Constitutive Equations 48
Model Identification and Finite Element Simulation 50
Results and Discussion 51
Summary and Conclusions 56
References 56
Modelling and Simulation of the Portevin-Le Chatelier Effect 58
Physical and Mechanical Characteristics of the PLC Effect 58
Experimental Findings 59
Micromechanical Mechanisms 60
Modelling of the PLC Effect 60
Comparison of Experimental Findings with Simulation 63
Further Numerical Results Compared to Experimental Findings in the Literature 64
Conclusions 65
References 65
Plastic Deformation Behaviour of Fe-Cu Composites 67
Introduction 67
Experiment 68
Polycrystal Modelling 69
Constitutive Model 69
Finite Element Simulation 71
Results and Discussion 72
Stress-Strain Flow Behaviour 72
Crystallographic Texture 76
Local Strain Distribution 77
Summary 79
References 79
Regularisation of the Schmid Law in Crystal Plasticity 81
Introduction 81
Framework of Non-hardening Crystal Plasticity 82
The Effect of Regularization in Polyslip Situations in Two Dimensions 85
Analytical Examination with a Reduction on Two Dimensions 85
Examination of the Parameters 88
Numerical Examination 91
Conclusion 93
References 94
A Lower Bound Estimation of a Twinning Stress for Mg by a Stress Jump Analysis at the Twin-Parent Interface 96
Introduction 96
Notation 98
Geometrical Description 98
A Schmid Law for Twinning 98
Stress Jump at the Twin Interface 100
Special Cases: $n_{IF}$ Equals $n_{T}$ or $d_{T}$ 103
Arbitrary Alignment of the Interface and the Effect on the Schmid Stress 104
Lower Bound Estimation of a Twinning Stress for Mg 104
Pole Figures of Some Interesting Quantities Regarding the Stress Jump 105
Conclusions 106
References 107
Appendix 108
Part II Fibre and Particle Reinforced Solids 110
Numerical Evaluation of Effective Material Properties of Piezoelectric Fibre Composites 111
Introduction 111
Piezoelectricity and Piezoelectric Composites 112
Numerical Homogenisation Technique 113
Generation of RVE Models 114
Periodic Boundary Conditions 114
Finite Element Modelling of RVE 116
Boundary Conditions for Evaluation of the Different Effective Coefficients 116
Results and Discussion 117
Effect of the Fibre Diameter on Effective Material Properties 118
Comparison of Effective Material Properties for Different Arrangement of Fibres 118
Conclusions 120
References 121
Evolutionary Optimisation of Composite Structures 123
Introduction 123
Evolution Strategies 125
Applications 126
First Example: Topology Optimisation 127
Second Example: Optimisation of Short Fibre Reinforced Composites 128
Third Example: Laminate Ply Angle Optimisation 131
Conclusions 132
References 132
Fibre Rotation Motion in Homogeneous Flows 134
Introduction 134
Basic Assumptions 135
Constitutive Equation for the Hydrodynamic Moment 137
Solutions to Equations of Motion 137
Resting Medium 138
Rotational Flow 139
Elliptic Flow 140
Shear Flow 141
Conclusions 142
References 143
Part III Solids under Thermal Stressing 144
Distortion and Residual Stresses during Metal Quenching Process 145
Introduction 145
Mathematical Formulation 146
Thermal Field 146
Phase Transformation Field 147
Displacement Field 148
Solution Methodology 151
Thermal Field Formulation 151
Phase Field Formulation 152
Displacement Field Formulation 152
Structural Application 153
Results and Discussions 154
Concluding Remarks 157
References 157
Micro Model for the Analysis of Spray Cooling Heat Transfer – Influence of Droplet Parameters 158
Introduction 158
Modelling of Heat Transfer 159
Micro-macro Interactions 159
Droplet Spreading with Time 161
Temperature Field 162
Evaporation Efficiency and HTC 164
Results and Discussion 165
Conclusions 169
References 170
Finite Element Simulation of an Impinging Liquid Droplet 172
Introduction 172
Model for an Impinging Droplet 172
Dynamic Contact Angle 173
Interface Capturing and Tracking Methods 174
Volume of Fluid (VOF) Method 175
Level Set Method 175
Front Tracking Method 176
Arbitrary Lagrangian Eulerian (ALE) Approach 176
Eulerian vs. Lagrangian 177
Topological Issues 177
Spurious Velocities 177
Algorithmic and Computational Issues 178
Verification and Validation 179
ALE Approach for Computations of an Impinging Droplet 179
References 182
Pore-Scale Modelling of Transport Phenomena in Drying 185
Introduction 185
Account of Pore Size Distribution in Continuous Modelling 186
Account of Pore Structure in Discrete Pore Network Model 191
Extension of Transport Phenomena in Pore Network Model 194
Viscous Effect on Capillary Flow 194
Thermal Effect on Capillary Flow and Vapour Diffusion 197
Conclusion and Outlook 199
References 200
Part IV Dynamics of Particles and Particle Systems 203
Micro and Macro Aspects of the Elastoplastic Behaviour of Sand Piles 204
Introduction 204
Simulation Method 205
Stress Calculation 206
Determining Strains 207
Analytic Descriptions 208
Simulation Results 210
Comparison with Theory 212
Conclusions 214
References 215
Micro-Macro Deformation and Breakage Behaviour of Spherical Granules 217
Introduction 217
Experimental Methods and Materials 218
Experimental Results 220
Force-Displacement Behaviour during Compression 220
Breakage Probability of Granules during Normal Impact 222
Simulation of the Granules Breakage with Discrete Element Method 224
Simulation Data 224
Simulation Results 225
Conclusions 228
References 228
Investigations of the Restitution Coefficient of Granules 230
Introduction 230
Testing Method and Material 231
Experimental Results and Discussion 233
Conclusions 235
References 236
Oblique Impact Simulations of High Strength Agglomerates 237
Introduction 237
Finite and Discrete Element Modelling 238
Result and Discussions 239
Finite Element Simulation 239
Discrete Element Simulation 241
Conclusions 246
References 247
Shear Dynamics of Ultrafine Cohesive Powders 248
Introduction 248
Contact Forces between Single Particles and Contact Constitutive Models 249
Reference Shear Experiments 250
Simulations 252
Conclusions 255
References 256
CFD-Modelling of the Fluid Dynamics in Spouted Beds 258
Introduction 258
CFD-Multiphase Modelling 258
Gas-Particle Drag Models 260
Simulation Results 262
Conclusions 267
References 267
Numerical Study of the Influence of Diffusion of Magnetic Particles on Equilibrium Shapes of a Free Magnetic Fluid Surface 269
Introduction 269
Mathematical Model 269
Computational Algorithm 273
Numerical Results 274
References 276
A Note on Sectional and Finite Volume Methods for Solving Population Balance Equations 277
Introduction 277
Numerical Methods for One-Dimensional PBEs 279
The Cell Average Technique 279
The Finite Volume Technique 282
Numerical Methods for Two-Dimensional PBEs 283
Reduced Model Approach 283
Complete Model Approach 287
Conclusions 287
References 288
Population Balance Modelling for Agglomeration and Disintegration of Nanoparticles 290
Introduction 290
Experimental Condition 291
Characterisation of TiO2 Nanoparticles 292
Population Balance Equation 294
Results and Discussion 296
Conclusions 298
References 299
Author Index 301