Bertram / Tomas Micro-Macro-Interactions

In Structured Media and Particle Systems
1. Auflage 2008
ISBN: 978-3-540-85715-0
Verlag: Springer Berlin Heidelberg
Format: PDF
Kopierschutz: 1 - PDF Watermark

E-Book, Englisch, 312 Seiten

Reihe: Engineering

Many materials or media in nature and technology possess a microstructure which determines their macroscopic behaviour. The knowledge of the relevant mechanisms is often more comprehensive on the micro than on the macro scale. On the other hand, not all information on the micro level is relevant for the understanding of this macro behaviour. Therefore, averaging and homogenization methods are needed to select only the specific information from the micro scale, which influences the macro scale. These methods also open the possibility to design or to influence microstructures with the objective to optimize their macro behaviour. This book presents the development of new methods in this interdisciplinary field of macro- micro-interactions of different engineering branches like mechanical and process engineering, applied mathematics, theoretical, and computational physics. In particular, solids with microstructures and particle systems are considered.

Autoren/Hrsg.

Bertram, Albrecht

Tomas, Jürgen

Inhaltsverzeichnis

1;Title Page;2
2;Preface;5
3;Contents;7
4;Part I Inelastic Material Behaviour of Polycrystals;10
4.1;Normal Grain Growth: Monte Carlo Potts Model Simulation and Mean-Field Theory;11
4.1.1;Introduction;11
4.1.2;Monte Carlo Potts Model Simulation;12
4.1.3;Monte Carlo Simulation Results;15
4.1.3.1;Coarsening Process: Growth Law, Scaling Regime and Grain Size Distribution;15
4.1.3.2;Topology: Number of Faces vs. Grain Size;17
4.1.3.3;Volumetric Rate of Change;18
4.1.4;Mean-Field Theory;20
4.1.5;Comparison of Simulation with Experimental Measurements and Analytical Theory;21
4.1.6;Conclusions;23
4.1.7;References;24
4.2;Microstructural Influences on Tensile Properties of hpdc AZ91 Mg Alloy;27
4.2.1;Introduction;27
4.2.2;Experimental Procedures;28
4.2.3;Results and Discussion;29
4.2.3.1;Macro Properties;29
4.2.3.2;Microstructure;31
4.2.3.3;Fracture Behaviour;34
4.2.3.4;Micro-Macro Interactions;34
4.2.4;Summary and Conclusions;37
4.2.5;References;38
4.3;On Different Strategies for Micro-Macro Simulations of Metal Forming;40
4.3.1;Introduction;40
4.3.2;The Isotropic Background Model (IB);42
4.3.3;The Continuous Taylor Model (CT);42
4.3.4;The Two Scale Model (TS);44
4.3.5;Conclusions;45
4.3.6;References;45
4.4;Simulation of Texture Development in a Deep Drawing Process;47
4.4.1;Introduction;47
4.4.2;Constitutive Equations;48
4.4.3;Model Identification and Finite Element Simulation;50
4.4.4;Results and Discussion;51
4.4.5;Summary and Conclusions;56
4.4.6;References;56
4.5;Modelling and Simulation of the Portevin-Le Chatelier Effect;58
4.5.1;Physical and Mechanical Characteristics of the PLC Effect;58
4.5.2;Experimental Findings;59
4.5.3;Micromechanical Mechanisms;60
4.5.4;Modelling of the PLC Effect;60
4.5.5;Comparison of Experimental Findings with Simulation;63
4.5.6;Further Numerical Results Compared to Experimental Findings in the Literature;64
4.5.7;Conclusions;65
4.5.8;References;65
4.6;Plastic Deformation Behaviour of Fe-Cu Composites;67
4.6.1;Introduction;67
4.6.2;Experiment;68
4.6.3;Polycrystal Modelling;69
4.6.3.1;Constitutive Model;69
4.6.3.2;Finite Element Simulation;71
4.6.4;Results and Discussion;72
4.6.4.1;Stress-Strain Flow Behaviour;72
4.6.4.2;Crystallographic Texture;76
4.6.4.3;Local Strain Distribution;77
4.6.5;Summary;79
4.6.6;References;79
4.7;Regularisation of the Schmid Law in Crystal Plasticity;81
4.7.1;Introduction;81
4.7.2;Framework of Non-hardening Crystal Plasticity;82
4.7.3;The Effect of Regularization in Polyslip Situations in Two Dimensions;85
4.7.3.1;Analytical Examination with a Reduction on Two Dimensions;85
4.7.3.2;Examination of the Parameters;88
4.7.3.3;Numerical Examination;91
4.7.4;Conclusion;93
4.7.5;References;94
4.8;A Lower Bound Estimation of a Twinning Stress for Mg by a Stress Jump Analysis at the Twin-Parent Interface;96
4.8.1;Introduction;96
4.8.1.1;Notation;98
4.8.1.2;Geometrical Description;98
4.8.2;A Schmid Law for Twinning;98
4.8.3;Stress Jump at the Twin Interface;100
4.8.3.1;Special Cases: $n_{IF}$ Equals $n_{T}$ or $d_{T}$;103
4.8.3.2;Arbitrary Alignment of the Interface and the Effect on the Schmid Stress;104
4.8.4;Lower Bound Estimation of a Twinning Stress for Mg;104
4.8.5;Pole Figures of Some Interesting Quantities Regarding the Stress Jump;105
4.8.6;Conclusions;106
4.8.7;References;107
4.8.8;Appendix;108
5;Part II Fibre and Particle Reinforced Solids;110
5.1;Numerical Evaluation of Effective Material Properties of Piezoelectric Fibre Composites;111
5.1.1;Introduction;111
5.1.2;Piezoelectricity and Piezoelectric Composites;112
5.1.3;Numerical Homogenisation Technique;113
5.1.3.1;Generation of RVE Models;114
5.1.3.2;Periodic Boundary Conditions;114
5.1.3.3;Finite Element Modelling of RVE;116
5.1.3.4;Boundary Conditions for Evaluation of the Different Effective Coefficients;116
5.1.4;Results and Discussion;117
5.1.4.1;Effect of the Fibre Diameter on Effective Material Properties;118
5.1.4.2;Comparison of Effective Material Properties for Different Arrangement of Fibres;118
5.1.5;Conclusions;120
5.1.6;References;121
5.2;Evolutionary Optimisation of Composite Structures;123
5.2.1;Introduction;123
5.2.2;Evolution Strategies;125
5.2.3;Applications;126
5.2.3.1;First Example: Topology Optimisation;127
5.2.3.2;Second Example: Optimisation of Short Fibre Reinforced Composites;128
5.2.3.3;Third Example: Laminate Ply Angle Optimisation;131
5.2.4;Conclusions;132
5.2.5;References;132
5.3;Fibre Rotation Motion in Homogeneous Flows;134
5.3.1;Introduction;134
5.3.2;Basic Assumptions;135
5.3.3;Constitutive Equation for the Hydrodynamic Moment;137
5.3.4;Solutions to Equations of Motion;137
5.3.4.1;Resting Medium;138
5.3.4.2;Rotational Flow;139
5.3.4.3;Elliptic Flow;140
5.3.4.4;Shear Flow;141
5.3.5;Conclusions;142
5.3.6;References;143
6;Part III Solids under Thermal Stressing;144
6.1;Distortion and Residual Stresses during Metal Quenching Process;145
6.1.1;Introduction;145
6.1.2;Mathematical Formulation;146
6.1.2.1;Thermal Field;146
6.1.2.2;Phase Transformation Field;147
6.1.2.3;Displacement Field;148
6.1.3;Solution Methodology;151
6.1.3.1;Thermal Field Formulation;151
6.1.3.2;Phase Field Formulation;152
6.1.3.3;Displacement Field Formulation;152
6.1.3.4;Structural Application;153
6.1.4;Results and Discussions;154
6.1.5;Concluding Remarks;157
6.1.6;References;157
6.2;Micro Model for the Analysis of Spray Cooling Heat Transfer – Influence of Droplet Parameters;158
6.2.1;Introduction;158
6.2.2;Modelling of Heat Transfer;159
6.2.2.1;Micro-macro Interactions;159
6.2.2.2;Droplet Spreading with Time;161
6.2.2.3;Temperature Field;162
6.2.2.4;Evaporation Efficiency and HTC;164
6.2.3;Results and Discussion;165
6.2.4;Conclusions;169
6.2.5;References;170
6.3;Finite Element Simulation of an Impinging Liquid Droplet;172
6.3.1;Introduction;172
6.3.2;Model for an Impinging Droplet;172
6.3.2.1;Dynamic Contact Angle;173
6.3.3;Interface Capturing and Tracking Methods;174
6.3.3.1;Volume of Fluid (VOF) Method;175
6.3.3.2;Level Set Method;175
6.3.3.3;Front Tracking Method;176
6.3.3.4;Arbitrary Lagrangian Eulerian (ALE) Approach;176
6.3.4;Eulerian vs. Lagrangian;177
6.3.4.1;Topological Issues;177
6.3.4.2;Spurious Velocities;177
6.3.4.3;Algorithmic and Computational Issues;178
6.3.4.4;Verification and Validation;179
6.3.5;ALE Approach for Computations of an Impinging Droplet;179
6.3.6;References;182
6.4;Pore-Scale Modelling of Transport Phenomena in Drying;185
6.4.1;Introduction;185
6.4.2;Account of Pore Size Distribution in Continuous Modelling;186
6.4.3;Account of Pore Structure in Discrete Pore Network Model;191
6.4.4;Extension of Transport Phenomena in Pore Network Model;194
6.4.4.1;Viscous Effect on Capillary Flow;194
6.4.4.2;Thermal Effect on Capillary Flow and Vapour Diffusion;197
6.4.5;Conclusion and Outlook;199
6.4.6;References;200
7;Part IV Dynamics of Particles and Particle Systems;203
7.1;Micro and Macro Aspects of the Elastoplastic Behaviour of Sand Piles;204
7.1.1;Introduction;204
7.1.2;Simulation Method;205
7.1.2.1;Stress Calculation;206
7.1.2.2;Determining Strains;207
7.1.3;Analytic Descriptions;208
7.1.4;Simulation Results;210
7.1.5;Comparison with Theory;212
7.1.6;Conclusions;214
7.1.7;References;215
7.2;Micro-Macro Deformation and Breakage Behaviour of Spherical Granules;217
7.2.1;Introduction;217
7.2.2;Experimental Methods and Materials;218
7.2.3;Experimental Results;220
7.2.3.1;Force-Displacement Behaviour during Compression;220
7.2.3.2;Breakage Probability of Granules during Normal Impact;222
7.2.4;Simulation of the Granules Breakage with Discrete Element Method;224
7.2.4.1;Simulation Data;224
7.2.4.2;Simulation Results;225
7.2.5;Conclusions;228
7.2.6;References;228
7.3;Investigations of the Restitution Coefficient of Granules;230
7.3.1;Introduction;230
7.3.2;Testing Method and Material;231
7.3.3;Experimental Results and Discussion;233
7.3.4;Conclusions;235
7.3.5;References;236
7.4;Oblique Impact Simulations of High Strength Agglomerates;237
7.4.1;Introduction;237
7.4.2;Finite and Discrete Element Modelling;238
7.4.3;Result and Discussions;239
7.4.3.1;Finite Element Simulation;239
7.4.3.2;Discrete Element Simulation;241
7.4.4;Conclusions;246
7.4.5;References;247
7.5;Shear Dynamics of Ultrafine Cohesive Powders;248
7.5.1;Introduction;248
7.5.2;Contact Forces between Single Particles and Contact Constitutive Models;249
7.5.3;Reference Shear Experiments;250
7.5.4;Simulations;252
7.5.5;Conclusions;255
7.5.6;References;256
7.6;CFD-Modelling of the Fluid Dynamics in Spouted Beds;258
7.6.1;Introduction;258
7.6.2;CFD-Multiphase Modelling;258
7.6.3;Gas-Particle Drag Models;260
7.6.4;Simulation Results;262
7.6.5;Conclusions;267
7.6.6;References;267
7.7;Numerical Study of the Influence of Diffusion of Magnetic Particles on Equilibrium Shapes of a Free Magnetic Fluid Surface;269
7.7.1;Introduction;269
7.7.2;Mathematical Model;269
7.7.3;Computational Algorithm;273
7.7.4;Numerical Results;274
7.7.5;References;276
7.8;A Note on Sectional and Finite Volume Methods for Solving Population Balance Equations;277
7.8.1;Introduction;277
7.8.2;Numerical Methods for One-Dimensional PBEs;279
7.8.2.1;The Cell Average Technique;279
7.8.2.2;The Finite Volume Technique;282
7.8.3;Numerical Methods for Two-Dimensional PBEs;283
7.8.3.1;Reduced Model Approach;283
7.8.3.2;Complete Model Approach;287
7.8.4;Conclusions;287
7.8.5;References;288
7.9;Population Balance Modelling for Agglomeration and Disintegration of Nanoparticles;290
7.9.1;Introduction;290
7.9.2;Experimental Condition;291
7.9.3;Characterisation of TiO2 Nanoparticles;292
7.9.4;Population Balance Equation;294
7.9.5;Results and Discussion;296
7.9.6;Conclusions;298
7.9.7;References;299
8;Author Index;301