Capolungo Atomistic and Continuum Modeling of Nanocrystalline Materials

Deformation Mechanisms and Scale Transition
1. Auflage 2010
ISBN: 978-0-387-46771-9
Verlag: Springer-Verlag
Format: PDF
Kopierschutz: Adobe DRM (»Systemvoraussetzungen)

E-Book, Englisch, 480 Seiten

Atomistic and Continuum Modeling of Nanocrystalline Materials develops a complete and rigorous state-of-the-art analysis of the modeling of the mechanical behavior of nanocrystalline (NC) materials. Among other key topics, the material focuses on the novel techniques used to predict the behavior of nanocrystalline materials. Particular attention is given to recent theoretical and computational frameworks combining atomistic and continuum approaches. Also, the most relevant deformation mechanisms governing the response of nanocrystalline materials are addressed and discussed in correlation with available experimental data.

Autoren/Hrsg.

Capolungo, Laurent

Inhaltsverzeichnis

1;Preface;6
2;Contents;8
3;Introduction;13
3.1;What Are Nanocrystalline Materials?;16
3.2;A Brief History;17
3.3;Modeling Tools;19
3.4;References;22
4;Fabrication Processes;23
4.1;1.1 One-Step Processes;25
4.1.1;1.1.1 Severe Plastic Deformation;25
4.1.1.1;1.1.1.1 ECAP;25
4.1.1.1.1;Microstructure;28
4.1.1.2;1.1.1.2 High-Pressure Torsion;29
4.1.1.2.1;Microstructure;30
4.1.2;1.1.2 Electrodeposition;31
4.1.3;1.1.3 Crystallization from an Amorphous Glass;32
4.2;1.2 Two-Step Processes;34
4.2.1;1.2.1 Nanoparticle Synthesis;34
4.2.1.1;1.2.1.1 Mechanical Alloying;34
4.2.1.1.1;Grain Refinement Mechanism;36
4.2.1.2;1.2.1.2 Physical Vapor Deposition;39
4.2.1.2.1;Evaporation of the Metal Source;40
4.2.1.2.2;Condensation of the Vaporized Metal;42
4.2.1.2.3;Growth and Collection of Nanoparticle Clusters;43
4.2.2;1.2.2 Powder Consolidation;44
4.2.2.1;1.2.2.1 Cold Compaction;45
4.2.2.2;1.2.2.2 Sintering;46
4.2.2.3;1.2.2.3 Hot Isostatic Pressing;46
4.3;1.3 Summary;47
4.4;References;47
5;Structure, Mechanical Properties, and Applications of Nanocrystalline Materials;50
5.1;2.1 Structure;50
5.1.1;2.1.1 Crystallites;51
5.1.1.1;2.1.1.1 Dislocations;51
5.1.1.2;2.1.1.2 Twins;53
5.1.1.3;2.1.1.3 Stacking Faults;53
5.1.2;2.1.2 Grain Boundaries;54
5.1.3;2.1.3 Triple Junctions;58
5.2;2.2 Mechanical Properties;58
5.2.1;2.2.1 Elastic Properties;60
5.2.1.1;2.2.1.1 Yield Stress;61
5.2.2;2.2.2 Inelastic Response;63
5.2.2.1;2.2.2.1 Ductility;63
5.2.2.2;2.2.2.2 Flow Stress;65
5.2.2.3;2.2.2.3 Strain Rate Sensitivity;66
5.2.2.4;2.2.2.4 Thermal Stability;67
5.3;2.3 Summary;71
5.4;References;72
6;Bridging the Scales from the Atomistic to the Continuum;74
6.1;3.1 Introduction;74
6.2;3.2 Viscoplastic Behavior of NC Materials;75
6.3;3.3 Bridging the Scales from the Atomistic to the Continuum in NC: Challenging Problems;79
6.3.1;3.3.1 Mesoscopic Studies;80
6.3.1.1;3.3.1.1 Computing Structure and Interfacial Energies of Boundaries;80
6.3.1.2;3.3.1.2 Kinetics of Dislocation Nucleation and Motion;83
6.3.1.3;3.3.1.3 Mesoscopic Simulations of Nanocrystals;85
6.3.2;3.3.2 Continuum Micromechanics Modeling;86
6.3.2.1;3.3.2.1 Thermodynamic Construct for Activation Energy of Nucleation and Competition of Bulk and Interface Dislocation Structures;86
6.3.2.2;3.3.2.2 Kinetics of Boundary-Bulk Interactions, Emission, and Absorption;92
6.3.2.3;3.3.2.3 Incorporation of Grain Boundary Network into Self-Consistent Scheme;94
6.4;References;96
7;Predictive Capabilities and Limitations of Molecular Simulations;101
7.1;4.1 Equations of Motion;102
7.2;4.2 Interatomic Potentials;105
7.2.1;4.2.1 Lennard Jones Potential;106
7.2.2;4.2.2 Embedded Atom Method;107
7.2.3;4.2.3 Finnis-Sinclair Potential;109
7.3;4.3 Relation to Statistical Mechanics;110
7.3.1;4.3.1 Introduction to Statistical Mechanics;111
7.3.2;4.3.2 The Microcanonical Ensemble (NVE);113
7.3.3;4.3.3 The Canonical Ensemble (NVT);115
7.3.4;4.3.4 The Isobaric Isothermal Ensemble (NPT);117
7.4;4.4 Molecular Dynamics Methods;117
7.4.1;4.4.1 Nosé Hoover Molecular Dynamics Method;117
7.4.2;4.4.2 Melchionna Molecular Dynamics Method;120
7.5;4.5 Measurable Properties and Boundary Conditions;121
7.5.1;4.5.1 Pressure: Virial Stress;121
7.5.2;4.5.2 Order: Centro-Symmetry;122
7.5.3;4.5.3 Boundaries Conditions;122
7.6;4.6 Numerical Algorithms;125
7.6.1;4.6.1 Velocity Verlet and Leapfrog Algorithms;125
7.6.2;4.6.2 Predictor-Corrector;126
7.7;4.7 Applications;128
7.7.1;4.7.1 Grain Boundary Construction;128
7.7.2;4.7.2 Grain Growth;130
7.7.3;4.7.3 Dislocation in NC Materials;132
7.7.3.1;4.7.3.1 Dislocation Nucleation and Propagation;132
7.7.3.2;4.7.3.2 Dislocation Twin Boundary Interaction;134
7.8;4.8 Summary;135
7.9;References;136
8;Grain Boundary Modeling;137
8.1;5.1 Simple Grain Boundaries;138
8.2;5.2 Energy Measures and Numerical Predictions;139
8.3;5.3 Structure Energy Correlation;141
8.3.1;5.3.1 Low-Angle Grain Boundaries: Dislocation Model;142
8.3.2;5.3.2 Large-Angle Grain Boundaries;146
8.3.2.1;5.3.2.1 CSL Model;147
8.3.2.1.1;Introduction to the O Lattice;149
8.3.2.1.1.1;Geometry;149
8.3.2.1.1.2;Significance;150
8.3.2.2;5.3.2.2 Structural Units Models;150
8.3.2.3;5.3.2.3 Disclination Models;154
8.3.2.3.1;Introduction to Disclination and Disclination Dipoles;154
8.3.2.3.2;Relationship to Excess Energy Between Cusps;157
8.4;5.4 Applications;158
8.4.1;5.4.1 Elastic Deformation: Molecular Simulations and the Structural Unit Model;158
8.4.2;5.4.2 Plastic Deformation: Disclination Model and Dislocation Emission;159
8.5;5.5 Summary;161
8.6;References;162
9;Deformation Mechanisms in Nanocrystalline Materials;163
9.1;6.1 Experimental Insight;163
9.2;6.2 Deformation Map;165
9.3;6.3 Dislocation Activity;167
9.4;6.4 Grain Boundary Dislocation Emission;171
9.4.1;6.4.1 Dislocation Geometry;173
9.4.2;6.4.2 Atomistic Considerations;174
9.4.3;6.4.3 Activation Process;175
9.4.4;6.4.4 Stability;177
9.5;6.5 Deformation Twinning;177
9.6;6.6 Diffusion Mechanisms;179
9.6.1;6.6.1 Nabarro-Herring Creep;181
9.6.2;6.6.2 Coble Creep;182
9.6.3;6.6.3 Triple Junction Creep;183
9.7;6.7 Grain Boundary Sliding;183
9.7.1;6.7.1 Steady State Sliding;183
9.7.2;6.7.2 Grain Boundary Sliding in NC Materials;185
9.8;6.8 Summary;187
9.9;References;187
10;Predictive Capabilities and Limitations of Continuum Micromechanics;189
10.1;7.1 Introduction;189
10.2;7.2 Continuum Micromechanics: Definitions and Hypothesis;190
10.2.1;7.2.1 Definition of the RVE: Basic Principles;191
10.2.1.1;7.2.1.1 Ergodic Condition;192
10.2.1.2;7.2.1.2 Macrohomogeneity Condition and Resulting Properties;194
10.2.2;7.2.2 Field Equations and Averaging Procedures;195
10.2.2.1;7.2.2.1 Field Equations and Boundary Conditions;195
10.2.2.2;7.2.2.2 Volume Averages of Stress and Strain Fields;198
10.2.2.2.1;Traction Boundary Conditions;198
10.2.2.2.2;Displacement Boundary Conditions;198
10.2.2.3;7.2.2.3 Hill Lemma;200
10.2.3;7.2.3 Concluding Remarks;202
10.3;7.3 Mean Field Theories and Eshelby’s Solution;203
10.3.1;7.3.1 Eshelby’s Inclusion Solution;204
10.3.2;7.3.2 Inhomogeneous Eshelby’s Inclusion: ‘‘Constraint’’ Hill’s Tensor;206
10.3.3;7.3.3 Eshelby’s Problem with Uniform Boundary Conditions;208
10.3.4;7.3.4 Basic Equations Resulting from Averaging Procedures;210
10.4;7.4 Effective Elastic Moduli for Dilute Matrix-Inclusion Composites;213
10.4.1;7.4.1 Method Using Equivalent Inclusion;213
10.4.2;7.4.2 Analytical Results for Spherical Inhomogeneities and Isotropic Materials;216
10.4.3;7.4.3 Direct Method Using Green’s Functions;219
10.5;7.5 Mean Field Theories for Nondilute Inclusion-Matrix Composites;221
10.5.1;7.5.1 The Self-Consistent Scheme;222
10.5.2;7.5.2 Interpretation of the Self-Consistent;226
10.5.3;7.5.3 Mori-Tanaka Mean Field Theory;228
10.5.3.1;7.5.3.1 Mori Tanaka’s Two-Phase Model;228
10.5.3.2;7.5.3.2 Mori Tanaka’s Mean Field Theory;232
10.6;7.6 Multinclusion Approaches;235
10.6.1;7.6.1 The Composite Sphere Assemblage Model;235
10.6.2;7.6.2 The Generalized Self-Consistent Model of Christensen and Lo;236
10.6.3;7.6.3 The n +1 Phases Model of Herve and Zaoui;239
10.7;7.7 Variational Principles in Linear Elasticity;240
10.7.1;7.7.1 Variational Formulation: General Principals;241
10.7.1.1;7.7.1.1 Extreme Variational Principle in Linear Elasticity;242
10.7.1.1.1;Minimum Potential Energy Principle;242
10.7.1.1.2;Application: The Voigt bound;245
10.7.1.1.3;Minimum Complementary Potential Energy Principle;246
10.7.1.1.4;Application: Reuss Bound;248
10.7.2;7.7.2 Hashin-Shtrikman Variational Principles;250
10.7.3;7.7.3 Application: Hashin-Shtrikman Bounds for Linear Elastic Effective Properties;257
10.8;7.8 On Possible Extensions of Linear Micromechanics to Nonlinear Problems;263
10.8.1;7.8.1 The Secant Formulation;266
10.8.1.1;7.8.1.1 The Classical Method;268
10.8.1.2;7.8.1.2 Modified Secant Method;270
10.8.2;7.8.2 The Tangent Formulation;276
10.8.2.1;7.8.2.1 The Kröner’s Approach;276
10.8.2.2;7.8.2.2 Hill’s Self-Consistent Model;279
10.8.2.3;7.8.2.3 Illustrations in the Case of Conventional Polycrystalline Materials;281
10.8.2.4;7.8.2.4 On Time-Dependent Behavior of Polycrystalline Materials;288
10.9;7.9 Illustrations in the Case of Nanocrystalline Materials;292
10.9.1;7.9.1 Volume Fractions of Grain and Grain-Boundary Phases;293
10.9.2;7.9.2 Linear Comparison Composite Material Model;293
10.9.2.1;7.9.2.1 Christensen and Lo’s Solutions;294
10.9.2.2;7.9.2.2 Luo and Weng’s Eigenstrain Problem;295
10.9.2.3;7.9.2.3 The Superposed Solution of Jiang and Weng;296
10.9.3;7.9.3 Constitutive Equations of the Grains and Grain Boundary Phase;297
10.9.4;7.9.4 Application to a Nanocystalline Copper;298
10.10;References;302
11;Innovative Combinations of Atomistic and Continuum: Mechanical Properties of Nanostructured Materials;305
11.1;8.1 Introduction;305
11.2;8.2 Surface/Interface Structures;309
11.2.1;8.2.1 What Is a Surface?;309
11.2.2;8.2.2 Dispersion, the Other A/V Relation;309
11.2.3;8.2.3 What Is an Interface?;310
11.2.4;8.2.4 Different Surface and Interface Scenarios;310
11.2.4.1;8.2.4.1 Liquid/Vapor Interface (Fig. 8.3);310
11.2.4.2;8.2.4.2 Solid/Vapor Interface (Fig. 8.4);311
11.2.4.3;8.2.4.3 Solid/Liquid Interface (Fig. 8.5);312
11.2.4.4;8.2.4.4 Liquid/Liquid Interface (Fig. 8.6);312
11.2.4.5;8.2.4.5 Solid/Solid Interface (Fig. 8.7);312
11.3;8.3 Surface/Interface Physics;313
11.3.1;8.3.1 Surface Energy;314
11.3.2;8.3.2 Surface Tension and Liquids;315
11.3.2.1;8.3.2.1 Physical Cause;316
11.3.2.2;8.3.2.2 Surface Tension in Everyday Life;316
11.3.2.3;8.3.2.3 Basic Physics Definitions;318
11.3.3;8.3.3 Surface Tension and Solids;319
11.3.3.1;8.3.3.1 Origin of Surface Tension for a Crystal;319
11.4;8.4 Elastic Description of Free Surfaces and Interfaces;320
11.4.1;8.4.1 Definition of Interfacial Excess Energy;321
11.4.2;8.4.2 Surface Elasticity;321
11.4.3;8.4.3 Surface Stress and Surface Strain;322
11.5;8.5 Surface/Interfacial Excess Quantities Computation;322
11.6;8.6 On Eshelby’s Nano-Inhomogeneities Problems;323
11.7;8.7 Background in Nano-Inclusion Problem;324
11.7.1;8.7.1 The Work of Sharma et al.;324
11.7.2;8.7.2 The Work by Lim et al.;325
11.7.3;8.7.3 The Work by Yang;327
11.7.4;8.7.4 The Work by Sharma and Ganti;330
11.7.5;8.7.5 The Work of Sharma and Wheeler;333
11.7.6;8.7.6 The Work by Duan et al.;335
11.7.6.1;8.7.6.1 Bulk Modulus;337
11.7.6.2;8.7.6.2 Shear Modulus;337
11.7.7;8.7.7 The Work by Huang and Sun;338
11.7.8;8.7.8 Other Works;339
11.8;8.8 General Solution of Eshelby’s Nano-Inhomogeneities Problem;340
11.8.1;8.8.1 Atomistic and Continuum Description of the Interphase;340
11.8.1.1;8.8.1.1 Atomic Level Caracterization;340
11.8.1.2;8.8.1.2 Interphase Stiffness Tensor;345
11.8.1.3;8.8.1.3 Particular Case of Isotropic Interface;346
11.8.1.4;8.8.1.4 Nano-Particles and Negative Stiffness Behavior;347
11.8.2;8.8.2 Micromechanical Framework for Coating-Inhomogeneity Problem;348
11.8.2.1;8.8.2.1 Integral Equation and Localization;349
11.8.2.2;8.8.2.2 Homogenization;354
11.8.2.3;8.8.2.3 Application to the Present Nano-Inhomogeneities Problem;355
11.8.2.4;8.8.2.4 Analitycal Solution for Spherical Isotropic Nano-Inhomogeneity;355
11.8.3;8.8.3 Numerical Simulations and Discussions;356
11.8.3.1;8.8.3.1 Spherical Inhomogeneities and Isotropic Material;356
11.8.3.2;8.8.3.2 Ellipsoidal Inhomogeneities and Isotropic Material;358
11.8.3.2.1;Oblate Spheroid Nano-Voids;359
11.8.3.2.2;Prolate Spheroid Nano-Void;361
11.8.3.2.3;Ellipsoidal Nano-inhomogeneity;361
11.8.3.3;8.8.3.3 Ellispsoidal inhomogeneities and anisotropic material;362
11.9;8.9 Appendix 1: ‘‘T’’ Stress Decomposition;364
11.10;8.10 Appendix 2: Atomic Level Description;366
11.11;8.11 Appendix 3: Strain Concentration Tensors: Spherical Isotropic Configuration;367
11.11.1;8.11.1 Parts of vartheta(i/j);368
11.11.2;8.11.2 Parts of Pij;368
11.11.3;8.11.3 Parts of a1;368
11.11.4;8.11.4 Parts of ak;368
11.11.5;8.11.5 Parts of AI;369
11.11.6;8.11.6 Parts of Ak;369
11.12;References;369
12;Innovative Combinations of Atomistic and Continuum: Plastic Deformation of Nanocrystalline Materials;373
12.1;9.1 Quasi-continuum Methods;374
12.2;9.2 Thermal Activation-Based Modeling;378
12.3;9.3 Higher-Order Finite Elements;381
12.3.1;9.3.1 Crystal Plasticity;383
12.3.2;9.3.2 Application via the Finite Element Method;386
12.4;9.4 Micromechanics;390
12.5;9.5 Summary;397
12.6;References;397
13;Subject Index;399