Chapter 1: Background and Significance
1.1 Framework of This Book
1.2 Polycrystalline and Single-Crystal Plasticity
1.3 Size Effect on Crystal Plasticity at Micron and Submicron Scales
1.3.1 Size Effect Observed in Material Experiments
1.3.2 Size Effect of Yield Stress
1.3.3 Strain Burst and Dislocation Avalanches
1.3.4 Size Effect of Submicron Crystal Under Cyclic Loading
1.3.5 Size Effect of Deformation Morphology of Compressed Micropillars
1.4 Method to Bridge Size Effect
1.4.1 Supersurface From Macro to Micron
1.4.2 Nonlocal Crystal Plasticity
1.4.3 Discrete Dislocation Dynamics Simulation Method
1.5 Content of This Book
Part 1 Continuum Dislocation Mechanism-Based Crystal Plasticity
Chapter 2: Fundamental Conventional Concept of Plasticity Constitution
2.1 Introduction
2.2 One-Dimensional Plasticity
2.2.1 Isotropic Hardening
2.2.2 Kinematic Hardening
2.2.3 Rate-Dependent Plasticity
2.3 Multiaxial Plasticity
2.3.1 Hypoelastic-Plastic Materials
2.3.2 Small Strain Plasticity
2.4 J2 Flow Theory Plasticity
2.4.1 Kirchhoff Stress Formulation of J2 Flow Theory Plasticity
2.4.2 Extension to Kinematic Hardening
2.4.3 Large Strain Viscoplasticity
2.5 Rock-Soil Constitutive Model
2.5.1 Mohr-Coulomb Constitutive Model
2.5.2 Drucker-Prager Constitutive Model
2.6 Gurson Model for Porous Elastic-Plastic Solids
2.7 Corotational Stress Formulation
2.8 Summary
Chapter 3: Strain Gradient Plasticity Theory at the Microscale
3.1 Size Dependence of Material Behavior at the Microscale
3.2 Couple Stress Theory
3.2.1 Couple Stresses
3.2.2 Rotation and Rotation Gradient
3.2.3 Virtual Work Principle
3.2.4 Constitutive Relation of Couple Stress Strain Gradient Plasticity Theory
3.2.5 Principles of Minimum Potential Energy and Minimum Complementary Energy
3.2.6 Equivalent Stress and Equivalent Strain
3.3 Stretch and Rotation Gradient Theory
3.3.1 Strain Gradient Tensor
3.3.2 Decomposition of Strain Gradient Partial Tensor h0 and Total Equivalent Strain ESG
3.3.3 Constitutive Relation of Stretch and Rotation Gradient Strain Gradient Plastic Theory
3.4 Microscale Mechanism-Based Strain Gradient Plasticity Theory
3.4.1 Experimental Law for Strain Gradient Plasticity Theory
3.4.2 Motivation for Microscale Mechanism-Based Strain Gradient Plasticity Theory
3.4.3 Microscale Computation Framework
3.4.4 Dislocation Model
3.4.5 Constitutive Equation of Mechanism-Based Strain Gradient Plasticity Theory
3.4.6 Size of Cell Element at the Microscale
3.4.7 Mechanism-Based Strain Gradient Plasticity Predicts Stress Singularity at Crack Tip
3.5 Summary
Chapter 4: Dislocation-Based Single-Crystal Plasticity Model
4.1 Introduction
4.2 General Constitutive Model for Single Crystals
4.2.1 Basic Kinematics of Crystal Plasticity
4.2.2 Slip Rate and Dislocation Density Evolution
4.2.3 Plastic Stress Required for Dislocation Motion
4.2.4 Update of Cauchy Stress in Single-Crystal Plasticity
4.3 Higher-Order Dislocation Dynamics-Based Crystal Plasticity Model
4.3.1 Governing Equations of Macroforces
4.3.2 Governing Equations of Microforces
4.3.3 Coupling of Macroscopic and Microscopic Equations
4.4 Size and Bauschinger Effect in Passivated Thin Films
4.4.1 Two Hardening Mechanisms Caused by Geometrically Necessary Dislocations
4.4.2 Model Description
4.4.3 Size Effect of Passivated Thin Films Under Tension
4.4.4 Bauschinger Effect of Passivated Thin Films During Unloading
4.5 Summary
Chapter 5: Revealing the Size Effect in Micropillars by Dislocation-Based Crystal Plasticity Theory
5.1 Introduction
5.2 Strain Burst and Size Effect in Compression Micropillars
5.2.1 Stochastic Crystal Plasticity Model
5.2.2 Determination of Size-Dependent Slip Resistance
5.2.3 Strain Bursts at Small Scales
5.2.4 Application to the Compression of Single-Crystal Ni Micron Pillars
5.3 Size-Dependent Deformation Morphology of Micropillars
5.3.1 Simulation Setups
5.3.2 Size-Dependent Deformation Morphology
5.3.3 Role of Short-Range Back Stress
5.3.4 Critical Transition Size
5.3.5 Discussions of Material Softening
5.4 Summary
Chapter 6: Microscale Crystal Plasticity Model Based on Phase Field Theory
6.1 Introduction
6.2 Theoretical Model
6.2.1 Basic Equations of Crystal Plasticity Theory
6.2.2 Phase Field Description of Plastic Slip
6.2.3 Stored Energy and Dissipated Energy
6.2.4 Principle of Virtual Power
6.2.5 Coupled Balance Equations
6.2.6 Finite Element Discretization
6.3 Computational Demonstrations
6.3.1 Dislocation Near a Free Surface
6.3.2 Dislocation in an Anisotropic Material
6.3.3 Dislocation Near a Bimaterial Interface
6.4 Applications to Heteroepitaxial Structures
6.4.1 Critical Shell Thickness of Core-Shell Nanopillars
6.4.2 Dislocations in Heteroepitaxial Thin Films
6.5 Summary
Part 2 Discrete Dislocation Mechanism-Based Crystal Plasticity Chapter 7: Discrete-Continuous Model of Crystal Plasticity at the Submicron Scale
7.1 Discrete Dislocation Dynamics
7.1.1 Dislocation Kinetic Equation
7.1.2 Dislocation Interactions and Topology Update
7.1.3 Dislocation Cross-Slip
7.1.4 Current Three-Dimensional Discrete Dislocation Dynamics Simulations
7.2 Coupling Discrete Dislocation Dynamics With Finite Element Method
7.2.1 Superposition Method
7.2.2 Discrete-Continuous Model
7.3 Improved Discrete-Continuous Model
7.3.1 Ef.cient Regularization Method
7.3.2 Image Force Calculation
7.3.3 Finite Deformation
7.4 Application to Heteroepitaxial Films
7.4.1 Thermoelastic Calculation to Determine Internal Stress Field
7.4.2 In.uence of Substrate Thickness on Dislocation Behavior
7.5 Application to Irradiated Materials
7.6 Summary
Chapter 8: Single-Arm Dislocation Source (SAS)-Controlled Submicron Plasticity
8.1 Introduction
8.2 Single-Arm Dislocation Source Mechanisms at Submicron Scales
8.3 Single-Arm Dislocation Source-Controlled Strain Burst and Dislocation Avalanche
8.4 Description of Single-Arm Dislocation Source-Controlled Plasticity
8.4.1 Single-Arm Dislocation Source-Controlled Dislocation Density Evolution
8.4.2 Effective Single-Arm Dislocation Source Length
8.4.3 Single-Arm Dislocation Source-Controlled Flow Stress
8.5 Summary
Contents
Chapter 9: Con.ned Plasticity in Micropillars
9.1 Insights into Coated Micropillar Plasticity
9.1.1 Stress-Strain Curves in Coated and Uncoated Pillars
9.1.2 Dislocation Source Mechanism in Coated Micropillars
9.1.3 Back Stress in Coated Micropillars
9.1.4 Evolution of Mobile and Trapped Dislocation
9.2 Implications for Crystal Plasticity Model
9.3 Theoretical Models for Coated Micropillars
9.3.1 Dislocation Density Evolution Model
9.3.2 Prediction of Stress-Strain Curve
9.4 Brief Discussion on Coating Failure Mechanism
9.4.1 High Hoop Stress of Coated Layer
9.4.2 Transmission Effect of Dislocations Across Coating
9.5 Summary
Chapter 10: Mechanical Annealing Under Low-Amplitude Cyclic Loading
10.1 Introduction
10.2 Cyclic Behavior of Collective Dislocations
10.3 Cyclic Instability of Dislocation Junction
10.3.1 Glissile Dislocation Junction
10.3.2 Sessile Dislocation Junction
10.4 Cyclic Enhanced Dislocation Annihilation Mechanism
10.5 Dislocation Density In.uenced by Cyclic Slip Irreversibility
10.6 Critical Size for Mechanical Annealing
10.7 Summary
Chapter 11: Strain Rate Effect on Deformation of Single Crystals at Submicron Scale
11.1 Introduction
11.2 Strain Rate Effect on Flow Stress in Single-Crystal Copper Under Compression Loading
11.2.1 Strain Rate Effect of Submicron Copper Pillars Under Uniaxial Compression
11.2.2 Strain Rate Effect of Dislocation Evolution in Copper Cubes Under Hydrostatic Pressure
11.3 Strain Rate Effect on Dynamic Deformation of Single-Crystal Copper Under Tensile Loading
11.3.1 Resolution of Discrete Dislocation Dynamics
11.3.2 Coupling Dislocation Dynamics Plasticity With Finite Element
11.3.3 Model Description and Simulation Results
11.4 Shock-Induced Deformation and Dislocation Mechanisms in Single-Crystal Copper
11.4.1 Dynamic Mechanical Behavior Corresponding to Dislocation Microstructure
11.4.2 Dynamic Multiscale Discrete Dislocation Plasticity Model
11.4.3 Coarse-Grained Homogeneous Nucleation Model
11.4.4 Shock-Induced Plasticity at the Submicron Scale
11.4.5 Discussion and Conclusion
11.5 Summary

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