Multiscale Modelling of Plasticity and Fracture by Means of Dislocation Mechanics

Cover -- Preface -- Table of Contents -- Atomistic Simulation Methods and Their Application on Fracture -- 1 Introduction -- 2 Description of Interatomic Bonds -- 2.1 Quantum Mechanics Based Descriptions of the Atomic Bound- Ing -- 2.2 Atomic Interaction Models, Potentials -- 3 The Molecular Dynamics Method -- 3.1 Force Calculation -- 3.2 Integrating the Equations of Motion -- 3.3 Relaxation Algorithms -- 3.4 Boundary and Initial Conditions -- 3.5 Stable Defects Under Load -- 3.6 Visualisation and Analysis of Defects -- 4 Comcurrent Multiscale Methods -- 4.1 Introduction and Classification of Multiscale Methods -- 4.2 The Finite Element Atomistic (Feat) Method -- 4.3 The Quasicontinuum-Method Based on the Cauchy Born Rule -- 4.4 The Fully Nonlocal Cluster-Based Quasicontinuum-Method -- 4.5 Other Concurrent Multiscale Methods -- 4.6 'Learn-On-The-Fly' -- Lotf -- 5 Atomistic Aspects of Fracture -- 5.1 Lattice Trapping and the Directional Cleavage Anisotropy -- 5.2 Metastable Fracture Surfaces -- 6 Dynamics of Brittle Crack Propagation -- 7 Summary -- Biblliography -- Fundamental Dislocation Theory and 3D Dislocation Mechanics -- 1 Basic Dislocation Theory -- 1.1 Heuristic Dislocation Creation -- 1.2 Basic Dislocation Types -- 1.3 Moving Dislocations -- 1.4 Dislocations In Real Crystals -- 2 Curved Dislocations -- 2.1 Line Tension Model -- 2.2 Dislocation Self-Interaction -- 3 2-D Applications -- 3.1 Simulation Technique -- 3.2 Static Simulations Using the Line Tension Model -- 3.3 Simulation Using Dislocation Self Interaction: Particle Strengthening -- 3.4 Simulations of Thermally Activated Dislocation Glide -- 4 3-D Aspects -- 4.1 Non-Elastic 3-D Effects -- 4.2 Computational Aspects for 3-D Simulations -- Bibliography -- Plasticity of Moderately Loaded Cracks and the Consequence of the Discrete Nature of Plasticity to Fatigue and Fracture -- 1 Introduction -- 2 Stress Field of a Crack in a Linear Elastic Material -- 3 Dislocation Crack Tip Interaction -- 3.1 Linear Elastic Analysis of the Stresses and Deformations Induced By An Edge Dislocation Near a Crack Tip -- 3.2 Moderate Cyclic Loading of a Crack -- 3.3 The Involved Length Scales -- 4 Modelling of Plasticity, Crack Propagation and Fracture Surface Contact -- 4.1 The Cyclic Plastic Deformation As a Function of Load Amplitude and Ber of Cycles -- 4.2 The Effect of Boundaries -- 4.3 The Threshold of Cyclic Plastic Deformation and the Effective Threshold of Stress Intensity Range -- 4.4 Other Discrete Discrete Dislocation Simulations of Fatigue Crack Propagation -- Bibliography -- Discrete Dislocation Plasticity Analysis of Cracks and Fracture -- 1 Introducton -- 2 Elastic Models of Dislocations -- 2.1 General Idea -- 2.2 Edge Dislocations -- 3 Boundary Value Problems -- 4 Dislocation Dynamics -- 4.1 Annihilation -- 4.2 Frank-Read Sources -- 5 Methodology for Crack Problems -- 6 Cracks in Single Crystals -- 6.1 Stationary Crack -- Tip Fields -- 6.2 Crack Propagation Under Monotonic Loading -- 7 Fatigue Crack Growth -- 8 Cracks in Polycrystals -- Bibliography -- Statistical Physical A.