Atomistic Modeling of Materials Failure

By: Markus J. Buehler

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Hardcover | 10 September 2008

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560 Pages

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Atomistic Modeling of Materials Failure is an introduction to molecular and atomistic modeling techniques applied to solid fracture and deformation. Focusing on a variety of brittle, ductile, geometrically confined and biological materials, this detailed overview includes computational methods at the atomic scale, and describes how these techniques can be used to model the dynamics of cracks and other deformation mechanisms.

A full description of molecular dynamics (MD) as a numerical modeling tool covers the use of classical interatomic potentials and implementation of large-scale massively parallelized computing facilities in addition to the general philosophies of model building, simulation, interpretation and analysis of results. Readers will find an analytical discussion of the numerical techniques along with a review of required mathematical and physics fundamentals. Example applications for specific materials (such as silicon, copper, fibrous proteins) are provided as case studies for each of the techniques, areas and problems discussed.

Providing an extensive review of multi-scale modeling techniques that successfully link atomistic and continuum mechanical methods, Atomistic Modeling of Materials Failure is a valuable reference for engineers, materials scientists, and researchers in academia and industry.

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You Can Find This Book In

Non-Fiction Engineering & Technology Technology in General Nanotechnology Science Physics Engineering in General Mechanical Engineering & Materials Materials Science Mechanics of Solids Mechanical Engineering Biochemical Engineering

Biotechnology

List of Figures	p. XVII
List of Tables	p. LXIII
Nomenclature	p. LXV
Introduction
Introduction	p. 3
Materials Deformation and Fracture Phenomena: Why and How Things Break	p. 5
Strength of Materials: Flaws, Defects, and a Perfect Material	p. 6
Crystal Structures and Molecular Packing	p. 8
Cracks	p. 10
Dislocations	p. 10
Other Defects in Crystals and Other Structures	p. 12
Brittle vs. Ductile Material Behavior	p. 12
The Need for Atomistic Simulations	p. 15
Applications: Experimental and Computational Mechanics	p. 18
Experimental Techniques	p. 18
Example Applications: The Significance of Mechanics	p. 20
Outline of This Book	p. 27
Basics of Atomistic, Continuum and Multiscale Methods
Basic Atomistic Modeling	p. 31
Introduction	p. 31
Modeling and Simulation	p. 32
Model Building and Physical Representation	p. 34
The Concept of Computational Experiments	p. 35
Basic Statistical Mechanics	p. 36
Formulation of Classical Molecular Dynamics	p. 37
Integrating the Equations of Motion	p. 39
Thermodynamic Ensembles and Their Numerical Implementation	p. 40
Energy Minimization	p. 43
Monte Carlo Techniques	p. 44
Classes of Chemical Bonding	p. 46
The Interatomic Potential or Force Field: Introduction	p. 48
Pair Potentials	p. 50
Multibody Potentials: Embedded Atom Method for Metals	p. 54
Force Fields for Biological Materials and Polymers	p. 56
Bond Order and Reactive Potentials	p. 59
Limitations of Classical Molecular Dynamics	p. 68
Numerical Implementation	p. 69
Periodic Boundary Conditions	p. 70
Force Calculation	p. 71
Neighbor Lists and Bins	p. 72
Property Calculation	p. 73
Temperature Calculation	p. 73
Pressure Calculation	p. 74
Radial Distribution Function	p. 74
Mean Square Displacement Function	p. 75
Velocity Autocorrelation Function	p. 76
Virial Stress Tensor	p. 76
Large-Scale Computing	p. 78
Historical Development of Computing Power	p. 79
Parallel Computing	p. 80
Discussion	p. 82
Visualization and Analysis Methods	p. 83
Energy Method	p. 85
Centrosymmetry Parameter	p. 86
Slip Vector	p. 88
Measurement of Defect Speed	p. 89
Visualization Methods for Biological Structures	p. 89
Other Methods	p. 90
Distinguishing Modeling and Simulation	p. 90
Application of Mechanical Boundary Conditions	p. 90
Summary	p. 93
Basic Continuum Mechanics	p. 95
Newton's Laws of Mechanics	p. 95
Definition of Displacement, Stress, and Strain	p. 97
Stress Tensor	p. 99
Equilibrium Conditions	p. 100
Strain Tensor	p. 103
Energy Approach to Elasticity	p. 105
Isotropic Elasticity	p. 107
Nonlinear Elasticity or Hyperelasticity	p. 108
Elasticity of a Beam	p. 110
Reduction Formulas	p. 110
Equilibrium Equations	p. 111
Example: Solution of a Simple Beam Problem	p. 112
Calculation of Internal Stress Field	p. 113
Differential Beam Equations	p. 116
The Need for Atomistic Elasticity: What's Next	p. 119
Atomistic Elasticity: Linking Atoms and Continuum	p. 121
Thermodynamics as Bridge Between Atomistic and Continuum Viewpoints	p. 121
The Atomic and Molecular Origin of Elasticity: Entropic vs. Energetic Sources	p. 122
The Virial Stress and Strain	p. 123
Elasticity Due to Energetic Contributions	p. 124
Cauchy-Born Rule	p. 124
Elasticity of a One-Dimensional String of Atoms	p. 126
Elasticity and Surface Energy of a Two-Dimensional Triangular Lattice	p. 128
Elasticity and Surface Energy of a Three-Dimensional FCC Lattice	p. 142
Concluding Remarks	p. 149
Elasticity Due to Entropic Contributions	p. 149
Elasticity of Single Molecules: Worm-Like-Chain Model	p. 150
Elasticity of Polymers	p. 152
Discussion	p. 154
Multiscale Modeling and Simulation Methods	p. 157
Introduction	p. 157
Direct Numerical Simulation vs. Multiscale and Multiparadigm Modeling	p. 158
Differential Multiscale Modeling	p. 159
Detailed Description of Selected Multiscale Methods to Span Vast Lengthscales	p. 160
Examples of Hierarchical Multiscale Coupling	p. 160
Concurrent Integration of Tight-Binding, Empirical Force Fields and Continuum Theory	p. 162
The Quasicontinuum Method and Related Approaches	p. 165
Continuum Approaches Incorporating Atomistic Information	p. 168
Hybrid ReaxFF Model: Integration of Chemistry and Mechanics	p. 169
Advanced Molecular Dynamics Techniques to Span Vast Timescales	p. 175
Discussion	p. 180
Material Deformation and Failure
Deformation and Dynamical Failure of Brittle Materials	p. 185
The Nature of Brittle Fracture	p. 186
Basics of Linear Elastic Fracture Mechanics	p. 189
Energy Balance Considerations: Griffith's Model of Fracture	p. 189
Asymptotic Stress Field and Stress Intensity Factor	p. 194
Crack Limiting Speed in Dynamic Fracture	p. 196
Atomistic Modeling of Brittle Materials	p. 197
A One-Dimensional Example of Brittle Fracture: Joint Continuum-Atomistic Approach	p. 201
Introduction	p. 202
Linear-Elastic Continuum Model	p. 204
Hyperelastic Continuum Mechanics Model for Bilinear Stress-Strain Law	p. 207
Molecular Dynamics Simulations of the One-Dimensional Crack Model: The Harmonic Case	p. 211
Molecular Dynamics Simulations of the One-Dimensional Crack Model: The Supersonic Case	p. 217
Discussion and Conclusions	p. 219
Stress and Deformation Field near Rapidly Propagating Mode I Cracks in a Harmonic Lattice	p. 223
Stress and Deformation Fields	p. 225
Energy Flow near the Crack Tip	p. 227
Limiting Velocities of Mode I Cracks in Harmonic Lattices	p. 229
Summary	p. 230
Crack Limiting Speeds of Cracks: The Significance of Hyperelasticity	p. 234
Modeling	p. 236
Crack Speed and Energy Flow	p. 238
Hyperelastic Area	p. 239
How Fast can Cracks Propagate?	p. 242
Characteristic Energy Length Scale in Dynamic Fracture	p. 244
Summary	p. 248
Crack Instabilities and Hyperelastic Material Behavior	p. 249
Introduction	p. 251
Design of Computational Model	p. 252
Computational Experiments	p. 255
Discussion and Conclusion	p. 258
Suddenly Stopping Cracks: Linking Atomistic Modeling, Theory, and Experiment	p. 260
Introduction	p. 260
Theoretical Background of Suddenly Stopping Cracks	p. 262
Atomistic Simulation Setup	p. 264
Atomistic Simulation Results of a Suddenly Stopping Mode I Crack	p. 268
Atomistic Simulation Results of a Suddenly Stopping Mode II Crack	p. 278
Discussion	p. 286
Crack Propagation Along Interfaces of Dissimilar Materials	p. 287
Mode I Dominated Cracks at Bimaterial Interfaces	p. 289
Mode II Cracks at Bimaterial Interfaces	p. 294
Summary	p. 297
Dynamic Fracture Under Mode III Loading	p. 299
Atomistic Modeling of Mode III Cracks	p. 300
Mode III Cracks in a Harmonic Lattice - The Reference Systems	p. 300
Mode III Crack Propagation in a Thin Stiff Layer Embedded in a Soft Matrix	p. 301
Suddenly Stopping Mode III Crack	p. 303
Discussion	p. 303
Brittle Fracture of Chemically Complex Materials	p. 304
Introduction	p. 305
Hybrid Atomistic Modeling of Cracking in Silicon: Mixed Hamiltonian Gormulation	p. 307
Atomistic Model	p. 307
Simulation Results	p. 308
Dynamical Fracture Mechanisms	p. 311
Reactive Chemical Processes and Fracture Initiation	p. 316
Summary	p. 317
Summary: Brittle Fracture	p. 320
Hyperelasticity can Govern Dynamic Fracture	p. 323
Interfaces and Geometric Confinement	p. 326
Deformation and Fracture of Ductile Materials	p. 327
Introduction	p. 327
Continuum Theoretical Concepts of Dislocations and Their Interactions	p. 328
Properties of Dislocations	p. 329
Forces on Dislocations	p. 331
Rice-Thomson Model for Dislocation Nucleation	p. 332
Rice-Peierls Model	p. 337
Link with Atomistic Concepts	p. 338
Generalized Stacking Fault Curves	p. 338
Linking Atomistic Simulation Results to Continuum Mechanics Theories of Plasticity	p. 339
Modeling Plasticity Using Large-Scale Atomistic Simulations	p. 341
Case Study: Deformation Mechanics of Model FCC Copper - LJ Potential	p. 343
Model Setup	p. 343
Visualization Procedure	p. 345
Simulation Results	p. 345
Summary	p. 355
Case Study: Deformation Mechanics of a Nickel Nanocrystal - EAM Potential	p. 357
Case Study: Multi-Paradigm Modeling of Chemical Complexity in Mechanical Deformation of Metals	p. 359
Atomistic Model and Validation	p. 360
Example Application: Modeling Hybrid Metal-Organic Systems	p. 364
Deformation and Fracture Mechanics of Geometrically Confined Materials	p. 373
Introduction	p. 373
Thin Metal Films and Nanocrystalline Metals	p. 381
Constrained Diffusional Creep in Ultra-Thin Metal Films	p. 385
Single Edge Dislocations in Nanoscale Thin Films	p. 390
Rice-Thompson Model for Nucleation of Parallel Glide Dislocations	p. 393
Discussion and Summary	p. 396
Atomistic Modeling of Constrained Grain Boundary Diffusion in a Bicrystal Model	p. 396
Introduction and Modeling Procedure	p. 397
Formation of the Diffusion Wedge	p. 400
Development of the Crack-Like Stress Field and Nucleation of Parallel Glide Dislocations	p. 402
Discussion	p. 404
Summary	p. 408
Dislocation Nucleation from Grain Triple Junction	p. 408
Atomistic Modeling of the Grain Triple Junction	p. 409
Atomistic Simulation Results	p. 410
Discussion	p. 414
Atomistic Modeling of Plasticity of Polycrystalline Thin Films	p. 414
Atomistic Modeling of Polycrystalline Thin Films	p. 415
Atomistic Simulation Results	p. 416
Plasticity of Nanocrystalline Bulk Materials with Twin Lamella	p. 422
Modeling of Constrained Diffusional Creep in Polycrystalline Films	p. 426
Discussion	p. 428
Summary: Results of Modeling of Thin Films	p. 430
Use of Atomistic Simulation Results in Hierarchical Multiscale Modeling	p. 432
Mechanisms of Plastic Deformation of Ultra-thin Uncapped Copper Films	p. 434
Deformation Map of Thin Films	p. 434
Yield Stress in Ultra-Thin Copper Films	p. 435
The Role of Interfaces and Geometric Confinement	p. 436
Deformation and Fracture Mechanics of Carbon Nanotubes	p. 438
Mesoscale Modeling of CNT Bundles	p. 441
Mesoscale Simulation Results	p. 444
Discussion	p. 445
Flaw-Tolerant Nanomaterials: Bulk Fracture and Deformation	p. 446
Strength of Brittle Nanoparticles	p. 446
Simulation Results	p. 450
Nanoscale Adhesion Systems	p. 452
Strength of Fibrillar Adhesion Systems	p. 453
Theoretical Considerations of Shape Optimization of Adhesion Elements	p. 455
Atomistic Modeling	p. 456
Simulation Results	p. 457
Summary	p. 460
References	p. 463
Index	p. 483
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Atomistic Modeling of Materials Failure

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