Computational Materials Engineering: An Introduction to Microstructure Evolution
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Table of contents
- Table of Contentsvii
- Prefacexiii
- Chapter 1. Introduction1
- 1.1 Microstructures Defined1
- 1.2 Microstructure Evolution2
- 1.3 Why Simulate Microstructure Evolution?4
- 1.4 Further Reading5
- Bibliography6
- Chapter 2. Thermodynamic Basis of Phase Transformations7
- 2.1 Reversible and Irreversible Thermodynamics8
- 2.2 Solution Thermodynamics18
- Bibliography45
- Chapter 3. Monte Carlo Potts Model47
- 3.1 Introduction47
- 3.2 Two-State Potts Model (Ising Model)48
- 3.3 Q-State Potts Model64
- 3.4 Speed-Up Algorithms80
- 3.5 Applications of the Potts Model87
- 3.6 Summary107
- 3.7 Final Remarks107
- 3.8 Acknowledgments108
- Bibliography108
- Chapter 4. Cellular Automata109
- 4.1 A Definition109
- 4.2 A One-Dimensional Introduction109
- 4.3 +2D CA Modeling of Recrystallization116
- 4.4 +2D CA Modeling of Grain Growth123
- 4.5 A Mathematical Formulation of Cellular Automata128
- 4.6 Irregular and Shapeless Cellular Automata129
- 4.7 Hybrid Cellular Automata Modeling136
- 4.8 Lattice Gas Cellular Automata140
- 4.9 Network Cellular Automata„A Development for the Future?144
- 4.10 Further Reading147
- Bibliography148
- Chapter 5. Modeling Solid-State Diffusion151
- 5.1 Diffusion Mechanisms in Crystalline Solids151
- 5.2 Microscopic Diffusion154
- 5.3 Macroscopic Diffusion160
- 5.4 Numerical Solution of the Diffusion Equation174
- Bibliography177
- Chapter 6. Modeling Precipitation as a Sharp-Interface Phase Transformation179
- 6.1 Statistical Theory of Phase Transformation181
- 6.2 Solid-State Nucleation185
- 6.3 Diffusion-Controlled Precipitate Growth197
- 6.4 Multiparticle Precipitation Kinetics206
- 6.5 Comparing the Growth Kinetics of Different Models215
- Bibliography216
- Chapter 7. Phase-Field Modeling219
- 7.1 A Short Overview220
- 7.2 Phase-Field Model for Pure Substances222
- 7.3 Case Study228
- 7.4 Model for Multiple Components and Phases241
- 7.5 Acknowledgments265
- Bibliography265
- Chapter 8. Introduction to Discrete Dislocation Statics and Dynamics267
- 8.1 Basics of Discrete Plasticity Models267
- 8.2 Linear Elasticity Theory for Plasticity268
- 8.3 Dislocation Statics284
- 8.4 Dislocation Dynamics298
- 8.5 Kinematics of Discrete Dislocation Dynamics310
- 8.6 Dislocation Reactions and Annihilation311
- Bibliography313
- Chapter 9. Finite Elements for Microstructure Evolution317
- 9.1 Fundamentals of Differential Equations317
- 9.2 Introduction to the Finite Element Method321
- 9.3 Finite Element Methods at the Meso- and Macroscale322
- Bibliography332
- Index335
Computational Materials Engineering is an advanced introduction to the computer-aided modeling of essential material properties and behavior, including the physical, thermal and chemical parameters, as well as the mathematical tools used to perform simulations. Its emphasis will be on crystalline materials, which includes all metals. The basis of Computational Materials Engineering allows scientists and engineers to create virtual simulations of material behavior and properties, to better understand how a particular material works and performs and then use that knowledge to design improvements for particular material applications. The text displays knowledge of software designers, materials scientists and engineers, and those involved in materials applications like mechanical engineers, civil engineers, electrical engineers, and chemical engineers.
Readers from students to practicing engineers to materials research scientists will find in this book a single source of the major elements that make up contemporary computer modeling of materials characteristics and behavior. The reader will gain an understanding of the underlying statistical and analytical tools that are the basis for modeling complex material interactions, including an understanding of computational thermodynamics and molecular kinetics; as well as various modeling systems. Finally, the book will offer the reader a variety of algorithms to use in solving typical modeling problems so that the theory presented herein can be put to real-world use.
•Balanced coverage of fundamentals of materials modeling, as well as more advanced aspects of modeling, such as modeling at all scales from the atomic to the molecular to the macro-material
•Concise, yet rigorous mathematical coverage of such analytical tools as the Potts type Monte Carlo method, cellular automata, phase field, dislocation dynamics and Finite Element Analysis in statistical and analytical modeling
•Companion web site will offer ample workable programs, along with suggested projects, resources for further reading, and useful classroom exercises
Readers from students to practicing engineers to materials research scientists will find in this book a single source of the major elements that make up contemporary computer modeling of materials characteristics and behavior. The reader will gain an understanding of the underlying statistical and analytical tools that are the basis for modeling complex material interactions, including an understanding of computational thermodynamics and molecular kinetics; as well as various modeling systems. Finally, the book will offer the reader a variety of algorithms to use in solving typical modeling problems so that the theory presented herein can be put to real-world use.
•Balanced coverage of fundamentals of materials modeling, as well as more advanced aspects of modeling, such as modeling at all scales from the atomic to the molecular to the macro-material
•Concise, yet rigorous mathematical coverage of such analytical tools as the Potts type Monte Carlo method, cellular automata, phase field, dislocation dynamics and Finite Element Analysis in statistical and analytical modeling
•Companion web site will offer ample workable programs, along with suggested projects, resources for further reading, and useful classroom exercises