Preface
Acknowledgments
Nomenclature
Chapter 1. Introduction
1.1 Classic Microstructure–Properties Relationships
1.2 Microstructure-Sensitive Design for Performance Optimization
1.3 Illustration of the Main Constructs of MSDPO
1.4 Implementation of MSDPO in Design Practice
1.5 The Central Challenge of MSDPO
1.6 Organization of the Book
Summary
Chapter 2. Tensors and Rotations
2.1 Definitions and Conventions
2.2 Tensor Operations
2.3 Coordinate Transformations
2.4 Rotations
2.5 Eigenvalues and Eigenvectors
2.6 Polar Decomposition Theorem
2.7 Tensor Gradients
Summary
Chapter 3. Spectral Representation: Generalized Fourier Series
3.1 Primitive Basis
3.2 Fourier Series
3.3 Fourier Transform
3.4 Generalized Spherical Harmonic Functions
3.5 Surface Spherical Harmonic Functions
Summary
Chapter 4. Description of the Microstructure
4.1 Local States and Local State Space
4.2 Measure of Local State Space
4.3 Local State Distribution Functions
4.4 Definition of the Microstructure Function
Summary
Chapter 5. Spectral Representation of Microstructure
5.1 Primitive Basis
5.2 Fourier Series and Fourier Transform Representations
5.3 Spherical Harmonic Function Representations
5.4 Primitive Basis Representation of the Microstructure Function
5.5 Representative Volume Element
Summary
Chapter 6. Symmetry in Microstructure Representation
6.1 Point Symmetry Subgroups of the Crystal Lattice
6.2 Symmetry Considerations in SO (3) and S2
Summary
Chapter 7. Structure–Property Relations: Continuum Mechanics
7.1 Potentials and Gradients
7.2 Stress
7.3 Strain and Motion
7.4 Conductivity
7.5 Elasticity
7.6 Crystal Plasticity
7.7 Macroscale Plasticity
Summary
Chapter 8. Homogenization Theories
8.1 Introduction
8.2 First-Order Bounds for Elasticity
8.3 Homogenization of Other Physical Properties
8.4 First-Order Bounds for Thermal Expansion
Summary
Chapter 9. Microstructure Hull and Closures
9.1 Microstructure Hull
9.2 Property Closures
Summary
Chapter 10. Design for Performance Optimization
10.1 Design Process Using GSH
10.2 Microstructure Design of a Compliant Mechanism
10.3 Microstructure Design of a Rotating Disk
10.4 Microstructure-Sensitive Design of a Composite Plate
10.5 Heterogeneous Design
Summary
Chapter 11. Microstructure Evolution by Processing
11.1 First-Order Crystal Plasticity Models in a Spectral Framework
11.2 Process Design Using Deformation Processing Operations
11.3 A Brief Outline for Heterogeneous Design
Summary
Chapter 12. Higher-Order Microstructure Representation
12.1 Correlation Functions and Microstructure Representation
12.2 Representation of Correlation Functions in the Primitive Basis
12.3 Discrete Fourier Transform Representation of Correlation Functions
12.4 Quantitative Representations of Interface Microstructure
12.5 Relationship between Two-Point Correlation Functions and the ICD
Summary
Chapter 13. Higher-Order Homogenization
13.1 Higher-Order Perturbation Estimates for Elastic Properties
13.2 Calculation of Second-Order Properties in the Primitive Basis
13.3 Homogenization in Discrete Fourier Transform Space
13.4 Extension of the Homogenization Method to Localization Problems
13.5 A Formulation for Strong-Contrast Materials
Summary
Chapter 14. Second-Order Hull, Property Closure, and Design
14.1 Hull of Two-Point Correlations
14.2 Second-Order Property Closure
14.3 Pareto-Front Techniques on the Property Closure
14.4 Second-Order Design
Summary
Chapter 15. Higher-Order Models of Deformation Processing
15.1 Higher-Order Model of Visco-Plasticity
15.2 Time- and Space-Dependent Modeling of Texture Evolution
Summary
Chapter 16. Electron Backscatter Diffraction Microscopy and Basic Stereology
16.1 Introduction
16.2 Pattern Formation
16.3 Automated Indexing
16.4 Phase Identification
16.5 Orientation Analysis
16.6 High-Resolution EBSD
16.7 Stereology: Volume Fractions Estimation
Summary
Appendix 1: Symmetry Point Operators
Nonhexagonal Lattices
Hexagonal Lattices
Bravais Lattices
Crystal Structures
Appendix 2: Tables of Spherical Harmonic Functions
References
Index
