Book contents
- Frontmatter
- Contents
- Preface
- Acknowledgements
- Frequently used symbols
- 1 Introduction
- 2 Basic elements of linear elasticity
- 3 Methods
- 4 Green's functions for unit point force
- 5 Interactions between defects and stress
- 6 Inclusions in infinite homogeneous regions
- 7 Interactions between inclusions and imposed stress
- 8 Inclusions in finite regions – image effects
- 9 Inhomogeneities
- 10 Point defects in infinite homogeneous regions
- 11 Point defects and stress – image effects in finite bodies
- 12 Dislocations in infinite homogeneous regions
- 13 Dislocations and stress – image effects in finite regions
- 14 Interfaces
- 15 Interactions between interfaces and stress
- 16 Interactions between defects
- Appendix A Relationships involving the ∇ operator
- Appendix B Integral relationships
- Appendix C The tensor product of two vectors
- Appendix D Properties of the delta function
- Appendix E The alternator operator
- Appendix F Fourier transforms
- Appendix G Equations from the theory of isotropic elasticity
- Appendix H Components of the Eshelby tensor in isotropic system
- Appendix I Airy stress functions for plane strain
- Appendix J Deviatoric stress and strain in isotropic system
- References
- Index
Preface
- Frontmatter
- Contents
- Preface
- Acknowledgements
- Frequently used symbols
- 1 Introduction
- 2 Basic elements of linear elasticity
- 3 Methods
- 4 Green's functions for unit point force
- 5 Interactions between defects and stress
- 6 Inclusions in infinite homogeneous regions
- 7 Interactions between inclusions and imposed stress
- 8 Inclusions in finite regions – image effects
- 9 Inhomogeneities
- 10 Point defects in infinite homogeneous regions
- 11 Point defects and stress – image effects in finite bodies
- 12 Dislocations in infinite homogeneous regions
- 13 Dislocations and stress – image effects in finite regions
- 14 Interfaces
- 15 Interactions between interfaces and stress
- 16 Interactions between defects
- Appendix A Relationships involving the ∇ operator
- Appendix B Integral relationships
- Appendix C The tensor product of two vectors
- Appendix D Properties of the delta function
- Appendix E The alternator operator
- Appendix F Fourier transforms
- Appendix G Equations from the theory of isotropic elasticity
- Appendix H Components of the Eshelby tensor in isotropic system
- Appendix I Airy stress functions for plane strain
- Appendix J Deviatoric stress and strain in isotropic system
- References
- Index
Summary
Preface
A unified introduction to the theory of anisotropic elasticity for static defects in crystals is presented. The term “defects” is interpreted broadly to include defects of zero, one, two, and three dimensionality: included are
Point defects (vacancies, self-interstitials, solute atoms, and small clusters of these species),
Line defects (dislocations),
Planar defects (homophase and heterophase interfaces),
Volume defects (inhomogeneities and inclusions).
The book is an outgrowth of a graduate course on “Defects in Crystals” offered by the author for many years at the Massachusetts Institute of Technology, and its purpose is to provide an introduction to current methods of solving defect elasticity problems through the use of anisotropic linear elasticity theory. Emphasis is put on methods rather than a wide range of applications and results. The theory generally allows multiple approaches to a given problem, and a particular effort is made to formulate and compare alternative treatments.
Anisotropic linear elasticity is employed throughout. This is now practicable because of significant advances in the theory of anisotropic elasticity for crystal defects that have been made over the last 35 years or so, including the development of Green's functions for unit point forces in infinite anisotropic spaces, half-spaces and joined dissimilar half-spaces. The use of anisotropic theory (rather than the simpler isotropic theory) is important, since, even though the results obtained by employing the two approaches often agree to within 25%, or so, there are many phenomena that depend entirely on elastic anisotropy. Unfortunately, however, the results obtained with the anisotropic theory are usually in the form of lengthy integrals that can be evaluated only using numerical methods and so lack transparency. To assist with this difficulty, isotropic elasticity is employed in parallel treatments of many problems where sufficiently simple conditions are assumed so that tractable analytic solutions can be obtained that are more transparent physically. Sections in the book where isotropic elasticity is employed are clearly distinguished to avoid confusion.
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- Introduction to Elasticity Theory for Crystal Defects , pp. xiii - xivPublisher: Cambridge University PressPrint publication year: 2012