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
11 - Point defects and stress – image effects in finite bodies
- 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
Introduction
In Chapter 10, the force multipole and small inhomogeneous models for point defects in infinite homogeneous regions were described. The interaction of inhomogeneous inclusions with various types of stresses has been treated in Chapters 7 and 8. Consequently, there is no need in this chapter to devote further attention to interactions between point defects and stress in terms of the small inhomogeneous inclusion model. Attention is therefore focused on these interactions in terms of the force multipole model.
Section 11.2 includes a treatment of the interaction between a single point defect (represented by a force multipole) and a general internal or applied stress. In Section 11.3, the force multipole model is used to investigate the volume change due to a single point defect in a finite body possessing a traction-free surface, where the defect image stress can play an important role. Then, with Section 11.3 in hand, Section 11.4 takes up the particularly interesting problem of the behavior of a finite traction-free body filled with a statistically uniform distribution of point defects, which may, for example, be vacancies in thermal equilibrium or solute atoms dispersed throughout a solid solution. Analyses are given of the volume changes, macroscopic shape changes and lattice parameter changes (as measured by X-ray diffraction) produced by the defects. A demonstration is given of the intuitive result that a uniform concentration of point defects in a finite body with a traction-free surface produces a uniform average strain throughout the body. If the centers are spherically symmetric and act as centers of pure dilatation, the macroscopic body either expands or contracts uniformly throughout the body (depending upon whether the centers possess positive or negative strengths) with no change in body shape. If the centers possess lower symmetry, the body again expands or contracts uniformly but undergoes a macroscopic shape change, reflecting the symmetry of the defects.
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- Information
- Introduction to Elasticity Theory for Crystal Defects , pp. 215 - 228Publisher: Cambridge University PressPrint publication year: 2012