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
15 - Interactions between interfaces and stress
- 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
An interface can experience a number of different types of force, including chemical forces (e.g., due to compositional differences across the interface), curvature forces (due to interface curvature) and mechanical forces (Sutton and Balluffi, 2006; Asaro and Lubarda, 2006). In view of the focus of this book, I consider only mechanical forces.
In general, an interface experiences a mechanical force when it lies between two adjoining regions containing different elastic fields and therefore different strain energy densities and elastic displacement fields. In such cases movement of the interface, in which one region grows at the expense of the other, can produce a decrease in the overall energy of the body and thereby give rise to a force on the interface, expressed by Eq. (5.38). Such a force can occur under a variety of circumstances. For example, during the recrystallization of a plastically deformed crystalline body, relatively strain-free crystals form and then grow into the surrounding plastically deformed and dislocated matrix. Here, the reduction in energy that occurs as the strain-free crystals grow at the expense of the dislocated matrix produces outward forces on the interfaces bounding the strain-free crystals. In other situations, elastic fields that differ across interfaces, and therefore generate a mechanical interface force, often occur in polycrystalline materials in the form of compatibility stresses, arising as a result of elastic anisotropy, anisotropic thermal expansion, and differing modes of plastic deformation in the crystals adjoining the interfaces (e.g., Sutton and Balluffi, 2006).
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- Information
- Introduction to Elasticity Theory for Crystal Defects , pp. 377 - 385Publisher: Cambridge University PressPrint publication year: 2012