Interactions Between Dislocations and Anisotropic Elastic Elliptical Inclusions

A general field solution for the stresses and displacements of the interactions between dislocations and inclusions has been derived in this paper by applying the Stroh’s formalism and the Muskhelishvili’s method of analytical continuation. The solutions are valid for general elastic anisotropic media under two-dimensional deformation. The interaction energy between dislocations and elastic inclusions is obtained explicitly. The solutions in general are expressed in series form for elastic inclusions. However, for the special cases when the elastic inclusions are replaced by a hole or rigid inclusion, simple closed-form solutions are derived. The general solutions are verified by considering the isotropic media since it is the only solution available in the literature. For the general anisotropic media, a series of contour diagrams for the glide component of the force on a dislocation are provided in this paper to study the effects of inclusion hardness, shape, and matrix anisotropy.