Interaction of a straight screw dislocation with a circular cylindrical inhomogeneity in the context of second strain gradient theory of elasticity

Abstract

In the context of Mindlin’s second strain gradient theory of elasticity, this paper presents an analysis of the elastic state of an infinite isotropic medium that contains a straight screw dislocation in the vicinity of a circular cylindrical inhomogeneity. For determination of the interaction fields of such an inhomogeneity–dislocation ensemble, first the dislocation is described by a proper eigenstrain field. Then, by applying a sufficient number of continuity conditions across the interface of the inhomogeneity with its surrounding matrix, analytical solutions are derived for the elastic displacement and strain fields of the interior and exterior points of the inhomogeneity. Furthermore, an expression will be determined for the image force acting by the inhomogeneity on the dislocation. The obtained solutions clearly exhibit the effect of the characteristic lengths of the constituent materials of the medium on the elastic fields developed therein. It is also demonstrated that such size-dependent elastic fields do not possess any classical singularities and, by increasing the size of the inhomogeneity relative to the characteristic lengths, all solutions tend to those obtained by classical elasticity.