Interaction of a Screw Dislocation With an Arbitrary Shaped Elastic Inhomogeneity

Abstract

In this paper, the interaction between a screw dislocation and an arbitrary shaped elastic inhomogeneity with different material properties than the surrounding matrix is investigated. The exact solution to this problem is derived by means of complex variable methods and Faber series expansion. Specifically, the conformal mapping function maps the matrix region surrounding the inhomogeneity onto the outside of a unit circle in the image plane, while the analytic function defined in the elastic inhomogeneity is expressed in terms of a Faber series expansion. Once the series form solution is obtained, the stress fields due to the screw dislocation can be obtained. Also the image force on the screw dislocation due to its interaction with the elastic inhomogeneity is derived. Three examples of a screw dislocation interacting with (1) an equilateral triangular inhomogeneity, (2) a square inhomogeneity, and (3) a five-pointed star-shaped inhomogeneity are presented to illustrate how the stiffness of the triangular, square or five-pointed star-shaped inhomogeneity can influence the mobility of the screw dislocation.