The steady-state response of a three-phase elliptical inhomogeneity with interface slip and diffusion under an edge dislocation in the matrix

Abstract

We study the steady-state response of a three-phase elliptical inhomogeneity in which the internal elliptical elastic inhomogeneity is bonded to the surrounding infinite matrix through an interphase layer with two confocal elliptical interfaces permitting simultaneous interface slip and diffusion. The matrix is subjected to an edge dislocation at an arbitrary position and uniform remote in-plane stresses. An analytical solution to the steady-state problem is derived using Muskhelishvili’s complex variable formulation. The effect of the edge dislocation and remote loading on the elastic fields in the inhomogeneity and the interphase layer is exhibited through a single loading parameter. More specifically, when divided by this loading parameter, the expressions for the stresses and strains in the inhomogeneity and the interphase layer are uninfluenced by the specific loading applied in the matrix. After excluding a particular common factor, the stresses and strains in the inhomogeneity and the interphase layer are also unaffected by the mismatch in shear moduli between the interphase layer and the matrix.