An edge dislocation interacting with a completely coated semi-infinite crack

Abstract

We derive an analytic solution to the plane problem associated with an edge dislocation interacting with a completely coated semi-infinite crack in the presence of remote in-plane loading. The semi-infinite crack and the parabolic coating–matrix interface are confocal, and the coating and the matrix have the same shear modulus but distinct Poisson’s ratios. Through the introduction of a conformal mapping function and the application of analytic continuation, a closed-form representation of a particular auxiliary function can be obtained leading to analytic expressions of the two pairs of analytic functions in the image plane characterizing the elastic fields in the two-phase composite. The local mode I and mode II stress intensity factors at the crack tip and the image force acting on the edge dislocation are then derived.