An Image Force Theorem for a Line Dislocation Near a Semi-Infinite Interfacial Crack in an Anisotropic Elastic Bimaterial

Abstract We use the Stroh sextic formalism to derive a real-form expression in terms of the Barnett–Lothe tensor L for the radial component of the image force acting on a line dislocation near a semi-infinite interfacial crack between two dissimilar anisotropic elastic half-spaces. The radial image force is always attractive and is independent of the elastic property of the half-space free of the dislocation, the angular position of the dislocation with respect to the interfacial crack plane, and the orientation of the interfacial crack plane. Furthermore, the radial image force is identical to that for a line dislocation in an anisotropic elastic half-space with a traction-free boundary. The Barnett–Lothe tensor appearing in the radial image force belongs to the half-space containing the dislocation, and the dislocation is attracted toward the interfacial crack.