Interaction between an infinitesimal glide dislocation loop coplanar with a penny-shaped crack

Abstract

This analysis develops a Green's function for a point shear dislocation coplanar with a penny-shaped crack. The solution procedure consists of using anti-symmetry conditions which allow the reduction to an asymmetric mixed boundary value problem for a half space. The mixed boundary conditions between the shear stresses and displacements on the surface are formulated in terms of a single pair and two coupled pairs of dual integral equations which have known solutions. Closed form expressions arc found for the shear displacement discontinuity inside the crack as well as for the shear stress on the crack -dislocation plane. The dislocation interaction solution is then used to formulate new integral equations for shear loading of multiple coplanar cracks or cracks with nonuniform crack fronts.