A Long Crack Penetrating a Circular Inhomogeneity

This paper presents the effects of elastic mismatch and crack-tip position on the stress intensity factors of a long crack penetrating a circular inhomogeneity. The analysis relies on closed-form solutions, derived using complex variable techniques, for the stresses and displacements produced by dislocations positioned inside and outside the inhomogeneity. Dislocation distributions are introduced to express the traction boundary condition along the crack surfaces as a system of singular integral equations, whose solution is obtained through a numerical procedure. It is shown that if the elastic mismatch is interpreted correctly, then the stress intensity factors of this micromechanical model are very good approximations to those computed using a Monte Carlo finite element model of a long crack in a polycrystalline plate with compliant grain boundaries.