A Long Crack Penetrating a Transforming Inhomogeneity

Abstract

This note presents the stress intensity factors of a long crack penetrating a circular transforming inhomogeneity. Using the Greens functions of dislocations interacting with a circular inhomogeneity experiencing an isotropic (free expansion) eigenstrain, the elasticity solution is reduced to a system of singular integral equations representing the traction boundary condition along the crack surfaces. The normalized stress intensity factor, obtained through a numerical solution of the integral equations, has a strong dependence on the elastic mismatch, and can be either negative or positive depending on the crack-tip location. The formulation and results generalize a previously published transformation-toughening model that assigns equal elastic moduli to the inhomogeneity and the surrounding medium.