Cracks and dislocation arrays in heterogeneous media

The paper considers the anti-plane strain model of a crack or dislocation array that is centrally situated within a circular cylindrical inhomogeneity surrounded by an infinite body, the elastic shear moduli of the two regions having different and unrestricted values; the appropriate shear stress at the crack or dislocation array and the applied stress at infinity have uniform values. The discussion of this general problem is restricted to the case where the crack or dislocation array size is small compared with the cylinder radius, the condition for crack extension and the number of dislocations within an array then being determined. Special situations are, however, considered in detail and for a crack within a cylinder it is shown that a close correspondence exists between the solutions for the cases where the surrounding material is either a rigid envelope or free space. This correspondence is even valid when the crack size is large compared with the cylinder radius; hence by determining separately the condition for extension of a crack of unrestricted size within a circular cylinder surrounded by a rigid envelope, the corresponding condition is derived for the case where the surrounding material is free space.