Weight functions and stress intensity factors for ring-shaped cracks

Ring-shaped cracks appear in many fracture mechanics problems of ceramic materials. In ceramics fracture is often caused by material inhomogeneities like spherical pores and inclusions. Failure of such inhomogeneities generally is modelled by failure of an annular crack extending around the inhomogeneity. A simple procedure to compute the stress intensity factors is the application of the weight function method. If the weight function for the special crack problem is available, the stress intensity factor can be obtained by integration of the product of weight function and stress distribution caused by the inclusion in the case of the uncracked structure over the crack length. In this report, the weight functions for a ring-shaped crack are derived and the stress intensity factors for remote tension and thermal loading are computed. These stress intensity factor solutions are then compared with K-factors available in literature.