Penny-shaped crack revisited: Closed-form solutions

Abstract

Closed-form solutions are obtained for a penny-shaped crack in a transversely isotropic elastic body, with the crack faces subjected to an arbitrary normal and shear loading. These results are important for investigating crack interactions. A simple and direct relationship is established between the limiting values of the tangential displacements and the stress intensity factors. A new governing integral equation is derived which is valid for an arbitrary crack under shear loading. This equation can be solved exactly and in an elementary manner for an elliptical crack under polynomial shear loading, and an approximate analytical solution is possible for a general crack under shear loading. Several illustrative examples are considered.