Buried penny-shaped cracks

Abstract

Penny-shaped cracks are commonly used mathematical models, generally used in the field of fracture mechanics. One specific application is the modeling of micro-structures, within elastic materials. From a purely mathematical perspective, a penny-shaped crack can be described as a flat, disk-shaped crack. In this work, we consider the buried penny-shaped crack problem, consisting of a single crack, buried below the surface of a half-space. Specifically, the flat surface of the crack is taken to be parallel to the boundary, and the radius of the crack is held constant. The primary point of interest in this problem is the depth dependence of the stress intensity factor, which characterizes the fracture conditions near the tip of the crack. Determining the stress intensity factor for this problem is reduced to solving a pair of dual integral equations, specifically looking at these equations evaluated at the upper bound of integration. These equations were amenable to numerical solution, where the distance between the crack and the boundary was allowed to become small. The values of these equations, at the upper bound of integration, both tend toward 0. Based on the numerical results, the stress intensity factors for this problem were dependent on the depth at which the penny-shaped crack is buried.