A three-dimensional stress analysis of a penny-shaped crack interacting with a spherical inclusion

Abstract

A three-dimensional elastic stress analysis is performed on an infinite solid to study the interaction between a penny-shaped crack and a spherical inclusion. In our derivation, a two-step superposition scheme is utilized to obtain the stress field over the imaginary crack site. The Duhamel-Neuman analogy is employed to transform an elasticity problem of a heterogeneous solid into an equivalent problem of a homogeneous solid in which the inclusion is replaced by the void and the boundary conditions modified accordingly. The effect. of the inclusion and the crack-inclusion interaction on crack propagation is interpreted in terms of the stress intensity factor for a penny-shaped crack. Finally, the proposed analytical approximations are compared with the noninteracting solution, the exact solution, and other theoretical approximations to validate the current framework.