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.