Three-dimensional stress analysis of composites considering interactions of cracks, inclusions and voids

Abstract

An analytical approach to calculate the stress of an arbitrary located penny-shaped crack interacting with other cracks, inclusions and voids is presented. First of all, the interaction between a penny-shaped crack and two spherical inclusions is analyzed by considering the three-dimensional problem of an infinite solid, composed of an elastic matrix, a penny-shaped crack and two spherical inclusions, under tension. Based on Eshelby`s equivalent inclusion method, superposition theory of elasticity and an approximation according to the Saint-Venant principle, the interaction between the crack and the inclusions is systematically analyzed. The stress intensity factor for the crack is evaluated to investigate the effect of the existence of inclusions and the crack-inclusions interaction on the crack propagation. To validate the current framework, the present predictions are compared with a noninteracting solution, an interacting solution for one spherical inclusion, and other theoretical approximations. The proposed analytical approach is extended to study the interaction of a crack with two voids and the interaction of a crack with an inclusion and a void. The current framework is used to derive formulations for the stress intensity factors and the strain energy release rate of interacting cracks in an infinite solid considering the influence of a spherical inclusion. In the solution process, the stress exerted on the cracks surfaces is assumed to be uniform for simplicity. The computational results in terms of stress intensity factors and strain energy release rate are presented for a variety of inclusion and cracks arrangements, relative muduli ratio among inclusion and matrix. The proposed approach and the two-point conditional probability function are applied together to analysis the stress over the crack considering the interaction of randomly located multiple cracks and inclusions. Numerical simulations of stress intensity factor for this case are also pr...