Microscopic analysis of crack propagation for multiple cracks, inclusions and voids

The elastic crack interaction with internal defects, such as microcracks, voids and rigid inclusions, is investigated in this study for the purpose of analyzing crack propagation. The elastic stress field is obtained using linear theory of elasticity for isotropic materials. The cracks are modeled as pile-ups of edge dislocations resulting into a coupled set of integral equations, whose kernels are those of a dislocation in a medium with or without an inclusion or void. The numerical solution of these equations gives the stress intensity factors and the complete stress field in the given domain. The solution is valid for a general solid, however the propagation analysis is valid mostly for brittle materials. Among different propagation models the ones based on maximum circumferential stress and minimum strain energy density theories, are employed. A special emphasis is given to the estimation of the crack propagation direction that defines the direction of crack branching or kinking. Once a propagation direction is determined, an improved model dealing with kinked cracks must be employed to follow the propagation behavior.