Effective toughness for bridged crack interacting with an arbitrary oriented and located microcrack

Abstract

The fracture problem for a brittle matrix reinforced by ductile particles is considered. As a crack propagates through the brittle matrix, it circumvents ductile particles which are left to form isolated bridges capable of supporting tractions across the crack faces and thus improve the fracture toughness of the matrix. The stress induced microcracking, which can provide another important toughening mechanism, is assumed to also take place. More specifically, a single microcrack arbitrary oriented and located ahead of the main crack tip is considered and the resulting combined toughening effect of crack bridging and crack–microcrack interaction is investigated. To make the problem mathematically tractable the restraining effect of bridging discrete forces is approximated by a continuum with an effective yield stress acting over a specified multiligament zone behind the crack tip. This zone is further simulated by an unknown continuous distribution of edge dislocations. The present work then proposes a self-consistent scheme, which relies on using a point-source representation for the microcrack and a simultaneous solution of integral equation for the unknown dislocation distribution. Both, the stress intensity factor (SIF) and crack opening displacement (COD) are derived for general orientation and position of microcrack and an effective fracture toughness of composite is assessed. This approximative solution is further tested using the exact solution for a collinear microcrack.