Fracture propagation near a frictionally - constrained fiber interface

Abstract

This work provides a three-dimensional numerical fracture mechanics analysis of a crack periphery as it propagates through a brittle matrix and encounters an individual brittle fiber. The surface integral method, based upon a distribution of singular fundamental solutions, is used to represent both the cracks and the coupled interfacial sliding zone. The interfacial frictional tractions are assumed to satisfy a Coulomb relationship and are determined iteratively from the stress induced by the matrix crack, the stress induced by the developing slip, and the initial normal compressive interfacial stress (i.e. from setting or thermal mismatch). Simulations of an initially long straight crack front moving toward and past a fiber for different interfacial frictional characteristics were conducted. The implications for tailoring fiber/matrix interfaces to optimize the global toughening effect are discussed. If the interface between fiber and matrix is cohesive enough (but not too cohesive) then tractions which develop at the interface may effectively retard the local growth of a matrix crack. Raising the friction coefficient (or cohesion) at the interface must, however, be balanced against the potential for fiber failure in the high stress zone near the matrix crack periphery. The implications frictional slippage holds for inhibiting and possibly arresting small matrix cracks are emphasized.