Crack Onset at the Spherical-inclusion Matrix Interface. Application of a Coupled Stress and Energy Criterion

Abstract

The problem of crack initiation at the interface of a spherical inclusion embedded in an infinite matrix subjected to a remote tension is studied by the means of the coupled criterion of the finite fracture mechanics. This allows us to predict the critical tension necessary to initiate the crack at the interface as a function of the elastic properties of the particle and matrix, the particle size and the main parameters defining the strength and fracture properties of the interface. The coupled criterion assumes that a crack of a finite length appears when the next two criteria are simultaneously fulfilled: on the one hand a stress criterion which imposes a condition over the stresses at points where the crack initiates and on the other hand the crack onset must be energetically allowed. The coupled criterion is applied with the aid of an axisymmetric boundary element method code. The numerical model shows a strong influence of the spherical-inclusion radius on the critical remote tension.