The effects of inter-surface cohesive tractions on linear and penny-shaped cracks

Abstract

A mesoscopic fracture model of equilibrium slit cracks in brittle solids, including inter-surface cohesive tractions acting near the crack tip, is analyzed and the effects of the cohesive tractions on the in-plane stress fields, crack-opening displacement profiles, and crack driving forces examined quantitatively for linear and penny-shaped cracks. The (numerical) analysis method is described in detail, along with results for four different cohesive forces. The assumed distribution of cohesive tractions were found to suppress the in-plane stress field adjacent to cracks in a homogeneous, isotropic medium when uniformly loaded in mode-I, and the suppression was a function of crack length. The crack-opening displacement profile was also perturbed and a new regime identified between the near-field Barenblatt zone and the far-field continuum zone. The extent of this ‘cohesive zone’ was quantified by use of an interpolating function fit to the calculated profiles and found to be independent of crack size for a given cohesive tractions distribution. Furthermore, the crack-opening displacement at the edge of the cohesive zone was found to be independent of crack size, implying that despite significant perturbations to the stress field, the crack driving force at unstable equilibrium remains unchanged with crack size.