A crack tip process zone formed by the action of a non-linear cohesive stress

Abstract

An analysis is made of a Dugdale-type process zone formed at a crack tip in which the cohesive stress is a non-linear function of the relative displacement of the crack faces. Two cases are considered: where the stress singularity at the crack tip is completely suppressed and where it is attenuated by the process zone. Numerical solutions were obtained for parabolic hardening (cohesive stress proportional to the square root of crack opening). The results are discussed in relation to process zone formation in fibre composites with brittle constituents. Considerable toughening can be produced by a process zone involving fibre pull-out, but the length of zone required to achieve a given level of toughness depends sensitively on the force-displacement relation.