Near-Tip Fields for Quasi-Static Crack Growth Along a Ductile-Brittle Interface

Abstract

As an analytical first study of the mechanics of ductile-brittle interfacial crack growth, I derive the stress and deformation fields near the tip of a crack that is growing quasi-statically along an interface joining material phases idealized as being rigid on one side and homogeneous, isotropic, elastic-ideally plastic on the other. Both the cases of antiplane strain and plane strain are treated, since it is some combination of these that pertains near an interface crack under general three-dimensional conditions. In the antiplane strain case, a family of solutions for the growing crack fields is found covering all admissible crack line shear stress ratios except for the case when the shearing is parallel to the crack; the Mode III homogeneous material solution is shown to be a limiting member of this family. Two distinct solution families are shown to exist for the growing crack fields in the plane strain case. One of these contains the Mode I homogeneous material solution and is characterized by large crack line stress triaxialities (up to 39 percent higher than that in homogeneous material solutions), while the other family has a limiting member that closely resembles (but is not identical to) the Mode II homogeneous material solution and is characterized by small and even negative crack line stress triaxialities. These solutions, which appear to constitute all possible that involve traction-free crack faces, are shown to cover large portions, but not the entire admissible range, of crack line near-tip shear/normal stress ratios (“mixities“).