Finite element analysis of crack growth in inelastic media

Abstract

In most materials, macrocrack extension is accompanied by inelastic phenomena (such as microcracking or plastic deformation) throughout a region surrounding the crack tip. Immediately ahead of the crack tip, strain localization occurs in a small volume of heavily damaged material referred to as the failure zone or fracture process zone. In this study, the failure zone and the surrounding zone of inelastic material are treated as two distinct regions. The failure zone is assumed to be thin relative to its length and is represented in a two-dimensional finite element model as tractions which act across the crack faces near the tip. An opening mode of crack tip deformation is assumed. The normal traction at any point on the crack surface in the failure zone is specified as a decreasing function of the crack opening displacement which vanishes after a critical value of displacement is reached. Two different rate-independent, inelastic continuum characterizations are used; one models metal plasticity and another represents microcracking in brittle materials. Both constitutive models allow for the definition of a generalized J-integral developed by Schapery, which has the same value for most paths around the crack tip for realistic distributions of plasticity or damage in the material surrounding a stationary or propagating crack. This path independence is verified numerically for a crack growing under conditions of small-scale inelasticity, and the equivalence between J and the work input to the last ligament of material in the failure zone is demonstrated. Steady-state crack growth is studied in two different specimen geometries. Simplified J-integral analyses arc used to estimate the work input to the failure zone for these steady-state problems. The J-integral estimations are compared with finite element results to determine the accuracy of the simplified analyses.