Elastic-plastic analysis of a collinear array of cracks on a bimaterial interface

Abstract

Abstract In previous studies, we found that although the near-tip fields of cracks on a bimaterial interface do not have a separable form of the Hutchinson-Rice-Rosengren (HRR) type, they appear to be nearly separable in an annular region well within the plastic zone. Furthermore, the fields bear interesting similarities to mixed mode HRR fields for homogeneous media. Over length scales comparable to the size of the dominant plastic zone, the stress levels in both materials are set by the yield strength of the weaker (lower yield strength) material. Over distances which are small compared with the smallest dimension of the plastic zone (or distances comparable with the crack tip opening displacement), the behavior of the stresses is governed by the strain hardening characteristics of the more compliant (lower hardening) material. Asymptotically, as the crack tip is approached, the material system responds like that of a plastically deforming solid bonded to a rigid substrate; in particular, the stress and the strain fields in the more compliant material behave like those of a material with identical plastic properties bonded to a rigid substrate. Guided by this observation, our attention is directed to the plane strain problem of a deformable material bonded to a rigid substrate. The bimaterial interface is populated by a row of collinear cracks. The body is loaded by remote tension so that the cracks remain effectively open over size scales that are physically relevant. Contained and large-scale yielding solutions for cracks with crack-length-to-ligament ratios that differ by more than two orders of magnitude are obtained by finite element analysis. The solutions reveal that the effects of load (or finite ligament plasticity) and geometry on the near-tip fields are adequately accounted for by the J integral. Furthermore, the near-tip fields appear to possess a structure which is similar to that already presented in previous publications on the small-scale yielding problem. Over the full range of loads considered, the relation between the crack opening displacement (measured at the center of the crack) and the J integral is not sensitive to differences in geometry associated with widely different crack-length-to-ligament ratios.