Elastic-plastic Crack Growth Along Ductile/Ductile Interfaces

Abstract

An analytical study is performed of the stress and deformation fields near the tip of a crack that grows quasi-statically along an interface between two generally dissimilar ductile materials. The materials are modeled as homogeneous, isotropic, incompressible, elastic-ideally plastic Prandtl-Reuss-Mises, and the analysis is carried out within a small-displacement-gradient formulation. The case of anti-plane shear deformations is considered first. We derive near-tip solutions for the full range of the ratio of the two materials’ yield stresses, and show that a near-tip family of solutions exists for each set of material properties; the implication is that far-field loading and geometrical conditions determine which specific near-tip solution governs in a particular problem. As a by-product of this analysis, we derive a new solution family for anti-plane shear crack growth in homogeneous material, one limiting member of which is the familiar Chitaley and McClintock (1971) solution. We also analyze the case of plane strain crack growth under applied tensile loading. Here, we account for curvature of inter-sector boundaries, in an attempt to obtain a complete set of solutions. When the material properties are identical, the solution family of Drugan and Chen (1989) for homogeneous material crack growth, which has an undetermined parameter in the near-tip field, is recovered. As the ratio of the two materials’ yield strengths, ĸ, deviates from unity, the near-tip solution structure is found to change, but the near-tip fields are shown to continue to possess a free parameter for a substantial range of ĸ. Below this range, a second solution structure develops for which the near-tip free parameter has a restricted range of freedom. Finally, a third near-tip solution structure develops for sufficiently low ĸ, for which there are no free parameters. The implications of these results appear to be that as the plastic yield strength mismatch of the two materials becomes larger, far-field loading and geometry have increasingly weaker effects on the leading-order near-tip fields, until finally a mismatch level is reached beyond which far-field conditions no longer affect the leading-order fields. However, conclusions are complicated by the fact that the analysis also implies the radius of validity of the leading-order fields to decrease continuously with increasing yield strength mismatch (beyond a certain level), so that below some ¯k value, it will become necessary to retain more than one term to describe the physical near-tip fields. Although not specifically explored here, our analysis also allows comparison of the effects of changing elastic and plastic properties of the two materials on crack growth propensity, so that perhaps this analysis could assist in the optimization of interfacial fracture properties.