Elastic-Plastic Analysis of Cracks on Bimaterial Interfaces: Part III—Large-Scale Yielding

In Parts I and II, the structure of small-scale yielding fields of interface cracks were described in the context of small strain plasticity and J₂ deformation theory. These fields are members of a family parameterized by the plastic phase angle ξ which also determines the shape or phase of the plastic zone. Through full-field analysis, we showed the resemblance between the plane-strain interface crack-tip fields and mixed-mode HRR fields in homogeneous material. This connection was exploited, to the extent possible, inasmuch as the interface fields do not appear to have a separable form. The present investigation is focused on “opening” dominated load states (| ξ | ≤ π/6) and the scope is broadened to include finite ligament plasticity and finite deformation effects on near-tip fields. We adopt a geometrically rigorous formulation of J₂ flow theory taking full account of crack-tip blunting. Our results reveal several surprising effects, that have important implications for fracture, associated with finite ligament plasticity and finite strains. For one thing the fields that develop near bimaterial interfaces are more intense than those in homogeneous material when compared at the same value of J or remote load. For example, the plastic zones, plastic strains, and the crack-tip openings, δ_t, that evolve near bimaterial interfaces are considerably larger than those that develop in homogeneous materials. The stresses within the finite strain zone are also higher. In addition, a localized zone of high hydrostatic stresses develops near the crack tip but then expands rapidly within the weaker material as the plasticity spreads across the ligament. These stresses can be as much as 30 percent higher than those in homogeneous materials. Thus, the weaker material is subjected to large stresses as well as strains—states which promote ductile fracture processes. At the same time, the accompanying high interfacial stresses can promote interfacial fracture.