A Finite Element Analysis of Mode III Quasi-Static Crack Growth at a Ductile-Brittle Interface

Steady-state quasi-static crack growth along a bimaterial interface is analyzed under Mode III, small-scale yielding conditions using a finite element procedure. The interface is formed by an elastic-plastic material and an elastic substrate. The top elastic-plastic material is assumed to obey the J₂ incremental theory of plasticity. It undergoes isotropic hardening with either a bilinear uniaxial response or a power-law response. The results obtained from the full-field numerical analysis compare very well with the analytical asymptotic results obtained by Castan˜eda and Mataga (1991), which forms one of the first studies on this subject. The validity of the separable form for the asymptotic solution assumed in their analysis is investigated. The range of dominance of the asymptotic fields is examined. Field variations are obtained for a power-law hardening elastic-plastic material. It is seen that the stresses are lower for a stiffer substrate. The potential of the bimaterial system to sustain slow stable crack growth along the interface is studied. It is found that the above potential is larger if the elastic substrate is more rigid with respect to the elastic-plastic material.