A cohesive zone model for cracks terminating at a bimaterial interface

Linear elastic fracture mechanics (LEFM) does not provide a realistic propagation criterion for a crack tip touching a bimaterial interface. In fact, LEFM predicts that the crack penetrates the interface at either zero or infinite value of the characteristic applied load, depending on the relative stiffness of the bonded materials. This paper presents a cohesive zone model that provides a propagation criterion for such cracks in terms of the parameters that define the relation between the crack opening displacement and the traction acting along the crack surfaces. Extensive numerical results are presented for the case of constant cohesive traction, 6, associated with a critical crack tip opening displacement, q<. A quantitative evaluation of the effective toughening resulting from the presence of the interface is presented, for both small scale and large scale bridging, in terms of the Dundurs parameters (9 and /I), and pn/L, where pZ is proportional to the small scale critical cohesive zone length and L is a characteristic length of the crack problem. In particular, universal results for small scale bridging are presented as where k,. and 6, are, respectively the critical stress intensity factor and critical cohesive zone length, i is the power of the stress singularity associated with the elastic crack touching the interface, and A and B* are universal functions. These equations generalize those derived from the Dugdale model for a homogeneous medium. It is shown through the analysis of a finite length crack that for a relatively wide range of LX$ and pz/L values, the presence of the interface has a rather insignificant effect on the critical stress, and the elastic singularity associated with a crack terminating at the interface between two dissimilar elastic materials dominates the stress field within an extremely small near-tip region, 0 1997 Elsevier Science Ltd. All rights reserved.