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 eit her zero or infinite value of the characteristic applied load, dependi ng: on the relative stiffness of the bonded materials. This paper pres ents a cohesive zone model that provides a propagation criterion for s uch cracks in terms of the parameters that define the relation between the crack opening displacement and the traction acting along the crac k surfaces. Extensive numerical results are presented for the case of constant cohesive traction, sigma(o) associated with a critical crack tip opening displacement, eta(c). A quantitative evaluation of the eff ective toughening resulting from the presence of the interface is pres ented, for both small scale and large scale bridging, in terms of the Dundurs parameters (alpha and beta), and rho(2)/L, where rho(2) is pro portional to the small scale critical cohesive zone length and L is a characteristic length of the crack problem. In particular, universal r esults for small scale bridging are presented as k(c) = sigma(o)(rho(2 )/B(alpha, beta))(lambda), delta(c) = A(alpha, beta)/B*(alpha, beta)r ho(2) where k(c) and delta(c) are, respectively the critical stress in tensity factor and critical cohesive zone length, lambda is the power of the stress singularity associated with the elastic crack touching t he interface, and A and B are universal functions. These equations ge neralize 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 alpha-beta and rho(2)/L values, the presence of the interface has a rather insignificant effect on the critical st ress, and the elastic singularity associated with a crack terminating at the interface between two dissimilar elastic materials dominates th e stress held within an extremely small near-tip region. (C) 1997 Else vier Science Ltd.