Stability of failure initiation by fracture for a bimaterial body with an edge crack

Abstract

Initiation of failure in a nonhomogeneous system made of two dissimilar materials that are bonded along a common interface is examined by considering both the local and global stationary values of the strain energy density function, dW dV . A length parameter, l, that represents the distance between [( dW dV ) min max ] l and [( dW dV ) min max ] g is determined for evaluating the stability of failure initiation by fracture. The subsscripts L and G on the maximum energy density refer, respectively, to the local and global stationary value. In particular, the combined influence of material inhomogeneity, position of load relative to an initial edge crack, and dimensional changes in the parameter l are analyzed. Both linear elastic and nonlinear elastic-plastic materials are considered. Predictions on the sites of potential fracture trajectories are made. The results led to a number of important conclusions. In the analysis, the following remain unchanged: the load and initial crack are always in separate material and the system is supported on the cracked side of the bimaterial body. A general trend is that fracture initiating from the crack tip tends to spread towards the concentrated load. Failure becomes more stable when the crack is moved closer to the support. The same can be accomplished by increasing the modulus of the material on which the load is applied. Plastic flow also enhances the failure stability, in contrast to crack front deformation that is purely elastic. Failure initiated by a uniform shear load is found to be more stable than that caused by loads applied normal to the boundary of the bimaterial system.