An Analytical Solution for the Interface Crack in a Quasi-Brittle Bonding Material

Abstract

An analytical solution to the problem of an interface crack in the presence of a small-scale process zone in a quasi-brittle bonding material near the crack tip is presented. In the process zone, a quadratic strength criterion of the Mises–Hill type is assumed. The problem of calculating the parameters of the process zone is reduced to a vector functional equation, for which a precise analyti-cal solution can be found using the Wiener–Hopf method. From the solution found, a closed system of transcendental equations is derived for determining the length of the process zone, the phase angle of the load, and the energy release rate in the zone, which form an accessible algorithm for estimating the limit loads that precede propagation of the crack along the interface. Numerical analysis of the developed model is performed, and the possibility of its application in fracture studies of some composite materials is demonstrated.