On analytical model of interface crack in bonding quasi-brittle material between distinct elastic media

Abstract

Developed is an analytical model of an interfacial crack in the quasi-brittle bonding material with a process zone near its tip. In the process zone, a quadratic strength criterion of the Mises-Hill type is assumed. Using the Mellin integral transformation, the problem of calculating the parameters of the process zone is reduced to a vector functional equation, for which an exact analytical solution was found using the Wiener-Hopf method. From the solution found, a closed system of transcendental equations and relationships 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.