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

Abstract

The purpose of this work is to build an analytical model of an interfacial crack in piecewise homogeneous elastic bodies to predict the conditions of its initiation. The treatment is based on the concept of the process zone, which takes into account the existence of a local region with a high level of stresses and strains in the bonding material before the crack front. In the process zone, a quadratic strength criterion of the Mises-Hill type is assumed. The use of this criterion provides consideration of the quasi-brittle mechanism of the bonding material fracture. Using the Mellin integral transformation, the problem of calculating the parameters of the process zone in the bonding material at the tip of the interfacial crack within the framework of the proposed model 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 and the opening of the crack at its tip, 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.