MODEL OF THE PROCESS ZONE IN A QUASI-BRITTLE MATERIAL OF A BIMATERIAL BODY NEAR THE TIP OF AN INTERFACIAL CRACK AT THE CORNER POINT OF A BROKEN INTERFACE

Abstract

A mathematical model of the process zone is developed, which under plane strain conditions is formed in a material with a quasi-brittle fracture mechanism near the apex of the interfacial crack at the corner point of the fractured interface. The process zone is modeled by a displacement discontinuity line on which the Mises—Hill strength condition is satisfied with the limit values of normal and tangential stresses in the quasi-brittle material as criterion parameters. The external load is taken into account by formulating the condition at infinity in the form of a requirement to cross-link the desired solution with the asymptotics of the known solution of a similar problem without a process zone. With the help of Mellin’s integral transformation, the problem of calculating the parameters of the process zone is reduced to a vector functional equation for the transformants of stress components and displacement gradients. For its solution, an approximate method based on the stepwise partition of the original equation into a pair of independent scalar functional equations, which are solved using the Wiener—Hopf method, is used. From the found approximate solution of the functional equation of the problem, a closed system of transcendental equations and relations for calculating the length of the process zone, the phase angle of stresses and the value of energy dissipation in the zone is obtained. The angle of inclination of the zone to the interface is determined from the condition of the maximum value of energy dissipation. An expression for the rate of energy dissipation in the zone is obtained, which provides the application of the energy criterion for estimating the ultimate load preceding crack nucleation in the direction determined by the orientation of the process zone at the time of nucleation.