Energy dissipation in the mixed mode growth of cracks at the interface between brittle materials

Abstract

In the present paper we compare the propagation of a crack in a homogeneous linear elastic material and the propagation of a geometrically identical crack located at the interface between two ideally brittle materials. Whereas the former crack is free to kink, the evolution of an interface crack results in a competition among the relative toughnesses of the surrounding layers and of the interface. By constraining cracks in homogeneous materials to propagate straight, as along an imaginary interface in a continuum, significant insights on the mixed mode growth of cracks at the interface between brittle materials are provided. It is shown that the collinear elongation in homogeneous materials under mixed mode conditions requires a higher amount of energy, which turns out to be dependent on the mode mixity. Such a surplus of energy has the same mathematical form of the expression widely used to model the increment of the fracture energy in layered materials. One can thus argue about which roles are played by thermodynamics constitutive prescriptions and which roles are played by geometrical constraints.