A comprehensive interpretation of the J-integral for cohesive interface cracks and interactions with matrix cracks

Abstract

In linear elastic fracture mechanics various loading quantities exist to describe the crack tip loading, like stress intensity factors, the energy release rate or the J-integral. The J-integral is calculated along an arbitrary integration path and is related to the other loading quantities. In non-standard problems including e.g. temperature gradients, material inhomogeneities or interfaces, the path independence of the J-integral is only ensured considering additional terms. Material interfaces can be strong (perfect) or weak (imperfect), whereas dissipative processes only arise in weak interfaces. In this paper a matrix crack with a classical crack tip stress singularity is investigated, interacting with an interface crack, in the latter case modelling the fracture process zone in front of the physical crack tip by cohesive zone theory. The dissipation in the interface due to delamination has an influence on the loading of the matrix crack in terms of the J-integral and thus on its deflection and path. In order to identify this influence, the matrix crack tip loading is calculated accurately applying the J-integral in connection with a large integration contour enclosing the interface. Additional terms on the one hand ensure path independence, on the other their physical interpretation is desirable. In particular the contribution of the cohesive zone is considered closely, revealing a generalized mixed-mode relation of the J-integral and crack tip opening displacements, depending on the cohesive law, as in the classical mode I case, and on the boundary value problem. With multiple dissipative processes, the global energy release rate of the multi-crack system is not trivially calculated either. Numerical examples reveal e.g. that the matrix crack tip loading in the presence of an imperfect interface may be increased, even though energy is dissipated. Crack growth simulations show the preference of a matrix crack to grow into the direction of lower stiffness giving rise to an extremely attracting effect of damaged interfaces.