Crack kinking from an initially closed, ordinary or interface crack, in the presence of friction

Abstract

One theoretically studies crack kinking from an ordinary crack (in some homogeneous solid) or an interface crack (between two dissimilar materials), in the situation where this crack is closed prior to kinking but open after it. This problem was recently considered by the authors with the simplifying, but physically quite unrealistic hypothesis of absence of friction between the crack lips. Their work is extended here to account for possible friction governed by Coulomb’s law. Problems of elastic fracture mechanics with unilateral contact and friction between the crack lips being not only non-linear, but incremental in nature, the theoretical treatment becomes notably more involved than without friction. It is still based, however, on the same basic ingredients, namely “homogeneity” properties of the type of problems considered, changes of scale and some reasonable hypotheses. It is shown that whatever the geometry of the body and the crack and whatever the loading, the asymptotic expression of the stress intensity factors (SIF) at the tip of a vanishingly small kinked crack extension depends solely upon the initial (mode II) SIF prior to kinking, the kink angle, Dundurs’s famous parameters α and β and the friction coefficient. The (history-independent) functions involved in the general formulae established are determined numerically through finite element computations. From there, using Goldstein and Salganik’s famous principle of local symmetry to predict the crack path, one derives a theoretical value for the kink angle. This value depends upon the loading only through the sign of the initial stress intensity factor; it also depends on the mismatch of elastic properties and the friction coefficient. However, its range of variation is numerically found to be rather narrow. Experiments conducted by various authors seem to confirm these theoretical predictions.