Development of fracture facets from a crack loaded in mode I+III: Solution and application of a model 2D problem

International audienceIt is experimentally well-known that a crack loaded in mode I+III propagates through formation of discrete fracture facets inclined at a certain tilt angle on the original crack plane, depending on the ratio of the mode III to mode I initial stress intensity factors. Pollard et al. (1982) have proposed to calculate this angle by considering the tractions on all possible future infinitesimal facets and assuming shear tractions to be zero on that which will actually develop. In this paper we consider the opposite case of well-developed facets; the stress field near the lateral fronts of such facets becomes independent of the initial crack and essentially 2D in a plane perpendicular to the main direction of crack propagation. To determine this stress field, we solve the model 2D problem of an infinite plate containing an infinite periodic array of cracks inclined at some angle on a straight line, and loaded through uniform stresses at infinity. This is done first analytically, for small values of this angle, by combining Muskhelishvili (1953)'s formalism and a first-order perturbation procedure. The formulae found for the 2D stress intensity factors are then extended in an approximate way to larger angles by using another reference solution, and finally assessed through comparison with some finite element results. To finally illustrate the possible future application of these formulae to the prediction of the stationary tilt angle, we introduce the tentative assumption that the 2D mode II stress intensity factor is zero on the lateral fronts of the facets. An approximate formula providing the tilt angle as a function of the ratio of the mode III to mode I stress intensity factors of the initial crack is deduced from there. This formula, which slightly depends on the type of loading imposed, predicts somewhat smaller angles than that of Pollard et al. (1982)