Toughening induced by the formation of facets in mode I+III brittle fracture: Experiments versus a two-scale Cohesive Zone model

Abstract

When subjected to some anti-plane shear mode III loading, segmentation of the crack front frequently occurs during propagation: even if the crack is initially planar, propagation produces facets/segments rotated toward the shear free direction. Here, we examine, both experimentally and theoretically, the effect of this microstructure on the effective macroscale brittle fracture toughness. Experiments performed on PMMA beams reveal that the critical load leading to abrupt rupture increases with mode III to mode I ratio. This apparent macroscopic toughening is usually taken into account by invoking a specific mode III toughness in addition to the mode I one. By applying thoroughfully a micro/macroscale Cohesive Zone (CZ) model that we have recently developed, we demonstrate that an additional material constant is useless here since this toughness increase can be attributed mainly to the presence of the facets at the microscale, whose geometry can be anticipated to depend on the classical mode I material constants. More precisely, two related physical mechanisms are generated due to the formation of a disconnected crack front: (i) changes in fractured surface area in comparison to a straight propagation, and (ii) crack shielding caused by the facets that reduce the effective crack opening. While the first effect is obvious to quantify, we show that the second plays an essential role but is more complex to take into account: it depends on the solution of the three-dimensional elasticity problem in presence of the facets, that is considered in the CZ model. We illustrate on the experiments how to use this approach in practice to determine the critical fracture threshold.