Fracture toughness of rough and frictional cracks emanating from a re-entrant corner

In mixed-mode conditions, the competing contribution of the different stress intensity factors predicts fracture initiation load as well as crack propagation direction. Commonly, mixed-mode fracture resistance is based on the assumption of smooth and frictionless cracks. However, the effect of friction and roughness cannot be neglected when mixed mode loading occurs, as in the case of a crack emanating from a re-entrant corner. In this paper, the effect of friction and roughness is evaluated through a simple saw-tooth model in a three-quarter-infinite plane (corresponding to a 90 degree re-entrant corner). The crack surfaces are assumed to be globally smooth, and roughness and friction are incorporated through a constitutive law between opposite crack surfaces. The solution is found using the distributed dislocation method, and an iterative algorithm is needed due to the non-linearity of the model. The effect of friction and roughness angle is discussed for a simple case.