The effect of cohesive-law parameters on mixed-mode fracture

Cohesive-zone models of fracture provide a framework that allows a smooth transition between a strength-based approach to fracture and an energy-based approach. At the heart of these models are traction–separation laws that are described by a cohesive strength and toughness. These cohesive-law parameters can be used to define a cohesive-length scale that, when compared to physical length scales in the problem, gives an indication of whether failure is controlled by strength or energy considerations. Mixed-mode fracture is described by a phase angle that provides a measure of the partition of the deformation energy into shear and normal components. It is shown that this phase angle can be calculated for a cohesive-zone model, and that, if the cohesive length is small enough, the phase angle agrees with the value predicted by linear-elastic fracture mechanics, irrespective of the shape of the cohesive-laws. It is further shown that the cohesive length derived from the cohesive parameters can be used to rationalize the concept of a phase angle for interfacial fracture in the presence of a modulus mismatch. In particular, the length scale required to define a phase angle for interfacial fracture can be identified with the cohesive length of a cohesive-zone model. This phase angle shifts with changes in the cohesive length in accordance to the predictions of linear-elastic interfacial fracture mechanics.