Cohesive-zone analyses with stochastic effects, illustrated by an example of kinetic crack growth

Cohesive-zone models of fracture are traditionally implemented using a deterministic failure criterion, with crack advance occurring when the work done against crack-tip tractions reaches a critical level. There are, however, many physical phenomena where crack growth is controlled by stochastic events ahead of the crack. These can include kinetic crack growth, stress-corrosion cracking, and void nucleation. In this paper, we show how a cohesive-zone model might be adapted to describe such stochastic phenomena. In particular, we have chosen to model kinetic crack growth by assuming that the probability of local failure, or bond rupture, depends on the difference between the level of local work done against the cohesive tractions and the equilibrium toughness of the interface. We have shown that if the cohesive parameters are within a range appropriate for linear-elastic fracture mechanics (LEFM), and the possibility of failure is limited to the crack tip, then the model accurately reproduces a classical analytical model for kinetic crack growth, with the crack velocity having an exponential relationship with respect to the level of the energy-release rate above a threshold. As with all cohesive-zone models, a transition between toughness-controlled fracture and strength-controlled fracture occurs as the cohesive length is increased. However, it is further noted that if failure is not limited to the crack tip, but is allowed to occur anywhere ahead of the crack tip, then the length scale controlling the crack velocity changes from the mesh size to the cohesive length. This mesh-independent result is associated with diffuse damage ahead of the crack tip. From a physical perspective, such a damage zone could correspond to a situation with a low activation energy for bond rupture, or to one where the a crack grows in response to spatially diffuse stochastic process in a damage zone such as void nucleation, crazing or micro-cracking.