Cohesive traction-separation relations for plate tearing under mixed mode loading

The present study investigates a sequence of failure events related to steady-state tearing of large-scale ductile plates by employing the micro-mechanics based Gurson-Tvergaard-Needleman (GTN) model. The fracture process in front of an advancing crack is approximated by a series of 2D plane strain finite element models to facilitate a comprehensive study of mixed mode fracture behavior as well as a parameter study of the cohesive energy and tractions involved in the process. The results from the conducted GTN model simulations are used to define cohesive zone models suitable for plate tearing simulations at large scale. It is found that mixed mode loading conditions can have a significant effect on the cohesive energy as well as relative displacement (in reference to pure mode I loading), while peak traction is practically unaffected. Specifically, increasing mode II contribution leads to monotonic increase of the cohesive energy. In contrast, the effect of mode III is more complicated as it leads to reduction of the mixed mode cohesive energy (in reference to pure mode I loading) at low to medium levels of mode mixity ratios (0-0.3). However, increasing mode III contribution beyond the mode mixity ratio of 0.3, reverses this trend with cohesive energy potentially exceeding the pure mode I level when at mode mixity ratio of 0.6 or higher. This behavior cannot be captured by the interactive cohesive zone models that rely on a simple rotational sweep of mode I traction-separation relation. Depending on the shear mode contribution, i.e., mode II or mode III, these models can lead to overly conservative (mode II) or unconservative (mode III) prediction of the crack growth resistance.