A Discussion on the Forms of Planar Mixed-Mode Fracture Criteria

Abstract

For the mixed-mode fracture on an original crack plane, the fracture criteria are usually based on the coupling of K I/K IC and K II/K IIC. Extended to general potential fracture planes, they become K I (θ)/K IC and K II (θ)/K IIC. Specifically, three forms have been widely used: linear, elliptical, and quadratic forms. The question of how these criteria perform is addressed by this research. This study does not intend to provide a general assessment but focused on only one case in which an analytical solution can readily be obtained. Specifically, we considered the performance of these criteria under Mode I loading, namely, K I ≠ 0, K II = 0. The analytical solution for fracture initiation angle under each of the three mixed-mode criteria were presented, where the results demonstrated that only the elliptical form yielded accurate results. That is, under Mode I loading, the initiation of pure Mode I fracture takes precedence that agrees well with standard results. What’s more, the mathematical requirements are obtained for the applicable mixed-mode fracture criteria.