A novel mixed-mode cohesive formulation for crack growth analysis

Modeling fracture with a cohesive zone model requires an appropriate cohesive law for correlating interfacial tractions and crack face separation, especially in mixed-mode loading scenarios. Various approaches have been employed in order to develop such a law which can be characterized into potential-based and non-potential-based formulations. A critical re-examination of these methods is presented here, followed by a novel mixed-mode formulation which satisfies a physical criterion for crack propagation. Specifically, as the crack propagates, the trailing current crack tip is defined through the vanishing of normal and tangential components of the interfacial tractions simultaneously. A general formulation for mixed-mode conditions is proposed in this paper. In particular, given normal and tangential traction separation laws for pure normal and tangential modes as being material properties, the normal and tangential traction separation laws in mixed-mode loading are formulated so that all traction components disappear at the same effective separation when the crack advances. The new mixed-mode law is used to analyze three standard fracture problems in laminated composites, including double cantilever beam (DCB), end-notch flexure (ENF), and mixed-mode bending (MMB). A comparison with predictions from some selected mixed-mode cohesive laws and experimental data available in the literature is also included to further validate the proposed mixed-mode law.