Finite Fracture Mechanics versus Phase Field: a case study on the crack onset from circular holes under biaxial loading conditions

The phenomenon of brittle crack onset stemming from a circular hole embodied in a biaxially loaded infinite plate is herein investigated. Three different approaches are used to determine the biaxial safety domains: Finite Fracture Mechanics, Cohesive Zone Model and Phase Field. In particular, the original formulation of Finite Fracture Mechanics (FFM) proves to be consistently more optimistic than its averaged-stress variant (FFM-avg); likewise, both agree in predicting the existence of a region in the loading space where failure is governed by the energy condition. Besides, failure predictions according to Dugdale’s Cohesive Zone Model (CZM) prove to be fairly close to those by FFM, whereas the differences between CZM and FFM-avg result more noticeable. Lastly, the Phase Field model of fracture is implemented paying special attention to the choice of the energy decomposition, being herein implemented two relevant options: No-Decomposition and No-Tension decomposition. In particular, the latter showcases reasonable agreement with FFM (and CZM), thus rendering it a solid contender for its use in applications in which combined tension-compression stress states appear, such as in the dynamic failure of brittle materials.