Cohesive Zone Interpretations of PhaseField Fracture Models

Abstract

Unlike micromechanics failure models that have a welldefined crack path, phasefield fracture models are capable of predicting the crack path in arbitrary geometries and dimensions by utilizing a diffuse representation of cracks. However, such models rely on the calibration of a fracture energy (Gc) and a regularization lengthscale (lc) parameter, which do not have a strong micromechanical basis. Here, we construct the equivalent cracktip cohesive zone laws representing a phasefield fracture model, to elucidate the effects of Gc and lc on the fracture resistance and crack growth mechanics under mode I Kfield loading. Our results show that the cohesive zone law scales with increasing Gc while maintaining the same functional form. In contrast, increasing lc broadens the process zone and results in a flattened tractionseparation profile with a decreased but sustained peak cohesive traction over longer separation distances. While Gc quantitatively captures the fracture initiation toughness, increasing Gc coupled with decreasing lc contributes to a rising fracture resistance curve and a higher steadystate toughness—both these effects cumulate in an evolving cohesive zone law with crack progression. We discuss the relationship between these phasefield parameters and process zone characteristics in the material.