A variationally-consistent phase-field cohesive zone model for mixed-mode fracture with directional energy decomposition scheme and modified-G criterion

Under complex stress-states, mixed-mode fracture is critical to the crack propagation. Additionally, in quasi-brittle materials, the toughness and strength can differ across fracture modes. Therefore, to analyze mixed-mode fracture behaviors under different stress conditions, we developed a new phase-field cohesive zone model (PF-CZM). A directional strain energy decomposition scheme with anisotropic constitution is applied to better describe the mechanical behaviors of damaged materials. A mixed-mode ratio is introduced to describe the relative contribution of mode I and mode II fracture to the crack propagation. Thus, the phase-field governing equation can be still derived by taking variation to the potential energy with respect to the phase-field. The crack orientation for propagation is assumed to be the direction that results in the maximum increase in crack area, which is demonstrated to be consistent with the modified G-criterion. The mode II crack orientation is determined using a deformation gradient-assistant approach. We also propose a new numerical frozen mechanism to take into account the interaction between the existing and incremental crack. Several numerical examples are provided to validate the current PF-CZM. The current study addresses when and how a crack will propagate in complex scenarios and significantly broadens the PFM’s applicability range for mixed-mode fracture, making it suitable for usage with a variety of materials.