A phase-field model for mixed-mode cohesive fracture in fiber-reinforced composites

The modeling of mixed-mode fracture within the phase field (PF) framework poses a challenge due to the difficulties in incorporating a reasonable mixed-mode cohesive law. This work proposes an innovative phase-field formulation to characterize mixed-mode cohesive fracture behaviors in fiber-reinforced composites (FRCs). The framework commences with the development of a multi-phase-field model capable of considering different failure mechanisms in FRCs within a thermodynamically consistent framework. Subsequently, a mixed-mode cohesive zone model (CZM) featuring the linear traction-separation law (TSL) is derived based on the careful construction of the PF driving force and degradation function. We mathematically prove that the proposed CZM effectively and rigorously characterizes the Hashin failure criteria for crack initiation and the power law criterion for crack propagation. Finally, several benchmark examples involving Mode-I/II and mixed-mode failures are investigated to demonstrate the model's capability in accurately predicting the cohesive fracture behaviors in FRCs, encompassing both the failure mechanisms dominated by fiber and matrix. This work paves the way for the PF modeling of fracture in FRCs that have previously been analyzed with sophisticated CZM-based approaches.