Modeling progressive failure and crack evolution in a randomly distributed fiber system via a coupled phase-field cohesive model

Despite the high microstructural heterogeneity of fiber-reinforced composites, few modeling framework provides a comprehensive and detailed understanding of the failure mechanisms of these materials. The aim of this work is to present a coupled phase-field cohesive-modeling framework that can precisely capture the progressive failure and damage behaviors of multiphasic microstructures and multifiber systems. Here, the phase-field method captures crack evolution in the matrix, and a coupled cohesive-zone model is introduced to characterize interfacial debonding. The novel model framework comprises the following novel aspects. (1) A newly developed scalar indicator that directly extracts inelastic strain from the total strain field and couples the cohesive traction-separation law with the phase-field model to determine the regularized interfacial displacement jump. (2) The periodic boundary conditions in the coupled phase-field cohesive framework are incorporated to characterize crack evolution in random fiber systems. (3) A complete set of failure modes, namely crack initiation, propagation, kinking, and coalescence are characterized in highly heterogeneous solids. Parametric studies of the novel framework yield numerical results that are highly consistent with experimental findings and reveal the effects of fiber distributions, fiber volume fractions, and boundary conditions on the nonlinear mechanical behaviors of fiber-reinforced composites. The results demonstrate the excellent potential of the novel numerical framework to evaluate the mechanical performances of composite materials in engineering applications.