A unified phase-field framework for matrix cracking and interfacial debonding in composites: Effects of interpolation function

Within the phase-field framework, matrix cracking and interfacial debonding in composites are simultaneously captured by introducing dual phase-field variables. To smooth a sharp interface, an interface-related phase-field variable is defined, and equivalent material parameters are formulated using interpolation functions that depend on the interface phase-field distribution. On the basis of the phase-field cohesive zone model, a crack phase-field variable is employed to capture material failure, enabling the characterization of various interfacial failure modes and quantification of the effect of interface strength on fracture behavior. Numerical results demonstrate that the interpolation function order significantly affects structural response: higher-order interpolations expand the low-fracture-energy region near the interface, reduce the predicted peak load, and promote a transition in the crack path from interfacial debonding to matrix cracking. This transition is attributed to the smoother variations in the local stiffness and fracture resistance introduced by higher-order interpolations. Moreover, increasing the interface strength enhances the load-bearing capacity and drives the fracture mode toward matrix-dominated cracking. For fiber-reinforced composite cases, the results obtained from higher-order interpolations closely match those derived from cohesive element models, validating the proposed approach. This framework offers a robust computational tool for investigating the interaction between interfacial debonding and matrix cracking, and provides deeper understanding of how interface parameterization influences fracture behavior in composites.