Extension and applications of rate-dependent cohesive zone models to mixed mode damage

Interfacial bonding failure between asphalt concrete and rail wrapping materials is a major challenge in tram track systems. The combination of complex stress conditions and the viscoelastic nature of asphalt makes traditional rate-dependent cohesive zone model (CZM) insufficient to describe mixed mode (I/II/III) fracture. In this study, a novel mixed mode rate-dependent CZM is proposed. The model integrates three orthogonal Maxwell elements with energy-driven damage initiation and evolution criteria, enabling a coupled description of multi-directional fracture in viscoelastic interfaces for the first time, and numerical implementation is accomplished via ABAQUS user material subroutine (UMAT). To address the high-dimensional parameter space of the proposed model, an inverse analysis framework is developed for efficient parameter identification. Experimental validation is performed through interfacial fracture tests on asphalt concrete-rail wrapping material composite specimens under varying loading rates and out-of-plane loading angles, confirming the model's ability to capture mixed-mode fracture behavior and rate-dependent failure mechanisms. The constitutive model is then implemented in a 3D solid finite element model of tram tracks to quantitatively evaluate interfacial bonding failure under typical operating speeds. Results indicate that that interface damage is increased with decreasing speed, that outer rail interface damage is more severe than inner rail damage, and that damage is propagated from the bottom to the top along the depth direction.