A cohesive zone model with rate-sensitivity for fast crack propagation

The subject of dynamic fracture has received increasing attention in recent years owing to its relevance in a variety of industrial applications where crack initiation cannot be precluded. In this context design and verification of safe crack arrest in structures is the primary risk management strategy against unwanted and possibly catastrophic events. Tackling the problem of dynamic fracture via the classical cohesive-zone (CZ) approach requires a special care. This is mainly due to the fact that in dynamic fracture additional dissipative mechanisms can manifest that, if not properly accounted for, prevent from obtaining accurate numerical results. In particular, recent contributions have shown that use of classical rate-independent CZ models to simulate dynamic fracture can produce unrealistic answers. Conceptually this is not surprising since dynamic fracture phenomena typically occur over a quite short time scale, whereby some form of rate-dependency at the crack tip region is expectable. Basically, two different approaches have been used in the literature to account for this rate-dependency, that is either by using the classical CZ model in conjunction with a rate-dependent constitution for the bulk material, either introducing rate-sensitivity directly into the cohesive law. In the present work we introduce a basic form of rate-dependency into the cohesive relationship initially developed in [Valoroso e Champaney, 2006] in a way to make it adjustable in run-time to account for variations in the dissipation power with the velocity of the running crack. This requires in turn a suitable modification of the traction-separation law in which one includes, though in a rather implicit form, also the dissipation mechanisms that come into picture with kinetic energy.