Influence of rate-dependent damage phase-field on the limiting crack-tip velocity in dynamic fracture

This contribution explores three thermodynamically-consistent damage phase-field formulations for rate-dependent dynamic fracture in viscoelastic materials. By means of a numerical study on a uniform displacement strip benchmark, the formulations and modelling assumptions are compared, and the corresponding limiting crack-tip speeds are discussed. In essence, in addition to recalling the existing phase-field model for viscoelastic materials, a damage phase-field formulation for rate-dependent toughness is introduced as a function of the damage-rate at the crack-tip and is contrasted to existing strain-rate dependent toughness models. Dynamic fracture simulations have demonstrated the significant role of rate dependency in suppressing crack branching and accelerating the crack propagation. The rate dependency is analysed through two main mechanisms: (i) the viscous dissipation, which can promote fracture, and (ii) an increase in the energy required to evolve a crack, through rate-dependent toughness models. Depending on the specific choice of parameters, the numerical simulations show crack propagation at speeds that exceed the theoretical limit depicted by the Rayleigh wave speed. Indeed, these high speeds are attributed to the viscoelastic and viscoelastic-like (observed in the case of strain-rate dependent fracture toughness) stiffening at the crack-tip, which translates to faster running surface waves and enables supersonic crack-speeds; a never-seen-before result in damage phase-field simulations.