A rate-dependent cohesive model for simulating dynamic crack propagation in brittle materials

Numerical investigations are conducted to simulate high-speed crack propagation in pre-strained PMMA plates. In the simulations, the dynamic material separation is explicitly modeled by cohesive elements incorporating an initially rigid, linear-decaying cohesive law. Initial attempts using a rate-independent cohesive law failed to reproduce available experimental results as numerical crack velocities consistently overestimate experimental observations. As proof of concept, a phenomenological rate-dependent cohesive law, which bases itself on the physics of microcracking, is introduced to modulate the cohesive law with the macroscopic crack velocity. We then generalize this phenomenological approach by establishing a rate-dependent cohesive law, which relates the traction to the effective displacement and rate of change of effective displacement. It is shown that this new model produces numerical results in good agreement with experimental data. The analysis demonstrates that the simulation of high-speed crack propagation in brittle structures necessitates the use of rate-dependent cohesive models, which account for the complicated rate-process of dynamic fracture at the propagating crack tip.