Analysis of a rate-dependent cohesive model for dynamic crack propagation

The effect of including rate-dependence in the cohesive zone modeling of steady-state and transient dynamic crack propagation is analyzed. Spontaneous crack propagation simulations are performed using a spectral form of the elastodynamic boundary integral equations, while the solution to the steady-state problem is obtained by solving the governing Cauchy singular equation on the crack plane. The steady-state analysis shows that the existing techniques for solving the Cauchy singular integral equation are not suitable. A solution technique for the underlying Riemann–Hilbert problem for the chosen rate and damage-dependent cohesive law is presented. Under spontaneous propagation conditions, quasi-steady-state speeds slower than the theoretically predicted shear wave speed are possible. Results also show that, due to the dissipation of energy inside the cohesive zone, the energy required for crack propagation increases with the crack speed.