Understanding the properties of the cohesive zone in dynamic shear fracture

The velocity and stability of dynamic crack growth in brittle solids are determined by complex, lower-scale structure-driven processes in the cohesive zone where crack increment is formed. To find out how the rate of these processes controls the evolution of the cohesive zone and finally crack propagation regime, we applied an original mechanical model of fracture that takes into account the finite incubation time of local fracture and the relationship between the fracture time and the rate of change of local stresses. With this model, we numerically investigated the evolution of the cohesive zone ahead of the propagating longitudinal shear (mode II) crack in brittle and quasi-brittle materials. To describe the fracture of brittle and quasi-brittle materials within a unified mathematical formalism, the local fracture time was scaled within two orders of magnitude. In the study, we showed for the first time that the generally accepted form of the dependence of the cohesive zone length on crack propagation velocity Vcrack ("Lorentz contraction") is violated at high Vcrack values close to the Rayleigh wave velocity (crack growth in brittle materials) as well as at low Vcrack values (quasi-brittle materials), where its transits to exponential decay. We also showed that an increase in the scale of local fracture incubation time, corresponding to the transition from the brittle to the quasi-brittle failure mode, leads to a qualitative change in the mode of the dynamic variations of cohesive zone length from regular (periodic) to irregular (chaotic). It was established that the dynamic variations of cohesive zone length during the course of the crack propagation are determined by the instability of the maximum (peak) shear stress value.