A Computational Investigation of the Speed of Crack Propagation in Elastic Brittle Materials

Abstract

Recent experimental observations have shown that crack speeds in elastic brittle materials subjected to Mode-I loading can surpass not only the material's Rayleigh wave speed, but also its shear wave speed. This work investigates the maximum crack speeds that are predicted by a complete phase-field model, referred to as the 2024 nucleation model, that accounts for both crack nucleation and propagation by considering the material's strength surface. To examine this, two numerical experiments with glass material properties are examined: a pre-strained crack propagation problem and a velocity boundary condition problem. Each experiment has two cases: one where the crack is able to branch freely, thus dissipating energy, and another where branching is suppressed by restricting it to a banded region, thus utilizing the energy to drive the crack to travel faster. In both experiments, allowing the crack to propagate freely and branch results in sub-Rayleigh crack-tip speeds. In the restricted problem, for the pre-strained case, the limiting speed of crack propagation appears to be the Rayleigh wave speed. However, with velocity boundary conditions, crack propagation speeds that surpass the shear wave speed are achieved. These results indicate that the 2024 nucleation model predicts the possibility of super-shear dynamic crack propagation.