Crack Motion Revisited

In our recent study of brittle fracture [1], we showed that hyperelasticity, the elasticity at large strain, plays a governing role in the onset of the crack instability from unidirectional motion. We discovered a simple, yet remarkable, scaling based on an effective elastic modulus for our modelled solid (the secant modulus at the stability limit) which led to successful predictions for the onset speed of the crack instability. We have now applied this scaling to the same modelled solid with the exception that the crack is constrained to travel unidirectional irrespective of its speed. This allows the crack to achieve a unique steady-state speed that has a dependence on hyperelasticity. Using our scaling law, we find that the steady-state crack speed scales to a constant value equal to a crack speed of a linear solid with our effective elastic modulus. We discuss how this finding is related to simple spring dynamics.