The critical velocity of mode-I fracture in a non-linear lattice in the absence of viscosity

Abstract

The high-velocity regime of mode-I fracture is interesting, especially because of the instability of the steady-state propagating crack to a more complex dynamics (such as micro-branching). In this article, we study mode-I fracture in a non-linear lattice in the absence of a viscous force. In earlier study, we had studied the effects of the bond potential parameters, including Kelvin viscous force, on the macroscopic behavior of the crack, including the high velocity regime instability. Recently, a new study has appeared using a very similar non-linear force but claiming quite different results. In this article, we seek to discover an explanation of these differences. We find that they do not result from the viscosity present in our previous study. At least part of the differences are attributable, rather, to the very wide system used in the recent study, which leads to long transients and a failure to probe the steady-state behavior. Our results confirm our previously claimed lack of agreement with the Yoffe prediction for the critical velocity of a steady-state crack, and neither do they match the predictions of Gao’s model.