Slow Cracklike Dynamics at the Onset of Frictional Sliding

We propose a friction model which incorporates interfacial elasticity and whose steady state sliding relation is characterized by a generic nonmonotonic behavior, including both velocity weakening and strengthening branches. In 1D and upon the application of sideway loading, we demonstrate the existence of transient cracklike fronts whose velocity is independent of sound speed, which we propose to be analogous to the recently discovered slow interfacial rupture fronts. Most importantly, the properties of these transient inhomogeneously loaded fronts are determined by steady state front solutions at the minimum of the sliding friction law, implying the existence of a new velocity scale and a “forbidden gap” of rupture velocities. We highlight the role played by interfacial elasticity and supplement our analysis with 2D scaling arguments.

Figure 1

A solution of Eqs. (4, 5, 6) with $\tilde{\rho }=0.01$, $\tilde{\mu }=300$, $\kappa =8$, $\alpha =1.05$, $\tilde{\eta }=0.1$, ${\tilde{K}}_d=2.5$, and ${\tilde{v}}_d=0.3$. (a) The driving force ${\tilde{\sigma }}_d(t)$. (b) The contact area $\tilde{A}(x,t)$. (c) $\tilde{\overline{\sigma }}(\tilde{x},\tilde{t})$. (d) The slip velocity $\tilde{v}(\tilde{x},\tilde{t})={\partial }_{\tilde{t}}{\tilde{u}}_x(\tilde{x},\tilde{t})$. For simplicity, the tildes are omitted from the axis labels.

Figure 2

Left: The steady friction law ${\tilde{\sigma }}_{xy}(\tilde{v})$ (parameters as in Fig. 1) (solid line). The horizontal lines correspond to homogeneous loading. Right: The transient front velocity $\tilde{c}$ vs the minimal steady state velocity ${\tilde{c}}_{ss}^m\sim \sqrt{\tilde{\mu }\alpha /\tilde{\eta }\kappa }$. The tildes are omitted from all quantities.