Survival of Heterogeneous Stress Distributions Created by Precursory Slip at Frictional Interfaces

We study the dynamics of successive slip events at a frictional interface with finite-element simulations. Because of the viscous properties of the material, the stress concentrations created by the arrest of precursory slip are not erased by the propagation of the following rupture but reappear with the relaxation of the material. We show that the amplitude of the stress concentrations follows an exponential decay, which is controlled by the bulk material properties. These results highlight the importance of viscosity in the heterogeneous stress state of a frictional interface and reveal the “memory effect” that affects successive ruptures.

Figure 1

(a) Two-dimensional model setup: a rectangular plate with rounded corners in contact with a rigid plane. The system is loaded on the top with a constant force $F_N$ and from the side with a constant velocity $V_x(t)$ applied to a rigid pusher via a spring. (b) Evolution of the global forces with time. Time of slip events (precursors and global sliding) is marked with vertical bars. Precursor events are color coded from blue to red, and global sliding events are in gray. (c) Location of slipping regions along the interface over time. Slip precursors of increasing length are observed. (inset) Local slip velocities ($\mathrm{m}/\mathrm{s}$) along the interface for the 6th precursor. The white line shows the position of the rupture front.

Figure 2

Propagation speed of the front (averaged over 5 mm) for precursors 7 (top) to 10 (bottom). Gray bars highlight acceleration of the front related to the location of arrested precursors.

Figure 3

(a) Local $\tau /\sigma$ ratio along the interface just prior to each slip event. Colors from blue to gray correspond to successive slip events (see Fig. 1 for color code). Lines are shifted along the $y$ axis for clarity. Continuous and dashed vertical lines correspond, respectively, to the positions $x_i$ and $x_i^{\prime }$. (inset) Zoom around the position $x_8$; ${\Delta }_i({\tau }_n/{\sigma }_n)$ is the variation in $\tau /\sigma$ between $x_8$ and $x_8^{\prime }$. Simplified notations correspond to $V_1={\Delta }_8({\tau }_9/{\sigma }_9)$, $V_2={\Delta }_8({\tau }_{10}/{\sigma }_{10})$, and $V_{\mathrm{ref}}={\Delta }_8({\tau }_{14}/{\sigma }_{14})$ and highlight the decreasing amplitude of stress concentrations $A_i^n$ [Eq. (2)]. (b) Normalized amplitude of stress concentration $A_i^n$ as a function of the number of slip events after event $i$. Colors correspond to different positions $x_i$. Dotted and continuous blue lines correspond to a decrease rate of $\gamma (E_v/E_0)$ with $\gamma =1$ and $\gamma =0.83$, respectively. (inset) Same data points with $A_i^n$ in log scale reveal the exponential decay of stress concentration. (c) Lines show the time evolution of $\tau /\sigma$ from blue (just after the 8th event) to red (just before the 9th event). The horizontal black line shows $x_7$, for which time evolution is shown in (d). (d) Time evolution of $\tau (x_7)$ [position of black line in (c)] during two slip event cycles. The modeled behavior [dashed cyan line, Eq. (3)] closely matches the data (thin black line). The amplitude between the two red lines is $\gamma \Delta {\tau }_n$ with $\gamma =0.83$.