Creep, stick-slip, and dry-friction dynamics: Experiments and a heuristic model

Abstract

We perform an extensive study of the dry-friction dynamics of a paper-on-paper system. We explore the dynamical phase diagram by systematically varying the relevant control parameters (driving velocity V, slider mass M, and loading machine stiffness k). A set of experimental results gives strong proof that the low-velocity dynamics is controlled by a creep process, in agreement with previous results from rock mechanics and metals [C. H. Scholz, The Mechanics of Earthquakes and Faulting (Cambridge University Press, Cambridge, 1990), Chap. 2 and references therein; E. Rabinowicz, Proc. Phys. Soc. 71, 668 (1958) and references therein]. At higher velocities, a crossover to inertial dynamics is observed. In each regime, when k is increased, the system bifurcates from periodic stick-slip to steady sliding: in the creep regime, the bifucation is a direct Hopf one; in the inertial regime it becomes subcritical. We identify, from comparison of the time dependence of the static friction coefficient ${\mathrm{\ensuremath{\mu}}}_{\mathit{s}}$(t) and of the velocity dependence of the stationary dynamic one, ${\mathrm{\ensuremath{\mu}}}_{\mathit{d}}$(V), a memory length of the order of 1 \ensuremath{\mu}m. The V dependence of ${\mathrm{\ensuremath{\mu}}}_{\mathit{d}}$(V) changes from V weakening to V strengthening at the creep-inertial crossover. We propose a heuristic model of low-velocity friction based on two main ingredients: (i) following and extending the ideas of Ruina [J. Geophys. Res. 88, 10 359 (1983)], we define a phenomenological contact age accounting for the renewal of physical contacts on the scale of the memory length, and (ii) we assume that the dynamics is controlled by the Brownian motion of an effective creeping volume in a pinning potential, the strength of which increases with age.The crossover from creep to inertial motion then naturally appears as the runaway threshold between thermally activated and free motion. The bifurcation analysis in the creep regime is compared in detail with experimental results, yielding a very satisfactory agreement. When confronted with rock mechanics results, this study strongly suggests that low-velocity creep is quite generic; further studies of this process should in particular bear on models of earthquake dynamics.