CREEP, STICK-SLIP, AND DRY-FRICTION DYNAMICS - EXPERIMENTS AND A HEURISTIC MODEL

We perform an extensive study of the dry-friction dynamics of a paper- on-paper system. We explore the dynamical phase diagram by systematica lly varying the relevant control parameters (driving velocity V, slide r mass M, and loading machine stiffness k). A set of experimental resu lts gives strong proof that the low-velocity dynamics is controlled by a creep process, in agreement with previous results from rock mechani cs 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 reference s therein]. At higher velocities, a crossover to inertial dynamics is observed. In each regime, when k is increased, the system bifurcates f rom periodic stick-slip to steady sliding: in the creep regime, the bi fucation is a direct Hopf one; in the inertial regime it becomes subcr itical. We identify, from comparison of the time dependence of the sta tic friction coefficient mu(s)(t) and of the velocity dependence of th e stationary dynamic one, mu(d)(V), a memory length of the order of 1 mum. The V dependence of mu(d)(V) changes from V weakening to V streng thening 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 o f physical contacts on the scale of the memory length, and (ii) we ass ume that the dynamics is controlled by the Brownian motion of an effec tive creeping volume in a pinning potential, the strength of which inc reases with age. The crossover from creep to inertial motion then natu rally 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 agr eement. When confronted with rock mechanics results, this study strong ly suggests that low-velocity creep is quite generic; further studies of this process should in particular bear on models of earthquake dyna mics.