F. Heslot et al., CREEP, STICK-SLIP, AND DRY-FRICTION DYNAMICS - EXPERIMENTS AND A HEURISTIC MODEL, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics, 49(6), 1994, pp. 4973-4988
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.