On the microphysical foundations of rate-and-state friction

Reference:

Putelat, T., Dawes, J. H. P. and Willis, J. R., 2011. On the microphysical foundations of rate-and-state friction. Journal of the Mechanics and Physics of Solids, 59 (5), pp. 1062-1075.

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Official URL:

http://dx.doi.org/10.1016/j.jmps.2011.02.002

Abstract

The rate-and-state formulation of friction is well established as a phenomenological yet quantitative description of friction dynamics, in particular the onset of stick-slip instabilities arising from an oscillatory bifurcation. We first discuss the physical origins of two theories for the derivation of friction coefficients used in rate-and-state models, both derived from thermally activated rate processes. Secondly, we propose a general expression for the state evolution law in the form of a first order kinetics which describes the relaxation to a velocity dependent equilibrium interfacial state {symbol}ss (v) over a velocity dependent dynamic rejuvenation time-scale t{symbol} (v). We show that the unknown relation {symbol}ss (v), defined as the ratio of t{symbol} to a constant interfacial stationary healing time-scale t* *, can be estimated directly from the experimental measurements of the steady-state friction coefficient and the critical stiffness for the onset of stick-slip behaviour of a spring-block system. Using a specific experimental dataset, we finally illustrate that this method provides the experimental measurements of the apparent memory length La (v) = v t* * {symbol}ss (v) and the constant characteristic relaxation time t* * from which a constant intrinsic memory length L = V* t* * can be defined once a slip rate of reference V* is chosen. As a result the complete state evolution law can be experimentally characterised.

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