Maximum micro-slip in tangential contact of randomly rough self-affine surfaces

Abstract

Many advanced laws of friction contain a characteristic length parameter defining the crossover from sticking to sliding. The physical sense and the scaling properties of this length, however, could not yet be clarified. In the present paper, the fact that any tangential contact of bodies with curved or rough surfaces naturally shows a preliminary slip at the micro scale is used. This is true even if the friction can be described locally by the simplest Coulomb law without preliminary micro-slip. This is suggested as the main physical mechanism for crossover from sticking to sliding. Under this assumption, it becomes possible to theoretically predict the value of the characteristic length of preliminary micro-slip. In this paper, based on recent advances in contact mechanics of self-affine fractal surfaces, the characteristic slip distance for such surfaces is estimated. We show that at low normal forces, the preliminary slip shows no dependence on the system size but only on the applied normal force. For the special case of randomly rough surfaces with a long wavelength roll-off or cut-off the preliminary slip length has the order of magnitude of the rms roughness multiplied with the coefficient of friction.