On a model of frictional sliding

A model of frictional sliding with an N-shaped curve for the sliding velocity dependence of the coefficient of Friction is considered. This type of friction law is shown to be related to dynamic i.e., velocity dependent 'ageing' of asperity junctions. Mechanisms of 'ageing' for ductile (Bowden-Tabor) and brittle(Byerlee) materials, though different in nature, lead to qualitatively similar N-shaped velocity dependencies of the coefficient of friction. Estimates for the velocities limiting the range of negative velocity sensitivity of the coefficient of friction are obtained for the ductile case and-albeit with a lesser degree of reliability-for the brittle one. It is shown by linear stability analysis that discontinuous sliding (stick-slip) is associated with the descending portion of the N-shaped curve. An instability criterion is obtained. An expression for the period of the attendant relaxation oscillations of the sliding velocity is given in terms of the calculated velocity dependence of the coefficient of friction. It is suggested that the micromechanically motivated friction law proposed should be used in models of earthquakes due to discontinuous frictional sliding on a crustal fault.