The characteristic displacement in rate and state-dependent friction from a micromechanical point of view

Abstract

The physical meaning of the characteristic displacement that has been observed in velocity-stepping friction experiments was investigated based on the micromechanics of asperity contact. It has been empirically found for bare rock surfaces that the magnitude of the characteristic displacement is dependent only on surface roughness and insensitive to both slip velocity and normal stress. Thus the characteristic displacement has been interpreted as the displacement required to change the population of contact points completely. Here arises a question about the physical mechanism by which the contact population changes. Because individual asperity contacts form, grow and are eliminated with displacement, there are at least two possible interpretations for the characteristic displacement: (1) it is the distance over which the contacts existing at the moment of the velocity change all fade away, being replaced by new asperity contacts, or (2) it is the distance required for a complete replacement in the real contact area that existed at the moment of the velocity change. In order to test these possibilities, theoretical models were developed based on the statistics of distributed asperity summits. A computer simulation was also performed to check the validity of the theoretical models using three-dimensional surface topography data with various surface roughnesses. The deformation was assumed to be elastic at each asperity contact. The results of both the simulation and the theoretical models show that the characteristic displacement in (1) is about three times longer than that in (2). Comparison of the results with the experimental observations obtained by others indicates that the possibility (2) is the correct interpretation. This means that the “state” in the rate and state variable friction law is memorized in a very confined area of real contact. Further, our results explain why the characteristic displacement is insensitive to normal stress: this comes from the fact that the microscopic properties such as the mean contact diameter are insensitive to normal stress. The approach based on the micromechanics of asperity contact is useful to investigate the underlying mechanism of various phenomena in rock friction.