An Effort to Reconcile Time- and Slip-Dependent Friction Evolution

Abstract

In rate and state friction (RSF) theory, time-dependent evolution (represented by the Aging law) and slip-dependent evolution (represented by the Slip law) both succeed in explaining some features of the friction curves while failing in explaining others. Nevertheless, experimental results provided strong evidence for the two ideas and suggested that they are both critical components in friction evolution. Making a first attempt toward reconciling these two ideas, we developed a new friction model for RSF evolution assuming combined physical mechanisms that highlight asperities' plastic behavior: the time-dependent growth of asperity contact area and the slip-dependent enhancement (slip strengthening) of asperity intrinsic strength. Our model adopts a two-scale mathematical structure developed by Li and Rubin (2017; https://doi.org/10.1002/2017JB013970), where the specification of the surface distribution of asperity ensembles and their geometry facilitates the numerical construction of the state variable in the RSF equation. Results show that this new model's fit to the slide-hold-slide experiments is similar to the best fits of the Slip law, while it provides an improved physical picture; however, for velocity steps it fails to match the symmetry of step ups and downs, although the general fit is acceptable. By introducing two new parameters to specify the slip-hardening mechanism, we allow the model to incorporate as a subset the pure time-dependent model discussed in Li and Rubin (2017). Although failing to completely reconcile time- and slip-dependent friction evolution, this study produced useful insights for future research; for example, a granular numerical description of the frictional surface might be convenient for modeling the physics of friction.