Frictional aging is observed at a wide range of length- and time-scales, and plays a crucial role in functioning of micro- and nanomachines, as well as in the nucleation and recurrence of earthquakes. Here, we developed an analytical model for description of frictional aging mediated by dynamical formation and rupture of microscopic interfacial contacts. The model accounts for the presence of various types of contacts at the frictional interface and exhibits three different aging regimes: (i) linear aging at short hold times, (ii) logarithmic (or logarithmic-like) aging for intermediate time scales and (iii) levelling off in the static friction for long hold times. It is demonstrated that the linear aging regime is a universal feature of frictional aging for the interfaces including various types of contacts, and the slope of variation of the static friction with the hold time depends on a distribution of energy barriers for contact formation. The conditions for the existence of a pronounced logarithmic aging regime, covering a long-time interval, have been established. Frictional aging has been found to manifest itself not only in slide-hold-slide measurements, but also in sliding experiments exhibiting stick-slip mode of motion, and a relationship has been established between these two regimes of aging. The predicted dependencies of frictional aging on the normal load and temperature are in good agreement with the experimental observations. Our work shows that experimental studies of load and temperature dependencies of aging, carried out over a wide range of time scales, offer promising opportunities for understanding the microscopic mechanisms of frictional aging and revealing the physical meaning of state variables that determine temporal evolution of friction described by phenomenological rate and state laws.
- Asymptotic analysis (C)
- Chemo-mechanical processes (A)
- Friction (B)
- Frictional aging
- Multi-contact model