Frictional constitutive law at intermediate slip rates accounting for flash heating and thermally activated slip process

A constitutive law in a rate- and state-dependent framework accounting for flash heating at microscopic contacts is proposed on the basis of a simple asperity model and a thermally activated slip process thought to cause logarithmic dependency of the friction coefficient on slip rate. This law is probably applicable in an intermediate slip rate regime (about 0.001-0.1 m/s), where contact time of asperities is shorter than a cutoff time for time-dependent healing, and a phase transformation such as melting does not take place at the microscopic contacts. The steady state friction coefficient, which is constructed numerically and derived analytically, depends on slip rate and background temperature, gives a good coverage of experimental data of gabbro friction at slip rate on the order of 0.1 m/s, and explains linear dependency of the friction coefficient of Al2O3 ceramics on temperature at around 0.1 m/s. Similar to the usual rate- and state-dependent friction law, the transition behavior on a sudden step in slip rate includes a positive direct effect and a following evolution effect, which are essential in considering the problems dealing with coupling of a frictional surface and surrounding elastic medium. This constitutive law illuminates the importance of the change in not only microscopic, but also macroscopic temperature; the latter, as well as the slip rate, probably changes dynamically during the nucleation of rupture and the coseismic phase.