The gradual evolution of friction following a normal stress step reflects changes in contact strength, not contact area

Pathikrit Bhattacharya, Terry E. Tullis, Allan M. Rubin, N. M. Beeler, & Nir Z. Badt

Published September 8, 2024, SCEC Contribution #13858, 2024 SCEC Annual Meeting Poster #138

Rate and state friction refers to the dependence of friction on the velocity of sliding, and on the ‘state’ of the frictional interface that has been poorly understood for fifty years. Empirically, the state of a frictional interface has been found to evolve with slip and/or time, and in response to abrupt changes in normal stress, but the microprocesses responsible for this evolution are unclear. Frictional interfaces are in contact only at numerous smaller regions called asperities, and the real contact area is expected to be only a fraction of the nominal area. Frictional resistance results from the shear strength of only these contacting asperities. It is commonly presumed that changes in state are due primarily to changes in the real contact area. An alternative explanation is that changes in state are due to changes in (some measure) of the strength of the contact area, for example due to changes in chemical bond strength or their area-averaged density. Here we show that although the eventual shear-stress level due to friction after a step-increase in normal stress depends on the increased contact area, the evolution of frictional strength with slip cannot be understood in terms of changes in contact area. Instead, changes in area-averaged contact strength play a more important role in this evolution. We formulate a state-evolution equation that encodes contrasts in the area-averaged strength between old and new regions of interfacial contact as a parameter and show that slip rate reductions of Westerly granite samples following moderate-to-large normal stress steps can be used to estimate this strength contrast. For our experiments, the area-averaged strength of the new contact area created rapidly by the abrupt increase in normal stress is found to be only 15-25 percent of the strength that the old contacts possessed at the pre-step steady state, and evolves to this old strength with slip. These experiments may lay the foundation for replacing our empirical descriptions of state evolution with an understanding of operative microprocesses that focuses on changes in contact strength as well as contact area.

Key Words
rate-state friction, earthquake mechanics, friction physics

Citation
Bhattacharya, P., Tullis, T. E., Rubin, A. M., Beeler, N. M., & Badt, N. Z. (2024, 09). The gradual evolution of friction following a normal stress step reflects changes in contact strength, not contact area. Poster Presentation at 2024 SCEC Annual Meeting.

Related Projects & Working Groups
Fault and Rupture Mechanics (FARM)