Quantifying the evolution of dynamic friction
The evolution of friction controls the dynamics of shear ruptures, which occur in a broad range of fields from engineering to nature. Examples include failure of composite materials and bimaterial structures, brakes and earthquakes. In particular, friction has a crucial importance in determining how ruptures propagate along faults in the Earth's crust and release waves that cause destructive shaking. Yet the evolution of dynamic friction is one of the main unknowns in earthquake science.
Recently, we have been able to measure the evolution of dynamic friction associated to spontaneously propagating dynamic ruptures (Rubino, Rosakis, Lapusta, Nature Communications, 2019), using our ultrahigh speed full-field imaging technique.
Measuring the local evolution of dynamic friction is an important achievement as previous friction experiments typically imposed slip-velocity histories to the sample, assumed uniform sliding along the interface, and measured the resulting averaged friction resistance.
The dependence of friction on slip and slip rate is shown in the figure below. The observed friction has a complex behavior, displaying initial velocity strengthening followed by substantial velocity weakening. Our measurements are consistent with rate-and-state friction laws supplemented with flash heating but not with widely used slip-weakening friction laws.
Evolution of friction with slip and slip rate. (a-b) Friction (given by the shear to normal stress ratio during slip) vs. slip on the interface for a point at the center of the field of view, reported for four different experimental configurations. See the schematics of the experimental configuration here. The four experimental ruptures have different dependence of friction on slip, indicating that friction cannot be described by a purely slip-dependent law. (c) Friction vs. slip rate, reported for the two ruptures in (a). Both cases show initial strengthening with slip rate (direct effect) followed by rate weakening, as captured by rate-and-state formulations. Note that the steady-state level of dynamic friction depends on the slip rate. Credit: Rubino, Rosakis, Lapusta, Nature Communications (2017).
The evolution of dynamic friction is visualized in the movie below for two of the experiments shown in the figure. The movie shows first how friction changes with slip and second how it evolves with slip rate, for each of the two cases. Another plot simultaneously shows the changes of slip rate vs. slip.
Evolution of dynamic friction
After the initial strengthening, friction weakens and transitions to a steady state dynamic level. The values of friction attained at steady state plotted vs. the corresponding levels of slip rate reveal a pronounced weakening with slip rate, not explained by simple rate-and-state friction models. We find that our results are consistent with a combined formulation of rate-and-state friction enhanced with flash heating weakening, as indicated by the figure below (left panel). It is interesting to note the remarkable similarity between our measurements, obtained on a polymer, and those obtained on quartzite rock (right panel) by Goldsby and Tullis, Science (2011), suggesting the generality of the flash heating formulation.
Steady-state friction versus slip rate. (a) Experimental measurements of steady-state friction coefficient vs. slip rate and fits with the standard rate-and-state friction formulation (green curve), and combined formulation of rate-and-state friction enhanced by flash heating (black curve). Our steady-state measurements are consistent with the combined formulation. Green dots are low-velocity measurements obtained in collaboration with Kilgore, Beeler, and Lu. Red, blue, black and purple solid symbols are measurements obtained with a higher level of accuracy (using a smaller field of view); the green, black and purple empty diamonds are measurements with lower levels of accuracy as they are obtained with larger fields of view. (b) Experimental measurements of dynamic friction on quartzite samples (Goldsby and Tullis, Science, 2011), showing similar behavior for rocks, with significant slip-rate dependence of friction for high steady-state slip rates, consistent with the flash heating formulation. Note the different horizontal scale for the two plots. Credit: Rubino, Rosakis, Lapusta, Nature Communications (2017).
This work proposes a new approach for measuring the local evolution of dynamic friction and has important implications for understanding earthquake hazard since laws governing frictional resistance of faults are vital ingredients in physically-based predictive models of the earthquake source.
Our findings have also been reported in the press in these articles: "The role of dynamic friction in earthquakes" in the magazine Tribology & Lubrication Technology (TLT), and "How friction evolves during an earthquake" in the Caltech news.