TY - JOUR
T1 - A microscopic model of rate and state friction evolution
AU - Li, Tianyi
AU - Rubin, Allan M.
N1 - Funding Information:
Tianyi thanks Pathikrit Bhattacharya for his sincere instructions and valuable discussion on rate and state friction. We thank Masao Nakatani for his extremely valuable reviews and important suggestions, which went above and beyond the call of duty and substantially improved the paper, and one anonymous reviewer for comments that helped with organization and clarity. All data used in this study are available upon request from the authors. This research was funded by the National Science Foundation under award EAR-1547286, and by the U.S. Geological Survey (USGS), Department of the Interior, under USGS award G16AP00028. The views and conclusions contained in this document are those of the authors and should not be interpreted as necessarily representing the official policies, either expressed or implied, of the U.S. Government.
Publisher Copyright:
©2017. American Geophysical Union. All Rights Reserved.
PY - 2017/8
Y1 - 2017/8
N2 - Whether rate- and state-dependent friction evolution is primarily slip dependent or time dependent is not well resolved. Although slide-hold-slide experiments are traditionally interpreted as supporting the aging law, implying time-dependent evolution, recent studies show that this evidence is equivocal. In contrast, the slip law yields extremely good fits to velocity step experiments, although a clear physical picture for slip-dependent friction evolution is lacking. We propose a new microscopic model for rate and state friction evolution in which each asperity has a heterogeneous strength, with individual portions recording the velocity at which they became part of the contact. Assuming an exponential distribution of asperity sizes on the surface, the model produces results essentially similar to the slip law, yielding very good fits to velocity step experiments but not improving much the fits to slide-hold-slide experiments. A numerical kernel for the model is developed, and an analytical expression is obtained for perfect velocity steps, which differs from the slip law expression by a slow-decaying factor. By changing the quantity that determines the intrinsic strength, we use the same model structure to investigate aging-law-like time-dependent evolution. Assuming strength to increase logarithmically with contact age, for two different definitions of age we obtain results for velocity step increases significantly different from the aging law. Interestingly, a solution very close to the aging law is obtained if we apply a third definition of age that we consider to be nonphysical. This suggests that under the current aging law, the state variable is not synonymous with contact age.
AB - Whether rate- and state-dependent friction evolution is primarily slip dependent or time dependent is not well resolved. Although slide-hold-slide experiments are traditionally interpreted as supporting the aging law, implying time-dependent evolution, recent studies show that this evidence is equivocal. In contrast, the slip law yields extremely good fits to velocity step experiments, although a clear physical picture for slip-dependent friction evolution is lacking. We propose a new microscopic model for rate and state friction evolution in which each asperity has a heterogeneous strength, with individual portions recording the velocity at which they became part of the contact. Assuming an exponential distribution of asperity sizes on the surface, the model produces results essentially similar to the slip law, yielding very good fits to velocity step experiments but not improving much the fits to slide-hold-slide experiments. A numerical kernel for the model is developed, and an analytical expression is obtained for perfect velocity steps, which differs from the slip law expression by a slow-decaying factor. By changing the quantity that determines the intrinsic strength, we use the same model structure to investigate aging-law-like time-dependent evolution. Assuming strength to increase logarithmically with contact age, for two different definitions of age we obtain results for velocity step increases significantly different from the aging law. Interestingly, a solution very close to the aging law is obtained if we apply a third definition of age that we consider to be nonphysical. This suggests that under the current aging law, the state variable is not synonymous with contact age.
KW - multicontact interface
KW - rate and state friction
KW - two-scale model
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U2 - 10.1002/2017JB013970
DO - 10.1002/2017JB013970
M3 - Article
AN - SCOPUS:85029623802
SN - 0148-0227
VL - 122
SP - 6431
EP - 6453
JO - Journal of Geophysical Research
JF - Journal of Geophysical Research
IS - 8
ER -