Abstract
A model of frictional sliding with anN-shaped curve for the sliding velocity dependence of the coefficient of friction is considered. This type of friction law is shown to be related to dynamic i.e., velocity dependent ‘ageing’ of asperity junctions. Mechanisms of ‘ageing’ for ductile (Bowden-Tabor) and brittle (Byerlee) materials, though different in nature, lead to qualitatively similarN-shaped velocity dependencies of the coefficient of friction. Estimates for the velocities limiting the range of negative velocity sensitivity of the coefficient of friction are obtained for the ductile case and—albeit with a lesser degree of reliability—for the brittle one. It is shown by linear stability analysis that discontinuous sliding (stick-slip) is associated with thedescending portion of theN-shaped curve. An instability criterion is obtained. An expression for the period of the attendant relaxation oscillations of the sliding velocity is given in terms of the calculated velocity dependence of the coefficient of friction. It is suggested that the micromechanically motivated friction law proposed should be used in models of earthquakes due to discontinuous frictional sliding on a crustal fault.
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References
Ashby, M. F., andJones, D. R. H.,Engineering Materials 2 (Pergamon Press, Oxford 1986).
Båk, P., andTang, C. (1989),Earthquakes as a Self-organized Critical Phenomenon, J. Geophys. Res.94, 15635–15637.
Barenblatt, G. I., Keilis-Borok, V. I., andVishik, M. M. (1981),Proc. Natl. Acad. Sci. USA 78, 5284–5291.
Bowden, F. P., andTabor, D.,The Friction and Lubrication of Solids, Part I (Clarendon Press, Oxford 1950).
Burridge, R., andKnopoff, L. (1967),Model and Theoretical Seismicity, Bull. Seismol. Soc. Am.57, 341–371.
Byerlee, J. D. (1967),Theory of Friction Based on Brittle Fracture, J. Appl. Phys.38, 2928–2934.
Carlson, J. M., andLanger, J. S. (1989),Mechanical Model of an Earthquake Fault, Phys. Rev.A 40, 6470–6484.
Chester, F. M., andHiggs, N. G. (1992),Multimechanism Friction Constitutive Model for Ultrafine Quartz Gouge at Hypocentral Conditions, J. Geophys. Res.97, 1859–1870.
Christiansen, K., andOlami, Z. (1992),Scaling, Phase Transitions and Nonuniversality in a Self-organized Critical Cellular-automaton Model, Phys. Rev.A46, 1829–1838.
Dieterich, J. H. (1979),Modeling of Rock Friction: 1. Experimental Results and Constitutive Equations, J. Geophys. Res.84, 2161–2175.
Dieterich, J. H. (1993),Earthquake Nucleation on Faults with Rate and State Dependent Strength, Tectonophysics211, 115–134.
Dieterich, J. H., andKilgore, B. D. (1994),Direct Observation of Frictional Contacts: New Insights for State-dependent Properties, Pure and Appl. Geophys.143, 283–302.
Dieterich, J. H., andLinker, M. F. (1992),Fault Stability under Conditions of Variable Normal Stress, Geophys. Res. Lett.19, 691–694.
Estrin, Y. (1995),Dynamic Ageing and Unstable Behaviour in Plastic Flow and in Frictional Sliding, AMD-Vol 200/MD-Vol. 57, Plastic and Fracture Instabilities in Materials, ASME, 189–201.
Gu, J.-C., Rice, J. R., Ruina, A. L., andTse, S. T. (1984),Slip Motion and Stability of a Single Degree of Freedom Elastic System with Rate and State Dependent Friction, J. Mech. Phys. Solids32, 167–196.
Kubin, L. P., andEstrin, Y. (1985),The Portevin-Le Chatelier Effect in Deformation with Constant Stress Rate, Acta Metallurgica33, 397–407.
Lebyodkin, M., Bréchet, Y., Estrin, Y., andKubin, L. (1995),Statistics of the catastrophic slip events in the Portevin-Le Chatelier effect, Phys. Rev. Lett.74, 4758–4761.
McCormick, P. G. (1988),Theory of Flow Localisation due to Dynamic Strain Ageing, Acta Metallurgica36, 3061–3069.
Rabinowicz, E.,Friction and Wear of Materials (John Wiley, New York 1965).
Rice, J. R. (1983),Constitutive Relations for Fault Slip and Earthquake Instabilities, Pure and Appl. Geophys.121, 443–475.
Rice, J. R. (1993) (private communication).
Scholz, C. H.,The Mechanics of Earthquakes and Faulting (Cambridge University Press, Cambridge, UK 1990).
Shimamoto, T. (1986),Transition between Frictional Slip and Ductile Flow for Halite Shear Zones at Room Temperature, Science231, 711–714.
Teufel, L. W. (1981),Frictional Instabilities in Rock: Effect of Stiffness, Normal Stress, Sliding Velocity, and Rock Type. Presented at the 18th Annual Meeting of Soc. for Eng. Sci., Brown University, Providence, RI, Sept. 2–4, 1981.
Timoshenko, S., andGoodier, J. N.,Theory of Elasticity (McGraw Hill, N.Y. 1951).
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Estrin, Y., Bréchet, Y. On a model of frictional sliding. PAGEOPH 147, 745–762 (1996). https://doi.org/10.1007/BF01089700
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DOI: https://doi.org/10.1007/BF01089700