Tribology Letters

, 57:23 | Cite as

Linear Elastic Fracture Mechanics Predicts the Propagation Distance of Frictional Slip

  • David S. Kammer
  • Mathilde Radiguet
  • Jean-Paul Ampuero
  • Jean-François Molinari
Original Paper


When a frictional interface is subject to a localized shear load, it is often (experimentally) observed that local slip events propagate until they arrest naturally before reaching the edge of the interface. We develop a theoretical model based on linear elastic fracture mechanics to describe the propagation of such precursory slip. The model’s prediction of precursor lengths as a function of external load is in good quantitative agreement with laboratory experiments as well as with dynamic simulations, and provides thereby evidence to recognize frictional slip as a fracture phenomenon. We show that predicted precursor lengths depend, within given uncertainty ranges, mainly on the kinetic friction coefficient, and only weakly on other interface and material parameters. By simplifying the fracture mechanics model, we also reveal sources for the observed nonlinearity in the growth of precursor lengths as a function of the applied force. The discrete nature of precursors as well as the shear tractions caused by frustrated Poisson’s expansion is found to be the dominant factors. Finally, we apply our model to a different, symmetric setup and provide a prediction of the propagation distance of frictional slip for future experiments.


Stick-slip Friction mechanisms Unlubricated friction Linear elastic fracture mechanics 



The research described in this article is supported by the European Research Council (ERCstg UFO-240332) and the Swiss National Science Foundation (grant PMPDP2-145448). JPA was funded by US NSF (grant EAR-1015704).


  1. 1.
    Rubinstein, S., Cohen, G., Fineberg, J.: Dynamics of precursors to frictional sliding. Phys. Rev. Lett. 98(22), 226103 (2007). doi: 10.1103/PhysRevLett.98.226103 CrossRefGoogle Scholar
  2. 2.
    Maegawa, S., Suzuki, A., Nakano, K.: Precursors of global slip in a longitudinal line contact under non-uniform normal loading. Tribol. Lett. 38(3), 313 (2010). doi: 10.1007/s11249-010-9611-7 CrossRefGoogle Scholar
  3. 3.
    Scheibert, J., Dysthe, D.K.: Role of friction-induced torque in stick-slip motion. Europhys. Lett. 92(5), 54001 (2010). doi: 10.1209/0295-5075/92/54001 CrossRefGoogle Scholar
  4. 4.
    Trømborg, J., Scheibert, J., Amundsen, D., Thøgersen, K., Malthe-Sørenssen, A.: Transition from static to kinetic friction: insights from a 2D model. Phys. Rev. Lett. 107(7), 074301 (2011). doi: 10.1103/PhysRevLett.107.074301 CrossRefGoogle Scholar
  5. 5.
    Bouchbinder, E., Brener, E.A., Barel, I., Urbakh, M.: Slow cracklike dynamics at the onset of frictional sliding. Phys. Rev. Lett. 107(23), 235501 (2011). doi: 10.1103/PhysRevLett.107.235501 CrossRefGoogle Scholar
  6. 6.
    Amundsen, D.S., Scheibert, J., Thøgersen, K., Trømborg, J., Malthe-Sørenssen, A.: 1D model of precursors to frictional stick-slip motion allowing for robust comparison with experiments. Tribol. Lett. 45(2), 357 (2012). doi: 10.1007/s11249-011-9894-3 CrossRefGoogle Scholar
  7. 7.
    Kammer, D.S., Yastrebov, V.A., Spijker, P., Molinari, J.F.: On the propagation of slip fronts at frictional interfaces. Tribol. Lett. 48(1), 27 (2012). doi: 10.1007/s11249-012-9920-0 CrossRefGoogle Scholar
  8. 8.
    Otsuki, M., Matsukawa, H.: Systematic breakdown of Amontons’ law of friction for an elastic object locally obeying Amontons’ law. Sci. Rep. 3, 1586 (2013). doi: 10.1038/srep01586 CrossRefGoogle Scholar
  9. 9.
    Lapusta, N., Rice, J.R.: Nucleation and early seismic propagation of small and large events in a crustal earthquake model. Geophys J. Res. Solid Earth 108(B4) (2003). doi: 10.1029/2001JB000793
  10. 10.
    Wu, Y., Chen, X.: The scale-dependent slip pattern for a uniform fault model obeying the rate-and state-dependent friction law. J. Geophys. Res. Solid Earth 119(6), 4890 (2014). doi: 10.1002/2013JB010779 CrossRefGoogle Scholar
  11. 11.
    Rubinstein, S.M., Cohen, G., Fineberg, J.: Cracklike processes within frictional motion: is slow frictional sliding really a slow process? MRS Bull. 33(12), 1181 (2008). doi: 10.1557/mrs2008.249 CrossRefGoogle Scholar
  12. 12.
    Freund, L.B.: The mechanics of dynamic shear crack propagation. J. Geophys. Res. Solid Earth 84(B5), 2199 (1979). doi: 10.1029/JB084iB05p02199 CrossRefGoogle Scholar
  13. 13.
    Ampuero, J.P., Ripperger, J., Mai, P.M.: In: Abercrombie, R., McGarr, A., Di Toro, G., Kanamori, H. (eds.) Earthquakes: Radiated Energy and the Physics of Faulting, pp. 255–261. American Geophysical Union, Washington, DC (2006). doi: 10.1029/170GM25
  14. 14.
    Kato, N.: Fracture energies at the rupture nucleation points of large interplate earthquakes. Earth Planet. Sci. Lett. 353–354(0), 190 (2012). doi: 10.1016/j.epsl.2012.08.015 CrossRefGoogle Scholar
  15. 15.
    Svetlizky, I., Fineberg, J.: Classical shear cracks drive the onset of dry frictional motion. Nature 509, 205 (2014). doi: 10.1038/nature13202 CrossRefGoogle Scholar
  16. 16.
    Palmer, A.C., Rice, J.R.: The growth of slip surfaces in the progressive failure of over-consolidated clay. Proc. R. Soc. Lond. A 332(1591), 527 (1973). doi: 10.1098/rspa.1973.0040 CrossRefGoogle Scholar
  17. 17.
    Andrews, D.: Rupture propagation with finite stress in antiplane strain. J. Geophys. Res. 81(20), 3575 (1976). doi: 10.1029/JB081i020p03575 CrossRefGoogle Scholar
  18. 18.
    Braun, O., Barel, I., Urbakh, M.: Dynamics of transition from static to kinetic friction. Phys. Rev. Lett. 103(19), 194301 (2009). doi: 10.1103/PhysRevLett.103.194301 CrossRefGoogle Scholar
  19. 19.
    Kaneko, Y., Ampuero, J.P.: A mechanism for preseismic steady rupture fronts observed in laboratory experiments. Geophys. Res. Lett. 38(21), L21307 (2011). doi: 10.1029/2011GL049953 CrossRefGoogle Scholar
  20. 20.
    Bar Sinai, Y., Brener, E.A., Bouchbinder, E.: Slow rupture of frictional interfaces. Geophys. Res. Lett. 39(3), L03308 (2012). doi: 10.1029/2011GL050554 CrossRefGoogle Scholar
  21. 21.
    Bar-Sinai, Y., Spatschek, R., Brener, E.A., Bouchbinder, E.: On the velocity-strengthening behavior of dry friction. J. Geophys. Res. Solid Earth 119(3), 1738 (2014). doi: 10.1002/2013JB010586 CrossRefGoogle Scholar
  22. 22.
    Radiguet, M., Kammer, D.S., Gillet, P., Molinari, J.F.: Survival of heterogeneous stress distributions created by precursory slip at frictional interfaces. Phys. Rev. Lett. 111(16), 164302 (2013). doi: 10.1103/PhysRevLett.111.164302 CrossRefGoogle Scholar
  23. 23.
    Radiguet, M., Kammer, D.S., Molinari, J.F.: The role of viscoelasticity on heterogeneous stress fields at frictional interfaces. Mech. Mater. 80, 276 (2015). doi: 10.1016/j.mechmat.2014.03.009
  24. 24.
    Freund, L.: Dynamic Fracture Mechanics. Cambridge University Press, New York (1990)CrossRefGoogle Scholar
  25. 25.
    Tada, H., Paris, P.C., Irwin, G.R.: The Stress Analysis of Cracks Handbook, 3rd edn. ASME, New York (2000)CrossRefGoogle Scholar
  26. 26.
    Rice, J.R.: In: Kelly, R. (ed.): Proceedings of the Eighth U.S. National Congress of Applied Mechanics. Western Periodicals Co., North Hollywood, California, pp. 191–216 (1979)Google Scholar
  27. 27.
    Uenishi, K., Rice, J.R.: Universal nucleation length for slip-weakening rupture instability under nonuniform fault loading. J. Geophys. Res. 108(B1), B12042 (2003). doi: 10.1029/2001JB001681 Google Scholar
  28. 28.
    Garagash, D.I., Germanovich, L.N.: Nucleation and arrest of dynamic slip on a pressurized fault. J. Geophys. Res. 117(B10), B10310 (2012). doi: 10.1029/2012JB009209 Google Scholar
  29. 29.
    Ciccotti, M., Mulargia, F.: Differences between static and dynamic elastic moduli of a typical seismogenic rock. Geophys. J. Int. 157(1), 474 (2004). doi: 10.1111/j.1365-246X.2004.02213.x CrossRefGoogle Scholar
  30. 30.
    Ben-David, O., Cohen, G., Fineberg, J.: The dynamics of the onset of frictional slip. Science 330(6001), 211 (2010). doi: 10.1126/science.1194777 CrossRefGoogle Scholar
  31. 31.
    Weertman, J.: Unstable slippage across a fault that separates elastic media of different elastic constants. J. Geophys. Res. 85(B3), 1455 (1980). doi: 10.1029/JB085iB03p01455 CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media New York 2015

Authors and Affiliations

  • David S. Kammer
    • 1
  • Mathilde Radiguet
    • 1
  • Jean-Paul Ampuero
    • 2
  • Jean-François Molinari
    • 1
  1. 1.Computational Solid Mechanics Laboratory, IIC-ENAC, IMX-STIEcole Polytechnique Fédérale de Lausanne, EPFLLausanneSwitzerland
  2. 2.Seismological LaboratoryCalifornia Institute of TechnologyPasadenaUSA

Personalised recommendations