Fracture and friction: A review

• Autorzy: Varotsos P.
• Języki publikacji: EN

Abstrakty

EN

Earlier reviews on fracture and friction, as well as relevant monographs (e.g., "Theory of Earthquake Premonitory and Fracture Processes" by R. Teis-seyre), presented the knowledge accumulated at that time. By putting emphasis on the physics of these phenomena, the present review summarizes the experi-mental and theoretical advances that have been achieved during the last years. This is preceded, in the description of each phenomenon, by a careful inspection of the problems envisaged in the frame of the earlier aspects. As a first example, we refer to the recent experiments which demonstrate that the cracks cannot ac-celerate up to the Rayleigh wave speed predicted by classic theories. Secondly, contrary to what had been thought previously, the most recent theoretical models of the crack propagation are intrinsically unstable against Yoffe-like deflections (i.e., deviations of the crack motion from a straight line) at all speeds. Recent laboratory experiments shed light on what happens during individual slip events in stick-slip phenomena (e.g., the frictional force is larger for increasing than for decreasing velocity within individual events due to memory effects). Further-more, measurements on laboratory scale reveal that the frequency of precursor events increases dramatically just before a major slip event (even when studying the friction between relatively smooth solids like). The latter effect is primarily due to defects (or disorder, in general), which are shown to play a major role in both phenomena investigated.

Słowa kluczowe

EN

friction constitutive law; weakening effect; fracture; precursory effects

• Wydawca: Instytut Geofizyki PAN
• Czasopismo: Acta Geophysica Polonica
• Rocznik: 2004
• Tom: Vol. 52, nr 2
• Strony: 105--142
• Opis fizyczny: Bibliogr. 104 poz.

Twórcy

autor

Varotsos P.

• Solid Earth Physics Institute, Department of Physics, University of Athens, Panepistimiopolis, Zografos, 157 84 Athens, Greece

Bibliografia

• 1. Beeler, N.M., T.E. Tullis and J.D. Weeks, 1994, The roles of time and displacement in the evolution effect in rock friction, Geophys. Res. Lett. 21, 1987-1990.
• 2. Bocquet, L., and HJ. Jensen, 1997, Phenomenological study of hysteresis in quasistatic friction, J. Physique I, 7, 1603-1625.
• 3. Bouchaud, J.P., E. Bouchaud, G. Lapasset and J. Planes, 1993, Models of fractal cracks, Phys Rev. Lett. 71, 2240-2243.
• 4. Boudet, J.F., and S. Ciliberto, 1998, Interaction of sound with fast crack propagation, Phys Rev. Lett. 80, 341-344.
• 5. Bowden, F.P., and D, Tabor, 1950, Friction and Lubrication of Solids, Part I, Clarendon Press, Oxford,
• 6. Bowden, F.P., and D, Tabor, 1964, Friction and Lubrication of Solids, Part 2, Clarendon Press, Oxford.
• 7. Brace, W.F., and J.D. Byerlee, 1966, Stick slip as a mechanism for earthquakes. Science 153, 990-992.
• 8. Buchel. A., and J.P. Sethna, 1996, Elastic theory has zero radius of convergence, Phys. Rev. Lett. 77, 1520-1523.
• 9. Cannelli. G., R. Cantelli and F. Cordero, 1993, Self-organized criticality of the fracture processes associated with hydrogen precipitation in niobium by acoustic emission, Phys. Rev. Lett. 70, 3923-3926.
• 10. Caroli, C., and P. Nozieres, 1996, Dry friction as a hysteretic elastic response. In: B.NJ. Persson and E. Tosatti (eds.), "Physics of Sliding Friction", Kluwer Academic Publishers, Dordrecht.
• 11. Caroli, C., and B. Velicky, 1997, Dry friction as an elasto-plastic response: Effect of compressive plasticity, J. Physique I, 7, 1391-1416.
• 12. Ching, E.S.C., J.S. Langer and H. Nakanishi, 1996, Dynamic instabilities in fracture, Phys. Rev. Lett. 76, 1087-1090.
• 13. Coulomb, C.A., 1785, Theorie des Machines simples, Memoire de Mathematique et de Physique de l' Academie Royale, Paris, 161-342.
• 14. Curtin, W.A., 1998, Size scaling of strength in heterogeneous materials, Phys. Rev. Lett. 80, 1445-1448.
• 15. Daguier. P., S. Henaux, E. Bouchaud and F. Creuzet, 1996, Quantitative analysis of a fracture surface by atomic force microscopy, Phys. Rev. E. 53, 5637-5642.
• 16. Daguier. P., B. Nghiem, E. Bouchaud and F. Creuzet, 1997, Pinning and depinning of crack fronts in heterogeneous materials, Phys. Rev. Lett. 78, 1062-J065.
• 17. Ertas, D., and M. Kardar, 1992, Dynamic roughening of directed lines Phys. Rev. Lett. 69, 929-932.
• 18. Ertas, D., and M. Kardar, 1993, Dynamic relaxation of drifting polymers: A phenomenological approach, Phys. Rev. E-48, 1228-1245.
• 19. Ertas, D., and M. Kardar, 1994, Anisotropic scaling in depinning of a flux line, Phys. Rev. Lett. 73,1703-1706.
• 20. Ertas, D., and M. Kardar, 1996, Anisotropic scaling in threshold critical dynamics of driven directed lines, Phys. Rev. B-53, 3520-3542.
• 21. Farkas, Z., G. Bartels, T. Unger and D.E. Wolf, 2003, Frictional coupling between sliding and spinning motion, Phys. Rev. Lett. 90, 4, 248-302.
• 22. Fineberg, J., S.P. Gross, M. Marder and H.L. Swinney, 1991, Instability in dynamic fracture. Phys. Rev. Lett. 67,457-460.
• 23. Fineberg. I, S.P. Gross, M. Marder and H.L. Swinney, 1992, Instability in the propagation of fast cracks, Phys. Rev. B-45, 5146-5154.
• 24. Freund, L.E., 1990, Dynamic Fracture Mechanics, Cambridge University Press, New York
• 25. Gao, H., and J.R. Rice, 1989, A first order perturbation crack trapping by arrays of obstacles, J. Appl. Mech. 56, 828-836.
• 26. Garcimartin, A., A. Guarino, L. Bellon and S. Ciliberto, 1997, Statistical properties of fracture precursors, Phys. Rev. Lett. 79, 3202-3205.
• 27. Gerde, E., and M. Marder, 2001, Friction and fracture. Nature 413,285-288.
• 28. Griffith, A.A., 1920, The phenomena of rupture and flow in solids, Philos. Trans. R. Soc. don A-221, 163-198.
• 29. Gross, S.P., J. Fineberg, M. Marder, W.D. McCormick and H. Swinney, 1993, Acoustic emissions from rapidly moving cracks, Phys. Rev. Lett. 71, 3162-3165.
• 30. Gueguen, Y., and V. Palciauskas, 1994, Introduction to the Physics of Rocks, Princeton University Press, Princeton, N J.
• 31. Gumbsch, P., S. J. Zhou and B.L. Holian, 1997, Molecular dynamics investigation of dynamic crack stability, Phys. Rev. B. 55, 3445-3455.
• 32. Hadjicontis, V., and C. Mavromatou, 1995, Electric signals recorded during uniaxial compression of rock samples: their possible correlation with preseismic electric signals, Acta Geophys. Pol. 43, 49-61.
• 33. Hadjicontis, V,, and C. Mavromatou, 1996, Laboratory investigation of the electric signals preceding earthquakes. In: Sir J. Lighlhill (ed.), "The Critical Review of VAN: Earthquake Prediction from Seismic Electric Signals", World Scientific, Singapore, 105-117.
• 34. Halsey, T.C., 2003, Friction in a spin. Nature 424, 1005-1006.
• 35. Hansen, A., and P.C. Hemmer, 1994, Burst avalanches in bundles of fibers: Local versus global load-sharing, Phys. Lett. A-184, 394-396.
• 36. Hauch, J.A., D. Hollant, M.P. Marder and H.L. Swinney, 1999, Dynamic fracture in single crystal silicon, Phys. Rev. Lett. 82, 3823-3826.
• 37. Heslot, F., T. Baumberger, B. Perrin, B. Caroli and C. Caroli, 1994, Creep, stick-slip, and dry friction dynamics: experiments and heuristic model, Phys. Rev. E-49,4973-4988.
• 38. Holian, B.L., and R. Ravelo, 1995, Fracture simulations using large-scale molecular dynamics, Phys. Rev. B-51, 11275-11288.
• 39. Holian, B.L., and R. Thomson, 1997, Crack limiting velocity, Phys. Rev. E-56, 1071-1079.
• 40. Holian, B.L., R. Blumenfeld and P. Gumbsch, 1997, An Einstein model of brittle crack propagation, Phys. Rev. Lett. 78,78-81.
• 41. Jackson, J.D., 1975, Classical Electrodynamics, 2nd ed., John Wiley, New York, 848 pp.
• 42. Johansen, A., and D. Sornette, 1999, Acoustic radiation controls friction: Evidence from a spring-block experiment, Phys. Rev. Lett. 82, 5152-5155.
• 43. Johansen, A., P, Dimon, C. Ellegaard, J.S. Larsen and H.H. Rugh, 1993, Dynamic phases in a spring-block system, Phys. Rev. E-48, 4779-4790.
• 44. Kessler, D.A., 2001, A new crack at friction. Nature 413, 260-261.
• 45. Kossecka, E., and R. DeWitt, 1977, Disclination kinematic, Arch. Mech. 29, 633-651.
• 46. Lockner, D.A., J.D. Byerlee, V. Kuksenko, A. Ponomarev and A, Sidorin, 1991, Quasi-static fault growth and shear fracture energy in granite, Nature 350, 39-42.
• 47. Lomnitz-Adler, J., 1991, Model for steady-state friction, J. Geophys. Res. 96, 6121-6131.
• 48. Lubkin, G.B., 1997, experiments find hysterisis and precursors in the stick slip friction of a granular system, Physics Today, Sep. 1997, p. 17-19 and references therein.
• 49. Mandelbrot, B.B., 1985, Self-affine fractals and fractal dimension, Phys. Ser. 32, 257-260.
• 50. Mandelbrot, B.B., D.E. Passoja and A.J. Paullay, 1984, Fractal character of fracture surfaces of metals. Nature 308, 721-722.
• 51. Marder, M., and J. Fineberg, 1996, How things break, Physics Today, Sep. 1996, p. 24-29.
• 52. Maveyraud, C., W. Benz, G. Ouillon, A. Sornette and D. Sornette, 1999, Solid friction at high sliding velocities: cm explicit 3D dynamical smooth particle hydrodynamics approach, J. Geophys. Res. 104, 28769-28788.
• 53. Milman, V.Y., R. Blumenfeld, N.A. Stelmashenko and R.C. Ball, 1993, Comment on "Experimental measurements of the roughness of brittle cracks", Phys. Rev. Lett. 71, 204.
• 54. Mura, T., 1963, On dynamic problems of continuous distribution of dislocations, Int. J. Eng.Sci. 1,371-381.
• 55. Muser, M.H,, L. Wenning and M.O. Robbins, 2001, Simple microscopic theory of Amontons's laws for static friction, Phys. Rev. Lett. 86, 1295-1298.
• 56. Nakano, A., R.K. Kalia and P. Vashishta, 1995, Dynamics and morphology of brittle cracks: A molecular-dynamics study of Silicon Nitride, Phys. Rev. Lett. 75, 3138-3141.
• 57. Narayan, O„ and D.S. Fisher, 1992a, Dynamics of sliding charge-density waves in 4-sdimen-sions, Phys. Rev. Lett. 68, 3615-3618.
• 58. Narayan, O., and D.S, Fisher, 1992b, Critical behaviour of sliding charge-density waves in 4-edimensions, Phys. Rev. B-46, 11520-11549.
• 59. Narayan, O., and D.S. Fisher, 1993, Threshold critical dynamics of driven interfaces in random media, Phys. Rev. B-48,7030-7042.
• 60. Narayan, O., and A.A. Middleton, 1994, Avalanches and the renormalization group for pinned charge-density waves, Phys, Rev. B. 49, 244-256.
• 61. Nasuno. S., A. Kudrolli and J. Gollub, 1997, Friction in granular layers: Hysteresis and precursors, Phys. Rev. Lett. 79, 949-952.
• 62. Omeltchenko, A., J. Yu, R.K. Kalia and P. Vashishta, 1997, Crack front propagation and fracture in graphite sheet: A molecular-dynamics study on parallel computers, Phys. Rev. Lett. 78, 2148-2151.
• 63. Petri, A-,G. Paparo, A. Vespignani, A. Alippi and M. Constantini, 1994, Experimental evidence for critical dynamics in microfracturing processes, Phys. Rev. Lett. 73, 3423-3426.
• 64. Pisarenko, D., and P. Mora, 1994, Velocity weakening in a dynamical model of friction, Pure Appl. Geophys. 142,447-466.
• 65. Ramanathan, S., and D.S. Fisher, 1998, On set of propagation of planar cracks in heterogeneous media, Phys. Rev. B-58, 6026-6046.
• 66. Ramanathan, S., D. Ertas and D.S. Fisher, 1997, Quasistatic crack propagation in heterogeneous media, Phys. Rev. Lett. 79, 873-876.
• 67. Renshaw, C.E., and E.M. Schulson, 2001, Universal behaviour in compressive failure of brittle materials, Nature 412, 897-900.
• 68. Schmittbuhl, J., and K.J. Maloy, 1997, Direct observation of a self-affine crack propagation, Phys. Rev. Lett. 78, 3888-3891.
• 69. Schmittbuhl, J., S. Roux, J.P. Vilotte and K.J. Maloy, 1995, Interfacial crack pinning: Effect of nonlocal interactions, Phys. Rev. Lett. 74, 1787-1790.
• 70. Scholz, C.H., 1998, Earthquakes and friction laws, Nature 391, 37-42.
• 71. Sharon, E., S.P. Gross and J. Fineberg, 1995, Local crack branching as a mechanism for instability in dynamic fracture, Phys. Rev. Lett. 74, 5096-5099.
• 72. Sharon, E., S.P. Gross and J. Fineberg, 1996, Energy dissipation in dynamic fracture, Phys. Rev. Lett. 76, 2117-2120.
• 73. Tanguy, A., and P. Nozieres, 1996, First-order bifurcation landscape in a 2D geometry - The example of solid friction, J. Physique, I (France) 6, 1251-1270.
• 74. Tanguy, A., and S. Roux, 1997, Memory effects in friction over correlated surfaces, Phys. Rev. E-55, 2166-2173.
• 75. Tanguy, A., M. Gounelle and S. Roux, 1998, From individual to collective pinning: Effect of long-range elastic interactions, Phys. Rev. E-58, 1577-1589.
• 76. Teisseyre, R., 1990, Earthquake premonitory and rebound theory: synthesis and revision of principles, Acta Geophys. Pol. 38, 3, 269-278.
• 77. Teisseyre, R., 1995, Theory of Earthquake Premonitory and Fracture Processes, PWN, War¬szawa, 648 pp.
• 78. Teisseyre, R., 1996, Motion and flow equation of stresses, Acta Geophys. Pol. 44, l, 19-29.
• 79. Teisseyre, R., 1997, Dislocation-stress relations and evolution of dislocation fields, Acta Geophys. Pol. 45, 3, 205-214.
• 80. Teisseyre, R., 2001 a, Evolution, propagation and diffusion of dislocation fields. In: R. Teisseyre and E. Majewski (eds.), "Earthquake Thermodynamics and Phase Transformations in the Earth’s Interior", 167-198, Academic Press, San Diego.
• 81. Teisseyre, R., 2001b, Shear band thermodynamic model of fracturing. In: R. Teisseyre and E. Majewski (eds.), "Earthquake Thermodynamics and Phase Transformations in the Earth's Interior", 279-292, Academic Press, San Diego.
• 82. Teisseyre, R., 2001c, Diffusion and desorption of O' radicals: anomalies of electric field, electric conductivity and magnetic susceptibility as related to earthquake processes. In: R. Teisseyre and E. Majewski (eds.), "Earthquake Thermodynamics and Phase Transformations in the Earth’s Interior", 519-552, Academic Press, San Diego.
• 83. Teisseyre, R., 2001d, Dislocation dynamics and related electromagnetic excitation, Acta Geophys. Pol. 49, l, 55-73.
• 84. Teisseyre, R., and H. Nagahama, 1998, Dislocation field evolution and dislocation source/sink function, Acta Geophys. Pol. 46, l, 13-33
• 85. Teisseyre, R., and H. Nagahama, 2001, Electric and electromagnetic fields related to earthquake formation. In: R. Teisseyre and E. Majewski (eds.), "Earthquake Thermodynamics and Phase Transformations in the Earth's Interior", 535-552, Academic Press, San Diego.
• 86. Teisseyre, R., and T. Yamashita, 1999, Splitting stress motion equation into seismic wave and fault-related fields, Acta Geophys. Pol. 47, 2, 135-148.
• 87. Teisseyre, R., T. Yamashita and Z. Czechowski, 1995b, Earthquake premonitory and fracture rebound theory: a synopsis. In: R. Teisseyre (ed.), "Theory of Earthquake Premonitory and Fracture Processes", 405-412, PWN, Warszawa.
• 88. Teodosiu, C., 1970, A dynamic theory of dislocations and its applications to the theory of the elastic-plastic continuum. In: J.A. Simmons, R. deWitt and R. Bullough (eds.), "Fundamental Aspect of Dislocation Theory", 837-876, Nat. Bur. Stand. (U.S.), Spec Publ. 317,11.
• 89. Thompson, P.A., and M. Robbins, 1990, Origin of stick-slip motion in boundary lubrication, Science 250,792-794.
• 90. Tsutsumi, A., and T. Shimamoto, 1996, Frictional properties of moniodiorite and gabbro during seismogenic fault motion, J. Geol. Soc. Japan 102, 240-248.
• 91. Tsutsumi. A., and T. Shimamoto, 1997, High-velocity frictional propenies of gabbro, Geophys. Res. Lett. 24,699-702.
• 92. Tullis, T.E., 1996, Rock friction and its implications for earthquake prediction examined via models of Park field earthquakes. Proc. Natl. Acad. Sci. USA 93, 3803-3810.
• 93. Varotsos, P., 2001, A review and analysis of electromagnetic precursory phenomena, Acta Geophys. Pol. 49, l, 1-42.
• 94. Varotsos, P., 2004, The Physics of Seismic Electric Signals, Terra Publ., Tokyo (in press).
• 95. Varotsos, P., and K. Alexopoulos, 1995, Solid State Physics, Savalas Eds., Athens, 384 pp.
• 96. Varotsos, P., N. Sarlis, M. Lazaridou and P. Kapiris, 1998, Transmission of stress induced electric signals in dielectric media, J. Appl. Phys. 83, 60-70.
• 97.Varotsos, P., N. Sarlis and M. Lazaridou, 2000, Transmission of stress induced electric signals: in dielectric media, Part II Acta Geophys. Pol. 48, 2, 141-177.
• 98. Varotsos, P., N. Sarlis and E. Skordas, 2002, Long range correlalions in the electric signals that precede rupture, Phys. Rev. E-66, 011902 (7).
• 99. Vicsek, T., 1989, Fractal Growth Phenomena, World Scientific, Singapore.
• 100. Virieux, J„ and R. Madariaga, 1982, Dynamic faulting studied by a finite difference method, Bull. Seism. Soc. Am. 72, 2, 345-369.
• 101. Walmann, T., A. Malthe-Sorenssen, J. Feder, T. Jossang and P. Meaking, 1996, Scaling relations for the lengths and widths of fractures, Phys. Rev. Lett. 77, 5393-5396
• 102. Yoffe E., 1951, The moving Griffith crack, Phil. Mag. 42, 739-750
• 103. Zapperi, S., P. Ray, H.E. Stanley and A. Vespignani, 1997, First-order transition in the break-down of disordered media, Phys. Rev. Lett. 78, 1408-1411.
• 104. Zhou, S.J., P.S. Lomdahl, R. Thomson, and B.L. Holian, 1996, Dynamic crack processes via, molecular dynamics, Phys. Rev. Lett. 76, 2318-2321