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Contact Mechanics, Friction and Adhesion with Application to Quasicrystals

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Fundamentals of Friction and Wear on the Nanoscale

Abstract

We discuss the origin of friction and adhesion between hard solids such as quasicrystals. We emphasize the fundamental role of surface roughness in many contact mechanics problems, in particular for friction and adhesion between solid bodies. The most important property of rough surfaces is the surface roughness power spectrum \(C(q)\). We present surface roughness power spectra of many surfaces of practical importance, obtained from the surface height profile measured using optical methods and the Atomic Force Microscope. We show how the power spectrum determines the contact area between two solids. We also present applications to contact mechanics and adhesion for rough surfaces, where the power spectrum enters as an important input.

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References

  1. D. Shechtman, I. Blech, D. Gratias, J.W. Cahn, Phys. Rev. Lett. 53, 1951 (1984)

    Article  ADS  Google Scholar 

  2. B.N.J. Persson, O. Albohr, F. Mancosu, V. Peveri, V.N. Samoilov, I.M. Sivebaek, Wear 254, 835 (2003)

    Article  Google Scholar 

  3. E. Riedo, H. Brune, Applied Physics Letters 83, 1986 (2003)

    Article  ADS  Google Scholar 

  4. J.M. Dubois, S.S. Kang, J. von Stebut, J. Mater. Sci. Lett. 10, 537 (1991)

    Google Scholar 

  5. J.M. Dubois, P. Brunet, W. Costin, A. Merstallinger, J. Non-Cryst. Solids 334–335, 475 (2004)

    Google Scholar 

  6. J.Y. Park, D.F. Ogletree, M. Salmeron, C.J. Jenks, P.A. Thiel, Trib. Lett. 17, 629 (2004)

    Google Scholar 

  7. J.S. Ko, A.J. Gellman, T.A. Lograsso, C.J. Jenks, P.A. Thiel, Surface Science 423, 243 (1999)

    Article  ADS  Google Scholar 

  8. C.F. McFadden, A.J. Gellman, Trib. Lett. 1, 201 (1995)

    Google Scholar 

  9. Y.-P. Zhao, L.S. Wang, T.X. Yu, J. Adhesion Sci. Technol. 17, 519 (2003)

    Article  ADS  Google Scholar 

  10. C.H. Mastrangelo, Trib. Lett. 3, 223 (1997)

    Article  Google Scholar 

  11. F. Bottiglione, G. Carbone, Langmuir 29, 599 (2013)

    Google Scholar 

  12. C. Gui, M. Elwenspoek, N. Tas, J.G.E. Gardeniers, J. Appl. Phys. 85, 7448 (1999)

    Google Scholar 

  13. See, e.g., A.-L. Barabasi, H.E. Stanley, Fractal Concepts in Surface Growth (Cambridge University Press, Cambridge, 1995)

    Google Scholar 

  14. See, e.g., J. Krug, Advances in Physics 46, 139 (1997)

    Google Scholar 

  15. J. Feder, Fractals (Plenum Press, New York, 1988)

    Google Scholar 

  16. M.V. Berry, Z.V. Lewis, Proc. R. Soc. London A 370, 459 (1980)

    Google Scholar 

  17. J. Krim, G. Palasantzas, Int. J. of Modern Phys. B 9, 599 (1995)

    Article  ADS  Google Scholar 

  18. P.R. Nayak, ASME J. Lubrication Technology 93, 398 (1971)

    Article  Google Scholar 

  19. E. Bouchaud, J. Phys.: Condens. Matter 9, 4319 (1997)

    ADS  Google Scholar 

  20. B.N.J. Persson, Sliding Friction: Physical Principles and Applications, Sec. edn. (Springer, Heidelberg, 2000)

    Google Scholar 

  21. H. Hertz, J. Reine Angew. Math. 92, 156 (1882)

    MATH  Google Scholar 

  22. J.F. Archard, Proc. R. Soc. A 243, 190 (1957)

    Google Scholar 

  23. J.A. Greenwood, in Fundamentals of Friction, Macroscopic and Microscopic Processes, Ed. by I.L. Singer and H.M. Pollack (Kluver, Dordrecht, 1992)

    Google Scholar 

  24. J.A. Greenwood, J.B.P. Williamson, Proc. R. Soc. A 295, 300 (1966)

    Google Scholar 

  25. K.L. Johnson, Contact Mechanics (Cambridge University Press, Cambridge, 1985)

    Google Scholar 

  26. A.W. Bush, R.D. Gibson, T.R. Thomas, Wear 35, 87 (1975)

    Google Scholar 

  27. A.W. Bush, R.D. Gibson, G.P. Keogh, Mech. Res. Commun. 3, 169 (1976)

    Google Scholar 

  28. B.N.J. Persson, Phys. Rev. Lett. 87, 1161 (2001)

    Google Scholar 

  29. B.N.J. Persson, J. Chem. Phys. 115, 3840 (2001)

    Google Scholar 

  30. We define the apparent contact area \(A(\lambda )\) on the length scale \(\lambda \) to be the area of real contact if the surface would be smooth on all length scales shorter than \(\lambda \). That is, considering the Fourier transform of the surface profile, all the components whose wave vector is larger that \(2\pi /\lambda \) have to be set to 0, and the contact area with this new surface is by definition \(A(\lambda )\)

    Google Scholar 

  31. B.N.J. Persson, F. Bucher, B. Chiaia, Phys. Rev. B 65, 184106 (2002)

    Article  ADS  Google Scholar 

  32. B.N.J. Persson, Eur. Phys. J. E 8, 385 (2002)

    Google Scholar 

  33. B.N.J. Persson, Phys. Rev. Lett. 89, 245502 (2002)

    Google Scholar 

  34. S. Hyun, L. Pei, J.-F. Molinari, M.O. Robbins, Phys. Rev. E 70, 026117 (2004)

    Google Scholar 

  35. C. Yang, U. Tartaglino, B.N.J. Persson, Eur. Phys. J. E 19, 47 (2006)

    Google Scholar 

  36. M. Borri-Brunetto, B. Chiaia, M. Ciavarella, Comput. Methods Appl. Mech. Engrg. 190, 6053 (2001)

    Article  ADS  MATH  Google Scholar 

  37. K.N.G. Fuller, D. Tabor, Proc. R. Soc. London A 345, 327 (1975)

    Article  ADS  Google Scholar 

  38. K. Kendall, Molecular Adhesion and it Applications (Kluwer, New York, 2001); D. Maugis, Contact, Adhesion and Rupture of Elastic Solids (Springer, Berlin, 1999)

    Google Scholar 

  39. K. Kendall, J. Phys. D: Appl. Phys. 4, 1186 (1971); 6, 1782 (1973); 8, 115 (1975). See also the beautiful review article of K. Kendall, Contemp. Phys. 21, 277 (1980)

    Google Scholar 

  40. G.A.D. Briggs, B.J. Briscoe, J. Phys. D: Appl. Phys. 10, 2453 (1977)

    Article  ADS  Google Scholar 

  41. K.N.G. Fuller, A.D. Roberts, J. Phys. D: Appl. Phys. 14, 221 (1981)

    Article  ADS  Google Scholar 

  42. S. Zilberman, B.N.J. Persson, J. Chem. Phys. 118, 6473 (2003)

    Article  ADS  Google Scholar 

  43. V.N. Samoilov, I.M. Sivebaek, B.N.J. Persson, J. Chem. Phys. 121, 9639 (2004)

    Article  ADS  Google Scholar 

  44. J.N. Israelachvili, Intermolecular and Surface Forces (Academic Press, London, 1995)

    Google Scholar 

  45. K.L. Johnson, K. Kendall, A.D. Roberts, Proc. R. Soc. Lond. A 324, 301 (1971)

    Google Scholar 

  46. G. Sperling, PhD thesis, Karlsruhe Technical University (1964)

    Google Scholar 

  47. N.P. Padture, M. Gell, E.H. Jordan, Science 296, 280 (2002)

    Article  ADS  Google Scholar 

  48. K.T. Turner, S.M. Spearing, J. Appl. Phys. 92, 7658 (2002)

    Google Scholar 

  49. L.D. Piveteau, B. Gasser, L. Schlapbach, Biomaterials 21, 2193 (2000)

    Article  Google Scholar 

  50. S. Gorb, B.N.J. Persson, J. Chem. Phys. 119, 11437 (2003)

    Google Scholar 

  51. B.N.J. Persson, J. Chem. Phys. 118, 7614 (2003)

    Article  ADS  Google Scholar 

  52. A.K. Geim, S.V. Dubonos, I.V. Grigorieva, K.S. Novoselov, A.A. Zhukov, S.Yu. Shapoval, Nature Materials 2, 461 (2003)

    Google Scholar 

  53. A. Peressadko, S.N. Gorb, Journal of Adhesion 80, 247 (2004)

    Article  Google Scholar 

  54. K.L. Johnson, Tribology International 31, 413 (1998); L. Zhang, Y.-P. Zhao, J. Adhesion Sci. Technol. 18, 715 (2004)

    Google Scholar 

  55. B.N.J. Persson, Wear 254, 832 (2003)

    Article  Google Scholar 

  56. H.J. Gao, H.M. Yao, Proceedings of the National Academy of Sciences of the United States of America 101, 7851 (2004)

    Article  ADS  Google Scholar 

  57. B.N.J. Persson, F. Mugele, J. Phys.: Condens. Matter 16, R295 (2004)

    Google Scholar 

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Persson, B. et al. (2015). Contact Mechanics, Friction and Adhesion with Application to Quasicrystals. In: Gnecco, E., Meyer, E. (eds) Fundamentals of Friction and Wear on the Nanoscale. NanoScience and Technology. Springer, Cham. https://doi.org/10.1007/978-3-319-10560-4_13

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