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Modeling of Thermal-Assisted Dislocation Friction

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Abstract

We generalize a model for friction at a sliding interface involving the motion of misfit dislocations to include the effect of thermally activated transitions across barriers. We obtain a comparatively simple form with the absolute zero-temperature Peierls barrier replaced by an effective Peierls barrier which varies exponentially with temperature, in agreement with recent experimental observations of thermally activated friction. Going further, we suggest a plausible method for generalizing the frictional drag at a more constitutive level by replacing the Peierls stress in a more general sense where the microstructure (e.g., dislocation density, grain size etc.) is built in. Last, but not least, we point out that when barriers are included the static coefficient of friction becomes larger than the dynamic coefficient of friction, which is an important connection to reality.

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References

  1. Bowden, F.P., Moore, A.J.W., Tabor, D.: The ploughing and adhesion of sliding metals. J. Appl. Phys. 14(80), 80–91 (1943)

    Article  ADS  Google Scholar 

  2. Tomlinson, G.A.: A molecular theory of friction. Philos. Mag. 7(46), 905–939 (1929)

    CAS  Google Scholar 

  3. Harrison, J.A., White, C.T., Colton, R.J., Brenner, D.W.: Molecular-dynamics simulations of atomic-scale friction of diamond surfaces. Phys. Rev. B 46(15), 9700–9708 (1992)

    Article  CAS  ADS  Google Scholar 

  4. Landman, U., Luedtke, W.D.: Nanomechanics and dynamics of tip–substrate interactions. J. Vac. Sci. Technol. B 9(2), 414–423 (1991)

    Article  CAS  Google Scholar 

  5. Merkle, A.P., Marks, L.D.: A predictive analytical friction model from basic theories of interfaces, contacts and dislocations. Tribol. Lett. 26(1), 73–84 (2007)

    Article  Google Scholar 

  6. Bollmann, W.: On the geometry of grain and phase boundaries: I. General Theory. Philos. Mag. 16(140), 363–381 (1967)

    Article  CAS  ADS  Google Scholar 

  7. Bollmann, W.: On the geometry of grain and phase boundaries, II. Applications of general theory. Philos. Mag. 16(140), 383–399 (1967)

    Article  CAS  ADS  Google Scholar 

  8. Grimmer, H., Bollmann, W., Warrington, D.H.: Coincidence-site lattices and complete pattern-shift in cubic crystals. Acta Cryst. A 30(MAR), 197–207 (1974)

    Article  Google Scholar 

  9. Barthel, E.: On the description of the adhesive contact of spheres with arbitrary interaction potentials. J. Colloid Interf. Sci. 200(1), 7–18 (1998)

    Article  CAS  Google Scholar 

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

    MATH  Google Scholar 

  11. Unertl, W.N.: Implications of contact mechanics models for mechanical properties measurements using scanning force microscopy. J. Vac. Sci. Technol. A 17(4), 1779–1786 (1999)

    Article  CAS  ADS  Google Scholar 

  12. Leibfried, G.: Über den Einfluß thermisch angeregter Schallwellen auf die plastische Deformation. Z. Phys. 127, 344 (1950)

    Article  MATH  CAS  MathSciNet  ADS  Google Scholar 

  13. Lubenets, S.V., Startsev, V.I.: Sov. Phys. Solid State 10, 15 (1968)

    Google Scholar 

  14. Alshits, V. I.: Progress in materials science. In: Indenbom, V. L., Lothe, J. Elastic Strain Fields and Dislocation, vol. 31, p. 625. Elsevier Science, Amsterdam (1992)

  15. Alshits, V.I.: Sov. Phys. Solid State Ussr 11(8), 1947 (1970)

    Google Scholar 

  16. Alers, G.A., Buck, O., Tittmann, B.R.: Measurements of plastic flow in superconductors and the electron-dislocation interaction. Phys. Rev. Lett. 23(6), 290–293 (1969)

    Article  CAS  ADS  Google Scholar 

  17. Kojima, H., Suzuki, T.: Electron drag and flow stress in niobium and lead at 4.2°K. Phys. Rev. Lett. 21(13), 896–898 (1968)

    Article  CAS  ADS  Google Scholar 

  18. Hikata, A., Elbaum, C.: Ultrasonic attenuation in normal and superconducting lead; electronic damping of dislocations. Phys. Rev. Lett. 18(18), 750–752 (1967)

    Article  CAS  ADS  Google Scholar 

  19. Tittmann, B.R., Bommel, H.E.: Amplitude-dependent ultrasonic attenuation in superconductors. Phys. Rev. 151(1), 178–189 (1966)

    Article  CAS  ADS  Google Scholar 

  20. Mason, W.P.: Effect of electron-damped dislocations on the determination of the superconducting energy gaps of metals. Phys. Rev. 143(1), 229–235 (1966)

    Article  CAS  ADS  Google Scholar 

  21. Huffman, G.P., Louat, N.: Interaction between electrons and moving dislocations in superconductors. Phys. Rev. Lett. 24(19), 1055–1059 (1970)

    Article  CAS  ADS  Google Scholar 

  22. Alshits, V.I., Shtolberg, A., Indenbom, V.L.: Stationary kink motion in the secondary Peierls relief. Phys. Stat. Sol. B 50(1), 59–69 (1972)

    Article  Google Scholar 

  23. Alshits, V.I., Sandler, Y.M.: Flutter mechanism of dislocation drag. Phys. Stat. Sol. 64, K45–K49 (1974)

    Google Scholar 

  24. Hiratani, M., Nadgorny, E.M.: Combined model of dislocation motion with thermally activated and drag-dependent stages. Acta Mater. 49(20), 4337–4346 (2001)

    Article  CAS  Google Scholar 

  25. Merkle, A.P., Marks, L.D.: Comment on “friction between incommensurate crystals”. Philos. Mag. Lett. 87(8), 527–532 (2007)

    Article  CAS  ADS  Google Scholar 

  26. Dienwiebel, M., Pradeep, N., Verhoeven, G.S., Zandbergen, H.W., Frenken, J.W.M.: Model experiments of superlubricity of graphite. Surf. Sci. 576(1–3), 197–211 (2005)

    Article  CAS  ADS  Google Scholar 

  27. Dienwiebel, M., Verhoeven, G.S., Pradeep, N., Frenken, J.W.M., Heimberg, J.A., Zandbergen, H.W.: Superlubricity of graphite. Phys. Rev. Lett. 92(12), 1261011–1261014 (2004)

    Article  Google Scholar 

  28. Merkle, A., Marks, L.D.: Friction in full view. Appl. Phys. Lett. 90, 641011–641013 (2007)

    Article  Google Scholar 

  29. Zhao, X., Phillpot, S.R., Sawyer, W.G., Sinnott, S.B., Perry, S.S.: Transition from thermal to athermal friction under cryogenic conditions. Phys. Rev. Lett. 102, 1861021–1861024 (2009)

    Google Scholar 

  30. Zhao, X., Perry, S. S.: Appl. Phys. Lett. (2009) (submitted)

  31. Weertman, J., Weertman, J.R.: Elementary Dislocation Theory, 2nd edn. Oxford University Press, Oxford (1992)

    Google Scholar 

  32. Hirth, J.P., Lothe, J.: Theory of Dislocations, 2nd edn. Krieger Publishing Company, Malabar (1982)

    Google Scholar 

  33. Bulatov, V.V., Kaxiras, E.: Semidiscrete variational Peierls framework for dislocation core properties. Phys. Rev. Lett. 78(22), 4221–4224 (1997)

    Article  CAS  ADS  Google Scholar 

  34. Hirth, J.P., Lothe, J.: Theory of Dislocations, 2nd edn. Krieger Publishing Company, Malabar, FL (1992)

    Google Scholar 

  35. Duesbery, M.: The influence of core structure on dislocation mobility. Philos. Mag. 19, 501 (1969)

    Article  CAS  ADS  Google Scholar 

  36. Guyot, P., Dorn, J.: Can. J. Phys. 45, 983 (1967)

    Google Scholar 

  37. Nadgorny, E.: Prog. Mater. Sci. 31, 1 (1989)

    Article  Google Scholar 

  38. Teichler, H.: Berechnung des Peierls-potentials im diamantgitter mit Hilfe der pseudopotential methode. Phys. Status Solidi b 23, 341 (1967)

    Article  CAS  Google Scholar 

  39. Wang, G., Strachan, A., Ҫğin, T., Goddard III, W.A.: Calculating the Peierls energy and Peierls stress from atomistic simulations of screw dislocation dynamics: application to bcc tantalum, Modelling Simul. Mater. Sci. Eng. 12, S371 (2004)

    CAS  ADS  Google Scholar 

  40. Landau, A.I.: The effect of dislocation inertia on the thermally activated low-temperature plasticity of materials. I. Theory. Phys. Status Solidi a 61(2), 555–563 (1980)

    Article  CAS  Google Scholar 

  41. Mura, T.: Micromechanics of Defects in Solid. Springer, New York (1987)

    Google Scholar 

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Acknowledgment

The authors would like to thank the U.S. Air Force Office of Scientific Research for funding this study on Grant number FA9550-08-1-0016.

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  1. Department of Materials Science and Engineering, Northwestern University, Evanston, IL, 60208, USA

    Y. Liao & L. D. Marks

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  1. Y. Liao
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  2. L. D. Marks
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Correspondence to Y. Liao.

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Liao, Y., Marks, L.D. Modeling of Thermal-Assisted Dislocation Friction. Tribol Lett 37, 283–288 (2010). https://doi.org/10.1007/s11249-009-9520-9

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