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Contact with Intermolecular Interaction for a Viscoelastic Layer (Self-Consistent Approach): Energy Dissipation under Indentation and Friction Force

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Abstract

A contact between an infinitely extended plane indenter and a viscoelastic layer in the scope of a self-consistent approach according to Derjaguin under the surface application (traditional formulation) and bulk application (refined formulation) of intermolecular interaction forces is considered. Using the first law of thermodynamics, the problem of determining the energy dissipation in a viscoelastic layer is solved for a preset indenter approach/retraction law. Based on this solution, friction force under sliding a rough counterbody over a viscoelastic layer has been calculated. The results of the calculations indicate a significant effect of abrupt changing in the contact gap over time exerted on the energy dissipation and the friction force.

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REFERENCES

  1. B. Derjaguin, “Untersuchungen über die Reibung und Adhäsion, IV. Theorie des Anhaftens kleiner Teilchen,” Kolloid-Z. 69 (2), 155–164 (1934).

    Article  Google Scholar 

  2. K. L. Johnson, K. Kendall, and A. D. Roberts, “Surface energy and the contact of elastic solids,” Proc. Roy. Soc. London, Ser. A 324 (1558), 301–313 (1971).

    Google Scholar 

  3. B. V. Derjaguin, V. M. Muller, and Yu. P. Toporov, “Effect of contact deformations on the adhesion of particles,” J. Colloid Interface Sci. 53 (2), 314–326 (1975).

    Article  ADS  Google Scholar 

  4. I. Sridhar, K. L. Johnson, and N. A. Fleck, “Adhesion mechanics of the surface force apparatus,” J. Phys. D: Appl. Phys. 30 (12), 1710–1719 (1997).

    Article  ADS  Google Scholar 

  5. A. O. Sergici, G. G. Adams, and S. Müftü, “Adhesion in the contact of a spherical indenter with a layered elastic half-space,” J. Mech. Phys. Solids 54 (9), 1843–1861 (2006).

    Article  ADS  MATH  Google Scholar 

  6. E. D. Reedy, “Thin-coating contact mechanics with adhesion,” J. Mater. Res. 21 (10), 2660–2668 (2006).

    Article  ADS  Google Scholar 

  7. F. M. Borodich, B. A. Galanov, N. V. Perepelkin, and D. A. Prikazchikov, “Adhesive contact problems for a thin elastic layer: asymptotic analysis and the JKR theory,” Math. Mech. Solids 24 (5), 1405–1424 (2018).

    Article  MATH  Google Scholar 

  8. J. A. Greenwood and K. L. Johnson, “The mechanics of adhesion of viscoelastic solids,” Philos. Mag. A 43 (3), 697–711 (1981).

    Article  ADS  Google Scholar 

  9. I. G. Goryacheva, M. M. Gubenko, and Yu. Yu. Makhovskaya, “Sliding of a spherical indenter on a viscoelastic foundation with the forces of molecular attraction taken into account,” J. Appl. Mech. Techn. Phys. 55 (1), 81–88 (2014).

    Article  ADS  Google Scholar 

  10. Y. Y. Lin and C. Y. Hui, “Mechanics of contact and adhesion between viscoelastic spheres: an analysis of hysteresis during loading and unloading,” J. Polym. Sci. Part B: Polym. Phys. 40, 772–793 (2002).

    Article  ADS  Google Scholar 

  11. G. Haiat, M. C. Phan Huy, and E. Barthel, “The adhesive contact of viscoelastic spheres,” J. Mech. Phys. Solids 51 (1), 69–99 (2003).

    Article  ADS  MATH  Google Scholar 

  12. V. M. Muller, V. S. Yushchenko, and B. V. Derjaguin, “On the influence of molecular forces on the deformation of an elastic sphere and its sticking to a rigid plane,” J. Colloid Interface Sci. 77 (1), 91–101 (1980).

    Article  ADS  Google Scholar 

  13. P. Attard and J. L. Parker, “Deformation and adhesion of elastic bodies in contact,” Phys. Rev. A 46 (12), 7959–7971 (1992).

    Article  ADS  Google Scholar 

  14. J. A. Greenwood, “Adhesion of elastic spheres,” Proc. R. Soc. London, Ser. A 453 (1961), 1277–1297 (1997).

  15. I. A. Soldatenkov, “The use of the method of successive approximations to calculate an elastic contact in the presence of molecular adhesion,” J. Appl. Math. Mech. 76 (5), 597–603 (2012).

    Article  Google Scholar 

  16. R. M. McMeeking, “A maxwell stress for material interactions,” J. Colloid Interface Sci. 199 (2), 187–196 (1998).

    Article  ADS  Google Scholar 

  17. R. A. Sauer and S. Li, “A contact mechanics model for quasi-continua,” Int. J. Numer. Meth. Eng. 71 (8), 931–962 (2007).

    Article  MATH  Google Scholar 

  18. L. H. He, “Stress and deformation in soft elastic bodies due to intermolecular forces,” J. Mech. Phys. Solids 61 (6), 1377–1390 (2013).

    Article  ADS  MATH  Google Scholar 

  19. I. A. Soldatenkov, “The contact problem with the bulk application of intermolecular interaction forces (a refined formulation),” J. Appl. Math. Mech. 77 (6), 629–641 (2013).

    Article  MATH  Google Scholar 

  20. N. A. Dolgov, S. N. Romashin, L. Yu. Frolenkova, and V. S. Shorkin, “A model of contact of elastic bodies with account for their adhesion,” Int. J. Nanomech. Sci. Tech. 6 (2), 117–133 (2015).

    Article  Google Scholar 

  21. J. T. G. Overbeek and M. J. Sparnaay, “Classical coagulation. London-van der Waals attraction between macroscopic objects,” Discuss. Faraday Soc. 18, 12–24 (1954).

    Article  Google Scholar 

  22. J.-J. Wu, “The jump-to-contact distance in atomic force microscopy measurement,” J. Adhesion 86 (11), 1071–1085 (2010).

    Article  Google Scholar 

  23. E. V. Teodorovich, “On the contribution of macroscopic van der Waals interactions to frictional force,” Proc. R. Soc. London, Ser. A 362, 71–77 (1978).

    Article  ADS  Google Scholar 

  24. J. B. Sokoloff, “Theory of energy dissipation in sliding crystal surfaces,” Phys. Rev. B 42 (11), 760–765 (1990).

    Article  ADS  Google Scholar 

  25. B. N. J. Persson and Z. Zhang, “Theory of friction: Coulomb drag between two closely spaced solids,” Phys. Rev. B 57 (12), 7327–7334 (1998).

    Article  ADS  Google Scholar 

  26. V. L. Popov, “Electronic and phononic friction of solids at low temperatures,” Tribol. Int. 34, 277–286 (2001).

    Article  Google Scholar 

  27. A. I. Volokitin and B. N. J. Persson, “Radiative heat transfer and noncontact friction between nanostructures,” Phys. Usp. 50 (9), 879–906 (2007).

    Article  ADS  Google Scholar 

  28. I. A. Soldatenkov, “Contact with intermolecular interaction forces for a viscoelastic layer (self-consistent approach): calculation of the stress-strain state and energy dissipation,” Mech. Solids 55 (7), 1077–1092 (2020). https://doi.org/10.3103/S0025654420070195

    Article  ADS  MATH  Google Scholar 

  29. I. A. Soldatenkov, “Contact with intermolecular interactions for a viscoelastic layer (self-consistent approach): feature analysis of the indenter approach/retract process,” Mech. Solids 56 (7), 1259–1276 (2021). https://doi.org/10.3103/S0025654421070232

    Article  ADS  MATH  Google Scholar 

  30. I. G. Kaplan, Intermolecular Interactions: Physical Picture, Computational Methods and Model Potentials (John Wiley&Sons, Chichester, 2006).

    Book  Google Scholar 

  31. J. N. Israelachvili, Intermolecular and Surface Forces (Academic, London, 2011).

    Google Scholar 

  32. R.M. Christensen, Theory of Viscoelasticity. An Introduction (Acad. Press, New York, 1971).

    Google Scholar 

  33. P. M. Ogibalov, V. A. Lomakin, and B. P. Kishkin, Mechanics of Polymers (MSU, Moscow, 1975) [in Russian].

    Google Scholar 

  34. A. A. Adamov, V. P. Matveenko, N. A. Trufanov, and I. N. Shardakov, Methods of Applied Viscoelasticity (Ural Branch RAS, Yekaterinburg, 2003) [in Russian].

    Google Scholar 

  35. G. M. Fikhtengol’ts, Course of Differential and Integral Calculus (Fizmatlit, Moscow, 2003), Vols. 1, 3 [in Russian].

    Google Scholar 

  36. N. N. Kalitkin, Numerical Methods (BKhV-Peterburg, St. Petersburg, 2011) [in Russian].

  37. H. G. Hahn, Elastizitätstheorie. Grundlagen der Linearen Theorie und Anwendungen auf Eindimensionale, Ebene und Räumliche Probleme (Teubner, Stuttgart, 1985).

    MATH  Google Scholar 

  38. J. D. Ferry, Viscoelastic Properties of Polymers (John Wiley&Sons, New York, 1961).

    Book  Google Scholar 

  39. I. A. Soldatenkov, “Calculation of the deformation component of the force of friction for a standard elastoviscous base,” J. Friction Wear 29 (1), 7–14 (2008).

    Article  Google Scholar 

  40. I. V. Kragelsky, M. N. Dobychin, and V. S. Kombalov, Friction and Wear: Calculation Methods (Mashinostroenie, Moscow, 1977; Pergamon, Oxford, 1982).

  41. Y. Wang and J. Wang, “Friction determination by atomic force microscopy in field of biochemical science,” Micromachines 9 (7), 313 (2018).

    Article  Google Scholar 

  42. Z. Deng, A. Smolyanitsky, Q. Li, X. Q. Feng, J. Rachel, and R. J. Cannara, “Adhesion-dependent negative friction coefficient on chemically modified graphite at the nanoscale,” Nat. Mater. 11, 1032–1037 (2012).

    Article  ADS  Google Scholar 

  43. M. Z. Baykara, M. R. Vazirisereshk, and A. Martini, “Emerging superlubricity: a review of the state of the art and perspectives on future research,” Appl. Phys. Rev. 5 (4), 041102 (2018).

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Funding

The work has been performed according to Sate Order No. AAAA-A20-120011690132-4 and under the financial support of the Russian Foundation for Basic Research and the Belarusian Republican Foundation for Fundamental Research within scientific project no. 20-58-00007.

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  1. Ishlinsky Institute for Problems in Mechanics, Russian Academy of Sciences, 119526, Moscow, Russia

    I. A. Soldatenkov

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  1. I. A. Soldatenkov
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Correspondence to I. A. Soldatenkov.

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Translated by O.Polyakov

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Soldatenkov, I.A. Contact with Intermolecular Interaction for a Viscoelastic Layer (Self-Consistent Approach): Energy Dissipation under Indentation and Friction Force. Mech. Solids 57, 1701–1716 (2022). https://doi.org/10.3103/S0025654422070160

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