Skip to main content
SpringerLink
Log in

Non-Steady Wear of a Two-Layer Coating Taking into Account Frictional Heating

  • Published:
Journal of Applied Mechanics and Technical Physics Aims and scope

Abstract—

The application of two-layer coatings is one of the most widely used ways to increase the performance capacity of heavily loaded frictional joints. Design of two-layer coatings for dry sliding friction surfaces and prediction of their efficiency involve the need to develop mathematical models of sliding contact allowing for wear and frictional heating. To achieve this goal, we consider a nonsteady quasi-static contact problem of uncoupled thermoelasticity of a rigid punch in the form of half-plane sliding with a constant velocity over the surface of a two-layer elastic coating bonded on its bottom face to a flat rigid substrate. During the sliding, the punch also penetrates into the two-layer coating in a direction normal to its surface. The punch friction against the coating surface is mathematically described by the Coulomb friction model. The heat flow generated by friction is directed into the coating depth. The frictional sliding contact gives rise to wear of the two-layer coating. The stated problem is solved using the Laplace integral transform. The basic characteristics of each layer, namely, displacements, temperature, and stresses, are presented in the form of the contour integrals of meromorphic functions. The analysis of the properties of the integrand poles in the complex plane of integration and determination of thermoelastic instability domains in the space of problem parameters are followed by evaluation of the contour integrals. The influence of the problem parameters on the sliding contact main characteristics, i.e., temperature, wear, and stresses, is studied. As an example, the wear of a two-layer coating with its upper layer made of titanium nitride and lower layer made of titanium (TiN/Ti) is considered. The numerical results show that by properly selecting the coating layer thicknesses, better wear resistance and lower contact temperature of the coating can be achieved.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1.
Fig. 2.

Similar content being viewed by others

REFERENCES

  1. Kolesnikov, V.I. and Ivanochkin, P.G., Dvukhsloinye kompozitsii tribotekhnicheskogo naznacheniya dlya tyazhelonagruzhennykh uzlov treniya (Bilayered Composites of Tribotechnical Purposes for Heavily Loaded Frictional Joints), Rostov-on-Don: RGUPS, 2009.

  2. Liu, L., Shen, H.H., Liu, X.Z., Guo, Q., Meng, T.X., Wang, Z.X., Yang, H.J., and Liu, X.P., Wear resistance of TiN(Ti2N)/Ti composite layer formed on C17200 alloy by plasma surface Ti-alloying and nitriding, Appl. Surf. Sci., 2016, vol. 388, pp. 103–108. https://doi.org/10.1016/j.apsusc.2016.03.059

    Article  ADS  Google Scholar 

  3. Shi C.-M., Wang T.-G., Pei Z.-L., Gong, J., and Sun, C., Effects of the thickness ratio of CrN vs Cr2O3 layer on the properties of double-layered CrN/Cr2O3 coatings deposited by arc ion plating, J. Mater. Sci. Tech., 2014, vol. 30, pp. 473–479. https://doi.org/10.1016/j.jmst.2014.01.007

    Article  Google Scholar 

  4. Zhang, J., Sun, K., Wang, J., Tian, B., Wang, H., and Yin, Y., Sliding wear behavior of plasma sprayed Fe3Al–Al2O3 graded coatings, Thin Solid Films, 2008, vol. 516, pp. 5681–5685. https://doi.org/10.1016/j.tsf.2007.07.126

    Article  ADS  Google Scholar 

  5. Murray, J.W., Cook, R.B., Senin, N., Algodi, S.J., and Clare, A.T., Defect-free TiC/Si multi-layer electrical discharge coatings, Mater. Des., 2018, vol. 155, pp. 352–365. https://doi.org/10.1016/j.matdes.2018.06.019

    Article  Google Scholar 

  6. Sharifahmadian, O., and Mahboubi, F., A comparative study of microstructural and tribological properties of N-DLC/DLC double layer and single layer coatings deposited by DC-pulsed PACVD process, Ceram. Int., 2019, vol. 45, pp. 7736–7742. https://doi.org/10.1016/j.ceramint.2019.01.076

    Article  Google Scholar 

  7. Feldshtein, E.E., Devojno, O.G., Kardapolava, M.A., Lutsko, N.I., Zurek, D., and Michalski M., Tribological characteristics of composite coatings formed by laser cladding of powders of nickel self-fluxing alloy and bronze, J. Frict. Wear, 2016, vol. 37, pp. 454–461. https://doi.org/10.3103/S1068366616050056

    Article  Google Scholar 

  8. Kozarez, I.V., Mikhal’chenkova, M.A., Lavrov, V.I., and Sinyaya N.V., Increase of abrasive wear resistance of parts by means of variation of welding technique of double-layer coatings with hard surface, Trakt. Sel’khozmash., 2016, no. 10, pp. 38–40.

  9. Ivanochkin, P.G., Kolesnikov, V.I., Flek, B.M., and Chebakov, M.I., Contact strength of a two-layer covering under friction forces in the contact region, Mech. Solids, 2007, vol. 42, pp. 157–165. https://doi.org/10.3103/S0025654407010190

    Article  ADS  Google Scholar 

  10. Goryacheva, I.G. and Torskaya, E.V., Modeling the contact wear fracture of a two-layer basement, Mech. Solids, 2008, vol. 43, pp. 426–436. https://doi.org/10.3103/S002565440803014X

    Article  ADS  Google Scholar 

  11. Azojan, A.I. and Ivanochkin, P.G., in Proceedings of the 18th International Conference on Current Problems of Continuum Mechanics, November 7–10, 2016, Rostov-on-Don: South. Fed. Univ., 2016, pp. 20–24.

  12. Vasiliev, A.S., Volkov, S.S., and Aizikovich, S.M., Approximated analytical solution of contact problem on indentation of elastic half-space with coating reinforced with inhomogeneous interlayer, Mater. Phys. Mech., 2018, vol. 35, pp. 175–180. https://doi.org/10.18720/MPM.3512018_20

    Article  Google Scholar 

  13. Vasiliev, A.S., Volkov, S.S., and Aizikovich, S.M., in Proceedings of the 11th International Conference on Shell Structures: Theory and Applications SSTA 2017, Gdansk, Poland, October 11–13, 2017, vol. 4, pp. 185–188. https://doi.org/10.1201/9781315166605-39

  14. Yilmaz, K.B., Comez, I., Yildirim, B., Guler, M.A., and El-Borgi, S., Frictional receding contact problem for a graded bilayer system indented by a rigid punch, Int. J. Mech. Sci., 2018, vol. 141, pp. 127–142. https://doi.org/10.1016/j.ijmecsci.2018.03.041

    Article  Google Scholar 

  15. Vasiliev, A.S., Volkov, S.S., Aizikovich, S.M., and Litvinenko, A.N., Indentation of an elastic half-space reinforced with a functionally graded interlayer by a conical punch, Mater. Phys. Mech., 2018, vol. 40, pp. 254–260. https://doi.org/10.18720/MPM.4022018_14

    Article  Google Scholar 

  16. Goldstein, R.V., Ustinov, K.B., and Chentsov, A.V., Influence of substrate compliance on stresses generating stability loss of a delaminated coating, Vychisl. Mekh. Splosh. Sred, 2011, vol. 4, no. 3, pp. 48–57. https://doi.org/10.7242/1999-6691/2011.4.3.26

    Article  Google Scholar 

  17. Kudish, I., Pashkovski, E., Volkov, S.S., Vasiliev, A.S., and Aizikovich, S.M., Heavily loaded line EHL contacts with thin adsorbed soft layers, Math. Mech. Solid., 2020, vol. 25, pp. 1011–1037. https://doi.org/10.1177/1081286519898878

    Article  MathSciNet  MATH  Google Scholar 

  18. Volkov, S.S., Vasiliev, A.S., Aizikovich, S.M., and Sadyrin, E.V., Contact problem on indentation of an elastic half-plane with an inhomogeneous coating by a flat punch in the presence of tangential stresses on a surface, AIP Conf. Proc., 2018, vol. 1959, p. 070037. https://doi.org/10.1063/1.5034712

    Article  Google Scholar 

  19. Babeshko, V.A. and Vorovich, I.I., Calculation of contact temperatures generated by the rotation of a shaft in a bearing, J. Appl. Mech. Tech. Phys., 1968, vol. 9, pp. 221–222. https://doi.org/10.1007/BF00913191

    Article  ADS  Google Scholar 

  20. Lifanov, I.K. and Saakian, A.V., Method of numerical solution of the problem of impressing a moving stamp into an elastic half-plane, taking heat generation into account, J. Appl. Math. Mech., 1982, vol. 46, pp. 388–394. https://doi.org/10.1016/0021-8928(82)90117-4

    Article  Google Scholar 

  21. Vorovich, I.I., Pozharskii, D.A., and Chebakov, M.I., The thermoelasticity of a moving punch when the heat release from friction is taken into account, J. Appl. Math. Mech., 1994, vol. 58, pp. 539–544. https://doi.org/10.1016/0021-8928(94)90103-1

    Article  MathSciNet  MATH  Google Scholar 

  22. Zelentsov, V.B. and Mitrin, B.I., Thermoelastic instability in the quasi-static coupled thermoelasticity problem dealt with the sliding contact with frictional heating, Mech. Solids, 2019, vol. 54, pp. 58–69. https://doi.org/10.3103/S0025654419010059

    Article  ADS  Google Scholar 

  23. Aleksandrov, V.M. and Annakulova, G.K., Interaction between coatings of a body with deformation, wear, and heat release due to friction, Trenie Iznos, 1992, vol. 13, no. 1, pp. 154–160.

    Google Scholar 

  24. Evtushenko, A.A. and Pyr’ev, Yu.A., Influence of wear on the development of thermoelastic instability of a frictional contact, Izv. Akad. Nauk, Mekh. Tverd. Tela, 1997, no. 1, pp. 114–121.

  25. Zelentsov, V.B., Mitrin, B.I., Lubyagin, I.A., and Kudish, I.I., Diagnostics of wear thermoelastic instability based on sliding contact parameter monitoring, IMA J. Appl. Math., 2019, vol. 84, pp. 345–365. https://doi.org/10.1093/imamat/hxy061

    Article  MathSciNet  MATH  Google Scholar 

  26. Al-Ethari, H., Al-Dulaimi, K.Y., Warcholinski, B., and Kuznetsova, T.A., Interrelation of surface temperature and tribological characteristics of a protective coating on a tool, J. Frict. Wear, 2019, vol. 40, pp. 603–608. https://doi.org/10.3103/S1068366619060229

    Article  Google Scholar 

  27. Broszeit, E., Matthes, B., Herr, W., and Kloos, K.H., Tribological properties of r.f. sputtered Ti–B–N coatings under various pin-on-disc wear test conditions, Surf. Coat. Technol., 1993, vol. 58, pp. 29–35. https://doi.org/10.1016/0257-8972(93)90171-J

    Article  Google Scholar 

  28. Zelentsov, V.B., Mitrin, B.I., and Lubyagin, I.A., Effect of wear on frictional heating and thermoelastic instability of sliding contact, Vychisl. Mekh. Splosh. Sred, 2016, vol. 9, no. 4, pp. 430–442. https://doi.org/10.7242/1999-6691/2016.9.4.36

    Article  Google Scholar 

  29. Vestyak, A.V., Igumnov, L.A., Tarlakovskii, D.V., and Fedotenkov, G.V., The influence of non-stationary pressure on a thin spherical shell with an elastic filler, Vychisl. Mekh. Splosh. Sred, 2016, vol. 9, no. 4, pp. 443–452. https://doi.org/10.7242/1999-6691/2016.9.4.37

    Article  Google Scholar 

  30. Kovalenko A.D., Thermoelasticity: Basic Theory and Applications, Groningen: Wolters-Noordhoff, 1970.

    MATH  Google Scholar 

  31. Ditkin, V.A. and Prudnikov, A.P., Operatsionnoe ischislenie (Operational Calculus), Moscow: Vysshaya Shkola, 1975.

  32. Hurwitz, A. and Courant, R., Lectures on General Function Theory and Elliptic Functions, Berlin: Springer, 1964. https://doi.org/10.1007/978-3-662-00750-1

  33. Pontryagin, L.S., Ordinary Differential Equations, Oxford: Pergamon, 1962.

    MATH  Google Scholar 

Download references

Funding

This work was financially supported by the Russian Foundation for Basic Research (project no. 18-57-00015-Bel_a) and Belarussian Foundation for Basic Research (project no. F18R-239).

Author information

Authors and Affiliations

  1. Don State Technical University, 344000, Rostov-on-Don, Russia

    V. B. Zelentsov & B. I. Mitrin

  2. Luikov Heat and Mass Transfer Institute of National Academy of Science of Belarus, 220072, Minsk, Republic of Belarus

    T. A. Kuznetsova & V. A. Lapitskaya

Authors
  1. V. B. Zelentsov
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. B. I. Mitrin
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. T. A. Kuznetsova
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. V. A. Lapitskaya
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to V. B. Zelentsov.

Additional information

Translated by V. Filatov

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Zelentsov, V.B., Mitrin, B.I., Kuznetsova, T.A. et al. Non-Steady Wear of a Two-Layer Coating Taking into Account Frictional Heating. J Appl Mech Tech Phy 62, 1088–1096 (2021). https://doi.org/10.1134/S002189442107021X

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1134/S002189442107021X

Keywords:

Search

Navigation