Skip to main content

Adhesive contact between a rigid body of arbitrary shape and a thin elastic coating

Abstract

Application of the principle of energy balance to a rigid indenter in contact with a thin elastic layer on a flat rigid substrate provides a very simple derivation of the detachment criterion which earlier has been obtained by much more complicated asymptotic analysis. The simple criterion is additionally confirmed by the fully three-dimensional simulations of contact with a coated rigid substrate using the recently developed formulation of the boundary element method for coated media. The found detachment criterion is applied to contact of indenters of various shape. In the case of flat-ended indenters, the adhesive strength occurs to be proportional to the area of the face of the indenter (independently of the shape). The asymptotic criterion is also used for calculation of the adhesion strength of indenters having arbitrary shape and is illustrated with a case study of a contact of a rough indenter with a coated substrate.

This is a preview of subscription content, access via your institution.

References

  1. 1.

    Matheson, R.R.: 20th-to 21st-century technological challenges in soft coatings. Science 297, 976–979 (2002). https://doi.org/10.1126/science.1075707

    Article  Google Scholar 

  2. 2.

    Mittal, K.L.: Adhesion Aspects of Polymeric Coatings. Springer, New York (2012)

    Google Scholar 

  3. 3.

    Pastewka, L., Robbins, M.O.: Contact between rough surfaces and a criterion for macroscopic adhesion. Proc. Natl. Acad. Sci. 111, 3298–3303 (2014). https://doi.org/10.1073/pnas.1320846111

    Article  Google Scholar 

  4. 4.

    Ciavarella, M., Papangelo, A.: A generalized Johnson parameter for pull-off decay in the adhesion of rough surfaces. Phys. Mesomech. 21, 67–75 (2018). https://doi.org/10.1134/S1029959918010095

    Article  Google Scholar 

  5. 5.

    Popov, V.L., Pohrt, R., Li, Q.: Strength of adhesive contacts: influence of contact geometry and material gradients. Friction 5, 308–325 (2017). https://doi.org/10.1007/s40544-017-0177-3

    Article  Google Scholar 

  6. 6.

    Li, Q., Popov, V.L.: Adhesive force of flat indenters with brush-structure. Facta Univ. Ser. Mech. Eng. 16, 1–8 (2018). https://doi.org/10.22190/FUME171220005L

    Article  Google Scholar 

  7. 7.

    Heepe, L., Gorb, S.N.: Biologically inspired mushroom-shaped adhesive microstructures. Annu. Rev. Mater. Res. 44, 173–203 (2014). https://doi.org/10.1146/annurev-matsci-062910-100458

    Article  Google Scholar 

  8. 8.

    Johnson, K.L., Kendall, K., Roberts, A.D.: Surface energy and the contact of elastic solids. Proc. R. Soc. Lond. A. 324, 301–313 (1971)

    Article  Google Scholar 

  9. 9.

    Hertz, H.: Über die Berührung fester elastischer Körper. J. für die reine und Angew. Math. 92, 156–171 (1882)

    MATH  Google Scholar 

  10. 10.

    Griffith, A.A.: VI. The phenomena of rupture and flow in solids. Philos. Trans. R. Soc. Lond. A Math. Phys. Eng. Sci. 221, 163–198 (1921). https://doi.org/10.1098/rsta.1921.0006

    Article  Google Scholar 

  11. 11.

    Borodich, F.M., Galanov, B.A., Suarez-Alvarez, M.M.: The JKR-type adhesive contact problems for power-law shaped axisymmetric punches. J. Mech. Phys. Solids. 68, 14–32 (2014). https://doi.org/10.1016/j.jmps.2014.03.003

    MathSciNet  Article  MATH  Google Scholar 

  12. 12.

    Johnson, K.L., Greenwood, J.A.: An approximate JKR theory for elliptical contacts. J. Phys. D. Appl. Phys. 38, 1042–1046 (2005). https://doi.org/10.1088/0022-3727/38/7/012

    Article  Google Scholar 

  13. 13.

    Johnson, K.L.: The adhesion of two elastic bodies with slightly wavy surfaces. Int. J. Solids Struct. 32, 423–430 (1995). https://doi.org/10.1016/0020-7683(94)00111-9

    Article  MATH  Google Scholar 

  14. 14.

    Yang, F.: Adhesive contact between a rigid axisymmetric indenter and an incompressible elastic thin film. J. Phys. D. Appl. Phys. 35, 2614–2620 (2002). https://doi.org/10.1088/0022-3727/35/20/322

    Article  Google Scholar 

  15. 15.

    Yang, F.: Asymptotic solution to axisymmetric indentation of a compressible elastic thin film. Thin Solid Films 515, 2274–2283 (2006). https://doi.org/10.1016/j.tsf.2006.07.151

    Article  Google Scholar 

  16. 16.

    Argatov, I.I., Mishuris, G.S., Popov, V.L.: Asymptotic modelling of the JKR adhesion contact for a thin elastic layer. Q. J. Mech. Appl. Math. 69, 161–179 (2016). https://doi.org/10.1093/qjmam/hbw002

    MathSciNet  Article  Google Scholar 

  17. 17.

    Papangelo, A.: Adhesion between a power-law indenter and a thin layer coated on a rigid substrate. Facta Univ. Ser. Mech. Eng. 16, 19–28 (2018). https://doi.org/10.22190/FUME180102008P

    Article  Google Scholar 

  18. 18.

    Ciavarella, M.: A very simple estimate of adhesion of hard solids with rough surfaces based on a bearing area model. Meccanica 53, 241–250 (2018). https://doi.org/10.1007/s11012-017-0701-6

    MathSciNet  Article  Google Scholar 

  19. 19.

    Ciavarella, M., Papangelo, A., Barber, J.R.: The role of adhesion in contact mechanics. J. R. Soc. Interface 16, 20180738 (2019). https://doi.org/10.1098/rsif.2018.0738

    Article  Google Scholar 

  20. 20.

    Popov, V.L.: Contact Mechanics and Friction. Physical Principles and Applications. Springer, Berlin (2017)

    Book  Google Scholar 

  21. 21.

    Li, Q., Pohrt, R., Lyashenko, I.A., Popov, V.L.: Boundary element method for non-adhesive and adhesive contacts of a coated elastic half-space. arXiv:1807.01885 (2018)

Download references

Acknowledgements

The authors acknowledge partial financial support of the Deutsche Forschungsgemeinschaft (DFG PO 810/55-1).

Author information

Affiliations

Authors

Corresponding author

Correspondence to Valentin L. Popov.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Li, Q., Popov, V.L. Adhesive contact between a rigid body of arbitrary shape and a thin elastic coating. Acta Mech 230, 2447–2453 (2019). https://doi.org/10.1007/s00707-019-02403-0

Download citation