Skip to main content
SpringerLink
Log in

Adhesion-Induced Instability in Asperities

  • Original Paper
  • Published:
Tribology Letters Aims and scope Submit manuscript

Abstract

Adhesive forces between two approaching asperities will deform the asperities, and under certain conditions this will result in a sudden runaway deformations leading to a jump-to-contact instability. We present finite element-based numerical studies on adhesion-induced deformation and instability in asperities. We consider the adhesive force acting on an asperity, when it is brought near a rigid half-space, due to van der Waals interaction between the asperity and the half-space. The adhesive force is considered to be distributed over the volume of the asperity (body force), thus resulting in more realistic simulations for the length scales considered. Iteration scheme based on a “residual stress update” algorithm is used to capture the effect of deformation on the adhesion force, and thereby the equilibrium configuration and the corresponding force. The numerical results are compared with the previous approximate analytical solutions for adhesion force, deformation of the asperity and adhesion-induced mechanical instability (jump-to-contact). It is observed that the instability can occur at separations much higher, and could possibly explain the higher value of instability separation observed in experiments. The stresses in asperities, particularly in case of small ones, are found to be high enough to cause yielding before jump-to-contact. The effect of roughness is considered by modeling a spherical protrusion on the hemispherical asperity. This small-scale roughness at the tip of the asperities is found to control the deformation behavior at small separations, and hence are important in determining the friction and wear due to the jump-to-contact instability.

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
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9

Similar content being viewed by others

References

  1. Pethica, J.B., Sutton, A.P.: On the stability of a tip and flat at very small separations. J. Vac. Sci. Technol. A 6(4), 2490–2494 (1988)

    Article  CAS  ADS  Google Scholar 

  2. Cappella, B., Dietler, G.: Force–distance curves by atomic force microscopy. Surf. Sci. Rep. 34, 1–104 (1999)

    Article  CAS  Google Scholar 

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

    Article  PubMed  ADS  Google Scholar 

  4. Landman, U., Luedtke, W.D., Burnham, N.A., Colton, R.J.: Atomistic mechanisms and dynamics of adhesion, nanoindentation and fracture. Science 248(4954), 454–461 (1990)

    Article  CAS  PubMed  ADS  Google Scholar 

  5. Attard, P.: Interaction and deformation of elastic bodies: origin of adhesion hysteresis. J. Phys. Chem. B 104, 10635–10641 (2000)

    Article  CAS  Google Scholar 

  6. Johnson, K.L.: Continuum mechanics modeling of adhesion and friction. Langmuir 12, 4510–4513 (1996)

    Article  CAS  Google Scholar 

  7. Roy Chowdhury, S.K., Ghosh, P.: Adhesion and adhesional friction at the contact between solids. Wear 174, 9–19 (1994)

    Article  ADS  Google Scholar 

  8. Smith, J.R., Bozzolo, G., Banerjea, A., Ferrante, J.: Avalanche in adhesion. Phys. Rev. Lett. 63(12), 1269–1272 (1989)

    Article  CAS  PubMed  ADS  Google Scholar 

  9. Bradley, R.S.: The cohesive force between solid surfaces and the surface energy of solids. Philos. Mag. 13(86), 853–862 (1932)

    CAS  Google Scholar 

  10. Israelachvili, J.N.: Intermolecular and Surface Forces, 2nd edn. Academic Press, San Diego (1992)

    Google Scholar 

  11. 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  CAS  ADS  Google Scholar 

  12. Derjaguin, B.V., Muller, V.M., Toporov, Y.P.: Effect of contact deformations on the adhesion of particles. J. Colloid Interface Sci. 53(2), 314–326 (1975)

    Article  CAS  Google Scholar 

  13. Maugis, D.: Adhesion of spheres: the JKR-DMT transition using a Dugdale model. J. Colloid Interface Sci. 150(1), 243–269 (1992)

    Article  CAS  Google Scholar 

  14. Johnson, K.L., Greenwood, J.A.: An adhesion map for the contact of elastic spheres. J. Colloid Interface Sci. 192, 326–333 (1997)

    Article  CAS  PubMed  Google Scholar 

  15. Muller, V.M., Yushchecko, V.S., Derjaguin, B.V.: 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  CAS  Google Scholar 

  16. Greenwood, J.A.: Adhesion of elastic spheres. Proc. R. Soc. Lond. A 453, 1277–1297 (1997)

    Article  CAS  MathSciNet  ADS  MATH  Google Scholar 

  17. Vinogradova, O.I., Feuillebois, F.: Interaction of elastic bodies via surface forces. 1. Power-law attraction. Langmuir 18, 5126–5132 (2002)

    Article  CAS  Google Scholar 

  18. Kizuka, T.: Atomic process of point contact in gold studied by time-resolved high-resolution transmission electron microscopy. Phys. Rev. Lett. 81(20), 4448–4451 (1998)

    Article  CAS  ADS  Google Scholar 

  19. Erts, D., Lohmus, A., Lohmus, R., Olin, H., Pokropivny, A.V., Ryen, L., Svensson, K.: Force interactions and adhesion of gold contacts using a combined atomic force microscope and transmission electron microscope. Appl. Surf. Sci. 188, 460–466 (2002)

    Article  CAS  ADS  Google Scholar 

  20. Bobji, M.S., Pethica, J.B., Inkson, B.J.: Indentation mechanics of Cu–Be quantified by an in situ TEM mechanical probe. J. Mater. Res. 20(10), 2726–2732 (2005)

    Article  CAS  ADS  Google Scholar 

  21. Anantheshwara, K., Bobji, M.S.: In situ transmission electron microscope study of single asperity sliding contacts. Tribol. Int. (in press)

  22. Maugis, D.: Contact, Adhesion and Rupture of Elastic Solids. Springer, New York (1999)

    Google Scholar 

  23. Kadin, Y., Kligerman, Y., Etsion, I.: Jump-in induced plastic yield onset of approaching microcontacts in the presence of adhesion. J. Appl. Phys. 103, 013513 (2008)

    Article  ADS  Google Scholar 

  24. Cho, S.S., Park, S.: Finite element modeling of adhesive contact using molecular potential. Tribol. Int. 37, 763–769 (2004)

    Article  Google Scholar 

  25. Sauer, R.A., Li, S.: An atomic interaction-based continuum model for adhesive contact mechanics. Finite Elem. Anal. Des. 43, 384–396 (2007)

    Article  MathSciNet  Google Scholar 

  26. Sauer, R.A., Wriggers, P.: Formulation and analysis of a three-dimensional finite element implementation for adhesive contact at the nanoscale. Comput. Methods Appl. Mech. Eng. 198, 3871–3883 (2009)

    Article  MathSciNet  Google Scholar 

  27. Archard, J.F.: Elastic deformation and the laws of friction. Proc. R. Soc. Lond. A 243, 190–205 (1957)

    Article  ADS  Google Scholar 

  28. Anantheshwara, K., Arul Selvan, K., Mishra, R.K., Bobji, M.S.: In situ transmission electron microscopy study of deformation of an aluminum alloy tribolayer. Scripta Mater. 60(8), 623–626 (2009)

    Article  CAS  Google Scholar 

  29. Wang, J.J., Bobji, M.S., Peng, Y., Xu X., Inkson, B.J.: In situ TEM characterisation of the tribology of nanostructured Au. In: Proceedings of NANO 2008 (2008)

  30. Yao, H., Ciavarella, M., Gao, H.: Adhesion maps of spheres corrected for strength limit. J. Colloid Interface Sci. 315, 786–790 (2007)

    Article  CAS  PubMed  Google Scholar 

  31. Johnson, K.L.: Contact Mechanics. Cambridge University Press, Cambridge (2003)

    Google Scholar 

  32. Roy Chowdhury, S.K., Pollock, H.M.: Adhesion between metal surfaces: effect of surface roughness. Wear 66, 307–321 (1981)

    Article  Google Scholar 

  33. Maugis, D., Pollock, H.M.: Surface forces, deformation and adherence at metal microcontacts. Acta Metall. 32(9), 1323–1334 (1984)

    Article  CAS  Google Scholar 

  34. Liu, D.L., Martin, J., Burnham, H.A.: Optimal roughness for minimal adhesion. Appl. Phys. Lett. 91, 043107 (2007)

    Article  ADS  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mechanical Engineering, Indian Institute of Science, Bangalore, India

    M. S. Bobji & C. S. Jog

  2. Structural Design and Engineering Division, Vikram Sarabhai Space Centre, Trivandrum, India

    Shijo Xavier

  3. Department of Mechanical Engineering, National Institute of Technology Calicut, Calicut, India

    U. B. Jayadeep

Authors
  1. M. S. Bobji
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Shijo Xavier
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. U. B. Jayadeep
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. C. S. Jog
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to M. S. Bobji.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Bobji, M.S., Xavier, S., Jayadeep, U.B. et al. Adhesion-Induced Instability in Asperities. Tribol Lett 39, 201–209 (2010). https://doi.org/10.1007/s11249-010-9637-x

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11249-010-9637-x

Keywords

Search

Navigation