Skip to main content
SpringerLink
Log in

Thin-coating contact mechanics with adhesion

  • Outstanding Meeting Paper
  • Article
  • Published:
Journal of Materials Research Aims and scope Submit manuscript

Abstract

An elementary theory for a rigid spherical indenter contacting a thin, linear elastic coating that is bonded to a rigid substrate was developed. This theory predicts that contact area varies as the square root of the compressive load in contrast to Hertz theory where contact area varies as the two-thirds power of the compressive load. Finite element analysis confirmed an approximate square root dependence of contact area on compressive load when the coating thickness-to-indenter radius ratio is less than 0.1 and when the coating Poisson’s ratio is less than 0.45. Thin-coating contact mechanics theories that use either the Derjaguin-Muller-Toporov (DMT) approximation or the Johnson-Kendall-Roberts (JKR) approximation were also developed. In addition, a finite element simulation capability that includes adhesion was developed and verified. Illustrative finite element simulations that include adhesion were then performed for a thin elastic coating (rigid indenter/substrate). Results were compared with the thin-coating contact theories and the transition from DMT-like to JKR-like response was examined.

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

Similar content being viewed by others

References

  1. C.-H. Hsueh, P. Miranda: Combined empirical-analytical method for determining contact radius and indenter displacement during Hertzian indentation of coating/substrate systems. J. Mater. Res. 19, 2774 (2004).

    CAS  Google Scholar 

  2. C.H. Hsueh, P. Miranda: Master curves for Hertzian indentation on coating/substrate systems. J. Mater. Res. 19, 94 (2004).

    CAS  Google Scholar 

  3. A. Perriot, E. Barthel: Elastic contact to a coated half-space: Effective elastic modulus and real penetration. J. Mater. Res. 19, 600 (2004).

    CAS  Google Scholar 

  4. F. Yang: Adhesive contact between a rigid axisymmetric indenter and an incompressible elastic thin film. J. Phys. D: Appl. Phys. 35, 2614 (2002).

    CAS  Google Scholar 

  5. T. Tang, C.Y. Hui: Decohesion of a rigid punch from an elastic layer: Transition from “flaw sensitive” to “flaw insensitive” regime. J. Polym. Sci., Part B: Polym. Phys. 43, 3628 (2005).

    CAS  Google Scholar 

  6. R.W. Carpick, E.E. Flater, K. Sridharan, D.F. Ogletree, M. Salmeron: Atomic-scale friction and its connection to fracture mechanics. JOM 56, 48 (2004).

    Google Scholar 

  7. K.L. Johnson, I. Sridhar: Adhesion between a spherical indenter and an elastic solid with a compliant elastic coating. J. Phys. D: Appl. Phys. 34, 683 (2001).

    CAS  Google Scholar 

  8. I. Sridhar, Z.W. Zheng, K.L. Johnson: A detailed analysis of adhesion mechanics between a compliant elastic coating and a spherical probe. J. Phys. D: Appl. Phys. 37, 2886 (2004).

    CAS  Google Scholar 

  9. M. Wang, K.M. Liechti, V. Srinivasan, J.M. White, P.J. Rossky, T.M. Stone: A hybrid molecular-continuum analysis of IFM experiments on a self-assembled monolayer. J. Appl. Mech.2004, (submitted).

    Google Scholar 

  10. F.W. delRio, M.P. de Boer, J.A. Knapp, E.D. Reedy Jr., P.J. Clews, M.L. Dunn: The role of van der Waals forces in adhesion of micromachined surfaces. Nat. Mater. 4, 629 (2005).

    CAS  Google Scholar 

  11. E.D. Reedy Jr., M.P. de Boer, A.D. Corwin, M.J. Starr, F. Bitsie, H. Sumali, J.M. Redmond, R.E. Jones, B.R. Antoun, G. Subhash, R.W. Carpick, E.E. Flater, M.D. Street, W.R. Ashurst: High Fidelity Frictional Models for MEMs. SAND2004-4791. (Sandia National Laboratories, Albuquerque, NM, 2004).

    Google Scholar 

  12. E.D. Reedy Jr., M.J. Starr, R.E. Jones, E.E. Flater, R.W. Carpick: Contact modeling of SAM-coated polysilicon asperities. (28th Annual Meeting of The Adhesion Society, Mobile, AL, February 13–16, 2005).

    Google Scholar 

  13. D.S. Grierson, E.E. Flater, R.W. Carpick: Accounting for the JKR-DMT transition in adhesion and friction measurements with atomic force microscopy. J. Adhes. Sci. Technol. 19, 291 (2005).

    CAS  Google Scholar 

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

    Book  Google Scholar 

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

    CAS  Google Scholar 

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

    CAS  Google Scholar 

  17. J.R. Rice: A path independent integral and the approximate analysis of strain concentration by notches and cracks. J. Appl. Mech. 35, 379 (1968).

    Google Scholar 

  18. P.A. Klein: Tahoe User Guide. (Sandia National Laboratories, Albuquerque, NM, 2003).

    Google Scholar 

  19. J.R. Koteras, A.S. Gullerud: Presto User’s Guide Version 1.05. (SAND2003-1089, Sandia National Laboratories, Albuquerque, NM, 2003).

    Google Scholar 

  20. K.L. Johnson: Continuum-mechanics modeling of adhesion and friction. Langmuir 12, 4510 (1996).

    CAS  Google Scholar 

  21. D. Maugis: Adhesion of spheres: The JRK-DMT transition using a Dugdale model. J. Colloid Interface Sci. 150, 243 (1992).

    CAS  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Sandia National Laboratories, Albuquerque, New Mexico, 87185, USA

    E. D. Reedy Jr.

Authors
  1. E. D. Reedy Jr.
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to E. D. Reedy Jr..

Rights and permissions

Reprints and permissions

About this article

Cite this article

Reedy, E.D. Thin-coating contact mechanics with adhesion. Journal of Materials Research 21, 2660–2668 (2006). https://doi.org/10.1557/jmr.2006.0327

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1557/jmr.2006.0327

Search

Navigation