Skip to main content
SpringerLink
Log in

Contact area determination in indentation testing of elastomers

  • Published:
Journal of Materials Research Aims and scope Submit manuscript

Abstract

To evaluate mechanical properties by means of nanoindentation, information on the contact area is crucial. However, the contact area is not directly accessible in experiments and is usually calculated according to the Oliver and Pharr procedure, which turned out to be unsatisfying when applied to viscoelastic materials like polymers. In this study, complementary in situ indentation testing and finite element analysis (FEA) were performed on silicone elastomers. Through this combination of techniques, several individual error sources in the conventional contact area determination have been identified and quantified. For shallow penetrations, contact areas after Oliver and Pharr were up to 40% smaller than the in situ testing results; for larger penetrations, the contact size was overestimated by approximately 6%. The deviations of the resulting mechanical properties were approximately 10%. Viscoelastic effects could be captured if dynamic indentation testing was performed.

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. J-L. Bucaille, E. Felder, and G. Hochstetter: Mechanical analysis of the scratch test on elastic and perfectly plastic materials with the three-dimensional finite element modeling. Wear 249, 422 (2001).

    Article  CAS  Google Scholar 

  2. S. Shim, W.C. Oliver, and G.M. Pharr: A critical examination of the Berkovich vs. conical indentation based on 3D finite element calculations, in Fundamentals of Nanoindentation and Nanotribology III, edited by K.J. Wahl, N. Huber, A.B. Mann, D.F. Bahr, and Y-T. Cheng (Mater. Res. Soc. Symp. Proc. 841, Warrendale, PA, 2005), R9.5.1.

  3. M. Li, W-M. Chen, N-G. Liang, and L-D. Wang: A numerical study of indentation using indenters of different geometry. J. Mater. Res. 19, 73 (2004).

    Article  CAS  Google Scholar 

  4. N. Yu, A.A. Polycarpou, and T.F. Corny: Tip-radius effect in finite element modeling of sub-50nm-shallow nanoindentation. Thin Solid Films 450, 295 (2004).

    Article  CAS  Google Scholar 

  5. Y. Sun, T. Bell, and S. Zheng: Finite element analysis of the critical ratio of coating thickness to indentation depth for coating property measurements by nanoindentation. Thin Solid Films 258, 198 (1995).

    Article  CAS  Google Scholar 

  6. H.F. Wang and H. Bangert: Three-dimensional finite element simulation of Vickers indentation on coated systems. Mater. Sci. Eng., A 163, 42 (1993).

    Article  Google Scholar 

  7. T.A. Laursen and J.C. Simo: A study of the mechanics of microt indentation using finite elements. J. Mater. Res. 7, 618 (1992).

    Article  CAS  Google Scholar 

  8. A. Bolshakov, W.C. Oliver, and G.M. Pharr: Influences of the stress on the measurement of mechanical properties using nanoin dentation: Part II. Finite element simulations. J. Mater. Res. 11, 760 (1996).

    Article  CAS  Google Scholar 

  9. M. Lichinchi, C. Lenardi, J. Hauptand, and R. Vitali: Simulation of Berkovich nanoindentation experiments on thin films using finite element method. Thin Solid Films 312, 240 (1998).

    Article  CAS  Google Scholar 

  10. K-D. Bouzakis and N. Michailidis: Indenter surface area and hardness determination by means of a FEM-supported simulation of nanoindentation. Thin Solid Films 494, 155 (2006).

    Article  CAS  Google Scholar 

  11. K. Li, T.W. Wu, and J.C.M. Li: Contact area evolution during an indentation process. J. Mater. Res. 12, 2064 (1997).

    Article  CAS  Google Scholar 

  12. P-L. Larsson, A.E. Giannakopoulos, E. Söderlund, D.J. Rowcliffe, and R. Vestergaard: Analysis of Berkovich indentation. Int. J. Solids Struct. 33, 221 (1996).

    Article  Google Scholar 

  13. S. Swaddiwudhipong, J. Hua, K.K. Tho, and Z.S. Liu: Equivalency of Berkovich and conical load-indentation curves. Modell. Simul. Mater. Sci. Eng. 14, 71 (2006).

    Article  CAS  Google Scholar 

  14. S. Swaddiwudhipong, L.H. Poh, J. Hua, Z.S. Liu, and K.K. Tho: Modeling nano-indentation test of glassy polymers using finite elements with strain gradient plasticity. Mater. Sci. Eng., A 404, 179 (2005).

    Article  CAS  Google Scholar 

  15. S. Gupta, F. Carillo, M. Balooch, L. Pruitt, and C. Puttlitz: Simulated soft tissue indentation: A finite element study. J. Mater. Res. 20, 1979 (2005).

    Article  CAS  Google Scholar 

  16. S.D. Chen and F.J. Ke: MD simulation of the effect of the contact area and tip radius on nanoindentation. Sci. China, Ser. G 47, 101 (2004).

    Article  CAS  Google Scholar 

  17. R. Komanduri, N. Chandrasekaran, and L.M. Raff: MD simulation of indentation and scratching of single crystal aluminum. Wear 240, 113 (2000).

    Article  CAS  Google Scholar 

  18. A. Hasnaoui, P.M. Derlet, and H. Van Swygenhoven: Interaction between dislocations and grain boundaries under an indenter-A molecular dynamics simulation. Acta Mater. 52, 2251 (2004).

    Article  CAS  Google Scholar 

  19. G. Päzold, A. Linke, T. Hapke, and D.W. Heermann: Computer simulation of nanoindentation into polymer films. Z. Phys. B: Condens. Matter 104, 521 (1997).

    Google Scholar 

  20. K. Yashiro, A. Furuta, and Y. Tomita: Nanoindentation on crystal/amorphous polyethylene: Molecular dynamics study. Commit. Mater. Sci. 38, 136 (2006).

    Article  CAS  Google Scholar 

  21. W.C. Oliver and G.M. Pharr: An improved technique for determining hardness and elastic modulus using load and displacement sensing indentation experiments. J. Mater. Res. 7, 1564 (1992).

    Article  CAS  Google Scholar 

  22. I.A. Sneddon: The relation between load and penetration in the axissymmetric Boussinesq problem for a punch of arbitrary profile. Int. J. Eng. Sci. 3, 47 (1965).

    Article  Google Scholar 

  23. L. Anand and N.M. Ames: On modeling the micro-indentation response of an amorphous polymer. Int. J. Plast. 22, 1123 (2006).

    Article  CAS  Google Scholar 

  24. P-L. Larsson and S. Carlsson: On microindentation of viscoelastic polymers. Polym. Test. 17, 49 (1998).

    Article  CAS  Google Scholar 

  25. Y-T. Cheng and C-M. Cheng: Relationship between initial unloading slope, contact depth, and mechanical properties for conical indentation in linear viscoelastic solids. J. Mater. Res. 20, 1046 (2005).

    Article  CAS  Google Scholar 

  26. A.E. Giannakopoulos and A. Triantafyllou: Spherical indentation of incompressible rubber-like materials. J. Mech. Phys. Solids 55, 1196 (2007).

    Article  CAS  Google Scholar 

  27. S.J. Jerrams, M. Kaya, and K.F. Soon: The effects of strain rate and hardness on the material constants of nitrile rubbers. Mater. Des. 19, 157 (1998).

    Article  CAS  Google Scholar 

  28. W. Kuhn: On the shape of fibrous molecules in solutions. Kolloid-Zeitschrift. 68, 2 (1934).

    Article  CAS  Google Scholar 

  29. E. Guth and H. Mark: Rubber elasticity and its relationship to the structural model. Naturwissenschaften 25, 353 (1937).

    Article  CAS  Google Scholar 

  30. L.R.G. Treloar: The elasticity of a network of longchain molecules I. Trans. Faraday Soc. 39, 36 (1943).

    Article  CAS  Google Scholar 

  31. L.R.G. Treloar: The elasticity of a network of longchain molecules II. Trans. Faraday Soc. 39, 241 (1943).

    Article  CAS  Google Scholar 

  32. ABAQUS Theory manual (ABAQUS Inc., Providence, RI, 2006).

  33. M. Mooney: A theory of large elastic deformation. J. Appl. Phys. 11. 582 (1940).

    Article  Google Scholar 

  34. R.S. Rivlin: Large elastic deformations of isotropic materials IV: Further developments of the general theory. Philos. Trans. A 241, 379 (1948).

    Google Scholar 

  35. R.W. Ogden: Large deformation isotropic elasticity-On the correlation of theory and experiment for incompressible rubberlike solids. Proc. R. Soc. London, Sect. A 326, 565 (1972).

    Article  CAS  Google Scholar 

  36. O.H. Yeoh: Characterization of elastic properties of carbon-black-filler rubber vulcanizates. Rubber Chem. Technol. 63, 792 (1990).

    Article  CAS  Google Scholar 

  37. E.M. Arruda and M.C. Boyce: A three-dimensional constitutive model for the large stretch behavior of rubberelastic materials. J. Mech. Phys. Solids 41, 389 (1993).

    Article  CAS  Google Scholar 

  38. L. Valenta and L. Molnar: Comparison of the Neo-Hooke model and the Mooney-Rivlin model in FEA. Periodica Polytechnica Mech. Eng. 45, 95 (2001).

    Google Scholar 

  39. P. Raos: Modelling of elastic behaviour of rubber and its application in FEA. Plast. Rubber and Compo. Process. Appl. 19, 293 (1993).

    CAS  Google Scholar 

  40. J. Deuschle, E.J. de Souza, S. Enders, and E. Arzt: Crosslinking and curing kinetics of PDMS studied by dynamic nanoindentation, to be published.

  41. B.N. Lucas, W.C. Oliver, G.M. Pharr, and J-L. Loubet: Time dependent deformation during indentation testing, in Thin Films: Stresses and Mechanical Properties VI, edited by W.W. Gerberich, H. Gao, J-E. Sundgren, and S.P. Baker (Mater. Res. Soc. Symp Proc. 436, Pittsburgh, PA, 1997), p. 233.

    CAS  Google Scholar 

  42. ABAQUS Analysis User’s Manual (ABAQUS Inc., Providence, RI, 2006).

  43. Z. Hicsasmaz and S.S.H. Rizvi: Effect of size and shape on modulus of deformability. LWT 38, 431 (2005).

    Article  CAS  Google Scholar 

  44. R. Brown: Physical Testing of Rubber, 4th ed. (Springer, New York, 2006), p. 151.

    Google Scholar 

  45. N. Chollacoop and U. Ramamurty: Experimental assessment of the representative strains in instrumented sharp indentation. Scr. Mater. 53, 247 (2005).

    Article  CAS  Google Scholar 

  46. L.R.G. Treloar: The Physics of Rubber Elasticity, 3rd ed. (Clarendon Press, Oxford, 1975).

    Google Scholar 

  47. Y. Choi, H-S. Lee, and D. Kwon: Analysis of sharp-tip indentation curve for contact area determination taking into account pile-up and sink-in effects. J. Mater. Res. 19, 3307 (2004).

    Article  CAS  Google Scholar 

  48. J. Deuschle, S. Enders, and E. Arzt: Surface detection in nanoindentation of soft polymers. J. Mater. Res. 22, 3107 (2007).

    Article  CAS  Google Scholar 

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

    Article  CAS  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Max-Planck-Institute for Metals Research, Stuttgart, Baden Wuerttemberg, 70569, Germany

    Julia K. Deuschle

  2. Institute of Statics and Dynamics of Aerospace Structures, University of Stuttgart, Stuttgart, Baden Wuerttemberg, 70569, Germany

    H. Matthias Deuschle

  3. Engineering Mechanics, University of Nebraska, Lincoln, NE, USA

    Susan Enders & Eduard Arzt

Authors
  1. Julia K. Deuschle
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. H. Matthias Deuschle
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Susan Enders
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Eduard Arzt
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Julia K. Deuschle.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Deuschle, J.K., Deuschle, H.M., Enders, S. et al. Contact area determination in indentation testing of elastomers. Journal of Materials Research 24, 736–748 (2009). https://doi.org/10.1557/jmr.2009.0093

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1557/jmr.2009.0093

Search

Navigation