Skip to main content
Log in

Measurement of hardness and elastic modulus by instrumented indentation: Advances in understanding and refinements to methodology

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

Abstract

The method we introduced in 1992 for measuring hardness and elastic modulus by instrumented indentation techniques has widely been adopted and used in the characterization of small-scale mechanical behavior. Since its original development, the method has undergone numerous refinements and changes brought about by improvements to testing equipment and techniques as well as from advances in our understanding of the mechanics of elastic–plastic contact. Here, we review our current understanding of the mechanics governing elastic–plastic indentation as they pertain to load and depth-sensing indentation testing of monolithic materials and provide an update of how we now implement the method to make the most accurate mechanical property measurements. The limitations of the method are also discussed.

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

Access this article

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. W.C. Oliver and G.M. Pharr, J. Mater. Res. 7, 1564 (1992).

    Article  CAS  Google Scholar 

  2. G.M. Pharr, W.C. Oliver, and F.R. Brotzen, J. Mater. Res. 7, 613 (1992).

    Article  CAS  Google Scholar 

  3. J.B. Pethica, R. Hutchings., and W.C. Oliver, Philos. Mag. A 48, 593 (1983).

    Article  CAS  Google Scholar 

  4. F. Frolich, P. Grau, and W. Grellmann, Phys. Status Solidi 42, 79 (1977).

    Article  Google Scholar 

  5. D. Newey, M.A. Wilkins, and H.M. Pollock, J. Phys. E: Sci. Instrum. 15, 119 (1982).

    Article  CAS  Google Scholar 

  6. G.M. Pharr and W.C. Oliver, MRS Bull. 17, 28 (1992).

    Article  Google Scholar 

  7. G.M. Pharr, Mater. Sci. Eng. A 253, 151 (1998).

    Article  Google Scholar 

  8. T.D. Shen, C.C. Koch, T.Y. Tsui, and G.M. Pharr, J. Mater. Res. 10, 2892 (1995).

    Article  CAS  Google Scholar 

  9. D. Stone, W.R. LaFontaine, P. Alexopoulos, T.W. Wu, and C-Y. Li, J. Mater. Res. 3, 141 (1988).

    Article  CAS  Google Scholar 

  10. W.D. Nix, Metall. Trans. 20A, 2217 (1989).

    Article  CAS  Google Scholar 

  11. S.V. Hainsworth, H.W. Chandler, and T.F. Page, J. Mater. Res. 11, 1987 (1996).

    Article  CAS  Google Scholar 

  12. M. Tabbal, P. Merel, M. Chaker, M.A. El Khakani, E.G. Herbert, B.N. Lucas, and M.E. O’Hern, J. Appl. Phys. 85, 3860 (1999).

    Article  CAS  Google Scholar 

  13. S.V. Hainsworth, M.R. McGurk, and T.F. Page, Surf. Coat. Technol. 102, 97 (1998).

    Article  CAS  Google Scholar 

  14. T.Y. Tsui and G.M. Pharr, J. Mater. Res. 14, 292 (1999).

    Article  CAS  Google Scholar 

  15. T.Y. Tsui, J.J. Vlassak, and W.D. Nix, J. Mater. Res. 14, 2196 (1999).

    Article  CAS  Google Scholar 

  16. S. Bec, A. Tonck, J-M. Georges, E. Georges, and J-L. Loubet, Philos. Mag. A 74, 1061 (1996).

    Article  CAS  Google Scholar 

  17. N.X. Randall, Philos. Mag. A 82, 1883 (2002).

    Article  CAS  Google Scholar 

  18. Y.Y. Lim and M.M. Chaudhri, J. Mater. Res. 14, 2314 (1999).

    Article  CAS  Google Scholar 

  19. K. Miyahara, N. Nagashima, and S. Matsuoka, Philos. Mag. A 82, 2149 (2002).

    Article  CAS  Google Scholar 

  20. R. Saha and W.D. Nix, Acta Mater. 50, 23 (2002).

    Article  CAS  Google Scholar 

  21. J.A. Knapp, D.M. Follstaedt, S.M. Myers, J.C. Barbour, and T.A. Friedman, J. Appl. Phys. 85, 1460 (1999).

    Article  CAS  Google Scholar 

  22. T.F. Page, G.M. Pharr, J.C. Hay, W.C. Oliver, B.N. Lucas, E. Herbert, and L. Riester, in Fundamentals of Nanoindentation and Nanotribology, edited by N.R. Moody, W.W. Gerberich, N. Burnham, and S.P. Baker (Mater. Res. Soc. Symp. Proc. 522, Warrendale, PA, 1998), p. 53.

  23. J. Mencik, D. Munz, E. Quandt, E.R. Weppelmann, and M.V. Swain, J. Mater. Res. 12, 2475 (1997).

    Article  CAS  Google Scholar 

  24. B.N. Lucas, W.C. Oliver, and J.E. Swindeman, in Fundamentals of Nanoindentation and Nanotribology, edited by N.R. Moody, W.W. Gerberich, N. Burnham, and S.P. Baker (Mater. Res. Soc. Symp. Proc. 522, Warrendale, PA, 1998), p. 3.

  25. A. Bolshakov and G.M. Pharr, J. Mater. Res. 13, 1049 (1998).

    Article  CAS  Google Scholar 

  26. J.C. Hay, A. Bolshakov, and G.M. Pharr, J. Mater. Res. 14, 2296 (1999).

    Article  CAS  Google Scholar 

  27. T.A. Laursen and J.C. Simo, J. Mater. Res. 7, 618 (1992).

    Article  CAS  Google Scholar 

  28. H. Gao, C-H. Chui, and J. Lee, Int. J. Solids Structures 29, 2471 (1992).

    Article  Google Scholar 

  29. Y-T. Cheng and C-M. Cheng, J. Appl. Phys. 84, 1284 (1998).

    Article  CAS  Google Scholar 

  30. Y-T. Cheng and C-M. Cheng, Int. J. Solids Structures 36, 1231 (1999).

    Article  Google Scholar 

  31. Y-T. Cheng and C-M. Cheng, Appl. Phys. Lett. 73, 614 (1998).

    Article  CAS  Google Scholar 

  32. P-L. Larsson, A.E. Giannakopoulos, E. Soderlund, D.J. Rowcliffe, and R. Vestergaard, Int. J. Solids Structures 33, 221 (1996).

    Article  Google Scholar 

  33. S.D.J. Mesarovic and N.A. Fleck, Proc. R. Soc. London A 455, 2707 (1999).

    Article  Google Scholar 

  34. B. Taljat, T. Zacharia, and G.M. Pharr, in Fundamentals of Nanoindentation and Nanotribology, edited by N.R. Moody, W.W. Gerberich, N. Burnham, and S.P. Baker (Mater. Res. Soc. Symp. Proc. 522, Warrendale, PA, 1998), p. 33.

  35. G.M. Pharr and A. Bolshakov, J. Mater. Res. 17, 2660 (2002).

    Article  CAS  Google Scholar 

  36. A. Bolshakov, W.C. Oliver, and G.M. Pharr, in Thin Films: Stresses and Mechanical Properties V, edited by S.P. Baker, C.A. Ross, P.H. Townsend, C.A. Volkert, and P. Børgesen (Mater. Res. Soc. Symp. Proc. 356, Pittsburgh, PA, 1995), p. 675.

  37. K.W. McElhaney, J.J. Vlassak, and W.D. Nix, J. Mater. Res. 13, 1300 (1998).

    Article  CAS  Google Scholar 

  38. J-L. Loubet, B.N. Lucas, and W.C. Oliver, NIST Special Publication 896: International Workshop on Instrumented Indentation (National Institute of Standards and Technology, San Diego, CA, 1995), pp. 31–34.

  39. B.N. Lucas, C.T. Rosenmayer, and W.C. Oliver, in Thin Films— Stresses and Mechanical Properties VII, edited by R.C. Cammarata, M. Nastasi, E.P. Busso, and W.C. Oliver (Mater. Res. Soc. Symp. Proc. 505, Warrebdale, PA, 1998), p. 97.

  40. W.H. Poisl, W.C. Oliver, and B.D. Fabes, J. Mater. Res. 10, 2024 (1995).

    Article  CAS  Google Scholar 

  41. B.N. Lucas, W.C. Oliver, J-L. Loubet, and G.M. Pharr, 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.

  42. B.N. Lucas and W.C. Oliver, Metall. Mater. Trans. 30A, 601 (1999).

    Article  CAS  Google Scholar 

  43. M.F. Doerner and W.D. Nix, J. Mater. Res. 1, 601 (1986).

    Article  Google Scholar 

  44. I.N. Sneddon, Int. J. Eng. Sci. 3, 47 (1965).

    Article  Google Scholar 

  45. A.E.H. Love, Q.J. Math. 10, 161 (1939).

    Article  Google Scholar 

  46. A.E.H. Love, Philos. Trans. A 228, 377 (1929).

    Google Scholar 

  47. J.W. Harding and I.N. Sneddon, Proc. Cambridge Phil. Soc. 41, 16 (1945).

    Article  Google Scholar 

  48. I.N. Sneddon, Fourier Transforms (McGraw-Hill, New York, 1951), pp. 450–467.

  49. J. Woirgard and J-C. Dargenton, J. Mater. Res. 12, 2455 (1997).

    Article  CAS  Google Scholar 

  50. C-M. Cheng and Y-T. Cheng, Appl. Phys. Lett. 71, 2623 (1997).

    Article  CAS  Google Scholar 

  51. H. Gao and T-W. Wu, J. Mater. Res. 8, 3229 (1993).

    Article  Google Scholar 

  52. H. Hertz, Miscellaneous Papers by H. Hertz (Macmillan, London, 1896).

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

  54. J.S. Field and M.V. Swain, J. Mater. Res. 8, 297 (1993).

    Article  CAS  Google Scholar 

  55. J.S. Field and M.V. Swain, J. Mater. Res. 10, 101 (1995).

    Article  CAS  Google Scholar 

  56. J.L. Hay, W.C. Oliver, A. Bolshakov, and G.M. Pharr, in Fundamentals of Nanoindentation and Nanotribology, edited by N.R. Moody, W.W. Gerberich, N. Burnham, and S.P. Baker (Mater. Res. Soc. Symp. Proc. 522, Warrendale, PA, 1998), p. 101.

  57. J.L. Hay and G.M. Pharr, in ASM Handbook Volume 8: Mechanical Testing and Evaluation, 10th ed., edited by H. Kuhn and D. Medlin (ASM International, Materials Park, OH, 2000), pp. 232–243.

  58. D. Tabor, The Hardness of Metals (Oxford University Press, London, 1951).

  59. R.B. King, Int. J. Solids Struct. 23, 1657 (1987).

    Article  Google Scholar 

  60. J.J. Vlassak and W.D. Nix, J. Mech. Phys. Solids, 42, 1223 (1994).

    Article  Google Scholar 

  61. B.C. Hendrix, J. Mater. Res. 10, 255 (1995).

    Article  CAS  Google Scholar 

  62. J.L. Loubet, J.M. Georges, O. Marchesini, and G. Meille, J. Tribology 106, 43 (1984).

    Article  CAS  Google Scholar 

  63. D.L. Joslin and W.C. Oliver, J. Mater. Res. 5, 123 (1990).

    Article  CAS  Google Scholar 

  64. D.S. Stone, K.B. Yoder, and W.D. Sproul, J. Vac. Sci. Technol. A 9, 2543 (1991).

    Article  CAS  Google Scholar 

  65. J.B. Pethica and W.C. Oliver, Phys. Scr. 19, 61 (1987).

    Article  Google Scholar 

  66. J.B. Pethica and W.C. Oliver, in Thin Films: Stresses and Mechanical Properties, edited by J.C. Bravman, W.D. Nix, D.M. Barnett, and D.A. Smith (Mater. Res. Soc. Symp. Proc. 130, Pittsburgh, PA, 1989), p. 13.

Download references

Author information

Authors and Affiliations

Authors

Additional information

This author was an editor of this focus issue during the review and decision stage. For the JMR policy on review and publication of manuscripts authored by editors, please refer to http://www.mrs.org/publications/jmr/policy.html

Rights and permissions

Reprints and permissions

About this article

Cite this article

Oliver, W.C., Pharr, G.M. Measurement of hardness and elastic modulus by instrumented indentation: Advances in understanding and refinements to methodology. Journal of Materials Research 19, 3–20 (2004). https://doi.org/10.1557/jmr.2004.19.1.3

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1557/jmr.2004.19.1.3

Navigation