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An improved technique for determining hardness and elastic modulus using load and displacement sensing indentation experiments

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Abstract

The indentation load-displacement behavior of six materials tested with a Berkovich indenter has been carefully documented to establish an improved method for determining hardness and elastic modulus from indentation load-displacement data. The materials included fused silica, soda–lime glass, and single crystals of aluminum, tungsten, quartz, and sapphire. It is shown that the load–displacement curves during unloading in these materials are not linear, even in the initial stages, thereby suggesting that the flat punch approximation used so often in the analysis of unloading data is not entirely adequate. An analysis technique is presented that accounts for the curvature in the unloading data and provides a physically justifiable procedure for determining the depth which should be used in conjunction with the indenter shape function to establish the contact area at peak load. The hardnesses and elastic moduli of the six materials are computed using the analysis procedure and compared with values determined by independent means to assess the accuracy of the method. The results show that with good technique, moduli can be measured to within 5%.

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References

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

    Article  CAS  Google Scholar 

  2. W. C. Oliver, R. Hutchings, and J. B. Pethica, in ASTM STP 889, edited by P. J. Blau and B. R. Lawn (American Society for Testing and Materials, Philadelphia, PA, 1986), pp. 90–108.

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

    Article  Google Scholar 

  4. J. B. Pethica, in Ion Implantation into Metals, edited by V. Ashworth, W. Grant, and R. Procter (Pergamon Press, Oxford, 1982), pp. 147–156.

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

    Article  CAS  Google Scholar 

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

    Article  CAS  Google Scholar 

  7. D. Stone, W. R. LaFontaine, P. Alexopoulos, T-W. Wu, and Che-Yu Li, J. Mater. Res. 3, 141 (1988).

    Article  CAS  Google Scholar 

  8. J. J. Oilman, in The Science of Hardness Testing and Its Research Applications, edited by J. H. Westbrook and H. Conrad (American Society for Metals, Metals Park, OH, 1973), pp. 51–74.

  9. W. C. Oliver, MRS Bulletin XI, 15 (1986).

  10. W. C. Oliver, C. J. McHargue, and S. J. Zinkle, Thin Solid Films 153, 185 (1987).

    Article  CAS  Google Scholar 

  11. J. Boussinesq, Applications des Potentiels a l’étude de équilibre et du mouvement des solides élastiques (Gauthier-Villars, Paris, 1885).

    Google Scholar 

  12. H. Hertz, J. reine und angewandte Mathematik 92, 156 (1882).

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

    Google Scholar 

  14. A. E. H. Love, Quart. J. Math. 10, 161 (1939).

    Article  Google Scholar 

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

    Book  Google Scholar 

  16. I. N. Sneddon, Int. J. Engng. Sci. 3, 47 (1965).

    Article  Google Scholar 

  17. J. W. Harding and I. N. Sneddon, Proc. Cambridge Philos. Soc. 41, 12 (1945).

    Article  Google Scholar 

  18. D. Tabor, Proc. R. Soc. A 192, 247 (1948).

    Google Scholar 

  19. N. A. Stillwell and D. Tabor, Proc. Phys. Soc. London 78, 169 (1961).

    Article  Google Scholar 

  20. A. P. Ternovskii, V. P. Alekhin, M.Kh. Shorshorov, M. M. Khrushchov, and V. N. Skvortsov, Zavod. Lab. 39, 1242 (1973).

    CAS  Google Scholar 

  21. S.I. Bulychev, V.P. Alekhin, M.Kh. Shorshorov, A.P. Ternovskii, and G.D. Shnyrev, Zavod. Lab. 41, 1137 (1975).

    CAS  Google Scholar 

  22. S.I. Bulychev, V.P. Alekhin, M.Kh. Shorshorov, and A.P. Ternovskii, Prob. Prochn. 9, 79 (1976).

    Google Scholar 

  23. M. Kh. Shorshorov, S. I. Bulychev, and V. P. Alekhin, Sov. Phys. Dokl. 26, 769 (1982).

    Google Scholar 

  24. S. I. Bulychev and V. P. Alekhin, Zavod. Lab. 53, 76 (1987).

    Google Scholar 

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

    Article  CAS  Google Scholar 

  26. R. B. King, Int. J. Solids Structures 3, 1657 (1987).

    Article  Google Scholar 

  27. A. K. Bhattacharya and W. D. Nix, Int. J. Solids Structures 24, 881 (1988).

    Article  Google Scholar 

  28. G. M. Pharr, W. C. Oliver, and D. R. Clarke, Scripta Metall. 23, 1949 (1989).

    Article  CAS  Google Scholar 

  29. G. M. Pharr, W. C. Oliver, and D. R. Clarke, J. Elec. Mater. 19, 881 (1990).

    Article  CAS  Google Scholar 

  30. G. M. Pharr, W. C. Oliver, and D. S. Harding, J. Mater. Res. 6, 1129 (1991).

    Article  CAS  Google Scholar 

  31. J. P. Hirth and J. Lothe, Theory of Dislocations, 2nd ed. (John Wiley and Sons, New York, 1982), p. 837.

    Google Scholar 

  32. J. B. Pethica and W. C. Oliver, Physica Scripta T19, 61 (1987).

    Article  Google Scholar 

  33. 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, 13 (1989).

  34. W. C. Oliver and J. B. Pethica, U.S. Patent No. 4848141, July 1989.

  35. G. Simmons and H. Wang, Single Crystal Elastic Constants and Calculated Aggregate Properties: A Handbook, 2nd ed. (The M.I.T. Press, Cambridge, MA, 1971).

  36. G.R. Anstis, P. Chantikul, B.R. Lawn, and D. B. Marshall, J. Am. Ceram. Soc. 64, 533 (1981).

    Article  CAS  Google Scholar 

  37. General Electric Fused Quartz Products Technical Data, general catalog number 7705–7725, April 1985.

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Authors and Affiliations

  1. Metals and Ceramics Division, Oak Ridge National Laboratory, 37831-6116, Oak Ridge, Tennessee, USA

    W. C. Oliver

  2. Department of Materials Science, Rice University, P. O. Box 1982, 77251, Houston, Texas, USA

    G. M. Pharr

Authors
  1. W. C. Oliver
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  2. G. M. Pharr
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Oliver, W.C., Pharr, G.M. An improved technique for determining hardness and elastic modulus using load and displacement sensing indentation experiments. Journal of Materials Research 7, 1564–1583 (1992). https://doi.org/10.1557/JMR.1992.1564

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  • DOI: https://doi.org/10.1557/JMR.1992.1564

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