Hostname: page-component-848d4c4894-nr4z6 Total loading time: 0 Render date: 2024-05-29T16:35:28.024Z Has data issue: false hasContentIssue false
  • English
  • Français

Small correction required when applying the Hertzian contact model to instrumented indentation data

Published online by Cambridge University Press:  31 January 2011

J. L. Hay  and
P. J. Wolff
J. L. Hay*
Affiliation:
MTS Systems Corporation, Nano Instruments Innovation Center, 1001 Larson Drive, Oak Ridge, Tennessee 37830
P. J. Wolff
Affiliation:
MTS Systems Corporation, Nano Instruments Innovation Center, 1001 Larson Drive, Oak Ridge, Tennessee 37830
*
a)Address all correspondence to this author.
Get access

Abstract

Instrumented indentation testing (IIT) is a relatively new form of mechanical testing which significantly expands on the capabilities of traditional hardness testing. In an IIT experiment, an indenter of known mechanical properties is pressed into contact and then withdrawn from a test material. The fundamental measurements during an IIT experiment are the applied load and the resulting penetration of the indenter into the test surface. The Hertzian contact model, or a derivative thereof, is often employed to relate these measurements to interesting mechanical properties of the test material. This article argues for a small correction to the Hertzian contact model when applied to instrumented indentation data. The magnitude of the correction primarily depends on Poisson's ratio of the test material and the contact radius normalized by the radius of the indenter tip. Neglecting this correction can cause significant errors in the calculation of elastic modulus and hardness from instrumented indentation data.

Type
Articles
Information
Journal of Materials Research , Volume 16 , Issue 5 , May 2001 , pp. 1280 - 1286
Copyright
Copyright © Materials Research Society 2001

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

1.Hay, J. and Pharr, G.M., in ASM Handbook: Mechanical Testing and Evaluation (ASM International, Materials Park, OH, 2000), Vol. 8 (in press).Google Scholar
2.Oliver, W.C. and Pharr, G.M., J. Mater. Res. 7, 1564 (1992).CrossRefGoogle Scholar
3.Hertz, H., Misc. Papers by Hertz, H. (Macmillan and Co., Ltd., London, U.K., 1896) pp. 147–162.Google Scholar
4.Field, J.S. and Swain, M.V., J. Mater. Res. 8, 297 (1993).CrossRefGoogle Scholar
5.Field, J.S. and Swain, M.V., J. Mater. Res. 10, 101 (1995).CrossRefGoogle Scholar
6.Swain, M.V., Mater. Sci. Eng. A 253, 160 (1998).CrossRefGoogle Scholar
7.Strojny, A., Lilleodden, E.T., Wang, G., Sivertsen, J.V., and Gerberich, W.W., in Thin Films: Stresses and Mechanical Properties VI, edited by Gerberich, W.W., Gao, H., Sundgren, J-E., and Baker, S.P. (Mater. Res. Soc. Symp. Proc. 436, Pittsburgh, PA, 1997), p. 281.Google Scholar
8.Tsui, T.Y., Oliver, W.C., and Pharr, G.M., in Thin Films: Stresses and Mechanical Properties VI, edited by Gerberich, W.W., Gao, H., Sundgren, J-E., and Baker, S.P. (Mater. Res. Soc. Symp. Proc. 436, Pittsburgh, PA, 1997), p. 147.Google Scholar
9.Bulychev, S.I., Alekhin, V.P., Shorshorov, M.Kh., Ternovskii, A.P., and Shnyrev, G.D., Zavod. Lab. 41, 1137 (1975).Google Scholar
10.Bulychev, S.I., Alekhin, V.P., Shorshorov, M.Kh., and Ternovskii, A.P., Probl. Prochn. 9, 79 (1976).Google Scholar
11.Pharr, G.M., Oliver, W.C., and Brotzen, F.R., J. Mater. Res. 7, 613 (1992).CrossRefGoogle Scholar
12.Love, A.E.H., Q. J. Math. 10, 161 (1939).CrossRefGoogle Scholar
13.Love, A.E.H., Philos. Trans. A 228, 377 (1929).Google Scholar
14.Harding, J.W. and Sneddon, I.N., Proc. Cambridge Philos. Soc. 41, 16 (1945).CrossRefGoogle Scholar
15.Sneddon, I.N., Int. J. Engng. Sci. 3, 47 (1965).CrossRefGoogle Scholar
16.Sneddon, I.N., Fourier Transforms (McGraw-Hill, New York, 1951), pp. 450–467.Google Scholar
17.Yoffe, E.H., Phil. Mag. A, 50, 813 (1984).CrossRefGoogle Scholar
18.Bolshakov, A. and Pharr, G.M., J. Mater. Res. 13, 1049 (1998).CrossRefGoogle Scholar
19.Bolshakov, A. and Pharr, G.M., in Thin Films: Stresses and Mechanical Properties VI, edited by Gerberich, W.W., Gao, H., and Sundgren, J-E. (Mater. Res. Soc. Symp. Proc. 436, Pittsburgh, PA, 1997), p. 141.Google Scholar
20.Hay, J.C., Bolshakov, A., and Pharr, G.M., J. Mater. Res. 14, 2296 (1999).CrossRefGoogle Scholar
21.Hay, J.C., Bolshakov, A., and Pharr, G.M., in Fundamentals of Nanoindentation and Nanotribology, edited by Moody, N.R., Gerberich, W.W., Burnham, N., (Mater. Res. Soc. Symp. Proc. 522, Warrendale, PA, 1998), p. 263.Google Scholar
22.Hay, J.C., Bolshakov, A., and Pharr, G.M., in Fundamentals of Nanoindentation and Nanotribology, edited by Moody, N.R., Gerberich, W.W., Burnham, N., (Mater. Res. Soc. Symp. Proc. 522, Warrendale, PA, 1998), p. 39.Google Scholar
23.Tabor, D., Hardness of Metals (Oxford University Press, New York, 1951), pp. 67–83, 105–106.Google Scholar
24.Johnson, K.L., Contact Mechanics (Cambridge University Press, Cambridge, U.K., 1985), pp. 61, 176.CrossRefGoogle Scholar