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 In an IIT experiment, an indenter of known mechanical properties is pressed into contact and then withdrawn from a test material.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.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
J. Hay and G.M. Pharr, in ASM Handbook: Mechanical Testing and Evaluation (ASM International, Materials Park, OH, 2000), vol. 8 (in press).
W.C. Oliver and G.M. Pharr, J. Mater. Res. 7, 1564 (1992).
H. Hertz, Misc. Papers by H. Hertz (Macmillan and Co., Ltd., London, U.K., 1896) pp. 147–162.
J.S. Field and M.V. Swain, J. Mater. Res. 8, 297 (1993).
J.S. Field and M.V. Swain, J. Mater. Res. 10, 101 (1995).
M.V. Swain, Mater. Sci. Eng. A 253, 160 (1998).
A. Strojny, E.T. Lilleodden, G. Wang, J.V. Sivertsen, and W.W. Gerberich, 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. 281.
T.Y. Tsui, W.C. Oliver, 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. 147.
S.I. Bulychev, V.P. Alekhin, M.Kh. Shorshorov, A.P. Ternovskii, and G.D. Shnyrev, Zavod. Lab. 41, 1137 (1975).
S.I. Bulychev, V.P. Alekhin, M.Kh. Shorshorov, and A.P. Ternovskii, Probl. Prochn. 9, 79 (1976).
G.M. Pharr, W.C. Oliver, and F.R. Brotzen, J. Mater. Res. 7, 613 (1992).
A.E.H. Love, Q. J. Math. 10, 161 (1939).
A.E.H. Love, Philos. Trans. A 228, 377 (1929).
J.W. Harding and I.N. Sneddon, Proc. Cambridge Philos. Soc. 41, 16 (1945).
I.N. Sneddon, Int. J. Engng. Sci. 3, 47 (1965).
I.N. Sneddon, Fourier Transforms (McGraw-Hill, New York, 1951), pp. 450–467.
E.H. Yoffe, Phil. Mag. A, 50, 813 (1984).
A. Bolshakov and G.M. Pharr, J. Mater. Res. 13, 1049 (1998).
A. Bolshakov and G.M. Pharr, in Thin Films: Stresses and Mechanical Properties VI, edited by W.W. Gerberich, H. Gao, and J-E. Sundgren (Mater. Res. Soc. Symp. Proc. 436, Pittsburgh, PA, 1997), p. 141.
J.C. Hay, A. Bolshakov, and G.M. Pharr, J. Mater. Res. 14, 2296 (1999).
J.C. Hay, A. Bolshakov, and G.M. Pharr, in Fundamentals of Nanoindentation and Nanotribology, edited by N.R. Moody, W.W. Gerberich, N. Burnham, (Mater. Res. Soc. Symp. Proc. 522, Warrendale, PA, 1998), p. 263.
J.C. Hay, A. Bolshakov, and G.M. Pharr, in Fundamentals of Nanoindentation and Nanotribology, edited by N.R. Moody, W.W. Gerberich, N. Burnham, (Mater. Res. Soc. Symp. Proc. 522, Warrendale, PA, 1998), p. 39.
D. Tabor, Hardness of Metals (Oxford University Press, New York, 1951), pp. 67–83, 105–106.
K.L. Johnson, Contact Mechanics (Cambridge University Press, Cambridge, U.K., 1985), pp. 61, 176.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Hay, J.L., Wolff, P.J. Small correction required when applying the Hertzian contact model to instrumented indentation data. Journal of Materials Research 16, 1280–1286 (2001). https://doi.org/10.1557/JMR.2001.0179
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1557/JMR.2001.0179