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Simple method and critical comparison of frame compliance and indenter area function for nanoindentation

Published online by Cambridge University Press:  01 December 2004

Motohiro Suganuma  and
Michael V. Swain
Motohiro Suganuma*
Affiliation:
Aichi Industrial Technology Institute, Department of Materials Science, Nishi-shinwari, Hitotsugi-cho, Kariya 448-0003, Japan
Michael V. Swain
Affiliation:
Biomaterials, Faculty of Dentistry, University of Sydney, United Dental Hospital, Surry Hills, NSW 2010, Australia
*
a) Address all correspondence to this author.e-mail: motohiro_suganuma@pref.aichi.lg.jp
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Abstract

A simple method has been proposed for an independent determination of the frame compliance Cf and the area function of a Berkovich indenter. Cf was determined from the unloading compliance of very large indentations in four test materials (fused silica, silicon nitride, high-carbon steel, and copper-zinc alloy) with known elastic properties, following the Oliver–Pharr method by assuming the ideal shape of Berkovich indenter. For a specific value of Cf (= 0.3 nm/mN in our case) all the specimens showed an hc (contact depth)-independent modulus, which agreed well with the expected value when the pile-up effect was taken into account. The contact area A(hc) was then estimated using fused silica as the standard specimen, according to two different procedures, i.e., the Oliver–Pharr method and the Field–Swain method. Both methods gave almost identical area functions over the whole range of the measurement. It was also found that such area functions can be described by two separate equations: A = 2πRehc for hc < Δh and A = g(hc + Δh)2 for hc ⩾ Δh, where Re is the effective tip radius, Δh the truncation depth, and g the geometrical factor for a Berkovich indenter. Based on the spherically truncated cone model, a simple procedure is presented to determine all these parameters from the analysis of a multiple partial unloading P-h curve.

Keywords

Elastic propertiesHardnessNanoindentation
Type
Articles
Information
Journal of Materials Research , Volume 19 , Issue 12 , December 2004 , pp. 3490 - 3502
Copyright
Copyright © Materials Research Society 2004

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References

REFERENCES

1Oliver, W.C. and Pharr, G.M.: An improved technique for determining hardness and elastic modulus using load and displacement sensing indentation experiments. J. Mater. Res. 7, 1564 (1992).CrossRefGoogle Scholar
2Sakai, M., Shimizu, S. and Ishikawa, T.: The indentation load-depth curve of ceramics. J. Mater. Res. 14, 1471 (1999).CrossRefGoogle Scholar
3Oliver, W.C. and Pharr, G.M.: Measurement of hardness and elastic modulus by instrumented indentation: Advances in understanding and refinements to methodology. J. Mater. Res. 19, 3 (2004).CrossRefGoogle Scholar
4Pethica, J.B., Hutchings, R. and Oliver, W.C.: Hardness measurement at penetration depths as small as 20 nm. Philos. Mag. A 48, 593 (1983).CrossRefGoogle Scholar
5Doerner, M.F. and Nix, W.D.: A method for interpreting the data from depth-sensing indentation instruments. J. Mater. Res. 1, 601 (1986).CrossRefGoogle Scholar
6Walls, M.G., Chaudhri, M.M. and Tang, T.B.: STM profilometry of low-load Vickers indentations in a silicon crystal. J. Phys. D 25, 500 (1992).CrossRefGoogle Scholar
7Scholl, D., Everson, M.P. and Jaklevic, R.C.: Measurement of surface topography and area-specific nanohardness in the scanning force microscope. J. Mater. Res. 10, 2503 (1995).CrossRefGoogle Scholar
8Field, J.S. and Swain, M.V.: A simple predictive model for spherical indentation. J. Mater. Res. 8, 297 (1993).CrossRefGoogle Scholar
9Field, J.S. and Swain, M.V.: Determining the mechanical properties of small volumes of material from submicrometer spherical indentations. J. Mater. Res. 10, 101 (1995).CrossRefGoogle Scholar
10Gerberich, W.W., Yu, W., Kramer, D., Strojny, A., Bahr, D., Lilleodden, E. and Nelson, J.: Elastic loading and elastoplastic unloading from nanometer level indentations for modulus determinations. J. Mater. Res. 13, 421 (1998).CrossRefGoogle Scholar
11Makino, H., Kamiya, N. and Wada, S. Grain size effect of Si3N4 on damage morphology induced by localized contact stress, in Science of Engineering Ceramics, edited by Kimura, S. and Niihara, K. (Ceram. Soc. Jpn. Symp. Proc. 1, Tokyo, Japan, 1991), p. 229Google Scholar
12Sakai, M. and Nakano, Y.: Elastoplastic load-depth hysteresis in pyramidal indentation. J. Mater. Res. 17, 2161 (2002).CrossRefGoogle Scholar
13King, R.B.: Elastic analysis of some punch problems for a layered medium. Int. J. Solids Structures 23, 1657 (1987).CrossRefGoogle Scholar
14Bolshakov, A. and Pharr, G.M.: Influences of pileup on the measurement of mechanical properties by load and depth-sensing indentation techniques. J. Mater. Res. 13, 1049 (1998).CrossRefGoogle Scholar
15McElhaney, K.W., Vlassak, J.J. and Nix, W.D.: Determination of indenter tip geometry and indentation contact area for depth-sensing indentation experiments. J. Mater. Res. 13, 1300 (1998).CrossRefGoogle Scholar
16Chudoba, T., Griepentrog, M., Dück, A., Schneider, D. and Richter, F.: Young’s modulus measurements on ultra-thin coatings. J. Mater. Res. 19, 301 (2004).CrossRefGoogle Scholar
17Algueró, M., Bushby, A.J. and Reece, M.J.: Direct measurement of mechanical properties of (Pb, La)TiO3 ferroelectric thin films using nanoindentation technique. J. Mater. Res. 16, 993 (2001).CrossRefGoogle Scholar
18Johnson, K.L.: Contact Mechanics (Cambridge Univ. Press, Cambridge, U.K., 1985), pp. 84, 106CrossRefGoogle Scholar
19Murakami, Y., Tanaka, K., Itokazu, M. and Shimamoto, A.: Elastic analysis of triangular pyramidal indentation by the finite-element method and its application to nano-indentation measurement of glasses. Philos. Mag. A 69, 1131 (1994).CrossRefGoogle Scholar
20Shimamoto, A., Tanaka, K., Akiyama, Y. and Yoshizaki, H.: Nanoindentation of glass with a tip-truncated Berkovich indenter. Philos. Mag. A 74, 1097 (1996).CrossRefGoogle Scholar
21Sawa, T. and Tanaka, K.: Simplified method for analyzing nanoindentation data and evaluating performance of nanoindentation instruments. J. Mater. Res. 16, 3084 (2001).CrossRefGoogle Scholar
22Xu, K.W., Hou, G.L., Hendrix, B.C., He, J.W., Sun, Y., Zheng, S., Bloyce, A. and Bell, T.: Prediction of nanoindentation hardness profile from a load-displacement curve. J. Mater. Res. 13, 3519 (1998).CrossRefGoogle Scholar
23Cheng, Y-T. and Cheng, C-M.: Further analysis of indentation loading curves: Effects of tip rounding on mechanical property measurements. J. Mater. Res. 13, 1059 (1998).CrossRefGoogle Scholar
24Malzbender, J., de With, G. and Toonder, J. den: The P-h2 relationship in indentation. J. Mater. Res. 15, 1209 (2000).Google Scholar
25Thurn, J. and Cook, R.F.: Simplified area function for sharp indenter tips in depth-sensing indentation. J. Mater. Res. 17, 1143 (2002).CrossRefGoogle Scholar
26Menčík, J. and Swain, M.V.: Errors associated with depth-sensing microindentation tests. J. Mater. Res. 10, 1491 (1995).CrossRefGoogle Scholar
27 M. Suganuma, H. Makino, and N. Kamiya: (unpublished work).Google Scholar