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Critical issues in making small-depth mechanical property measurements by nanoindentation with continuous stiffness measurement

Published online by Cambridge University Press:  31 January 2011

G.M. Pharr ,
J.H. Strader  and
W.C. Oliver
G.M. Pharr*
Affiliation:
Department of Materials Science and Engineering, University of Tennessee, Knoxville, Tennessee 37996-2200; and Materials Science and Technology Division, Oak Ridge National Laboratory, Oak Ridge, Tennessee 37831
J.H. Strader
Affiliation:
Department of Materials Science and Engineering, University of Tennessee, Knoxville, Tennessee 37996-2200
W.C. Oliver
Affiliation:
Agilent Technologies, Nanotechnologies Measurement Division, Oak Ridge, Tennessee 37830
*
a) Address all correspondence to this author. e-mail: pharr@utk.eduThis 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/jmr_policy
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Abstract

Experiments were performed on a (100) copper single crystal to examine the influences that small displacement oscillations used in continuous stiffness measurement techniques have on hardness and elastic-modulus measurements in nanoindentation experiments. For the commonly used 2-nm oscillation, significant errors were observed in the measured properties, especially the hardness, at penetration depths as large as 100 nm. The errors originate from the large amount of dynamic unloading that occurs in materials like copper that have high contact stiffness resulting from their high modulus-to-hardness ratios. A simple model for the loading and unloading behavior of an elastic–plastic material is presented that quantitatively describes the errors and can be used to partially correct for them. By correcting the data in accordance with model and performing measurements at smaller displacement oscillation amplitudes, the errors can be reduced. The observations have important implications for the interpretation of the indentation size effect.

Keywords

CuHardnessNanoindentation
Type
Articles
Information
Journal of Materials Research , Volume 24 , Issue 3 , March 2009 , pp. 653 - 666
Copyright
Copyright © Materials Research Society 2009

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References

REFERENCES

1.Oliver, W.C. and Pharr, G.M.: An improved technique for determining hardness and elastic modulus by load and displacement sensing indentation experiments. J. Mater. Res. 7, 1564 (1992).CrossRefGoogle Scholar
2.Oliver, 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
3.Asif, S.A.S., Wahl, K.J., and Colton, R.J.: Nanoindentation and contact stiffness measurement using force modulation with a capacitive load-displacement transducer. Rev. Sci. Instrum. 70, 2408 (1999).CrossRefGoogle Scholar
4.Asif, S.A.S., Wahl, K.J., Colton, R.J., and Warren, O.L.: Quantitative imaging of nanoscale mechanical properties using hybrid nanoindentation and force modulation. J. Appl. Phys. 90, 1192 (2001).CrossRefGoogle Scholar
5.Field, J.S. and Swain, M.V.: A simple predictive model for spherical indentation. J. Mater. Res. 8, 297 (1993).CrossRefGoogle Scholar
6.Field, 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
7.Durst, K., Franke, O., Böhner, A., and Gökin, M.: Indentation size effect in Ni-Fe solid solutions. Acta Mater. 55, 6825 (2007).CrossRefGoogle Scholar
8.Nix, W.D. and Gao, H.: Indentation size effects in crystalline materials: A law for strain gradient plasticity. J. Mech. Phys. Solids 46, 411 (1998).CrossRefGoogle Scholar
9.Swadener, J.G., George, E.P., and Pharr, G.M.: The correlation of the indentation size effect measured with indenters of various shape. J. Mech. Phys. Solids 50, 681 (2002).CrossRefGoogle Scholar
10.Feng, G. and Nix, W.D.: Indentation size effect in MgO. Scr. Mater. 51, 599 (2004).CrossRefGoogle Scholar
11.Strader, J.H., Shim, S., Bei, H., Oliver, W.C., and Pharr, G.M.: An experimental evaluation of the constant b relating the contact stiffness to the contact area in nanoindentation. Philos. Mag. 86, 5285 (2006).CrossRefGoogle Scholar
12.Vlassak, J.J. and Nix, W.D.: Measuring the elastic properties of anisotropic materials by means of indentation experiments. J. Mech. Phys. Solids 42, 1223 (1994).CrossRefGoogle Scholar
13.Vlassak, J.J. and Nix, W.D.: Indentation modulus of elastically anisotropic half-spaces. Philos. Mag. A 67, 1045 (1993).CrossRefGoogle Scholar
14.Malzbender, J., de With, G., and den Toonder, J.: The P-h 2 relationship in indentation. J. Mater. Res. 15, 1209 (2000).CrossRefGoogle Scholar
15.Oliver, W.C.: Alternative technique for analyzing instrumented indentation data. J. Mater. Res. 16, 3202 (2001).CrossRefGoogle Scholar
16.Pharr, G.M. and Bolshakov, A.: Understanding nanoindentation unloading curves. J. Mater. Res. 17, 2660 (2002).CrossRefGoogle Scholar
17.Hainsworth, S.V., Chandler, H.W., and Page, T.F.: Analysis of nanoindentation load-displacement loading curves. J. Mater. Res. 11, 1987 (1996).CrossRefGoogle Scholar
18.Pharr, G.M., Oliver, W.C., and Brotzen, F.R.: On the generality of the relationship among contact stiffness, contact area, and elastic modulus during indentation. J. Mater. Res. 7, 613 (1992).CrossRefGoogle Scholar
19.Hay, J.C., Bolshakov, A., and Pharr, G.M.: A critical examination of the fundamental relations in the analysis of nanoindentation data. J. Mater. Res. 14, 2296 (1999).CrossRefGoogle Scholar
20.Thurn, J. and Cook, R.F.: Indentation-induced deformation at ultramicroscopic and macroscopic contacts. J. Mater. Res. 19, 124 (2004).CrossRefGoogle Scholar
21.Bei, H., George, E.P., Hay, J.L., and Pharr, G.M.: Influence of indenter tip geometry on elastic deformation during nanoindentation. Phys. Rev. Lett. 95, 045501 (2005).CrossRefGoogle ScholarPubMed