Skip to main content Accessibility help
×
Home

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

  • G.M. Pharr (a1), J.H. Strader (a2) and W.C. Oliver (a3)

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.

Copyright

Corresponding author

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

References

Hide All
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).
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).
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).
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).
5.Field, J.S. and Swain, M.V.: A simple predictive model for spherical indentation. J. Mater. Res. 8, 297 (1993).
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).
7.Durst, K., Franke, O., Böhner, A., and Gökin, M.: Indentation size effect in Ni-Fe solid solutions. Acta Mater. 55, 6825 (2007).
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).
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).
10.Feng, G. and Nix, W.D.: Indentation size effect in MgO. Scr. Mater. 51, 599 (2004).
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).
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).
13.Vlassak, J.J. and Nix, W.D.: Indentation modulus of elastically anisotropic half-spaces. Philos. Mag. A 67, 1045 (1993).
14.Malzbender, J., de With, G., and den Toonder, J.: The P-h 2 relationship in indentation. J. Mater. Res. 15, 1209 (2000).
15.Oliver, W.C.: Alternative technique for analyzing instrumented indentation data. J. Mater. Res. 16, 3202 (2001).
16.Pharr, G.M. and Bolshakov, A.: Understanding nanoindentation unloading curves. J. Mater. Res. 17, 2660 (2002).
17.Hainsworth, S.V., Chandler, H.W., and Page, T.F.: Analysis of nanoindentation load-displacement loading curves. J. Mater. Res. 11, 1987 (1996).
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).
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).
20.Thurn, J. and Cook, R.F.: Indentation-induced deformation at ultramicroscopic and macroscopic contacts. J. Mater. Res. 19, 124 (2004).
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).

Keywords

Metrics

Full text views

Total number of HTML views: 0
Total number of PDF views: 0 *
Loading metrics...

Abstract views

Total abstract views: 0 *
Loading metrics...

* Views captured on Cambridge Core between <date>. This data will be updated every 24 hours.

Usage data cannot currently be displayed