Hostname: page-component-848d4c4894-sjtt6 Total loading time: 0 Render date: 2024-06-28T13:16:24.313Z Has data issue: false hasContentIssue false
  • English
  • Français

Penetration depth and tip radius dependence on the correction factor in nanoindentation measurements

Published online by Cambridge University Press:  31 January 2011

J.M. Meza ,
F. Abbes  and
M. Troyon
J.M. Meza
Affiliation:
Grupo de Investigación en Nuevos Materiales, Universidad Pontificia Bolivariana, Medellín, Antioquia 333, Colombia
F. Abbes
Affiliation:
Laboratoire de Microscopies et d’Etude de Nanostructures, EA 3799, Université de Reims Champagne-Ardenne, 51685 Reims Cedex 2, France
M. Troyon*
Affiliation:
Laboratoire de Microscopies et d’Etude de Nanostructures, EA 3799, Université de Reims Champagne-Ardenne, 51685 Reims Cedex 2, France
*
a)Address all correspondence to this author. e-mail: michel.troyon@univ-reims.fr
Get access

Abstract

Dimensional analysis is used to show that the maximum penetration depth and the tip radius affect the β correction factor appearing in the Sneddon relationship between unloading contact stiffness, contact area, and elastic modulus. A simple analytical model based on elasticity theory is derived that predicts the variation of β with penetration depth. This model shows that β increases at low penetration depth and decreases with the tip radius. The β(h) curve given by the model is compared with that calculated by finite element analysis for an elastic material and also with that deduced from experimental measurements performed on fused quartz with two Berkovich indenters: a sharp one and a blunted one. It is also demonstrated that the correction factor can be expressed as two multiplicative contributions, a contribution related to the mechanical properties of the material and a contribution related to the indenter geometry. Implications of these findings on nanoindentation test are also discussed.

Keywords

Elastic properties
Type
Articles
Information
Journal of Materials Research , Volume 23 , Issue 3 , March 2008 , pp. 725 - 731
Copyright
Copyright © Materials Research Society 2008

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

1King, R.B.: Elastic analysis of some punch problems for a layered medium. Int. J. Solids Struct. 23, 1657 1987Google Scholar
2Hendrix, M.T.: The use of shape correction factors for elastic indentation measurements. J. Mater. Res. 10, 255 1995Google Scholar
3Woirgard, J.: Some results on the indentation of an elastic half space. Philos. Mag. 86, 5199 2006CrossRefGoogle Scholar
4Hay, J.C., Bolshakov, A., Pharr, G.M.: A critical examination of the fundamental relations used in the analysis of nanoindentation data. J. Mater. Res. 14, 2296 1999Google Scholar
5Cheng, Y-T., Cheng, C-M.: Scaling, dimensional analysis, and indentation measurements. Mater. Sci. Eng., R 44, 91 2004CrossRefGoogle Scholar
6Dao, M., Chollacoop, N., Van Vliet, K.J., Venkatesh, T.A., Suresh, S.: Computational modeling of the forward and reverse problems in instrumented sharp indentation. Acta Mater. 49, 3899 2001Google Scholar
7Oliver, W.C., Pharr, G.M.: Measurement of hardness and elastic modulus by instrumented indentation: Advances in understanding and refinements to methodology. J. Mater. Res. 19, 3 2004CrossRefGoogle Scholar
8Troyon, M., Huang, L.: About the correction factor for contact area in nanoindentation measurements. J. Mater. Res. 20, 610 2005CrossRefGoogle Scholar
9Troyon, M., Huang, L.: Comparison of different analysis methods in nanoindentation and influence on the correction factor for contact area. Surf. Coatings Technol. 201, 1613 2006CrossRefGoogle Scholar
10Troyon, M., Lafaye, S.: About the importance of introducing a correction factor in the Sneddon relationship for nanoindentation measurements. Philos. Mag. 86, 5299 2006CrossRefGoogle Scholar
11Cao, Y.P., Dao, M., Lu, J.: A precise correcting factor for the study of the superhard material using nanoindentation tests. J. Mater. Res. 22, 1255 2007CrossRefGoogle Scholar
12Cheng, Y-T., Cheng, C-M.: Further analysis of indentation loading curves: Effects of tip rounding on mechanical property measurements. J. Mater. Res. 13, 1059 1998CrossRefGoogle Scholar