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Correction factor for contact area in nanoindentation measurements

Published online by Cambridge University Press:  01 March 2005

Michel Troyon*
Affiliation:
Laboratoire de Microscopies et d'Etude de Nanostructures, EA 3799, Université de Reims, 51685 Reims Cedex 2, France
Liye Huang
Affiliation:
Laboratoire de Microscopies et d'Etude de Nanostructures, EA 3799, Université de Reims, 51685 Reims Cedex 2, France
*
a)Address all correspondence to this author. e-mail: michel.troyon@univ-reims.fr
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Abstract

In the relationship between unloading contact stiffness, elastic modulus, and contact area, which is the fundamental basic equation for nanoindentation analysis, a multiplicative correction factor is generally needed. Sometimes this correction factor is called γ to take into account the elastic radial inward displacements, and sometimes it is called β to correct for the fact that the indenter shape is not a perfect cone. In reality, these two effects simultaneously coexist and thus it is proposed that this correction factor is α = βγ. From nanoindentation data measured on three materials of different elastic moduli with a sharp Berkovich indenter and a worn one, the tip of which was blunt, it is demonstrated that the correction factor α does not have a constant value for a given material and indenter type but depends on the indenter tip rounding and also on the deformation of the indenter during indentation. It seems that α increases with the tip radius and also with the elastic modulus of the measured materials.

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Articles
Copyright
Copyright © Materials Research Society 2005

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References

REFERENCES

1.Oliver, 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, 564 (1992).Google Scholar
2.Martin, M. and Troyon, M.: Fundamental relations used in nanoindentation: Critical examination based on experimental measurements. J. Mater. Res. 17, 2227 (2002).Google Scholar
3.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
4.King, R.B.: Elastic analysis of some punch problems for a layered medium. Int. J. Solids Structures 23, 1657 (1987).CrossRefGoogle Scholar
5.Hay, J.C., Bolshakov, A. and Pharr, G.M.: A critical examination of the fundamental relations used in the analysis of nanoindentation data. J. Mater. Res. 14, 2296 (1999).CrossRefGoogle Scholar
6.Cheng, 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).Google Scholar
7.Troyon, M. and Martin, M.: A critical examination of the P-h2 relationship in nanoindentation. Appl. Phys. Lett. 83, 863 (2003).CrossRefGoogle Scholar
8.Gong, J., Miao, H. and Peng, Z.: On the contact area for nanoindentation tests with Berkovich indenter: Case study on soda-lime glass. Mater. Lett. 58, 1349 (2004).Google Scholar
9.Shih, C.W., Yang, M. and Li, J.C.M.: Effect of tip radius on nanoindentation. J. Mater. Res. 6, 2623 (1991).Google Scholar
10.Lim, Y.Y. and Chaudhri, M.M.: Experimental investigations of the normal loading of elastic spherical and conical indenters on to elastic flats. Philos. Mag. 83, 3427 (2003).Google Scholar
11.Chaudhri, M.M.: A note on a common mistake in the analysis of nanoindentation data. J. Mater. Res. 16, 336 (2001).CrossRefGoogle Scholar
12.Bolshakov, A. and Pharr, G.M.: Influences of pile-up on the measurement of mechanical properties by load and depth-sensing indentation techniques. J. Mater. Res. 13, 1049 (1998).CrossRefGoogle Scholar