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An expanding cavity model incorporating pile-up and sink-in effects

Published online by Cambridge University Press:  01 December 2011

Xavier Hernot  and
Olivier Bartier
Xavier Hernot*
Affiliation:
L.A.R.M.A.U.R-Indentation, E.A. 42.82, Université de Rennes 1, 35402 Rennes Cedex, France
Olivier Bartier
Affiliation:
L.A.R.M.A.U.R-Indentation, E.A. 42.82, Université de Rennes 1, 35402 Rennes Cedex, France
*
a)Address all correspondence to this author. e-mail: Xavier.Hernot@univ-rennes1.fr
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Abstract

A new expanding cavity model (ECM) for describing conical indentation of elastic-ideally plastic material is developed. For the proposed ECM, it is assumed that the volume of material displaced by the indenter is equal to the volume loss, due to elastic deformation, in the material and depends on the pile-up or sink-in. It was shown that the proposed ECM matches very well numerical data in the final portion of the transition regime for which the contact pressure lies between approximately 2.5Y and 3Y. For material of large E/Y ratio, the new ECM also provides results which are very close to the numerical data in the plastic-similarity regime (regime in which Cf = 3). For material of smaller E/Y ratio, the proposed ECM gives better results than the Johnson’s ECM because pile-up or sink-in is taken into account.

Keywords

NanoindentationSimulationHardness

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Type
Articles
Information
Journal of Materials Research , Volume 27 , Issue 1: Focus Issue: Instrumented Indentation , 14 January 2012 , pp. 132 - 140
Copyright
Copyright © Materials Research Society 2011

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References

REFERENCES

1.Love, A.E.H.: Boussinesq’s problem for a rigid cone. Q. J. Math. 10, 161 (1939).Google Scholar
2.Johnson, K.L.: Contact Mechanics (Cambridge University Press, Cambridge, England, 1985), pp. 171.Google Scholar
3.Tabor, D.: The Hardness of Metals (Clarendon Press, Oxford, England, 1951), pp. 101.Google Scholar
4.Mata, M. and Alcala, J.: Mechanical property evaluation through sharp indentations in elastoplastic and fully plastic contact regimes. J. Mater. Res. 18, 1705 (2003).CrossRefGoogle Scholar
5.Marsh, D.M.: Plastic flow in glass. Proc. R. Soc. London, Ser. A 279, 420 (1964).Google Scholar
6.Gao, X-L.: New expanding cavity model for indentation hardness including strain-hardening and indentation size effects. J. Mater. Res. 21, 1317 (2006).Google Scholar
7.Mata, M., Casals, O., and Alcala, J.: The plastic zone size in indentation experiments: The analogy with the expansion of a spherical cavity. Int. J. Solids Struct. 43, 5994 (2006).Google Scholar
8.Johnson, K.L.: The correlation of indentation experiments. J. Mech. Phys. Solids 18, 115 (1970).Google Scholar
9.Hill, R.: The Mathematical Theory of Plasticity (Oxford University Press, London, England, 1950).Google Scholar
10.Studman, C.J., Moore, M.A., and Jones, S.E.: On the correlation of indentation experiments. J. Phys. D: Appl. Phys. 10, 949 (1977).CrossRefGoogle Scholar
11.Chiang, S.S., Marshall, D.B., and Evans, A.G.: The response of solids to elastic/plastic indentation. I. Stresses and residual stresses. J. Appl. Phys. 53, 298 (1982).Google Scholar
12.Feng, G., Qu, S., Huang, Y., and Nix, W.D.: An analytical expression for the stress field around an elastoplastic indentation/contact. Acta Mater. 55, 2929 (2007).Google Scholar
13.Yoffe, E.H.: Elastic stress fields caused by indenting brittle materials. Philos. Mag. A 46, 617 (1982).CrossRefGoogle Scholar
14.Fischer-Cripps, A.C.: Elastic–plastic behaviour in materials loaded with a spherical indenter. J. Mater. Sci. 32, 727 (1997).Google Scholar
15.Kramer, D., Huang, H., Kriese, M., Robach, J., Nelson, J., Wright, A., Bahr, D., and Gerberich, W.W.: Yield strength predictions from the plastic zone around nanocontacts. Acta Mater. 47, 333 (1999).Google Scholar
16.Hernot, X. and Pichot, F.: Influence du coefficient de Poisson sur les régimes d’indentation sphérique. Mat. Tech. 96, 31 (2009).Google Scholar
17.Bartier, O. and Hernot, X.: Etude des régimes de déformation de matériaux élastiques parfaitement plastiques au cours de l’indentation parabolique et sphérique. Mat. Tech. 96, 20 (2009).Google Scholar
18.Alcala, J., Barone, A.C., and Anglada, M.: The influence of plastic hardening on surface deformation modes around Vickers and spherical indents. Acta Mater. 48, 3451 (2000).Google Scholar
19.Felder, E.: Analytical correlation of indentation experiments. Philos. Mag. 86, 5239 (2006).CrossRefGoogle Scholar
20.Malherbe, S., Benayoun, S., Morel, S., and Iost, A.: Caractérisation mécanique de matériaux élastoplastiques—utilisation d’indenteurs axisymétriques. Mater. Tech. 93, 213 (2005).CrossRefGoogle Scholar
21.Pelletier, H.: Étude de la formation du bourrelet autour des empreintes de nanoindentation. Mater. Tech. 93, 229 (2005).Google Scholar
22.Zielinski, W., Huang, H., and Gerberich, W.W.: Microscopy and microindentation mechanics of single crystal Fe-3 wt. % Si: Part II. TEM of the indentation plastic zone. J. Mater. Res. 8, 1300 (1993).Google Scholar
23.Mata, M. and Alcala, J.: The role of friction on sharp indentation. J. Mech. Phys. Solids 52, 145 (2004).Google Scholar
24.Gao, X-L.: An expanding cavity model incorporating strain-hardening and indentation size effects. Int. J. Solids Struct. 43, 6615 (2006).Google Scholar