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A precise correcting method for the study of the superhard material using nanoindentation tests

Published online by Cambridge University Press:  03 March 2011

Yan Ping Cao
Affiliation:
Laboratoire des Systèmes Mécaniques et d’ingénierie Simultanée, Université de Technologie de Troyes, 10010 Troyes, France; and Forschungszentrum Karlsruhe, Institut für Materialforschung II, D-76344 Eggenstein-Leopoldshafen, Germany
Ming Dao
Affiliation:
Department of Materials Science and Engineering, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139
Jian Lu*
Affiliation:
Department of Mechanical Engineering, Hong Kong Polytechnic University, Hung Hom, Kowloon, Hong Kong
*
a) Address all correspondence to this author. e-mail: mmmelu@inet.polyu.edu.hk
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Abstract

The accurate description of the indentation load–displacement relationship of an elastic sharp indenter indenting into an elastic half-space is critical for analyzing the nanoindentation data of superhard materials using the procedure proposed by Oliver and Pharr [J. Mater. Res.7, 1564 (1992)]. A further discussion on this issue is made in the present work to reconcile the apparent inconsistencies that have appeared between the experimental results reported by Lim and Chaudhri [Philos. Mag.83, 3427 (2003)] and the analysis performed by Fischer-Cripps [J. Mater. Res.18, 1043 (2003)]. It is found that the indenter size effect is responsible for this large discrepancy. Moreover, according to our analysis, we found that when the deformation of the indenter is significant, besides the errors caused by the Sneddon’s boundary condition as addressed by Hay et al. [J. Mater. Res.14, 2296 (1999)], the errors induced by the application of reduced modulus should be considered at the same time in correcting the modified Sneddon’s solution. In the present work, for the diamond indenter of 70.3° indenting into an elastic half-space with its Poisson’s ratio varying from 0.0 to 0.5 and the ratio of the Young’s modulus of the indented material to that of the diamond indenter, Ematerial/Eindenter, varying from 0 to 1, a set of new correction factors are proposed based on finite element analysis. The results reported here should provide insights into the analysis of the nanoindentation load–displacement data when using a diamond indenter to determine the hardness and Young’s modulus of superhard materials.

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Copyright
Copyright © Materials Research Society 2007

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References

REFERENCES

1Doerner, M.F. and Nix, W.D.: A method for interpreting the data from depth-sensing indentation instruments. J. Mater. Res. 1, 601 (1986).CrossRefGoogle Scholar
2Oliver, 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, 1564 (1992).CrossRefGoogle Scholar
3Tabor, D.: Hardness of Metals (Clarendon Press, Oxford, UK, 1951).Google Scholar
4Johnson, K.L.: Contact Mechanics (Cambridge University, Cambridge, UK, 1985) .CrossRefGoogle Scholar
5Field, 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
6Huber, N. and Tsakmakis, C.: Determination of constitutive properties from spherical indentation data using neural networks: Part I and II. J. Mech. Phys. Solids 47, 1569 (1999).CrossRefGoogle Scholar
7Giannakopoulos, A.E. and Suresh, S.: Determination of elastoplastic properties by instrumented sharp indentation. Scripta Mater. 40, 1191 (1999).CrossRefGoogle Scholar
8Dao, M., Chollacoop, N., Van Vliet, K.J., Venkatesh, T.A., and Suresh, S.: Computational modelling of the forward and reverse problems in instrumented sharp indentation. Acta Mater. 49, 3899 (2001).CrossRefGoogle Scholar
9Bucaille, J.L., Stauss, S., Felder, E., and Michler, J.: Determination of plastic properties of metals by instrumented indentation using different sharp indenters. Acta Mater. 51, 1663 (2003).CrossRefGoogle Scholar
10Chollacoop, N., Dao, M., and Suresh, S.: Depth-sensing instrumented indentation with dual sharp indenters. Acta Mater. 51, 3713 (2003).CrossRefGoogle Scholar
11Mata, M. and Alcalá, J.: Mechanical property evaluation through sharp indentations in elastoplastic and fully plastic contact regimes. J. Mater. Res. 18, 1705 (2003).CrossRefGoogle Scholar
12Mata, M. and Alcalá, J.: The role of friction on sharp indentation. J. Mech. Phys. Solids 52, 145 (2004).CrossRefGoogle Scholar
13Cao, Y.P. and Lu, J.: A new method to extract the plastic properties of metal materials from an instrumented spherical indentation loading curve. Acta Mater. 52, 4023 (2004).CrossRefGoogle Scholar
14Cao, Y.P. and Lu, J.: Size-dependent sharp indentation: I and II. J. Mech. Phys. Solids 53, 33 (2005).CrossRefGoogle Scholar
15Cao, Y.P., Qian, X.Q., Lu, J., and Yao, Z.H.: An energy-based method to extract plastic properties of metal materials from conical indentation tests. J. Mater. Res. 20, 1194 (2005).CrossRefGoogle Scholar
16Chudoba, T., Schwarzer, N., and Richter, F.: Determination of elastic properties of thin films by indentation measurements with a spherical indenter. Surf. Coat. Technol. 127, 9 (2000).CrossRefGoogle Scholar
17Saha, R. and Nix, W.D.: Effects of the substrate on the determination of thin film mechanical properties by nanoindentation. Acta Mater. 50, 23 (2002).CrossRefGoogle Scholar
18Giannakopoulos, A.E., Larsson, P.L., and Vestergaard, R.: Analysis of Vickers indentation. Int. J. Solids Struct. 31, 2679 (1994).CrossRefGoogle Scholar
19Larsson, P.L., Giannakopoulos, A.E., Soderlund, E., Rowcliffe, D.J., and Vestergaard, R.: Analysis of Berkovich indentation. Int. J. Solids Struct. 33, 221 (1996).CrossRefGoogle Scholar
20Hay, 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
21Chaudhri, M.M.: A note on a common mistake in the analysis of nanoindentation data. J. Mater. Res. 16, 336 (2001).CrossRefGoogle Scholar
22Fischer-Cripps, A.C.: Use of combined elastic modulus in depth-sensing indentation with a conical indenter. J. Mater. Res. 18, 1043 (2003).CrossRefGoogle Scholar
23Lim, Y.Y. and Chaudhri, M.M.: Experimental investigations of the normal loading of elastic spherical and conical indenters on elastic flats. Philos. Mag. 83, 3427 (2003).CrossRefGoogle Scholar
24Fischer-Cripps, A.C., Karvankova, P., and Veprek, S.: On the measurement of hardness of super-hard coatings. Surf. Coat. Technol. 200, 5645 (2006).CrossRefGoogle Scholar
25Sneddon, I.N.: The relation between load and penetration in the axisymmetric Boussinesq problem for a punch of arbitrary profile. Int. J. Eng. Sci. 3, 47 (1965).CrossRefGoogle Scholar
26Friedmann, T.A., Sullivan, J.P., Knapp, J.A., Tallant, D.R., Follstaedt, D.M., Medlin, D.L., and Mirkarimi, P.B.: Thick stress-free amorphous tetrahedral carbon films with hardness near that of diamond. Appl. Phys. Lett. 71, 3820 (1997).CrossRefGoogle Scholar
27Sjostrom, H., Stafstrom, S., Boman, M., and Sundgren, J.E.: Superhard and elastic carbon nitride thin film having fullerene like microstructure. Phys. Rev. Lett. 75, 1336 (1995).CrossRefGoogle Scholar
28Veprek, S., Nesladek, P., Niederhofer, A., Glatz, F., Jilek, M., and Sima, M.: Recent progress in the superhard nanocrystalline composites towards their industrialization understanding of the origin of the superhardness. Surf. Coat. Technol. 108–109, 138 (1998).CrossRefGoogle Scholar
29Veprek, S. and Argon, A.S.: Towards the understanding of the mechanical properties of super- and ultrahard nanocomposites. J. Vac. Sci. Technol., B 20, 650 (2002).CrossRefGoogle Scholar
30 ABAQUS Theory Manual Version 6.4 (Hibbitt, Karlsson and Sorensen Inc, Pawtucket, RI, 2004).Google Scholar
31Lim, Y.Y. and Chaudhri, M.M.: Indentation of elastic solids with rigid cones. Philos. Mag. 84, 2877 (2004).CrossRefGoogle Scholar
32Xu, Z.H. and Li, X.: Sample size effect on nanoindentation of micro-/nanostructures. Acta Mater. 54, 1699 (2006).CrossRefGoogle Scholar
33Fu, G.H. and Fischer-Cripps, A.C.: On Sneddon’s boundary conditions used in the analysis of nanoindentation data. J. Mater. Sci. 40, 1789 (2005).CrossRefGoogle Scholar
34Barenblatt, G.I.: Scaling, Self-Similarity, and Intermediate Asymptotics (Cambridge University Press, Cambridge, 1996).CrossRefGoogle Scholar
35Cheng, Y.T. and Cheng, C.M.: Scaling, dimensional analysis, and indentation measurements. Mater. Sci. Eng., R 44, 91 (2004).CrossRefGoogle Scholar
36Oliver, 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
37King, R.B.: Elastic analysis of some punch problems for a layered medium. Int. J. Solids Struct. 23, 1657 (1987).CrossRefGoogle Scholar
38Vlassak, 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