Hostname: page-component-78c5997874-4rdpn Total loading time: 0 Render date: 2024-11-17T16:45:23.483Z Has data issue: false hasContentIssue false

Comment to paper “Penetration depth and tip radius dependence on the correction factor in nanoindentation measurements” by J.M. Meza et al. [J. Mater. Res. 23(3), 725 (2008)]

Published online by Cambridge University Press:  20 March 2012

Karsten Durst*
Affiliation:
Department of Materials Science and Engineering, University of Erlangen-Nürnberg, 91058 Erlangen, Germany
Hamad ur Rehman
Affiliation:
Department of Materials Science and Engineering, University of Erlangen-Nürnberg, 91058 Erlangen, Germany
Benoit Merle
Affiliation:
Department of Materials Science and Engineering, University of Erlangen-Nürnberg, 91058 Erlangen, Germany
*
a)Address all correspondence to this author. e-mail: karsten.durst@ww.uni-erlangen.de
Get access

Abstract

[Meza et al. J. Mater. Res.23(3), 725 (2008)] recently claimed that the correction factor beta for the Sneddon equation, used for the evaluation of nanoindentation load-displacement data, is strongly depth- and tip-shape-dependent. Meza et al. used finite element (FE) analysis to simulate the contact between conical or spheroconical indenters, and an elastic material. They calculated the beta factor by comparing the simulated contact stiffness with Sneddon’s prediction for conical indenters. Their analysis is misleading, and it is shown here that by applying the general Sneddon equation, taking into account the true contact area, an almost constant and depth-independent beta factor is obtained for conical, spherical and spheroconical indenter geometries.

Type
Comments and Reply
Copyright
Copyright © Materials Research Society 2012

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

1.Meza, J.M., Abbes, F., and Troyon, M.: Penetration depth and tip radius dependence on the correction factor in nanoindentation measurements. J. Mater. Res. 23(3), 725731 (2008).Google Scholar
2.Abbes, F., Troyon, M., Meza, J.M., and Potiron, S.: Finite element analysis of the penetration depth/tip radius ratio dependence on the correction factor β in instrumented indentation of elastic-plastic materials. J. Micromech. Microeng. 20, 65003 (2010).CrossRefGoogle Scholar
3.Sneddon, I.N.: The relation between load and penetration in the axisymmetric boussinesq problem for a punch of arbitrary profile. Int. J. Eng. Sci. 3, 4757 (1965).Google Scholar
4.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, 613617 (1992).Google Scholar
5.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, 320 (2004).Google Scholar
6.King, R.B.: Elastic analysis of some punch problems for a layered medium. Int. J. Solids Struct. 23, 16571664 (1987).CrossRefGoogle Scholar
7.Vlassak, J.J. and Nix, W.D.: Measuring the elastic properties of anisotropic materials by means of indentation experiments. J. Mech. Phys. Solids 42, 12231245 (1994).Google Scholar
8.Hay, J.C., Bolshakov, A., and Pharr, G.M.: Critical examination of the fundamental relations used in the analysis of nanoindentation data. J. Mater. Res. 14, 22962305 (1999).CrossRefGoogle Scholar
9.Hay, J.L. and Wolff, P.J.: Small correction required when applying the Hertzian contact model to instrumented indentation data. J. Mater. Res. 16, 12801286 (2001).CrossRefGoogle Scholar
10.Larsson, P.-L., Giannakopoulos, A.E., Söderlund, E., Rowcliffe, D.J., and Vestergaard, R.: Analysis of Berkovich indentation. Int. J. Solids Struct. 33, 221248 (1996).CrossRefGoogle Scholar
11.Durst, K., Göken, M., and Pharr, G.M.: Indentation size effect in spherical and conical indentation. J. Phys. D: Appl. Phys. 41, 074005 (2008).Google Scholar
12.Strader, J.H., Shim, S., Bei, H., Oliver, W.C., and Pharr, G.M.: An experimental evaluation of the constant β relating the contact stiffness to the contact area in nanoindentation. Philos. Mag. 86, 52855298 (2006).Google Scholar
13.Bolshakov, A., Oliver, W.C., and Pharr, G.M.: Explanation for the shape of nanoindentation unloading curves based on finite element simulation, in Thin Films: Stresses and Mechanical Properties V, edited by Baker, S.P., Ross, C.A., Townsend, P.H., Volkert, C.A., and Børgesen, P. (Mater. Res. Soc. Symp. Proc. 356, Pittsburgh, PA, 1995) pp. 675680.Google Scholar
14.Chudoba, T. and Jennett, N.M.: Higher accuracy analysis of instrumented indentation data obtained with pointed indenters. J. Phys. D: Appl. Phys. 41, 215407 (2008).Google Scholar
15.Cheng, Y.-T. and Cheng, C.-M.: Scaling approach to conical indentation in elastic-plastic solids with work hardening. J. Appl. Phys. 84, 12841291 (1998).Google Scholar
16.Pharr, G.M. and Bolshakov, A.: Understanding nanoindentation unloading curves. J. Mater. Res. 17, 26602671 (2002).CrossRefGoogle Scholar
17.Woirgard, J. and Dargenton, J.-C.: An alternative method for penetration depth determination in nanoindentation measurements. J. Mater. Res. 12, 24552458 (1997).CrossRefGoogle Scholar
18.Merle, B., Maier, V., Göken, M., and Durst, K.: Experimental determination of the effective indenter shape and ε-factor for nanoindentation by continuously measuring the unloading stiffness. J. Mater. Res. 27(1), 214221 (2012), DOI: 10.1557/jmr.2011.245.Google Scholar