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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)]

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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.

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References

  1. J.M. Meza, F. Abbes, and M. Troyon: Penetration depth and tip radius dependence on the correction factor in nanoindentation measurements. J. Mater. Res. 23 (3), 725–731 (2008).

    Article  CAS  Google Scholar 

  2. F. Abbes, M. Troyon, J.M. Meza, and S. Potiron: 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).

    Article  Google Scholar 

  3. I.N. Sneddon: The relation between load and penetration in the axisymmetric boussinesq problem for a punch of arbitrary profile. Int. J. Eng. Sci. 3, 47–57 (1965).

    Article  Google Scholar 

  4. G.M. Pharr, W.C. Oliver, and F.R. Brotzen: On the generality of the relationship among contact stiffness, contact area, and elastic modulus during indentation. J. Mater. Res. 7, 613–617 (1992).

    Article  CAS  Google Scholar 

  5. W.C. Oliver and G.M. Pharr: Measurement of hardness and elastic modulus by instrumented indentation: Advances in understanding and refinements to methodology. J. Mater. Res. 19, 3–20 (2004).

    Article  CAS  Google Scholar 

  6. R.B. King: Elastic analysis of some punch problems for a layered medium. Int. J. Solids Struct. 23, 1657–1664 (1987).

    Article  Google Scholar 

  7. J.J. Vlassak and W.D. Nix: Measuring the elastic properties of anisotropic materials by means of indentation experiments. J. Mech. Phys. Solids 42, 1223–1245 (1994).

    Article  Google Scholar 

  8. J.C. Hay, A. Bolshakov, and G.M. Pharr: Critical examination of the fundamental relations used in the analysis of nanoindentation data. J. Mater. Res. 14, 2296–2305 (1999).

    Article  CAS  Google Scholar 

  9. J.L. Hay and P.J. Wolff: Small correction required when applying the Hertzian contact model to instrumented indentation data. J. Mater. Res. 16, 1280–1286 (2001).

    Article  CAS  Google Scholar 

  10. P.-L. Larsson, A.E. Giannakopoulos, E. Söderlund, D.J. Rowcliffe, and R. Vestergaard: Analysis of Berkovich indentation. Int. J. Solids Struct. 33, 221–248 (1996).

    Article  Google Scholar 

  11. K. Durst, M. Göken, and G.M. Pharr: Indentation size effect in spherical and conical indentation. J. Phys. D: Appl. Phys. 41, 074005 (2008).

    Article  Google Scholar 

  12. J.H. Strader, S. Shim, H. Bei, W.C. Oliver, and G.M. Pharr: An experimental evaluation of the constant β relating the contact stiffness to the contact area in nanoindentation. Philos. Mag. 86, 5285–5298 (2006).

    Article  CAS  Google Scholar 

  13. A. Bolshakov, W.C. Oliver, and G.M. Pharr: Explanation for the shape of nanoindentation unloading curves based on finite element simulation, in Thin Films: Stresses and Mechanical Properties V, edited by S.P. Baker, C.A. Ross, P.H. Townsend, C.A. Volkert, and P. Børgesen (Mater. Res. Soc. Symp. Proc. 356, Pittsburgh, PA, 1995) pp. 675–680.

    CAS  Google Scholar 

  14. T. Chudoba and N.M. Jennett: Higher accuracy analysis of instrumented indentation data obtained with pointed indenters. J. Phys. D: Appl. Phys. 41, 215407 (2008).

    Article  Google Scholar 

  15. Y.-T. Cheng and C.-M. Cheng: Scaling approach to conical indentation in elastic-plastic solids with work hardening. J. Appl. Phys. 84, 1284–1291 (1998).

    Article  CAS  Google Scholar 

  16. G.M. Pharr and A. Bolshakov: Understanding nanoindentation unloading curves. J. Mater. Res. 17, 2660–2671 (2002).

    Article  CAS  Google Scholar 

  17. J. Woirgard and J.-C. Dargenton: An alternative method for penetration depth determination in nanoindentation measurements. J. Mater. Res. 12, 2455–2458 (1997).

    Article  CAS  Google Scholar 

  18. B. Merle, V. Maier, M. Göken, and K. Durst: Experimental determination of the effective indenter shape and ε-factor for nanoindentation by continuously measuring the unloading stiffness. J. Mater. Res. 27 (1), 214–221 (2012), DOI: 10.1557/jmr.2011.245.

    Article  CAS  Google Scholar 

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ACKNOWLEDGMENTS

Svitlana Rosen’s support for the FE simulations is gratefully acknowledged.

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Authors and Affiliations

  1. Department of Materials Science and Engineering, University of Erlangen-Nürnberg, 91058, Erlangen, Germany

    Karsten Durst, Hamad ur Rehman & Benoit Merle

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  1. Karsten Durst
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  2. Hamad ur Rehman
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  3. Benoit Merle
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Correspondence to Karsten Durst.

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Durst, K., ur Rehman, H. & Merle, B. 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)]. Journal of Materials Research 27, 1205–1207 (2012). https://doi.org/10.1557/jmr.2012.41

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  • DOI: https://doi.org/10.1557/jmr.2012.41

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