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Implications of the idea of effective tip shape on nanoindentation unloading curves: AFM measurements and FE simulation

Published online by Cambridge University Press:  26 August 2011

Karim R. Gadelrab ,
Matteo Chiesa  and
Flavio A. Bonilla
Karim R. Gadelrab*
Affiliation:
Laboratory for Energy and Nano Science (LENS), Masdar Institute, Abu Dhabi 54224, United Arab Emirates
Matteo Chiesa
Affiliation:
Laboratory for Energy and Nano Science (LENS), Masdar Institute, Abu Dhabi 54224, United Arab Emirates
Flavio A. Bonilla
Affiliation:
Asylum Research, Santa Barbara, California 93117
*
a)Address all correspondence to this author. e-mail: kgadelrab@masdar.ac.ae
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Abstract

The analysis of nanoindentation force data are based on Sneddon’s solution for a linear elastic half space with a rigid axisymmetric indenter. Berkovich indenters commonly used in indentation experiments are normally modeled as cones. The idea of effective tip shape was presented to better explain the behavior of the unloading curve and pressure distribution under the tip in real experiments. We examine the concept of effective tip in three dimensions by importing real indenter metrology by atomic force microscope directly into finite element analysis and simulate fused silica indentation experiments. We show that fitting the elastic reloading curves overestimates the elastic modulus of fused silica. This is explained by studying the pressure distribution at maximum depth under the effective tip. While the effective tip describes the problem geometrically, it is believed that neglecting the deformed zone in the indented material is responsible for over estimating the modulus value.

Keywords

NanoindentationAmorphousSimulation
Type
Articles
Information
Journal of Materials Research , Volume 27 , Issue 1: Focus Issue: Instrumented Indentation , 14 January 2012 , pp. 126 - 131
Copyright
Copyright © Materials Research Society 2011

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References

REFERENCES

1.Pharr, G. and Bolshakov, A.: Understanding nanoindentation unloading curves. J. Mater. Res. 17, 2660 (2002).CrossRefGoogle Scholar
2.Oliver, W. and Pharr, G.: Improved technique for determining hardness and elastic modulus using load and displacement sensing indentation experiments. J. Mater. Res. 7, 1564 (1992).CrossRefGoogle Scholar
3.Oliver, W. and Pharr, G.: Measurement of hardness and elastic modulus by instrumented indentation: Advances in understanding and refinements to methodology. J. Mater. Res. 19, 3 (2004).CrossRefGoogle Scholar
4.Poon, B., Rittel, D., and Ravichandran, G.: An analysis of nanoindentation in linearly elastic solids. Int. J. Solids Struct. 45, 6018 (2008).CrossRefGoogle Scholar
5.Martin, M. and Troyon, M.: Fundamental relations used in nanoindentation: Critical examination based on experimental measurements. J. Mater. Res. 17, 2227 (2002).CrossRefGoogle Scholar
6.Troyon, M. and Martin, M.: A critical examination of the P–h relationship in nanoindentation. Appl. Phys. Lett. 83, 863 (2003).CrossRefGoogle Scholar
7.Troyon, M. and Huang, L.: Correction factor for contact area in nanoindentation measurements. J. Mater. Res. 20, 610 (2005).CrossRefGoogle Scholar
8.Sneddon, I.N.: Boussinesq’s problem for a rigid cone. Math. Proc. Cambridge Philos. Soc. 44, 492 (1948).CrossRefGoogle Scholar
9.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, 47 (1965).CrossRefGoogle Scholar
10.Bolshakov, A., Oliver, W.C., and Pharr, G.M.: An 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), p. 675.Google Scholar
11.Galin, L.A.: Contact Problems in the Theory of Elasticity. (Dept. of Mathematics, School of Physical Sciences and Applied Mathematics, North Carolina State College, NC, 1961).Google Scholar
12.Borodich, F.M. and Keer, L.M.: Contact problems and depth-sensing nanoindentation for frictionless and frictional boundary conditions. Int. J. Solids Struct. 41, 2479 (2004).CrossRefGoogle Scholar
13.Fu, G. and Cao, L.: On the effective indenter shape used in the analysis of nanoindentation unloading curves. J. Mater. Sci. 40, 9 (2005). pp. 2683–2684.CrossRefGoogle Scholar
14.Shim, S., Oliver, W.C., and Pharr, G.M.: A critical examination of the Berkovich vs. conical indentation based on 3D finite element calculation, in Fundamentals of Nanoindentation and Nanotribology III, edited by Wahl, K.J., Huber, N., Mann, A.B., Bahr, D.F., and Cheng, Y-T. (Mater. Res. Soc. Symp. Proc. 841, Warrendale, PA, 2005), p. 39.Google Scholar
15.Shim, S., Oliver, W.C., and Pharr, G.M.: A comparison of 3D finite element simulations for Berkovich and conical indentation of fused silica. Int. J. Surf. Sci. Eng. 1, 259 (2007).CrossRefGoogle Scholar
16.Gadelrab, K.R. and Chiesa, M.: Influence of nanoindenter tip radius on the estimation of the elastic modulus, in Deformation Mechanisms, Microstructure Evolution and Mechanical Properties of Nanoscale Materials, edited by Greer, J.R., Zhu, T., Clark, B.G., Gianola, D.S., and Ngan, A.H.W. (Mater. Res. Soc. Symp. Proc. 1297, Warrendale, PA, 2011), P03-47, p. 53.Google Scholar
17.Hermann, K., Hasche, K., Pohlenz, F., and Seeman, R.: Characterization of the geometry of indenters used for the micro- and nanoindentation method. Measurement 29, 201 (2001).CrossRefGoogle Scholar
18.Chudoba, T. and Jennett, N.: Higher accuracy analysis of instrumented indentation data obtained with pointed indenters. J. Phys. D Appl. Phys. 41, 215407 (2008).CrossRefGoogle Scholar
19.VanLandingham, M., Juliano, T., and Hagon, M.: Measuring tip shape for instrumented indentation using atomic force microscopy. Meas. Sci. Technol. 16, 2173 (2005).CrossRefGoogle Scholar
20.Gadelrab, K.R., Bonilla, F.A., and Chiesa, M.: Densification modeling of fused silica under nanoindentation. J. Mech Phys Solids (2011, under review).Google Scholar
21.Gadelrab, K.R., Bonilla, A., and Chiesa, M.: Numerically assisted nanoindentation analysis. J. Mater. Res. (2011, under review).Google Scholar
22.Jennett, N.M. and Meneve, J.: Depth-sensing indentation of thin hard films: A study of modulus measurement sensitivity to indentation parameters, in Fundamentals of Nanoindentation and Nanotribology, edited by Moody, N.R., Gerberich, W.W., Burnham, N., and Baker, S.P. (Mater. Res. Soc. Symp. Proc. 522, Warrendale, PA, 1998), p. 239.Google Scholar
23.Shuman, D.J., Costa, A.L.M., and Andrade, M.S.: Calculating the elastic modulus from nanoindentation and microindentation reload curves. Mater. Charact. 58, 380 (2007).CrossRefGoogle Scholar