Skip to main content Accessibility help

Effects of mechanical properties on the contact profile in Berkovich nanoindentation of elastoplastic materials

  • Jiangting Wang (a1), Peter D. Hodgson (a1) and Chunhui Yang (a2)


Pile-up or sink-in is always a concern in a nanoindentation test because it gives rise to errors in the estimation of the projected contact area when it is theoretically analyzed with the classic Oliver–Pharr method. In this study, a three-dimensional finite element model is developed to simulate nanoindentation with a perfect Berkovich tip. The variation of the contact profile with respect to the work-hardening rate n and the ratio of yield stress to elastic modulus σy/E has been studied for a wide range of elastoplastic materials. The numerical results show that a low σy/E not only facilitates the pile-up for materials with little or no work-hardening but also enhances the sink-in for materials with a high work-hardening rate. It is attributed to the lateral-flow dominated plastic deformation in low work-hardening materials and the normal-flow dominated plastic deformation in high work-hardening materials, respectively. Because of the large sink-in, for the materials with high n and low σy/E, significant errors in the calculation of the projected contact area can be generated by using the classic Oliver–Pharr method.


Corresponding author

a)Address all correspondence to this author. e-mail:


Hide All
1.Doerner, M. and Nix, W.: A method for interpreting the data from depth-sensing indentation instruments. J. Mater. Res. 1, 601 (1986).
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).
3.Pharr, G.: Measurement of mechanical properties by ultra-low-load indentation. Mater. Sci. Eng., A 253, 151 (1998).
4.Bhushan, B. and Li, X.: Nanomechanical characterisation of solid surfaces and thin films. Int. Mater. Rev. 48, 125 (2003).
5.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).
6.Cheng, Y-T. and Cheng, C-M.: Scaling, dimensional analysis, and indentation measurements. Mater. Sci. Eng., R 44, 91 (2004).
7.Gouldstone, A., Chollacoop, N., Dao, M., Li, J., Minor, A., and Shen, Y.: Indentation across size scales and disciplines: Recent developments in experimentation and modeling. Acta Mater. 55, 4015 (2007).
8.Tabor, D.: The Hardness of Metals (Clarendon Press, Oxford, 1951).
9.Lim, Y.Y. and Chaudhri, M.M.: The effect of the indenter load on the nanohardness of ductile metals: An experimental study on polycrystalline work-hardened and annealed oxygen-free copper. Philos. Mag. A 79, 2979 (1999).
10.Bec, S., Tonck, A., Georges, J., Georges, E., and Loubet, J.: Improvements in the indentation method with a surface force apparatus. Philos. Mag. A 74, 1061 (1996).
11.Mata, M. and Alcala, J.: Mechanical property evaluation through sharp indentations in elastoplastic and fully plastic contact regimes. J. Mater. Res. 18, 1705 (2003).
12.Giannakopoulos, A.E., Larsson, P.L., and Vestergaard, R.: Analysis of Vickers indentation. Int. J. Solids Struct. 31, 2679 (1994).
13.Larsson, P.L., Giannakopoulos, A.E., SÖderlund, E., Rowcliffe, D.J., and Vestergaard, R.: Analysis of Berkovich indentation. Int. J. Solids Struct. 33, 221 (1996).
14.McElhaney, K., Vlassak, J., and Nix, W.: Determination of indenter tip geometry and indentation contact area for depth-sensing indentation experiments. J. Mater. Res. 13, 1300 (1998).
15.Bolshakov, A. and Pharr, G.: Influences of pileup on the measurement of mechanical properties by load and depth-sensing indentation techniques. J. Mater. Res. 13, 1049 (1998).
16.Chen, X. and Vlassak, J.: Numerical study on the measurement of thin film mechanical properties by means of nanoindentation. J. Mater. Res. 16, 2974 (2001).
17.Dao, M., Chollacoop, N., Van Vliet, K.J., Venkatesh, T.A., and Suresh, S.: Computational modeling of the forward and reverse problems in instrumented sharp indentation. Acta Mater. 49, 3899 (2001).
18.Taljat, B. and Pharr, G.M.: Development of pile-up during spherical indentation of elastic-plastic solids. Int. J. Solids Struct. 41, 3891 (2004).
19.Randall, N.: Direct measurement of residual contact area and volume during the nanoindentation of coated materials as an alternative method of calculating hardness. Philos. Mag. A 82, 1883 (2002).
20.Swaddiwudhipong, S., Hua, J., Tho, K., and Liu, Z.: Equivalency of Berkovich and conical load-indentation curves. Model. Simul. Mater. Sci. Eng. 14, 71 (2006).
21.Dieter, G.: Mechanical Metallurgy (McGraw-Hill, New York, 1986).
22.Cheng, Y. and Cheng, C.: Relationships between hardness, elastic modulus, and the work of indentation. Appl. Phys. Lett. 73, 614 (1998).
23.Tsui, T. and Pharr, G.: Substrate effects on nanoindentation mechanical property measurement of soft films on hard substrates. J. Mater. Res. 14, 292 (1999).
24.Cheng, Y-T.S. and Cheng, C-M.: Effects of ‘sinking in’ and ‘piling up’ on estimating the contact area under load in indentation. Philos. Mag. Lett. 78, 115 (1998).



Full text views

Total number of HTML views: 0
Total number of PDF views: 0 *
Loading metrics...

Abstract views

Total abstract views: 0 *
Loading metrics...

* Views captured on Cambridge Core between <date>. This data will be updated every 24 hours.

Usage data cannot currently be displayed