Hostname: page-component-8448b6f56d-wq2xx Total loading time: 0 Render date: 2024-04-18T19:22:25.868Z Has data issue: false hasContentIssue false
  • English
  • Français

On the determination of spherical nanoindentation stress–strain curves

Published online by Cambridge University Press:  03 March 2011

Sandip Basu ,
Alexander Moseson  and
Michel W. Barsoum
Sandip Basu
Affiliation:
Department of Materials Science and Engineering, Drexel University, Philadelphia, Pennsylvania 19104
Alexander Moseson
Affiliation:
Department of Materials Science and Engineering, Drexel University, Philadelphia, Pennsylvania 19104
Michel W. Barsoum*
Affiliation:
Department of Materials Science and Engineering, Drexel University, Philadelphia, Pennsylvania 19104
*
a) Address all correspondence to this author.e-mail: barsoumw@drexel.edu
Get access

Abstract

Instrumented nanoindentation experiments, especially with sharp tips, are a well-established technique to measure the hardness and moduli values of a wide range of materials. However, and despite the fact that they can accurately delineate the onset of the elasto-plastic transition of solids, spherical nanoindentation experiments are less common. In this article we propose a technique in which we combine (i) the results of continuous stiffness measurements with spherical indenters – with radii of 1 μm and/or 13.5 μm, (ii) Hertzian theory, and (iii) Berkovich nanoindentations, to convert load/depth of indentation curves to their corresponding indentation stress–strain curves. We applied the technique to fused silica, aluminum, iron and single crystals of sapphire and ZnO. In all cases, the resulting indentation stress–strain curves obtained clearly showed the details of the elastic-to-plastic transition (i.e., the onset of yield, and, as important, the steady state hardness values that were comparable with the Vickers microhardness values obtained on the same surfaces). Furthermore, when both the 1 μm and 13.5 μm indenters were used on the same material, for the most part, the indentation stress–strain curves traced one trajectory. The method is versatile and can be used over a large range of moduli and hardness values.

Keywords

HardnessNanoscaleStress/strain relationship
Type
Articles
Information
Journal of Materials Research , Volume 21 , Issue 10 , October 2006 , pp. 2628 - 2637
Copyright
Copyright © Materials Research Society 2006

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.Oliver, W.C., 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).Google Scholar
2.Tabor, D.: Hardness of Metals (Clarendon Press, Oxford, 1951).Google Scholar
3.Li, X., Bhusan, B.: A review of nanoindentation continuous stiffness measurement technique and its applications. Mater. Charact. 48, 11 (2002).Google Scholar
4.Field, J.S., Swain, M.V.: The indentation characterisation of the mechanical properties of various carbon materials: Glassy carbon, coke and pyrolytic graphite. Carbon 34, 1357 (1996).Google Scholar
5.Field, J.S., Swain, M.V.: Determining the mechanical properties of small volumes of material from submicrometer spherical indentations. J. Mater. Res. 10, 101 (1995).Google Scholar
6.Bradby, J.E., Williams, J.S., Swain, M.V.: Pop-in events induced by spherical indentation in compound semiconductors. J. Mater. Res. 19, 380 (2004).Google Scholar
7.Herbert, E.G., Pharr, G.M., Oliver, W.C., Lucas, B.N., Hay, J.L.: On the measurement of stress-strain curves by spherical indentation. Thin Solid Films 398–399, 331 (2001).Google Scholar
8.Iwashita, N., Swain, M.V., Field, J.S., Ohta, N., Bitoh, S.: Elasto-plastic deformation of glass-like carbons heat-treated at different temperatures. Carbon 39, 1525 (2001).Google Scholar
9.Iwashita, N., Field, J.S., Swain, M.V.: Indentation hysteresis of glassy carbon materials. Philos. Mag. A 82, 1873 (2002).Google Scholar
10.Field, J.S., Swain, M.V.: A simple predictive model for spherical indentation. J. Mater. Res. 8, 297 (1993).Google Scholar
11.Bradby, J.E., Kucheyev, S.O., Williams, J.S., Jagadish, C., Swain, M.V., Munroe, P., Phillips, M.R.: Contact-induced defect propagation in ZnO. Appl. Phys. Lett. 80, 4537 (2002).Google Scholar
12.Kucheyev, S.O., Bradby, J.E., Williams, J.S., Jagadish, C., Swain, M.V.: Mechanical deformation of single-crystal ZnO. Appl. Phys. Lett. 80, 956 (2002).Google Scholar
13.Murugaiah, A., Barsoum, M.W., Kalidindi, S.R., Zhen, T.: Spherical Nanoindentations in Ti3SiC2. J. Mater. Res. 19, 1139 (2004).Google Scholar
14.Barsoum, M.W., Murugaiah, A., Kalidindi, S.R., Zhen, T.: Kinking nonlinear elastic solids, nanoindentations and geology. Phys. Rev. Lett. 92, 255508-1 (2004).Google Scholar
15.Barsoum, M.W., Murugaiah, A., Kalidindi, S.R., Gogotsi, Y.: Kink bands, nonlinear elasticity and nanoindentations in graphite. Carbon 42, 1435 (2004).Google Scholar
16.Sneddon, I.N.: The relaxation between load and penetration in the axisymmetric boussinesq problem for a punch of arbitrary profile. Int. J. Eng. Sci. 3, 47 (1965).Google Scholar
17.Lucas, B.N., Oliver, W.C.: Indentation power-law creep of high-purity indium. Metall. Mater. Trans. A 30, 601 (1999).Google Scholar
18.Basu, S., Barsoum, M.W., Kalidindi, S.R.: Sapphire: A kinking nonlinear elastic solid. J. Appl. Phys. 99, 063501 (2006).Google Scholar
19.Ozgur, U., Alivov, Y.I., Liu, C., Teke, A., Reshchikov, M.A., Dogan, S., Aurutin, V., Cho, S.J., Morkoc, H.: A comprehensive review of ZnO materials and devices. J. Appl. Phys. 98, 041301 (2005).Google Scholar
20.Wachtman, J.B.J., Tefft, W.E., Lam, D.C.J., Stenchfield, R.P.: Elastic constants of synthetic single crystal corundum at room temperature. J. Res. Natl. Bur. Stand. 64A, 213 (1960).Google Scholar