Hostname: page-component-7b7567c8c-2n9c9 Total loading time: 0 Render date: 2026-11-14T03:26:28.715Z Has data issue: false hasContentIssue false
  • English
  • Français

New relationship between Young's modulus and nonideally sharp indentation parameters

Published online by Cambridge University Press:  03 March 2011

Dejun Ma,
Chung Wo Ong and
Sing Fai Wong
Dejun Ma
Affiliation:
Surface Engineering Research Institute, Chinese Mechanical Engineering Society, Beijing 100072, People’s Republic of China
Chung Wo Ong*
Affiliation:
Department of Applied Physics and Materials Research Center, The Hong Kong Polytechnic University, Hung Hom, Kowloon, Hong Kong, People’s Republic of China
Sing Fai Wong
Affiliation:
Department of Applied Physics and Materials Research Center, The Hong Kong Polytechnic University, Hung Hom, Kowloon, Hong Kong, People’s Republic of China
*
a) Address all correspondence to this author. e-mail: apacwong@inet.polyu.edu.hk
Get access

Abstract

Both analysis and numerical calculations have been carried out to investigate the relationship between Young’s modulus and nonideally sharp indentation parameters. The results confirm that there exists an approximate one-to-one correspondence between the ratio of nominal hardness/reduced Young’s modulus (Hn/Er) and the ratio of elastic work/total work (We/W) for any definite bluntness ratio (Δh/hm) of a nonideally sharp indenter. Based on this relationship, the Young’s modulus of the indented material can be determined just from the values of Hn, We, and W, which are directly measurable quantities in an indentation test.

Keywords

Elastic propertiesIndentationHardness

Information

Type
Articles
Information
Journal of Materials Research , Volume 19 , Issue 7 , July 2004, pp. 2144 - 2151
Copyright
Copyright © Materials Research Society 2004

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.)

Article purchase

Temporarily unavailable

References

REFERENCES

1.Pethica, J.B., Hutchings, R. and Oliver, W.C.: Hardness measurement at penetration depth as small as 20nm. Philos. Mag. A 48, 593 (1983).CrossRefGoogle Scholar
2.Loubet, J.L., Georges, J.M., Marchesini, O. and Meille, G.: Vickers indentation curves of magnesium oxide (MgO). J. Tribology 106, 43 (1984).CrossRefGoogle Scholar
3.Newey, D., Wilkens, M.A. and Pollock, H.M.: An ultra-low-load penetration hardness tester. J. Phys. E. Sci. Instrum. 15, 119 (1982).CrossRefGoogle Scholar
4.Oliver, W.C. and Pharr, G.M.: An improved technique for determining hardness and elastic modulus using load and displacement sensing indentation experiments. J. Mater. Res. 7, 1564 (1992).CrossRefGoogle Scholar
5.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, 613 (1992).CrossRefGoogle Scholar
6.Cheng, Y-T., Li, Z. and Cheng, C-M. Scaling approach to modeling indentation measurements, in Fundamentals of Nanoindentation and Nanotribology II, edited by Baker, S.P., Cook, R.F., Corcoran, S.G., and Moody, N.R. (Mater. Res. Soc. Symp. Proc. 649, Warrendale, PA, 2001), p. Q1.1.Google Scholar
7.Cheng, Y-T. and Cheng, C-M.: Relationships between hardness, elastic modulus, and the work of indentation. Appl. Phys. Lett. 73, 614 (1998).CrossRefGoogle Scholar
8.Giannakopoulos, A.E. and Suresh, S.: Determination of elastoplastic properties by instrumented sharp indentation. Scripta Mater. 40, 1191 (1999).CrossRefGoogle Scholar
9.Venkatesh, T.A., Van Vliet, K.J., Giannakopoulos, A.E. and Suresh, S.: Determination of elasto-plastic properties by instrumented sharp indentation: guidelines for property extraction. Scripta Mater. 42, 833 (2000).CrossRefGoogle Scholar
10.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).CrossRefGoogle Scholar
11.Ni, W.Y., Cheng, Y.T., Cheng, C.M. and Grummon, D.S.: An energy-based method for analyzing instrumented spherical indentation experiments. J. Mater. Res. 19, 149 (2004).CrossRefGoogle Scholar
12.Cheng, Y-T. and Cheng, C-M.: Further analysis of indentation loading curves: effect of tip rounding on mechanical property measurements. J. Mater. Res. 13, 1059 (1998).CrossRefGoogle Scholar
13.Yu, W. and Blanchard, J.P.: An elastic-plastic indentation model and its solutions. J. Mater. Res. 11, 2358 (1996).CrossRefGoogle Scholar
14.Timoshenko, S. and Goodier, J.N.: Theory of Elasticity (McGraw Hill, New York, 1951).Google Scholar
15.Loubet, J.L., Bauer, M., Tonck, A., Bec, S. and Gauthier-Manuel, B. Nanoindentation with a surface force apparatus, in Mechanical Properties and Deformation Behaviour of Materials Having Ultra-Fine Microstructures, edited by Nastasi, M.A., Parkin, D.M., and Gleiter, H. (Kluwer Academic Publishers, Dordrecht, The Netherlands, 1993).Google Scholar
16.Tabor, D., The Hardness of Metals (Claredon Press, Oxford, U.K., 1951).Google Scholar
17.Alcala, J., Giannakopoulos, A.E. and Suresh, S.: Continuous measurements of load-penetration curves with spherical microindenters and the estimation of mechanical properties. J. Mater. Res. 13, 1390 (1998).CrossRefGoogle Scholar
18.ABAQUS Version 6.2 (Hibbitt, Karlsson & Sorensen, Inc., Pawtucket, RI, 2001).Google Scholar
19.Bucaille, J.L., Stauss, S., Felder, E. and Michler, J.: Determination of plastic properties of metals by instrumented indentation using different sharp indenters. Acta Mater. 51, 1663 (2003).Google Scholar
20.Mesarovic, S.Dj. and Fleck, N.A.: Spherical indentation of elastic-plastic solids. Proc. R. Soc. London. 455, 2707 (1999).CrossRefGoogle Scholar