Hostname: page-component-586b7cd67f-r5fsc Total loading time: 0 Render date: 2024-11-20T06:35:19.206Z Has data issue: false hasContentIssue false
  • English
  • Français

Further analysis of energy-based indentation relationship among Young’s modulus, nominal hardness, and indentation work

Published online by Cambridge University Press:  31 January 2011

Dejun Ma  and
Chung Wo Ong
Dejun Ma*
Affiliation:
Department of Mechanical Engineering, The Academy of Armored Forces Engineering, 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
*
a)Address all correspondence to this author. e-mail: [email protected]
b)Address all correspondence to this author. e-mail: [email protected]
Get access

Abstract

In our previous study, we modeled the indentation performed on an elastic–plastic solid with a rigid conical indenter by using finite element analysis, and established a relationship between a nominal hardness/reduced Young’s modulus (Hn/Er) and unloading work/total indentation work (We/Wt). The elasticity of the indenter was absorbed in Er ≡ 1/[(1 − ν2)/E + (1 − νi2)/Ei], where Ei and νi are the Young’s modulus and Poisson’s ratio of the indenter, and E and ν are those of the indented material. However, recalculation by directly introducing the elasticity of the indenter show that the use of Er alone cannot accurately reflect the combined elastic effect of the indenter and indented material, but the ratio η = [E/(1 − ν2)]/[Ei/(1 − νi2)] would influence the Hn/Er–We/Wt relationship. Thereby, we replaced Er with a combined Young’s modulus Ec ≡ 1/[(1 − ν2)/E + 1.32(1 − νi2)/Ei] = Er/[1 + 0.32η/(1 + η)], and found that the approximate Hn/Ec–We/Wt relationship is almost independent of selected η values over 0–0.3834, which can be used to give good estimates of E as verified by experimental results.

Keywords

Elastic propertiesNanoindentation
Type
Articles
Information
Journal of Materials Research , Volume 25 , Issue 6 , June 2010 , pp. 1131 - 1136
Copyright
Copyright © Materials Research Society 2010

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.Pethica, J.B., Hutchings, R., Oliver, W.C.Hardness measurement at penetration depth as small as 20 nm. Philos. Mag. A 48, 593 (1983)CrossRefGoogle Scholar
2.Loubet, J.L., Georges, J.M., Marchesini, O., Meille, G.Vickers indentation curves of magnesium oxide (MgO). J. Tribol. 106, 43 (1984)CrossRefGoogle Scholar
3.Newey, D., Wilkens, M.A., Pollock, H.M.An ultra-low-load penetration hardness tester. J. Phys. E: Sci. Instrum. 15, 119 (1982)CrossRefGoogle Scholar
4.Oliver, W.C., 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., 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.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)CrossRefGoogle Scholar
7.Cheng, Y-T., Cheng, C-M.Relationships between hardness, elastic modulus, and the work of indentation. Appl. Phys. Lett. 73, 614 (1998)CrossRefGoogle Scholar
8.Cheng, Y-T., Cheng, C.M.Scaling, dimension analysis, and indentation measurements. Mater. Sci. Eng., R 44, 91 (2004)CrossRefGoogle Scholar
9.Ma, D., Ong, C.W., Zhang, T.An improved energy method for determining Young’s modulus by instrumented indentation using a Berkovich tip. J. Mater. Res. 23, 2106 (2008)CrossRefGoogle Scholar
10.Ma, D., Ong, C.W., Zhang, T.An instrumented indentation method for Young’s modulus measurement with accuracy estimation. Exp. Mech. 49, 719 (2009)CrossRefGoogle Scholar
11.Dao, M., Chollacoop, N., Van Vliet, K.J., Venkatesh, T.A., Suresh, S.Computational modeling of the forward and reverse problems in instrumented sharp indentation. Acta Mater. 49, 3899 (2001)CrossRefGoogle Scholar
12.Lichinchi, M., Lenardi, C., Haupt, J., Vitali, R.Simulation of Berkovich nanoindentation experiments on thin films using finite element method. Thin Solid Films 312, 240 (1998)CrossRefGoogle Scholar
13.Fischer-Cripps, A.C.Use of combined elastic modulus in depth-sensing indentation with a conical indenter. J. Mater. Res. 18, 1043 (2003)CrossRefGoogle Scholar
14.ABAQUS version 6.2 (Hibbitt, Karlsson & Sorensen, Inc, Pawtucket, RI 2001)Google Scholar
15.Lan, H., Venkatesh, T.A.Determination of the elastic and plastic properties of materials through instrumented indentation with reduced sensitivity. Acta Mater. 55, 2025 (2007)CrossRefGoogle Scholar
16.Liu, L., Ogasawara, N., Chiba, N., Chen, X.Can indentation technique measure unique elastoplastic properties? J. Mater. Res. 24, 784 (2009)CrossRefGoogle Scholar