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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: dejunma@yahoo.com
b)Address all correspondence to this author. e-mail: apacwong@inet.polyu.edu.hk
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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

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