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Relation between the ratio of elastic work to the total work of indentation and the ratio of hardness to Young's modulus for a perfect conical tip

Published online by Cambridge University Press:  31 January 2011

J. Chen  and
S.J. Bull
J. Chen
Affiliation:
School of Chemical Engineering and Advanced Materials, Newcastle University, Merz Court, Newcastle upon Tyne, NE1 7RU, United Kingdom
S.J. Bull*
Affiliation:
School of Chemical Engineering and Advanced Materials, Newcastle University, Merz Court, Newcastle upon Tyne, NE1 7RU, United Kingdom
*
a) Address all correspondence to this author. e-mail: s.j.bull@ncl.ac.uk
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Abstract

A linear relationship between the ratio of elastic work to the total indentation work and hardness to reduced modulus, i.e., We/Wt = λ H/Er, has been derived analytically and numerically in a number of studies and has been widely accepted. However, the scaling relationship between We/Wt and H/Er has recently been questioned, and it was found that λ is actually not a constant but is related to material properties. In this study, a new relationship between We/Wt and H/Er has been derived, which shows excellent agreement with numerical simulation and experimental results. We also propose a method for obtaining the elastic modulus and hardness of a material without invoking the commonly used Oliver and Pharr method. Furthermore, it is demonstrated that this method is less sensitive to tip imperfections than the Oliver and Pharr approach is.

Keywords

Elastic propertiesHardnessNanoindentation
Type
Articles
Information
Journal of Materials Research , Volume 24 , Issue 3 , March 2009 , pp. 590 - 598
Copyright
Copyright © Materials Research Society 2009

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References

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