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A new approach of the Oliver and Pharr model to fit the unloading curve from instrumented indentation testing

Published online by Cambridge University Press:  17 April 2017

Stephania Kossman*
Affiliation:
Univ. Lille, FRE 3723—LML—Laboratoire de Mécanique de Lille, Lille F-59000, France; and Arts et Métiers ParisTech, MSMP, Lille 59800, France
Thierry Coorevits
Affiliation:
Arts et Métiers ParisTech, MSMP, Lille 59800, France
Alain Iost
Affiliation:
Arts et Métiers ParisTech, MSMP, Lille 59800, France
Didier Chicot
Affiliation:
Univ. Lille, FRE 3723—LML—Laboratoire de Mécanique de Lille, Lille F-59000 France
*
a) Address all correspondence to this author. e-mail: stephaniakossman@gmail.com
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Abstract

The unloading part of a load–displacement curve from instrumented indentation tests is usually approximated by a power law (Oliver and Pharr model), where the load is the dependent variable. This approach generally fits well the data. Nevertheless, the convergence is occasionally quite questionable. In this regard, we propose a different approach for the Oliver and Pharr model, called the inverted approach, since it assigns the displacement as the dependent variable. Both models were used to fit the unloading curves from nanoindentation tests on fused silica and aluminum, applying a general least squares procedure. Generally, the inverted methodology leads to similar results for the fitting parameters and the elastic modulus (E) when convergence is achieved. Nevertheless, this approach facilitates the convergence, because it is a better conditioned problem. Additionally, by Monte Carlo simulations we found that robustness is improved using the inverted approach, since the estimation of E is more accurate, especially for aluminum.

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Copyright
Copyright © Materials Research Society 2017 

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Footnotes

Contributing Editor: George M. Pharr

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