Scaling Relationships in Nanoindentation

  • Anthony C. Fischer-CrippsEmail author
Part of the Mechanical Engineering Series book series (MES)


An interesting fundamental approach to the analysis of load-displacement data is provided by dimensional analysis [1–9]. Consider the indentation of an elastic–plastic specimen with a rigid conical indenter. The mechanical properties of the specimen can be approximated by a uniaxial stress–strain response given by Eqs. 4.28 and 4.29, here repeated for convenience:

$$ \begin{aligned} \sigma &= E\varepsilon \qquad\quad\varepsilon\le {\rm{Y/E}} \\ \sigma &= K{\varepsilon ^x}\qquad\;\; \varepsilon\ge {\rm{ Y/E}} \end{aligned} $$

where σ is the applied stress and e is the resulting strain and K is equal to:

$$ K = Y{\left[ {\frac{E}{Y}} \right]^x} $$


Finite Element Analysis Dimensional Analysis Indentation Depth Indentation Test Indentation Size Effect 
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Copyright information

© Springer Science+Business Media, LLC 2011

Authors and Affiliations

  1. 1.Fischer-Cripps Laboratories Pty Ltd.Killarney HeightsAustralia

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