Abstract
An analytical model was developed in a previous work to relate the normalized indenter displacement to both the coating-to-substrate Young's modulus ratio and the coating-thickness-to-contact-radius ratio for Hertzian indentation on coating/substrate systems. However, application of this model is contingent upon the determination of the contact radius during indentation. Using the data from finite element analyses, an empirical equation is proposed in this paper to determine the normalized contact radius. Combining this empirical equation with the previous analytical equation, both the contact radius and the indenter displacement for Hertzian indentation on coating/substrate systems are predicted. The predictions obtained by this combined empirical–analytical method are shown to agree with the finite element results in general although the indenter displacement is over-estimated when the coating is stiffer than the substrate. Finally, the potential applications of this method to determine the elastic properties of coatings from the indentation data are envisaged.
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