A contact area function for Berkovich nanoindentation: Application to hardness determination of a TiHfCN thin film

• Hardness and elastic modulus of TiHfCN thin film have been determined by indentation.
• A simple area function describing the contact area in indentation is proposed.
• The function only considers the truncation length of the tip defect.
• The hardness of the film is found to be close of 35.5 GPa.
• The elastic modulus of the film is found to be close of 490 GPa.

In nanoindentation, especially at very low indenter displacements, the indenter/material contact area must be defined in the best possible way in order to accurately determine the mechanical properties of the material. One of the best methodologies for the computation of the contact area has been proposed by Oliver and Pharr [W.C. Oliver, G.M. Pharr, J. Mater. Res. 7 (1992) 1564], which involves a complex phenomenological area function. Unfortunately, this formulation is only valid when the continuous stiffness measurement mode is employed. For other conditions of indentation, different contact area functions, which take into account the effective truncation length or the radius of the rounded indenter tip, as well as some fitting parameters, have been proposed. However, most of these functions require a calibration procedure due to the presence of such parameters. To avoid such a calibration, in the present communication a contact area function only related to the truncation length representative of the indenter tip defect, which can be previously estimated with high resolution microscopy, has been proposed. This model allows the determination of consistent indentation data from indenter displacements of only few nanometers in depth. When this proposed contact area function is applied to the mechanical characterization of a TiHfCN film of 2.6 μm in thickness deposited onto a tool steel substrate, the direct determination of the hardness and elastic modulus of the film leads to values of 35.5 ± 2 GPa and 490 ± 50 GPa, respectively.