Hertzian analysis of the self-consistency and reliability of the indentation hardness measurements on superhard nanocomposite coatings

The measurement of elastic properties of superhard nanocomposite coatings can be subject to a number of possible errors, such as indentation size effects (indenter tip blunting, non-representative small volume of the material to be tested upon nanoindentation and a too small stress under the indenter which does not reach the yield stress of that material if a too low load is used), the composite effect of the system of superhard coating on a softer substrate, high compressive or tensile stress in the coatings, drifts and/or stiffness of the indenter etc. We shall present a systematic study of these possible artefacts on superhard coatings using a large range of applied loads on a number of super- and ultrahard samples. The hardness values obtained from the indentation measurements are compared with the Vickers hardness calculated from the projected area of the plastic deformation. The data will be also compared with finite element method computer modeling in order to obtain a deeper insight into the complex problems. It will be shown that reliable results can be obtained if sufficiently thick coatings are used which allows one to obtain load independent values of hardness measured at sufficiently large indentation depths. Hertzian analysis of the non-linear elastic response upon unloading provides analytical solutions that can be used in order to check if the hardness values measured on the super- and ultrahard coatings are self-consistent. In particular, it is possible to estimate the maximum tensile stress that the coatings survive without failure. This stress occurs at the periphery of the contact between the coating and the indenter and, in the case of ultrahard coatings, it can reach values in the range of tens of GPa. The results show a very good agreement with the theoretical predictions based on the Universal Binding Energy Relation.