Hardness measurements of Ti and TiC multilayers: a model

Microhardness measurements of thin films have to face the problem of the influence of the substrate on the measurement. Numerous models which take into account this behaviour are available in the literature. When the film is composed of several layers of different properties, it is more difficult to solve this problem because of the multiple influences of the different layers and the substrate. Little work on this subject has been already done; we propose here an extension to multilayers of two models: that of Jonsson and Hogmark, based on the relative deformed areas under the indent, and a model we have developed on the basis of plastically deformed volumes in the substrate and in the film. Starting from the hardness determination of Ti and TiC monolayer films, it is shown that it is possible to use either one or the other model to determine the composite superficial hardness of multilayer Ti–TiC films.