Modelling the hardness response of bulk materials, single and multilayer coatings

A number of models exist for determining the hardness of a coating from experimental data that contain a contribution from the substrate. These models are not always easy to apply and, as the complexity of the coating increases and the thickness of the layers are reduced, it becomes almost impossible to extract meaningful data from the experimental results. Even for simple systems the models cannot be regarded as predictive except in a restricted range of circumstances. Furthermore, existing models cannot help the designer answer important questions, like what order should coatings be in a multilayer stack to achieve the best hardness response over a range of contact loads. This paper outlines the development of a simple predictive model that can be used to explain experimental results and answer such questions. The model uses work of indentation divided by deforming volume to define hardness. The deforming volume for most systems of interest is approximately hemispherical; the model sums all the contributions to the work of indentation which take place within this hemispherical region. The model can explain indentation size effect behaviour, coating/substrate system hardness and hardening effects in multilayer and superlattice coatings. (C) 2001 Elsevier Science B.V. All rights reserved.