On the computation of the absolute hardness of thin solid films

A study has been conducted in order to evaluate the descriptive capability of a modified form of the models advanced by Jönsson and Hogmark, Burnett and Rickerby, Chicot and Lesage and Korsunsky et al., regarding the composite hardness measurements carried out on different substrate–film systems. The modification that has been introduced involves the incorporation of the indentation size effect on both the substrate and film hardness through the power relationship, for the description of the change in hardness with the indentation diagonal, earlier proposed by Meyer. The modified models were first evaluated employing the data already published by Chicot et al., for Ti and TiC films formed on the surface of a chromium steel of a high carbon content. Subsequently, they were tested employing the data obtained experimentally with three under stoichiometric TiNx coatings, deposited by PVD magnetron sputtering on 316L stainless steel. It has been determined that the composite hardness measured on such systems can be satisfactorily described by means of any of the four models analyzed. However, it has also been found that the model proposed by Korsunsky and co-workers not only gives rise to the minimum quadratic difference between most of the measured and predicted values of the composite hardness, but also provides useful information regarding the film toughness. An optimization procedure is outlined which can be used in order to compute unambiguously and simultaneously all the constants involved in any of the four modified models, taking into consideration all the experimental measurements. The models advanced by Burnett and Rickerby, Chicot and Lesage and Korsunsky et al. have been found to predict a smooth increase in hardness as the indentation diagonal decreases, outside the range of experimental measurements. On the contrary, it has been shown that the model advanced by Jönsson and Hogmark breaks down when tested outside the range of experimental values of hardness, particularly at low indentation diagonal values.