A new model for the computation of the composite hardness of coated systems

The present communication proposes a new model for the computation of the composite hardness of coated systems as a function of the relative indentation depth, the hardness of both coating and substrate and two material constants that characterize the performance of the film during the indentation test. The model is developed from several important considerations which can be summarized as follows: (1) The substrate starts to contribute to the composite hardness at penetration depths of the order of 0.07-0.2 times the coating thickness, as suggested in the literature. (2) Above such a boundary the composite hardness depends mainly on the intrinsic hardness of the coating, whereas below it such a hardness is determined essentially by the hardness of the mixture that encompasses the remaining part of the film and the plastically deformed substrate material. (3) The hardness of such a mixture is assumed to be constant, except for the possible indentation size effect that could be displayed by the substrate. (4) The composite hardness is given by a linear law of mixtures in terms of the hardness of the coating and such a mixture, and the volume fraction of both materials under the indenter, at any given depth of the latter. It is shown that the model proposed describes very well the hardness data obtained in different systems including: Ti and TiC formed on a chromium steel of a high carbon content; TiN; TiCN and CrN deposited on M2 steel; and TiN0.55, TiN0.65, TiN0.75, ZrN0.50, ZrN0.60 and ZrN0.70 deposited on 316L stainless steel substrate. The results are also compared with those derived from the models earlier advanced by Jonsson and Hogmark, Burnett and Rickerby, Chicot and Lesage and Tuck et al., without taking into consideration the indentation size effect of the film. It is shown that the modified version of the earlier model put forward by Korsunsky et al., published recently by Tuck et al., constitutes a particular form of the model here proposed. (C) 2002 Elsevier Science B.V. All rights reserved.