Toward an optimization of hardness models for thin films

Thin films hardness measurement has to face some difficulties to interpret the apparent hardness value. In effect, for a wide range of indentation loa ds, the substrate undergoes a part of the deformation induced by the indent or. In these conditions, the apparent hardness is the result of both contri butions of the substrate and of the film. Some models are available in lite rature in order to describe these contributions. The hypothesis which are s tated by the authors are quite different in nature. For example, the model of Buckle is based on a discrete description of the deformation zone under the indent add to some experimental considerations (1). The model of Jonsso n and Hogmark is based on the load supporting areas of the indent in the fi lm and in the substrate (2). More recently some models (Burnett and Rickerb y (3, 4) and Chicot and Lesage (5)) searched to represent the real behaviou r; that is to say to describe the plastic deformation under the indent in t he film and in the substrate. Whatever are the considerations of the models , all consider the following relationship expressing linearly the apparent hardness value He in function of the respective hardness of the film and of the substrate H-C = a H-F + b H-S [1] Knowing that (a + b) has to be 1, it is more interesting in practice to use the following relation which involves an only one coefficient: H-C = H-S + a(H-F - H-S) [2] When these models are applied to different configurations of films and subs trates, the predicted H-F, values may be very different This article has th e objective to give responses to the following questions : What is the more appropriate model and what credit can be allowed to its estimations ? Usin g some experimental data from work on titanium nitride thin film by Burnett and Rickerby: it is possible to compare the predictions of the models beca use a precise hardness of the film has been deduced independently from thic ker film for which hardness measurements may be performed independently on the action of the substrate for a sufficient range of loads. Useful compari sons between the models are deduced from the calculation of the influence c oefficient a which appears in relation [2] and the influence coefficient ex perimental a deduced from the experimental data. The main conclusions are the following : Buckle's model does not give very satisfactory predictions especially when the ratio between the indentation depth D and the thickness e is lower than 0.5. The model of Jonsson and Hog mark does not give useful predictions when the constant C takes the value 1 . It is shown that the other possibility for C (i.e. 0.5) cannot represent all the results and that C should take values lower than 0.5 (i.e. until 0. 35) in relation to the film and the substrate hardnesses ratio. The model o f Burnett and Rickerby cannot be applied because it involves a fitting para meter which eliminates the predictional character of the model. Only our mo del fit correctly all the experimental data, that is why it will used in th e following of the article as a base for the comparisons. From experimental results on chromium films obtained by Jonsson and Hogmark for which the au thors stated that a value of I. It seems that this hypothesis should be tak en cautiously in accordance with the previous remarks. From experimental results obtained in our laboratory on titanium and titani um carbide films, we confirm the preceeding remarks for the model of Jonsso n and Hogmark and we propose an adaptation of the model of Buckle taking in to account the real shape of the deformed plastic zone under the indent.