A model for coated surface hardness

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Abstract

The authors present a model that predicts the hardness of a film deposited on the surface of a substrate. The model is based on a simple mathematical relationship involving the hardness of the film and the hardness of the substrate, together with the hardness of the composite film/substrate at a given film thickness/penetration depth ratio. The parameters of the present model depend on the mechanical properties of the film/substrate pair and can be experimentally determined by using depth-sensing hardness instruments. In the models found in the literature, the equation parameters are constants typical for each model. The present model is proposed and validated for the case of a film (W–C–Co coating) harder than the substrate (various metallic materials) and it allows determination of the film hardness without the need to determine either the film thickness or the substrate hardness.

Introduction

The characterization of the mechanical behaviour of thin coatings is often made using indentation hardness tests. If the ratio of the indentation depth to the thickness of the film is small enough, the observed behaviour is only due to the properties of the coating. In many cases, most experimental apparatus, including ultramicrohardness tester, are not sufficiently sensitive to allow the needed accuracy in the load and penetration measurements to assess only the behaviour of the coating. To overcome this, higher load hardness tests should be used, on the condition that the contributions of substrate and thin film in the final result can be conveniently separated.

A large number of models have been used for this purpose [1], [2], [3], [4], [5], [6], [7], [8], [9], [10], [11], [12], [13], [14], [15], [16], [17], [18], [19]. Most of them can be summed up by the following general equation:Hc−HsHf−Hs=Fthwhere Hc, Hs and Hf are the composite, substrate and film hardnesses, respectively, t is the thickness of the film and h is the depth of the indentation. F is a function that depends on the type of mathematical model; its parameters are related to the properties of the film and the substrate materials, size and geometry of the deformed region, etc.

In a recent work by Fernandes et al. [19], the kinematic model was applied to the case of a spherical cavity problem in order to undertake a theoretical study of the mechanical behaviour of a bilayer, during the hardness test. The authors concluded that the size of the plastically deformed region and its evolution during the hardness test strongly influences the behaviour of the composite, this being the reason why the former models fail, in general, to produce reasonable results because they do not give any guarantee for the values of their characteristic parameters, which are not specific to each film/substrate pair. The formulation of an appropriate model must, directly or indirectly, take into consideration that, during the indentation test of a material, the size of the plastically deformed region depends on the elastic and plastic properties of the material under indentation.

In the present research, a model to predict the hardness of the film from the hardness value of the composite was developed and validated for the case of W–C–Co films on six different softer substrates. In the model, the values of the parameters are not imposed a priori, but they can be determined experimentally, from the results obtained using a depth sensing indentation apparatus.

Section snippets

A hardness model for the composite film/substrate

The formulation of the present model is based on the following two hypotheses.

The composite follows a simple behaviour described by the linear equation (the validity of such a linear relationship has been discussed elsewhere [20], [21], [22]):Hc−HsHf−Hs=AthD+Bwhere Hc, Hs and Hf are the composite, substrate and film hardnesses, respectively, t is the thickness of the film and hD is the plastic penetration depth of the indentation. A and B are equation parameters that depend on the film and

Experimental details

Vickers hardness tests were performed on several coating/substrate systems. Six different substrates were used: 1-mm-thick sheet samples of copper in annealed condition (ACu samples), mild steel, rolled up to 80% reduction (RS samples), and AISI M2 steel samples, submitted to four different heat treatments in order to obtain different hardness values (Table 1). The AISI M2 sample A (M2A) was used in an as-received annealed condition. The other three samples M2B, M2C and M2D were water-quenched

Results and validation

For each coating/substrate system, the data for the hardness of the composite, Hc, were obtained as a function of hD, normalized to the unity of thickness t (Fig. 1). The hardness of the film is assumed to be 18.5 GPa by considering the value of the hardness for small indentations for which no contribution of the substrate to the hardness of the composite is expected. So, the ratio between the hardness of the film Hf and the hardness of the substrate Hs is within the range 2.05<Hf/Hs<18.5 (

Conclusion

A model to predict film hardness when performing hardness tests on a composite material is presented. This model allows the determination of an accurate value of the hardness of a hard film on a soft substrate, without the need to previously determine the thickness of the film and the hardness of the substrate. Using a depth sensing hardness instrument, the following procedure is used to apply the model:

  • 1.

    To perform two different nominal indentation loads and determining the respective pairs

Acknowledgements

The authors are indebted to Fundação para a Ciência e a Tecnologia do Ministério da Ciência e Tecnologia and Program PRAXIS XXI, for financial support. A grant to A. Cavaleiro from Fundação Oriente is also acknowledged.

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