Elsevier

Mechanics of Materials

Volume 42, Issue 2, February 2010, Pages 166-174
Mechanics of Materials

Depth-sensing indentation modeling for determination of Elastic modulus of thin films

https://doi.org/10.1016/j.mechmat.2009.11.016Get rights and content

Abstract

There are various methods to address the problem of determining the hardness of thin films when the substrate is involved in the deformation process produced during conventional indentation tests. For the determination of the elastic modulus using depth-sensing indentation methods, the problem is more complex due to the deformation of the equipment that comes in addition to the effect of the substrate.

In the paper we discuss the use of Oliver and Pharr’s method to take into account the deformation of the equipment for the measurement of the elastic modulus of TiCN thin films.

For micro-indentation tests we proposed a new model to precise the effect of the substrate. The elastic moduli that are calculated are in very good agreement to those found in literature. For nano-indentation tests it is necessary to correct the data to take into account the shape of the indenter tip. We show that this correction, proposed at the origin for massive materials, is not able to explain the discrepancies between the calculated values and those coming from the literature for the elastic modulus of thin films.

Introduction

During the last decades, numerous works have been conducted to develop new surface modification process in order to increase the resistance of mechanical components to surface damage. Among them, physical and chemical vapor deposition provide very hard films of thickness of the order of micrometer. In addition to the hardness, Leyland and Matthews, 2000, Batista et al., 2003 have shown that the elastic modulus of the film is an important parameter to consider when studying the performance of such coated materials. Mechanical properties of thin films cannot be determined using conventional tensile test. A popular solution is to deform the coating at a very small scale using depth-sensing indentation. For the thicker films, the method of Oliver and Pharr (1992) proposed to analyze nano-indentation experiments, allows a direct determination of the elastic modulus of the film. For the thinner films, this method cannot be applied and direct determination is not possible due to the interaction with the substrate. Chudoba et al., 2002, Cleymand et al., 2005 have observed that the influence of the substrate begins to be noticeable for indentation depth as low as 1% of the film thickness. This is much lower than the influence observed which begins to be noticeable for indentation depths near 10% of the film thickness depending on the hardness and nature of the film (Sun et al., 1995, Cai and Bangert, 1995). Following these observation, it is clear that any measurement performed either in the nano or the micro-indentation range, would involve the substrate for films of thickness near and above 1 μm that are the range of thickness used for mechanical applications. Models to separate the contributions of film substrate to the global deformation were proposed recently for the analysis of load–depth indentation curves. These models (Doerner and Nix, 1986, Mencik et al., 1997, Gao et al., 1992, Antunes et al., 2007) are based on the best fit analysis of the load–depth curve by an appropriate function. These very simple functions cannot describe properly the two asymptotic tendencies that should be observed for the very low loads for which the elastic modulus tends toward that of the film and for the higher loads for which the modulus tends toward that of the substrate. In addition, from the experimental point of view, it is important to keep in mind that indentation depth measured during the indentation test is due to the deformation of the specimen itself and to the deflection of the whole instrument. In a recent paper, Fischer-Cripps (2006) considered that the compliance of the equipment frame involves also the specimen mounting. As a consequence, the compliance is not a constant value but have to be estimated for each specimen when applying Oliver and Parr’s (1992) method.

The objective of the present work is to propose a new model based on two requirements

  • (1)

    to represent the two asymptotic tendencies for the film and the substrate;

  • (2)

    to propose a general method for the evaluation of the compliance of the global system.

The model will be applied to the mechanical characterization of TiCN thin films, of thickness near to 2 μm, deposited on a steel substrate.

Section snippets

Measurement on a massive material

For depth-sensing indentation analysis, Oliver and Pharr (1992) proposed to determine a “reduced elastic modulus” as a function of the indentation parameters deduced from the unloading part of the load–depth curve (Fig. 1):ER=1βπ21A1Cwhere ER is the reduced modulus, β a correction factor, A the contact area and C is the compliance.

The reduced modulus, ER, depends on the elastic modulus and Poisson’s coefficient of the specimen and those of the indenter as follows:1ER=1-ν2E+1-νi2EiFor a diamond

Material and experiments

A micro-hardness Tester CSM 2-107 equipped with a Vickers diamond indenter was used for the micro-indentation experiments. The tests were performed at maximum loads chosen within the range 50–10,000 mN. Loading and unloading rates (in mN/min) were set up at twice the maximum applied load. A dwell time of 15 s was imposed according to the standard CSM test procedure. Fig. 2 shows an example of loading-unloading curves obtained for a TiCN film of 2.19 μm thick.

For nanoindentation experiments, the

Application of the models for the determination of TiCN films elastic modulus

As known from the “rule of 1%”, it is not possible to determine 1/SF directly from the micro-indentation data because, even for the lowest applied loads, the indentation depth is higher than 1% of the film thickness and consequently, the substrate participates to the measured deformation. For, the nanoindentation measurements, the minimum indentation depths recorded were equal to 2.1% of the film thickness. Direct determination of the elastic modulus is impossible in this case too. The

The new model

According to the preceding remarks, a relevant model should take into account the compliance of the equipment frame as well as the two asymptotic film and substrate tendencies that constitute boundaries for the apparent Young modulus. In addition for nanoindentation results, the rounded tip of the indenter should be taken into account.

Let us examine first what have proposed Oliver and Pharr (1992) to deal with the compliance of the frame.

Application to micro-indentation experiments

Experimental results presented in Fig. 4a show clearly that the experimental curve does not intercept the axes at the origin of 1/Sc  1/hc diagram. This is the manifestation of the deformation of the frame during the test. As a matter of fact, the intercept is found to be near 1 × 10−5 mm N−1 for 1/hc = 0 in accordance to previous results obtained by Chicot and Mercier (2007) in our laboratory on a standard fused silica specimen (Cf = 2.8 × 10−5 mm N−1) using the same equipment.

Application of the model

Conclusions

A new model is proposed to calculate the elastic modulus of thin films from Oliver and Pharr’s method applied to depth-sensing nano and micro-indentation experiments. This model takes into account the actual frame compliance. Moreover, the two tendencies observed at low and high loads, corresponding to film and substrate tendencies respectively, are introduced through a weight function similarly to that of Korsunsky’s model developed for hardness film determination.

Applied to micro-indentation

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