Determination of elastoplastic properties of TiO2 thin films deposited on dual phase stainless steel using nanoindentation tests

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Abstract

In recent years, the extraction of mechanical behaviour of thin films by nanoindentation using sharp indenter geometry has been extensively studied. This work investigates the mechanical properties of TiO2 thin film (1 µm thickness) deposited by spin coating on dual phase Duplex stainless steel and glass substrates. Experiments are carried out with different sharp triangular pyramids (a Cube corner and a Berkovich indenter) using a commercial Nano Indenter® XP apparatus. The substrate effect has been counteracted and an inverse method proposed in literature for bulk material has been adapted to assess the elastoplastic parameters of the tested thin film directly from estimation of the hardness and elastic modulus values determined experimentally. This experimental method, coupled with two dimensional finite elements modelling, allows the determination of the mechanical behaviour of the film over the Duplex steel.

Introduction

Instrumented nanoindentation has become a powerful tool to assess the mechanical properties of bulk materials and thin films [1]. In recent years, inverse methods which allow the complete determination of a bulk material true stress–true strain curve from load–displacement curves obtained with one or two indenter geometries have been built [1], [2], [3]. In most of the inverse models, a mathematical trick is used to reduce the number of unknown variables in the expression of the loading curvature of the load–displacement curve: the representative strain [2], [3]. Dao et al. [2] have constructed dimensionless functions which link the curvature, Cθ, of only one load–displacement curve to the elastic modulus and stress within the tested material for a given strain level. From the load–displacement curvature and the material elastic modulus, those functions allow determining the representative stress, σr, at εr, and then a point in the stress–strain curve. Bucaille et al. [1] have extended the Dao's method and determine two points in the true stress–true strain curve from load–displacement curves obtained with two different indenter's geometries.

If mechanical properties of bulk material can be assessed relatively easily using inverse methods, it is not the case of thin films ones. In this case indeed, the major difficulty encountered in the extraction of its mechanical behaviour is to avoid the disruption of measured properties by the effect of the underlying substrate [4], [5], [6]. This can be done by restricting the maximum penetration depth, ht, to less than 10% of the film thickness t [7]. Bucaille et al. [8] have applied their inverse model to extract mechanical properties of a Ni film. However the film was thick enough for it to be considered as a bulk material. In the case of hard film deposited on a soft substrate, this tenth rule cannot be easily applied on less than 1 µm thickness films, except with an apparatus equipped with a Dynamic Contact Module (DCM®, Agilent Technologies), which allows very low loads tests with high resolution. For such thin films, composite mechanical properties (Emes, Hmes) are measured, which are combinations of the film's properties, (Ef, Hf), and the substrate's properties (Es, Hs)[4], [9]. In recent years, authors have built models which allow the extraction of the properties of the film from the composite ones [9], [10], [11], [12].

Korsunsky et al. [9] are using an energetic approach and assume that the total energy used up during the test is composed of the deformation energy in the substrate, and the deformation and fracture energy in the coating [11]:Hmes=Hs+(HfHs)·(11+k·d249·t2)

In Eq. (1) d refers to the diagonal of the indenter, and k is a dimensionless materials parameter which takes into account the system response mode during indentation. In the case of elastic modulus, Bec et al. [4] proposed a model based on the assumption that the system is equal to two springs in series:1Emes=2·ac1+2·tπ·ac·[tπ·ac2·Ef+12·ac·Es]

Once the substrate effect has been counteracted, an inverse method can be applied to built the entire true stress–true strain curve of the film.

The objective of this work is to extract the mechanical behaviour of a titanium dioxide (TiO2) thin film, 1 µm thickness, deposited on a Duplex stainless steel substrate. On one hand, Korsunsky and Bec models will be applied on TiO2 thin films deposited on two different substrates in order to counteract the substrate effect. On the other hand, inverse methods are used to extract the mechanical behaviour of the film.

Section snippets

Nanoindentation tests

Experimental tests were performed with a commercial Nano Indenter® XP (MTS Nano Innovation Center, Oak Ridge, TN) using Berkovich and cube corner indenters. The cube corner indenter tip has been calibrated with the help of the Oliver and Pharr method [13], but we assumed that the frame compliance was equal to zero and that the elastic modulus of the tested material is constant in its thickness. We used three samples to calibrate our indenter: Al, Si, and SiO2. We then used the identified area

Substrate effect removal on Berkovich indentation tests

Fig. 2 shows the evolutions of the measured (or combined) elastic modulus and hardness extracted from experiments performed on TiO2/Duplex sample tested with the Berkovich indenter, and on TiO2/glass sample.

All curves are divided into three parts, well described by Fischer Cripps [16]. Korsunsky et al. [9] propose to determine the film hardness using Eq. (1) and the knowledge of the substrate hardness. Fig. 2(b) shows the application of this model on TiO2/Duplex sample tested with the Berkovich

Conclusion

In this work, we have determined a set of mechanical properties for the TiO2 thin film (1 µm thickness) deposited by spin coating on dual phase Duplex stainless steel. With the help of Korsunsky and Bec's models applied on experimental data obtained with a Berkovich and cube corner indenters, we assessed hardness and elastic modulus of the thin film. The inverse method proposed by Bucaille et al. and the Johnson's model was employed to assess the elastoplastic parameters of the tested thin film,

Acknowledgments

This work has been realised as part of the ANR project Meloxel. Authors would like to express their thanks to all the project partners.

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