A new paradigm in thin film indentation
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A new method to accurately and reliably extract the actual Young’s modulus of a thin film on a substrate by indentation was developed. The method involved modifying the discontinuous elastic interface transfer model to account for substrate effects that were found to influence behavior a few nanometers into a film several hundred nanometers thick. The method was shown to work exceptionally well for all 25 different combinations of five films on five substrates that encompassed a wide range of compliant films on stiff substrates to stiff films on compliant substrates. A predictive formula was determined that enables the film modulus to be calculated as long as one knows the film thickness, substrate modulus, and bulk Poisson’s ratio of the film and the substrate. The calculated values of the film modulus were verified with prior results that used the membrane deflection experiment and resonance-based methods. The greatest advantages of the method are that the standard Oliver and Pharr analysis can be used, and that it does not require the continuous stiffness method, enabling any indenter to be used. The film modulus then can be accurately determined by simply averaging a handful of indents on a film/substrate composite.
I. INTRODUCTION
Accurately assessing the properties of thin film coatings with modestly intrusive indents remains a strong desire of the scientific and engineering communities. These measurements can be problematic as the deformation field emanating from the indent usually propagates in both the film and the substrate, rendering any property interrogated as a composite value influenced by both components. Various experimental and theoretical approaches have been applied to decoupling these effects,1–20 yet a complete and accurate picture has been challenging to obtain. Recently, the authors proposed a new model called the discontinuous elastic interface transfer model21 that accounted for an apparent discontinuity in elastic strain transfer at the film/substrate interface. The physical basis of this model is best illustrated in Fig. 1, which shows that values of strain are not numerically equivalent across the film-substrate interface. Figure 1(a) is a schematic of the spherically symmetric strain field emanating from an indent in a film/ substrate composite that is representative of the interplay of stress and strain between the film and substrate in the leading models of Doerner and Nix2 and Gao,3 see our prior work for a discussion on this point.21 In this case there is a continuous transfer of strain from the film to the substrate, in other words, values of strain are a)
Address all correspondence to this author. e-mail: [email protected] DOI: 10.1557/JMR.2010.0228 J. Mater. Res., Vol. 25, No. 9, Sep 2010
numerically equivalent on both sides at the interface. However, our numerical simulations indicated that a discontinuity in elastic strain transfer should exist at the film/substrate interface, see Figs. 1(b) and 1(c). The new model was constructed based on this discontinuity by adapting th
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