Measuring Substrate-Independent Young’s Modulus Application Note Introduction The problem of determining intrinsic film properties from indentation data that are influenced by both film and substrate is an old one. If the film is thick enough to be treated as a bulk material, then the analysis of Oliver and Pharr (1992) is typically used [1]. When the film is so thin that indentation results at all practical depths are substantially affected by the substrate, the influence of the substrate must be accurately modeled in order to extract the properties of the film alone. Since 1986, many such models have been proposed [2-12]. In 1992, Gao, Chiu, and Lee proposed a simple approximate model for substrate influence. They derived two functions, I 0 and I 1 , to govern the transition in elastic properties from film to substrate [5]. Beginning with his Ph.D. dissertation in 1999, Song and his colleagues took an alternate solution path which was originally suggested by Gao et al . but not followed [7-9]. This alternate path yielded a simpler model which is called the “Song-Pharr model” in the literature. The Song-Pharr model predicts substrate effect reasonably well when the film is more compliant than the substrate. Unfortunately, none of the available models works well when the film is stiffer than the substrate. This shortcoming motivated the present work. Finite-element analysis (FEA) is essential to the development and verification of analytic contact models, because FEA idealizes experiment. In a finite-element model, the film thickness, film properties, and substrate properties are all well known, because they are required inputs. Also, there is little ambiguity about the true contact area under load, because it is determined from the last node(s) in contact. So before turning to experimentation, the worth of an analytic model is first assessed by means of FEA. For example, an elastic finite-element model may be constructed with a film of thickness t on a substrate, with the input properties being the Young’s modulus and Poisson’s ratio of the film ( E f , f ), and the Young’s modulus and Poisson’s ratio of the substrate ( E s , s ). Then, indentation into the material is simulated, and the simulated force- displacement data are analyzed in order to achieve a value for the Young’s modulus of the film, i.e. E f-out . What is the difference between this output value and the value that was used as an input to the finite-element model? FEA allows this question to be answered systematically over the domain of situations that might be encountered experimentally: thick films, thin films, stiff films on compliant substrates, compliant films on stiff substrates, etc. If an analytic model applied to simulated data fails to return the input properties Jennifer Hay
Measuring Substrate-Independent Young’s Modulus
Jun 04, 2023
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