Abstract
Coatings used in tribological applications often exhibit high hardness and stiffness to achieve high wear resistance. One coating characterization method frequently used is nanoindentation which allows the determination of indentation hardness and indentation modulus among other material properties. The indentation modulus describes the elastic surface behavior during indentation and is, among hardness, a direct indicator for wear resistance. To obtain the true indentation modulus of a coating, it must be measured with varying loads and then extrapolated to zero load. Current recommendation of the standard ISO 14577-4:2016 is a linear extrapolation which fits poorly for nonlinear curves. Such nonlinear curves are commonly found for high hardness mismatches between coating and substrate, for example, superhard tetrahedral amorphous carbon coatings (ta-C) on a steel substrate. In this study, we present a new empirical fit model, henceforth named sigmoid. This fit model is compared to several existing fit models described in the literature using a large number of nanoindentation measurements on ta-C coatings with wide ranges of indentation modulus and coating thickness. This is done by employing a user-independent and model agnostic fitting methodology. It is shown that the sigmoid model outperforms all other models in the combination of goodness of fit and stability of fit. Furthermore, we demonstrate that the sigmoid model’s fit parameter directly correlates with coating thickness and thus allows for a new approach of determining ta-C coating thickness from nanoindentation.
Highlights
NanoindentationUsually, the indentation modulus EIT can be reliably measured with the Oliver–Pharr method from the unloading curve [1]
Additional fit models described by Mencık et al [4] and Doerner and Nix [9] were not considered due to their unsuitable curve progression. These models could not adequately describe the quasi-continuous stiffness measurement (QCSM) results of our samples; we propose a new fit model for an improved extrapolation
The roughness of tetrahedral amorphous carbon coatings (ta-C) coatings is influenced by their thickness, so the sample surfaces were polished lightly for comparable measurements
Summary
NanoindentationUsually, the indentation modulus EIT can be reliably measured with the Oliver–Pharr method from the unloading curve [1]. Unlike hardness it is not possible to give a limit where the substrate influence can be neglected For this reason, the indention standard ISO 14577 part 4 [2] describes a method how the pure EIT of the coating can be obtained. The indention standard ISO 14577 part 4 [2] describes a method how the pure EIT of the coating can be obtained It requires a series of indention measurements with different forces and depths and the extrapolation of the function EITðaÞ or the normalized function EITða=tcÞ to zero depth with a as contact radius and tc as coating thickness. According to the standard [2], a minimum of 10 indents should be performed per force and at least 50 measurements are required This is a relatively time-consuming procedure; other methods have been developed:
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