Scratch testing and instrumented indentation are well established methods for mechanical characterization of surfaces. The Nano Scratch Tester (NST) and the Ultra Nanoindentation Tester (UNHT) are advanced instruments that use more sophisticated measurement procedures to provide accurate data .
The “Oliver & Pharr Method” (, ) is a very common technique to examine indentation data, which utilizes the unloading-part of the load-displacement curve in order to extract mechanical material properties such as the Hardness HIT and Elastic Modulus EIT. Since this model presumes the sample to be a monolithic halfspace, it cannot consider the influence of the substrate in the combined response of the coated surface to the load- induced deformations and stresses, and hence, the results are effective values of the entire sample (Eeff, Heff). Thus, by utilizing this standard “Oliver & Pharr Method”, it is rather difficult to get the precise mechanical properties of the coating (EO, HO). This model has been extended in various ways and substantiated with a general solution for contact situations on arbitarily layered materials [4, 5, 6]. The “Oliver & Pharr extended for coatings” model enables a physical analysis of indentation measurements, as it not only analyzes the exact values of generic material properties of each coating layer such as the elastic modulus (EO1, EO2, etc.), but also the yield strength (YO1, YO2, etc.) as it measures the complete elastic contact field at the point of initial unloading.
Due to the generality of this model, it can be applied to scratch test data as well, because it considers the extra load component (lateral load) and measurement effects (e.g. tilting of the stylus). Therefore, one is no longer bound to non-physical and non-generic parameters such as scratch hardness or critical loads (LC1, LC2, and LC3) using such a physical analysis of scratch tests, but can now get generic and, hence, more universal material properties, such as the critical stresses of each fracture mode (I, II, and III). Figure 1 shows the effect of the differences between the extended and standard model on the Von Mises stress distribution. Even though the classic “Oliver & Pharr Method” does not even enable one to calculate the entire elastic field and its stress- strain components.
Figure 1. Von Mises stress distribution of an assumed monolithic halfspace without considering additional loads and measurement effects (a) in comparison to the Von Mises stress distribution (b) taking all those conditions into account like the “Extended Oliver & Pharr Method”.
This article shows how this can be used to physically analyze scratch tests and indentation measurements on different surface structures, i.e. a 250 nm thin optical anti-reflex (AR) coating on a polymer substrate and a 10-µm thick double-layer tribological coating on a Tungsten Carbide (WC) substrate (Table 1). The elastic moduli, layer thicknesses, and material compositions of the substrates have been determined beforehand – the former through indentation into a bulk sample. These systems are not only different with regard to their coating thicknesses, but also with regard to their mechanical structure: the WC substrate is much stiffer compared to the polymer substrate. Therefore, it is presumed that the substrates variably influence the effective mechanical parameters acquired through the standard "Oliver & Pharr Method".
Table 1. Known sample parameters
Figure 2. A flow chart of the procedure of mechanical characterization and optimization of arbitrary structured surfaces.
Dimensioning of Indentation Measurements
Prior to performing an indentation measurement on a coated substrate, it should be – as any physical experiment – appropriately dimensioned so as to obtain optimum data from the sample constituent of interest (in this case the coating). Since the same principle is applied for the following scratch test, this measurement procedure can be summed up as a scheme as shown in Figure 2.
However, it should be noted that the mechanical properties of the coating are believed to be completely unknown in this flowchart, as the procedure starts with a non-dimensioned indentation into the coated substrate so as to determine the initial values of its mechanical parameters EC1 and YC1. These preliminary values are used for the initial dimensioning of the final indentation measurement. In case this dimensioning showed that the sensitivity of this initial measurement is focused on the coating and the uncertainty of the results is considerably low, then the initial phase of this mechanical characterization procedure is over.
Otherwise, values of Elastic Modulus and Poisson’s ratio can be obtained from literature in order to begin with a rough dimensioning prior to undertaking the initial indentation measurement . A non-dimensioned measurement can be eliminated if the exact coating properties are close to the used literature values.
Physical Analysis of Indentation Measurements
Since an indentation measurement was performed using the UNHT, measurement data that includes the results of the standard “Oliver & Pharr Method” will be given in the “Oliver&Pharr for Coatings” (O&PfC) project file format with the extension “fdop”. In this format, measurement data can be easily opened by the software FilmDoctor® Studio , O&PfC® , and ISA , as shown in Figure 3, so as to begin the physical analysis.
Figure 3. Measurement data of the AR sample (a) and TR sample (b) as exported by UNHT® loaded into the FilmDoctor® Studio to begin the physical analysis.
It should be noted that both measurements appear to be well dimensioned for the coating of interest as the contact radius, a, of 34 nm and 382 nm for the AR and TR samples, respectively, are well below the respective layer thicknesses of 250 nm and 3.2 µm – almost only 10% of the layer thickness, which is an initial indication for a well-dimensioned measurement.
The software follows the corresponding steps:
1. Fits a power-law function to the unloading part of the load-displacement curve,
2. Computes the most effective indenter as explained in , and
3. Calculates the distribution of normal stress in indentation direction for a given number of fit points within the fit range.
Secondly, as shown in Figure 4, the surface structures need to be defined since the FilmDoctor® must take into account the exact structure of the sample so as to measure the effect of the other structure constituents on the measurement data. This other material information is calculated beforehand. For example, the elastic modulus of the substrate has been measured on a bulk sample of the substrate material, while the layer thicknesses have been measured using the Anton Paar Calotest.
Figure 4. Sample structure definition by means of number of layers, Poisson’s ratio, Young’s modulus, and layer thickness for the AR sample (a) and TR sample (b). As can be seen from these figures, more layers, gradient layer structures, and intrinsic stresses can be defined if applicable.
Thirdly, the software FilmDoctor® determines the exact elastic modulus EIT of the layer in question by using both the measurement data and the previously defined material structure data. The results are summed up in Table 2. The difference between the effective elastic modulus being 39.5 GPa for the monolithic halfspace presumed by the classic “Oliver & Pharr Method” and the exact elastic modulus of the layer being 70.3 GPa is as significant as expected due to the thin layer thickness. However, it should be noted that despite the dissimilarity between effective and exact elastic modulus for the relatively thick Al1.4Cr0.6O3, the top layer on the TR sample is rather small, Eeff is slightly influenced and, and as a result, increased by the stiffer underlying interlayer and substrate.
Table 2. Summary of calculated properties for each sample
Layer 1 (Al1.4Cr0.6O3)
Layer 1 (SiO2)
In summary, while E is underestimated by the standard “Oliver & Pharr Method” for the AR coating because of the extremely compliant substrate, E is overestimated by it for the top layer of the TR coating due to the stiffer underlying structure.
Figure 5. The true elastic modulus of the layer of interest has been calculated by FilmDoctor® Studio and is shown in the left-hand panel (green underlined).
Although the so called “Bückle rule” or “10% rule”, which suggests that the ratio of maximum indentation depth to layer thickness must be less than 10%, is realized as the maximum indentation depth is about 170 nm on the TR sample and 13 nm on the AR sample (both approximately 5.2% only), the calculation of EIT through the standard “Oliver & Pharr Method” fails in both cases. Therefore, this rule is not suitable for determining Young’s modulus in that case.
It should be noted that ISO 14577 recommends to conduct a series of measurements at different loads, plot the resulting effective elastic moduli as a function of ac/h, and linearly extrapolate them to ac/h = 0. As shown in Figure 6, this process could cause an elastic modulus of the AR coating of 42.5 GPa. Hence, the ISO 14577 is not perfectly adapted for such complicated surface structures either.
Figure 6. Calculation of the Young’s modulus of the AR coating (as recommended by ISO 14577) results in 42.5 GPa what is undoubtedly far too low.
Finally, the software FilmDoctor® Studio calculates 28 field components of the complete elastic field at the beginning of unloading and enables one to determine the yield strength Y (or σY) which is the maximum Von Mises stress in the layer of interest if plastic flow occurred only in this sample constituent. Figure 7 shows, among other results, the distribution of Von Mises stress as cross section by means of the sample at the sample surface and center of indentation. It is clear that the stress concentrates only in the top layer as both stress plots reveal only a part of the top layer in depth. Therefore, the maximum Von Mises stress is equal to the yield strength that is 5.4 GPa and 20.7 GPa for the AR coating and top layer of the TR sample, respectively, as plastic deformation occurred according to the residual contact depth revealed by the load-displacement curves. However, this result supports the previously mentioned indication that both are well-dimensioned measurements.
Figure 7. Results of the physical analysis by FilmDoctor® for the AR sample (a) and TR sample (b) including the elastic modulus E, yield strength (if applicable), distribution of von-Mises stress as cross section through the sample from the center of indentation to the contact edge, and the share of measurement information for each constituent.
Furthermore, this is supported by the measured share of measurement data as 41.8% and 75.5% for the AR coating and TR top layer, respectively, as shown in the right column of Figure 7, while the noise floor of 1% is sufficiently low in both cases.
 CSM Instruments SA, “Ultra Nanoindentation Tester (UNHT),” 2010. [Online]. Available: http://www.csm-instruments.com/en/webfm_send/ 167. [Accessed 2011].
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 N. Schwarzer, “Arbitrary load distribution on a layered half space,“ ASME Journal of Tribology, 122, No. 4, p. 672-681, 2000.
 N. Schwarzer, “Elastic Surface Deformation due to Indenters with Arbitrary symmetry of revolution,“ Journal of Physics D: Applied Physics, 37, No. 19, p. 2761-2772, 2004.
 N. Schwarzer, “The extended Hertzian theory and its uses in analysing indentation experiments,“ Philosophical Magazine, 86, No 33-35, p. 5179-5197, 2006.
The Authors would like to thank the Saxonian Institute of Surface Mechanics for the strong collaboration (Dr Norbert Schwarzer and Nick Bierwisch)
This information has been sourced, reviewed and adapted from materials provided by Anton Paar TriTec SA.
For more information on this source, please visit Anton Paar.