Acta Polytechnica CTU Proceedings https://doi.org/10.14311/APP.2024.50.0001 Acta Polytechnica CTU Proceedings 50:1–6, 2024 © 2024 The Author(s). Licensed under a CC-BY 4.0 licence Published by the Czech Technical University in Prague MODULUS ESTIMATION OF POLYMERS VIA NANOINDENTATION – IMPACT OF SURFACE ROUGHNESS, PEAK FORCE AND TESTING SPEED Michael Huszara,∗, Gernot Oreskib, Florian Arbeitera a Montanuniversität Leoben, Chair of Materials Science and Testing of Polymers, Otto-Glöckel-Straße 2, 8700 Leoben, Austria b Polymer Competence Center Leoben, Sauraugasse 1, 8700 Leoben, Austria ∗ corresponding author: michael.huszar@unileoben.ac.at Abstract. Nanoindentation is widely used to study small-scale structures in materials. The impact of varying testing conditions on the measurement’s accuracy is of high interest, and their influence on the characterization of polymeric materials is still quite scarce. Therefore, this study investigates varying loading and unloading rates paired with maximum loads ranging from 0.5 to 20mN on Polyethylene samples with varying surface finishes after wet grinding. The indentation Data was analyzed using the Oliver & Pharr Method, and the resulting Modulus was compared with those obtained from macroscopical tensile tests. The hardness was compared to Shore hardness measurements. A correlation between the measured modulus values and the surface Quality was explored. The results prove the already established rule that the best surface finish (Sa = 0.07µm) leads to the smallest standard deviation. However, they show that the modulus characterization is less influenced by surface roughness than hardness evaluations. Keywords: Polymer, nanoindentation, roughness. 1. Introduction Nanoindentation did prove itself a valuable measuring technique for the characterization of localized mechan- ical properties on a micro-scale [1]. Recently, it has started to become more interesting for the field of non-linear elastic, or even visco-elastic materials [2]. One of this fields is polymer science, where foils or products with many different layers are often used. So far, these materials are most often only tested on a macroscopical scale as a whole and only limited attention is paid to the exact mechanical properties at the interfaces [3]. To successfully apply nanoin- dentation to polymers, several adaptations had to be introduced [4–7]. The time-dependent behavior of the materials has proven especially difficult in the past. Nevertheless, adhering to established testing routines, it is possible to accurately describe the mechanical properties of polymers on a small scale, e.g. mechan- ical properties resulting from small changes of local morphological properties, curing state of elastomers, or localized, time dependent behavior [8–12]. Recent studies have demonstrated the potential of nanoinden- tation to be used to characterize aging of polymers, which is a highly localized phenomenon [13, 14]. However, to explore localized processes while ensur- ing the reliability of the data obtained, it is essential to minimize possible sources of errors. Previous research on hard materials shows that the surface quality of the examined samples greatly influences results of nanoin- dentation [15, 16]. However, these studies focus on the hardness of metals, which exhibit different me- chanical behavior compared to softer materials, such as polymers. Therefore, the influence of roughness on nanoindentation of visco-elastic materials remains a question to be addressed. The most commonly used method to characterize the surface quality from an en- gineering perspective is its roughness. This study uses the roughness parameter Sa to describe the different surface finishes. The focus is put on the influence of Sa on the resulting quality of nanoindentation curves and evaluated values (modulus and hardness) of a visco- elastic material. Due to the viscous nature of the tested materials, the applied maximum force and load- ing rate were varied to check the impact on the quality of the results as well. 2. Materials and methods 2.1. Material and sample preparation A high-density polyethylene (PE) plate, as is often used in different polymer industries, was used in this study. Samples were cut out from this plate and wet- ground on a Struers Labopol-30 with a Laboforce-100 specimen mover (Struers, Denmark). 600, 1200, 2500, and 4000 sandpaper grits with water as lubricant and cooling agent were used for the grinding steps. One sample was polished with 3µm diamond paste (DiaMaxx Poly, 3 µm, Akasel, Denmark) together with a lubricant for soft materials (Aka-Lube Red, Akasel, Denmark). And end-polishing was done with a fumed Silica OP-S solution (fumed silica suspension 0.2µm water free, Akasel, Denmark) and water. 1 https://doi.org/10.14311/APP.2024.50.0001 https://creativecommons.org/licenses/by/4.0/ https://www.cvut.cz/en M. Huszar, G. Oreski, F. Arbeiter Acta Polytechnica CTU Proceedings Sample finish Ra [µm] Rz [µm] Sa [µm] Sz [µm] Str Spc [l mm−1] Sandpaper 600 1.51 14.7 1.62 25.4 0.15 3 969.49 Sandpaper 2500 0.70 7.0 0.72 13.19 0.63 2 390.63 Sandpaper 4000 0.08 1.0 0.08 2.93 0.06 1590.87 OP-S 0.05 0.8 0.07 8.3 0.31 92.89 Table 1. Results of the roughness measurements via confocal laser microscope. To obtain parallel surfaces necessary for the inden- tation tests, a custom-made sample holder was used. The samples were glued to the holder with a commer- cially available ethyl-cyanoacrylate superglue (UHU GmbH & Co. KG, Germany, Sekundenkleber, flüssig). Nanoindentation measurements were performed on samples with last steps of 600, 2500, 4000, and end- polished finish. The surface roughness was measured on an area of 0.9mm2 using a confocal laser scan- ning microscope VHK-1000 (Keyence, Belgium). To describe the height differences of the surface Sa (arith- metic mean) and Sz (maximum height) are used. For surface morphology, Str (texture aspect ratio) is used to characterize isotropy, and Spc (arithmetic mean peak curvature) is determined to distinguish the “sharpness” of peaks. A surface with uniform roughness in all directions will have a Str near 1, while a surface with directional roughness will result in a value near 0. Sharp peaks will result in a high Spc value, while a low value means more rounded, flat peaks. Additionally, within this area 10 profile lines were measured for easy comparison with the commonly used roughness values Ra and Rz. 2.2. Nanoindentation and evaluation following the Oliver Pharr approach The nanoindentation measurements were performed on a UNHT3 Nanoindenter (Anton Paar, Graz Aus- tria). Subsequent evaluation was done with the soft- ware Indentation Ver.: 8.0.24 (Anton Paar, Graz Aus- tria). A Berkovich indenter was used for all experi- ments. The maximum loads (Fmax) that were used during indentations were 0.5, 1, 5, 10, 15 and 20mN. For each load level, five indentations were made. To avoid possible interactions between indentation sites, a distance of 250µm was used. The indentation was performed with a loading speed of 2 times Fmax per minute, a holding period of 10 s at Fmax and subsequent unloading with the same speed as the loading step. The holding period is introduced to decrease the influence of visco-elastic creep on the results [17]. The unloading curve was fitted between 98% and 40% of Fmax to determine the modulus. The upper and lower bounds were empirically deter- mined in order for the tangent to describe the actual unloading curve best. The evaluation subsequently followed the method devised by Oliver and Pharr [1]. The obtained reduced modulus (Er) is proportional to the Young´s modulus (E) of the indenter (Eind) and of the sample material (in our case EP E). The indenter properties are the modulus and Poisson´s ratio of diamond (Eind = 1141GPa; νind = 0.07), and for the Poisson´s ratio of PE, νP E = 0.4 [18] was used. Hardness (H) is calculated using the projected area of the indenter at the contact indentation depth di- vided by the maximum load Fmax [1]. Since the hard- ness of polymers is typically measured using a Shore durometer [19], a direct comparison of the obtained values is not possible. To achieve at least some level of comparability, the spring constant of the durom- eter used (Zwick, Germany) was measured, and an area function of the indenter was determined. The standard Shore D indenter features a cone-shaped tip with a 30° opening angle, and a tip radius of 0.1mm, mounted on a cylinder with a diameter of 1.25mm. Shore hardness is defined in a way that 100 Shore D corresponds to no penetration and 0 Shore D cor- responds to no resistance, meaning the full 2.5mm length of the indenter is pressed into the sample. Us- ing this, the indentation depth can be calculated, and the measured spring constant of 16.77Nmm−1 allows the evaluation of the load at this depth to be used to calculate the hardness following [1]. 3. Results and discussion The results from the roughness measurements are shown in Table 1. For comparison, typical evaluations via line scans (Ra and Rz) and area scans (Sa, Sz, Str and Spc) were used. Sa and Sz can be compared to indentation depth. Since Sz is the maximum height difference of the complete measured surface, which is much larger than the actual indentation site, it is more likely to have a height difference close to the value of Sa at the indentation area. Therefore, comparisons focus on Sa in all further analysis. The scratches caused by the grinding of the sam- ples led to an anisotropic surface structure. This anisotropy is especially distinct for the sample fin- ished with the sandpaper 4000. As can be seen in Table 1, the sample shows a value of Sa = 0.08µm while Str is close to zero (0.06). Keeping the same indentation time settings is crucial for comparable results with different maxi- mum loads on viscoelastic materials and their time- dependent material response. This results in different loading and unloading speeds relative to the max- imum load used. In our case, speeds were set at 2Fmax min−1. Figure 1 shows four indentation curves 2 vol. 50/2024 Modulus estimation of polymers via nanoindentation. . . (a). Indentation curves with different Fmax and loading and unloading speeds. (b). The corresponding creep curves from the holding period at Fmax. Figure 1. Comparison of material response due to different Fmax and loading and unloading speeds of 2Fmax min−1 on the Sa = 0.07 µm sample. of the Sa = 0.07µm sample with different maximum loads, loading/unloading speeds, and a small “creep” analysis via a 10 s holding time. As shown in Figure 1a, the loading curves of all loading speeds are almost identical. Figure 1b shows the normalized indentation depth as a function of time for all applied load levels. Similarly, there is no evi- dent difference between the curves. While a holding segment of 10 s is insufficient for a full creep analysis, it can be used to see large deviations in the deforma- tion and showcase different responses to the previous loading speed. These curves indicate that there is no substantial difference in the time depending material response, and therefore, the evaluations are compara- ble. Furthermore, the absence of a “nose” (increase of deformation depth during unloading due to viscous material effects [20]) implies that the 10 s holding time is sufficient for a precise analysis of PE samples. After addressing the effects of loading level and speeds, the impact of surface quality was examined. Figure 2 shows a representative indentation curve of the 20mN and 5mN Fmax indentations for each surface quality. These indentation curves show that the slope of the load and unload process is strongly affected by the sur- (a). Maximum load of 20mN. (b). Maximum load of 5mN. Figure 2. Indentation curves on the different surface finishes. face roughness. This is especially visible for the sample with the highest surface roughness of Sa = 1.62µm. Only one successful indentation with Fmax of 20mN maximum load was possible for this sample. Further- more, it shows an unconventional loading segment. The indentation curve features a long plateau, and no rising load is detected. This can indicate a badly fixed sample or indenter, and the contact point must be manually adjusted. This was done by setting the contact point after establishing a clear contact and a visible, stable growth of the indentation depth in the measured curve. This curve was evaluated for E and H before and after manually setting the contact point to compare to the other results. Besides this faulty measurement, the influence of roughness can be seen clearly in the result from the same surface with Fmax = 5mN (Figure 2b). There are two different slopes visible in the loading regime. The region of the first slope can be affiliated with the bending and slipping of the top of the rough surface when it comes into contact with the indenter, while the later slope starts when there is more contact with the bulk material. The same behavior can also be noticed with the Sa = 0,72µm surface indentation curves. Evaluation of these curves leads to “wrong” indentation depths, resulting in high standard devia- tions for the calculated E and H values, as shown in Figure 3. In contrast, there is a nearly perfect over- 3 M. Huszar, G. Oreski, F. Arbeiter Acta Polytechnica CTU Proceedings (a). The calculated values of EP E compared to the Young’s modulus from tensile tests. (b). H compared to a converted shore hardness result. Figure 3. Dependency of indentation results on Fmax and Sa. lapping of the two curves of the smooth surfaces using the 20mN maximum load and very low deviation at the 5mN maximum load. Based on all performed measurements, the calculated values of E and H are compared in Figure 3. For comparison of the results, the Young´s mod- ulus of 1.14GPa, measured in uniaxial tensile tests in a previous research [18] and the shore hardness measured following ISO 48-4 resulting in 55.4 Shore D are used. The Shore D result was converted, following the procedure explained in section 2.2 to HP E−Shore = 49MPa. The results for Hardness and Young´s modulus fol- low the same trend with the two smooth surfaces, Sa = 0.07 µm (EP E = 1.17GPa; HP E = 49MPa) and Sa = 0.08 µm (EP E = 1.20GPa; HP E = 46MPa), having the lowest standard deviation and the best agreement with the macroscopic measured values. Only at the lowest value of Fmax = 0.5mN slight differences are detectable between these surface qualities. This devi- ation can most likely be attributed to the differences in Spc, and the smoother peaks of the polished sur- face. This explains why the Sa = 0.08µm surface is measured more compliant with the small maximum load. The Sa = 0.72 surface finish shows only good agreement for EP E at a maximum load of > 10mN, with a generally lower HP E of around 40MPa. The Figure 4. The ratio of Sa to the measured maximum indentation depth for the different surface finishes and maximum loads. roughest surface in this study (Sa = 1.62µm) shows overall lower values for EP E and HP E with a high standard deviation. Only the corrected contact point at Fmax = 20mN, resulting in EP E = 1.12GPa and HP E = 61MPa, would fit the known properties, but the chosen contact point can strongly influence the results. A not fully developed indentation due to the high surface roughness can explain these results (compare Figure 2 for Fmax = 5mN, where maximum indentation depth (hmax) is already around 25% of Sa). They indicate that H seems more sensitive to effects caused by roughness than E. Therefore, the evaluation of H can be used more profoundly to deter- mine if the results for the indent are correct. Overall, surface roughness strongly affects the standard devia- tion of both hardness and modulus characterization, with the biggest deviation on the roughest surface. To give further insights into the exact dependency of the evaluated values on the surface quality and applied Fmax (and subsequent hmax), the ratios of Sa to hmax were assessed for all samples. Figure 4 shows the results for a quantitative comparison. Based on the EP E results presented in Figure 3 and the measurements that yielded acceptable out- comes, we can consider the ratio of approximately 20%, achieved at a Fmax of 10mN for the surface with Sa = 0.72 µm as a rough threshold value for character- izing the Young’s Modulus of PE via nanoindentation. The threshold for valid results seems to be much lower for hardness measurements. The level of acceptance appears to be around 8%, reached with Sa = 0.08 µm and 0.5mN. Since the Sa = 0.07 µm surface shows the same Sa/hmax ratio, the hardness results still seem to fit quite well. This is an evident sign that Sa, com- pared to indentation depth, is only a rough but still valuable criterion for seeing if the surface quality is good enough for specific nanoindentation evaluations. Figure 5 depicts three indents with a maximum load of 10mN on the surfaces with Sa = 0.72µm, 0.08µm, and 0.07µm obtained with a SEM Tescan Clara (Tescan, Czech Republic). 4 vol. 50/2024 Modulus estimation of polymers via nanoindentation. . . (a). Sa = 0.72 µm. (b). Sa = 0.08 µm. (c). Sa = 0.07 µm. Figure 5. SEM images from lasting impression of indentations with 10mN maximum load on P E samples with different surface roughness. While the impression can easily be seen on the best surface quality, the rougher surfaces make it hard or impossible to distinguish the indent from surface features. This can make it impossible to evaluate the correct orientation of the indenter to the surface and the tested region. The comparison between Sa = 0.08µm and Sa = 0.07µm shows the necessity of considering more than one roughness parameter. The lower Spc of the polished surface (Figure 5c) is visible as the smoother appearance. At the same time, the difference in the Str shows the high orientation of the surface features of the Sa = 0,08µm finish. Both differences affect the visibility of the persistent impression and the contact of the indenter to the sample material. 4. Conclusion In this work, it was shown, that the applied sur- face preparation and subsequent roughness can sig- nificantly influence the evaluated modulus values de- termined via nanoindentation testing of visco-elastic materials. It has been demonstrated that with a load and unload rate below 40mN/min, along with a 10 s holding time at maximum load, there is no significant rate-dependent effect for PE. It was possible to get reasonable results for hardness measurements with a Sa to hmax ratio of around 8%, while for the modu- lus, a ratio of up to 20% provided acceptable results. The results confirm that the ISO 14577 recommended Ra to indentation depth ratio of 5% used for hard- ness measurements can be safely applied for polymers. Overall, it could be shown that a higher roughness increases scatter, and better statistics are required to measure the mechanical properties correctly. Acknowledgements The work was funded from the Polymer Competence Cen- ter Leoben GmbH and performed within the framework of the COMET-program (grant number 854178) of the Federal Ministry for Climate Action, Environment, En- ergy, Mobility, Innovation and Technology and the Federal Ministry for Digital and Economic Affairs, Austria. The help from the Chair of Functional Materials and Materials Systems, in regard to roughness testing on their confocal laser scanning microscope is highly appreciated. 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Journal of Physics D: Applied Physics 31(19):2395, 1998. https://doi.org/10.1088/0022-3727/31/19/006 6 https://doi.org/10.1016/j.polymertesting.2020.106978 https://doi.org/10.1016/j.polymertesting.2020.106978 https://doi.org/10.1016/j.polymertesting.2024.108417 https://doi.org/10.1016/j.polymertesting.2024.108417 https://doi.org/10.1016/j.polymertesting.2011.02.002 https://doi.org/10.1016/j.polymertesting.2011.02.002 https://doi.org/10.1016/j.actamat.2006.12.031 https://doi.org/10.1007/s11837-022-05278-0 https://doi.org/10.1016/j.solmat.2019.110082 https://doi.org/10.1557/JMR.1998.0438 https://doi.org/10.1007/s10853-017-0961-5 https://doi.org/10.1016/S0257-8972(01)01340-8 https://doi.org/10.3390/ma15093273 https://doi.org/10.1007/s11249-016-0805-5 https://doi.org/10.1088/0022-3727/31/19/006 Acta Polytechnica CTU Proceedings 50:1–6, 2024 1 Introduction 2 Materials and methods 2.1 Material and sample preparation 2.2 Nanoindentation and evaluation following the Oliver Pharr approach 3 Results and discussion 4 Conclusion Acknowledgements References