## 3 Results and Discussion
### Quasi-Static Nanoinindentation
3D plots of nanoindentation imprints of the composite specimen modified with 4 wt% carbon nanotubes and the neat polymer sample were made by _in-situ_ SPM imaging over a surface area of 10 \(\upmu\)m \(\times\) 10 \(\upmu\)m. The scans have been done forth after the performance of the relevant indentation test and are indicative of mended surface morphology of the monofilier nanocomposite concerning the in-plane recovery at the modified HDPE-based material (see Figure 3). The measured residual penetration depth in the HDPE is 228 nm against 155 nm for the nanocomposite sample. Bearing in mind the experimental values of the contact depths (see Table 2), it can be inferred that the composite structure containing MWCNTs exhibits more expressed elastic behavior. There has to be noted the identical degree of average surface roughness of both samples-14.2 nm for the pure HDPE and 11.3 nm for the nanocomposite 4 wt%MWCNT/HDPE, defined by the plotted blue lines in the topography forward SPM images (see Figure 3b,d). Therefore, any negative impact of potential rough surface engendering doubt over the impecability of the nanoindentation data can be excluded. The nanoindentation pile-up which is formed above the bulk surface of both samples and is more distinct over the pure polymer could be due to the elastic-plastic nature of the region around the tip under load [26]. That difference in the pile-up characteristics between the nanocomposite material and the polymer means that the tailored with carbon nanoparticles HDPE matrix may act on the mechanism of plastic deformation. Wear behavior, as a key property of each one nanocomposite, could be investigated by means of the plasticity index [16], which is an important parameter in the descrying of material lifetime. Extraction of plasticity index from the relevant load-displacement data imposes a subtraction of the creep segment when using the compliance method referring to viscoelastic-plastic material [27]. Calculation of the plasticity index (\(\up\)) of a solid body according the equation, proposed in the paper in question, showed an enhancement in wear resistance of the nanocomposite samples. The values were obtained by taking the ratio between the mathematical area below the indentation loading-unloading curve (corresponding to the plastic work done during the test) and the sum of that area added to the mathematical area situated under the unloading curve referring to the viscoelastic recovery of the material. As expected, the highest reduction in the plasticity index compared to the neat polymer was found for the composition 4 wt%MWCNT/HDPE--0.63 against 0.68. The other two polymer-based compositions--4 wt%GNP/HDPE and 2 wt%GNP2 wt%MWCNT/HDPE--were determined to have plasticity indexes of 0.66 and 0.65, respectively. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Sample** & \begin{tabular}{c} **Contact Depth [nm] at** \\ **100 \(\upmu\)N Peak Load** \\ \end{tabular} & \
\begin{tabular}{c} **Contact Depth [nm] at** \\ **1000 \(\upmu\)N Peak Load** \\ \end{tabular} &
\begin{tabular}{c} **Contact Depth [nm] at** \\ **10,000 \(\upmu\)N Peak Load** \\ \end{tabular} \\ \hline HDPE & 179 \(\pm\) 10 & 662 \(\pm\) 35 & 2411 \(\pm\) 67 \\ \hline
4 wt\%GNP/HDPE & 159 \(\pm\) 19 & 657 \(\pm\) 77 & 2280 \(\pm\) 86 \\ \hline
4 wt\%MWCNT/HDPE & 149 \(\pm\) 22 & 622 \(\pm\) 46 & 2104 \(\pm\) 118 \\ \hline
2 wt\%GNP2 wt\%MWCNT/HDPE & 166 \(\pm\) 23 & 651 \(\pm\) 52 & 2269 \(\pm\) 157 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Average contact depth in the nanocomposite surface as a function of nanoindentation peak load. The relative vicinity of the \(\uppsi\) values could be explained by the high loading rate of 10,000 \(\upmu\)N leading to higher penetration depth and therefore to more expressed elastic-plastic response of the composite material that is partially depending on the interaction polymer chains \(-\) nanofiller in the nanocomposite structure [28].