## 3 Results and Discussion  
### Quasi-Static Nanoinindentation  
The mathematical calculations of the received experimental data were performed by the aid of the instrumental software as their essence rests on the analysis of the unloading part of the indentation load vs. indentation depth curve by using the Oliver and Pharr method [21], thoroughly depicted in a preceding article [22]. The nanoindentation experiments have shown better mechanical properties as nanohardness and reduced modulus of elasticity of the composite samples compared to the pure HDPE, regardless of the exerted peak load (see Figures 1 and 2). Each one symbol in the figures is a mean value corresponding to successful completion of at least 49 indentations laid down in the experimental grid. The standard deviation of the measured parameters has been added in the graph, though the presented average values are based on indentation curves picked up from optically selected surface areas with high flatness, as confirmed by the _in-situ_ SPM imaging (see Figure 3). Moreover, the estimation of the test data was made after careful removal of the wrong nanoindentation curves impeding the precise formulation of the results. No matter of the applied peak force, the composite filled with MWCNTs demonstrated best nanohardness, while the values of the neat HDPE were at the bottom. These results suggest good dispersion of the carbon nanotubes in the polymer matrix, leading to improved mechanical behavior. Similar finding has been reported in another article dealing with HDPE-based materials reinforced with a relatively low content of carbon nanofillers [6]. A glance into the dependence of nanocomposite mechanical parameters on the indentation load, plotted in Figures 1 and 2, prompts for a presence of size effects that become more noticeable when going deeper in the polymer material [23] reaching to the elastic zone, where these effects, being elastic in nature, are mostly set down by the complex molecular structure of the semi-crystalline polyethylene matrix [24]. As expected, an increase in contact depth with increment of the applied indentation force was observed as regards all tested nanocomposite samples (Table 2). Except the fact that the penetration of the probe is higher in the pure HDPE at every exerted maximum load, the impact of the carbon nanof fillers on the composites' mechanical response is more distinguishable when the peak force is set to 100 \(\upmu\)N by receiving values that are more sensible to the plastic behavior of the materials coming from the top layer of the samples. The effect of the hybrid nanocomposite structure on the determined mechanical properties of the composite samples is shown in Fig. 1.  
Figure 1: Nanohardness of the nanocomposite samples, including pure HDPE as a reference, measured at three different peak loads—100 \(\upmu\)N, 1000 \(\upmu\)N, and 10,000 \(\upmu\)N.  
Figure 2: Reduced modulus of elasticity of the nanocomposite samples, including pure HDPE as a reference, measured at three different peak loads—100 \(\upmu\)N, 1000 \(\upmu\)N, and 10,000 \(\upmu\)N.  
parameters is more visible at peak loads of 1000 \(\upmu\)N and 10,000 \(\upmu\)N, though in most of the experimental data, the bifiller composition has fainter nanomechanical behavior than the polymer composite filled with 4 wt% MWCNTs. This could be due to several factors as worst nanoparticles distribution in the specimen 2 wt%GNP2 wt%MWCNT/HDPE and the superior role of carbon nanotubes with respect to the input of higher hardness in the composite matrix [25]. Regardless the contrasting contact depths at 10,000 \(\upmu\)N the calculated mechanical parameters are in relatively tight range meaning that there is a presence of more combined elastic-plastic deformation influencing the measurement of hardness and reduced modulus of elasticity.