## 1 Introduction  
Recently, the use of polymer-based nanocomposites in the research activities of the scientific community all over the world is widespread because of the common striving to produce a new class of high-quality multifunctional materials that would be able to replace the conventional ones [1]. High-density polyethylene (HDPE) is one of the promising semi-crystalline thermoplastic polymers in the field, standing out with its notable physical and mechanical properties [2; 3; 4; 5]. Though some aspects of its nanomechanical characterization have already been referred [6], the detailed study of important nanosurface properties as indentation size effect, nanoharness, and reduced modulus of elasticity, as well as the nanoscratch behavior of HDPE-based composite materials, has yet to be done. The inclusion of inorganic nanofillers with high mechanical strength in thermoplastic polymer die hasbeen investigated in terms of enhancement of the nanocomposite mechanical parameters by applying depth-sensing indentation technique [7] and, thereafter, an attempt to correlate the mechanical properties with the structural characterization of the composite material has been reported [8]. The resulting modified polymer samples have shown improved values of hardness and modulus of elasticity, but there has to be noted that these studies are constrained mainly over the quasi-static and dynamic nanoindentation behavior of HDPE-based specimens. Using a polyethylene matrix offers many advantages, such as low-cost processing and low energy consumption, that make it favorable for different applications, especially in electronic packaging [9] due to the matching of good mechanical and thermal properties [10; 11]. In the last few years, graphene nanoplatelets and carbon nanotubes have rather barely been applied as carbon nanofillers in HDPE matrix in spite of their potentially positive effect on the nanocomposite mechanical, thermal, and electrical performance. However, [PERSON] et al. [6] have made a nanomechanical examination of carbon nanocomposite samples with hybrid structure based on HDPE and produced using the injection-molding method. Though the authors have picked a low level of nanofiller loading of 0.1 wt%, they established a significant increase of the hardness at the hybrid composite sample combining GNPs and nanodiamonds in the polymer die. In addition to the inclusion in nanocomposite systems, HDPE has also been subjected to nanomechanical testing as a part of incompatible polymer blends [12]. As outcome, there has been suggested a correlation between the interfacial and mechanical properties of the polymer mixture. The sophisticated hierarchical structure of high-density polyethylene, consisting of both crystalline and amorphous phases [13], has an impact on its nanomechanical surface behavior that could be modified in positive sense by adding carbon nanoparticles as reinforcement. [PERSON] et al. [14] observed an increment in nanohardness and elastic modulus of about 10% as a result of the addition of MWCNTs in HDPE die. In general, up to now, the nanoindentation research on HDPE-based materials has been predominantly centered on nanocomposites incorporated with carbon nanotubes [15] or nitride types of nanofillers [7; 16], and to find a study dealing with a hybrid carbon structure in a polyethylene matrix is rather a rareness. In the present article, it was made an attempt to explore the elastic-plastic response of polymer nanocomposite samples by applying a quasi-static nanoindentation method with setting of three separate peak forces in the trapezoid load function. For achieve a better understanding of the wear properties of the new material, it was performed an experimental approach consisting of estimation of COF through nanoscatch testing of the specimens' surface. Assessment of the pile-up formed by the lateral displacement of the indenter disclosed the impact of the carbon nanofillers on the mechanical behavior of the composite materials.