## 3 Results and Discussion
### Tensile Properties  
The mechanical properties of the compounds used in FFF are of vital importance [11; 12; 77]. Sufficient strength and flexibility are required to spool and de-spool the filament for its production and for printing. Moreover, the filaments must be stiff enough to avoid buckling during printing. Furthermore, high strength and stiffness are also required in the PIM process for the de-molding and handling of the parts [78]. Therefore, tensile tests were conducted on filaments produced with all the evaluated compounds. This method enables a rapid screening and comparison of similar materials processed under the same conditions [12; 46]. Figure 7 shows representative strain-stress curves of filaments of the materials evaluated, together with the average ultimate tensile strength (_UITS_) and the corresponding average strain value (\(\varepsilon_{UITS}\)). The secant modulus (\(E_{S}\)) was calculated in the strain range between 0.1% and 0.3% in order to avoid the initial stage of the test, in which the slight curvature of the specimens (due to the processing and handling of the filaments) could influence the results. Table 6 summarizes the average and standard deviation values for the three parameters. Figure 6: Viscoelastic properties as a function of angular frequency measured in parallel plate rotational rheometer at 160 \({}^{\circ}\)C for HDPE00, HDPE30, AAHDPE00 and AAHDPE30: (**a**) Complex viscosity, (**b**) Storage modulus and (**c**) Loss factor. Lines are included to facilitate the visualization of the results. Even though the flowability of the unfilled polyethylene was the only parameter employed to select the two types of high density polyethylene (see Section 2.2), no significant differences existed in the _UTS_ and _E\({}_{S}\)_ of HDPE00 and AAHDPE00 (Table 6). In fact, the _\(\varepsilon_{UTS}\)_ was the only parameter significantly different between HDPE00 and AAHDPE00 (Figure 7) with the non-grafted polymer having a significantly larger value. The incorporation of the particles should result in an increase in the strength and stiffness of the composites [21, 22, 23, 27, 74]. This behavior is observed for AAHDPE30 with an increase of 18% in _UTS_ and 98% in _E\({}_{S}\)_ with respect to the values of AAHDPE00 (Table 6). In the case of HDPE30, the _E\({}_{S}\)_ is 137% higher than the values of HDPE00, whereas no significant difference in the _UTS_ was found between HDPE00 and HDPE30 (Table 6). The presence of the zirconia particle results in a decrease in the _\(\varepsilon_{UTS}\)_ of 91% in HDPE30 compared to HDPE00 and of 46% in AAHDPE30 compared to AAHDPE00 (Table 6). The decrease in the _\(\varepsilon_{UTS}\)_ is produced by the restriction of movement of the polymer by the rigid particles which do not elongate, resulting in a reduction in the ductility of the material [21, 22, 23, 27, 74]. When comparing the properties of the nanocomposites, the _E\({}_{S}\)_ of HDPE30 is significantly higher than that of AAHDPE30 (Table 6). The secant modulus, calculated in the strain range from 0.1% to 0.3%, is highly dependent on the polymer structure and factors such as the crystallinity. In order to determine the crystallinity, Differential Scanning Calorimetry (DSC) tests were conducted on five samples of each material. The crystallinity of HDPE00 is 76.21% \(\pm\) 2.16% and increases to 77.65% \(\pm\) 0.31% for HDPE30. For AAHDPE00 the crystallinity is 63.42% \(\pm\) 1.52% and decreases to 57.92% \(\pm\) 0.85% for AAHDPE30. In polymer nanocomposites with a semicrystalline polymeric matrix, the nanoparticle surface can act as a heterogeneous nucleating site [14]. Smaller nanoparticles are less able to act as nucleating agents than larger fillers [14, 79]. Additionally, the improvement of the dispersion of adhesion reduces the mobility of the crystallisable chain segments [68, 80]. Therefore, the high dispersion and adhesion to the zirconia results in a lower crystallinity of the matrix in AAHDPE30 than in HDPE30 and consequently in a lower secant modulus [80].