## 3 Results and Discussion
### Fracture Toughness  
Figures 3-5 illustrate the average values of \(\mathrm{K_{ic}}\) and \(\mathrm{G_{ic}}\) for specimens with CNTs and Carbon Black, as well as the Ternary systems for all of the studied dispersion conditions. As can be observed, a general increase in the fracture toughness (\(\mathrm{K_{ic}}\)) took place for all the systems (binary and ternary). Specifically, \(\mathrm{G_{ic}}\) increased for the binary systems with CNTs and the ternary systems. However, it remained unaffected within experimental error for the binary systems modified with CB. Figure 3: \(\mathrm{K_{ic}}\) and \(\mathrm{G_{ic}}\) mean values for specimens with CNTs. In more detail, the \(\rm K_{ic}\) for the systems with 0.1 wt. % CNTs increased by almost 40% after three hours of dispersion when compared with the neat system, while further dispersion for one more hour led to a deterioration of the average \(\rm K_{ic}\) values by ca. 15% for the CNTs0.1-III specimens. This phenomenon can be attributed to the achievement of a threshold at the dispersion duration after which no further improvement can be observed. After the third hour, the agglomerates were eliminated at such an extent that their size could not prevent crack propagation. Similar behavior was exhibited by the specimens with 0.3 wt. % CNTs, which led to a more pronounced increase by 53% after the third hour of dispersion when compared to the neat systems. Conversely, for the specimens with 0.5 wt. % CNTs, only one hour of dispersion was sufficient to cause an almost 34% improvement in \(\rm K_{ic}\) while further dispersion led to even lower \(\rm K_{ic}\) values. In terms of \(\rm G_{ic}\) values, all systems with CNTs had the same behavior with the \(\rm K_{ic}\) values except for CNTs0.1-I, which presented an increase of 142% from the first hour of dispersion. This notable improvement can be attributed to the large scale of agglomerates, which can increase the energy required until the fracture of the specimens. However, for all the CNT modified specimens, the fourth hour of dispersion resulted in a degradation of the \(\rm G_{ic}\) values compared to the neat specimens. In the case of the binary systems with CB, a total increase of the \(\rm K_{ic}\) values was observed as the percentage of the filler and the dispersion duration increased (Figure 4). However, when each CB content was examined separately, only small differences in the average \(\rm K_{ic}\) values were observed with increasing duration of dispersion, possibly due to the characteristics of the CB. Therefore, no correlation with the dispersion duration was observed for the CB specimens inversely to the case of the CNT modified systems. Furthermore, an amount of 0.5 wt. % CB was found to cause a small  
Figure 4: \(\rm K_{ic}\) and \(\rm G_{ic}\) mean values for specimens with CB. Figure 5: \(\rm K_{ic}\) and \(\rm G_{ic}\) mean values for ternary specimens. decrease in the average G\({}_{\rm ic}\) values, while higher CB percentages (1 or 2 wt. %) led to only insignificant increments in the mean G\({}_{\rm ic}\) values in comparison to the neat system. Figure 5 presents the mean values of K\({}_{\rm ic}\) and G\({}_{\rm ic}\) for the ternary systems. As can be observed, all the ternary systems exhibited a total increase of K\({}_{\rm ic}\) when compared with the neat systems. The average K\({}_{\rm ic}\) values increased by 40% after four hours of dispersion for the CNTs0.5_CB1 specimens, while a more pronounced enhancement of about 81% was exhibited by the CNTs0.5_CB2 specimens in comparison to the neat specimens. The combination of the two fillers, which possess nano and micro dimensions, respectively, created a synergetic effect which is capable of hindering crack propagation and producing crack bifurcation phenomena. Moreover, the average G\({}_{\rm ic}\) values of the CNTs0.5_CB1 were not affected in comparison to the neat specimens. However, a significant improvement by about 65% was observed for the CNTs0.5_CB2-III and the CNTs0.5_CB2-IV systems when compared to the neat specimens.