## 4 Results and Discussion
### Fracture Pattern and Load-Displacement Curves
The information in Figure 11 shows the normalized fracture toughness ratio (\(\text{K}_{\text{lc}}/\text{K}_{\text{lc}\ (\text{SCB})}\)) for the tested samples. This figure reveals that the ENDB and SENB test samples can also provide nearly the same fracture toughness results as obtained by the standard SCB testing method. However, the ENDC test shows an underestimated evaluation for the resistance of asphalt mixture materials against cracking compared to the standard SCB mode I test method. The influence of test temperature on the measured \(\text{K}_{\text{lc}}\) value is illustrated and compared in Figure 12a. According to this figure, which shows the variations of \(\text{K}_{\text{lc}}\) versus temperature, the mode I fracture toughness value is enhanced by reducing the test temperature. By decreasing the test temperature from \(-5\ ^{\circ}\text{C}\) to \(-25\ ^{\circ}\text{C}\), in all specimens  
Figure 10: Comparison of fracture toughness data obtained from different mode I testing methods. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Researcher** & **Temperature (\({}^{\circ}\)C)** & **Specimen** & **Asphal Type** &
\begin{tabular}{c} **Fracture** \\ **Toughness (MPa\(\surd\)m)** \\ \end{tabular} \\ \hline [PERSON] et al. [4] & \(-15\) & SCB & HMA & 0.8 \\ \hline [PERSON] et al. [12] & \(-18\) & SENB & HMA & 0.52 and 0.61 \\ \hline [PERSON] et al. [32] & \(-15\) & ENDB & HMA & 0.67 \\ \cline{2-5}  & \(-15\) & ENDC & HMA & 0.54 \\ \hline [PERSON] and [PERSON] [36] & \(-5\) & ENDB & HMA & 0.67 \\ \cline{2-5}  & \(-20\) & ENDB & HMA & 0.78 \\ \hline [PERSON] et al. [37] & \(-15\) & ENDB & HMA & 0.86 \\ \hline [PERSON] et al. [62] & \(-15\) & ENDB & HMA & 0.95 \\ \cline{2-5}  & \(-15\) & SCB & HMA & 0.75 \\ \cline{2-5}  & \(-25\) & ENDB & HMA & 1.05 \\ \cline{2-5}  & \(-25\) & SCB & HMA & 0.83 \\ \hline [PERSON] et al. [66] & \(-20\) & ENDC & HMA & 0.65 \\ \cline{2-5}  & \(-20\) & ENDB & HMA & 0.75 \\ \hline [PERSON] [67] & \(0\) & SCB & \multirow{2}{*}{Dense Graded Asphalt} & 0.88 \\ \cline{2-5}  & \(-10\) & SCB & & 0.98 \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Mode I fracture toughness values obtained by different researchers. the K\({}_{\text{lc}}\) values increases by approximately 40%. As a viscoelastic material, the asphalt binder becomes stiffer by reducing the temperature. The stiffness of a bituminous material increases due to the reduction of temperature up to the lower performance grade temperature of bitumen. According to the literature, the stress intensity factor increases by increasing the stiffness or elastic modulus of bitumen [27; 28; 68] and consequently such behavior can result in the increase of stiffness of the HMA mixture as well. Hence, due to the stiffer HMA mixture at \(-25\)\({}^{\circ}\)C compared to \(-5\)\({}^{\circ}\)C, the enhancement of the low-temperature crack growth resistance for asphalt mixtures is expected. Such trends observed for the variations of fracture toughness with the temperature are also reported in other published papers [6; 15; 38]. The fracture toughness ratio at two testing temperatures (i.e., (K\({}_{\text{lc}}\)(\(\theta\)\(-25\)\({}^{\circ}\)C)/K\({}_{\text{lc}}\)(\(\theta\)\(-5\)\({}^{\circ}\)C)) are also shown in Figure 12b. This figure demonstrates that a simple shift occurs in the low temperature cracking resistance of the asphalt mixtures by changing the temperature. Indeed, the (K\({}_{\text{lc}}\)(\(\theta\)\(-25\)\({}^{\circ}\)C)/K\({}_{\text{lc}}\)(\(\theta\)\(-5\)\({}^{\circ}\)C)) ratio changes in a narrow range for the tested geometries and specimens and it can be concluded that the (K\({}_{\text{lc}}\)(\(\theta\)\(-25\)\({}^{\circ}\)C)/K\({}_{\text{lc}}\)(\(\theta\)\(-5\)\({}^{\circ}\)C)) ratio is approximately equal to 1.4 as shown in Figure 12b. Figure 11: Normalized mode I fracture toughness ratio (K\({}_{\text{lc}}\)/K\({}_{\text{lc}}\)(SCB)) for the tested samples.