## 4 Results and Discussion  
### Fracture Pattern and Load-Displacement Curves  
Figure 7 shows the samples of broken ENDB, SCB, SENB and ENDC specimens fracture under mode I. It is seen that in all samples the fracture trajectory is straight without significant kinking, which extends throughout both aggregates and mastic or fine aggregate mastic. This reveals that all investigated test samples are symmetrically broken into two halves after fracturing. Comparison of the fracture trajectories of ENDB and ENDC samples that have the exact same geometry (or shape) but loaded in two different manners (i.e., bending and compression) showed that the fracturing of both samples is similar and the loading type has no effect on the fracture trajectory. However, the load bearing capacity and fracture load of the tested samples were different and this shows the effect of geometry and loading type on the fracture behavior of the asphalt mixtures. Some typical load-displacement curves obtained for the tested specimens are shown in Figure 8. From these curves it can be concluded that the low temperature fracture behavior of the tested asphalt mixture is linear and brittle and, after the peak load, a sudden drop in the loading curve is observed. The ENDC and SENB samples presented the highest and lowest fracture loads, respectively. In Table 3, the fracture loads (i.e., the maximum load values) obtained from different replicates are presented for the tested ENDB, SCB, SENB and ENDC samples at two low temperatures. the experiments into Equations (1)-(4), the corresponding values of K\({}_{\text{lc}}\) were determined. The required geometry factors (Y\({}_{\text{I}}\)) for using these equations are also presented in Table 4 for the tested conditions (determined from numerical analyses). Figure 9 presents the mode I fracture resistance (or K\({}_{\text{lc}}\)) value of the tested HMA material at \(-25\)\({}^{\circ}\)C and \(-5\)\({}^{\circ}\)C.  
The fracture toughness value obtained using the ENDB and SCB specimens varies in the range between 0.87 and 1.13 MPa\(\surd\)m and 0.89 to 1.06 MPa\(\surd\)m with an average value of 1.05 MPa\(\surd\)m and 0.99 MPa\(\surd\)m, respectively. The minimum and maximum band for the mode I fracture toughness obtained from the SENB specimen varies from 0.83 to 1.0 MPa\(\surd\)m with an average value of 0.93 MPa\(\surd\)m. Similarly, from the tests conducted at \(-5\)\({}^{\circ}\)C, the fracture toughness value obtained using the ENDB and SCB specimens varies \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Specimen** & **Dimentions** & **Test Condition** & **Mode I Geometry Factor** \\ \hline \multirow{2}{*}{ENDB} & R = 50 mm & S/R = 0.9 & \multirow{2}{*}{Y\({}_{\text{I}}\) = 1.25} \\  & t = 30 mm & a/t =0.4 & \\ \hline \multirow{2}{*}{SCB} & R = 50 mm & S/R = 0.66 & \multirow{2}{*}{Y\({}_{\text{I}}\) = 4.0} \\  & t = 30 mm & a/R = 0.33 & \\ \hline \multirow{2}{*}{SENB} & L = 400 mm & \multirow{2}{*}{S/L = 0.9} & \multirow{2}{*}{Y\({}_{\text{I}}\) = 0.79} \\  & W = 50 mm & & & \\ \hline \multirow{2}{*}{ENDC} & R = 50 mm & \multirow{2}{*}{\(\beta\) = 0\({}^{\circ}\)} & \multirow{2}{*}{Y\({}_{\text{I}}\) = 0.65} \\  & t = 30 mm & & & \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Corresponding values of geometry factor (Y\({}_{\text{I}}\)) for the investigated test specimens. Figure 8: Typical load-displacement curves of the tested ENDB, SCB, SENB and ENDC specimens at \(-25\)\({}^{\circ}\)C.