## 4 Results and Discussion
### Fracture Trajectory Results
#### 4.2.2 Mixed Mode Fracture Trajectory  
As expected, the trajectory of the asphalt fracture under mixed mode loading is not self-similar and a curved in-plane and out-of-plane fracture path is often seen for the tested mixed mode I/II and I/III, respectively. Figure 9 presents some of the observed fracture paths for the mixed mode I/II of the tested asphalt specimens. Again, according to this figure, the propagating curve crack may alter its route to round the coarse aggregates located in front of the crack. The fracture trajectory deviation depends on the mode mixity, distribution of aggregates and also the test temperature. Compared to the mode I case, mixed mode I/II fracture grows mostly through the interface and soft mastic parts and the propagating crack rarely breaks the aggregates. Figure 8: (**a**) Fracture surface of broken asphalt samples under mode I loading; (**b**) the fraction of different cracking mechanisms observed by the image processing for the tested mixtures. Figure 9: \(Cont.\)Figure 10 compares the fracture trajectories of investigated asphalt samples with a brittle homogenous material (e.g., PMMA) for mixed mode I/II. Different manners are seen for the fracture trajectory of mixed mode as seen from this figure. The heterogeneity of the asphalt mixture can affect the fracture initiation direction and even concavity or convexity of the fracture path and indeed, depending on the distribution of aggregates, the interface fracture (or rounding the aggregates) is the preferred trajectory for propagation of crack under mixed mode I/II. The difference between the fracture paths of isotropic PMMA material and heterogeneous visco-elastic asphalt material becomes more at higher temperatures and mixtures containing greater amount of large size aggregates in the ligament of tested samples. Similar to the mode I case, the fracture surface observed for the mixed mode I/II shows a rough surface passing mainly through the soft mastic and boundary of aggregates (or interface of aggregate/mastic). Observation of fracture surface under mixed mode loading indicates that more than 85% of the fracture path grows through the mastic or interface of aggregate/mastic. The roughness of fracture surface in the heterogeneous asphalt mixture is also greater than the surface of isotropic material with the same mode mixity. Figure 9: Fracture trajectories observed for mixed mode I/II in different asphalt test samples. The mode III and mixed mode I/III fracture grows in a twisted manner and out-of the plane of the initial crack. Figure 11 shows the mode III fracture trajectory observed for the ENDB specimen made of asphalt mixture for low and medium temperatures. Close observation of the mixed mode I/III and mode III fracture surface reveals that by contributing the mode III component on the fracture behavior of the heterogeneous asphalt mixture, the fracture grows mainly through the interface of aggregate/mastic or the mastic part. In other words, the coarse aggregates are rarely broken during the propagation of mode III fracture. This can be attributed to the lower resistance of the binder and soft mastic against the tear type deformation compared to its tensile resistance. In addition, the roughness of the fracture surface made of the asphalt samples is greater than the isotropic PMMA material tested under mode III as compared in Figure 12. The fracture tends to round the aggregates instead of breaking the aggregates and this behavior is more pronounced for the intermediate temperature condition. As a conclusion, the influence of some affecting parameters such as heterogeneity, loading mode and temperature was investigated in this research for identifying the fracture mechanism of the propagating crack in the ligament of the asphalt concrete composites. Table 6 compares and summarizes the percentages and contribution of the passing fracture path through different locations (aggregates, mastic or interface of aggregate/mastic) for different test specimens, fracture modes and test temperatures.