## 5 Conclusions  
* The fracture resistance, fracture trajectory and fracture surface of the asphalt samples were investigated under different mode mixities and testing conditions using different test samples and configurations.
* The fracture resistance values (i.e., critical stress intensity factors, K\({}_{\text{Hf}}\), K\({}_{\text{Hf}}\) and K\({}_{\text{IIIf}}\)) were dependent to the shape of test sample, applied loading type, loading mode, and temperature. Generally, the fracture resistance was decreased by increasing the test temperature and changing the loading mode from tensile type to shear type.
* The heterogeneity of the asphalt mixture and location of the coarse aggregates in the route of fracture propagation along the ligament can noticeably affect the trajectory of fracture. The fracture path shows more deviations relative to the path observed for a model brittle and isotropic material, when the coarser aggregates are located in front of the trajectory of propagating crack. Indeed, the crack tends to round the aggregates in most of the cases and propagate through the softer mastic part or the interface of aggregate/mastic.
* Increasing the temperature can result in more deviation in the fracture trajectory because of the reduction in the stiffness of mastic and bitumen relative to the aggregate and tendency of the crack to not grow through the aggregates by rounding them.  
\begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline \multirow{2}{*}{**Specimen**} & \multirow{2}{*}{**Fracture Path Location**} & \multicolumn{3}{c}{**Mode-I**} & \multicolumn{3}{c}{**Mode-II or Mixed**} & \multicolumn{3}{c}{**Mode-III or Mixed**} \\ \cline{3-8}  & & & & & **Mode I/II** & \multicolumn{3}{c}{**Mode I/III**} \\ \cline{3-8}  & & **Low** & **Medium** & **Low** & **Medium** & **Low** & **Medium** \\  & & **Temp** & **Temp** & **Temp** & **Temp** & **Temp** & **Temp** \\ \hline \multirow{3}{*}{SCB} & mastic & 60 & 80 & 75 & 90 & - & - \\  & aggregates & 30 & 12 & 5 & 0 & - & - \\  & interface of aggregate/mastic & 10 & 8 & 20 & 10 & - & - \\  & mastic & 70 & 85 & - & - & 90 & 95 \\ ENDB & aggregates & 15 & 10 & - & - & 5 & 0 \\  & interface of aggregate/mastic & 15 & 5 & - & - & 5 & 5 \\  & mastic & 70 & 90 & 85 & 90 & - & - \\ BD & aggregates & 20 & 5 & 10 & 2 & - & - \\  & interface of aggregate/mastic & 10 & 5 & 5 & 8 & - & - \\  & mastic & 65 & 90 & 90 & 93 & - & - \\ SENB & aggregates & 15 & 2 & 5 & 2 & - & - \\  & interface of aggregate/mastic & 20 & 8 & 5 & 5 & - & - \\ \hline \hline \end{tabular}
\end{table}
Table 6: Contribution of aggregate, mastic and interface of aggregate/mastic on the fracture path of tested asphalt concrete materials under different mode mixities and temperatures.  
Figure 12: Comparison of fracture surface roughness after mode III failure obtained from (**a**) asphalt concrete and (**b**) Polymethylmethacrylate.  
Observation of fracture surface for all mode mixities revealed that a significant part of the fracture surface (i.e., greater than 80% of the fracture surface) propagates through the mastic and interface of aggregates/mastic. This percentage increases with increasing the test temperature or adding the contribution of mode II or mode III in the process of asphalt cracking.  
Conceptualization, L.L. and M.R.M.A.; methodology, M.R.M.A.; validation, H.R.K. and J.H.; formal analysis, J.H., L.L. and H.R.K.; investigation, L.L., H.Y. and H.R.K.; writing--original draft preparation, M.R.M.A.; writing--review and editing, M.R.M.A.; visualization, H.R.K. and H.Y.; supervision, M.R.M.A. and L.L. All authors have read and agreed to the published version of the manuscript.  
This research received no external funding.  
This study did not involve tests on humans or animals.  
Informed Consent Statement: Informed consent was obtained from all subjects involved in the study.  
The data presented in this study are available on request from the corresponding author.  
The authors declare no conflict of interest.