## 3 Results and Discussion
### Pre-Peak Strain Energy Density  
Table 6 and Figures 9 and 10 show the pre-peak strain energy density results versus test temperature for AC-13 and SMA-13 under different degrees of aging. As shown in Figures 9 and 10, at the same test temperature, the strain energy density of AC-13 and SMA-13 both increase after short-term aging and gradually decay as the aging degree deepens into long-term aging. The reason for this phenomenon may be as follows: after thermo-oxidative aging, the content of the carbonyl group, carbonyl group, sulfoxide group, and aromatic group increases to some degree. During short-term aging, the content of the former two groups, which are beneficial for boosting the association between molecules, jumps with a greater degree so that the toughness of the overall structure of the asphalt mixture is enhanced, and more energy is required for cracking [41]. In comparison, the growth of the aromatic group, which has a high rigidity, dominates in the long-term aging process. The results may reduce the toughness of the overall structure of the asphalt mixture and the energy required for cracking under external loads. Specifically, for AC-13,  
the pre-peak strain energy density under short-term aging ascends by 2% (10 \({}^{\circ}\)C), 14% (20 \({}^{\circ}\)C), 17% (30 \({}^{\circ}\)C) and 35% (40 \({}^{\circ}\)C). When the degree of aging extends to LTOA2d, there is a descent in the pre-peak strain energy density by 10% (10 \({}^{\circ}\)C and 40 \({}^{\circ}\)C), 16% (20 \({}^{\circ}\)C) and 19% (30 \({}^{\circ}\)C). However, when the degree of aging extends further, the tendency to decrease slows down and becomes steadier, with a decrease rate of 11% (10 \({}^{\circ}\)C), 13% (20 \({}^{\circ}\)C and 30 \({}^{\circ}\)C) and 20% (40 \({}^{\circ}\)C). Likewise, for SMA-13, the pre-peak strain energy density under short-term aging ascends by 35% (10 \({}^{\circ}\)C), 60% (20 \({}^{\circ}\)C) and 39% (30 \({}^{\circ}\)C) and 62% (40 \({}^{\circ}\)C). When the degree of aging extends to LTOA2d, there is a violent descent in the pre-peak strain energy density, by 11% (10 \({}^{\circ}\)C and 20 \({}^{\circ}\)C) 21% (30 \({}^{\circ}\)C) and 34% (40 \({}^{\circ}\)C). With the continuous deepening of the degree of aging, the decrease trend becomes steadier by a decrease rate of only 8.5%. Figure 10: Pre-peak strain energy density versus test temperature for SMA-13 under different degrees of aging. Figure 9: Pre-peak strain energy density versus test temperature for AC-13 under different degrees of aging. For asphalt mixtures with the same aging duration, the pre-peak strain energy density of AC-13 and SMA-13 slightly increases as the test temperature rises from 10 \({}^{\circ}\)C to 20 \({}^{\circ}\)C, while it descends as the test temperature continues to rise to 40 \({}^{\circ}\)C. The reason for this phenomenon may be that the increase in temperature can increase the amplitude of molecular motion, and thus cause a corresponding increase in the heat energy, which activates the rotation of the segment around the main chain axis and exhibits a crimped and stretched conformation [26]. Thus, more energy is required to fracture the overall macrostructure of the asphalt mixture. Furthermore, asphalt mixture exhibits a leather state in the temperature range of 20-40 \({}^{\circ}\)C, in which there is a mutual slide between molecules, and the slip becomes more intense with the increase in temperature [33]. Therefore, the energy required to break the interaction between molecular chains eventually drops. As the test temperature rises from 10 \({}^{\circ}\)C to 20 \({}^{\circ}\)C, the pre-strain energy density of AC-13 grows slightly by 4% (UA), 17% (STOA), 12% (LTOA2d), 6% (LTOA5d) and 3% (LTOA8d).