# Evaluation of Low-Temperature Performance of Recycled
## 3 Results and Discussion
### Flexural-Tensile Strain and Strain Energy Density  
Studies have indicated a direct correlation between asphalt pavement cracks and the flexural-tensile strain of an asphalt mixture [13; 33]. Exceeding the threshold of this strain can lead to low-temperature cracking. Therefore, the flexural-tensile strain serves as an evaluation metric. As shown in Figure 11, the trabecular bending test demonstrates that the flexural-tensile strain of RAMs gradually decreases as the temperature drops. The strain reduction between \(-10\)\({}^{\circ}\)C and \(-20\)\({}^{\circ}\)C is notably greater than that between \(0\)\({}^{\circ}\)C and \(-10\)\({}^{\circ}\)C. This trend is attributed to reduced Brownian motion in asphalt molecules and a decrease in free volume between them as the temperature declines. Consequently, the viscous flow of asphalt mortar increases, causing a decline in flexural-tensile strains [34]. When considering the impact of RAP content on the LTP of RAMs, it is observed that an increase in RAP content at \(-10\)\({}^{\circ}\)C leads to a progressive decrease in the flexural-tensile  
Figure 10: Fracture temperature and transition temperature of asphalt mixture. Figure 9: Fracture strength of asphalt mixture. strain of RAMs. This decrease is due to the diminished capacity of RAMs to absorb energy before failure when RAP is incorporated [35]. Although this reduction weakens the LTP of RAMs, the trend is less pronounced at 0 \({}^{\circ}\)C and \(-\)20 \({}^{\circ}\)C. Furthermore, when comparing the influence of different thermal histories of the RAP content on the LTP of mixtures, it is noted that at 0 \({}^{\circ}\)C and \(-\)10 \({}^{\circ}\)C, when the RAP content is 40%, the flexural-tensile strain of RAMs with THRAP exceeds that of those with UVRAP, indicating superior low-temperature deformation ability at these temperatures. However, as the RAP content increases or the temperature drops to \(-\)20 \({}^{\circ}\)C, the LTP of RAMs with UVRAP is relatively better than that of those with THRAP. Strain energy density is a measure of the amount of strain energy consumed per unit volume at the center bottom of a trabecular specimen during fracture. It accounts for both strength and strain, providing a more accurate assessment of the LTP of RAMs compared to relying solely on failure strength or failure strain [26]. Research has shown that strain energy density closely reflects the actual behavior of asphalt mixtures under low-temperature tensile failure [36]. When an asphalt mixture is damaged, the higher the bending strain energy density is, the better is the LTP of an asphalt mixture. The strain energy density function can be represented by Equation (8), as follows:  
\[\omega_{\text{f}}=\frac{\text{d}\text{w}}{\text{d}\text{v}}=\int_{0}^{\epsilon _{\text{c}}}\sigma(\varepsilon)\text{d}\varepsilon \tag{8}\]  
where \(\omega_{\text{f}}\) is the strain energy density function, that is, the envelope area under the \(\sigma\)-\(\varepsilon\) curve when the stress reaches its peak; \(\sigma(\varepsilon)\) is the function of stress concerning strain; and \(\varepsilon_{\text{c}}\) is the strain corresponding to the maximum stress. By using a cubic polynomial to fit the rising section of the stress-strain curve before the peak, Formula (9) can be utilized to calculate the strain energy density of seven types of asphalt mixtures. \[\omega_{\text{f}}=\frac{\text{d}\text{w}}{\text{d}\text{v}}=\int_{0}^{\epsilon _{\text{c}}}\text{A}\varepsilon^{3}+\text{B}\varepsilon^{2}+\text{C} \varepsilon+\text{D}\text{d}\varepsilon \tag{9}\]  
The strain energy density results in Figure 12 show that with an increase in RAP content, the asphalt mixture becomes less flexible and deformable. The destruction occurs at a lower energy. A comparison of the effects of different thermal histories of RAPs on the LTP of asphalt mixtures reveals that the RAM with 20% THRAP exhibits better low-temperature crack resistance than that with 20% UVRAP. However, as the RAP content further increases, the LTP shows the opposite trend.