# Coupled Thermomechanical Responses of Zirconium Alloy System Claddings under Neutron Irradiation
## 4 Results and Discussion  
### The Thermomechanical Behavior  
The temperature field distribution in \({}^{\circ}\)C of the fuel elements after irradiation for 1200 days is shown in Figure 2, which are pure Zr, N36, Zr-4, and Zr-2.5 Nb-0.5 Cu. The temperature distribution in the radial direction at the middle part of the cladding and the axial direction at the ends of the cladding are presented, respectively. It was observed from the simulation results that the temperature of the inner surface was the highest under irradiation, and that this decreased gradually from the inner to outer surface along the radial direction due to the action of the coolant. The distribution of temperature showed a gradient increasing trend at the end of the cladding in the axial direction. In the simulation, the temperature of the four cladding materials was maintained at 300 to 320 \({}^{\circ}\)C under the action of the coolant, which was consistent with the value and distribution of the cladding temperature of the LWR fuel rod [27]. The distribution of temperature was the same for pure Zr and Zr alloy. The results show that the composition of alloying elements has little effect on the temperature distribution and magnitude of the cladding tube under neutron irradiation. In the present study, the thermomechanical behavior of the cladding was studied under normal operating conditions. In the initial stage, the pressure on the cladding was due to the compressive stress from the outer surface to the inner surface, induced by the coolant pressure (15.5 MPa) and the helium pressure (2 MPa) in the gap. Figure 3 shows the Mises stress field distributions in the MPa of cladding for different alloy systems during stable operation for 1200 days under irradiation conditions; these data can be employed to evaluate the cladding safety. It may be observed from the simulation results that the stress field distribution of the cladding was similar to the temperature field distribution; namely, the stress gradually decreased from the inner to the outer surface of the cladding in the radial direction. The distribution of stress along the radial direction was the same for the four alloys, which is consistent with the SiC/SiC composite cladding at the end of its life [28]. The stress was related to the temperature of the cladding produced by fuel burnup. Therefore, the gradient distribution of stress along the radial direction was shown to be independent of the alloys of cladding materials. However, the axial stress distribution of the cladding was found to be dependent on the alloy element. In the pure Zr and Zr-4 alloy, the stress level was low at the end. The stress gradually increased from the end to center, along the axial direction, as shown in Figure 3a,c. The maximum magnitudes of both pure Zr and Zr-4 alloys were about 30.2 MPa on the 1200 th day. In contrast, the stress was high at the end for the N36 alloy. The stress distribution of the N36 alloy showed that the stress decreased from the end to the center along the axial direction, as shown in Figure 3b. Uniform stress distribution was observed along the axial direction for the Zr-2.5 Nb-0.5 Cu alloy, as shown in Figure 3d. The \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Density** & **Temperature** & **Neutron Injection** & **Young’s Modulus** & **Thermal Conductivity** & **Poisson’s** & **Specific Heat Capacity** \\
**g/cm\({}^{3}\)** & \({}^{\circ}\)C** & **Quantiy n/mm\({}^{2}\)** & **GPa** & **W/ (m\({}^{\circ}\)C)** & **Ratio** & **J/(kg\({}^{\circ}\)C)** \\ \hline
6.49 & 100 & 224 & 95 & 7.46 & 0.3 & 283 \\ - & 200 & 899 & 89 & 11.17 & - & 314 \\ - & 300 & 3376 & 83 & 12.68 & - & 333 \\ - & 400 & 1,746,000 & 77 & 14.03 & - & 345 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: N36 alloy parameters of fuel rod cladding.