# Coupled Thermomechanical Responses of Zirconium Alloy System Claddings under Neutron Irradiation
## 4 Results and Discussion
### The Change of Gap Distance  
The displacement fields, in mm distribution of cladding, of different alloy systems irradiated under stable operation for 1200 days, are shown in Figure 4. The results show that the displacement field of the four cladding materials presented a gradient distribution along the radial direction. It was found that the outer surface of the cladding had a large displacement deformation due to the irradiation of pure Zr, N36, and Zr -2.5 Nb-0.5 Cu alloys. In contrast, a large displacement deformation was observed on the inner surface for the Zr-4 alloy, as shown in Figure 4c. The change of the displacement deformation was affected by the alloy system due to thermal expansion and irradiation-induced growth. Normally, there is no contact between the inner surface of the cladding and the outer surface of the fuel pellet for safety reasons; however, this may occur due to displacement deformation along radial direction. There is typically a gap between pellet and cladding (i.e., the difference between the radial distance on the inner surface of the cladding and the radial distance on the outer surface of the pellet). In order to study the change of gap distance between the pellet and the cladding, the radial distance between the outer surface of the pellet and the inner surface of the cladding is also an important index. The radial distances of cladding and pellet are presented in Figure 5. It was shown that the radial distance increased with running time. At the beginning of the simulation, the radial distance of the fuel increased rapidly, which was ascribed to the heating and expansion of the fuel. The gap distance gradually decreased due to irradiation growth from the simulation results. The initiation of Pellet Cladding Mechanical Interaction (PCMI) can take place at the end due to burnups of pellets, which will induce additional cladding growth from pellet expansion [29]. The change rule of the gap is consistent with the reactor behavior of PWR SiC cladding fuel rods [30]. This is mainly due to the rapid increase of the local thickness of the pellet under irradiation. As the irradiation time increases, the gas distance decreases, which leads to a  
Figure 3: Stress field of different Zr alloy systems irradiated for 1200 days (unit: MPa). fuel elements. The thermal mechanical coupling behavior of different system alloys under irradiation was simulated and calculated. The distribution and evolution laws of temperature field, displacement field, and stress field were analyzed:  
1. The temperature field and stress field of the fuel element decreased gradually from the center to the surface along the radial direction, and the maximum value appeared in the core of the pellet. 2. The results show that the distribution of the displacement field along the radial direction increased gradually from the center to the outer surface. The increase of the displacement of the outer surface of the pellet was due to the increase of the local thickness, which was due to the irradiation effect. 3. Different alloy systems did not affect the distribution of the temperature field, displacement field, or stress field of the UO\({}_{2}\)/Zr fuel element under irradiation. The values of temperature, displacement, and stress change with the change of alloy system. The displacement and stress fields were more sensitive to the alloy system; that is, the macroscopic mechanical properties of the fuel element under irradiation were shown to be sensitive to alloy elements. Conceptualization, L.W. and B.S. ; data curation, H.Z. and C.Y. ; formal analysis, D.G. and R.P. ; funding acquisition, L.W. and B.S. ; investigation, H.Z. and C.Y. ; methodology, J.M., J.Q. and H.Z. ; project administration, B.S. ; software, H.Z. ; supervision, B.S. and L.W. ; validation, H.Z. and C.Y. ; visualization, R.P., J.Q. and J.M. ; writing--original draft, C.Y. and H.Z. ; writing--review & editing, C.Y., H.Z. and B.S. All authors have read and agreed to the published version of the manuscript.