# Coupled Thermomechanical Responses of Zirconium Alloy System Claddings under Neutron Irradiation
## 1 Introduction  
With sources of fossil fuels becoming increasingly exhausted and the environmental challenges associated with their use, efficient and clean nuclear energy will become a promising energy source in the future. The most significant issue with nuclear power is its safety and controllability in the long term. Cladding is one of the most important components in a nuclear reactor. It has been used in extreme environments with high radiation levels, high temperatures, and high pressure levels for a long time [1]. Zirconium (Zr) alloys have been applied as a cladding material because of their high temperature mechanical properties, small neutron absorption cross section, strong radiation resistance, and good irradiation stability [2]. The properties of the Zr alloy clad and UO\({}_{2}\) fuel are critical issues to be resolved for nuclear power [3, 4]. However, the effects that extreme environments--e.g., with high irradiation levels, high temperatures, and high pressure levels--have on the mechanical and thermal properties of Zr alloy cannot be determined through conventional experimental methods [5, 6]. Experimental data on optimizing component structure properties is lacking. Numerical simulations provide an effective method for performance analyses of nuclear materials in extreme environments. Bison, a three-dimensional finite element analysis program developed by the National Laboratory of Idaho, USA, has been usedto simulate the thermal mechanical behavior of fuel rods in the reactor [7]. Alcyone, a three-dimensional finite element analysis program developed by the CEA of France, has been used to study the high burnup performance of fuel [8]. The user subroutine UMAT of ABAQUS finite element software was employed to study the radiation-thermal-mechanical coupling behavior of fuel rods by [PERSON] et al. [9]. The effects of a nonhomogeneous irradiation environment were studied using the UMAT of ABAQUS. The three-dimensional deformation of a typical 17 \(\times\) 17 fuel assembly was determined by numerical simulation [10]. The thermomechanical behavior simulation, coupled with the hydrostatic-pressure-dependent, grain-scale fission gas swelling calculation for a monolithic UMo fuel plate, was studied under heterogeneous neutron irradiation [11]. The thermomechanical behavior of a Zr-4 fuel rod was studied by experiments and a simulation. It was found that the creep behavior was not captured by a simple law [12]. The deformation behavior of Zr alloys was also investigated at the microscale level. A physically-based crystal plasticity model was proposed to study the contact force and gap opening of fuel rod assembly by [PERSON] and [PERSON] [13]. The effects of fast neutron irradiation on the tensile deformation mechanism of Zr-2.5 pressure tube samples was studied by in situ neutron diffraction [14]. It was found that the starting stress of base plane <a> slip and cylinder <a> slip increased due to neutron diffraction, while the influence of cone < c + a > slip was small and became the dominant deformation mechanism. After the model was established, the SRIM/TRIM software could be used to conduct an ion energy analysis on the thickness of the model to evaluate its safety and stability, and provide a scientific basis for the subsequent behavior model in the fuel rod reactor [15]. Irradiation-induced hardening was confirmed for the Zr alloy cladding. An increase of Nb was shown to be able to retard the formation of irradiation defects [16]. The thermomechanical behavior of Zr alloys with UO\({}_{2}\)/Zr fuel element is key for nuclear reactors. At the same time, the alloying elements in the Zr alloy for the nuclear reactor can also affect the properties of Zr alloys. For example, tin can improve the strength of Zr, reduce its plasticity, and improve its creep and corrosion.