## 1 Introduction
Compared to the experimental work, the visualization of thermal cycles, surface features and material flow after each stage of the FSW can be easily determined with low effort and cost through numerical modeling. Moreover, numerical simulation can be used to choose the proper welding parameters from a wide range with low cost [23]. Accordingly, different modeling methods such as computational fluid dynamics (CFD), Lagrangian, Eulerian, and arbitrary Lagrangian Eulerian (ALE) methods have been used to study the FSW process. [PERSON] et al. [24] developed a 3D CFD model to simulate FSW of a 6 mm thick DH36 steel plate in a Eulerian domain. They found that the temperature measured by the thermocouple and CFD model was in good agreement at high welding speed. In addition, the strain rate was enhanced with increasing tool rotation, while increasing the welding speed resulted in increasing the shear stress on the tool surface. Moreover, the optimum range of the tool rotation and welding speed was below 550 rpm and between 100 to 350 mm/min, respectively. [PERSON] and [PERSON] [25] developed a CFD code, FLUENT, to simulate the material flow around two tools with trivex-based geometry. They reported that the traversing and down forces decreased when using the trivex tools compared to the trifilute one. Additionally, they used the streamline planes to understand the material flow around the tool pin and found that the trifilute tool has a strong augering action. Although the CFD method had been used successfully to simulate the FSW process [26; 27], CFD cannot model the material hardening and elastic properties. In addition, the full sticking conditions assumed between the tool and workpiece material lead to simulation errors in tool reactions and joining temperature [23]. Lagrangian and Eulerian approaches are other methods to simulate the FSW process. The material position relative to nodes remains fixed in the Lagrangian method, while nodes stay fixed and material moves inside the fixed mesh in the Eulerian one. Thus, the Lagrangian method is suitable to simulate the process outside the processed zone, while the Eulerian approach is good in modeling the material flow [28]. With advances in numerical simulation, the arbitrary Lagrangian Eulerian (ALE) method was developed. [PERSON] and [PERSON] [29] developed an adaptive ALE formulation to simulate the temperature distribution and material flow during the FSW of 6061 aluminum alloy. They used the Forge 3 FE software to develop their model. Non-steady phases of FSW were simulated as well as the steady phase. [PERSON] et al. [30] utilized the same software used by [PERSON] and [PERSON] [29] to model the FSW defect. [PERSON] et al. [31] used ALE and a smoothed particle hydrodynamics (SPH) formulation to study the FSW of 6061-T6 aluminum alloy. The results showed that the temperature distribution was symmetric, and the peak temperature increased with increasing the tool rotation. However, the weld surface features and equivalent plastic strain were not studied. Simulation of FSW of aluminum and lightweight alloys was successfully done by the ALE method. However, severe plastic deformation in the SZ caused severe mesh distortion and precocious simulation failure with the ALE formulation [32]. Unlike the ALE formulation, the Coupled Eulerian Lagrangian (CEL) method can simulate the FSW process with severe plastic deformation without precocious failure of the simulation. The CEL method aims to capture the advantages of the Lagrangian and Eulerian approaches. [PERSON] et al. [32] developed a CEL model to simulate the defects formed during friction stir processing (FSP) of AA 5083-H111 aluminum plate. They did not study the effect of the FSP parameters on the thermal cycle and surface appearance or flash formation. In the present study, a 3D thermo-mechanical finite element model based on the Coupled Eulerian Lagrangian (CEL) method was developed, using Abaqus/Explicit, to simulate the FSW of 1 Cr11 Ni2W2 MoV heat-resistant martensitic stainless steel.