## 3 Simulation of Tube-Cap Welding
### Simulation Steps
#### 3.3.2 Simulation Modeling and Material Used  
The main parameter used in the simulation was the current (A), as shown in Table 5. The fixed parameters were set as follows: the squeeze time, which refers to the duration of the application of the initial pressure, was set to 20 cycles; the welding time, such as the time during which the current flows, was set to 1 cycle; and the holding time, which is the time during which the applied pressure is maintained after the welding time, was set to 5 cycles. A 60 Hz single-phase AC thyristor welding machine was used in the welding process. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Symbol** & **Nomenclature** & **Symbol** & **Nomenclature** \\ \hline \(\overline{\sigma}\) & Effective stress & \(k\) & Thermal conductivity \\ \hline \(\dot{\tilde{z}}\) & Effective plastic strain rate & \(\rho_{m}\) & Mass density \\ \hline \(K\) & Large positive number & \(c_{m}\) & Heat capacity \\ \hline \(\dot{\tilde{z}}_{ii}\) & Volumetric strain rate & \(\ddot{\tilde{T}}\) & Temperature rate \\ \hline \(t_{i}\) & Surface traction & \(\dot{q}_{V}\) & Heat generation rate in volume \\ \hline \(u_{i}\) & Velocity on the surface & \(\dot{q}_{S}\) & Heat generation rate along surface \\ \hline \(\Phi\) & Electric potential & & \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Properties used in the simulations. \begin{table}
\begin{tabular}{c c c} \hline \hline
**No.** & **Components** & **Material** \\ \hline
1 & Cladding Tube (CT) & ZIRLO \\ \hline
2 & CT Electrode & CuBe2 \\ \hline
3 & End Plug (EP) & Zircaloy-4 \\ \hline
4 & EP Electrode & CuBe\({}_{2}\) \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Materials used in the simulation. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Type** & \begin{tabular}{c} **Yield** \\ **Strength** \\ **(MPa)** \\ \end{tabular} & \begin{tabular}{c} **Tensile** \\ **Strength** \\ **(MPa)** \\ \end{tabular} & \
\begin{tabular}{c} **Elongation (\%)** \\ **Ratio** \\ \end{tabular} &
\begin{tabular}{c} **Poisson’s** \\ **Point (\({}^{\circ}\)C)** \\ \end{tabular} \\ \hline ZIRLO & 613.88 & 819.04 & 14.67 & 0.10 & 1834 \\ \hline Zircaloy4 & 597.50 & 794.40 & 15.6 & 0.18 & 1834 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Mechanical properties of the used material (%) [19]. Figure 3: Simulation modeling and location of substance (tungsten). \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Factor** & \multicolumn{3}{c}{**Range**} \\ \hline Over lapping (mm) & \multicolumn{3}{c}{0.8 (fixed)} \\ \hline Force (kN) & \multicolumn{3}{c}{4.3 (fixed)} \\ \hline Current (kA) & 11 & 12 & 14 & 15 \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Variable factor for butt welding. is a critical factor during the entire welding process. To analyze this flow phenomenon, Figure 3 assumes that a foreign substance (tungsten) with a melting temperature higher than the melting temperature is included in the tube material and analyzes how this foreign substance moves within the weld pass depending on the welding variables. It is assumed that the foreign substance is introduced into the tube rather than the end plug (cap), as the tube undergoes significant melting and shape changes compared to the end plug. Table 6 shows the melting temperatures of the materials used, including the end plug, the tube, and the foreign substance (tungsten). The displacement of the substance was measured by setting the green dot (tungsten) inside the tube as the initial position and measuring the displacement of the substance during the welding process with respect to this position, as shown in Figure 4. In addition, the measurement intervals for analyzing the position of the foreign substance during welding were shown, and the welding time was divided into five intervals, with the first half cycle divided into four intervals and the remaining one interval being the point at which welding ended.