# Torsional Fatigue Performance of a Spot-Welded Structure: An XFEM Analysis
## 3 Results and Discussion
### Influence of the Total Number of Spot Wells  
The total number of spot welds is one of the important parameters affecting the performance of the box. This study examined five distinct cases with eight, nine, ten, eleven, and twelve spot weld twins. Table 3 presents the obtained respective \(N_{f}\) and crack propagation rate (\(da/dN\)) values. They were 23,606, 27,466, 42,375, 176,660, and \(10^{6}\) cycles when the number of spot weld twins was increased from 8 to 12, where the relative changes between them were 16.3%, 54.28%, 417%, and 566%. It was seen that when an additional spot weld twin was added to the box, its effect kept increasing. Finally, it was observed that no fatigue failure was observed for 12 spot weld twins, as no crack nucleation was observed throughout the joined sample. Fatigue life larger than \(10^{6}\) cycles was regarded as the run-out in this investigation. It was concluded that it was possible to eliminate the fatigue failure in such boxes when they were subjected to torsional loading by increasing the number of spot welds. The average crack propagation rate was observed to increase from 3.10 \(\times\)\(10^{-5}\) mm/cycle to 2.33 \(\times\)\(10^{-4}\) mm/cycle, more than 7.5 times when the number of spot weld twins was decreased from 11 to 8. Figure 5 shows the crack patterns around spot welds for each configuration when \(N\) reaches to \(N_{f}\). It was observed that the two central spot welds were subjected to fatigue failure when the number of spot weld twins was 8 and 10, while there were three central welding regions for the others. It appeared to be that for 9 and 11 spot weld twins, the central spot-welded region (5 th and 6 th rows from the fixed end, respectively) could not compensate for the whole fatigue deformation, the closer two spot weld twins were also subjected to the failure. Here it was concluded that for the given loading amount, the central two and three spot weld twins accommodate the fatigue failure for the even and odd numbers of the total number of spot weld twins, respectively. Obviously, for a larger amount of loading provided that it does not result in plastic deformation, the fatigue deformation expands from the central twins to the ones located around them.  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Number of Spot** & \(D\) **(mm)** & \(R\) **(mm)** & \(N_{f}\) **(Cycle)** & \(\begin{array}{c}da/dN\\ \text{(mm/Cycle)}\end{array}\) \\ \hline
8 & & & & 23,607 & 2.33 \(\times\)\(10^{-4}\) \\ \hline
9 & & & & 27,466 & 2.00 \(\times\)\(10^{-4}\) \\ \hline
10 & 5.5 & \(-\)1.0 & & 42,375 & 1.30 \(\times\)\(10^{-4}\) \\ \hline
11 & & & & 177,660 & 3.10 \(\times\)\(10^{-5}\) \\ \hline
12 & & & & 10\({}^{6}\) & - \\ \hline  & 4.5 & & & 20,524 & 2.2 \(\times\)\(10^{-4}\) \\ \cline{2-5}
10 & 5.5 & \(-\)1.0 & & 42,375 & 1.30 \(\times\)\(10^{-4}\) \\ \cline{2-5}  & 6.5 & & & 211,845 & 3.07 \(\times\)\(10^{-5}\) \\ \hline  & & & \(-\)1.0 & & 42,375 & 1.30 \(\times\)\(10^{-4}\) \\ \cline{2-5}
10 & 5.5 & & & 0.0 & 48,058 & 1.14 \(\times\)\(10^{-4}\) \\ \cline{2-5}  & & & & 0.5 & 93,900 & 5.85 \(\times\)\(10^{-5}\) \\ \hline \end{tabular}
\end{table}
Table 3: Numerically obtained \(N_{f}\) and \(da/dN\) for different assembly configurations (\(t=1.5\) mm).