## 3 Results  
As mentioned above, for an enhanced visualization of the results, separate graphs were created for each weld thickness. The type of line of the legend indicates the working pressure (dashed = 5 bar, solid = 6 bar, and dotted = 7 bar). The different colors indicate the welding times used in the second pulse as explained in the methodology (in ascending order, the machine times are represented in %) and range from the smallest value in grey, through the middle value in blue, to the largest value in orange. The axes of each graph correspond to the failure force on the Y axis and intensity on the X axis. In the case of smaller thicknesses (Figure 10) with low cycle times, higher intensities were necessary to achieve optimum welds. Increasing the working pressure improved the weld performance primarily in longer cycle times. These joints failed due to a lack of strength and a reduction in the thickness of the resulting joint. In both cases, joints with failure forces above 9800 N were achieved. When the joint thickness increased (Figure 11) with low cycle times, the 20 mm thickness did not admit the maximum intensity; as the thickness increased, the maximum intensity could be used. Figure 10: Force necessary for failure. Weld thickness: 16 mm (**a**) and 18 mm (**b**). \begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline
\begin{tabular}{c} **Welding** \\ **Parameters** \\ \end{tabular} & \multicolumn{2}{c}{**Shear Force(Tn)**} & \multicolumn{2}{c}{**Average**} & \multicolumn{2}{c}{**Pulling Force(Tn)**} & \multicolumn{2}{c}{**Average**} & \multicolumn{2}{c}{**Weld Failure**} \\  & & & & & & & & **(Tn)** \\ \hline A+B Thickness & \(\tau_{1}\) & \(\tau_{2}\) & \(\tau_{3}\) & \(\tau\) & \(\sigma_{1}\) & \(\sigma_{2}\) & \(\sigma_{3}\) & \(\sigma\) & \(F=\sqrt{\sigma^{2}+\tau^{2}}\) \\ \cline{2-9} (mm) & \multicolumn{5}{c}{**Real Thickness (mm)**} & \multicolumn{5}{c}{**Average**} & \multicolumn{2}{c}{**OK**} & \multicolumn{2}{c}{**Invalid**} \\ Intensity (\%) & \multicolumn{5}{c}{**Real Thickness (mm)**} & \multicolumn{5}{c}{**Average**} & \multicolumn{2}{c}{**OK**} & \multicolumn{2}{c}{**Invalid**} \\ Time (\%) & \multicolumn{5}{c}{**Real Thickness (mm)**} & \multicolumn{5}{c}{**Real Thickness (mm)**} & \multicolumn{5}{c}{**Real Thickness (mm)**} & \multicolumn{2}{c}{**Real Thickness (mm)**} & \multicolumn{2}{c}{**Real Thickness (mm)**} \\ Time (\%) & \(\Delta_{1}\) & \(\Delta_{2}\) & \(\Delta_{3}\) & \(\Delta_{4}\) & \(\Delta_{5}\) & \(\Delta_{6}\) & \(\Delta_{\text{real}}\) & \(\Delta_{\text{real}}>0.85\) & \(\Delta_{\text{real}}<0.85\) \\ Pressure (bar) & \multicolumn{5}{c}{**Real Thickness (mm)**} & \multicolumn{5}{c}{**Real Thickness (mm)**} & \multicolumn{5}{c}{**Real Thickness (mm)**} & \multicolumn{2}{c}{**OK**} & \multicolumn{2}{c}{**Invalid**} \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Assessment of weld performance. The input energy was determined by combining the time and intensity. The combination of high energy and excess pressure led to deficient welds. For the 20 mm thickness, failures occurred due to a lack of strength and a reduction in the thickness of the resulting joint. With 22 mm joint thickness, the welding had enough material, and, at low energy levels, the work pieces were not dented. By keeping the test electrical energy constant and varying the pressure, we observed that, with excessive pressure, the joints began to dent. With joint thicknesses above 22 mm (Figure 12), low cycle times tests obtained joints with a failure force greater than 14,700 N, when the maximum intensity was used. This proved that excess pressure did not bring improvements to the resultant piece. In the case of the 24 mm thickness, the best results (greater failure forces) were obtained for medium and high cycle times and 6 bars of pressure. For thicknesses of more than 24 mm, only high cycle times produced failures, due to the reduced thickness of the resulting joint. In the case of high cycle times, the use of high pressure improved the obtained welds.