## 6 Results and Discussion  
In the present study, we compared the springback shape predicted by the models and that experimentally obtained. Figure 13 shows the comparison for the AR H-BHF as a reference. To illustrate  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Model Designation** & **Elasticity** & **Yielding** & **Hardening** \\ \hline Iso & Constant & Hill48 & Isotropic \\ Kinematic & Constant & Hill48 & Isotropic + kinematic \\ Young & Variable & Hill48 & Isotropic \\ Full & Variable & Hill48 & Isotropic + kinematic \\ \hline \hline \end{tabular}
\end{table}
Table 9: Summary of the analysed models.  
the differences between the models in terms of springback predictions, the whole channel is shown in Figure 13a, where only the flange area of the left side of the channel is depicted in Figure 13b. In these figures, X and Y represent space coordinates.  
As can be seen from the results, the full and Young models had the highest accuracy. To evaluate the accuracy of each model in every case, the springback angle \(\Delta\Theta\)i (final angle minus 90 degrees of the forming angle) was evaluated for each model and analysed case. The angle measurement followed the protocol defined in the Numisheet benchmark of 1993 [28]. Table 10 summarises the values of the springback angles.  
In the case of the PSTT, the simulations were carried out as follows:  
1. The first drawing was simulated using the AR material model (35 mm drawing).
2. The springback of that step was then simulated.
3. Next, the post-springback geometry was imported, without any residual stress or strain, and the second drawing (until reaching a drawing depth of 70 mm) was performed with the AR material model.
4. Finally, the last springback was simulated.  
To evaluate the accuracy of each model, the error of accuracy (in %) between the predicted springback angle and experimental springback angle was calculated. Figures 14 and 15 show the accuracy of the springback angle prediction for \(\Delta\Theta\)1 and \(\Delta\Theta\)2, respectively.  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Material State** & **Model** & \multicolumn{2}{c}{**L-BHF**} & \multicolumn{2}{c}{**H-BHF**} \\ \hline  & & \(\Delta\Theta\)1 & \(\Delta\Theta\)2 & \(\Delta\Theta\)1 & \(\Delta\Theta\)2 \\ \hline  & Exp & 7.6 & 3.45 & 7.28 & 3.45 \\  & Full & 7.31 & 2.14 & 7.02 & 2.56 \\ AR & Young & 6.92 & 1.82 & 6.39 & 1.12 \\  & Kine & 5.44 & 1.85 & 4.66 & 0.57 \\  & Iso & 4.84 & 0.29 & 4.36 & 0.34 \\ \hline  & Exp & 2.04 & 4.13 & 1.56 & 3.85 \\  & Full & 1.18 & 3.65 & 0.77 & 3.02 \\ PSTT & Young & 1.06 & 1.15 & 0.53 & 1.24 \\  & Kine & 0.25 & 0.98 & 0.43 & 0.75 \\  & Iso & 0.18 & \(-\)0.04 & 0.21 & 0.67 \\ \hline \hline \end{tabular}
\end{table}
Table 10: Summary of the springback angles after forming for each model and experiment.  
Figure 13: Springback prediction of the different models for the AR H-BHF case. (**a**) Whole profile and (**b**) left side of the profile.  
From the results, it can be concluded that, in every case, the full model was the most accurate, followed by the Young model. This was expected as the full model was the most complete one. However, for the PSTT, at a H-BHF, errors of up to 50% were found in the \(\Delta\)01. In terms of the springback angle, the angles differed in the various models between 91.57 degrees and 90.77 degrees. However, these values were within the accuracy of springback simulations of sheet metal forming [16].