## 4 Discussion
### Geometric Dimension Consistency  
The consistency of the geometric dimensions of the TWBs serves as a criterion for assessing their forming performance. [PERSON] conducted numerical simulations and experimental verifications involving pre-deformation rolling (PDR) on the TWBs before deep drawing, effectively enhancing the uniformity of wall thickness in the TWBs post-deep drawing [35]. The AW TWBs exhibit weld excess metals on their upper and lower surfaces, leading to sudden changes in the dimension of the FZ and the BM cross-section thickness direction, thereby impacting the formability of the TWBs. Consequently, the Erichsen cupping test was conducted on the TWBs with retained weld excess metals, and their performance was compared with that of the TWBs without excess metal. Simultaneously, ABAQUS finite analysis was carried out on the TWBs models both with and without excess metal, utilizing the coupling Euler-Lagrangian method (CEL) to simulate the surface stress distribution of the TWBs during the cupping process. Relevant parameters for the BM and the FZ materials were provided in the literature [36]. Model plate thickness and the FZ size are consistent with actual dimensions, along with an outer diameter matching the inner diameter of the upper half of the die and employing encastre conditions; the punch model size corresponds to actual dimensions, defined as a rigid body. For a more intuitive analysis of the impact of weld excess metal on stress distribution during the TWBs forming, the model was simplified, neglecting thermal stresses generated during welding and aligning relevant parameters of the HAZ and the BM materials.  
Figure 17a shows the surface after the cupping test of the AW TWBs with retained excess metal. The rupture position is at the weld toe and runs parallel to the welding direction. The corresponding figure on the right illustrates the simulation results of the surface stress state, with the highest stress concentration centered at the weld toe. Figure 17b shows the surface after the cupping test of the AW TWBs without excess metal. The corresponding figure on the right shows that the highest stress is uniformly distributed across the central area of the TWBs. When both the TWBs reach the same forming depth, the uniformly distributed stress is lower than the stress concentrated at the weld toe.  
Figure 18 shows the force-displacement curves of the AW TWBs with and without excess metal and the stress concentration locations at the cross-section. The TWBs with retained excess metal exhibit an ultimate punch load of 7.85 kN and a cupping value of 5.16 mm, notably lower than that of the TWBs without excess metal. Compared to the TWBs without excess metal, those with retained excess metal experience advanced stress concentration at the weld toe during the cupping test. This premature stress concentration can result in early cracking and reduce the formability of the TWBs. Therefore, the CR process diminishes the non-uniformity of the cross-sectional ge  
Figure 17: The AW-TWBs cupping surface failure mode and stress distribution simulation results: (**a**) with retained excess metal and (**b**) without excess metal.  
FZ and the BM, and the subsequent SHT eliminates the local strain-hardening induced by the CR. Consequently, the PWCR-SHT process enhances the uniformity of mechanical properties and geometric dimensions, facilitating uniform plastic deformation in each area during the force process, thereby improving the formability of the aluminum alloy TWBs.