## 4 Discussion
### Mechanical Property Consistency  
As shown in Figure 9, the PWCR process enables the FZ to achieve higher hardness through strain hardening caused by the CR. According to the formula [26],  
\[\sigma=\alpha\text{Gb}\rho^{1/2}, \tag{1}\]  
\(\sigma\) is the critical stress required for dislocations to escape from the pinning point and \"bow out\"; \(\alpha\) is a constant; G is the shear modulus; b is the Burgers vector; and \(\rho\) is the dislocation density. When external forces deform the weld excess metal, internal dislocations become mobilized and entangled, activating dislocation sources and promoting dislocation propagation, that is, the dislocation density \(\rho\) increases. This, in turn, enhances the pinning capability between dislocations, that is, the critical stress \(\sigma\) increases, resulting in a strengthening effect. According to the formula [27],  
\[\text{H}=\text{C}\rho\text{Gb}^{2}\text{Vr}, \tag{2}\]  
H is strain storage energy (SE); C is a material parameter; and Vr is the molar volume. Figure 14: The surface of TWBs after cupping test (**a**) the AW TWBs; (**b**) the PWCR TWBs; (**c**) the PWSHT TWBs; (**d**) the PWCR-SHT TWBs; and (**e**) the BM. Figure 13: (**a**) Force–displacement curve during cupping test and (**b**) cupping depth and formability ratio. The high-density dislocations induced by the CR are transformed into a high SE. In the subsequent PWCR-SHT process, the SHT temperature is set at 520 \({}^{\circ}\)C, which exceeds the critical recrystallization temperature. SE serves as the driving force for recrystallization. When SE surpasses the critical SE threshold, it triggers static recrystallization (SRX) behavior. With a greater SE and a smaller initial grain size, the resulting recrystallization size becomes smaller. For example, as shown in Figure 7, the W1 region of the FZ experiences a higher rolling force, resulting in a higher SE. The original grains in this region are equiaxed and smaller, leading to smaller recrystallized grains than the original ones. In the W3 region, the rolling force is lower, resulting in a lower SE. Despite the smaller original grain size, the extended SHT duration leads to larger recrystallized grains than the original ones. In the W2 region, the original grains are larger columnar grains, and the rolling force is more evenly distributed, resulting in a smaller SE. Consequently, the recrystallized grain size in the W2 region is larger, retaining some of the original grain morphology. When SE falls within the critical SE range, recrystallization does not occur, and the original grains grow directly. For example, as shown in Figure 8a, for HAZ1, this area experiences only lateral extrusion force from the FZ, resulting in a relatively small SE. The original grains coalesce and grow above the recrystallization temperature, and the newly formed grains do not retain the original grain shape. When SE is smaller than the critical SE range, there is no significant change in the original grains, as shown in Figure 8a for HAZ2. During the welding process, the gas trapped within the molten pool cannot be promptly released, resulting in the formation of macroscopic pores within the FZ. The subsequent CR process is crucial in eliminating these pores by extruding and reshaping the FZ. In the solidification phase of the molten pool, microcracks often develop at the grain boundaries. However, the recrystallization process leads to the regeneration of new grains based on the original ones, effectively eliminating these grain boundary microcracks [28]. Hence, the PWCR-SHT process offers a dual benefit by concurrently addressing macroscopic defects (pores) and microscopic defects (microcracks) within the FZ. Throughout the part's loading cycle, pores and microcracks can act as potential sources of cracks. Therefore, the PWCR-SHT process enhances its overall ductility by delaying the occurrence of the FZ cracks. The PWSHT and the PWCR-SHT process exhibit similarities in changes in the composition and content of precipitated phases.