## 4 Discussion
### Formability Evaluation  
Figure 8a-c shows that for the limit strain values corresponding to uniaxial strain, the highest major strain values are observed in the RD and DD directions (Figure 8a,b), while the lowest value occurs in the TD (Figure 8c). Theoretically, according to Hollomon's Law \(\sigma=k\)\", the major strain values should reach approximately twice the strain hardening exponent (n) [28]. However, the limit strain values in the three directions are notably lower than the theoretical prediction, with reductions of approximately 21%, 27%, and 37% for RD, DD, and TD, respectively. Similarly, upon comparing the experimental values of the minor strain with the theoretically predicted values based on the strain hardening coefficient (n)  
with minor strain equal to once the coefficient of the strain hardening exponent \(n\), varying degrees of deviation across different orientation directions were observed. For instance, in the RD, where \(n=0.14\), the experimental value exhibited a deviation of approximately 29% from the theoretically value. Similarly, in the DD and TD directions, with respective strain hardening indices of \(n=0.15\) and \(n=0.16\), the deviation was 32% and 43%, respectively. In this context, similar trends to those observed under uniaxial strain conditions were expected for plane strain conditions. Specifically, it was theoretically expected that the major limit strain value would approach approximately \(n\), representing the strain hardening coefficient, while ideally, the minor limit strain would be null. The findings demonstrate a close alignment between the major limit strain values and the strain hardening coefficient, supporting theoretical expectations. Additionally, the minor limit strain values are significantly close to null, with only a negligible displacement to the right of the major strain axis, on the order of \(\sim 10^{-3}\), in the DD. Furthermore, the limit strain value along the DD exhibits the closest proximity to the theoretical relationship line \(\rho=-0.5\), which aligns with the obtained experimenatal anisotropy value of \(R=1.09\). In contrast, although the limit strain values in the RD and TD directions are also situated near the \(\rho=-0.5\) line, they deviate from the corresponding anisotropy values obtained, specifically \(R=0.82\) for the RD and \(R=0.93\) for the TD [29]. Finally, there is a noticeable departure from the \(\rho=1\) relationship line when analyzing the limit strain values under the balanced biaxial strain path. Every value that is obtained is shifted to the left, and none of the values match this line. This displacement points to a deformation process influencing the behavior of the material, most likely caused by the crystallographic texture reorienting due to dislocation movement by applied loads [45]. [PERSON] et al. [4] studied the effect of heat treatment on the forming limit curve and compared the results with the as-received material (T3). They concluded that precipitation hardening achieved within two days of aging improved the deformation capacity under plane strain conditions in comparison with the as-received forming limit curve but has no notable improvement on the results obtained by heat treatments. However, it is important to mention that the formability limit curve results were not associated with the anisotropy results. [PERSON] et al. [6] analyzed the plastic deformation of the 2024-O aluminum alloy at cryogenic temperatures, examining different yield criteria. The experimental results were compared with simulated results using the Norton-Hoff constitutive model and the YId2000-2d yield criterion. They observed that lower temperatures resulted in increased strain hardening. Therefore, they concluded that strain hardening plays an important role in the capacity to withstand plastic deformation. While both studies examined different thicknesses, the results showed a good agreement with the findings of this study.