## 4 Discussion
### Formability Evaluation
However, it should be noted that neither study considered the mechanical response under different strain paths or the effects of anisotropy on some directions. For example, there is no relationship between the uniaxial strain path in the diagonal direction (45\({}^{\circ}\) with respect to the rolling direction) and the anisotropy value in that direction. Figure 8d shows the forming limit curves in the three directions. In the left-sided scenario, ranging from the uniaxial strain value to the plane strain value, the three curves exhibit a behavior that tends toward linearity, which is notably similar across all three. This similarity is a consequence of the mechanical properties, particularly the coefficients of strain hardening n and R-values. In the case of the right side, Figure 8d reveals that the biaxial strain values, ranging from the plane strain value to the balanced biaxial strain value, associated with the limit strains of the three curves, are remarkably similar, with a clear parabolic trend. The slight discrepancies in strain values can be attributed to various factors, including sample geometry, material properties and crystallographic texture evolution on different strain paths and different sample orientations. [PERSON] et al. [29] reported that a high value of normal anisotropy decreases the limiting strain values. In this study, only one alloy was analyzed, but for comparison, [PERSON] et al. [7] reported their results by simulating the deformation of an aluminum 2024-O alloy. In their study, they showed an increase in the limiting strain values with a normal anisotropy value of \(\overline{R}=0.83\) (\(R_{0}=0.68\), \(R_{45}=1.05\)  
\(R_{90}=0.54\)), which is lower than the anisotropy value in this study, demonstrating good agreement with the results obtained (\(\overline{R}=0.97\)). [PERSON] et al. [46] explored the influence of strain hardening index n and anisotropy coefficient R on AA7020 aluminum sheets. They concluded that both parameters have great relevance on the limit strain results, where they reported that the higher the n value, the higher the limit strain values, as reported by [PERSON] et al. [29]. In comparison, the results of this study are in good agreement, with the difference that the n values they obtained were very different in the three directions. On the other hand, lower R-values, which indicate greater plastic anisotropy, were associated with reduced formability, particularly in the transverse direction, where the limit strains were notably lower. In summary, the relationship among the microstructural, mechanical, and formability properties is as follows:  
Firstly, the reflected microstructural properties were not predominant in the results of either the mechanical properties or the formability. Figure 4 only shows changes in the geometry of the grain on the three strain paths, which is why only the microstructures in the rolling direction (RD) are shown. Furthermore, the intermetallic phases observed in the SEM images do not show significant changes that could be attributed to the deformations. As can be observed in the stress-strain curves (Figure 6a) and the respective mechanical properties (Table 1) for the three directions with respect to the rolling direction, only a few differences can be observed, resulting in low dispersion of mechanical properties. In the same way, the anisotropy coefficients obtained in the three directions show a low anisotropy trend, with similar values for each direction (\(R_{0}=0.82\), \(R_{45}=1.07\), \(R_{90}=0.93\)). It should be noted that, due to the similarity of the anisotropy values, they are also reflected in the similarity of the strain limit curves (see Figure 8). The slight differences that can be observed, specifically in Figure 8a, are attributed to the slight differences in the anisotropy values. For example, the limit strain in the uniaxial strain path in the DD direction is the value that is closest to the \(\rho\) ratio lines, where theoretically, a value \(R=1\) should coincide with this line.