## 1 Introduction  
Given the crucial role of 2024-T3 aluminum alloy in producing lightweight yet high-strength components in aerospace and automotive industries, understanding its mechanical behavior under various loading conditions is essential. The anisotropic nature of this alloy, specifically, significantly influences its mechanical properties and formability. This makes the study of anisotropy and its impact on the forming limit curve (FLC) a vital area of research for optimizing the material's performance in critical applications. It is well known that 2024-T3 aluminum has a strong presence in the automotive and aerospace industries to produce components and spares due to its excellent hardness, strength, and lightweight characteristics. The analysis of the mechanical characteristics and resistance to the plastic deformation of aluminum alloy sheets has been the focus of research in recent decades. The impact of artificial aging on the mechanical characteristics of aircraft aluminum alloy 2024 was documented by [PERSON] et al. [1]. [PERSON] et al. [2] investigated how processing variables affected the flow, formability, and hardness of the alloy material. During the deep drawing process, the materials were subjected to cold working with a hemispherical punch to assess their formability. [PERSON] et al. [3] experimented on sheets of 2024 aluminum alloy using hot forming techniques with synchronous cooling (HFSC). According to their analysis, HFSC significantly reduced spring back, resulting in better final geometries with less distortion while maintaining constant hardening levels. The effects of heat treatment on the microstructure, crystallographic texture, and formability of sheets made of 2024 aluminum alloy were examined by [PERSON] et al. [4]. Their research showed that precipitation-induced alterations in the microstructure of the aluminum alloy sheet were caused by solution treatment and artificial aging. They also concluded that heat treatment, which involved solution treatment at 150 \({}^{\circ}\)C for two days and artificial aging at the same temperature for two days, improved the forming characteristics of the sheets. The expected failure of 2024 aluminum sheets under biaxial stretching circumstances was examined by [PERSON] et al. [5]. Their analysis showed that shear forces are the main factors controlling material failure, and that these forces are concentrated in the through-thickness plane. Tensile and formability tests were used by [PERSON] et al. [6] to conduct an experimental and numerical analysis of 2424 aluminum sheets that were subjected to cryogenic forming procedures. Their research showed that testing conducted at low temperatures can enhance strain limits. The formability test is widely utilized in the production of sheet metal components, encompassing various operational types and conditions, such as cold forming or hot forming processes. The forming limit diagram (FLD), initially introduced by [PERSON] and [PERSON] [7] and later refined by [PERSON] [8], serves as a crucial tool in assessing sheet metal formability. The FLD delineates the maximum values of major (\(\epsilon_{1}\)) and minor (\(\epsilon_{2}\)) principal strains that a sheet metal can withstand before neccling occurs, signifying a localized thinning of the material. To determine the experimental FLD, several mechanical tests are employed, with the Marciniak [9] and Nakazima [10] tests being the most frequently utilized. In the Marciniak test, flat-tip punches induce plastic straining on the sheet metal, while round-tip punches are employed in the Nakazima test. Different sample geometries are utilized in these tests, resulting in diverse strain paths. The primary distinction lies in the geometry of the punch used, influencing the deformation behavior of the material. Various methodologies are employed to identify neccling onset and the corresponding limit strain. One approach, proposed by [PERSON] et al. [11] and [PERSON] et al.