## 4 Discussion
### Assessment of the Numerical Models  
This section explores four criteria to evaluate the studied numerical models, namely safety for the ISF equipment, the complexity of FEM models, the solution time required by the numerical simulations, and their accuracy in predicting both the peak and the evolution of the force. Figure 8: (**a**) Flow chart of Hollomon’s hardening rule adjustment process; (**b**) The two Hollomon’s hardening curves compared to the engineering and true stress–strain curves. Figure 9: Improved axial force prediction based on “optimal” parameters for the AISI304 material. Safety: This criterion reflects the capability to provide conservative estimations regardless of accuracy. A certain overestimation is expected since the actual loads are higher than the filtered-studied data; still, they should not become a limitation for utilizing the equipment. On the other hand, minor underestimations could pose a risk for the machinery and tools. Table 5 indicates that safe results were obtained in all cases where the FEM hardening model was refined. Complexity: The complexity of FEM models necessitates specialized software, hardware, inputs, and knowledge. While the initial geometry of the SPIF system is straightforward, the subsequent modeling steps involve selecting from a long list of numerical alternatives to achieve accurate results. The process can be automated for simple geometries, such as the frusta studied in this work. Nevertheless, the hardening variability of different materials requires exploring diverse modeling approaches, like the ones shown in this study. Solution time: Unlike the instantaneous response provided by analytical models, numerical simulations of SPIF are time-consuming, ranging from hours to even days, depending on part complexity. All cases simulated in this study required a computational time below five hours. However, fitting the hardening model of the AISI-SAE 304 material took approximately 70 h, making it difficult to justify the use of simulations only for peak force estimation. Accuracy: In addition to accurately predicting peak force values, numerical models should also replicate the transient development of the force response for each case, especially when used for applications like failure prediction and stiffness compensation. Figure 9 highlights that the AISI-SAE 304 model requires additional refinement to accurately represent both the qualitative and quantitative aspects of the physical force data. Although the results obtained from the introduced regression model are promising, they also indicate the necessity of incorporating alternative isotropic or combined isotropic-kinematic hardening models. These additional models may provide a more comprehensive description of the loads induced by the SPIF process on this material. However, advanced characterization tests such as the uniaxial tension-compression cyclic tests are necessary for their parameter identification. Combined with the hardening model, the heating effect caused by the contact between the tool and the blank may be another reason for the numerical results discrepancy. [PERSON] et al. [9] found a difference of around 13% in the axial forces of variable wall angle cones formed with AISI-SAE 304 when the spindle speed was varied from 1000 rpm to free spindle rotation. On the other hand, the Vocc hardening law, with parameters identified from uniaxial tensile tests, accurately represents the experimental load response of the AA1050-H24 material. The achieved numerical force curves, gathered in Figure 10, reproduce the experimental trend of components formed with SPIF at different wall angles [7; 8]. In this case, simulations could be helpful for discerning, before forming the first component, between successful parts and those at risk of failure.