## 5 Results and Discussion
The comparison of the FEM results with the experimental results is given in Table 4, wherein the maximum error was successfully controlled within 5%. Figure 7: Geometry representation in 3D of MMC fracture model. Figure 8: _Cont_. Through the failure curves of different experiment groups, the die-cast aluminum A356 showed a weak necking phenomenon before fracture and a short cumulative stage of failure, indicating a possible brittle fracture characteristic. We observed the same results through FEM simulation, as shown in Figure 6. In the plastic stage before fracture, the triaxiality remained basically consistent, and there was no obvious necking phenomenon at the fracture position. In previous studies, [PERSON] [29] and [PERSON] [39] reported that A356 has the characteristic of brittle fracture. The characteristic of an insignificant necking phenomenon is related to the casting process and microstructure of A356. Defects such as inclusions, porosity, and shrinkage produced by casting can lead to stress concentrations within the material. These casting defects will accelerate the formation and expansion of cracks. Under the action of stress, the cracks will expand in a very short period of time, leading to fracture of the material. In addition, A356 is a hypoeutectic Al-Si alloy, and \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multirow{2}{*}{**Experiment**} & \multicolumn{3}{c}{**Displacement at Fracture (mm)**} & \multicolumn{3}{c}{**Ultimate Force (N)**} \\ \cline{2-7}  & **Experiment** & **FEM** & **Error** & **Experiment** & **FEM** & **Error** \\ \hline Static tensile & 2.76 & 2.8 & 1.5\% & 15,545 & 15,645 & 0.64\% \\ R5 notch & 0.55 & 0.546 & 0.72\% & 18,083 & 18,201 & 0.65\% \\ R20 notch & 0.755 & 0.756 & 0.13\% & 16,673 & 16,554 & 0.71\% \\ D10 center & 0.536 & 0.511 & 4.6\% & 16,317 & 16,349 & 0.196\% \\ hole & 45\({}^{\circ}\) shear & 0.923 & 0.946 & 2.49\% & 1768.36 & 1770.72 & 0.13\% \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Comparison of FEM and experiment results of force–displacement curves. Figure 8: Comparison of FEM and experiment results. coarse eutectic silicon particles can lead to stress concentration phenomena, thus increasing the possibility of material fracture [29]. A reduction of casting defects, refinement and modification of eutectic silicon by improving the casting process can improve the ductility of A356 [40; 41]. In numerical calculations, the element size effect must be considered, and is shown in Figure 9. The material in the finer elements showed a more delayed fail than that in the coarser elements. An element dependence factor which scales the failure strain of the material according to the element size was thus calculated. The element dependence factor \(\alpha(scale_{el})\) was defined as a function of the relative element size, and the relative element size was defined as:  
\[scale_{el}=\frac{Size_{el}}{Size_{ref}} \tag{9}\]  
where \(Size_{el}\) is the reference element size, which is usually the element size used in the material test calibration model; \(Size_{ref}\) is the actual size of each element applied in the whole model. According to the strain hardening curve of A356 (Figure 5a), the strain rate had a significant effect on the failure pattern. Using the failure strain value in the quasi-static condition as the reference failure strain, a strain rate correction factor was calculated to correct the failure strain at different strain rates using the following equation:  
\[\beta(\hat{\epsilon})=\frac{\hat{\epsilon}}{\hat{\epsilon}_{ref}} \tag{10}\]  
where \(\hat{\epsilon}_{ref}\) is the reference strain rate, and \(\hat{\epsilon}\) is the strain rate with a different condition. After introducing the strain rate correction factor, the FEM results under different strain rates are shown in Figure 10. The established FEM model can simulate the experimental results well, and the errors of the numerical results are all below 5%.