## 5 Results and Discussion
After experimental and FEM simulation analysis, we obtained the average triaxiality during loading and the equivalent plastic strain at the onset of fracture for each specimen, as shown in Table 3. In agreement with the previous research literature on the fracture phenomena of metals [36; 37], the average triaxiality of the tensile specimens was approximately 0.33. Since hydrostatic stresses were introduced into the notched region, the stress triaxiality value at the smallest cross section was 0.5 for the R5 specimen, and similar findings were reported in the previous literature [24]. \begin{table}
\begin{tabular}{c c c} \hline
**Specimen** & **Stress triaxiality** & **Equivalent Plastic Strain at Fracture** \\ \hline Uniaxial tensile & 0.33 & 0.065 \\ R5 notch & 0.5 & 0.081 \\ R20 notch & 0.42 & 0.12 \\ D10 center hole & 0.37 & 0.067 \\
45\({}^{\circ}\)shear & 0.25 & 0.13 \\ \hline \end{tabular}
\end{table} 
Table 3: Experiment fracture strain at different stress triaxiality. Figure 6: The simulated stress triaxiality at different stress states. In the MMC equation, the parameters to be determined were: \(k\), \(n\), \(c_{1}\), \(c_{2}\) and \(c_{\theta}^{s}\). For the plane strain condition, \(c_{\theta}^{s}\) = 1. The MMC model could thus be simplified as follows:  
\[\bar{\epsilon}_{p}^{f}=\left\{\frac{A}{c_{2}}\times\left[\sqrt{\frac{1+c_{1}^{ 2}}{3}}\cos\left(\frac{\overline{\theta}\pi}{6}\right)+c_{1}\left(\eta+\frac{1 }{3}\sin\left(\frac{\overline{\theta}\pi}{6}\right)\right)\right]\right\}^{- \frac{1}{\pi}} \tag{8}\]  
According to the stress triaxiality and the equivalent plastic strain at fracture in Table 3, unknown parameters in the MMC equation were fitted by a Python script. The MMC fracture surface obtained after fitting is shown in Figure 7.  
In the GISSMO failure model, the nonlinear damage accumulation exponent \(k\), the equivalent plastic strain when instability deformation occurs \(\varepsilon_{crit}\), and the stress recession exponent \(m\) are unknown parameters. A parameter inversion method [38] in LS_OPT was used to obtain the value of each parameter in the GISSMO failure model based on the force-displacement data. The mean square error of the load-displacement data in the parameter inversion was less than 3%. Figure 8 shows the comparison of force-displacement curves and failure modes between the simulation calculation and experiment results for five specimens. As shown in Figure 8a, according to the force-displacement curve, there was no softening stage before material fracture, and similarly no significant necking was observed before material fracture during the simulation and experiment. In Figure 8b,c, the minimum cross-sectional positions of the R5 and R20 notched specimens are in the middle of the specimen. The stress concentration phenomenon caused the specimen to fracture first at the edge of the notch. The fracture displacement was about 0.55 mm and 0.75 mm. During the tensile deformation process, the specimen first experienced elastic-plastic deformation and fracture occurred instantaneously at the maximum strength. Similarly to the static tensile experiment, after the tensile force reached the maximum value, the material almost did not soften and no significant necking occured; instead, fracture occured directly. Figure 8d shows the force-displacement curve of the D10 center hole specimen. The fracture was first generated at the internal hole wall of the middle section, and then extended along the hole wall normal to the axial load until the complete fracture. Figure 8e shows a sheared 45\({}^{\circ}\) specimen with fracture starting at the arc edge of the least cross section. With the tensile deformation, the crack at the edge propagated into the matrix and eventually led to a complete fracture. Compared with the notched specimen, the tensile displacement of the shear specimen was larger, about 0.92 mm. A significant stress concentration was observed before the fracture under all test conditions.