## 3 Simulation of the Stress Intensity Factor Correction Factor
### Analysis of the Influencing Factors  
The factors affecting the stress intensity include the radius of curvature \(R\) of the bottleneck joint bottle body, the wall thickness \(h\) of the pressure vessel, the length of the crack \(L\), and the crack angle \(\alpha\). In order to express the influence of multiple factors on  
Figure 3: Crack growth model.  
Figure 2: Pressure vessel simulation structure diagram: (**a**) stress load diagram and (**b**) pressure vessel grid simulation model.  
the stress intensity factor, the relationship between each factor and \(F\) is presented in the following figures.  
The curvature radius of the bottleneck surface is set to 220 mm, 245 mm, 270 mm, 295 mm, 320 mm, and the wall thickness \(h\) and the crack length \(L\) are fixed values. Under different initiation angles, \(F\) and \(R\) are plotted. The law of change is shown in Figure 4a. The nonlinear regression method is used to calculate the fitting expression curve of \(F\) and \(R\) when the pressure vessel wall thickness \(h\), crack length \(L\), and the angle \(\alpha\) between the crack direction and the axial direction are fixed values, as shown in Figure 4b.  
It can be observed from Figure 4a,b that the stress intensity factor correction factor \(F\) increases with the increase in the curvature radius \(R\) of the joint surface between the bottleneck of the pressure vessel and the bottle body.  
The wall thickness of the pressure vessel is set at 4 cm, 6 cm, 8 cm, 10 cm, and 12 cm; the radius of curvature \(R\) and the crack length \(L\) are fixed values; and the change law of \(F\) and \(h\) is shown in Figure 5a. Similarly, when the radius of curvature \(R\) of the bottleneck of the pressure vessel, the crack length \(L\), and the angle \(\alpha\) between the crack direction and the axial direction are fixed values, the fitting relationship between \(F\) and \(h\) is shown in Figure 5b.  
It can be observed from Figure 5a,b that the stress intensity factor correction factor \(F\) decreases as the wall thickness \(h\) increases.  
Set the initial state of the crack, take the length of the crack as 6 mm, 8 mm, 10 mm, 12 mm, and 14 mm, the radius of curvature \(R\) and the wall thickness have fixed values,  
Figure 4: The relationship curve between \(F\) and \(R\) (**a**) under different crack initiation angles, the law of change of \(F\) with \(R\), and the (**b**) fitting curve of \(F\) and \(R\) when \(h\), \(L\) and \(\alpha\) are fixed values.  
Figure 5: The relationship curve between \(F\) and \(h\) (**a**) under different initiation angles, the law of change of \(F\) with \(h\), and the (**b**) fitting curve of \(F\) and \(h\) when \(R\), \(L\), and \(\alpha\) are fixed values.  
and draw the law of change between \(F\) and \(L\) under different initiation angles, as shown in Figure 6a. Calculated when the pressure vessel bottleneck radius of the curvature \(R\), wall thickness \(h\), and the angle \(\alpha\) between the crack direction and the axial direction are fixed values, the fitting relationship between \(F\) and \(L\) is shown in Figure 6b.  
It can be observed from Figure 6a,b that the stress intensity factor correction factor \(F\) increases as the crack length \(L\) increases.  
Taking the radian of the angle between the crack direction and the axial direction as the independent variable, calculate the fitting relationship between \(F\) and \(\alpha\) when the radius of curvature of the bottleneck of the pressure vessel \(R\), the crack length \(L\), and the wall thickness \(h\) of the pressure vessel are fixed values.  
It can be observed from Figure 7 that the stress intensity factor correction coefficient \(F\) rapidly decreases, with the increase in \(\alpha\), and then there is little change in the fluctuation.