## 1 Introduction
When the SIF of this type of crack reaches a certain critical value, i.e., the material's fracture toughness, the crack propagates rapidly (called instability propagation) and causes the structure fracture of the component [14]. The early research mainly aimed at the calculation of the SIF of two-dimensional cracks. In practical engineering applications, the forcing components create instability and the fracture is due to the existence of three-dimensional cracks. For the opening of the ampoule bottle, its non-penetrating crack mostly occurs in three-dimensional cracks. Even if the final form of the crack is a through crack, in most cases, its initial state is also in the form of a non-penetrating crack. At present, the main solutions to the three-dimensional crack's SIF include: [PERSON]'s function method, the finite element method, the dual boundary element method, the multi-zone method, the displacement discontinuity method, etc. [15]. Among them, the FEM has the advantages of high efficiency, low cost, good reliability and is not restricted by the load and geometric shape of the cracked body, so it has been widely used. The literature [16; 17; 18] demonstrated the applicability and reliability of using the FEM to analyze and evaluate the SIF. Therefore, several important parameters for calculating cracks in fracture mechanics can be easily studied by the FEM, such as the coefficient \(K\) of the SIF and the coefficient \(F\) of shape factor. As an extremely important parameter to characterize the stress-strain field at the crack tip, the accurate and reliable calculation of the coefficient \(K\) is the main criterion for predicting the fracture of cracks in linear elastic materials [19]. [PERSON] et al. [20] demonstrated the empirical SIF equation for surface cracks, which was used to predict crack propagation under tensile or flexural fatigue loading in components of various crack shapes and crack sizes. [PERSON] et al. [21] studied the effect of component geometry and residual stress on the SIF of surface cracks, and the SIF was a good estimate of crack propagation behavior in stress corrosion cracking. Many scholars' studies have shown that the SIF playsan important role in predicting crack propagation and component fracture. The crack shape coefficient \(F\) is a key parameter for the calculation of the coefficient \(K\), which is closely related to the geometry of the cracks and the loading patterns. [PERSON] et al. [22] presented the effect of semi-elliptical cracks on several types of SIFs at different relative depths and at various aspect ratios, suggesting that that crack shape had a significant effect on the fracture. [PERSON] et al. [23] investigated the effects of a notch shape and different cracks on the SIF under tensile and bending loads. [PERSON] et al. [24] measured the SIF of the V-shaped mouth of the component under different loads by the focal ray method. Since the body of ampoule bottle is a cylinder and the head presents a convex-shaped surface, the neck can be regarded as a V-shaped notch which is prone to stress concentration, and it makes the analysis of the coefficients \(K\) and \(F\) become more complicated. Generally, the SIF calculation method of a typical cracked body model can be approximated by querying the manual. However, under complex loads, for structural components like an ampoule bottle with complex crack shapes or structures, the SIF in many cases is difficult to find from the manual. The main form of load in the opening process of an ampoule bottle is a combined load including both tensile stress and bending moment. However, there are few studies on the crack under the combined loads and few reports on the crack of the neck with a V-shaped notch.