## 3 Results and Discussion  
### Finite Element Model Validation  
The FIPP liner material in the finite element model adopts the elastic-plastic constitutive model tested according to ISO 178. The relationship between the true strain and stress in the plastic phase of the FIPP material is shown in Figure 4, which will be used to define the plastic constitutive model of the finite element model. The elastic limit of the FIPP material is 41.8 MPa. However, bending failure in the specimen did not occur during the test and the ultimate bending strength was considered 62.62 MPa in the configuration of the finite element model. The comparison of the pressure-displacement curve of the FIPP liner is shown in Figure 5. According to the curve, the buckling behavior of the liner can be divided into three stages. At first (stage AB), the deformation displacement versus the pressure is linear during the increase of hydrostatic pressure. At this stage, the liner did not form a buckling lobe. Then (stage BC), as the pressure increases, the deformed part of liner formed a bulge, which can be called the buckling lobe. When the pressure value approaches the critical buckling pressure, the deformation increases and rate of the buckling lobe is significantly increased, while the pressure increase rate remains unchanged. The buckling lobe continues deformation with no enhancement of the ability to withstand the external pressure, but the liner still has the bearing capacity until the pressure reaches the critical buckling pressure which will cause the buckling failure at the buckling lobe. The liner has a buckling failure at the end (stage CD). During stage AB, the test result and simulation result both indicate that the linear relationship between pressure and displacement is ended when the displacement reaches 12.53 mm, but the pressure of the test is 19.4% greater than simulation. At stage BC, the liner material may have had errors in the manufacturing process and the constraints of the flange on the liner in the test limited the displacement of the liner at both ends of the liner, producing end effects affecting the buckling cross-section in the test. When the displacement of the buckling lobe was equal, the pressure of the test result was greater than  
Figure 4: True stress versus true strain curve of FIPP material. the numerical result during the buckling process. Hence, the liner stiffness in the test was significantly greater than the simulation. At point C, the liner reached the critical buckling pressure of 38.08 kPa when the displacement of the buckling lobe was 52.77 mm in the test and the liner reached the critical buckling pressure of 35.94 kPa when the displacement of the buckling lobe reached 76.39 mm in the numerical results. The critical buckling pressure in the test was 5.6% greater than the simulation and the displacement of buckling lobe in the simulation was 30.9% greater than in the test. In stage CD, when the displacement of the buckling lobe increased to 74.4 mm in the test, the buckling lobe began to move axially to the port along the liner and the liner eventually failed (Figure 6), while the buckling lobe continued to deform in the numerical results. This paper mainly studied the influence of changing geometric parameters on critical buckling pressure. Although the pressure of the simulation result was lower than the test result during the buckling process, the accuracy of the critical buckling pressure was still reliable. Figure 5: Comparing the pressure–displacement curves of test and simulation divided into floating-stage (AB), buckling stage (BC) and failure stage (CD).