pressure. As can be seen, before the yielding of the pressure armor, the results of the two methods are in good agreement. After the yielding occurs, the errors of the two methods begin to appear. The growth rate of the Mises stress obtained from FEM is slower than that from the theory. The main reason is that the self-locking of the pressure armor in the finite element method will cause the redistribution of stress in the section, which makes it difficult to predict the stress. While the theoretical method doesn’t take this change into consideration. After yielding, the maximum von Mises stress of two models keep increasing slowly and the Matlab’s reaches to the ultimate strength firstly. Generally speaking, the difference between the two methods is not very big. The analytical result is 71 MPa while numerical result is 74 MPa when the maximum von Mises stress reaches to the yield strength. As for getting to the ultimate strength, the analytical result is 75 MPa while the numerical result is 80 MPa.
Figure 3.10 Mises stress of Z-shaped section.
Figure 3.11 Pressure-maximum von Mises stress curve.
Figure 3.12 Pressure-axial displacement curve.
If the deformation of pipe is not restricted, the pipe cannot function normally. Figures 3.12 and 3.13 show the relationship between the axial displacement and the internal pressure and between the radial displacement and the internal pressure, respectively. The axial displacement takes the value of the coupling point RP2, and the radial displacement takes the value of the middle node of the Z-section selected. It can be found that the theoretical curve is in same trend with the finite element curve. While, FEM always lags behind the theoretical curve. This is because the deformation of the pressure armor will be limited by its self-locking structure, but this effect is not considered in the theoretical model. Therefore, in the subsequent deformation development, the finite element method needs more internal pressure to obtain the same deformation as the theoretical model. When the internal pressure continues to increase and reaches to the ultimate strength, the axial displacement and radial displacement begin to increase sharply. This also indicates that the pressure armor is the main internal pressure resistant structure. When it fails, it is considered that the pipe will soon fail.
Figure 3.13 Pressure-radial displacement curve.
3.5 Design
It can be found that the results in two models are in good agreement and the theoretical model has high accuracy in predicting the burst pressure of pipe. The results may be of interest to the manufacture factory engineers. It is convenient to design the structure of pipes by using the theoretical model under different internal pressure and different given radius. Other most simplify formulas are proposed in Handbook [6] which are shown in the below. The contribution of tensile armor to burst pressure resistance is expressed by
(3.15)
where ttot is the total thickness of the double tensile armor layers, R is the mean radius of layer, a is the winding angle, and σu is the ultimate tensile strength of the layer. The contribution of the tensile armor to end cap pressure resistance is expressed by
(3.16)
where Rint is the inner radius of the layer. The contribution of the pressure armor to burst pressure resistance is expressed by
(3.17)
where tj denotes the thickness of pressure spiral with layer number j and R is the mean radius of the Np pressure layers, respectively. The fill factor Ffj for pressure spiral wire layer j. The total hoop pressure resistance is the obtained by summing the contribution from each layer as
(3.18)
The burst pressure is then given by the smallest of phoop and pa:
(3.19)
It can be seen that R, ttot, and a take most significant roles in influencing the burst pressure. In the design procedure, we can adjust these parameters to meet the design requirement. In shallow water, steel strip reinforced thermoplastic pipe (related materials are shown in Table 3.3) is often used. Bai [11] has done some researches on the mechanical responses of SSRTP under pressure loads. In order to design structure of pipes economically and safely, this chapter uses two theoretical models to predict burst pressure in more models (shown in Table 3.4) to illustrate the procedure of designing under different serve conditions.
Table 3.3 Steel strip geometrical properties.
| Models | 207 GPa |
| Ultimate stress | 960 MPa |
| Poisson radio | 0.3 |
| Profile | 0.5 mm × 52 mm |
| Winding angle | 54.7° |
Table 3.4 Models with different inner radius.
| Model | Inner radius | Layers |
|---|---|---|
| A1 | 25 mm | Internal sheath + four layers steel strips + out sheath |
| A2 | 25 mm | Internal sheath + six layers steel strips + out sheath |
| B1 | 50 mm | Internal sheath + pressure armor + two tensile armors = out sheath |
