of the plastic layers corresponds to 5.74% of the total tensile strength, as shown in Figure 4.20, where W stands for tensile wire strength, while WP accounts also for HDPE layers. This result demonstrates the neglection of their influence is reasonable for further studies in order to get conservative results.
Figure 4.20 Tensile force comparison.
The comparison in terms of radial displacement does not provide reliable results if the interlocked pressure armor is included in the pipe profile. Several reasons could be attributed to this deficiency. The assumption of equivalent pressure armor as an orthotropic cylinder leads to the hypothesis of continuous geometry in the theoretical model, while gaps, rough surfaces and winding angle appear in the FEM simulation. Besides, they could also be affected by the thickness variation in different layers, which is not considered in the analytical model.
In order to get acceptable results from FEM, points which are not in correspondence of the gaps between wires are chosen to investigate the contact pressure, and the selected points are shown in Figure 4.19.
The average results among the outcomes are compared to the theoretical ones, as shown in Figures 4.21 and 4.22. As they show good accordance, Eq. (4.9) could be used as a rough estimation to carry out the contact pressure between the two different layers.
Figure 4.21 Contact pressure between pressure armor and inner tensile armor layer.
Figure 4.22 Contact pressure between tensile armor layers.
The evaluation in terms of stresses regards the tensile armor is conducted, being the one that provides most of the strength in the longitudinal direction. The theoretical model assumes that strain and stress is axisymmetric, i.e., the stress for all the wires at the same pipe cross section is assumed to be the same. Von Mises stress contour plot of the outer tensile armor layer is shown in Figure 4.23, with its active view cut in z plane. Selecting the points from all the wires located at the mid-span and comparing their stresses and strain with the theoretical results as shown in Figure 4.24, it can be observed that, even if there are some fluctuations, their amplitude is still not high.
A random wire from each layer was chosen to conduct the comparison between the Mises stress and the elongation, as shown in Figures 4.25 and 4.26. The comparison between the trends leads to a remarkable confidence in terms of stress behavior.
Once the validity of the theoretical model is proved, it is extended in order to consider the contribution of the external pressure. Longitudinal displacements are applied at a constant rate until 20 mm, while constant pressure equal to 20 MPa is applied on the outer surface of the tensile armor layer. Only the contribution of the tensile armor is considered as previously explained in Figure 4.20. As it was expected, the presence of the pressure armor in the profile of the pipe makes the structure stiff enough in radial direction so that the hydrostatic pressure does not affect the tensile capacity of the pipe in a notable way, which is just slightly reduced, as shown in Figure 4.27, where T stands for pure tensile load and TP stands for combined tensile and external pressure loads.
Figure 4.23 Mises stress—outer layer of wires.
Figure 4.24 Strain and stress distribution for outer tensile armor layer.
Figure 4.25 Mises stress comparison for inner tensile armor layer.
Figure 4.26 Mises stress comparison for outer tensile armor layer.
Figure 4.27 Tensile strength comparison for the pipe subjected to pure tension and combined external and tensile loads.
4.5 Parametric Study
In this section, the reference case of “metallic strip flexible pipes” subjected to pure tensile load is included, which is regarded as Case 1. The study has already been developed in [16] for a range of MSFP which does not include the pressure armor layer in the profile. It has been observed that, found out that, for this kind of pipe, the tensile force is mainly due to the PE layers.
Based on MSFP’s structure, the extra pressure armor layer is added in its inner reinforcement cross-section design, regarded as Case 2. As previously shown, the contribution to the overall radial stiffness induced by the pressure armor allows the possibility of neglecting the innermost and outermost HDPE layers. The tensile armor layers, existing in Case 3, are substituted by four steel strip reinforced layers accounting for thickness h = 0.5 mm. The detailed longitudinal profile of Case 2 is illustrated in Figure 4.28. For this numerical campaign, the inner diameter and the loading condition are the same as the previous case. The theoretical model is extended to the new geometry, for which the coefficients expressed in Eqs. (4.11) and (4.12) should be modified by considering the variation in terms of number of layers and thickness, which can be expressed as
(4.15)