1. Introduction
Fiber-reinforced flexible pipes are a new type of offshore composite pipes manufactured by companies such as Technip [
1] and DeepFlex [
2] in recent years. These pipes comprise multiple reinforcement and polymer layers, similar to metal-reinforced flexible pipe [
3]. However, metal-reinforced spiral belts are replaced by composite-reinforced spiral belts in fiber-reinforced flexible pipes, resulting in lower weight and better chemical and fatigue resistance.
The glass fiber-reinforced unbonded flexible pipe investigated in this study comprises nine layers, as shown in
Figure 1. The liner, membrane, and outer sheath are PE (Abbreviations are all listed in notation list, see
Table 1) layers formed by extrusion molding that separate the transmission medium from the external seawater. The inner hoop layer is a cylindrical structure comprising two sublayers formed by curing after cross-winding of glass fiber. The tensile and hoop reinforcement layers comprise GFRP spiral belts wound in a single direction via wet winding. Owing to the different winding angles and thicknesses, the tensile and hoop reinforcement layers contribute primarily to the axial and radial stiffness, respectively.
The excessive deformation of pipes and the rupture of tensile armors caused by axial tensile loads are typical failure modes of flexible pipes [
4]. Although the weight of fiber-reinforced flexible pipes is lower than that of typical flexible pipes, the axial tensile loads caused by the gravity of pipes in deep water are non-negligible. Therefore, the tensile stiffness and ultimate capacity of fiber-reinforced flexible pipes under axial tension must be investigated.
Some scholars have proposed analytical models to predict the tensile behavior of flexible pipes. Oliveira et al. [
5] proposed a simple analytical formula based on strain and geometrical relationships to evaluate the axial stiffness of flexible pipes. Lu et al. [
6] and Yue et al. [
7] established theoretical models considering the radial contractions of the liner and pressure armor layers to describe the axial tensile behavior of a shallow-water flexible pipe. Tang et al. [
8] proposed equations based on the tension and axial deformation relationship to calculate the tensile stiffness of umbilicals. Wang et al. [
9] introduced an analytical model based on the curved beam theory to investigate the tensile mechanical behavior of flexible pipes and cables with helically wound structures.
Numerical models that considered the detailed geometries and interactions of different pipe layers were used to simulate the tensile behavior of flexible pipes. Bahtui et al. [
10] performed a finite element analysis using ABAQUS/Explicit, and the results showed the hysteresis of the tensile response of a flexible pipe under a high radial pressure. Merino et al. [
11] established a flexible pipe model based on beam and shell elements using ANSYS to predict the effect of end constraints and friction coefficients on the tensile response. Ren et al. [
12] established a detailed finite element model based on ABAQUS/Explicit. In consideration of the interaction between all layers, the axial tensile stiffness of an eight-layer unbonded flexible riser was predicted.
In terms of experimental research, Ramos Jr. et al. [
13] conducted an axial tensile test on a flexible pipe to measure the axial and transverse strains of the outer tensile spiral belts and the axial displacement of the pipe. Lopez et al. [
14] conducted a dynamic tension test on a flexible pipe and identified the rupture of tensile armors using accelerometers, inclinometers, and strain gauges. Bai et al. [
15] investigated the axial tensile behavior of a steel strip-reinforced flexible pipe through a full-scale test to determine the effects of the loading rate and friction coefficient on the ultimate capacity and failure mode of the pipe. In consideration of internal pressure on the tensile response of steel strip-reinforced flexible pipes, Chen et al. [
16] investigated the typical failure characteristics of the pipe via full-scale tests. A full-scale axial tensile test was conducted by Liu et al. [
17] to investigate the effect of the internal friction and viscoelastic properties of polymeric layers on the axial behavior of the flexible pipe.
In consideration of the stress concentration of flexible pipes, Dong et al. [
18] investigated the effects of end restraints on the stresses of the tensile armors under axial tensile loads using the finite element method. An analytical model based on strain energy and the Euler equation was also derived by Dong et al. [
19] to clarify the effects of end restraints. Nassiraei and Rezadoost [
20] investigated the effect of fiber-reinforced polymer layers and joint geometry on the stress concentration factors of tubular joints using finite element models and empirical formulas. Zhu et al. [
21] demonstrated that ovality exerted a limited effect on the tensile stiffness of flexible pipes but resulted in stress concentrations on tensile armors. De Sousa et al. [
22] and Zhu et al. [
23] investigated the axial tensile response of a flexible pipe with damaged tensile armor wires; subsequently, stress concentration was observed in wires adjacent to the damaged wires.
The tensile strength of flexible pipe has also been investigated by some scholars. Goto et al. [
24] proposed an equation based on the force equilibrium between the axial and circumferential directions to calculate the tensile strength of the pipe. Yim et al. [
25] equated the carcass and pressure armor layer to orthotropic shells, and proposed constitutive, compatibility and force equilibrium equations for a flexible pipe; subsequently, the ultimate strength of the tensile layer was obtained using a regression analysis. Considering the plastic behavior of materials, Cornacchia et al. [
26] proposed a theoretical model using the secant modulus to calculate the tensile strength of unbonded flexible pipes.
The tensile behavior of flexible pipes with composite layers has received attention in recent years. Xu et al. [
27] investigated the effect of the filament winding angle, fiber volume ratio, and diameter–thickness ratio on the tensile stiffness of glass fiber-reinforced bonded flexible pipes using theoretical and finite element models. Fang et al. [
28] proposed analytical and numerical models by embedding glass fibers into a matrix to simulate the mechanical behavior of a glass fiber-reinforced bonded flexible pipe under tension and internal pressure. Zhou et al. [
29] investigated the tensile behavior of a flexible pipe with partial composite reinforcement layers using the finite element method, where predefined beam elements and laminated shell elements were selected for spiral belts and fiber-reinforced inner jackets, respectively. Liu et al. [
30] proposed a theoretical model based on the energy method and a numerical model using ABAQUS to simulate the tensile behavior of flexible pipes with partial composite reinforcement layers.
Past research on the tensile behavior of flexible pipes has mostly focused on metal-reinforced flexible pipes, while little relevant research has been performed on fiber-reinforced unbonded flexible pipes, which are entirely composed of composite and polymer materials. The mechanical properties of composites are more complex than metal materials due to anisotropy, which leads to difficulties in research. The axial tensile behavior of a glass fiber-reinforced unbonded flexible pipe within the elastic deformation range was investigated in this study using established analytical models, while considering the anisotropy of materials and the effect of radial deformation. The classical laminate theory was used in the analytical model to obtain the engineering constants of the inner hoop layer. A 3D numerical model was established to validate the analytical model; subsequently, the distribution characteristics of the strains, stresses, and axial displacement of the pipe were obtained. Additionally, a prototype test was performed to measure the fiber-direction strain of the spiral belts in the outer tensile reinforcement layer.
4. Conclusions
In this study, the mechanical characteristics of a glass fiber-reinforced flexible pipe under an axial tensile load were investigated using analytical, numerical, and experimental methods. Based on the load–strain relationship of different layers, analytical equations considering the anisotropy of the material and the effect of radial compression deformation were derived to calculate the axial tensile stiffness of the pipe. A 3D numerical model was established to simulate the axial tensile behavior of the pipe; thus, the distributions of strain and stress in different layers and the axial displacement of the pipe were obtained. An axial tensile test was performed to measure the fiber-direction strains of the multiple spiral belts in two sections of the pipe. Based on a comparative analysis of the results of different methods, the following conclusions were inferred:
The winding angle significantly affected the axial load capacity of the spiral belts in the tensile reinforcement layers because the stiffness of GFRP is mainly provided by fibers. A smaller winding angle is more conducive to the axial load capacity.
The errors between the results of the average fiber-direction strains of the outer tensile reinforcement layer in Sections S1 and S2 by the numerical model and test are insignificant, which indicates the high accuracy of the finite element model.
The distribution of the fiber-direction stress in Layer L8 is relatively uniform along the axial and circumferential directions of the pipe, except for the regions near the end sections. The inner hoop and hoop reinforcement layers are subjected to compressive stress in the fiber direction, which indicates the radial compression effect of the pipe under an axial tensile load.
The result of axial tensile stiffness calculated by the analytical model considering radial compression is very close to that obtained by the numerical model; thus, the accuracy of analytical model is proved.
In summary, the analytical model considering the radial compression of the pipe has high accuracy in predicting the axial tensile stiffness of fiber-reinforced flexible pipes. The finite element model can also provide accurate descriptions of the distribution characteristics of strain and stress. Nevertheless, the analytical and numerical models proposed in this study can only be used for the elastic deformation range of fiber-reinforced flexible pipes. When the pipe is subjected to a larger axial tensile load, the spiral belts may rupture or other damage may occur. In future studies, the ultimate strength of GFRP should be considered such that the tensile failure behavior of fiber-reinforced flexible pipes can be investigated.