1. Introduction
Fiber-reinforced polymer (FRP) pipes are typically fabricated using polymers as the matrix and fibers as the reinforcing material [
1]. The performance characteristics of these pipes can be customized by adjusting the type of polymers as well as the type, volume fraction, and winding angle of the fibers [
2]. Compared to traditional steel pipes, FRP pipes exhibit outstanding chemical and physical properties such as corrosion resistance and a high strength-to-weight ratio. Consequently, they have found extensive applications in the petrochemical industry, marine engineering, and civil engineering [
3,
4,
5,
6]. Researchers have extensively investigated the mechanical properties of FRP pipes under various environmental conditions, including temperature [
7,
8], medium [
9,
10], and humidity [
11]. Studies have explored pipes’ behavior under internal pressure loads [
3,
4], axial loads [
12], radial loads [
13], and combined external forces [
14,
15]. The fiber-reinforced rubber (FRR) pipe is one of such pipes.The balanced performance of FRR pipes has also garnered attention. The balanced performance index measures the axial deformation capacity of the pipe under internal pressure [
16]. Pipes with good balanced performance can not only provide displacement compensation when transmitting pressurized media but also avoid exerting additional forces and displacements on connected equipments or pipelines. This balanced performance index represents a higher standard in the custom design of FRR pipes to meet specific application requirements compared to traditional criteria such as stiffness and failure.
In studying the balanced performance of FRR pipes, Gao et al. [
17] utilize thin shell theory to investigate the effects of fiber winding angles and pipe curvature radii on the balanced performance of the pipe, disregarding the influence of the rubber matrix. Based on the finding of Jaszak et al. [
18], which identified that the maximum stress in FRR pipes occurs in the fiber-reinforced layer, Xu et al. [
19] similarly ignored the impact of the rubber matrix in their theoretical study of the axial and lateral stiffness of self-balancing FRR pipes. However, Fang et al. [
20] use the finite element method to reveal that, despite the higher Young’s modulus of the reinforcing fiber, the larger volumetric proportion of the polymer matrix makes its influence on the mechanical properties of FRP pipes significant and non-negligible. Consequently, the impact of the rubber matrix on the balanced performance of FRR pipes has not been adequately addressed to date.
The “netting-analysis” method, which assumes that the internal pressure is borne solely by the reinforcing fibers and neglects the contribution of the matrix material, can be used to assess the stress state of FRP pipes [
21]. This theory suggests that the optimal fiber winding angle is 54.7°. However, Evans and Gibson [
22] point out that the accuracy of the “netting-analysis” results is valid only when the stiffness of the matrix is significantly lower than that of the reinforcing fibers. Nonetheless, they did not provide the specific stiffness ratio between the matrix and the reinforcing fibers for different materials. Gu et al. [
23], utilizing the three-dimensional anisotropic elasticity theory, derive the analytical solutions for the stress and strain distribution in steel-wire-wound reinforced rubber pipes.They attributed the discrepancies between their theoretical and experimental results to the simplification of the rubber matrix as a linear elastic material. In addition, researchers have employed various analytical methods to study the mechanical behavior of fiber-reinforced composites. For randomly oriented graphene nanoplatelet-reinforced 2D notched epoxy plates, Kabir et al. use a meshless technique combining a Gaussian quadrature technique and a Bezier based multi-step method to investigate the stress of the plates [
24]. Wang et al. apply the generalized finite difference method combined with domain decomposition techniques and the meshless generalized finite difference method for the stress analysis of 3D elastic composites [
25]. The simulation results demonstrate that this method is accurate and efficient in numerical simulations of multi-layered materials.
Gao et al. [
3] employ numerical methods utilizing the embedded element technique to simulate the embedding of reinforcing fibers within the rubber matrix. This study examines the effects of different fiber and rubber materials on pipes’ deformation, stress distribution, and failure mechanisms under internal pressure, accounting for the nonlinear characteristics of both the fiber and rubber materials. The reliability of the numerical results is verified through experiments. Similarly, Wei et al. [
26] investigate the impact of fiber winding angles and twisting directions on the torsional stiffness of FRP pipes using numerical methods, considering the nonlinearity of materials. The numerical results are also validated against experimental findings. Moreover, the literature [
27,
28,
29,
30] includes in-depth analyses of the mechanical properties of FRP pipes, incorporating material nonlinearity into their numerical methods and validating these findings through experimental results. In conclusion, these studies indicate that the numerical method can accurately simulate the mechanical behavior of FRP pipes made from various polymers and fibers under different loading conditions. Furthermore, numerical methods enhance the intuitive and detailed understanding of deformation, stress, and strain, thereby serving as a valuable tool for studying the balanced performance of FRR pipes.
The winding angle of fibers is a critical parameter influencing the mechanical properties of FRP pipes [
2]. Consequently, the balanced performance of pipes can be achieved through specific winding angles of fibers [
19]. According to the literature [
31], the sensitivity of a pipe’s leakage and fracture strength are significantly affected by the fiber winding angle. Krishnan et al. [
32,
33] employed experimental methods to study the failure modes of glass/epoxy pipes with fiber-reinforced layers wound at
,
, and
under multiaxial cyclic loads. The results demonstrated that the optimal winding angle differs for pure hydrostatic loading, hoop to axial loading, and quad hoop to axial loading. Beyond the investigation of single winding angles, Xia et al. [
34] explore the axial and torsional strength of multi-layered filament-wound pipes under internal pressure, concluding that the stacking sequence of fiber-reinforced layers plays a crucial role in determining the stress and deformation of the pipes. Further studies have combined the winding angle of fibers with other structural parameters to explore the impact on the mechanical properties of FRP pipes under multivariable influences [
35,
36]. However, the influence of fiber winding angle on the balanced performance of FRR pipes has not been sufficiently explored in the existing literature.
The purpose of this study is to investigate the balanced performance and axial stiffness of the FRR pipe under internal pressure. To achieve this, experiments are conducted to reveal the structural response of the pipe under maximum working pressure, and to investigate the combined influence of internal pressure and axial load. To characterize the nonlinear mechanical properties of the rubber material, the strain energy density model is fitted based on deformation test results. Subsequently, a numerical model considering the interaction between the rubber matrix and reinforcing fibers is developed. The reliability of this numerical model is verified through experimental validation. Additionally, this study reveals the influence of fiber winding angles on the balanced performance and axial stiffness of the FRR pipe.