Theoretical and experimental study on the continuum damage mechanical (CDM) behavior of RTPs under axial tension
Introduction
Composite materials have been used to build pipes for oil exploration in the field of ocean engineering due to practical advantages such as good corrosion resistance, good thermal insulation and light weight (Martins et al., 2013; Bai et al., 2014; Toh et al., 2018). Among various composite pipes, reinforced thermoplastic pipes (RTPs) received considerable attention from the engineers and researchers. Until now, RTPs have been used as water injection pipes, oil gathering pipes and gas export pipes in some shallow-water areas of the Middle East and Southeast Asia for years, which held out a cheerful application prospect (Dalmolen et al., 2009). As shown in Fig. 1, the liner and the coating made of homogenous materials such as PE, PA and PVDF are used to resist the corrosion from the transported fluids and saline seawater. As main load-bearing layers, laminates normally are made of polymer matrix and reinforced fibers which wound in different angles (Bai et al., 2015; Yu et al., 2015).
As the exploration of oil and gas moves into deep water, prediction on the load-bearing capacity and stiffness characteristics of RTPs are becoming more important. Lekhnitskii (1981) proposed the theory of elasticity of an anisotropic body, which provided a basis for numerous theoretical research including studies on the bending stiffness, the axial stiffness and the prediction of stress field (Jolicoeur and Cardou, 1994; Zhang and Hoa, 2012; Sun et al., 2014a). Sun et al. (2014b) proposed the homogenization assumption, in which RTPs are assumed as homogenized pipes. Because of this, RTPs can be described by nine homogenized elastic constants, which improves the efficiency of evaluating RTPs a lot. By summarizing a large number of previous experimental and theoretical work, NASA SP-8007 (1986) gave many classical formulae to predict the load-bearing capacity of orthotropic cylinders subjected to axial compression, bending, torsion and lateral pressure. However, there is no any relatively complete analytical model to predict the mechanical response of RTPs under ultimate tension including the elastic stiffness, the first-ply-failure load, the CDM and plastic behavior.
For experimental research on RTPs under axial loads, Khalifa et al. (2012) conducted tensile test on four specimens made of glass fiber and vinyl ester resin. According to ASTM-D 2105-01 standard (2007), the test loading rate was determined as 10 mm/min. Meanwhile, acoustic emission and Scanning Electron Microscope were used to identify the damage mode. It divided the damage process into four steps: matrix cracking, microscopic cracks to fiber/matrix interface, propagation in the matrix and fiber failure, and also verified that acoustic emission is a reliable method to observe the behavior of RTPs. özbek et al. (2019) performed quasi-static compression tests on the basalt, glass and basalt/glass fiber reinforced pipes and identified three distinct failure mode including transverse shearing, lamina bending and local buckling. The discussion about the energy absorption capability illustrated that composite pipes can be used to improve crashworthiness of structures. Betts et al. (2019) conducted compression and tension tests on filament wound glass fiber-reinforced polymer pipes, which were verified by an analytical model based on existing methods. Experiments can give accurate results, but would cost a lot on some special-designed testing devices. For numerical simulation, Ren et al. (2013) conducted ABAQUS Explicit quasi-static analyses on unbonded flexible risers to predict the axial stiffness. Compared with previous experimental results, it had high accuracy. Liu and Wang (2020) used the same numerical method to predict the homogenized axial moduli of RTPs, which agreed well with analytical results. Compared with experimental research, numerical simulation can give accurate results with a lower cost, and provide a much simpler way to observe stress field.
When composite laminates are under ultimate loads, the nonlinear response related to continuum damage mechanical (CDM) behavior would play a key role on determining the life of marine structures. Hashin and Rotem (1973), Hashin (1980) divided the damage mode of composite materials into tensile fiber mode, tensile matrix mode, compressive fiber mode and compressive matrix mode according to stress conditions. Yeh and Kim (1994), Yeh and Chern (1998) proposed a similar formula to evaluate the delamination of adjacent composite laminates. Based on Hashin and Yeh's work, a nonlinear stiffness degradation model in the open literatures (Zhang et al., 2013; Yao et al., 2019; He et al., 2019) was developed and used to simulate the CDM behavior of composite sheets, which coincided with experimental results. Because of accessible concept and high accuracy, the Hashin-Yeh failure criterion and this nonlinear degradation model were widely used to evaluate the damage condition of composites in open literatures.
This research focuses on the linear and nonlinear mechanical behavior of RTPs under axial tension. To predict the CDM response, an analytical model is proposed by combing the existing homogenization method, failure criteria and material degradation models in a cyclic program. According to the existing homogenization method, stress distributions are obtained by replacing original RTP models with homogenized pipes. As the homogenization method ignores the effect of cross-sectional curvature on damage sequences, a stress correction factor is defined to take it into account. Once corrected stresses of homogenous layers satisfy von Mises criterion, Ramberg-Osgood curve is used to update elastic constants of isotropic materials. For composite laminates, a nonlinear stiffness degradation model is adopted to update the stiffness matrix if Hashin-Yeh failure criterion is satisfied. To verify the proposed model, quasi-static uniaxial tension tests and numerical simulation calling a VUMAT subroutine were conducted to observe the stress field. The proposed model was found to give accurate prediction on stiffness characteristics and stress field, and have functions including identifying damage location, predicting failure mode, and analyzing damage propagation. Furthermore, the effects of winding angles are studied, which showed that dominant failure mode would change from tensile fiber to tensile matrix as winding angles increase.
Section snippets
The analytical CDM model
Normally, RTPs are made of many cylindrical fiber-reinforced laminates. As shown in Fig. 2, all layers are bonded together, so voids and delamination are not considered in the elastic phase of the theoretical model. The cross-sectional feature of a RTP can be described by the internal radius of the ith layer ri, the winding angle of fibers in the ith layer ϕi, the number of layers n, the internal radius of RTPs a and the external radius b.
Axial tension test
Axial tension test was performed on two RTP specimens to verify the CDM model developed in the present paper. The specimens were produced by Weihai Nacheon Pipeline Co., Ltd., which consisted of liner, coating and four composite laminates. Coating and liner are made of PE, and composite laminates are made of glass-fiber/PE tapes. The winding angles of fibers in adjacent layer are 55°/-55°. The internal diameter is 47.5 mm. Other geometrical and material parameters are listed in Table 1 and
Numerical simulation
As composite layers are in the middle of liner and coating, it is difficult to observe the stress field during the experiment process. Compared with experimental methods, numerical simulation provides a simple and effective way to understand stress distribution of composites.
The comparison of different methods
The comparison of different methods is shown in Fig. 8. It is clear to see that RTPs firstly comes into the elastic phase, so the first part of the tension-strain curve is linear. It means that the elastic stiffness keeps constant in the elastic phase, so the winding angle change during the loading process has few influences on the elastic stiffness and could be ignored. When the tension increases to a critical point, the first ply failure (FPF) occurs. The numerical and analytical results
Conclusions
This work investigates the mechanical response of RTPs under axial tension by analytical, experimental and numerical methods. In the present paper, an analytical CDM model is proposed to predict the linear and nonlinear behavior of RTPs by executing the existing homogenization method, failure criteria and material degradation models in an iterative and cyclic way. Stress distributions are obtained by using the existing homogenization method. As the homogenization method ignores the effect of
Acknowledgements
This work is supported by the National Science Fund for Distinguished Young Scholars, China [No.51625902], the Offshore Flexible Pipe Project from Ministry of Industry and Information Technology, China, the Taishan Scholars Program of Shandong Province, China [TS201511016], and National Natural Science Foundation of China [No.51879249]. The help from Dr. Wentao He for numerical simulation is also greatly appreciated.
References (37)
- et al.
Collapse of reinforced thermoplastic pipe under combined external pressure and bending moment
Ocean. Eng.
(2015) - et al.
Buckling stability of steel strip reinforced thermoplastic pipe subjected to external pressure
Compos. Struct.
(2016) - et al.
Investigation of the stress-strain constitutive behavior of ±55° filament wound GFRP pipes in compression and tension
Compos. B Eng.
(2019) - et al.
Effect of structural parameters on low-velocity impact behavior of aluminum honeycomb sandwich structures with CFRP face sheets
Thin-Walled Struct.
(2019) - et al.
Mechanical characterization of glass/vinylester ±55° filament wound pipes by acoustic emission under axial monotonic loading
CR Mecanique
(2012) - et al.
Three-dimensional progressive failure modeling of glass fiber reinforced thermoplastic composites for impact simulation
Compos. Struct.
(2017) - et al.
An elastic stability-based method to predict the homogenized hoop elastic moduli of reinforced thermoplastic pipes (RTPs)
Compos. Struct.
(2019) - et al.
Analytical prediction of buckling collapse for reinforced thermoplastic pipes based on hoop stress analysis of crushed rings
Ocean. Eng.
(2019) - et al.
The effect of stress ratio on the fracture morphology of filament wound composite tubes
Mater. Des.
(2013) - et al.
An experimental study on intraply fiber hybridization of filament wound composite pipes subjected to quasi-static compression loading
Polym. Test.
(2019)
Material characterization of filament-wound composite pipes
Compos. Struct.
Investigation on impact behavior of FMLs under multiple impacts with the same total energy: experimental characterization and numerical simulation
Compos. Struct.
Analysis of flexural behavior of reinforced thermoplastic pipes considering material nonlinearity
Compos. Struct.
A limit-based approach to the stress analysis of cylindrically orthotropic composite cylinders (0/90) subjected to pure bending
Compos. Struct.
Response of sandwich structures with pyramidal truss cores under the compression and impact loading
Compos. Struct.
A method to analyze the pure bending tubes of cylindrically anisotropic layers with arbitrary winding angles including 0° or 90°
Compos. Struct.
Behavior of reinforced thermoplastic pipe (RTP) under combined external pressure and tension
Ships Offshore Struct.
A theory of elastic, plastic and creep deformations of an initially isotropic material showing anisotropic strain hardening, creep recovery and secondary creep
Appl Mech
Cited by (21)
Multi-time scale thermal tribological dynamics coupling model of the helicopter intermediate reducer under severe loss of lubrication
2024, Simulation Modelling Practice and TheoryInvestigation on fracture behaviour of UHPFRC using a mesoscale computational framework
2024, Computer Methods in Applied Mechanics and Engineering3D concrete fracture simulations using an explicit phase field model
2024, International Journal of Mechanical Sciences