A review of the design and analysis of reinforced thermoplastic pipes for offshore applications

Liner and cover

The liner and cover are designed to contain the internal transported product and protect the reinforcing layers from external corrosion damage, respectively. Various thermoplastics, such as polyethylene (PE), cross-linked polyethylene (PEX), polyamide (PA) and polyvinylidenefluoride (PVDF), can be used to manufacture the liner and cover. Pipe-grade PE is widely used to manufacture the liner and cover as it is a commonly adopted material in oil and gas production while the use of other thermoplastics for more specialised fluid services is under development.^37,38 The properties of some thermoplastics available in the market are given in Table 2.^39–45

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Table 2.

Properties of commercially available thermoplastics.^39–45

Thermoplastic	Density (kg/m3)	Elastic modulus (MPa)	Tensile strength (MPa)	Elongation to failure (%)	Maximum service temperature (℃)
PP	917	1300	35	225	104
LLDPE	922	600	16.1	659	70
LDPE	850	204	20	537	70
MDPE	950	800	23.7	522	70
HDPE	1040	953	22.5	651	70
PA 66	1700	2800	80	50	98.9
PPS	1430	3800	65	16.4	227
PEEK	1400	3600	92	24.4	240

Reinforcing layer

The structural reinforcing of an RTP consists of several angle-ply layers made from fibre reinforcements and thermoplastic matrix materials with a winding angle of 54.7°. This winding angle is commonly adopted in the design of RTPs to fully utilise the strength properties of the fibre reinforcements in the reinforcing layers based on the ‘netting analysis’, ⁴³ which is often used as an effective tool in the design of composite pressure vessels. However, it should be noted that this analysis is only valid when the resultant hoop to axial stress ratio is 2:1 but gives no indication of the strength of the pipe if the ratio of applied stresses varies, which can be caused by even small changes in operational conditions. ⁴⁶ Obviously, the winding angles that result in the best performances of composite pipes under other loading cases could be different from 54.7°. Also, apart from structures with single winding angles of ± θ , it has been reported that angle-ply reinforcement layer systems with two different angles of the reinforcement orientation [ ± φ / ± ϕ ] can also be successfully employed in composite pipes due to the balanced nature of this type of composite structure and could improve the axial load-bearing capacity of a pipe. ⁴⁷

Reinforcement materials

The reinforcements in the reinforcing layers, which are the principal load-bearing components of an RTP, can be constructed using either high-strength fibres (e.g. glass, carbon or aramid) or metallic materials (e.g. steel wires or tapes). The latter can also be classified into whiskers, metal wools (e.g. steel wool) and metal filament-length fibres, with metals such as beryllium, steel and tungsten commonly used. A beryllium reinforcement has a low density and high modulus while the density of a tungsten wire is higher. Steel wires are the most important metallic reinforcements and exhibit high and consistent strength. It has been reported that a new type of plastic-matrix steel composite pipe, a plastic pipe reinforced by cross-helically wound steel wires (PSP), has been developed in China for use in several areas, including petroleum transportation, chemical engineering and municipal water supplies. ⁴⁸

Glass fibre

Glass fibres are the most widely used reinforcements in the manufacture of composite materials due to their cheap prices. Also, they have good temperature and chemical resistance, low moisture absorption and high tensile strength. Generally, there are several types of glass fibres: A-glass (A for ‘alkali’), E-glass (E for ‘electrical’), C-glass (C for ‘chemical’), D-glass and S-glass. A-glass is the original type of glass fibre, which has been almost completely replaced by other types, with E-glass the most popular because of its excellent properties and relatively low cost. As S-glass fibres are designed to possess a high strength and modulus to meet the requirements of very technical applications, such as in the aerospace and military industries, they are more expensive than E-glass. Other types of glass fibres have been developed to meet specific demands; for instance, C-glass fibres are employed mainly for surface tissue due to their good chemical resistance.

Carbon fibre

Carbon fibres are generally considered to be high-performance reinforcements with high strength and modulus but are expensive. They are produced mainly from polyacrylonitrile (PAN) heat-treated at temperatures ranging from 1000 to 3000℃, which control their tensile strength and elastic modulus, according to which they can be roughly divided into high-strength (HS) and high-modulus (HM) carbon fibres (e.g. AS4 and P75, respectively). Apart from their high strength and modulus, these fibres also improve the fatigue characteristics of FRP composites as they can reduce the strain in the polymer matrix material for a given load. ⁴⁹ In addition, their low coefficient of thermal expansion (CTE) and high corrosion resistance enhance their attraction as reinforcements for FRP composites. ⁵⁰ Therefore, even though applications of carbon fibre-reinforced composites (i.e. AS4-carbon fibre-PEEK) are currently limited mainly to the aerospace industry, they are increasingly being employed in offshore applications, especially those in deep water, as they can maintain their mechanical properties in seawater and provide additional cost savings in terms of weight in comparison with steel. ⁶ However, the impact resistance of composites reinforced by carbon fibres is not as good as that of glass fibre-reinforced composites.

Aramid fibre

Aramid is the generic name for a family of organic fibres with low density and high tensile strength. These fibres are usually produced as filament yarns, rovings or chopped fibres, all of which have a characteristic bright golden-yellow colour. They are commonly used in the military industry, especially in anti-ballistic applications, due to their light weight, and high impact and abrasion resistance; for instance, Kevlar™ is the trade name of aramid fibres manufactured by DuPont, which was originally a gunpowder producer and famous for military helmets and body armours. ⁵¹ Nevertheless, applications of aramid fibres are no longer restricted to the military industry as they are now widely used as reinforcements in RTPs for offshore oil and gas applications. Twaron™ is the brand name of Teijin Aramid, which is developing lightweight, flexible Twaron-RTPs to overcome many of the issues which affect existing steel-based pipe systems. ⁵²

Summary of fibre properties

Other fibres which could be used as reinforcements in FRP composites include boron, ceramic, silica and ultra-high molecular weight PE (UHMW-PE). The mechanical properties of different types of fibres are given in Table 3.^48,52–56

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Table 3.

Properties of different types of fibres.

Fibre	Density (kg/m3)	Tensile strength (MPa)	Elastic modulus (GPa)	Elongation to failure (%)
Steel wires 48	–	1832	210 53	5
E-glass 54	2541	3450	72.4	1.8–3.2
C-glass 54	2492	3160	68.9	4.8
S-glass 54	2492	4590	85.5	5.7
AS4 55	1750	3590	235.0	–
P75 56	2160	1900	517.0	–
Twaron 52	420–3360	–	60–80	3.0–4.4

Matrix materials

Two main classes of resins are usually used as matrix materials in FRP composites: thermoset plastics and thermoplastics. The stress–strain relationships of most thermoset plastics, such as polyester, vinylester and epoxy, are almost linear in the elastic range, as shown in Figure 2. Thus, their mechanical behaviours can be successfully described by the classic laminate theory.^57,58 Due to their attractive properties, such as high chemical resistance, low processing temperatures and good fibre impregnation, thermoset plastics are commonly used matrix materials in FRP composites. However, it has been reported that glass fibre-reinforced polyester pipes show fluid weepage at about 20% of their burst pressure due to the transverse cracking of the matrix materials. ⁵⁹ This brittle failure mode is commonly observed in fibre-reinforced thermosetting composites, which prevents the strength properties of the fibre reinforcements being fully utilized. ⁶⁰ In contrast to fibre-RTPs, glass fibre-reinforced PE pipes can remain fluid tight up until the time of failure of the reinforcements. ⁶¹ Also, in contrast to the linear stress–strain relationships of thermoset plastics, PE has shown highly nonlinear responses to loading which creates difficulties in accurately modelling its mechanical behaviours. The stress–strain curves of PE are shown in Figure 3.

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Figure 2.

Stress–strain curves of polyester and epoxy resin.^62,63

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Figure 3.

Stress–strain curves of MDPE (PC2040) subjected to uniaxial loading. ⁶¹

The mechanical properties of thermoset plastics and thermoplastics during heating are also different. Thermoset plastics can retain their shape over a wide range of temperatures as their microstructure consists of an irreversible molecular chain. However, high temperatures soften thermoplastics, which harden again when cooled, a property that is important as it enables thermoplastic pipes to be repaired. ⁶⁴ Also, the elastic modulus of PE changes substantially with temperature. Alawaji ⁶⁵ conducted full-scale experiments to investigate the effects of temperature on HDPE pipes. According to the results, the elastic modulus of a pipe is reduced by 62% when the temperature is raised from 30 to 70℃, an almost linear decrease. Bilgin et al. ⁶⁶ presented robust equations for calculating the elastic moduli of PEs (HDPE and MDPE) at different temperatures, which follow the basic trends of the data reported in the literature and experiments. They also found that the temperature has negligible effects on PE’s Poisson’s ratio and CTE.

The strength and failure mechanism of PE have been well documented.^67,68 According to API 17J, ⁶⁹ the maximum allowable strain for PE in static applications is 7.7% while a more conservative value of 5.5% is applied for the design of an RTP, which can be considered the strain limits of its liner and cover. ⁷⁰ Unfortunately, very little information on the strength characteristics of fibre-reinforced PE composites is openly available. Benjamin ⁷¹ tested the properties of MDPE (PC2040) and fibre-reinforced MDPE composites (DeLama DL/3 tape), with the results shown in Table 4.

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Table 4.

Properties of MDPE and fibre-reinforced MDPE composites.

	MDPE (PC2040)	DeLama DL/3 tape
Initial tensile modulus (MPa)	716.0	–
Ultimate tensile strength (MPa)	17.5	–
Transverse modulus (MPa)	–	691.0
Transverse strength (MPa)	–	15.2

Current commercial RTP products for offshore applications

At present, most commercial RTPs for offshore oil and gas applications are manufactured using pipe-grade HDPE (PE 80 or PE 100) and aramid fibre reinforcements.

Coflexip RTP

Coflexip® is the offshore branch of Technip-Coflexip, which has over 25 years of experience in manufacturing continuous flexible steel pipes for offshore oil and gas applications. They have developed a lightweight Coflexlite® RTP, which has inner and outer sheaths made from HDPE and middle layers consisting of double cross-wound aramid fibre tapes that provide a high pressure rating. Also, in collaboration with Technip, Cosmoplast® produces RTPs for offshore oil and gas applications, which can be supplied in coils with lengths of up to 500 m and enable easy and fast installation. ⁷⁶ The technical specifications of Coflexlite® RTPs are given in Table 5.

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Table 5.

Data sheet of Coflexlite® RTPs. ⁷⁷

Nominal diameter		3″	4″	5″	6″
Internal diameter	mm	74	101	127	152
External diameter	mm	102	135	162	191
Design pressure at 60℃	Bar	55	43	37	32
Burst pressure at 20℃	Bar	284	218	189	165
Burst pressure at 60℃	Bar	210	161	140	122
Minimum bending radius at 20℃	m	0.7	0.9	1.1	1.2
Weight in air empty	Kg/m	3.7	5.8	7.5	9.6
Thermal exchange coeff. at 20℃	W/m.K	4.6	5.7	6.7	7.5
Maximum length on one reel	m	1800	1000	500	250

Offshore pipes under internal pressure

The load-bearing capacity of pipes under internal pressure, usually referred to as the pressure capacity, is a primary concern for designing offshore pipes. Overestimating this capacity could lead to catastrophic failures of a pipe while underestimating the amount of product that could be transported, thereby lowering production and causing extra cost. The pressure capacity of a metallic pipe is well-documented in some industrial standards^82–84 and is determined mainly by its wall thickness and the yield strength of its material as: ⁸⁵

Due to the anisotropy of a composite material, it is more difficult to predict the pressure capacity of a composite pipe. As described above, the ‘netting analysis’ is primarily used to design cylindrical pressure vessels and shows that winding angles of ± 54.7° are the optimum ones for closed-end composite pipes based on the assumption that only fibres carry loads. ⁴³ Meiras ⁸⁶ conducted a series of experiments using filament-wound pipes with polyester and epoxy resin to demonstrate the effect of their matrix materials on their pressure capacity. He reported a knee in the axial stress/strain curve when a pipe is subjected to internal pressure and weepage, which he attributed to resin failure before fibre breakage. Hull et al. ⁵⁹ investigated failures of glass/polyester filament-wound pipes with winding angles of ±54.44° using closed-end and unrestrained-end internal pressure tests, with the experimental results agreeing well with most of the conclusions reported by Meiras. ⁸⁶ Weepage resulting from transverse cracking of the resin and resin/matrix interface occurs at about 20% of its burst pressure due to fractures of the fibres. This observation was confirmed by Jones and Hull ⁸⁷ who used standard microscopic technologies to examine failure mechanisms in filament-wound pipes. Then, Spencer and Hull ⁸⁸ studied the influence of winding angles of ± 35°, ± 45°, ± 65° and ± 75°, on the failures of filament-wound pipes under internal pressure. It was shown that the micro-mechanisms associated with deformation, weepage and fracture depend strongly on the winding angles under both closed-end and unrestrained-end boundary conditions. Rosenow ⁸⁹ extended Spencer and Hull’s study ⁸⁸ to six different winding angles varying from ± 15° to ± 85° using both the classic laminate theory and an experimental approach, which showed that the optimum winding angles which lead to the highest pressure capacity depend primarily on the state of loading. From his study, winding angles of ± 55° should be used as the optimum angles for only the closed-end loading case in which the hoop-to-axial stress is 2:1, and is consistent with the ‘netting analysis’. ⁴³ However, it should be noted that, in his experiments, even though the winding angles are set to ± 55°, the pipes still fail due to weepage before fibre breakage. Xia et al. ⁹⁰ obtained similar results as filament-wound pipes with winding angles of ± 30° and ± 70° showed brittle breaking behaviours caused by transverse tensile stresses. Evans and Gibson ⁹¹ investigated the effect of the matrix materials on the optimum winding angles in more detail. They showed that the actual optimum winding angles deviate from those predicted by the ‘netting analysis’ depending on the ratio of the matrix to reinforcement stiffness. Also, Parnas and Katirci ⁹² demonstrated that the optimum winding angle for filament-wound composite vessels ranges from 52.1° to 54.2° depending on the geometry and failure criteria used.

Studies of the mechanical behaviours of RTPs under internal pressure have been reported in recent years. Kruijer et al. ⁹³ developed a mathematical model based on a plane strain characterisation and conducted experiments to study the deformation behaviour of an RTP constructed of a PE liner pipe over-wrapped with two layers of non-impregnated twisted aramid cords when pressurised. The modelled hoop and axial strains showed considerable deviations from the measured values, which they suggested could be caused by the nonlinear behaviour of PE and, therefore, it is necessary to take into account material nonlinearity when modelling the mechanical behaviours of RTPs. They also indicated that the ratio between the average hoop and axial stresses is in the order of 2.25:1 for a closed-end RTP due to its geometry, which results in too much stiffness being applied in the axial direction and too little in the hoop direction when employing winding angles of ± 54.7°. Bai et al. ⁹⁴ studied the burst capacity of an RTP consisting of HDPE and a combination of aramid fibre reinforcements and HDPE matrix materials under internal pressure through experimental, numerical and theoretical approaches. The values of the STBPs predicted by the numerical simulations and theoretical calculations are shown to be 19.6% and 16.5% larger than the experimental results, respectively. This is caused by not considering the nonlinear mechanical behaviour of PE in either the numerical simulation or theoretical calculation. Then, Bai et al. ⁹⁵ investigated the mechanical behaviour of an RTP, the material and structure of which are similar to those of the RTP presented in Bai et al., ⁹⁴ under internal pressure using a FE model, an analytical solution and experiments. In the FE model, they adopted the progressive damage model proposed by Linde et al., ⁹⁶ which was originally used to model fibre-metal laminates, to determine the failure initiation and damage progression in the reinforced tapes with the HDPE modelled as a linear elastic material. The values of the burst pressure predicted by the FE model and analytical solutions are compared with the experimental results from which they show 18.1% and 26.4% deviations, respectively. It can be seen in the experiment that the orientation of the crack in the outer layer of the RTP is almost parallel to the fibre direction in the reinforced tape, which suggests that fibre breakage is the cause of failure of the entire pipe. The same results are observed in the pressure testing conducted by Gibson et al. ⁶¹ in which all specimens achieve the full strength of the reinforcements. They also demonstrated a modified laminate theory for analysing the mechanical behaviours of fibre-reinforced PE composites in which the nonlinear mechanical behaviour of the matrix materials are modelled numerically. Their approach shows reasonable agreement with most pressure-strain data from their experiments.

Offshore pipes under bending

Research on the flexural behaviour of long metallic and composite cylinders has been actively undertaken, with several studies on the reeling of metallic pipes reported in the literature.^97–99 It has been shown that the minimum allowable bend radius of a metallic pipe can be limited by the elastic strain limit of the metallic material as the pipe may bend into the plastic range during the winding and unwinding processes. Brazier ¹⁰⁰ studied the flexural behaviour of a long metallic pipe subjected to pure bending. Due to the induced bending moment, an ovalisation occurs in the cross-section of the pipe, resulting in a progressive reduction in its flexural stiffness, which is known as the Brazier effect. The pipe then buckles when the induced bending moment becomes larger than the critical moment. Kedward ¹⁰¹ extended Brazier’s approach to thin-walled orthotropic cylinders and presented theoretical solutions, which enable calculation of the critical moment for pipes made from orthotropic materials. Although Chan and Demirhan ¹⁰² created a closed-form solution to determine the bending stiffness of laminated composite pipes, their work was shown to be appropriate for only pipes with small diameters.

With the aid of Finite Element Analysis (FEA), Rodriguez and Ochoa ¹⁰³ conducted numerical studies to analyse the flexural behaviours of carbon fibre/epoxy and glass fibre/epoxy pipes, which showed that failures of the pipes are characterised by damage initiation in their composite layers. They analysed the progressive development of damage which indicated that, as expected, epoxy-based composite pipes cannot be used as spoolable pipes as they fail easily in the brittle mode under bending. Xia et al. ¹⁰⁴ developed analytical means of studying the stress–strain responses and deflections of filament-wound fibre-reinforced sandwich pipes subjected to pure bending but did not perform any failure modelling. Most recently, Ashraf et al. ⁴⁷ presented numerical studies investigating the spoolability of RTPs made from PEEK and AS4-carbon fibre-reinforced PEEK composites. Similar to the findings from Rodriguez and Ochoa’s analysis, the spoolability of this RTP is rather limited as it fails at a large radius due to a matrix failure in the transverse direction in the fibre-reinforced layers. Although the aforementioned studies provide effective methods for evaluating the flexural behaviours of pipes, most considered the mechanical behaviours of the materials to be linear elastic.

Offshore pipes under combined bending and external pressure

In the past, RTPs have primarily been used in relatively shallow water, at depths from 30 to 900 m, due to their low resistance to external pressure as excessive external pressure results in their catastrophic collapse. ¹⁰⁵ However, it has recently been reported that its light weight, high performance and good spoolability enable an RTP to be an ideal design for deep-water riser applications in which a pipe is expected to experience significant bending and high external pressure during its installation and operational phases.^106–108 The mechanical behaviour of offshore pipes subjected to combined bending and external pressure has attracted substantial attention over the last few decades. Corona and Kyriakides^109,110 investigated the collapse of long, relatively thick-walled metal pipes under combined bending and external pressure through experimental and numerical efforts, which showed that the nature of their instability and corresponding critical loads is dependent on their loading paths. Stephens et al. ¹¹¹ studied the nonlinear collapse of long, cylindrical shell structures subjected to combined bending and uniform normal pressure loads. They demonstrated that the circumferential flattening of a pipe’s cross-section is the dominant collapse mode for those with higher length/radius ratios. Experimental results of collapses of aluminium and steel pipes under combined bending and external pressure were reported by Kyriakides ¹¹² and Johns et al. ¹¹³ who showed that the nature of instability of a pipe also depends on its D / t ratio. In addition, Johns et al. ¹¹³ presented an approach for analysing the bifurcation type of pipe instability. Kyriakides and Shaw ¹¹⁴ developed theoretical methods for investigating the limit-load type of instability of a pipe. Bai et al.^115,116 published articles discussing the collapse of metal pipes under combined external pressure, tension and bending which showed that the material properties of a pipe are crucial for determining its collapse response and envelopes. Gong et al. ¹¹⁷ conducted a similar study considering different D / t ratios, which demonstrated that the values of the critical external pressure of pipes with lower D / t ratios are larger than those with higher D / t ratios.

Nevertheless, research results for the mechanical behaviours of composite pipes under combined bending and external pressure are limited. Starbuck and Eberle ¹¹⁸ developed an analytical technique for the design of spoolable composite pipes considering loading scenarios including bending strain, axial force, internal and external pressures, elevated temperature and combinations of them. Their study showed that different angle-ply laminate architectures are required for different loading scenarios to achieve better performances. Pavlou ⁶⁴ also presented theoretical means of predicting the failures of composite pipes under combined bending and external pressure for design purposes. According to his research, two types of failure, material failure of the pipe wall and buckling of the structure, can occur.

Offshore pipes under combined bending and tension

As previously discussed, RTPs can be installed by the reel-lay method which involves spooling a pipe onto a transportable reel, during which it experiences significant bending in the presence of axial tension, ¹¹⁹ transporting the reel to the site of the pipeline and unwinding the pipe from the reel. Substantial attention has been paid to studying the responses of offshore pipes under combined bending and tension. Wilhoit and Merwin ¹²⁰ presented theoretical solutions to identify the effect of axial tension on the moment-carrying capacity of a pipe. They found that axial tension reduces the pipe’s moment-carrying capability but also decreases the moment acting on the pipe. Dyau and Kyriakides ¹²¹ investigated the ovalisation in cross-sections of elastic-plastic pipes caused by combined bending and tension through a combination of experiments and theoretical analyses, which showed that it depends on the loading path, material and geometric properties of the pipe (e.g. yield strengths and D / t ratios). Similar results were obtained in a study conducted by Bai et al. ¹²² Gong et al. ¹¹⁷ studied the buckling responses of offshore pipes subjected to combined bending and tension through both analytical and numerical efforts. Their results indicated that, in addition to a pipe’s loading paths and material properties, different values of its load combination lead to significant differences in its load-carrying capacity and buckling deformation. Therefore, the applied tension should be minimised to achieve a better load-carrying capacity.

Since the use of composite pipes for offshore applications is increasing rapidly, many studies concerning the mechanical behaviours of composite pipes under the loads encountered during installation and combinations of these loads have been reported. Bai et al. ¹²³ analysed the load-bearing capacity of an RTP under axial loads, which showed that the tearing caused by the axial tension can occur on its outside face. Most recently, the ovality of an RTP based on PE subjected to combined bending and tension was investigated by Bai et al. ¹²⁴ using a theoretical method and FE simulations. Their study showed that the axial tension slows down and even reduces the ovalisation of the pipe’s cross-section. It should be noted that they studied a short RTP (20 mm), with the material nonlinearity of PE ignored in their FE model, which could have resulted in an inadequate analysis. In addition, their theoretical model was based on the model presented by Dyau and Kyriakides, ¹²¹ which was originally developed for metallic pipes. Therefore, an approach considering the plasticity of the material may not be suitable for RTPs as they will not deform plastically.

Offshore pipes under combined external pressure and tension

Except for the loads incurred during the reeling and unreeling processes, the installation of RTPs in water also adds substantial loads to the pipes. It has been shown that sections of the pipe laid on or near the seabed are subjected to a significant combination of external pressure and tension apart from bending and external hydrostatic pressure. ¹²⁵

The responses of cylindrical pipes under combined external pressure and tension has been studied by many researchers for a long time. Earlier studies^126–128 on the collapse of metallic pipes under combined external pressure and axial tension were developed to create design criteria for the oil-well casings recommended by API BUL 5C3. ¹²⁹ They showed that the equation provided by the API recommendation provides a conservative estimate of the collapse strength. Babcock and Madhaven ¹³⁰ studied the collapse of a metallic pipe under combined external pressure and axial tension analytically and experimentally, and their pressure-tension interaction collapse envelope is shown in Figure 4. It is obvious that the axial tension results in a reduction in the resistance of the pipe to external pressure. Later, Madhavan et al. ¹³¹ extended their study to pipes with D / t ratios ranging from 10 to 40. They found that the extent of the reduction in the collapse pressure of the pipe and the nature of the collapse pressure-tension interaction profile are strongly dependent on the stress–strain behaviour of the pipe’s material. Kyriakides and Corona ¹³² analysed the buckling and collapse of metallic pipes under this combined loading through an additional parametric study, which showed that buckling and collapse are affected mainly by the D / t ratio, material elastic modulus and yield stress. Also, the loading path generally has a small influence on the collapse envelopes.

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Figure 4.

Pressure-tension interaction collapse envelope for pipe with D/t ratio = 25. ¹³¹

Mistry et al. ¹³³ conducted experimental and theoretical investigations into the failure of ± 55° filament-wound glass-fibre/epoxy cylindrical pipes with D / t ratios ranging from 2.5 to 20 under combined external pressure and axial loading. They observed both buckling and material failures (first-ply failures) in their samples, with the buckling pressure decreasing rapidly with increasing D / t ratios and the pressure for the first-ply failure not sensitive to the D / t ratio. Mistry ¹³⁴ theoretically studied the failures of filament-wound glass fibre-reinforced plastic pipes under combined external pressure and axial compression as well as the effect of the winding angle on their strength, which demonstrated that the failure of the pipe under this loading case could be caused by either a buckling or material failure. It also showed that the winding angle required to achieve the optimal performance depends on the hoop-to-axial membrane stress ratio. Dong and Mistry ¹³⁵ confirmed Mistry’s findings ¹³⁴ through conducting experiments to examine the failure of ± 55° filament-wound glass reinforced plastic cylinders with D / t ratios ranging from 48 to 54 under a combination of external pressure and axial compression. Both longitudinal cracks resulting from buckling and shear cracks caused by the failure of the material occurred in their tests. Bai et al. ¹³⁶ developed a two-dimensional (2D) theoretical model based on the theory initially proposed by Kyriakides et al. ¹³² and a three-dimensional (3D) FE model to study the behaviours of RTPs under combined external pressure and tension. The RTPs were assumed to be made from PE and combinations of aramid fibres and PE matrix materials. However, the nonlinear behaviours of PE and fibre-reinforced PE composites were not considered in their study. They found that the RTP collapses due to buckling at a low axial tension whereas, at high tension levels, its maximum strain in the RTP reaches the allowable strain of the material which causes the pipe to fail. In addition, the loading paths have considerable effects on the failure of RTPs.

Offshore pipes under combined torsion, bending, axial tension and external pressure

The earliest publication on the mechanical behaviours of homogeneous orthotropic cylindrical shells under torsion can probably be traced back to Shaw and Simitses ¹³⁷ who analysed the instability of laminated cylindrical shells under torsion. Since then, several studies investigating the torsional buckling of composite pipes have been published.^138–141 As these studies considered buckling to be the most important failure mechanism when composite pipes are subjected to torsion, they focused on determining the critical load. Wall and Card ¹⁴² investigated the torsional shear strength of filament-wound glass-epoxy tubes experimentally and theoretically and, in their experiments, observed evident delamination in some specimens. Putić et al. ¹⁴³ further studied the torsional properties of, and damage in, glass/epoxy composite pipes, which showed that excessive torsion can cause damage, such as fracture of the fibres and matrix delamination, which results in the appearance of cracks on the pipes and, in many cases, complete breakage of them.

With the rising demand to improve the effectiveness of aircraft structures in the aerospace industry, substantial efforts^144–146 have been made to investigate the buckling and post-buckling responses of carbon fibre-reinforced polymer (CFRP) composite cylinders under combined axial tension and torsion. These studies have identified the effect of the laminate’s orientation on buckling and demonstrated that buckling loads are strongly dependent on the loading sequence. Crate et al. ¹⁴⁷ examined the effect of internal pressure on the buckling of thin-walled cylinders under torsion and found that applying internal pressure raises the shear buckling stress. Chouchaoui^148,149 conducted a similar study of a laminated cylindrical pipe under tension, torsion, bending and internal and external pressures, which roughly described some characteristics of the mechanical behaviours of the pipe under these loads. Holston et al. ¹⁵⁰ developed a combined analytical and experimental investigation of the stability of composite cylindrical shells. They considered five loadings: (a) uniform axial compression; (b) torsion; (c) bending; (d) combined torsion and uniform axial compression and (e) combined bending and uniform axial compression. The experimental buckling loads showed 10 to 33% differences from the analytical solutions in which the effects of boundary conditions were not considered. This demonstrates the significance of taking into account boundary conditions for determining the mechanical behaviours of composites pipes under combined loadings, which could be achieved by employing FEA.