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Marine Structures journal homepage: http://www.elsevier.com/locate/marstruc

Fatigue behaviour and life prediction of filament wound CFRP pipes based on coupon tests Zhenyu Huang a, b, Wei Zhang a, b, Xudong Qian b, *, Zhoucheng Su c, Dinh-Chi Pham c, Narayanaswamy Sridhar c a

Guangdong Provincial Key Laboratory of Durability for Marine Civil Engineering, Shenzhen University, Shenzhen, 518060, China Department of Civil and Environmental Engineering, National University of Singapore, 1 Engineering Drive 2, 1175762, Singapore c Engineering Mechanics Department, Institute of High Performance Computing, A*STAR Research Entities, 1 Fusionopolis Way, 138632, Singapore b

A R T I C L E I N F O

A B S T R A C T

Keywords: CFRP Fatigue behaviour Composite riser Delamination Fatigue life Filament wound

This paper investigates the fatigue behaviour of filament wound Toray T700/Epotech X4201 composite pipes with different lay-ups. The present work compares the fatigue behaviour of coupon specimens manufactured with two different fiber orientations under tension-tension and tension-compression cyclic actions. The test results show that the lay-up and stress ratio have significant effect on the failure mechanism and fatigue life of carbon fiber reinforced polymer (CFRP) composite coupons. This paper develops an empirical model, which integrates the effect of stress ratio in a fatigue damage parameter, to evaluate the fatigue life of the CFRP filament wound coupons. Combined with the numerically calculated stresses at the critical locations corresponding to the fatigue damage locations, the proposed empirical model developed from the coupon test database predicts successfully the fatigue life of full diameter CFRP pipes, using stresses computed at critical locations in the CFRP pipe.

1. Introduction Future missions of the offshore industry in the deep and ultra-deep waters create exciting demands for light-weight systems, which generate significant savings in their construction and operation. The weight of riser, through which the oil is transported from the wellbore at the seabed to the connecting rig on the surface, imposes a critical concern in the weight saving solutions. The use of con ventional steel risers becomes infeasible and un-economical for deep water applications due to the high density of metallic materials. In contrast, carbon fiber reinforced polymer (CFRP) composite risers [1] represent an attractive alternative with enhanced properties, such as lightweight, high specific strength, good durability, low thermal conductivity and good corrosion resistance [2–6]. As the risers experience cyclic actions induced mainly by vortex-induced vibrations over its entire life [7,8], typically greater than 20 years, detailed understanding on the fatigue behaviour becomes essential to develop reliable approaches to estimate the fatigue life of CFRP risers, which further promotes the economic design of deep-water risers for marine applications. Typical failure modes of fiber reinforced polymer (FRP) composites due to fatigue include the matrix cracking, debonding, delamination, and fiber fracture [9]. Damage grows initially in small increments and maintains a constant growth rate thereafter before accelerating in the final stage [10–12]. Unlike the fatigue behaviour of metals, the stiffness degradation of composites is

* Corresponding author. E-mail address: [email protected] (X. Qian). https://doi.org/10.1016/j.marstruc.2020.102756 Received 17 May 2019; Received in revised form 6 February 2020; Accepted 4 March 2020 Available online 7 April 2020 0951-8339/© 2020 Elsevier Ltd. All rights reserved.

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Nomenclature D ¼ E ¼ E0 ¼ I ¼ L1 ¼ L2 ¼ M ¼ N ¼ Nf ¼ P ¼ d0 ¼ di ¼ f ¼ α; β ¼ θ ¼ σ ¼ σ 11 ¼

Fatigue damage factor Young’s modulus at any number of cycles N (GPa) Initial Young’s modulus (GPa) Moment of inertia (mm4) The length of load span (mm) The length of support span (mm) Moment introduced at the mid-span (kN.m) Number of cycles Total number of cycles at failure Force applied by the actuator (kN) Outer diameter of the pipe (mm) Inner diameter of the pipe (mm) Loading frequency (Hz) Curve fitting parameters Smallest angle between the loading direction and fiber direction (o) Stress at the middle bottom of the pipe (MPa) Maximum principal stress (MPa) σ 11 max ¼ Maximum principal stress corresponding to the maximum load (MPa) σ 11 min ¼ Maximum principal stress corresponding to the minimum load (MPa) σ max ¼ Maximum stress in cyclic loading (MPa) σ min ¼ Minimum stress in cyclic loading (MPa) σ ult ¼ Ultimate tensile stress (MPa) ðσ eff ÞSWT ¼ Effective stress amplitude based on SWT model (MPa) ðσ eff ÞGoodman ¼ Effective stress amplitude based on Goodman model (MPa) Δσ ¼ Stress range (MPa)

noticeable in the initial stage of fatigue loading and may potentially lead to major stiffness reductions during the subsequent fatigue process [13,14]. Wu et al. [15] have conducted tensile fatigue tests on various FRP sheets [carbon, glass, polyparaphenylenl benzo bisoxazole (PBO), basalt], and demonstrated the superior fatigue performance of CFRP and PBO composites compared to the glass fiber reinforced polymer (GFRP) and basalt fiber reinforced polymer (BFRP) composites. Zhao et al. [16] show that the different tensile moduli of fibers affect the damage mechanisms in the composites. For BFRP composites, the low modulus of the basalt fiber distributes the applied cyclic stresses to the epoxy adhesive, causing transverse matrix cracking. For CFRP composites, in contrast, the relatively high modulus of the carbon fibers retains large stresses along the fibers, initiating the longitudinal matrix cracking. The fatigue life of composite materials depends on a number of critical factors including the matrix material, fiber material, fiber orientation, and stress amplitude, stress ratio, and load frequency [17–20]. Reifsnider and Gao [21] have proposed a micromechanics fatigue criterion based on an average stress function. The fatigue criterion covers the failure of all the composite constituents and represents the constituent interactions by involving the volume fraction, the constituent properties and the interfacial bond. Fawaz and Ellyin [22] have presented a semi-log linear model to predict the fatigue failure of composites with different fiber orientations under multiaxial stresses. The correlation between the model and the published data is quite accurate. Harris and his co-workers [23,24] have built a normalized constant-life model, describing the relationship between the alternating and mean stresses, for fatigue life pre diction, which is not only applicable to various undamaged composite laminates, but also applicable to impact-damaged laminates. Plumtree and Cheng [25] have proposed a fatigue damage parameter based on the Smith Watson Topper (SWT) parameter to predict the fatigue life of off-axis unidirectional fiber composites. The parameter quantified through microstress analysis takes into account the effect of fiber orientation and mean stress. El Kadi and Ellyin [26] have studied the effects of stress ratio and concluded that the fatigue life of composites increases with the amplitude of stress ratio for a tension-tension loading, but decreases with the magnitude of the stress ratio for a tension-compression loading. Huybrechts [27] has demonstrated that CFRP composite risers often entail a long fatigue life when the fatigue failure is predominantly governed by the fiber-failure. The lack of experimental database for long-term damage mechanisms required by the accurate fatigue life prediction remains one of the basic technical barriers for wide industrial applications of composite risers [28]. A reliable S–N curve has not yet evolved for composite risers. The lack of experimental efforts on the composite risers leads to a large safety factor in the offshore design rec ommendations [29], although some researchers have reported limited fatigue tests on composite riser specimens [30–32]. The development of a comprehensive fatigue design procedure requires extensive experimental data for composite riser prototypes fabricated following the exact procedure as that for commercial products. An alternative method is to investigate the fatigue behaviour using coupon level specimens, and subsequently develop a convenient approach to estimate the fatigue life of composite risers, for which the fatigue failure initiates from the same material failure as the coupon specimens. Previous researchers have proposed different models to predict the fatigue life of composite materials using the coupon test data. Most of these models do not accurately 2

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Table 1 Material configuration of composite pipe. Carbon fiber Epoxy system

Lay-up A Lay-up B Complex Oven curing Weight fractions Pipe dimension

Tensile strengthen:4900 MPa Tensile modulus:230 GPa Density:1.8 g/cm3 Glass transition temperature:148.7 � C Tensile strength:59.7 MPa Tensile modulus:2.712 Gpa Density:1.13 g/cm3 [�45]28 [90]56 [(90/�15/90/�453)5/�453] 90 � C/2 h þ 130 � C/2 h þ 150 � C/5 h Epoxy:24.3%; Carbon fiber:75.7% Internal diameter:208.8 mm; Thickness:11.2 mm/5 mm Length: 2000 mm

consider the effects of stress ratios and loading frequencies, and thus require significant amount of experimental data to establish a set of characteristic fatigue curves for a given composite. In order to overcome this, Epaarachchi and Clausen [33] have developed a fatigue model including the nonlinear effect of stress ratio and load frequency to predict the fatigue life for GFRP composite materials. Helmi et al. [34] have applied this fatigue model to assess the fatigue life of GFRP tubes based on coupon tests. Their empirical model shows excellent accuracy in predicting the fatigue life of both coupons and tubes for GFRP composites with a maximum thickness of 11.2 mm. The current study aims to investigate the fatigue performance of CFRP pipes fabricated with the filament wound T700/X4201 composites and propose a convenient method to predict the fatigue life of full diameter composite risers. This paper starts with a review of previous studies on the fatigue behaviour of FRP composites. The next section introduces the experimental program including the static tension test of coupon specimens, fatigue test of coupon specimens, and fatigue test of full-diameter composite pipes. The third section discusses the coupon test results and the effects of different parameters in determining the fatigue life of CFRP composites. The fourth section proposes an empirical approach to predict the fatigue life of the CFRP composites based on the model originally developed for GFRP by Epaarachchi and Clausen [33]. The fifth section discusses the fatigue test results of 6 full-diameter composite pipes, and compares the fatigue life estimations based on the proposed empirical model. The last section summarizes the conclusions drawn from the study. 2. Experimental program 2.1. CFRP pipe specimens The CFRP pipe specimens utilize the filament wound Toray T700/Epotech X4201 composites. The fabrication employs the continuous filament winding process, using carbon fiber roving and anhydride epoxy resin, where the carbon fiber volume fraction is 75.7%. The filament-wound process involves winding filaments under tension over a rotating prepared mandrel. The mandrel rotates around the spindle while a delivery eye on a carriage traverses horizontally in line with the axis of the rotating mandrel, laying down carbon fibers in the desired angle. The carbon filaments are impregnated in a bath with resin as they are wound onto the mandrel. Once the mandrel is completely covered to the desired thickness, the resin is cured in a radiant heater. After curing, the internal pipe finishing is conducted. The mandrel mould is removed and the internal surfaces of two pipe ends are machined to finishing. Table 1 presents the material configurations of the composite riser as provided by the manufacturer. The composite pipe specimens employ three separate stacking sequences, including [�45]28, [90]56 and [(90/�15/90/�453)5/�453]. The number inside the bracket of a lay-up, e.g., [�45]28, represents the angle between the fiber layers and the longitudinal axis while the subscript “28” denotes the number of plies in each layup recommended by ISO standard [35]. The 90� winding angle has wide applications for pipes subjected to internal pressures. This study covers this winding angle to compare its performance against the other two winding sequences, i.e., [45/-45] and the complex layup [(90/�15/90/�453)5/�453]. The complex layup design [(90/�15/90/�453)5/�453] combines three different fiber orientations i.e., [90], [15/-15] and [45/-45]. The ratio of [90]: [15/-15]: [45/-45] is about 1:1:3. This specific layup design proposal is for flexible composite riser for deep-water applications, considering the loading cases of high tensile load, internal oil and gas pressure, external water pressure and fatigue bending that a riser may experience in its service life. Huang et al. [36] have verified this lamination sequence design under static loading conditions. Fig. 1 illustrates the experimental setup for the CFRP pipe. The specimen has a length of 2000 mm, an internal diameter of 208.8 mm and a wall thickness of 11.2 mm. Each CFRP pipe contains 56 plies, with a thickness of 0.2 mm for each ply. Fig. 1b and c shows the CFRP composite pipes with different lay-ups. 2.2. CFRP coupon specimens The CFRP coupons are extracted from the undamaged zone in the tested CFRP composite pipes along the longitudinal direction by waterjet cutting. The coupons extracted in the longitudinal direction of the pipe are 30 mm wide and 250 mm long, as shown in Fig. 2. The dimensions of the coupons comply with ASTM D3039 [37]. Table 2 lists the designed lay-up of the CFRP materials. 3

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Fig. 1. CFRP composite riser pipes: (a) dimensions and instrumentations of the pipes; (b) pipe of [�45]28 lay-up and complex lay-up; and (c) pipe of [90]56 lay-up. 4

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Fig. 2. CFRP coupons extracted from composite pipe and testing fixture: (a) [�45]28 lay-up coupons; (b) [90]56 lay-up coupons; (c) complex lay-up coupons; and (d) test set-up for coupons.

Table 2 CFRP coupon specimens with different lay-up sequence. Manufactural technique

Lay-up sequence

Length (mm)

Width (mm)

Thickness (mm)

Filament wound

[�45]28 [90]56 [(90/�15/90/�453)5/�453]

250

30

11.2

Table 3 Test matrix of fatigue coupons. Lay-up

Loading type

f (Hz)

Stress range (MPa)

σmax =σult

σmin =σmax

Quantity

[�45]28

Tension-Tension

2.0 2.0 2.0 2.0 2.0 2.0 2.0 2.0 2.0 2.0 2.0 2.0

72.0 58.5 85.5 85.5 72.0 85.5 174.0 150.0 128.6 193.4 193.4 240.0

0.55 0.44 0.65 0.39 0.25 0.29 0.80 0.69 0.59 0.40 0.53 0.66

0.1 0.1 0.1 0.5 1.0 1.0 0.1 0.1 0.1 1.0 0.5 0.5

5 6 5 6 5 6 6 6 6 5 5 5

Tension-Compression complex

Tension-Tension Tension-Compression

σmax =σult ¼ maximum-to-ultimate stress ratio; σmin =σmax ¼ minimum-to-maximum stress ratio.

2.3. Test set-up, instrumentation and loading procedure The experimental program consists of the monotonic tension test on CFRP coupon specimens, the fatigue test on CFRP coupon specimens, as well as the fatigue test on CFRP pipe specimens. The monotonic tension test on CFRP coupon specimens employs a 500 kN MTS testing machine equipped with hydraulic grips for all specimen types. Fig. 2d illustrates the test set-up with 50 mm 5

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Table 4 Summary of monotonic test results of CFRP coupons. Specimen No.

Lay-up

Ultimate Strength (MPa)

Average Ultimate Strength (MPa)

Elastic modulus (GPa)

Average Elastic modulus (GPa)

T [�45]28-1 T [�45]28-2 T [�45]28-3 T [90]56-1 T [90]56-2 T [90]56-3 T [complex]-1 T [complex]-2 T [complex]-3

[�45]28

141.2 140.9 158.1 17.4 14.6 17.5 250.9 229.5 245.1

146.7 (9.8)

11.2 12.0 16.0 8.0 8.8 9.7 35.4 37.8 38.5

13.1 (2.6)

[90]56 complex

16.5 (1.6) 241.8 (11.1)

8.8 (0.9) 37.2 (1.6)

The value in the bracket represents the standard deviation. [complex] ¼ [(90/�15/90/�453)5/�453].

extensometer and strain gauges to measure displacements and strains in the coupon specimen. The strain gauges locate in the middle of the front and back surfaces of the coupon specimen. Both coupon ends are strengthened using the aluminum plates. A data acquisition system collates the applied load, displacements from the extensometer and the strain gauge data during the test. The uniaxial, monotonic tension test covers three types of CFRP coupon specimens with [�45]28, [90]56 and [(90/�15/90/�453)5/�453] lay-ups extracted from the tested filament wound composite pipes. Each lay-up consists of three duplicated pieces of CFRP coupons for the monotonic tension test. The fatigue test set-up of coupon specimens is similar to that under monotonic tension test, with different instrumentation. The strain gauge may not be able to survive the entire fatigue test due to the high temperature induced during the cyclic loading. Therefore, the instrumentation relies on the extensometer and thermal couples attached to the specimen. Table 3 lists the 12 cases with different layups, loading types and loading conditions considered in the fatigue test program, with 5 or 6 duplicated specimens for each case. The cyclic fatigue test covers the [�45]28 lay-up and the complex [(90/�15/90/�453)5/�453] lay-up. For each layup, the σmin =σ max ratio varies among 0.1, 0.5 and 1.0, of which the positive value represents the tension-tension cyclic loading, while the negative values correspond to the tension-compression cyclic loading. The fatigue test also includes different σ max =σ ult ratios, where σult denotes the average ultimate tensile strength of the respective monotonic tension coupons. The σmax =σ ult ratio ranges from 0.25 to 0.65 for the coupon specimens with the [�45]28 lay-up, and from 0.40 to 0.80 for the coupon specimens with the complex lay-up. The loading

Fig. 3. Monotonic tension test results of CFRP coupons: (a) stress-strain curve for [�45]28 lay-up; (b) stress-strain curve for [90]56 lay-up; (c) stressstrain curve for complex lay-up; (d) failure modes for [�45]28 lay-up and complex lay-up.

6

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Table 5 Test results of fatigue coupons (under tension-tension). Group

Lay-up

NO.

Temp. at failure

Max stress (MPa)

Min stress (MPa)

Stress range (MPa)

σmin =σmax

σmax =σult

N

Log(N)

TT1

[�45]28

1/5 2/5 3/5 4/5 5/5

~90 C

80 80 80 80 80

8 8 8 8 8

72 72 72 72 72

0.1 0.1 0.1 0.1 0.1

0.55 0.55 0.55 0.55 0.55

TT2

[�45]28

1/6 2/6 3/6 4/6 5/6 6/6

~90 � C

65 65 65 65 65 65

6.5 6.5 6.5 6.5 6.5 6.5

58.5 58.5 58.5 58.5 58.5 58.5

0.1 0.1 0.1 0.1 0.1 0.1

0.44 0.44 0.44 0.44 0.44 0.44

TT3

[�45]28

1/5 2/5 3/5 4/5 5/5

<40 � C

95 95 95 95 95

9.5 9.5 9.5 9.5 9.5

85.5 85.5 85.5 85.5 85.5

0.1 0.1 0.1 0.1 0.1

0.65 0.65 0.65 0.65 0.65

TT4

complex

1/6 2/6 3/6 4/6 5/6 6/6

<40 � C

193.4 193.4 193.4 193.4 193.4 193.4

19.3 19.3 19.3 19.3 19.3 19.3

174 174 174 174 174 174

0.1 0.1 0.1 0.1 0.1 0.1

0.80 0.80 0.80 0.80 0.80 0.80

TT5

complex

1/6 2/6 3/6 4/6 5/6 6/6

<40 � C

166.7 166.7 166.7 166.7 166.7 166.7

16.7 16.7 16.7 16.7 16.7 16.7

150 150 150 150 150 150

0.1 0.1 0.1 0.1 0.1 0.1

0.69 0.69 0.69 0.69 0.69 0.69

TT6

complex

1/6 2/6 3/6 4/6 5/6 6/6

<40 � C

142.9 142.9 142.9 142.9 142.9 142.9

14.3 14.3 14.3 14.3 14.3 14.3

128.6 128.6 128.6 128.6 128.6 128.6

0.1 0.1 0.1 0.1 0.1 0.1

0.59 0.59 0.59 0.59 0.59 0.59

1531 1749 1120 1420 1220 Average 20018 3033 3491 112753 9495 1950 Average 231547 7219 342197 41407 352330 Average 983 4453 9144 7752 111 6844 Average 128501 92798 19654 54781 76272 81587 Average 533006 264329 813786 169600 981212 871281 Average

3.185 3.243 3.049 3.152 3.086 3.143 4.301 3.482 3.543 5.052 3.977 3.290 3.941 5.365 3.858 5.534 4.617 5.547 4.984 2.993 3.649 3.961 3.889 2.045 3.835 3.395 5.109 4.968 4.293 4.739 4.882 4.912 4.817 5.727 5.422 5.911 5.229 5.992 5.940 5.703

�

“N” represents the number of fatigue cycles.

frequency remains fixed at 2 Hz for all tests. The fatigue test of CFRP pipes follows the four-point bend setup, performed in a 1000 kN universal testing machine operated in a displacement-controlled mode. Each pipe has a clear span of 1800 mm as shown in Fig. 1a. The pipe specimen experiences pure bending in the central span of 600 mm between the two loading points, applied via a specially designed spread beam on top of two saddles placed on the pipes. The two ends of the composite pipe sit upon two saddle supports, with a pin support on one side (ux ¼ uy ¼ uz ¼ 0) and a roller on the other side (ux ¼ uy ¼ 0), as shown in Fig. 1d. The finite life fatigue test has a target life of 1 million cycles. The cyclic loading follows the sinusoidal load excitation with a frequency of 1–2 Hz. 3. Results and discussion for CFRP coupon tests 3.1. Monotonic behaviour Table 4 lists the test results including the ultimate strength and elastic modulus of coupon specimens for each lay-up group. The experiment aims to investigate the tensile behaviour of composite coupons with different fiber orientations through monotonic tension tests. According to ASTM D3039 [37], the ultimate strength equals the ultimate load divided by the average sectional area measured before the tests, while the strain in the stress-strain curve is the average of the strain gauge and the extensometer measurements. The elastic modulus of the coupon derives from the stress difference Δσ divided by the strain difference (0.002 as recommended in Table 3 in ASTM D3039). 3.1.1. Stress-strain responses under monotonic tension Fig. 3a shows the average stress-strain relationship for the [�45]28 lay-up coupons, which exhibits three distinctive stages of 7

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Table 6 Test results of fatigue coupons (under tension-compression). Group

Lay-up

NO.

Temp. at failure

Max stress (MPa)

σmax =σult

N

Log(N)

TC7

[�45]28

1/6 2/6 3/6 4/6 5/6 6/6

<40 C

57 57 57 57 57 57

28.5 28.5 28.5 28.5 28.5 28.5

85.5 85.5 85.5 85.5 85.5 85.5

0.5 0.5 0.5 0.5 0.5 0.5

0.39 0.39 0.39 0.39 0.39 0.39

72 72 72 72 72

1.0 1.0 1.0 1.0 1.0

0.25 0.25 0.25 0.25 0.25

42.8 42.8 42.8 42.8 42.8 42.8

85.5 85.5 85.5 85.5 85.5 85.5

1.0 1.0 1.0 1.0 1.0 1.0

0.29 0.29 0.29 0.29 0.29 0.29

96.7 96.7 96.7 96.7 96.7

96.7 96.7 96.7 96.7 96.7

193.4 193.4 193.4 193.4 193.4

1.0 1.0 1.0 1.0 1.0

0.40 0.40 0.40 0.40 0.40

<40 � C

128.9 128.9 128.9 128.9 128.9

64.5 64.5 64.5 64.5 64.5

193.4 193.4 193.4 193.4 193.4

0.5 0.5 0.5 0.5 0.5

0.53 0.53 0.53 0.53 0.53

<40 � C

160 160 160 160 160

80 80 80 80 80

240 240 240 240 240

0.5 0.5 0.5 0.5 0.5

0.66 0.66 0.66 0.66 0.66

408 313 620 207 328 349 Average 2332 5488 3050 8385 5704 Average 1572 932 876 1213 2053 674 Average 13410 240549 218988 89025 146244 Average 28080 201715 99046 52890 2286 Average 2504 2104 4199 2308 7176 Average

2.611 2.496 2.792 2.316 2.516 2.543 2.546 3.368 3.739 3.484 3.924 3.756 3.654 3.196 2.969 2.943 3.084 3.312 2.829 3.056 4.127 5.381 5.340 4.950 5.165 4.993 4.448 5.305 4.996 4.723 3.359 4.566 3.399 3.323 3.623 3.363 3.856 3.513

TC8

[�45]28

1/5 2/5 3/5 4/5 5/5

<40 � C

36 36 36 36 36

36 36 36 36 36

TC9

[�45]28

1/6 2/6 3/6 4/6 5/6 6/6

<40 � C

42.8 42.8 42.8 42.8 42.8 42.8

TC10

complex

1/5 2/5 3/5 4/5 5/5

<40 � C

TC11

complex

1/5 2/5 3/5 4/5 5/5

TC12

complex

1/5 2/5 3/5 4/5 5/5

�

Min stress (MPa)

Stress range (MPa)

σmin =σmax

responses, including the linear, nonlinear and the hardening stages. The average tensile strength and elastic modulus are 146.7 MPa and 13.1 GPa, respectively. Fig. 3b and c plot the stress-strain curves of the lay-up [90]56 and the complex lay-up [(90/�15/90/ �453)5/�453] respectively, both of which experience a sharp drop after the peak stress. The average ultimate strengths are 16.5 MPa and 241.8 MPa, while the elastic moduli are 8.8 GPa and 37.2 GPa, respectively. 3.1.2. Failure mode of monotonic tension coupons Fig. 3d shows the failure modes for the [�45]28 lay-up coupons and the complex lay-up coupons respectively. The filament wound coupons with the [�45]28 lay-up fail initially by fiber splitting along the fiber directions at the early loading stage, followed by interlaminar delamination and later fiber fracture in a localized region. For the complex [(90/�15/90/�453)5/�453] lay-up, the failure mode is the typical interlaminar delamination in the specimens. The fibers bulk out after reaching the peak load. The filament wound coupons with the [90]56 lay-up exhibit a very brittle behaviour and fail by matrix cracking, as reported in Ref. [36]. Filament wound coupons with the complex lay-up have a higher elastic modulus (average value of 37.2 GPa) than that of the other two lay-ups (8.0–16 GPa) while the [�45]28 lay-up specimens show significant nonlinearity due to fiber scissoring effect, as the [�45]28 layup provides effective interaction between fiber plies. These findings indicate that the fiber orientation have pronounced effects on the ultimate strength and failure modes of the coupon specimens. 3.2. Fatigue behaviour This section aims to examine experimentally the fatigue behaviour of CFRP coupon specimens and determine the effect of different parameters on the fatigue life, including the minimum-to-maximum (σ min =σmax ) stress ratio, the maximum-to-ultimate (σmax =σult ) stress ratio and the fiber orientation. According to the monotonic tension test, the coupon specimens with the [90]56 lay-up exhibit a brittle behaviour and the corresponding ultimate strength is much lower than the other two lay-ups. Thus, the [90]56 lay-up does not demonstrate good potential for engineering applications and is thus excluded in the fatigue test program. 8

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Fig. 4. Relation between temperature and fatigue cycles of TT2-[�45]28-6/6.

Fig. 5. Failure modes of CFRP coupons in fatigue test: (a) [ �45]28 lay-up under tension-tension; (b) complex lay-up under tension-tension; (c) [ �45]28 lay-up under tension-compression; (d) complex lay-up under tension-compression.

3.2.1. Fatigue life and failure modes Tables 5 and 6 summarize the fatigue test results with the number of cycles to failure for each coupon specimen. For the first two groups (TT1 and TT2) of coupon specimens with the [�45]28 lay-up, no obvious failure occurs prior to the fatigue damage initiation when the temperature in the specimen remains below 40 � C. As the damage initiates and propagates, the temperature in the specimen increases due to the interfacial friction between fiber and matrix, and splitting along the fiber direction (45� /-45� ) in the internal surface. Complete fatigue failure occurs when the fiber failure extends from the internal surface to the outer surface, and the 9

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Fig. 6. Effect of fiber orientation on fatigue life: (a) in terms of Δσ ; (b) in terms of σmax ; (c) in terms of ðσ eff ÞSWT ; (d) in terms of ðσ eff ÞGoodman .

temperature of the specimen increases up to 90 � C. Fig. 4 shows the variation in the measured temperature with respect to the number of applied cycles. The temperatures at the coupon surface start to increase rapidly from the ambient temperature at 25% of the total fatigue life to around 90 � C at failure. However, the fatigue life thus obtained may underestimate the real fatigue life of composite materials operating in a sea environment with an ambient temperature below 20 � C. Since the high temperature in the specimen arises from the high loading frequency, an effective approach to curb the temperature rise in the specimen is to maintain a low loading frequency. Therefore, the subsequent tests choose a loading frequency of 2 Hz as indicated in Table 3, which keeps the specimen temperature below 40 � C according to ASTM D3039 [37]. An alternative to reduce the specimen temperature is to use cooling by compressed air, which is often practiced for the fatigue test under the very high cycle fatigue (VHCF) conditions, which often entails a loading frequency of 1000 times higher than the typical high cycle fatigue (HCF) tests. Fig. 5 presents the failure modes of the composite coupon specimens with different lay-ups and different loading types. For coupon specimens with the complex lay-up both under tension-tension and tension-compression fatigue loadings, the fiber pull-out and sig nificant delamination between the plies cause the failure of the specimen, as shown in Fig. 5b and d. For the coupon specimens with the [�45]28 lay-up under tension-tension loading, ply delamination occurs at the early loading stage, followed by fiber fracture in the 45� / 45� direction accumulated in a local zone, as shown in Fig. 5a. The failure modes of these three cases are similar to those of the coupons under monotonic tension. In the complex lay-up coupons (Fig. 5b), ply delamination spreads along the coupon length in contrast to the local delamination in the [�45]28 lay-up coupons. For the coupon specimens with the [�45]28 lay-up, the tensioncompression fatigue loading initiates the buckling of the coupons without significant interlaminar delamination, as shown in Fig. 5c, despite the efforts to minimize geometric imperfections in the fabrication and setup of the coupon specimens. 3.2.2. Effect of fiber orientation Fig. 6 compares the fatigue life of the [�45]28 lay-up coupons and the complex lay-up coupons under tension-compression actions with four different loading parameters, Δσ , σ max , ðσeff ÞSWT , and ðσ eff ÞGoodman . The effective stress amplitude ðσeff ÞSWT proposed by Smith et al. [38], named as the S–W-T model, and another conservative and frequently used model proposed by Goodman [39] quantify the mean stress effect, similar to the energy approach [40]. Equations (1) and (2) illustrate the effective stresses in the S–W-T model and in the Goodman model, respectively, pffiffiffiffiffiffiffiffiffiffiffiffiffiffi � (1) σ eff SWT ¼ σmax Δσ

σ eff

� Goodman

¼ σ ult Δσ = ðσ ult

(2)

σ mean Þ 10

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Fig. 7. Effect of loading type on fatigue life: (a) in terms of Δσ ; (b) in terms of σ max ; (c) in terms of ðσeff ÞSWT ; (d) in terms of ðσeff ÞGoodman .

Different fiber orientations lead to different failure modes and hence different fatigue lives. Fig. 6 indicates that the coupon specimens with the complex lay-up failed by global ply delamination along the coupon length show longer fatigue lives than those with the [�45]28 lay-up, which fail by buckling. The complex lay-up coupons also exhibit a more significant scatter than the [�45]28 lay-up coupons, when assessed by all four stress parameters in Fig. 6. 3.2.3. Effect of loading type The fatigue test includes two different loading types: the tension-tension cyclic loading and tension-compression cyclic loading. Fig. 7 presents the comparison of fatigue life for the complex lay-up coupons under these two different loading types. In terms of the stress range Δσ , the fitting curve for the coupons under tension-compression loading is higher than the fitting curve for the coupons under tension-compression loading. However, based on the maximum stress σ max , the presence of a compression component in the loading program decreases the fatigue strength with a large scatter. The S–W-T stress model leads to a rather flat fatigue assessment curve. Although the scatter in the S–W-T model remains relatively small compared to other fatigue indicators in Fig. 7, the fatigue life estimation relies heavily on the accuracy of the stress amplitude ðσeff ÞSWT due to the flatness of the curve in Fig. 7c. The Goodman model leads to two separate curves for the two loading types with a relatively large scatter. Most of the above fatigue indicators require separate treatments for the tension-tension and tension-compression loading conditions. Such separate treatments create challenges in assessing fatigue performance of engineering structures under complex loading conditions. The current study, hence, seeks to estimate the fatigue life of CFRP composites using a fatigue damage factor (to be presented in Section 4.1), which embeds the effect of the above loading type quantified by the stress ratios (σ min =σmax and σ max =σult ), as detailed in Section 4.1. 3.2.4. Stiffness degradation Fig. 8 plots the stiffness degradation curves of selected coupons under different σ min =σmax and σmax =σult ratios. The stiffness degradation behaviour is measured by the normalized Young’s modulus ratio (E=E0 ) against the normalized fatigue cycles (N=Nf ), where E is the Young’s modulus in the current cycle N, while E0 and Nf are the initial Young’s modulus and the total number of cycles at failure, respectively. Fig. 8a–c shows the degradation in the [�45]28 layup coupons under tension-compression loading, while Fig. 8d–e illustrate that for the complex lay-up coupons under tension-tension loading, and Fig. 8f–h presents the stiffness degradation for the complex lay-up coupons under tension-compression loading. The stiffness degradation curves of the [�45]28 lay-up coupons are much steeper than those of the complex lay-up coupons. The damage indicated by the reduced stiffness is permanent. At the final fatigue failure, the material stiffness degrades to around 80% of the initial stiffness for the complex lay-up coupons, and approximately 20% of the initial stiffness for the [�45]28 lay-up coupons. The difference in the stiffness degradation rate originates from the different 11

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Fig. 8. Stiffness degradation of CFRP coupons: (a) group TC7; (b) group TC8; (c) group TC9; (d) group TT4; (e) group TT5; (f) group TC10; (g) group TC11; (h) group TC12.

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failure modes in the two different lay-ups. The [�45]28 lay-up coupons exhibit combined interlaminar delamination and splitting along the fiber orientation which reduce the cross-sectional area of coupons under cyclic loading, leading to the progressive stiffness degradation. While for complex lay-up coupons failed by interlaminar delamination only, the cross-sectional area of the coupon specimen does not indicate a significant reduction. The loading types (tension-tension or tension-compression) impose marginal effects on the stiffness degradation based on the curves for the complex lay-up coupons, as shown in Fig. 8d–h. 4. Fatigue life assessment of composite pipes This section aims to develop an approach to estimate fatigue life of the CFRP pipes with the two different lay-ups based on the fatigue test results of CFRP coupon specimens. As discussed above, for the coupon specimens with the [�45]28 lay-up, the first two groups (TT1 and TT2) under tension-tension loading are under the influence of the temperature effect, thus the failure mode of these two groups does not reflect the true fatigue failure of composite materials in a sea environment. The third group (TT3) under tensiontension loading indicates a different failure mode compared to the other three groups (TC7-TC9) under tension-compression loading. The former fails by interlaminar delamination and fiber fracture in a local zone, while the latter three groups fail by buckling. One group of five fatigue test data in TT3 is insufficient to determine the fatigue life curve for the [�45]28 lay-up governed by the interlaminar delamination and fiber fracture under the tension-tension loading. Therefore, the current study focuses on the [�45]28 lay-up with the final buckling failure under tension-compression actions. For the coupon specimens with the complex lay-up, both the three groups (TT4-TT6) under tension-tension loading and the three groups (TC10-TC12) under tension-compression loading exhibit a similar failure mode, i.e., significant delamination between the plies. Thus, all these six groups of data are included in developing the fatigue life curve for the complex lay-up based on this failure mode. 4.1. Empirical model for fatigue life prediction Most of the existing models in predicting the fatigue life of composites have not accurately considered the effect of stress ratios (σmin =σ max and σmax =σ ult ). These models usually require considerable experimental data to plot a set of characteristic fatigue curves for a given composite material. In order to quantify the stress ratios in the fatigue life estimation, Epaarachchi and Clausen [33] have proposed a fatigue model incorporating the nonlinear effects of stress ratios. They have proposed the following relationship to estimate the fatigue damage factor, D, D ¼ αðN β

(3)

1Þ

where � D¼

σult σ max

8 σmin > <ψ ¼ σ max > : ψ ¼ σ max

σmin

�� � σult 0:6 1

ψ jsin θj �

σmax

for

∞<

for 1 <

ð1

1 1:6 ψ jsin θj

ψÞ

� fβ

(4)

σ min <1 σmax

(5)

σ min <∞ σmax

where f is the loading frequency, θ is the smallest angle between the loading direction and fiber direction (for the [�45]28 lay-up, θ equals 45� ; for the complex [(90/�15/90/�453)5/�453] lay-up, θ equals 15� ), α and β represent fitting parameters based on experimental data. To determine the values of α and β, Epaarachchi and Clausen [33] recommend a trial-and-error process, starting with a trial value of β to calculate D and ðNβ 1Þ for all data points. By indexing the parameter D as the Y axis against ðNβ 1Þ as the X axis, the fitted curve becomes a straight line. The fitting procedure changes the value of β until the linear regression line passes through the origin, i.e., D ¼ 0 for Nβ ¼ 1, with a least square error. Equations (4) and (5) embed the effect of stress ratios in the calculation of the damager factor D. In the current study, the loading frequency in the coupon fatigue tests equals 2 Hz for all cases. By fitting the α and β values against the reported coupon test results in Section 3.2, the equations of fatigue life prediction for the [�45]28 lay-up CFRP material and the complex lay-up CFRP material follow, � ½�45�28 layup: D ¼ 0:89 N 0:21 1 (6) � � � ð90= � 15=90= � 453 Þ5 � 453 layup:

D ¼ 0:20 N 0:14

1

�

(7)

Figs. 9a and 10a plot D against ðN 1Þ for the [�45]28 lay-up coupons and the complex lay-up coupons respectively. The curve fitting for the [�45]28 lay-up includes 17 test data with the goodness of fit values R2 equal to 0.86. The curve fitting for the complex lay-up utilizes 33 test data with an R2 value of 0.77. Fig. 9b–c plot σ max against N for the [�45]28 lay-up coupons with σ min =σmax ¼ 0:5 and σmin =σ max ¼ 1:0 respectively. Also included in Fig. 9b–c are the comparisons with the ISO fatigue life curves [41,42]. The ISO fatigue curves, shown in Eqs. (8) and (9), predict the fatigue life of GFRP materials, derived separately from two batches of experi mental results of plate GFRP materials, namely the Phase I and Phase II, respectively, β

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Fig. 9. Prediction of fatigue life for the CFRP composites with the [ �45]28 lay-up: (a) estimation of parameters in the empirical model; (b) fatigue life for σ min =σ max ¼ 0:5; (c) fatigue life for σ min =σmax ¼ 1:0.

ISO Phase I: ISO Phase II:

σ max ¼ 169:16N σ max ¼ 139:64N

(8)

1 11:06

(9)

1 12:34

The ISO curves overestimate the fatigue life for the [�45]28 lay-up CFRP coupons; while the proposed curve fits more closely to the data points. Fig. 10b–d plot σ max against N for the complex lay-up coupons with σ min =σmax equals 0.1, 0.5 and 1.0 respectively. The comparison in these figures also proves the accuracy of the proposed curve. The ISO curves, although not directly applicable to the complex lay-up, underestimate the fatigue life for the complex lay-up CFRP coupons. The comparison between Figs. 9 and 10 dem onstrates the superior fatigue performance of the complex lay-up compared to the [�45]28 lay-up. 4.2. Fatigue life prediction of full-diameter CFRP flexural pipes The steps below detail the procedure to assess the fatigue life of CFRP pipes. The subsequent section reports the experimental program on CFRP pipes and examines the feasibility of the below steps in estimating the fatigue life of full diameter CFRP pipes. Step I: Obtain the maximum and minimum stresses (σmax ; σ min ) at the critical region of CFRP pipe for a given loading condition. The σmax and σ min value can be derived from the force equilibrium equations or from the measured strains according to the stress-strain relationship. Step II: Determine the ultimate strength (σ ult ) of the CFRP material using uniaxial tension tests. Step III: Calculate the values of σmin =σ max , σmax =σ ult , and the damage parameter D based on Eq. (4). Step IV: Calculate the number of cycles to failure N according to Eq. (6) for the [�45]28 lay-up CFRP pipe or Eq. (7) for the complex lay-up CFRP pipe. 5. Fatigue test on CFRP pipes The fatigue test program includes a total of 6 full-diameter CFRP pipe specimens with the complex lay-up under four-point bending, which creates a constant bending moment in the center span. Table 7 lists the test matrix, of which PC1-PC3 are CFRP pipes with 11.2 mm thick complex lay-up, and PC4-PC6 are CFRP pipes with 5 mm thick complex lay-up. The minimum-to-maximum stress ratio remains fixed at 0.1 for all cases, and the maximum-to-ultimate stress ratio ranges from 0.2 to 0.4. The maximum and minimum stresses derive from the equilibrium equations, 14

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Fig. 10. Prediction of fatigue life for the CFRP composites with the complex lay-up: (a) estimation of parameters in the empirical model; (b) fatigue life for σ min =σ max ¼ 0:1; (c) fatigue life for σmin =σmax ¼ 0:5; (d) fatigue life for σ min =σmax ¼ 1:0.

Table 7 Test matrix of CFRP pipes with the complex lay-up. Specimen

d0 (mm)

t0 (mm)

Max load (kN)

Max stress (MPa)

Min load (kN)

Min stress (MPa)

Stress range (MPa)

σmin =σmax

σmax =σult

f (Hz)

PC1

230.5

11.1

98.2

72.5

9.82

7.25

65.25

0.1

0.30

PC2

230.7

11.2

65.5

48.4

6.55

4.84

43.56

0.1

0.20

PC3

231.2

11.2

129.5

96.7

12.95

9.67

87.03

0.1

0.40

PC4

218.8

5.0

42.4

72.5

4.24

7.25

65.25

0.1

0.30

PC5

219.0

5.1

28.3

48.4

2.83

4.84

43.56

0.1

0.20

PC6

218.8

5.0

56.6

96.7

5.66

9.67

87.03

0.1

0.40

1.0/ 2.0 1.0/ 2.0 1.0/ 2.0 1.0/ 2.0 1.0/ 2.0 1.0/ 2.0

σ¼

Md0 2I

(10)

where M ¼ PðL2 I¼

π 64

d04

L1 Þ=4

(11)

�

(12)

di4

and M denotes the moment introduced at the center span, P refers to the force applied by the actuator, σ defines the stress at the bottom of the pipe at the mid-span, I represents the moment of inertia, L1 equals the length of load span, and L2 is the length of support span as shown in Fig. 1a d0 and di are the outer diameter and inner diameter of the pipe respectively.

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Fig. 11. Status of PC2 after test at the left and right loading locations.

Fig. 12. Failure mode of PC3 after test (a)front view; (b)left; (c)right.

5.1. Failure mode The specimens PC1 and PC2 experience relatively small stress levels, as indicated in Table 6. The fatigue test stops after reaching a target life of 1 million cycles, while there is no obvious failure along the pipes after the test even at the loading locations, as illustrated in Fig. 11. However, the specimen PC3, subjected to a larger stress level, reaches only 6149 cycles before the final fatigue failure. 16

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Table 8 Fatigue test results of CFRP pipes with the complex lay-up. Specimen

Stress range (MPa)

σmin =σmax

σmax =σult

Status

Log(N)_test

Log(N)_proposed

PC1 PC2 PC3 PC4 PC5 PC6

65.25 43.56 87.03 65.25 43.56 87.03

0.1 0.1 0.1 0.1 0.1 0.1

0.30 0.20 0.40 0.30 0.20 0.40

Stop Stop Fail Stop Stop Fail

6.10þ 6.03þ 3.79 6.03þ 6.04þ 4.18

6.73 8.29 5.54 6.73 8.29 5.54

þ indicates the real life cycles should be larger than the current value. Log(N)_proposed is calculated based on the stresses at the bottom of the pipe at the mid-span.

Fig. 12 shows the failure mode of the composite pipe in which the damage initiates locally from the loading points. The damage propagates thereafter along the winding direction of the woven fabric. Fig. 12a and b shows that the crack propagates from the top surface to the bottom surface of the pipe. For the 5 mm thick CFRP pipes, PC4 and PC5 under the small stress levels exhibit the same behaviour as PC1 and PC2 without obvious failure after 1 million cycles. For PC6 subjected to a larger stress level, the same failure mode as PC3 occurs when the number of cycles reaches 15086. 5.2. Fatigue life cycles Table 8 lists the fatigue test results of CFRP pipes with the complex lay-up, compared with the estimated fatigue life based on the proposed model. The estimation of fatigue life in Table 8 uses the nominal stresses at the bottom of the pipe at the mid-span calculated according to Eqs. (10)–(12). Among the 11.2 mm thick pipes and the 5.0 mm thick pipes, the stress levels for PC1, PC2, PC4 and PC5 are small and the tests are terminated when the number of cycles has reached the target life, 1 million cycles. The real fatigue life cycles of these four pipes should be larger than the target life cycles. For PC3 and PC6, Table 7 indicates that the proposed model overpredicts the fatigue life of PC3 and PC6, since a high stress concentration near the contact region between the loading saddle and the pipe triggers the fatigue damage initiation in the pipe. Such a damage initiation does not correspond to the calculated maximum strain position at the mid-span, at which the stress values are used in the proposed model to estimate the fatigue life. In order to calculate the stresses at the failure location, this section presents the finite element (FE) analysis using ABAQUS solver [43]. 5.2.1. Finite element analysis The FE model simulates the deformation of the composite pipe to extract the stresses at the failure locations corresponding to the maximum load and the minimum load. The representation of the pipe deploys one layer of 3D continuum shell elements with reduced integration (SC8R) in the thickness direction. The whole composite pipe is modeled with a total of 56 plies in the pipe thickness. The composite pipe contains only one integration point in the thickness direction to optimize the computational cost of the large composite pipe model. The numerical investigation includes a mesh convergence study to identify a suitable mesh size for the CFRP component based on the convergence of the stresses at the failure locations. The benchmark FE model with a biased mesh density of 2–10 mm element size is adequate for the FE analysis. The details in building the FE model and determining the material parameters are available in Huang et al. [36]. In Fig. 13, Points 1–4 lie along the fracture initiation location of the pipe in the FE model. An in-house Python script extracts the normal stresses in the axial direction and the transverse direction, as well as the shear stress for a selected element. To calculate the equivalent stresses at the fracture initiation region, the Python script transforms the normal stresses and shear stress to the maximum principal stress and minimum principal stress based on the lay-up angles. The shear stress around the fracture initiation region is relatively small compared to the other two normal stresses. Further investigation discovers that the maximum principal stress (pos itive) corresponds to the normal stress in the transverse direction, while the minimum principal stress (negative) corresponds to the normal stress in the axial direction. Fig. 13 displays the contour of the maximum principal stress around the loading location for both PC3 and PC6. 5.2.2. Pipe fatigue life prediction Table 9 lists the results of fatigue life prediction for CFRP pipes based on the location of fracture initiation. σ 11_max represents the maximum principal stress corresponding to the maximum load, and σ11_min represents the maximum principal stress at the minimum load. The stresses at the point 1–4 are extracted respectively, and the average value of the stresses at the four points is used to calculate the fatigue life according to the proposed model. The comparison presented in Table 9 and Fig. 14 shows that the fatigue life predicted by the proposed model using stresses at the location of fracture initiation is reasonably close to the fatigue life measured in the test for both the composite pipe PC3 and PC6. This indicates that the empirical fatigue model based on the coupon level predicts well the fatigue life of the composite pipes. 6. Conclusions This paper investigates the fatigue behaviour of filament wound CFRP pipes and proposes an empirical approach to estimate the 17

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Fig. 13. The contour of the maximum principal stress around the loading location for PC3 and PC6.

fatigue life based on the coupon test results. The monotonic tension tests examine the failure mode and ultimate strength of CFRP coupons with different lay-ups. The fatigue test program examines the effects of lay-up and stress ratio on the fatigue life of CFRP composites. By extending the empirical model proposed by Epaarachchi and Clausen [33] for GFRP plates, this paper develops empirical equations to predict the fatigue life of CFRP composites with two different lay-ups. The fatigue test program also examines 6 full-diameter CFRP pipe specimens with the complex lay-up under cyclic loading. The study summarized above supports the following conclusions:

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Table 9 Prediction of fatigue life of CFRP pipes based on the location of fracture initiation. Specimen

Max load (kN)

Min load (kN)

PC3

129.5

12.95

PC6

56.6

5.66

σ11 (MPa) Region

σ11_max

σ11_min

Point 1 Point 2 Point 3 Point 4 Average Point 1 Point 2 Point 3 Point 4 Average

160 181 201 218 190 135 168 206 221 183

13.7 19.2 26.5 43.7 25.8 6.0 14.9 28.7 39.1 22.2

Log(N)_ proposed

Log(N)_test

3.57

3.79

3.99

4.18

σ11 is the maximum principal stress. Point 1–4 correspond to the four points in Fig. 13. Log(N)_proposed is calculated based on the average values of σ11_max and σ11_min at the failure location.

Fig. 14. Comparison of predicted and experimental fatigue lives of PC3 and PC.

(1) The composite lay-up has significant effect on the tensile strength of coupon specimens. Coupons with the [�45]28 lay-up offer approximately 8.8 times the tensile strength of that with the [90]56 lay-up, which indicates that the [�45]28 lay-up demon strates pronounced interactions between fiber plies. The complex lay-up coupons exhibit the highest tensile strength among the three lay-ups, with a sharp drop after the peak load, caused by interlaminar delamination. (2) For the complex [(90/�15/90/�453)5/�453] lay-up coupons under tension-tension or tension-compression loading, and the [�45]28 lay-up coupons under tension-tension loading, the failure modes are similar to those of the coupons under static tension. However, for the [�45]28 lay-up coupons under tension-compression loading, the specimens experience buckling failure. (3) The coupon specimens with the complex lay-up exhibit better fatigue performance than the coupon specimens with the [�45]28 lay-up. The [�45]28 lay-up coupon specimens suffer more severe stiffness degradation than the complex lay-up coupon spec imens up to failure. In addition, the presence of a compression component in the loading program decreases the fatigue life of the coupon specimens. (4) The empirical model originally proposed by Epaarachchi and Clausen [33] for GFRP composites have incorporated the effects of stress ratios and load frequencies in estimating the fatigue damage. The fatigue life curves plotted by the proposed equations fit the test data of the [�45]28 lay-up coupons and the complex lay-up coupons quite well. (5) CFRP pipes with the complex lay-up designed in this paper exhibit an excellent performance in resisting fatigue load. The failure of the two damaged pipes originate from the stress concentration at the contact region between the loading beam and the pipe. The fatigue life predicted by the proposed model using stresses computed at the location of fracture initiation matches reasonably close with the test result. Future test investigations should strengthen the loading locations of the pipes to avoid the loading point failure and to examine the fatigue life of CFRP pipes under the failure of interlaminar delamination.

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Acknowledgement The authors would like to acknowledge the research grant SERC 132 183 0024 received from the Agency for Science, Technology and Research (A*STAR), Singapore, the research grant received from the National Natural Science Foundation of China (NSFC, Grant No.51978407) and Shenzhen Basic Research Project (Grant No. JCYJ20180305124106675), China. References [1] Toh W, Long BT, Jaiman RK, Tay TE, Tan VBC. A comprehensive study on composite risers: material solution, local end fitting design and global response. Mar Struct 2018;61:155–9. [2] Sakr M, Ei Naggar MH, Nehdi M. Interface characteristics and laboratory constructability tests of novel fiber reined polymer/concrete piles. J Comps Constr 2005;9(3):274–83. � Optimization of composite catenary risers. Mar Struct 2003;33:1–20. [3] Da Silva RF, Te� ofilo FAF, Parente E, Cartaxo de Melo AM, Silva de Holanda A. [4] Guades Ernesto, Thiru Aravinthan, Allan Manalo, Islam Mainul. 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