Axial crush behavior and energy absorption capability of foam-filled GFRP tubes manufactured through vacuum assisted resin infusion process

Thin-Walled Structures 98 (2016) 263–273

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Axial crush behavior and energy absorption capability of foam-filled GFRP tubes manufactured through vacuum assisted resin infusion process Lu Wang n, Weiqing Liu, Yuan Fang, Li Wan, Ruili Huo College of Civil Engineering, Nanjing Tech University, Nanjing 211816, China

art ic l e i nf o

a b s t r a c t

Article history: Received 5 May 2015 Received in revised form 18 September 2015 Accepted 6 October 2015 Available online 19 October 2015

Foam-filled circular metallic tube has been widely used in safety design of automobile, space craft recovery and so on due to its advantage of high energy absorption. But poor chemical stability and easily oxidized of metal materials seriously threaten the durability and safety of the traditional metallic tube. The application of fiber reinforcement polymer (FRP) can effectively address these issues. In this paper, a simple and innovative foam-filled GFRP tube, fabricated by vacuum assisted resin infusion process, is proposed to enhance the durability and improve the energy absorption capacity. An experimental study was conducted to validate the effectiveness of this kind of absorptor for increasing the energy absorption capacity. Meanwhile, the influences of GFRP skin thickness, diameter of tube, foam density and fiber orientation angle of GFRP mat on failure mode, initial stiffness, stroke efficiency and specific energy absorption were also investigated. An analytical model, considered the confinement effect on foam core and local buckling of GFRP skin, was also developed to predict the ultimate peak strength of foam-filled GFRP tubes. The experimental and analytical results were shown to be well matched. & 2015 Elsevier Ltd. All rights reserved.

Keywords: GFRP tube Foam-filled Axial crush behavior Energy absorption Analytical model

1. Introduction A large number of practical engineering structures, such as vehicles, airplanes and space crafts, must absorb various amounts of energy during impact events. The structural crashworthiness, defined as the capability of a vehicle to protect its occupants from serious injury or death in case of accidents of a given proportion [1], has been adopted to evaluate the safety of the structures. Among all the crashworthy components, thin-walled aluminum alloy tubes has been widely used due to their advantages of ease of fabrication and excellent energy absorption efficiency. The progressive buckling and plastic deformation of thin-walled aluminum alloy skins can dissipate much energy. Many studies on the behaviors of aluminum alloy energy absorber with and without foam filled subjected to axial quasi-static compression loading or dynamic loading have been conducted [2–20]. In the meantime, a number of researchers investigated the energy absorption capacity of tubes with different cross section types under quasi-static lateral loading. Morris et al. [21]. conducted a numerically and experimentally study on the quasi-static lateral compression of nested tubes with vertical and inclined side constraints. The n

Corresponding author. Fax: þ 86 25 58139862. E-mail address: [email protected] (L. Wang).

http://dx.doi.org/10.1016/j.tws.2015.10.004 0263-8231/& 2015 Elsevier Ltd. All rights reserved.

energy absorbing capacity of nested systems can be enhanced due to the use of external constraints. Olabi et al. [22]. presented an overview of energy absorbers in the form of metal tubes under axial and lateral compressive loading. Baroutaji et al. [23,24] investigated the energy absorption capacity of circular and oblong tubes under quasi-static lateral loading. Moreover, the crashworthiness optimization of thin-walled tubes under quasi-static lateral loading was established. It can be concluded that the multiobjective optimization design of tube can be obtained if the minimum tube diameter, the minimum tube width and the maximum tube thickness were chosen. However, many researchers demonstrated that it is difficult to produce aluminum parts due to its characteristics of strain concentration and low ductility [25]. These issues can seriously threaten the durability and safety of the thin-walled aluminum alloy tubes. To address these issues, a kind of hybrid tubes was developed, which was traditional metal tubes wrapped with FRP composites. Various experimental and analytical investigations of the behaviors of hybrid tubes have been carried out. Shin et al. [25] investigated quasi-static axial crushing behavior of hybrid tubes produced by wrapping GFRP around square aluminum tubes. The ply orientations were 0°, 90°, 0/90° and 745° to the tube axis. The test results proved that the mean crush load and specific energy absorption of the hybrid tubes were significantly larger than those of the aluminum tubes. Han et al. [26]. numerically studied the

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Fig. 1. The foam-filled GFRP tube.

energy absorbing capacity of hybrid composite pultruded tubes with 745° fiber orientation. In their study, the influences of the height of the tube, the skin thickness and type of braid on the crushing behavior of the tubes have been summarized. Huang et al. [27]. conducted the numerical study on energy absorbing capacity of cylindrical metal tubes under static and dynamic loading. The results showed that the crushing characteristics and energy absorbing capacity of the tubes were enhanced by the use of FRP composites to confine the metal tubes. The thicker composites can generate the larger mean force and the specific energy absorption under both static and dynamic loading. It also pointed that the energy absorption capacity and the failure mode of the hybrid tubes were significantly affected by the ply pattern. Bouchet et al. [28] carried out dynamic compression tests on circular hybrid tubes in which the CFRP was employed as the wrapping. The specific energy absorption improved when the diameter to thickness ratio of the aluminum tube was 48, while reduced when it was equal to 25. Babbage and Mallick [29]. investigated the crushing behavior of hybrid tubes with circle and square sections under static compression loading. The influences of fiber orientation, composite thickness and with and without foam filled on the energy absorption capacity were examined. The test results indicated that the largest energy absorption capacity can be achieved by use of the foam-filled circle hybrid tubes with the thickest FRP skin. However, the manufacturing process of hybrid tubes is much more complicated than that of aluminum alloy tubes, meanwhile the bond behavior between composites and aluminum alloy is sensitive to the temperature, and moreover the cost of hybrid tubes is higher than aluminum alloy tubes. These issues cannot be ignored in the design procedure. Hence, many researchers have proposed that using composite tubes to instead the hybrid tubes. In recent years, a series of studies on foam-filled composite tubes been conducted. The effects of fiber orientation, thickness of tube and geometrical shape of the cross section on crush behavior and energy absorption performance have been investigated. Mamalis et al. [30]. and Palanivelu et al. [31]. investigated the effects of geometrical shape of cross sections on energy absorption performance of composite tubes. The test results showed that the energy absorption capability of circular cross sectional composite tubes are much higher than that of square and rectangular cross sectional composite tubes. Elgalai et al. [32]. studied the effects of type of fiber and corrugation angle on crushing behavior of axially crushed composite corrugated tubes. The results proved that the crushing behavior of composite corrugated tube was affected significantly by the corrugation angle. Carbon/epoxy tubes with corrugation angle of 40° exhibited the highest specific energy absorption capability. Melo et al. [33] investigated the effect of the vacuum processing conditions on the specific energy absorption

capacity of composite tubes. The test results demonstrated that the compressive strength of specimens manufactured under the vacuum condition was not improved significantly, while the specific energy absorption capacity was enhanced compared to that of specimens manufactured under the atmospheric condition. Although the composite tubes are excellent for energy absorption and have been extensively used in such engineering structures as automobiles, aircraft, military facilities, bridge structures and others, in the majority of the studies the composite tubes usually fabricated by a pultrusion or bonding processes. Furthermore, most previous studies of the crushing behavior and specific energy absorption capability of composite tubes were purely experimental. There are hardly any analytical studies on axial strength and local buckling of composite skins considering the foam core restriction. To enrich the type of crashworthy tubes and provide more choices about manufacture process, a simple and innovative foam-filled GFRP tube is proposed, which is fabricated by vacuum assisted resin infusion process (VARI). As shown in Fig. 1, the foams are cut into cylinders according to the design dimensions. Before vacuum infusing resin, the foam cores were wrapped by GFRP mats. When the resin reached curing time, the manufacture of foam-filled GFRP tubes is completed, and then cut them into specimens in accordance with design parameters. The details of vacuum assisted resin infusion process was introduced in our companion papers [34–37]. In this investigation, an experimental study was conducted to validate the effectiveness of this foam-filled GFRP tubes. The influences of GFRP skin thickness, diameter of tube, foam density and fiber orientation on failure mode, initial stiffness, stroke efficiency and specific energy absorption were also investigated. An analytical model, considered the confinement effect of foam core and local buckling of GFRP skin, was developed.

2. Experimental study 2.1. Specimen Details In this study, 18 specimens were fabricated and tested. All specimens were divided into two groups in accordance with the fiber orientation angle. Specimens H1D5T1C, H1D5T3C, TH1D5T1C and TH1D5T3C were control tubes without foam core to demonstrate the structural performance of GFRP thin-walled tubes. The other specimens were filled by polyurethane foam (PU foam) with varying thickness of the GFRP tube (t), diameter of the GFRP tube (d) and foam density (ρ). The design parameters for all specimens are summarized in Table 1. Specimens H1D5T1P6, H1D5T2P6 and H1D5T3P6 and Specimens TH1D5T1P6, TH1D5T2P6 and TH1D5T3P6 were fabricated

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Table 1 Details of specimens. Group

A

B

265

Table 3 Material properties of GFRP skin.

Specimen

H (mm)

d (mm)

t (mm)

ρ ( kg/m3)

m (g)

H1D5T2C H1D5T1P6 H1D5T2P6 H1D5T3P6 H1D5T2P4 H1D5T2P10 H1D7T3P6 H1D3T3P6

80 80 80 80 80 80 80 80

50 50 50 50 50 50 75 30

2.4 1.6 2.4 3.2 2.4 2.4 3.2 3.2

– 60 60 60 40 100 60 60

41.7 35.7 46.5 65.5 41.6 55.4 85.8 47.2

TH1D5T3C TH1D5T1P6 TH1D5T2P6 TH1D5T3P6 TH1D5T3P4 TH1D5T3P10 TH1D7T2P6 TH1D3T2P6

80 80 80 80 80 80 80 80

50 50 50 50 50 50 75 30

3.2 1.6 2.4 3.2 3.2 3.2 2.4 2.4

– 60 60 60 40 100 60 60

51.9 34.7 48.5 64.5 43.4 57.4 91.6 40.2

with H ¼100 mm, d¼ 50 mm and ρ ¼60 kg/m3, respectively, which were used to investigate the influence of thickness of the GFRP tube. Specimens H1D5T2P4, H1D5T2P6 and H1D5T2P10 and Specimens TH1D5T3P4, TH1D5T3P6 and TH1D5T3P10 were fabricated with H¼ 100 mm and d¼ 50 mm, respectively, which were used to investigate the influence of foam density. Specimens H1D5T3P6, H1D7T3P6 and H5D7T3P6 and Specimens TH1D5T2P6, TH1D7T2P6 and TH5D5T2P6 were fabricated with H ¼100 mm and ρ ¼ 60 kg/m3, respectively, which were used to investigate the influence of length-to-diameter ratio of the tube. Specimens H1D5T1P6 and TH1D5T1P6 and Specimens H1D5T3P6 and TH1D5T3P6 were fabricated with H ¼100 mm and ρ ¼ 60 kg/m3, respectively, which were used to investigate the influence of fiber orientation. 2.2. Material properties The polyurethane foams with different density (40 kg/m3, 60 kg/m3 and 100 kg/m3) were employed in this study. For each density, five cubic foam samples of 50 mm thick were made and tested in accordance with ASTM D1621-10 [38]. to obtain the compressive strength and the Young's modulus. Table 2 shows the cube compressive strength and the Young's modulus for each foam. Tensile and compressive tests, based on ASTM D3039/D3039M08 [39] and ASTM D695-10 [40]. respectively, were carried out to determine the tensile strength, the tension Young's modulus, the compressive strength and the compression Young's modulus of GFRP face sheet. The material tension and compression properties of web are summarized in Table 3.

Compressive strength (MPa) Compressive modulus (GPa) Tensive strength (MPa) Tensive modulus (GPa)

0/90°

7 45°

168.6 6.26 301.5 6.61

72.8 3.09 225.7 4.39

strong floor of the Structural Engineering Laboratory at Nanjing Tech University. Compression was applied by a hydraulic actuator with an axial capacity of 100 kN. Prior to the compressive test, two surfaces of the specimen were connected to 20-mm-thick steel plates and the specimens were placed at the center of the loading system. The applied load was applied under displacement control with a displacement rate at 0.01 mm per second. 2.4. Instrumentation Vertical loading data was collected via a five-channel load cell which was mounted directly beneath the panels. Axial shortening was measured by two linear variable displacement transducers (LVDTs) which were internal to the vertical actuator. The displacement data reflected the total displacement of the top surface of the specimen with respect to the bottom surface. For each specimen, two bi-directional strain rosettes with a gauge length of 10 mm were symmetrically distributed around the circumference of the outer face sheet to measure the axial and hoop strains at mid-height of the tube. The strain readings measured were then used to identify the failure mode and analyze the axial force distribution between face sheet and foam core. 2.5. Test procedure The specimen was installed vertically at the center of the loading system. The bottom surface of the specimen was coated with plaster to form a layer of bedding, which was used to ensure absolutely vertical during the test. The plaster was composed of plaster, potassium sulfate, and water, with a 37.5∶1∶15 proportion by weight [41]. Because the GFRP skin and foam are sensitive to the temperature, all the specimens were stored in the laboratory for a month to ensure that the temperature difference between GFRP skin and foam core of the specimen would be minimized at the time of the axial load tests. All tests were conducted in a constant temperature environment. The room temperature was kept at 25 °C. The tests were stopped when the shortening length reached roughly half of the clear height of specimen. The machine recorded the axial shortening and the crush force. Based on these data, the load–displacement curve were outlined. The energy absorbed by the specimens was obtained by the numerical integration of the area under the load–displacement curve.

2.3. Test setup Fig. 2 shows the test setup. The support system consisted of a steel framed structure. The base of the frame was bolted to the

3. Experimental results and discussion 3.1. Strength and stiffness

Table 2 Material properties of foams. Foam density (ρ) (kg/m3)

Yield strength (ffy) (MPa)

Young's modulus (Ef) (MPa)

40 60 100

0.171 0.366 0.637

5.02 9.87 15.17

The axial stiffness of a tube is defined as the slope of the load– displacement curve. The axial stiffness Keis given by Eq. (1)

Ke =

Pu ∆y

(1)

where Pu and Δy are ultimate load and corresponding displacement, respectively.

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Fig. 2. Test setup. Table 4 Experimental and analytical results of specimens. Specimen

Pu (kN)

Ke (kN/mm)

Ste (%)

W (Δst) (J)

Se (J/g)

Ppre (kN)

Ppre/Pu

H1D5T2C H1D5T1P6 H1D5T2P6 H1D5T3P6 H1D5T2P4 H1D5T2P10 H1D7T3P6 H1D3T3P6 TH1D5T3C TH1D5T1P6 TH1D5T2P6 TH1D5T3P6 TH1D5T3P4 TH1D5T3P10 TH1D7T2P6 TH1D3T2P6 Mean

22.72 42.33 59.43 76.76 49.95 66.01 120.26 38.58 21.85 31.33 55.72 72.70 61.23 75.47 81.69 33.92

11.29 12.16 20.63 43.58 18.28 24.47 87.74 18.84 12.11 10.06 23.21 41.60 26.27 54.24 28.04 14.43

37.51 60.02 53.76 51.25 56.23 47.48 40.24 57.51 41.23 56.25 52.49 46.25 52.78 42.02 43.74 58.76

199.85 1062.81 1168.59 1560.97 1034.73 1622.47 2121.52 808.02 254.59 740.92 888.62 1156.76 714.65 1412.09 1940.20 728.69

4.79 29.77 25.13 23.83 24.87 29.29 24.73 17.12 4.91 21.35 18.32 17.93 16.47 24.60 21.18 14.80

20.55 37.28 55.34 73.16 55.08 56.99 111.02 43.04 20.16 33.78 50.15 66.38 66.12 66.99 75.97 29.67

0.90 0.88 0.93 0.95 1.10 0.86 0.92 1.12 0.92 1.08 0.90 0.91 1.08 0.89 0.93 0.87 0.95

The test results of all the specimens, including the peak strength (Pu), axial stiffness (Ke), stroke efficiency (Ste) and specific energy absorption (Se), are summarized in Table 4. Fig. 3 shows the influences of GFRP skin thickness on the Pu of tubes. Compared to Specimen H1D5T1P6 (Pu ¼42.33 kN, Ke ¼12.16 kN/mm), the Pu of

Specimens H1D5T2P6 and H1D5T3P6 increased by 40.4% and 81.3%, respectively, and the Ke of Specimens H1D5T2P6 and H1D5T3P6 increased by 69.6% and 258.4%, respectively. Compared to Specimen TH1D5T1P6 (Pu ¼ 31.33 kN, Ke ¼10.06 kN/mm), the Pu of Specimens TH1D5T2P6 and TH1D5T3P6 increased by 77.8% and 132.1%, respectively, and the Keof Specimens TH1D5T2P6 and TH1D5T3P6 increased by 130.7% and 313.4%, respectively. This may be due to the fact that thicker GFRP skin can provide a higher lateral confining pressure to the foam as presented in Eq. (6), then the compressive strength of the confined foam can be enhanced. Meanwhile, the thicker web can lead to a larger axial stiffness. Thus, using thicker GFRP skin can improve the peak strength and axial stiffness of tubes significantly. Fig. 4 shows the influences of foam density on the Pu of the tubes. Specimens H1D5T2C and TH1D5T3C were the control tubes without foam core, so the values of Pu and Ke of them were the smallest in each group. In Group A, compared to Specimen H1D5T2P4 (Pu ¼ 49.95 kN, Ke ¼18.28 kN/mm), the Pu of Specimens H1D5T2P6 and H1D5T2P10 increased by 19.0% and 32.2%, respectively, and the Ke of Specimens H1D5T2P6 and H1D5T2P10 increased by 12.8% and 33.9%, respectively. In Group B, compared to Specimen TH1D5T3P4 (Pu ¼61.23 kN, Ke ¼26.27 kN/mm), the Pu of Specimens TH1D5T3P6 and TH1D5T3P10 increased by 18.7% and 23.3%, respectively, and the Keof Specimens TH1D5T3P6 and TH1D5T3P10 increased by 77.4% and 106.5%, respectively. The foam with larger density also behaves stiffer. In the meantime,

Fig. 3. The influences of GFRP skin thickness (a) h ¼ 50 mm, s ¼ 70 mm, ρ ¼ 60 kg/m3 and (b) h ¼ 50 mm, s ¼ 50 mm, ρ¼ 60 kg/m3.

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267

Fig. 4. The influences of foam density (a) h ¼50 mm, t ¼2.4 mm, s ¼50 mm and (b) h ¼ 100 mm, t¼ 2.4 mm, s¼ 100 mm.

Fig. 5. The influences of diameter of the GFRP tube (a) h ¼ 70 mm, t¼ 2.4 mm, ρ ¼ 60 kg/m3 and (b) h ¼ 70 mm, t ¼7.2 mm, ρ ¼ 60 kg/m3.

larger density foam can provide much more resistance to the compression. Therefore, a larger foam density can generate a larger peak strength and axial stiffness. Fig. 5 shows the influences of diameter of tube on the Pu and Ke of specimens. According to Fig. 5(a), for the specimens with 80 mm height, 3.2 mm GFRP skin thickness and 60 kg/m3 foam density, the Pu and Ke of Specimen H1D7T3P6 (d¼ 75 mm) were 120.26 kN and 87.74 kN/mm, respectively, which were 211.75 and

56.7% larger than the Pu of Specimen H1D3T3P6 (d¼ 30 mm) and H1D5T3P6 (d ¼50 mm), respectively, and 365.6% and 101.3% larger than the Ke of Specimen H1D3T3P6 and H1D5T3P6, respectively. According to Fig. 5(b), for the specimens with 80 mm height, 2.4 mm GFRP skin thickness and 60 kg/m3 foam density, the Pu and Ke of Specimen TH1D7T2P6 (d ¼75 mm) were 81.69 kN and 58.68 kN/mm, respectively, which were 140.8% and 46.6% larger than the Pu of Specimen TH1D3T2P6 (d¼ 30 mm) and TH1D5T2P6

Fig. 6. The influences of fiber orientation (a) h ¼50 mm, t¼ 2.4 mm, s¼ 50 mm and (b) h ¼ 100 mm, t¼ 2.4 mm, s¼ 100 mm.

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H1D5T1P6 and H1D5T3P6 were 12.16 kN/mm and 43.58 kN/mm, respectively, which were 20.8% and 4.8% larger than those of Specimens TH1D5T1P6 and TH1D5T3P6, respectively. 3.2. Compressive behavior and failure modes

Fig. 7. The idealized load–axial shortening curve.

(d ¼50 mm), respectively, and 306.8% and 152.8% larger than the Ke of Specimen TH1D3T2P6 and TH1D5T2P6, respectively. The larger diameter of tube can lead to a larger axial stiffness, hence, the peak strength of tubes can be improved. Fig. 6 shows the influences of fiber orientation of GFRP skin on the Pu and Ke of specimens. For Specimens H1D5T1P6 and H1D5T3P6 with 80 mm height, 0/90° fiber orientation of GFRP skin thickness and 60 kg/m3 foam density, the Puof them were 42.33 kN and 76.76 kN, respectively, which were 35.1% and 5.6% larger than those of Specimens TH1D5T1P6 and TH1D5T3P6 with 80 mm height, 745° fiber orientation of GFRP skin thickness and 60 kg/m3 foam density. For the value of Ke, the Ke of Specimens

According to the load-axial shortening curves (see Figs. 3–6), the deformation of tubes can be divided into three stages: linearelastic stage, post-yield stage and foam densification stage, as shown in Fig. 7. All specimens exhibited a linear-elastic response up to failure at the elastic stage (Line OM). In the post-yield stage, the compressive load capacity decreased sharply, which was associated with compressive failure of GFRP tube. The compressive load capacity of specimens roughly stayed at a half of peak strength level (Line NU). In the foam densification stage, the compressive load capacity of specimens increased, but the axial shortening of panels was very large. With an increasing compression, the fractured tubes violently extruded the foam, which resulted in crushing of the foam core (Line UV). According to the readings of strain gauges, the failure mode of all tubes was compressive failure of GFRP skin accompanied with fiber fracture. The direction of fracture was determined by the fiber orientation of GFRP mats. For specimens in Group A, the direction of fracture of GFRP skin was horizontal, as shown in Fig. 8 (a). For specimens in Group B, the direction of fracture of GFRP skin was 45°, as shown in Fig. 8(b). For all specimens, the first fracture crack usually occurred at the mid-height of the tube in the linear-elastic stage. During the post-yield stage, the specimen shortened sharply and the foam core was extruded by GFRP skin. Then and GFRP skin was fragmentation and the foam was densificated at the third stage.

Fig. 8. Failure modes (a) specimen with 0/90° fiber orientation; (b) specimen with 7 45° fiber orientation.

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Fig. 9. The stroke efficiency of the tubes (a) the influences of GFRP skin thickness; (b) the influences of foam density; (c) the influences of diameter of the GFRP tube and (d) the influences of fiber orientation.

3.3. Stroke efficiency The stroke efficiency (Ste) is employed to evaluate the deformability of a tube, which is defined as the ratio of the stroke length to the height of a tube (H) [42],

Ste =

∆st H

(2)

Fig. 9(a) illustrates a decrease of the obtained stroke efficiencies with increasing GFRP skin thickness, although the fiber orientation was different. The Ste of Specimens H1D5T1P6 and TH1D5T1P6 (t ¼1.6 mm) were 60.00% and 56.25%, respectively, which were 11.6% and 17.1% larger than those of Specimens H1D5T2P6 and TH1D5T2P6 (t ¼2.4 mm), respectively, and 7.1% and 21.6% larger than those of Specimens H1D5T3P6 and TH1D5T3P6 (t ¼3.2 mm), respectively. The tubes with the thickest GFRP skins had the lowest values of Ste (51.25% for H1D5T3P6, and 46.25% for TH1D5T3P6). The reason why this phenomenon occurred was that the thicker GFRP skin can give a larger axial stiffness of the tube, therefore, the stroke length become small for a given compression. Fig. 9(b) shows a slightly decrease of the obtained stroke efficiencies with increasing foam density. In each group, the Ste of Specimens H1D5T2C and TH1D5T3C (without foam filled) were the lowest compared to corresponding specimens, which were 37.50% and 41.25%, respectively. Although the difference in the GFRP skin thickness, both curves in Fig. 9(b) show a similar trend. Compared to Specimens H1D5T2P4 (Ste ¼ 56.25%) and TH1D5T3P4 (Ste ¼58.75%) with 40 kg/m3 foam density, the Steof Specimens

H1D5T2P6 and TH1D5T3P6 (ρ ¼60 kg/m3) decreased by 4.5% and 21.3%, respectively, which equaled to 53.75% and 46.25%, respectively. When the foam density increased to 80 kg/m3, the Steof Specimens H1D5T2P10 and TH1D5T3P10 decreased by 15.5% and 23.4%, respectively, which equaled to 47.5% and 45.0%, respectively. With the increase in foam density, the compression starts to increase sharply at the foam densification stage. Hence, the foam core suffered very large compressive strains and prevented the deformation of GFRP skins, which decreased the stroke length of tubes. Fig. 9(c) shows a distinct reduction of the obtained stroke efficiencies with increasing diameter of tubes. In Group A, compared to Specimen H1D7T3P6 (d ¼75 mm), the Ste of Specimens H1D5T3P6 (d¼ 50 mm) and H1D3T3P6 (d ¼30 mm) increased by 10.8% and 24.3%, respectively. The similar phenomenon can be found in Group B. Compared to Specimen TH1D7T2P6 (d ¼75 mm), the Ste of Specimens TH1D5T2P6 (d ¼50 mm) and TH1D3T2P6 (d ¼ 30 mm) increased by 20.0% and 34.3%, respectively. Because the larger diameter can lead to a larger axial stiffness of tubes, hence a small stroke length can be achieved under a given compression. Fig. 9(d) shows a slightly reduction of the obtained stroke efficiencies when the fiber orientation angle of GFRP skin changed to 745°. For Specimens H1D5T1P6 and H1D5T3P6 with 80 mm height, 0/90° fiber orientation of GFRP skin and 60 kg/m3 foam density, the Ste were 60.00% and 51.25%, respectively, which were 6.7% and 10.8% larger than those of Specimens TH1D5T1P6 and TH1D5T3P6 with 80 mm height, 7 45° fiber orientation of GFRP

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Fig. 10. The specific energy absorption of the tubes (a) the influences of GFRP skin thickness; (b) the influences of foam density; (c) the influences of diameter of the GFRP tube and (d) the influences of fiber orientation.

skin and 60 kg/m3 foam density. 3.4. Specific energy absorption The specific energy absorption (Se) was introduced to evaluate the “mass efficiency” of a tube, which is defined as [42].

Se =

W (∆st ) m

(3)

where m is the total mass of a tube, and W(Δ) is the energy dissipated by plastic deformation because the contribution due to elastic deformations is negligible, which can be calculated by Eq. (4)

W(∆)=

∫0

Δ

P(Δ¯ )ΔdΔ¯

(4)

where P is the applied compression, and Δ is the displacement of specimen (with integration variable Δ¯). Fig. 10(a) shows the influences of GFRP skin thickness on the specific energy absorption of the tubes. For the specimens with 80 mm height, 50 mm diameter, 60 kg/m3 foam density and 0/90° fiber orientation of GFRP skin, the Se of Specimen H1D5T1P6 (t ¼1.6 mm) was 29.77, which was 18.5% and 24.9% larger than that of Specimen H1D5T2P6 (t¼ 2.4 mm) and H1D5T3P6 (t ¼3.6 mm), respectively. For the specimens with 80 mm height, 50 mm diameter, 60 kg/m3 foam density and 745° fiber orientation of GFRP skin, the Se of Specimen TH1D5T1P6 (t¼1.6 mm) was 21.35, which was 16.5% and 19.1% larger than that of Specimen TH1D5T2P6 (t ¼2.4 mm) and TH1D5T3P6 (t¼3.2 mm), respectively. Hence, the

GFRP skin thickness can play an important role in increasing the energy absorption of the tubes. Fig. 10(b) shows the influences of foam density on the specific energy absorption of the tubes. For the specimens with 80 mm height, 2.4 mm GFRP skin thickness, 50 mm diameter and 0/90° fiber orientation of GFRP skin, the Se of Specimen H1D5T2P10 (ρ ¼ 100 kg/m3) was largest, which was equal to 29.29, the Se of Specimens H1D5T2P4 (ρ ¼ 40 kg/m3) and H1D5T2P6 (ρ ¼ 60 kg/ m3) were 24.87 and 25.13, respectively. For the specimens with 80 mm height, 3.2 mm GFRP skin thickness, 50 mm diameter and 745° fiber orientation of GFRP skin, the Se of Specimen TH1D5T3P10 (ρ ¼100 kg/m3) was largest, which was equal to 24.60, the Se of Specimens TH1D5T3P4 (ρ ¼40 kg/m3) and TH1D5T3P6 (ρ ¼60 kg/m3) were 16.47 and 17.93, respectively. The test results indicated that the higher foam density of the tubes can achieve the larger energy absorption. Fig. 10(c) shows the influences of diameter of tube on the specific energy absorption of specimens. For the specimens with 80 mm height, 3.2 mm web thickness, 60 kg/m3 foam density and 0/90° fiber orientation of GFRP skin, the Se of Specimen H1D7T3P6 (d ¼75 mm) was 24.73, which was 44.5% and 3.8% larger than that of Specimen H1D3T3P6 (d ¼30 mm) and H1D5T3P6 (d ¼50 mm), respectively. For the specimens with 80 mm height, 2.4 mm web thickness, 60 kg/m3 foam density and 745° fiber orientation of GFRP skin, the Se of Specimen TH1D7T2P6 (d¼ 75 mm) was 21.18, which was 43.1% and 15.6% larger than that of Specimen TH1D3T2P6 (d¼ 30 mm) and TH1D5T2P6 (d ¼50 mm), respectively. Thus, the energy absorption of the tubes can be enhanced using the tube with the larger diameter.

L. Wang et al. / Thin-Walled Structures 98 (2016) 263–273

Fig. 10(d) shows the influences of fiber orientation of GFRP skin on the specific energy absorption of specimens. For the specimens with 80 mm height, 1.6 mm GFRP skin thickness, 60 kg/m3 foam density and 50 mm diameter, the Se of Specimen H1D5T1P6 (0/90° fiber orientation) was 29.77, which was 39.4% larger than that of Specimen TH1D5T1P6 (7 45° fiber orientation). For the specimens with 80 mm height, 3.2 mm GFRP skin thickness, 60 kg/m3 foam density and 50 mm diameter, the Se of Specimen H1D5T3P6 (0/90° fiber orientation) was 23.83, which was 32.9% larger than that of Specimen TH1D5T3P6 ( 745° fiber orientation). Therefore, the tubes with 0/90° fiber orientation of GFRP skin can effectively improve the energy absorption. 3.5. Comparison with available experimental results Mondal et al. [18,19] and Goel [20]. conducted an experimental and numerical study of the axial crush performance of foam-filled aluminum tubes with 56.42 mm out diameter. Three specimens, called Circle-single tube/foam, Circle-two tubes/foam and Circlethree tubes/foam, were adopted to analyze their energy absorbing capacity, which consisted of single tube, double tubes and triple tubes, respectively. Circular configuration has equivalent diameters of 33.85 mm, 45.14 mm and 56.42 mm for innermost, central and outermost tubes, respectively. Table 5 compares the peak strength and specific energy absorption presented in Mondal et al. [18,19] and Goel [20]. with those of Specimens H1D5T1P6 and H1D5T2P6 because the out diameter of Specimens H1D5T1P6 and H1D5T2P6 are roughly close to those of their specimens. In the Table 5, φ is the ratio of total area of skins to cross sectional area of each specimen. As presented in Table 5, compared to Specimen H1D5T1P6, the Pu of Specimens Circle-single tube/foam, Circle-two tubes/foam and Circle-three tubes/foam decrease to 14.9%, 34.7% and 30.9%, respectively, even the value of φ of Specimen H1D5T1P6 (φ ¼0.12) was smaller than those of their specimens. In a similar manner, compared to Specimen H1D5T2P6, the Pu of Specimens Circle-two tubes/foam and Circle-three tubes/foam decrease to 34.7% and 30.9%, respectively, although the value of φ of Specimen H1D5T2P6 (φ ¼0.18) was smaller than those of their specimens. In the meantime, it can be found that compared to Specimen H1D5T1P6, the Se of Specimens H1D5T1P6 and H1D5T2P6 were approximately twenty times larger than that of Specimen Circlesingle tube/foam, twelve times larger than that of Specimen Circletwo tubes/foam and thirty times larger than that of Specimen Circle-three tubes/foam, respectively. Therefore, even the out diameter of Specimens H1D5T1P6 and H1D5T2P6 are slightly smaller, larger peak strength and energy absorbing capacity can be achieved. Table 5 Comparison of available test results and present test results. Specimens

d

t

φ

(mm) (mm) H1D5T1P6 H1D5T2P6 Circle-single tube/ foam Circle-two tubes/foam Circle-three tubes/ foam

m

Pu

W (Δst)

Se

(g)

(kN)

(J)

(J/g)

50 1.6 50 2.4 56.42 2.0

0.12 0.18 0.14

35.7 42.33 1062.81 29.77 46.5 59.43 1168.59 25.13 340.3 6.3 458.40 1.35

56.42 2.0 56.42 2.0

0.25 438.8 0.33 512.1

14.7 13.1

963.13 453.36

2.19 0.89

Note: Circle-single tube/foam, Circle-two tubes/foam and Circle-three tubes/foam are the specimens tested by Mondal et al. [18,19] and Goel [20].

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4. Ultimate axial load capacity 4.1. Confinement model for foam CORE The foam core was confined by the GFRP skin, thus the compressive strength of the confined foam core (fF’) should be adopted, which can be calculated by Eq. (5) [43].

f F‘ fF

= 1 + k1

fl fF

(5)

where fF is the compressive strength of the unconfined foam, k1 is the effectiveness coefficient of confinement, which is equal to 0.93 [44], fl is the lateral confining pressure. Teng et al. [44] proposed the following formula to calculate the lateral confining pressure fl of confined foam:

fl =

2fFRP t d

=

ρFRP fFRP (6)

d

where fFRP is the tensile strength of FRP in the hoop direction, t is the thickness of the FRP confinement, d is the diameter of tube, and ρFRP is FRP volumetric ratio. 4.2. Local buckling of GFRP skin Timoshenko and Gere [45]. indicated that the critical buckling stress of GFRP skin (fcr) can be calculated by Eq. (7),

‵ fr fcr = 3(1−vs2) f cr

(7)

where vs is the Poisson ratio of GFRP skin, and fcr’ is the critical stress of the corresponding cylindrical shell without foam-filled, which can be determined by Eq. (8).

‵ = f cr

Ests R 3(1−vs2)

(8)

where Es and ts are the Young's modulus and thickness of GFRP skin, respectively, and R is the radius of a tube. The value of fr can be obtained by Eq. (9).

fr =

1 12(1−vs2)

R

2

( ) λcr

+

2

( ) λcr

ts ts

R

ts

2 +

ts

( )( )( ) Ec

Es

λcr

ts

R

(3−vc ) (1 + vc )

ts

(9)

where Ec and vc are the Young's modulus and Poisson ratio of the foam core, respectively, and λcr is the buckling half wave length. 4.3. Ultimate axial load capacity Then, the ultimate axial load capacity (Ppre) of foam-filled GFRP tube can be calculated using the following formula:

Ppre = 0. 67f F‵ AF + fFRP AFRP

(10)

where AF and AFRP are cross-sectional areas of the foam and GFRP skin, respectively. Table 4 summarized the analytical ultimate peak strength of tubes. The largest variation between predicted and experimental results in the ultimate peak strength was 9.24 kN, which occurred in Specimen H1D7T3P6. Comparing the analytical and experimental results shows that the proposed analytical model is generally able to conservatively estimate the actual ultimate axial load capacity of the foam-filled GFRP tubes under compression with an average underestimation of 5.0%. 5. Conclusions This paper presents an experimental and analytical study on

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the foam-filled GFRP tubes under quasi-static axial compression loading. The main findings of this study are summarized as follows: (1) A kind of foam-filled GFRP tubes applied to engineering structures was developed via vacuum assisted resin infusion process. The test results proved that these foam-filled GFRP tubes had the characteristics of high compressive stiffness and strength, and strong energy absorbing capacity. Compared to the foam-filled metal tubes tested by Mondal et al. [18–19] and Goel [20], an approximately 190% increase in the peak strength and an approximately 1050% in the energy absorbing can be achieved. Furthermore, the weight of foam-filled GFRP tubes can be decreased to 11% roughly. (2) The thicker GFRP skin and larger diameter can enhance the peak load and axial stiffness of tubes significantly, but the influences of foam density on the peak load of tubes are small. The test results show that an approximately 132.1% and 313.4% increase in the peak strength and initial stiffness can be achieved due to the use of 3.2 mm-thick skin rather than 1.6 mm-thick skin. Moreover, the peak strength and axial stiffness of tubes with 0/90° fiber orientation angle are larger than those of tubes with 745° fiber orientation angle. (3) The larger diameter can sharply decrease the stroke efficiency of tubes, while the thicker GFRP skin and higher foam density can slightly decrease the stroke efficiency of tubes. Hence, at least 10% decrease in the stroke efficiency when the diameter enlarge to 75 mm. In the meantime, the stroke efficiency of tubes are hardly affected by the fiber orientation angle. (4) The energy absorption of tubes is affected by skin thickness, diameter of tube and foam density. Larger energy absorption can be achieved by increasing the skin thickness and diameter of tube and choosing the foam with larger density. (5) An analytical model, considered the confinement effect of foam core and local buckling of GFRP skin, is proposed to predict the peak load. It can be found that the analytical results agree will with the experimental results. The average error between analytical and experimental results is not larger than 5.0%. The analytical model has been shown to be able to accurately predict the strength, stiffness and deflection of foam-filled GFRP tubes. (6) This type of foam-filled GFRP tubes is still under development; the corresponding finite element model will be established to investigate the performance of GFRP webs, and the minimum weight design procedure will also be provided after conducting more experimental or numerical testing of specimens. Meanwhile, the flammability of tubes should be researched in future because the mechanical performance of GFRP tubes are affected significantly by the high temperature.

Acknowledgment The research described here was supported by the National Natural Science Foundation for the Youth of China (Grant no. 51408305), Key Program of National Natural Science Foundation of China (Grant no. 51238003), Natural Science Foundation of Jiangsu Province (Grant no. BK20140946) and National Natural Science Foundation for the Youth of China (Grant no. 51208251).

References [1] G.C. Jacob, J.F. Fellers, S. Simunovic, J.M. Starbuck, Energy absorption in polymer composites for automotive crashworthiness, J. Compos. Mater. 36 (7)

(2002) 813–850. [2] A.G. Mamalis, et al., Crashworthy capability of composite material structures, Compos. Struct. 37 (1997) 109–134. [3] H. Song, Z. Wan, Z. Xie, X. Du, Axial impact behavior and energy absorption efficiency of composite wrapped metal tubes, Int. J. Impact Eng. 24 (2000) 385–401. [4] A.A.A. Alghamdi, Collapsible impact energy absorbers: an overview, ThinWalled Struct. 39 (2001) 189–213. [5] N. Jones, Several phenomena in structural impact and structural crashworthiness, Eur. J. Mech.: A/Solids 22 (2003) 693–707. [6] H. El-Hage, P. Mallick, N. Zamani, A numerical study on the quasi-static axial crush characteristics of square aluminum tubes with chamfering and other triggering mechanisms, Int. J. Crashworth. 10 (2005) 183–196. [7] G.M. Nagel, D.P. Thambiratnam, Dynamic simulation and energy absorption of tapered thin-walled tubes under oblique impact loading, Int. J. Impact Eng. 32 (2006) 1595–1620. [8] V. Tarigopula, M. Langseth, O.S. Hopperstad, A.H. Clausen, Axial crushing of thin-walled high-strength steel sections, Int. J. Impact Eng. 32 (2006) 847–882. [9] B. Wang, G. Lu, Mushrooming of circular tubes under dynamic axial loading, Thin-Walled Struct. 40 (2) (2002) 167–182. [10] X. Huang, G. Lu, T. Yu, Energy absorption in splitting square metal tubes, ThinWalled Struct. 40 (2) (2002) 153–165. [11] G. Nagel, D. Thambiratnam, Computer simulation and energy absorption of tapered thin-walled rectangular tubes, Thin-Walled Struct. 43 (8) (2004) 1225–1242. [12] A. Rossi, Z. Fawaz, K. Behdinan, Numerical simulation of the axial collapse of thin-walled polygonal section tubes, Thin-Walled Struct. 43 (10) (2005) 1646–1661. [13] P. Guegan, D. Lebreton, F. Pasco, R. Othman, S. Le Corre, A. Poitou, Metallic energy absorbing inserts for Formula One type barriers, Proc. Inst. Mech. Eng. Part D: J. Automob. Eng. 222 (2008) 699–704. [14] S. Chung Kim Yuen, G.N. Nurick, The energy-absorbing characteristics of tubular structures with geometric and material modifications: an overview, Appl. Mech. Rev. 61 (2008) 409–420. [15] Z. Ahmed, D.P. Thambiratnam, A.C.C. Tan, Dynamic energy absorption characteristics of foam-filled conical tubes under oblique impact loading, Int. J. Impact Eng. 37 (2010) 475–488. [16] A. Toksoy, M. Guden, The strengthening effect of polystyrene foam filling in aluminum thin-walled cylindrical tubes, Thin-Walled Struct. 43 (2) (2005) 333–350. [17] A. Ghamarian, H. Zarei, M. Abadi, Experimental and numerical crashworthiness investigation of empty and foam-filled end-capped conical tubes, ThinWalled Struct. 49 (10) (2011) 1312–1319. [18] M. Goel, Deformation, energy absorption and crushing behavior of single-, double- and multi-wall foam filled square and circular tubes, Thin-Walled Structures 90 (2015) 1–11. [19] D. Mondal, M. Goel, S. Das, Effect of strain rate and relative density on compressive deformation behavior of closed cell aluminum-fly ash composite foam, Mater. Des. 30 (2009) 1268–1274. [20] D. Mondal, M. Goel, S. Das, Compressive deformation and energy absorption characteristics of closed cell aluminum-fly ash particle composite foam, Mater. Sci. Eng. A 507 (1–2) (2009) 102–109. [21] E. Morris, A. Olabi, M. Hashmi, Analysis of nested tube type energy absorbers with different indenters and exterior constraints, Thin-Walled Struct. 44 (8) (2006) 872–885. [22] A. Olabi, E. Morris, M. Hashmi, Metallic tube type energy absorbers: a synopsis, Thin-Walled Structures 45 (2007) 706–726. [23] A. Baroutaji, E. Morris, A. Olabi, Quasi-static response and multi-objective crashworthiness Optimization of oblong tube under lateral loading, ThinWalled Structures 82 (2014) 262–277. [24] A. Baroutaji, M. Gilchrist, D. Smyth, A. Olabi, Crush analysis and multi-objective optimization design for circular tube under quasi-static lateral loading, Thin-Walled Struct. 86 (2015) 121–131. [25] K.C. Shin, J.J. Lee, K.H. Kim, M.C. Song, J.S. Huh, Axial crush and bending collapse of an aluminum/GFRP hybrid square tube and its energy absorption capability, Compos. Struct. 57 (2002) 279–287. [26] H. Han, F. Taheri, N. Pegg, Y. Lu, A numerical study on the axial crushing response of hybrid pultraded and 7 45° braided tubes, Compos. Struct. 80 (2) (2007) 253–264. [27] M.Y. Huang, Y.S. Tai, H.T. Hu, Numerical study on hybrid tubes subjected to static and dynamic loading, Appl. Compos. Mater. 19 (2012) 1–19. [28] J. Bouchet, E. Jacquelin, P. Hamelin, Dynamic axial crushing of combined composite aluminum tube: the role of both reinforcement and surface treatments, Compos. Struct. 56 (2002) 87–96. [29] J. Babbage, P. Mallick, Static axial crush performance of unfilled and foamfilled aluminum–composite hybrid tubes, Compos. Struct. 70 (2005) 177–184. [30] A.G. Mamalis, D.E. Manolakos, M.B. Ioannidis, D.P. Papapostolou, On the response of thin-walled CFRP composite tubular components subjected to static and dynamic axial compressive loading: experimental, Compos. Struct. 69 (4) (2005) 407–420. [31] S. Palanivelu, W.V. Paepegem, J. Degrieck, J. Vantomme, D. Kakogiannis, J. V. Ackeren, D.V. Hemelrijck, J. Wastiels, Crushing and energy absorption performance of different geometrical shapes of small-scale glass/polyester composite tubes under quasi-static loading conditions, Compos. Struct. 93 (2011) 992–1007. [32] A.M. Elgalai, E. Mahdi, A.M.S. Hamouda, B.S. Sahari, Crushing response of

L. Wang et al. / Thin-Walled Structures 98 (2016) 263–273

[33]

[34]

[35]

[36]

[37]

[38]

composite corrugated tubes to quasi-static axial loading, Compos. Struct. 66 (1–4) (2004) 665–671. J.D.D. Melo, A.L.S. Silva, Villena JEN. The effect of processing conditions on the energy absorption capability of composite tubes, Compos. Struct. 82 (2008) 622–628. L. Wang, W.Q. Liu, L. Wan, H. Fang, D. Hui, Mechanical performance of foamfilled lattice composite panels in four-point bending: Experimental investigation and analytical modeling, Compos. Part B: Eng. 67 (2014) 270–279. L. Wang, W.Q. Liu, H. Fang, L. Wan, Behavior of sandwich wall panels with GFRP face sheets and a foam-GFRP web core loaded under four-point bending, J. Compos. Materi. 49 (2015) 2765–2778, http://dx.doi.org/10.1177/ 0021998314554124. L. Wang, W.Q. Liu, D. Hui, Compression strength of hollow sandwich columns with GFRP skins and a paulownia wood core, Compos. Part B: Eng. 60 (2014) 495–506. Z.M. Wu, W.Q. Liu, L. Wang, H. Fang, D. Hui, Theoretical and experimental study of foam- filled lattice composite panels under quasi-static compression loading, Compos. Part B: Eng. 60 (2014) 329–340. ASTM D1621-10, Standard Test Method for Compressive Properties of Rigid

273

Cellular Plastics, ASTM, PA, USA, 2010. [39] ASTM D3039/D3039M-08, Standard Test Method for Tensile Properties of Polymer Matrix Composite Materials, ASTM, PA, USA, 2008. [40] ASTM D695-10, Standard Test Method for Compressive Properties of Rigid Plastics, ASTM, PA, USA, 2010. [41] L. Wang, R.K.L. Su, Repair of fire-exposed preloaded RC rectangular columns by post-compressed steel plates, J. Struct. Eng.: ASCE 140 (2014) 329–340. [42] M. Seitzberger, F.G. Rammerstorfer, R. Gradinger, H.P. Degischer, M. Blaimschein, C. Walch, Experimental studies on the quasi-static axial crushing of steel columns filled with aluminum foam, Int. J. Solids Struct. 37 (30) (2000) 4125–4147. [43] R. Kumutha, R. Vaidyanathan, M.S. Palanichamy, Behaviour of reinforced concrete rectangular columns strengthened using GFRP, Cem. Concr. Compos. 29 (8) (2007) 609–615. [44] J.G. Teng, L. Lam, Behaviour and modelling of fiber reinforced polymer-confined concrete, J. Struct. Eng.: ASCE 130 (11) (2004) 1713–1723. [45] S.P. Timoshenko, J.M. Gere, Theory of Elastic Stability, 2nd ed., McGraw-Hill, New York, 1961.