Flexural performance of sandwich beams with lattice ribs and a functionally multilayered foam core

Composite Structures 152 (2016) 704–711

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Flexural performance of sandwich beams with lattice ribs and a functionally multilayered foam core Weiqing Liu a,⇑, Fubin Zhang b,⇑, Lu Wang a, Yujun Qi a, Ding Zhou a, Bo Su b a b

College of Civil Engineering, Nanjing Tech University, Nanjing, China Faculty of Civil Engineering and Mechanics, Jiangsu University, Zhenjiang, China

a r t i c l e

i n f o

Article history: Received 29 September 2015 Revised 27 April 2016 Accepted 16 May 2016 Available online 17 May 2016 Keywords: Lattice ribs Functionally multilayered Flexural Sandwich beam Energy dissipation VARTM

a b s t r a c t This study focused on the flexural behavior of an innovative sandwich beams with GFRP skins, lattice ribs, and a functionally multilayered PU foam core (GLF beams). The lattice ribs, consisted of longitudinal and horizontal ribs, were arranged along the longitudinal direction of the beam. Eight beams, involving a control specimen, were tested under four-point bending to validate the effectiveness of the lattice ribs and functionally multilayered foam core for increasing the ultimate bending strength, stiffness and energy dissipation ability. Test results showed that compared to control specimen, a maximum of 143% increase in the ultimate bending strength can be achieved. The energy dissipation ability of the beam was increased greatly by the use of lattice ribs and functionally multilayered foam core. Meanwhile, unlike the conventional sandwich beam, GLF beams failed in a ductile manner. Furthermore, an analytical model was proposed to predict the bending stiffness and ultimate bending strength of GLF beams. The analytical results were agreed well with test results. Ó 2016 Elsevier Ltd. All rights reserved.

1. Introduction Fiber reinforced polymer (FRP) composite sandwich beams have been extensively used in aerospace, ships, and automobile applications [1–9]. However, very limited attempts have been made to use these materials for structural beam element applications. The main reason could be that the currently used core materials are foam or light-weight woods, once the sandwich beams subject to out-of-plane bending loads, the deflection of sandwich beams are large due to their low Young’s modulus. To overcome these obstacles, a lot of studies have been conducted by many researchers. Sharaf et al. [10] studied the flexural behavior of sandwich beams with different polyurethane (PU) foam core densities. Test results suggested that the ultimate bending strength and stiffness of beams were improved significantly with the increase in foam density, but the beam costs and dead loads were also increased. Reis and Rizkalla [11] and Dawood et al. [12] developed a kind of sandwich beams consisted of glass fiber reinforced plastics (GFRP) skins, PU foam core and throughthickness fiber insertions. The interface delamination was prevented due to the use of the fiber insertions. However, the initial

⇑ Corresponding authors. E-mail addresses: [email protected] (W. Liu), [email protected] (F. Zhang). http://dx.doi.org/10.1016/j.compstruct.2016.05.050 0263-8223/Ó 2016 Elsevier Ltd. All rights reserved.

bending stiffness was hardly improved. Marasco et al. [13] proposed a novel sandwich panel strengthened with Z-fiber pins. The out-of-plane tension, shear and compression properties were studied. Tests results indicated that the beams with Z-pinned cores exhibited higher specific stiffness than conventional sandwich beams. Dweib et al. [14] proposed a sandwich beam consisted of GFRP skins, PU foam core and longitudinal GFRP ribs. Keller et al. [15] and Fam and Sharaf [16] investigated the flexural behavior of the novel kind of sandwich beams. Additionally, Wang et al. [17] studied the effects of longitudinal ribs thickness, space and height on the flexural behavior of the sandwich beams. These studies demonstrated that the longitudinal ribs can significantly increase the ultimate bending strength and stiffness of beams. However, all beams failed in a brittle manner, and in the meantime, energy dissipation abilities of them were low. In order to improve the ultimate bending strength, stiffness and energy dissipation ability of the sandwich beams, a kind of sandwich beams consisted of GFRP skins, lattice ribs and functionally multilayered PU foam core (GLF beams) was developed in this study. The lattice ribs, composed of longitudinal and horizontal ribs, were arranged along the longitudinal direction to improve the bending and shear stiffnesses and the ultimate bending strength. The functionally multilayered PU foam core with gradient densities (150, 250, 350 kg/m3) was adopted to improve the ultimate bending strength and stiffness. The high density foam core

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W. Liu et al. / Composite Structures 152 (2016) 704–711

(350 kg/m3) was placed at the compressive region and the lower density foam core (150 kg/m3) was placed at the tensile region (see Fig. 1). The flexural behavior of GLF beams was studied. Eight beams with the same dimensions (1400
120
80 mm) were tested under four-point bending to investigate the ultimate bending strength, stiffness, failure mode, and energy dissipation ability. Meanwhile, an analytical model was proposed to predict the initial bending stiffness and ultimate bending strength under four-point bending. The accuracy of the model was verified through a comparison of the analytical and experimental results.

Table 2 Material properties of GFRP laminate and lattice ribs. GFRP laminate

Yield strength (MPa)

Young’s modulus (GPa)

Compression Tension Shear

168.21 291.60 52.13

21.09 22.68 8.80

Table 3 Material properties of PU foam core. 150 (kg/m3)

250 (kg/m3)

350 (kg/m3)

Yield strength Young’s modulus

1.22 35.42

2.83 80.59

4.87 117.96

Yield strength Young’s modulus

0.54 16.22

0.79 24.32

1.03 32.68

PU foam core

2. Experimental program

Compression

2.1. Material properties

Shear

The GFRP skins and lattice ribs consisted of [0/90] symmetric Eglass woven fiber (800 g/m2) and HS-2101-G100 unsaturated polyester resin. The densities of the PU foam core are 150, 250, and 350 kg/m3, respectively. The specimens were manufactured by means of vacuum assisted resin transfer molding (VARTM) process. The mechanical properties of the GFRP skins were performed using tensile, compressive, and shear tests following the ASTM D3039 [18], ASTM D3410 [19], and ASTM D3518 [20] standards, respectively. The PU foam was performed using compressive and shear tests following the ASTM C365 [21] and ASTM C273 [22] standards, respectively. The details of test procedure were shown in our companion paper [9]. Tables 2 and 3 summarized the material properties of the GFRP laminate and PU foam core, respectively.

2.2. Description of test beams and parameters Eight beams with the identical dimensions (1400
120
80 mm) were fabricated and manufactured by the VARTM process in the Advanced Composite Structures Research Center at Nanjing Tech University (Fig. 1). The GFRP laminates and HS-2101-G100 unsaturated polyester resin were used for the skins and lattice ribs. The functionally multilayered foam core with 150, 250, and 350 kg/m3 densities were gradient distributed along the height of a beam. The skins thickness (ts = 4.8 mm) and lattice ribs thickness (tr = 1.2 mm) of all specimens were identical. Table 1 shows a summary of the test matrix and details of specimens. Specimen GLF-CON was a control beam with GFRP skins

Fig. 1. The GLF beam with lattice ribs and different foam core densities.

Table 1 Summary of test matrix and parameters. Specimena

a

Illustration

L (mm)

B (mm)

Core thickness (mm)

Core density (kg/m3)

Weight (kg)

Space of lattice ribs (mm) Horizontal (sh)

Longitudinal (sl)

GLF-CON

1400

120

70

150

4.58

–

–

GLF-L1

1400

120

70

150

4.83

–

120

GLF-L2

1400

120

70

150

5.10

–

60

GLF-H2

1400

120

23/46

150

5.13

23

–

GLF-H2F3

1400

120

23/23/23

350/250/150

6.10

23

–

GLF-L1H2

1400

120

23/23/23

150

5.45

23

120

GLF-L2H2

1400

120

23/23/23

150

5.73

23

60

GLF-L2H2F3

1400

120

23/23/23

350/250/150

6.85

23

60

GLF-La-Hb-Fc: a means the number of the longitudinal ribs, b means the number of the horizontal ribs, and c means the number of the foam core densities.

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Fig. 2. Fabrication process of the GLF beams. (a) assemble the PU foam and GFRP ribs, (b) VARTM process, and (c) test beams.

Fig. 3. Flexural test setup for GLF beams (units: mm): (a) schematic illustrations and (b) actual test setup.

and PU foam core. Specimen GLF-L1 and Specimen GLF-L2 fabricated with longitudinal ribs. The spacing of ribs were is 120 and 60 mm, respectively. Specimen GLF-H2 fabricated with horizontal ribs. Specimen GLF-H2F3 fabricated with both horizontal ribs and the functionally multilayered foam core. Specimen GLF-L1H2 and Specimen GLF-L2H2 fabricated with lattice ribs. Specimen GLFL2H2F3 fabricated with lattice ribs and functionally multilayered foam core. Fig. 2 shows the fabrication process of Specimen GLF-L2H2F3. First, the PU foam core are cut into the designed dimensions and slotted with a distance of 25 mm, a width of 2 mm, and a depth of 2 mm, to ease resin flow (Fig. 2(a)). Second, the PU foam cores are wrapped with one layer of [0/90] woven fabric, then the wrapped core was assembled with the GFRP skins (Fig. 2(b)). Third, before infusing resin, the stripping and diversion cloth are installed, respectively. Finally, the unsaturated polyester resin is injected into the vacuum bag due to the effect of atmospheric pressure. The tested beams are shown in Fig. 2(c). 2.3. Test set-up and instrumentation Four-point bending configuration tests were carried out according to ASTM C393 [23]. Fig. 3 presents the test set-up. The clear span (L) between the two roller supports was 1200 mm. A 300 mm-length pure bending zone was formed in the middle of a beam. Two 20 mm-thick rubber pads were placed between the two steel plates and the beam. Beams were loaded to failure using a 980 kN MTS hydraulic universal testing machine (with a precision of 0.22 N) at a displacement rate of 2 mm/min. To measure the deflection of the beam, three linear variable displacement transducers (LVDTs) with a stroke of 100 mm were

installed at middle span and support locations. Fig. 3(a) shows the arrangement of LVDTs and the electric resistance strain gauges pasted on the top and bottom skins. 3. Test results and discussion 3.1. Test results 3.1.1. Failure mode The macroscopic failure modes of beams can be categorized as three primary types (Fig. 4): (1) core shear failure and core-skin delamination failure, which occurred in specimens GLF-CON, GLF-H2 and GLF-H2F3; (2) core shear failure with through shear crack, which occurred in specimens GLF-L1 and GLF-L2; (3) core shear failure and skin delamination failure, which occurred in specimens GLF-L1H2, GLF-L2H2 and GLF-L2H2F3. The microscopic phenomena that result in the corresponding macroscopic failure modes can be described as: (2) the maximum shear strain of the foam core exceeds its crushing strain, core shear failure occurred. Then, all the forces transfer to the skin. The shear stress in the interface was larger than the adhesive strength, hence the core-skin delamination failure between skins and foam core occurred; (2) the maximum shear strain of the foam core exceeds its crushing strain, core shear failure occurred; (3) the shear stress in the skin interface was larger than its adhesive strength, then the delamination phenomenon between skins can be observed. Unlike the control Specimen GLF-CON, the core-skin delamination failure did not occur in the GLF beams (Specimen GLF-L1 and Specimen GLF-L2) due to the presence of the longitudinal ribs, which can improve the adhesive strength between the skins and foam core. Meanwhile, the through shear crack did not occur in

W. Liu et al. / Composite Structures 152 (2016) 704–711

707

Fig. 4. Failure modes of GLF beams.

the GLF beams (Specimen GLF-L1H2, Specimen GLF-L2H2 and Specimen GLF-L2H2F3) due to the presence of the lattice ribs and functionally multilayered foam core, which can improve the shear stiffness and strength of the beams. Comparison of Specimen GLFCON and Specimen GLF-L2H2F3 reveals that the failure mode changes from a brittle to a ductile failure manner, which indicated that the lattice ribs and functionally multilayered foam core can enhance the ductility of sandwich beams. 3.1.2. Load–deflection behavior Fig. 5 presents the mid-span load–deflection curves of the GLF beams. Specimen GLF-CON exhibited almost linearly up to final load of 10.8 kN (Fig. 5(a)). A similar load–deflection behavior was observed in Specimen GLF-H2 (Fig. 5(b)), which failed until the

loading reached 10.6 kN. For Specimen GLF-H2F3, core-skin delamination failure occurred when the applied load was equal to 16.7 kN. The load dropped by 66% after failure, then the load increased almost linearly with the deflection increase, the specimen continued to carry load until 15 kN (Fig. 5(b)). The load–deflection behavior of Specimen GLF-L1 increased almost linearly, but the bending stiffness was decreased when the applied load was 10 kN, as shown in Fig. 5(a). The beam failed when the applied load was 18.3 kN. A similar load–deflection behavior was observed in Specimens GLF-L2, GLF-L1H2, and GLFL2H2, which failed when the applied loads reached 24.1 kN, 18.9 kN and 25.3 kN, respectively (Fig. 5(b)). For Specimen GLF-L2H2F3, the load-defection curve was almost linearly up to failure. The ultimate bending strength was 26.2 kN,

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Fig. 5. Load–deflection behavior of GLF beams with different configurations. (a) longitudinal ribs, (b) lattice ribs and functionally multilayered foam core.

while the load dropped by 27% after failure (Fig. 5(b)). The curve behaved non-linearly with a reduced stiffness up to failure. It can be found that an increase in deflection occurred before the final failure, even without an increase in applied load due to progressive failure of the lattice ribs and functionally multilayered foam core. 3.1.3. Load–strain behavior Fig. 6 presents the mid-span load–strain curves of the GLF beams. It can be found that the measured maximum tensile and compressive strains were 0.71% and 0.76%, respectively, which were lower than the values obtained in material tests. This showed that the GFRP skin was underutilized in this system. The average tensile strain of the bottom skin of Specimen GLFH2F3 and Specimen GLF-L2H2F3 were 34% and 39% higher than the average compressive strain of the top skin, respectively (see Table 4), which demonstrated that the tensile property of the GFRP material can be fully utilized when beams with functionally multilayered foam core. 3.2. Discussion 3.2.1. Strength analysis Table 5 summarizes the ultimate bending strength and the strength-to-weight ratio of the GLF beams. The load bearing capacity of Specimen GLF-H2 was almost equal to those of Specimen GLF-CON, which illustrated that the horizontal ribs cannot affect the ultimate bending strength. Compared to the control specimen, the load bearing capacities of Specimen GLF-L1 and Specimen GLF-L2 were increased by 69% and 123%, respectively; while the load bearing capacities of Specimen GLF-L1H2 and Specimen GLF-L2 H2 were increased by 75% and 134%, respectively. The test results indicated that the lattice ribs can greatly increase the ultimate bending strength.

The load bearing capacity of Specimen GLF-H2F3 was 58% higher than that of Specimen GLF-CON, and the load bearing capacity of Specimen GLF-L2H2F3 was 58% higher than that of Specimen GLF-L2H2. The test results demonstrated that the functionally multilayered foam core can significantly improve the ultimate bending strength. The load bearing capacity of Specimen GLF-L2H2F3 was 147% higher than these of Specimen GLF-CON, and also higher than the other beams. The test results proved that the beam with lattice ribs and functionally multilayered foam core exhibited the highest ultimate bending strength. Meanwhile, the beam with lattice ribs can achieved the highest strength-to-weight ratio. 3.2.2. Stiffness analysis Manalo et al. [7] stated that the effective bending stiffness EIex can be obtained based on the deflection formulae of a composite beam under four-point bending, which was determined by experimental results. Using the initial linear elastic portion of the load– deflection curve (Fig. 5), the effective bending stiffness EIeff can be calculated using the following equation:

EIex ¼


 468 3 DP L 24; 576 Dd

ð1Þ

where (DP/Dd) is the slope of the initial linear-elastic portion of the experimental load–deflection curves, and L is the span of the beam. Table 4 shows the effective bending stiffness EIex and stiffnessto-weight ratio. The effective bending stiffness EIex of Specimen GLF-H2 was almost equal to that of Specimen GLF-CON. It can be found that the horizontal ribs cannot affect the effective bending stiffness EIex. The effective bending stiffness EIex of Specimen GLF-H2F3 was 38% larger than that of Specimen GLF-CON, which indicated that the functionally multilayered foam core can increase the beam bending stiffness.

Fig. 6. Load–strain curves of GLF beams. (a) longitudinal ribs, (b) lattice ribs and different foam core densities.

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W. Liu et al. / Composite Structures 152 (2016) 704–711 Table 4 Summary of the bending stiffness and maximum strain.

a

Specimen

Weight (kg)

DP/Dd (N/mm)

EIex (
1010) (N. mm2)

EIpre(
1010) (N. mm2)

EIpre/EIex

EIex/W

GLF-CON GLF-L1 GLF-L2 GLF-H2 GLF-H2F3 GLF-L1H2 GLF-L2H2 GLF-L2H2F3

4.58 4.83 5.10 5.13 6.10 5.45 5.73 6.85

607 806 1008 611 840 897 970 1019

2.00 2.65 3.32 2.01 2.76 2.95 3.19 3.35

2.85 3.29 3.52 2.79 3.27 3.42 3.56 3.62

1.43 1.24 1.06 1.39 1.18 1.16 1.12 1.08

0.44 0.55 0.65 0.39 0.45 0.54 0.56 0.49

a

(
1010)

Maximum strain (mm/mm) Tensile (%)

Compressive (%)

0.21 0.32 0.35 0.22 0.39 0.37 0.44 0.57

0.19 0.31 0.33 0.21 0.29 0.36 0.42 0.41

EIex/W: Strength-to-weight ratio.

Table 5 Summary of the ultimate bending strength and energy ductility coefficient.

a b

Specimen

Weight (kg)

Pu (kN)

Pu/W

GLF-CON GLF-L1 GLF-L2 GLF-H2 GLF-H2F3 GLF-L1H2 GLF-L2H2 GLF-L2H2F3

4.58 4.83 5.10 5.13 6.10 5.45 5.73 6.85

10.8 15.6 19.4 10.6 16.7 18.9 25.3 26.2

2.36 3.23 3.80 2.07 2.74 3.47 4.42 3.82

a

Ppre (kN)

Ppre /Pu

Failure mode

10.58 17.2 22.3 10.27 14.85 16.70 22.52 24.78

0.98 1.10 1.15 0.97 0.89 0.88 0.89 0.95

CS CS CS CS CS CS CS CS

& CSD

& & & & &

CSD CSD SD SD SD

b

Eu

Efinal

l

151.74 290.75 508.90 149.43 214.47 456.81 681.27 633.49

151.74 529.40 1244.85 149.43 651.97 894.12 1607.85 2649.14

1.00 1.55 1.50 1.00 1.00 1.82 2.24 3.61

Pu/W: Strength-to-weight ratio. CS: core shear failure; CSD: core-skin delamination failure; SD: skin delamination failure.

The effective bending stiffness EIex of Specimen GLF-L1 and Specimen GLF-L2 were 25% and 66% higher than that of Specimen GLF-CON, respectively; while the effective bending stiffness EIex of Specimen GLF-L1H2 and Specimen GLF-L2H2 were 48% and 60% higher than that of Specimen GLF-CON, respectively. The test results illustrated the lattice ribs can increase the bending stiffness of beams. The effective bending stiffness EIex of Specimen GLFL2H2F3 was 81% higher than that of Specimen GLF-CON. The test results indicated that the beam with both lattice ribs and functionally multilayered foam core shows the highest bending stiffness. Table 4 also suggests that beams only with longitudinal ribs had the highest strength-to-weight ratio.

4. Analytical results The traditional sandwich beam analysis methods, based on the homogeneous continuous core materials, were not suitable for the GLF beams. A simplified analytical model using the equivalent method was proposed to predict the bending stiffness and equivalent shear stiffness in this paper, which the semi-continuous core effects were considered. The following section presents the results of the equivalent Young’s modulus of foam core with lattice ribs, initial bending stiffness analysis, and ultimate bending strength of specimens. 4.1. Equivalent Young’s modulus of core materials

3.2.3. Energy dissipation According to Sun et al. [24], the energy ductility coefficient (l) was proposed to evaluate the post yield deformation of the beams, which can be expressed as:

l¼

df du

ð2Þ

where du means the displacement corresponding to the specimen reached its ultimate bending strength; and df means the displacement corresponding to the load dropped to 50% of the ultimate bending strength. As presented in Table 5, the value of l of Specimen GLF-H2 and Specimen GLF-H2F3 were equal to that of Specimen GLF-CON. Compared to Specimen GLF-CON, the value of l of Specimen GLF-L1 and Specimen GLF-L2 were increased by 55% and 50%, respectively; and the value of l of Specimen GLF-L1H2, Specimen GLF-L2H2 and Specimen GLF-L2H2F3 were increased by 82%, 124%, and 261%, respectively. These findings showed that the horizontal ribs cannot affect the energy dissipation ability of beams, while the lattice ribs can increase the energy dissipation ability substantially. Above all, the beams with lattice ribs and functionally multilayered foam core shows the best energy dissipation ability.

Consider a foam core element with longitudinal ribs cut out of a GLF beam, as shown in Fig. 7, the length and width are l and d, respectively. When the element subjected to the force Px in the x-direction, by considering force equilibrium (Fig. 7(b)), the Px can be expressed as:

Px ¼ rx;r Ar þ rx;f Af

ð3Þ

where rx,r and rx,f are the stresses of ribs and foam core in the x-direction, respectively; Ar and Af are the total cross-sectional areas of longitudinal ribs and foam core, respectively. Each of the terms in Eq. (3) is divided by exAx gives:

Ex ¼

rx;r Ar rx;f Af þ ex Ax ex Ax

ð4Þ

where ex is the strain of equivalent foam core in the x-direction, and Ax is the cross-sectional area of the element in the x-direction. The ribs and foam core are assumed to have perfect bonding through the resin. Then, the strain of them are the same in the x-direction. Hence, the equivalent Young’s modulus of the foam core in the x-direction (Ex) can be expressed as:

Ex ¼ Er V r þ Ef V f

ð5Þ

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Fig. 7. Analytical model: (a) element of the GLF foam core, and (b) force equilibrium of section 1–1.

where Er and Ef are the Young’s modulus of GFRP ribs and the foam core, respectively; Vr and Vf are the volume ratio of ribs and foam, respectively. The main function of horizontal GFRP ribs is to improve the bending strength and provide the elastic supports to the longitudinal ribs to avoid the occurrence of local wrinkling failure. Hence, we assume that the equivalent shear modulus of the core is not affected by the horizontal GFRP ribs in the z-direction. Based on the static relationship:

sxz ¼ sr V r þ

X

ð6Þ

sf V f

where sxz, sr and sf are the shear stresses of equilibrium core, ribs and foam, respectively, which can be obtained by the geometrical relationship:

cxz ¼ cr ¼ cr

ð7Þ

where cxz, cr and cf are the shear strain of equilibrium core, ribs and foam, respectively. Using Hooke’s law, the corresponding stresses are:

sxz ¼ cxz Gxz

ð8Þ

sr ¼ cr Gr

ð9Þ

sf ¼ cf Gf

ð10Þ

where Gr and Gf are the shear modulus ribs and foam, respectively, Gxz is the equivalent shear stiffness. Substituting Eqs. (8)–(10) into Eq. (7) gives:

Gxz ¼ Gr V r þ

X

ð11Þ

Gf V f

4.2. Analysis of stiffness and deflection By applying the parallel axis theorem and considering the contribution of the horizontal ribs, the equivalent flexural rigidity (EIpre) can be expressed as:

EIpre ¼

j n k X X X Es;i Is;i þ Er;i Ir;i þ Ex;i Ix;i i¼1

i¼1

ð12Þ

i¼1

where Es, Er and Ex are the Young’s modulus of skins, horizontal ribs and equivalent foam core, respectively; n, j, and k are the number of the skins, horizontal ribs, and the equivalent foam core. Taking into consideration of the core mechanical properties variations, the equivalent shear rigidity GApre can be expressed as:

GApre

k X ¼ Ai Gxz;i

ð13Þ

i¼1

where Gxz and A are the equivalent shear stiffness and area of the equivalent foam core, and k is the number of the equivalent foam core.

The predicted bending stiffness EIpre and the effective bending stiffness EIex are summarized in Table 4. Comparing the analytical and experimental results reveals that the predicted initial bending stiffness (EIpre) of GLF beams were larger than the experimental results. The maximum deviation was 43%, which occurred in Specimen GLF-CON. The reason is that soft PU foam core materials with lower shear modulus, which resulted in large shear deformation. While bending stiffness of beams with lattice ribs and functionally multilayered foam core reduced to 8–19%. These findings indicated that the lattice ribs and functionally multilayered foam core can significantly decrease the shear deformation. 4.3. Analysis of ultimate bending strength For the core shear failure, the failure load can be calculated by:

Ppre ¼ 2sc hc b

ð14Þ

where sc and hc are the shear strength and height of the foam core, respectively; and b is the width of the beam. For specimens with lattice ribs, the effect of longitudinal ribs in the shear force calculation was considered in the analytical model. The failure load can be calculated by:

Ppre ¼ 2



sc hc b þ

X

t r hr



ð15Þ

where tr and hr are the thickness and height of longitudinal ribs, respectively. For specimens with functionally multilayered foam core, the failure load can be calculated by:

Ppre ¼

X

2Gci cc;min hci b

ð16Þ

where Gci and hci are the shear modulus and height of the ith layer foam core, and cci is the shear strain of the foam core with the minimum density. The predicted ultimate bending strength of GLF beams were presented in Table 5. In general, the proposed analytical model is able to conservatively estimate the actual bending strength of the GLF beams with an average underestimation of 7%. The predicted value of beams with longitudinal ribs is consistent with the observed experimental behavior. On the other hand, the beams with lattice ribs are underestimated by approximately 5–12% because the proposed analytical model did not consider the effect of the horizontal ribs. The largest variation between analytical and experimental results in the ultimate bending strength was 2.2 kN, which occurred in Specimen GLF-L1H2. 5. Conclusions The flexural behavior of the sandwich beams with GFRP skins, lattice ribs and functionally multilayered foam core were investigated using a four-point bending configuration test. Based on experimental and analytical results, we can draw the following conclusions:

W. Liu et al. / Composite Structures 152 (2016) 704–711

(1) Beams composed of GFRP skins and PU foam core failed in a brittle failure mode, while beams with lattice ribs and functionally multilayered foam core failed in a ductile failure mode. (2) Compared to control specimen, beams with lattice ribs and functionally multilayered foam core exhibited a substantially increase in the bending stiffness and strength. (3) The deformation ability can be increased substantially due to the use of lattice ribs. Beams with lattice ribs and functionally multilayered foam core exhibited the best energy dissipation ability. (4) An analytical model was proposed to predict the bending stiffness and ultimate bending strength. Moreover, the analytical results agreed well with experimental results. (5) The lattice ribs and functionally multilayered foam core can sharply reduce the shear deformation of GLF beams. (6) The GLF beams had the characteristics of high bending strength and stiffness, and high energy dissipation ability. However, this new type of GLF beams is still under development, the effects of the shear span-to-depth ratios on flexural behavior of GLF beams should be studied in more detail. The corresponding design criterion will be established and the minimum weight design procedure will also be proposed in future study.

Acknowledgement The research described here was supported by the Key Program of National Natural Science Foundation of China (Grant No. 51238003); the National Natural Science Foundation of China (Grant No. 51308287). the National Natural Science Foundation for the Youth of China (Grant No. 51408305); Natural Science Foundation of Jiangsu Province (Grant No. BK20140946); the Scientific Research Start-up Fund for Senior Specialized Talents of Jiangsu University (Grant No. 16JDG016), and the Post-doctoral Fund of Jiangsu Province (Grant No. 1301048C). References [1] Hollaway LC. A review of the present and future utilisation of FRP composites in the civil infrastructure with reference to their important in-service properties. Constr Build Mater 2010;24:2419–55. [2] Jin MM, Hu YC, Wang B. Compressive and bending behaviors of wood-based two-dimensional lattice truss core sandwich structures. Compos Struct 2015;124:337–44.

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