Composites: Part B 60 (2014) 329–340

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Composites: Part B

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Theoretical and experimental study of foam-filled lattice compositepanels under quasi-static compression loading

1359-8368/$ - see front matter � 2014 Elsevier Ltd. All rights reserved.http://dx.doi.org/10.1016/j.compositesb.2013.12.078

⇑ Corresponding authors. Tel.: +86 25 58139862; fax: +86 25 58139863 (W. Liu).Tel.: +86 25 58139871; fax: +86 25 58139877 (L. Wang).

E-mail addresses: wqliu@njut.edu.cn (W. Liu), kevinlwang@hotmail.com (L.Wang).

Zhimin Wu a, Weiqing Liu a,⇑, Lu Wang b,⇑, Hai Fang a, David Hui ca College of Civil Engineering, Nanjing University of Technology, Nanjing, Chinab Advanced Engineering Composites Research Center, Nanjing University of Technology, Nanjing, Chinac Dept. of Mechanical Engineering, University of New Orleans, New Orleans, LA 70124, USA

a r t i c l e i n f o a b s t r a c t

Article history:Received 7 September 2013Received in revised form 11 November 2013Accepted 30 December 2013Available online 7 January 2014

Keywords:A. Glass fibersA. FoamsB. StrengthD. Mechanical testing

In this paper, a simple and innovative foam-filled lattice composite panel is proposed to upgrade the peakload and energy absorption capacity. Unlike other foam core sandwich panels, this kind of panels is man-ufactured through vacuum assisted resin infusion process rather than adhesive bonding. An experimentalstudy was conducted to validate the effectiveness of this panel for increasing the peak strength. Theeffects of lattice web thickness, lattice web spacing and foam density on initial stiffness, deformabilityand energy absorbing capacity were also investigated. Test results show that compared to the foam-corecomposite panels, a maximum of an approximately 1600% increase in the peak strength can be achieveddue to the use of lattice webs. Meanwhile, the energy absorption can be enhanced by increasing latticeweb thickness and foam density. Furthermore, by using lattice webs, the specimens had higher initialstiffness. A theoretical model was also developed to predict the ultimate peak strength of panels.

� 2014 Elsevier Ltd. All rights reserved.

1. Introduction

Sandwich panels have been widely used for constructing bridgedecks, temporary landing mats and thermal insulation wall boardsdue to better performance in comparison to other structuralmaterials in terms of enhanced stability, higher strength to weightratios, better energy absorbing capacity and ease of manufactureand repair. In sandwich panels, low density material, knownas core, is usually adopted in combination with high stiffness facesheets to resist high loads [1]. The most common types ofcore materials include polyvinyl chloride (PVC) foam, polyurethane(PU) foam, balsa wood, honeycombs, polyester foam coremat etc.The main functions of core materials are to absorb energy and pro-vide resistance to face sheets to avoid local buckling.

Extensive experimental studies of composite sandwich panelswith balsa wood core have been conducted in the past two decades[2–5]. Osei-Antwi et al. [6] investigated the shear mechanical char-acterization of composite sandwich panels with balsa wood core.Six specimens, cut from the panels in accordance with the threeprincipal shear planes, were tested. The test results indicated thatshear stiffness and strength increased with increasing density ofthe balsa wood, but they did not change with the use of different

adhesive joints in the balsa panels between the lumber blocks.Bekisli and Grenestedt [7] developed a new manufacturing methodfor the balsa sandwich cores by vacuum assisted resin infusion, andconducted the experimental study on these cores under shearforce. The test results revealed that the new manufacturing meth-od can increase stiffness and strength of the balsa sandwich cores.However, the compressive and shear stiffness and strength of balsawood have very large variations due to the natural and anisotropiccharacteristics of the material. Hence, a lot of material tests haveto be carried out to obtain reliable values for practical design.Furthermore, appropriate fire and corrosion protections shouldbe provided due to the use of wood.

Up to now, many investigations of geometric configurationshave been conducted to find more effective lightweight energyabsorbing structures [8–21]. Cartié and Fleck [22] studied the com-pressive strength of foam-cored sandwich panels with pin-rein-forcements. The test results showed the compressive strengthand energy absorption capacity of the sandwich panels were in-creased. In the buckling analysis of pin-reinforcements, the foamcore was considered as an elastic Winkler foundation in supportingthe pins. The compressive strength was governed by elastic buck-ling of the pins. Furthermore, the relationship between the com-pressive strength and loading rate was studied. Fan et al. [23]tested a series of multi-layered glass fiber reinforced compositewoven textile sandwich panels under quasi-static compressionloading. Their test results revealed that energy absorption of themulti-layered panel was greatly improved and far exceeded that

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330 Z. Wu et al. / Composites: Part B 60 (2014) 329–340

of the monolayer panel of the same thickness, and the failure modewas progressively monolayer collapses. The authors also con-ducted the bending tests of multi-layered glass fiber reinforcedcomposite woven textile sandwich panels [24]. The failure modewas associated with the crippling and shear failure within the facesheets, and the load capacity was dictated by the fracture strengthof the face sheets. Meanwhile, the authors pointed that the plastichinge mechanism made the panels to possess a long deflectionplateau after the peak strength. As an effectively kind of energyabsorbing structures, the egg-box shape has also extensively beeninvestigated [25–27]. Yoo et al. [28] carried out the compressivetests on foam-filled composite egg-box panels to evaluate the en-ergy absorbing capacity. The crack initiation and propagation ofcomposite egg-box cores without foam were observed and ana-lyzed. Furthermore, the possible use of foam-filled compositeegg-box panels as a thermal insulation wall board for membranetype liquefied natural gas ships was also evaluated. Although alot of geometric configurations for energy absorbing structureshave been developed in recent years, the majority of them havebeen applied to various protective packaging and crashworthinessstructures for automobiles, ships and aero planes rather than civilengineering structures, because the compressive, shear and bend-ing stiffness of these composite panels are low, the manufacturingprocess of these geometric configurations is complicated, and thecost of production may stay at a relative high level. Choy et al.[29] developed two types of sandwich panels, namely the fiber in-serted foam panels and the aluminum foil covered panels. Theirtest results proved that the bending stiffness of these panels wasincreased. However, these panels were used to reduce the noiseand isolate the vibration in the air conditioning. Hence, the com-posite panels with these geometric configurations are hardly ex-tended to civil engineering field.

Chen and Davalos have investigated the strength and stiffnessproperties of composite sandwich deck panels with sinusoidal coregeometry in the past few years. The compressive and shear tests ofFRP sandwich deck panels with sinusoidal core geometry havebeen conducted [30]. Chopped strand mat, composed of E-glass fi-bers and polyester resin, was used for the core material. The testresults showed that the typical shear failure mode was delamina-tion at the core-face sheet bonding interface, and the maximumstrength of these panels was determined by the number of bondinglayers and core thickness. An analytical model for the bucklingcapacity of FRP panels with two loaded edges partially constrainedwas proposed by Davalos and Chen [31]. By considering the skin ef-fect, Chen and Davalos [32] obtained an accurate solution of thetransverse shear modulus and the interfacial stress distributionfor sandwich structures with sinusoidal core. However, in theirstudies, the critical buckling stress of sinusoidal core is usuallylow, which is obviously caused by the absence of restriction from

Face sh

Foam

Lattice we(a)

Fig. 1. The foam-filled lattice composite panels (a) photo

foam core. Hence the compressive strength of panels cannot be im-proved. Meanwhile, the energy absorbing capacity of panels wasnot evaluated.

To address the aforementioned shortcoming, a simple and inno-vative foam-filled lattice composite panel, manufactured throughvacuum assisted resin infusion process [33], is developed in thisstudy, as shown in Fig. 1. The face sheets, lattice webs and foamcores are combined by vacuum infusing resin, which can enhancethe peel resistance between face sheets and foam cores. Unlikeother foam-core sandwich composite panels, the compressivestrength of foam is improved due to the confinement effects pro-vided by lattice webs, and the foam cores can also restrict the localbuckling of the lattice webs. Hence, the compressive strength offoam-filled lattice composite panels can be improved significantly.An experimental study was conducted to validate the effectivenessof this new type of panel. The peak strength, initial stiffness, defor-mability and energy absorbing capacity were investigated. A theo-retical model was also developed to predict the ultimate peakstrength of panels.

2. Manufacture process

The manufacture process can be divided into the following sixsteps: (i) four GFRP mats are placed on a large flat board as shownin Fig. 2(a), and the fiber orientation angle is 0/90� to the panel hor-izontal axis; (ii) the foams are cut into cubes according to the de-sign dimensions, and then wrapped using GFRP with ±45� fiberorientation angle see Fig. 2(b); (iii) to place four GFRP mats onthe foam cores, and the fiber orientation angle is also 0/90� tothe panel horizontal axis; (iv) before vacuum infusing UPR, thestripping cloth, diversion cloth and a thicker cover plate which isused to make the face board flat are installed, respectively, asshown in Fig. 2(d); (v) the unsaturated polyester resin is infusedinto the vacuum bag due to the effect of atmospheric pressure(see Fig. 2(e)); (vi) After UPR curing, the manufacture of foam-filledlattice composite panels is completed, and then the panels are cutin accordance with special requirements, as shown in Fig. 2(f).

3. Theoretical model

3.1. Local buckling of the GFRP web

The local buckling of the GFRP web can be analyzed using elas-tic foundation model, as shown in Fig. 3(a). The foam is repre-sented by the spring with a stiffness of k (per unit width andlength). In accordance with classical theory of elastic stability[34], the governing differential equation for the stability analysisof web is expressed as

eet

b (b)

of Specimen H5T2S5D6 and (b) schematic diagram.

Stripping cloth

Diversion cloth

GFRP mat

(a) (b)

(c) (d)

(e) (f)Fig. 2. The vacuum infusion molding process (a) manufacturing step i, (b) manufacturing step ii, (c) manufacturing step iii, (d) manufacturing step iv, (e) manufacturing step vand (f) manufacturing step vi.

GFRP Web

b

a

(a) (b) (c)Fig. 3. Theoretical model (a) elastic foundation model; (b) local buckling calculation and (c) closed web-foam core element (Part I) and unclosed web-foam core element(Part II).

Z. Wu et al. / Composites: Part B 60 (2014) 329–340 331

332 Z. Wu et al. / Composites: Part B 60 (2014) 329–340

D@4w@x4þ 2 @

4w@x2@y2

þ @4w@y4

!¼ Nx

@2w@x2

!þ 2Nxy

@2w@x@y

þ Ny@2w@y2

ð1Þ

where D is the bending stiffness of the web, which can be deter-mined by

D ¼ Et3

12ð1� v2Þ ð2Þ

where E and v are Young’s modulus and Poisson ratio of web,respectively.

The energy associated with the web deforming (U1) and theenergy associated with the applied loading (U2) are respectivelygiven by

U1 ¼D2

Z Z@2w@x2þ @

2w@y2

!28<:

� 2ð1� vÞ @2w@x2

@2w@y2� @

2w@x@y

!224359=;dxdy ð3Þ

U2 ¼12

Z ZNx

@w@x

� �2þ 2Nxy

@w@x

@w@y

� �þ Ny

@w@y

� �2" #dxdy ð4Þ

The loaded edges of web are fixed supports, and unloaded edges aresimply supports. The web is only subjected to a uniform axial com-pression in the x-direction. A half buckling wave length in the x-direction is h, as shown in Fig. 3(b). By considering a half wave inthe x-direction, the boundary conditions of web at the loaded andunloaded edges are

when x ¼ 0 or x ¼ h;w ¼ 0 and dw=dx ¼ 0

when y ¼ 0 or y ¼ b;w ¼ 0 and d2w=dx2 ¼ 0

Assuming that the deflection functions in the x and y directions arethe cosine and sine functions, respectively, the deformed shape canbe expressed as

w ¼X1m¼1

X1n¼1

Amn 1� cos2mpx

h

� �sin

npyb

ð5Þ

The total potential energy of the GFRP web (E) is given as

E ¼ U1 þ U2 þ U3 ð6Þ

where U3 is the energy associated with elastic foundation, definedas

U3 ¼12

Z Zkw2dxdy ð7Þ

According to the principle of minimum potential energy,

@E@Amn

¼ 0 ð8Þ

The critical buckling stress (fcr) can be calculated by

fcr ¼Dp4ð16b4m4 þ 8h2b2m2n2 þ 6h4n4Þ þ 3kh4b4

4p2h2b4m2tð9Þ

3.2. Ultimate axial load capacity

The panel can be considered as consisting of closed web-foamcore (CWFC) element (Part I) and unclosed web-foam core (UWFC)element (Part II), as shown in Fig. 3(c). For the CWFC element, thedepth and width are a and b, respectively. The thickness of web ist/2. By considering force equilibrium, the theoretical peak strengthof the CWFC element (Pc,pre) can be expressed as

Pc;pre ¼ 0:85f 0F AF þ fW AW ð10Þ

where AW and AF are cross-sectional areas of the web and foam,respectively, fW is the axial compressive strength of web, and f 0F isthe axial compression strength of the confined foam, which canbe calculated by

f 0FfF¼ 1þ k1ks

flfF

ð11Þ

where fF is the compressive strength of the unconfined foam, k1 isthe effectiveness coefficient of confinement, which is equal to2.98 [35], fl is the lateral confining pressure, and ks is the shapefactor, which can be calculated by

ks ¼ba

AeAF

ð12Þ

AeAF¼ 1� ½ðb=aÞða� 2RFÞ

2 þ ða=bÞðb� 2RFÞ2�3AF

ð13Þ

where Ae is the effective confinement area, and RF is the cornerradius.

Teng et al. [35] proposed the following formula to calculate thelateral confining pressure fl of confined foam:

fl ¼fWtt

2ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffia2 þ b2

p ð14Þwhere fWt is the tension strength of web.

For the UWFC element, because the GFRP web cannot providethe effective lateral confining pressure to the foam, the effect ofcompressive strength of foam on the ultimate peak strength canbe ignored. Hence, the theoretical peak strength of the UWFC ele-ment (Pu,pre) can be expressed as

Pu;pre ¼ fW AW ð15Þ

If a local buckling failure occurs, the fW should be replaced by fcr inEq. (15).

Then, the theoretical ultimate peak strength of panels (Ppre) canbe expressed as

Ppre ¼X

Pc;pre þX

Pu;pre ð16Þ

4. Experimental program

4.1. Test specimens

The specimens were manufactured using a vacuum assisted re-sin infusion process at Nanjing University of Technology. The E-glass weave fabrics, referred to simply as GFRP, and HS-2101-G100 unsaturated polyester resin (UPR) were used for face sheetsand webs. The panels were filled urethane foams (UF) with varia-tion density (40 kg/m3, 60 kg/m3 and 80 kg/m3). During vacuuminfusion molding process, methyl ethyl ketone peroxide (MEKP)was used to be the initiator of the unsaturated polyester resin.

In this study, 20 specimens were manufactured and tested. Thespecimen was cut from the panels, and it was representative of asymmetric volume element of the structure when subjected tocompression loading, as shown in Fig. 1(a). All specimens had thesame width (w = 200 mm) and length (d = 200 mm). SpecimensH5D4, H5D6, H7D6 and H5D8 were control specimens withoutwebs to demonstrate the mechanical performance of the normalfoam core GFRP sandwich panels. The other specimens werestrengthened by webs with varying foam density (q), thicknessof the lattice web (t) and spacing of the lattice web (s). The detailsof specimens are given in Table 1.

Table 1Details of specimens.

Specimen H (mm) s (mm) h (mm) t (mm) q (kg/m3)

H5D4 54.8 – 50 – 40H5D6 54.8 – 50 – 60H7D6 74.8 – 70 – 60H5D8 54.8 – 50 – 80H5T2S5D4 54.8 50 50 2.4 40H5T2S5D6 54.8 50 50 2.4 60H5T2S5D8 54.8 50 50 2.4 80H5T2S7D6 54.8 75 50 2.4 60H5T4S7D6 54.8 75 50 4.8 80H5T7S7D6 54.8 75 50 7.2 80H1T2S1D4 104.8 100 100 2.4 40H1T2S1D6 104.8 100 100 2.4 60H1T2S1D8 104.8 100 100 2.4 80H7T2S5D6 74.8 50 70 2.4 60H7T2S7D6 74.8 75 70 2.4 60H7T2S1D6 74.8 100 70 2.4 60H7T7S5D6 74.8 50 70 7.2 60H7T4S7D6 74.8 75 70 4.8 60H7T7S7D6 74.8 75 70 7.2 60H7T7S1D6 74.8 100 70 7.2 60

Table 2Material properties of foams.

Foam densityD (kg/m3)

Yield strengthffy (MPa)

Young’smodulus Ef (MPa)

40 0.163 4.8360 0.358 9.3880 0.609 14.70

Table 3Material properties of lattice webs.

Compression Yield strength fcy (MPa) Young’s modulus Ec (GPa)

59.76 5.66Tension Yield strength fty (MPa) Young’s modulus Et (GPa)

296.31 6.41

Specimen

Load cell

Fig. 4. Test set-up.

Z. Wu et al. / Composites: Part B 60 (2014) 329–340 333

(1) Webs with either 50 mm, 75 mm or 100 mm height, desig-nated as H5, H7 and H1, respectively.

(2) Webs with either 2.4 mm, 4.8 mm or 7.2 mm thickness, des-ignated as T2, T4 and T7, respectively.

(3) Panels with either 50 mm, 75 mm or 100 mm web spacing,designated as S5, S7 and S1, respectively.

(4) Foam density with either 40 kg/m3, 60 kg/m3 or 80 kg/m3,designated as D4, D6 and D8, respectively.

4.2. Material properties

The urethane foams with different density (40 kg/m3, 60 kg/m3

and 80 kg/m3) were used in this study. For each density, five cubicfoam samples of 50 mm thick were made and tested in accordancewith ASTM D1621-10 [36] to obtain the compressive strength andthe Young’s modulus. Table 2 shows the cube compressive strengthand the Young’s modulus for each foam.

Tensile and compressive tests, based on ASTM D3039/D3039M-08 [37] and ASTM D695-10 [38] respectively, were carried out todetermine the tensile strength, the tension Young’s modulus, thecompressive strength and the compression Young’s modulus ofweb. The material tension and compression properties of web aresummarized in Table 3.

4.3. Test set-up and Instrumentation

Fig. 4 shows the test set-up. The support system consisted of asteel framed structure. The base of the frame was bolted to thestrong floor of the Structural Engineering Laboratory at NanjingUniversity of Technology. Loading was applied by a hydraulic actu-ator with an axial capacity of 500 kN. Prior to the compressive test,two surfaces of the specimen were connected to 20-mm-thick steelplates, and the specimens were placed at the center of the loading

system. The load was applied under displacement control with adisplacement rate at 0.015 mm/s.

Vertical loading data was collected via a five-channel load cellwhich was mounted directly beneath the panels. Axial shorteningwas measured by four linear variable displacement transducers(LVDTs) which were internal to the vertical actuator. The displace-ment data reflected the total displacement of the top surface of thepanel with respect to the bottom surface.

5. Test results and evaluation

5.1. Strength and stiffness

The initial stiffness of a panel is defined as the slope of the load–displacement curve. The initial stiffness K1 is given by Eq. (17):

K1 ¼PyDy

ð17Þ

where Py and Dy are yield load and corresponding yield displace-ment, respectively. According to the load–displacement curves asshown in Figs. 5–7, it should be noted that the specimens exhibitedan approximate linear behavior until failure occurs, hence, the yieldload (Py) could be replaced by peak load (Pu) in Eq. (17).

The test results of all the specimens, including the peak strength(Pu), initial stiffness (K1), stroke efficiency (Ste) and specific energyabsorption (Se), are summarized in Table 4. Figs. 5 and 8(a) showthe effects of lattice web thickness on the Pu and K1 of panels.Compared to Specimen H5D6 (Pu = 18.09 kN, K1 = 2.99 kN/mm),the Pu of Specimens H5T2S7D6, H5T4S7D6 and H5T7S7D6increased by 447.8%, 1317.3% and 2377.3%, respectively, and theK1 of Specimens H5T2S7D6, H5T4S7D6 and H5T7S7D6 increasedby 2051.8%, 4535.1% and 6416.4%, respectively. Compared toSpecimen H7D6 (Pu = 20.15 kN, K1 = 4.01 kN/mm), the Pu ofSpecimens H7T2S7D6, H7T4S7D6 and H7T7S7D6 increased by698.9%, 1523.7% and 1581.3%, respectively, and the K1 ofSpecimens H5T2S7D6, H5T4S7D6 and H5T7S7D6 increased by1375.8%, 3062.3% and 4700.2%, respectively. Compared to

Fig. 5. The effects of lattice web thickness (a) h = 50 mm, s = 70 mm, q = 60 kg/m3; (b) h = 70 mm, s = 70 mm, q = 60 kg/m3; (c) h = 50 mm, s = 50 mm, D = 40 kg/m3 and (d)h = 50 mm, s = 50 mm, q = 80 kg/m3.

Fig. 6. The effects of web spacing (a) h = 70 mm, t = 2.4 mm, q = 60 kg/m3 and (b) h = 70 mm, t = 7.2 mm, q = 60 kg/m3.

334 Z. Wu et al. / Composites: Part B 60 (2014) 329–340

Specimen H5D4 (Pu = 4.66 kN) and H5D8 (Pu = 35.23 kN), the Pu ofSpecimens H5T2S5D4 and H5T2S5D8 increased by 5314.4% and807.2%, respectively. This may be due to the fact that thickerweb can provide higher lateral confining pressure to the foam aspresented in Eq. (14), then the compressive strength of the con-fined foam can be enhanced. Meanwhile, the thicker web can leadto a larger axial stiffness. Hence, the use of thicker web can im-prove the strength and initial stiffness of panels significantly.

Figs. 6 and 8(b) illustrate the effects of lattice web spacing onthe Pu and K1 of panels. According to Figs. 6(a) and 8(b), for thespecimens with 70 mm web height, 2.4 mm web thickness and60 kg/m3 foam density, the Pu and K1 of Specimen H7T2S5D6(s = 50 mm) were 278.23 kN and 102.67 kN/mm, respectively,which were 72.8% and 1700.5% larger than the Pu of SpecimenH7T2S7D6 (s = 70 mm) and H7T2S1D6 (s = 100 mm), respectively,and 73.5% and 84.4% larger than the K1 of Specimen H7T2S7D6

Fig. 7. The effects of foam density (a) h = 50 mm, t = 2.4 mm, s = 50 mm and (b) h = 100 mm, t = 2.4 mm, s = 100 mm.

Table 4Experimental and theoretical results of specimens.

Specimen Pu (kN) K1 (kN/mm) Ste (%) m (g) W(Dst) (kJ) Se (kJ/kg) Ppre (kN) Ppre/Pu

H5D4 4.66 1.86 68.5 771 0.13 0.2 6.52 1.40H5D6 18.09 2.99 67.2 811 0.57 0.7 14.32 0.79H7D6 20.15 4.01 73.5 859 1.23 1.4 14.32 0.71H5D8 35.23 7.03 64.3 851 1.07 1.3 24.36 0.69H5T2S5D4 252.31 162.78 56.1 1109 2.88 2.6 229.84 0.91H5T2S5D6 265.11 186.7 49.3 1147 3.55 3.1 240.33 0.91H5T2S5D8 319.61 202.28 44.7 1191 4.16 3.5 261.10 0.82H5T2S7D6 99.09 64.34 62.6 1062 1.77 1.7 113.65 1.15H5T4S7D6 56.39 138.59 60.2 1312 4.58 3.5 284.33 1.11H5T7S7D6 448.14 194.84 57.9 1563 6.34 4.1 489.69 1.09H1T2S1D4 308.1 174.07 28 1109 4.12 3.7 260.34 0.84H1T2S1D6 27.84 188.41 24.9 1134 4.55 4.0 272.36 0.83H1T2S1D8 357.13 212.58 24.3 1195 5.29 4.4 299.32 0.84H7T2S5D6 278.23 102.67 65.1 1327 5.15 3.9 230.97 0.83H7T2S7D6 160.97 59.18 67.9 1102 3.65 3.3 175.56 1.09H7T2S1D6 103.03 55.69 73 1093 2.64 2.4 117.89 1.14H7T7S5D6 624.31 219.06 56 2267 11.73 5.2 689.82 1.10H7T4S7D6 327.18 126.81 65.8 1687 6.52 3.9 347.63 1.06H7T7S7D6 338.79 192.49 59.8 1912 8.19 4.3 325.41 0.96H7T7S1D6 285.55 114.22 64.3 1560 5.66 3.6 310.63 1.09Mean – – – – – – – 0.97

Z. Wu et al. / Composites: Part B 60 (2014) 329–340 335

and H7T2S1D6, respectively. According to Figs. 6(b) and 8(b), forthe specimens with 70 mm web height, 6.8 mm web thicknessand 60 kg/m3 foam density, the Pu and K1 of Specimen H7T7S5D6(s = 50 mm) were 624.31 kN and 219.09 kN/mm, respectively,which were 84.3% and 118.6% larger than the Pu of SpecimenH7T7S7D6 (s = 70 mm) and H7T7S1D6 (s = 100 mm), respectively,and 13.8% and 91.8% larger than the K1 of Specimen H7T2S7D6and H7T2S1D6, respectively. According to Eq. (14), the smallerweb spacing can result in a larger lateral confining pressure tothe foam, which can improve the compressive strength of the con-fined foam. Therefore, decreasing the web spacing can increase thepeak strength of panels.

Figs. 7 and 8(c) illustrate the effects of foam density on the Puand K1 of the panels. Compared to Specimen H5T2S5D4 (Pu =252.31 kN, K1 = 162.78 kN/mm), the Pu of Specimens H5T2S5D6and H5T2S5D8 increased by 5.1% and 26.7%, respectively, and theK1 of Specimens H5T2S5D6 and H5T2S5D8 increased by 14.7%and 24.3%, respectively. Compared to Specimen H1T2S1D4(Pu = 308.10 kN, K1 = 174.07 kN/mm), the Pu of SpecimensH1T2S1D6 and H1T2S1D8 increased by 6.4% and 15.9%, respec-tively, and the K1 of Specimens H1T2S1D6 and H1T2S1D8increased by 8.2% and 22.1%, respectively. The foam with higherdensity also behaves stiffer. Hence higher density foam can provide

much more resistance to the applied loads. Therefore, a larger foamdensity can give a higher peak strength and initial stiffness.

5.2. Compressive behavior and failure modes

According to the load–displacement curves, the deformation ofspecimens can be divided into three stages: linear-elastic stage,post-yield stage and foam densification stage. All specimens exhib-ited a linear-elastic response up to failure at the elastic stage. In thepost-yield stage, the compressive load capacity decreased sharply,which was associated with buckling of lattice webs, as shown inFig. 9(b). The compressive load capacity of lattice composite panelsroughly stayed at a half of peak strength level, while the compres-sive load capacity of control specimens kept peak load level. In thefoam densification stage, the compressive load capacity of panelsincreased, but the deformation of panels was very large. With anincreasing applied load, the buckled webs violently extruded thefoam, which resulted in crushing of the foam, as shown in Fig. 9(c).

For the sandwich members, there are usually five failure modesincluding face sheet compressive/tensile failure, core shear failure,delamination, face sheet wrinkling and core indentation failure.But all of them usually occurred in the bending tests. The coreshear and indentation failure usually occurred when the sandwich

Fig. 8. The initial stiffness of the panels (a) the effects of lattice web thickness; (b) the effects of lattice web spacing and (c) the effects of the foam density.

(a)

(b)

(c)

Local buckling Local

buckling

Fig. 9. Compressive behavior of Specimen H7T7S5D6 (a) linear-elastic stage; (b)post-yield stage and (c) foam densification stage.

336 Z. Wu et al. / Composites: Part B 60 (2014) 329–340

panels subjected to the concentrated compression loading. In thisstudy, the failure mode of all the specimens was quite similar.However, the mentioned failure modes were not observed in thisstudy because sandwich panels were tested under uniform distrib-uted axial compression loading. Due to the use of the GFRP web,

the failure modes can be categorized as two primary types: (1)GFRP web compressive failure and (2) GFRP web local bucklingfailure. The microscopic phenomena which originate the corre-sponding failure modes can be summarized, respectively, as fol-lows: (1) the compressive stress of the web reaches its yieldstress before the occurance of the local buckling, and (2) the criticalbuckling stress of the web is less than its yield stress. According tothe critical buckling stress obtained from Eq. (9), the failure modeof panels can be judged.

5.3. Stroke efficiency

The stroke efficiency (Ste) is introduced to evaluate the defor-mability of a panel. The load–displacement responses of the spec-imens as shown in Figs. 4–6 can be idealized as a quadri-linearcurve (Fig. 10). Because specimens exhibited an approximate linearresponse up to failure, a line OA can be considered as a tangent lineto the load–displacement curve before reaching the peak strength.The line BC can be drawn according to the average value of thecompressive strength in the post-yield part. A tangent line CD tothe load–displacement curve in the region of densification of foamcan be drawn and its intersection point with line BC is point C. Thehorizontal coordinate value corresponding to point C is the strokelength (Dst). The stroke efficiency [39] is defined as the ratio of thestroke length to the height of a panel (H), thus

Ste ¼DstH

ð18Þ

Quatri-linear approx.

Actural Behavior

B

A

C

D

Fig. 10. The idealized load–displacement curve.

Z. Wu et al. / Composites: Part B 60 (2014) 329–340 337

Fig. 11(a) shows a distinct decrease of the measured stroke efficien-cies with increasing web thickness. The Ste of Specimens H5D6 andH7D6 (without web) were largest compared to the correspondinglattice web composite panels. The Ste of Specimens H5T2S7D6 andH7T2S7D6 with 2.4 mm lattice web thickness reduced to 62.6%and 67.9%, respectively. The panels with the thickest lattice webshad the lowest values of Ste (57.9% for H5T7S7D6, and 59.8% forH7T7S7D6). The reason of this phenomenon was that the thickerwebs can lead to the larger axial stiffness of the panel, hence, thestroke length become small for a given compressive load.

Fig. 11(b) shows a slight increase of the measured strokeefficiencies with increasing lattice web spacing. Compared toSpecimen H7T2S5D6 (s = 50 mm), the Ste of Specimens H7T2S7D6(s = 70 mm) and H7T2S1D6 (s = 100 mm) increased by 4.3% and12.1%, respectively. Compared to Specimen H7T7S5D6 (s =

Fig. 11. The stroke efficiency of the panels (a) the effects of lattice web thicknes

50 mm), the Ste of Specimens H7T7S7D6 (s = 70 mm) andH7T7S1D6 (s = 100 mm) increased by 6.9% and 14.9%, respectively.Because the larger web spacing can give a smaller volume ratio ofthe web to the whole panel, hence the axial stiffness of the paneldecrease, which lead to an increase in the stroke length.

Fig. 11(c) shows a reduction of the measured stroke efficiencieswith increasing foam density.

For Specimen H5T2S5D4 with 40 kg/m3 foam density, the mea-sured stroke efficiency was 56.1%, while for Specimen H5T2S5D8,the Ste reduced to value of 44.7% due to the higher foam density(q = 80 kg/m3). Although the difference in the web height andspacing, both curves in Fig. 10(c) shows a similar trend. The Steof Specimen H1T2S1D4 with 40 kg/m3 foam density was 28.0%,which was 12.4% and 15.1% larger than that of SpecimenH1T2S1D6 (q = 60 kg/m3) and Specimen H1T2S1D6 (q = 60 kg/m3), respectively. Seitzberger et al. [39] proposed that the reduc-tion of the stroke efficiency is related to the foam behavior. Withincreasing foam density, the region of densification, where thecompressive force starts to increase steeply, was shifted to lowervalues of the compressive strain. The foam suffered very large com-pressive strains and prevented the deformation of the lattice webs,which reduced the stroke length of the panels.

5.4. Specific energy absorption

The specific energy absorption (Se) was adopted to evaluate the‘‘mass efficiency’’ of a panel, which is defined as [39]:

Se ¼WðDstÞ

mð19Þ

s; (b) the effects of lattice web spacing and (c) the effects of foam density.

338 Z. Wu et al. / Composites: Part B 60 (2014) 329–340

where m is the total mass of a panel, and W is the total energy,which is given by Eq. (20):

WðDÞ ¼Z P

0ð�DÞd�D ð20Þ

where P is the applied compressive force, and D is the displacementof specimen (with integration variable �D). Assuming that the contri-bution due to elastic deformations is negligible, W can approxi-mately be regarded as the energy dissipated by plastic deformation.

Fig. 12(a) shows the effects of lattice web thickness on the spe-cific energy absorption of the panels. For the specimens with70 mm web height, 70 mm web spacing and 60 kg/m3 foam den-sity, the Se of Specimen H7T7S7D6 (t = 7.2 mm) was 4.3, whichwas 207.1%, 30.3% and 10.3% larger than that of Specimen H7D6(without lattice webs), H7T2S7D6 (t = 2.4 mm) and H7T4S7D6(t = 4.8 mm), respectively. For the specimens with 50 mm webheight, 70 mm web spacing and 60 kg/m3 foam density, the Se ofSpecimen H5T7S7D6 (t = 7.2 mm) was 4.1, which was 485.7%,141.2% and 17.1% larger than the Se of Specimen H5D6 (withoutlattice webs), H5T2S7D6 (t = 2.4 mm) and H5T4S7D6 (t =4.8 mm), respectively. Hence, the lattice web thickness can playan important role in increasing the energy absorption of the panels.

Fig. 12(b) shows the effects of lattice web spacing on the spe-cific energy absorption of the panels. For the specimens with70 mm web height, 2.4 mm web thickness and 60 kg/m3 foam den-sity, the Se of Specimen H7T2S5D6 (s = 50 mm) was largest, whichwas equal to 3.9, the Se of Specimens H7T2S7D6 (s = 70 mm) andH7T2S1D6 (s = 100 mm) were 3.3 and 2.4, respectively. For thespecimens with 70 mm web height, 7.2 mm web thickness and

Fig. 12. The specific energy absorption of the panels (a) the effects of lattice web thi

60 kg/m3 foam density, the Se of Specimen H7T7S5D6(s = 50 mm) was largest, which was equal to 5.2, the Se of Speci-mens H7T7S7D6 (s = 70 mm) and H7T7S1D6 (s = 100 mm) were4.3 and 3.6, respectively. The test results indicated that the smallerlattice web spacing of the panels can achieve the larger energyabsorption.

Fig. 12(c) shows the effects of foam density on the specific en-ergy absorption of the panels. For the specimens with 50 mmweb height, 2.4 mm web thickness and 50 mm web spacing, theSe of Specimen H5T2S5D4 (q = 40 kg/m3) was 2.6, which was19.2% and 34.6% smaller than that of Specimen H5T2S5D6(q = 60 kg/m3) and H5T2S5D8 (q = 80 kg/m3), respectively. Forthe specimens with 100 mm web height, 2.4 mm web thicknessand 100 mm web spacing, the Se of Specimen H1T2S1D4(q = 40 kg/m3) was 3.7, which was 8.1% and 18.9% smaller thanthat of Specimen H1T2S1D6 (q = 60 kg/m3) and H1T2S1D8(q = 80 kg/m3), respectively. Thus, the energy absorption of thepanels can be enhanced using the foam with the higher density.

6. Comparison with available experimental results

Chen and Davalos [30] tested three FRP sandwich deck panelswith sinusoidal core geometry under compression loading. Theface sheets and cores consisted of chopped strand mat. For eachspecimen, the volume ratio of the core respect to the whole panel(g) was calculated. Table 5 compares the peak strength and initialstiffness presented in Chen and Davalos [30] with those of Speci-men H5T7S7D6 because the value of g of Specimen H5T7S7D6 issimilar with their specimens. Compared to Specimen H5T7S7D6,

ckness; (b) the effects of lattice web spacing and (c) the effects of foam density.

Table 5Comparison of available test results and present test results.

Specimens Pu,chen (kN) K1,chen (kN/mm) g (%) Pu,chen/Pu,H5T7S7D6 (%) K1,chen/K1,H5T7S7D6 (%)

B1C2 155.54 86.41 24.4 34.7 44.3B2C2 163.07 148.25 23.1 36.4 76.1B3C2 177.22 136.32 22.1 39.5 70.0H5T7S7D6 448.14 194.84 19.7

Note: Pu,chen is the peak load; K1,chen is the initial stiffness, both from Chen and Davalos [30].

Z. Wu et al. / Composites: Part B 60 (2014) 329–340 339

the Pu of Specimens B1C2, B2C2 and B3C2 decrease to 34.7%, 36.4%and 39.5%, respectively, meanwhile, the K1 of Specimens B1C2,B2C2 and B3C2 decrease to 44.3%, 76.1% and 70.0%, respectively.The reason is that for the specimen H5T7S7D6, the critical bucklingstress of web can be increased due to the restriction from foamcores, and the compressive strength of the foam is also improvedbecause of the confinement provided by webs. Hence, even the va-lue of g of Specimen H5T7S7D6 is slightly smaller, larger peakstrength and initial stiffness can be achieved.

7. Comparison with available experimental results

Table 4 summarized the theoretical ultimate peak strength ofpanels. During the calculation, Specimens H5T2S5D4, H5T2S5D6,H5T2S5D8 and H7T2S5D6 failed by local buckling of web. The crit-ical buckling stresses of them were 36 MPa, 40 MPa, 54 MPa and51 MPa, respectively. For the foam-filled lattice composite panels,the largest variation between theoretical and experimental resultsin the ultimate peak strength was 18%, which occurred in Speci-men H5T2S5D8. In general, comparing the theoretical and experi-mental ultimate peak strengths reveals that the proposedtheoretical model is able to conservatively estimate the actual ulti-mate peak strength of panels under quasi-static compression load-ing with an average underestimation of 3%.

8. Conclusions

This paper presents an experimental investigation on the foam-filled lattice composite panels under quasi-static axial compressionloading. The main findings of this study are summarized asfollows:

(1) A kind of foam-filled lattice composite panels applied to civilengineering field was developed through vacuum assistedresin infusion process. The comparison between the avail-able test results of Chen and Davalos [30] and the test resultswas presented. These panels had the characteristics of highcompressive stiffness and strength, and strong energyabsorbing capacity.

(2) The experimental results show that compared to the foam-filled composite panels, a maximum of an approximately1600% increase in the peak load of panels can be achieveddue to the use of lattice webs.

(3) The thicker lattice web and smaller lattice web spacing canenhance the peak load of panels significantly, but the effectsof foam density on the peak load of panels are small.

(4) A quadri-linear curve was proposed to idealize the load–displacement responses of panels. The stroke length can bedetermined according to the quadri-linear curve.

(5) The thinner lattice web and larger lattice web spacing canthe improve stroke efficiency of panels, while the largerfoam density can decrease the stroke efficiency of panelsbecause the larger density foam, suffered larger compressivestrain, can provide much more resistance to prevent thefolds from touching each other.

(6) The energy absorption of panels is affected by lattice webthickness, lattice web spacing and foam density. Largerenergy absorption can be achieved by increasing the latticeweb thickness and foam density and decreasing the webspacing.

(7) Overall, it has been demonstrated that the foam-filledlattice composite panels exhibited better performancethan the normal foam-core sandwich panels. It isexpected that the foam-filled lattice composite panelscan be widely used as bridge decks, formworks and wallboards.

Acknowledgements

The research described here was supported by the Key Programof National Natural Science Foundation of China (Grant No.51238003), Natural Natural Science Foundation for the Youth(Grant No. 51008157) and Key University Science Research Projectof Jiangsu Province (Grant No. 12KJA580002).

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Theoretical and experimental study of foam-filled lattice composite panels under quasi-static compression loading1 Introduction2 Manufacture process3 Theoretical model3.1 Local buckling of the GFRP web3.2 Ultimate axial load capacity

4 Experimental program4.1 Test specimens4.2 Material properties4.3 Test set-up and Instrumentation

5 Test results and evaluation5.1 Strength and stiffness5.2 Compressive behavior and failure modes5.3 Stroke efficiency5.4 Specific energy absorption

6 Comparison with available experimental results7 Comparison with available experimental results8 ConclusionsAcknowledgementsReferences