Composites: Part B 67 (2014) 270–279

Contents lists available at ScienceDirect

Composites: Part B

journal homepage: www.elsevier .com/locate /composi tesb

Mechanical performance of foam-filled lattice composite panelsin four-point bending: Experimental investigation and analyticalmodeling

http://dx.doi.org/10.1016/j.compositesb.2014.07.0031359-8368/� 2014 Elsevier Ltd. All rights reserved.

⇑ Corresponding author. Address: College of Civil Engineering, Nanjing TechUniversity, Pu Zhu South Road 30, Nanjing 211816, China. Tel.: +86 25 58139862;fax: +86 25 58139863.

E-mail address: wqliu@njtech.edu.cn (W. Liu).

Lu Wang a, Weiqing Liu a,⇑, Li Wan a, Hai Fang a, David Hui ba College of Civil Engineering, Nanjing Tech University, Nanjing, Chinab Department of Mechanical Engineering, University of New Orleans, New Orleans, USA

a r t i c l e i n f o

Article history:Received 1 May 2014Received in revised form 21 June 2014Accepted 6 July 2014Available online 23 July 2014

Keywords:A. FoamsA. Glass fibersB. StrengthC. Analytical modelingD. Mechanical testing

a b s t r a c t

This study focused on the bending behavior of an innovative sandwich panels with GFRP face sheets and afoam-web core (GFFW panels), manufactured by vacuum assisted resin infusion process. An experimentalstudy was carried out to validate the effectiveness of this panel for increasing the ultimate bendingstrength. Compared to the control specimen, a maximum of an approximately 410% increase in the ulti-mate bending strength can be achieved. The influences of web thickness, web height and web spacing onfailure mode, initial bending stiffness and mid-span deflection were also investigated. Test results dem-onstrated that the ultimate bending strength and initial bending stiffness can be enhanced by increasingweb thickness and web height. In the meantime, the indentation failure and local wrinkling failure didnot occur due to the presence of the GFRP webs. Furthermore, an analytical model was proposed to pre-dict the mid-span deflection and initial bending stiffness of GFFW panels. A comparison of the analyticaland experimental results showed that the analytical model accurately predicted the ultimate bendingstrengths and min-span deflections of the GFFW panels loaded in four-point bending.

� 2014 Elsevier Ltd. All rights reserved.

1. Introduction

Recently, composite sandwich panels have been used increas-ingly in the structural engineering due to their advantages of lowcost, high strength to weight ratios and convenient usage. In sand-wich panels, low density materials, such as foam, paulownia woodand honeycombs, have been usually adopted to be the cores, whichare combined with high stiffness face sheets to resist applied load-ing. The face sheets provide major contribution to the bendingstiffness while the core provides the major of shear stiffness ofsandwich structures.

A large number of experimental and analytical studies on sand-wich members with different type of foam core have been con-ducted in the past three decades [1–12]. Steeves and Fleck[13,14] conducted the experimental, numerical and analyticalstudies on the collapse mechanisms for simply supported sand-wich beams with GFRP face sheets and a PVC foam core. Twenty-nine sandwich beams were tested under three-point bending.

The test results indicated that collapse was significantly influencedby the sandwich beam geometry and the density of the foam core.Tagarielli et al. [15] studied the initial collapse modes of sandwichbeams with clamped and simply supports under three-point bend-ing. Initial collapse was by three competing mechanisms: micro-buckling of face sheet, core shear and indentation. The testresults demonstrated that the simply supported beams displayeda softening post-yield response, but the clamped beams exhibitedhardening behavior because of membrane stretching of the facesheets. An theoretical model to predict the deflection of clampedbeams were also developed. Sharaf et al. [16] tested ten wall sand-wich panels with a foam core under one-way bending. The testresults showed that bending strength and stiffness of the panelsimproved significantly with the increase in foam density. However,the horizontal slip was measured between the top and bottom facesheets. The foam core with a smaller toughness can lead to a largerhorizontal slip. Wang and Shen [17] studied the nonlinear bendingof a sandwich panel with carbon nanotube-reinforced compositeface sheets resting on an elastic foundation in thermal environ-ments. The influences of nanotube volume fraction, core-to-skinthickness ratio, temperature change, foundation stiffness and in-plane boundary conditions on the nonlinear bending behaviors ofsandwich plates were investigated. Dawood et al. [18] evaluated

http://crossmark.crossref.org/dialog/?doi=10.1016/j.compositesb.2014.07.003&domain=pdfhttp://dx.doi.org/10.1016/j.compositesb.2014.07.003mailto:wqliu@njtech.edu.cnhttp://dx.doi.org/10.1016/j.compositesb.2014.07.003http://www.sciencedirect.com/science/journal/13598368http://www.elsevier.com/locate/compositesb

L. Wang et al. / Composites: Part B 67 (2014) 270–279 271

the behavior of 3-D GFRP sandwich panels with fiber insertionssubject to two-way bending. The test results showed that thebehavior of the panels was determined by the panel thicknessand the shear stiffness of the core. The dominant failure mode ofthe panels was buckling of the panel at the support locations. Acorresponding finite element model was also developed to investi-gate the effects of face sheet thickness, face sheet modulus, fiberinsertion density, panel thickness and aspect ratio on the bendingstrength of the panels. Reis [19] and Reis and Rizkalla [20] devel-oped a new type of sandwich panels consisted of composite facesheets, foam core and through-thickness fiber insertions. The inter-face delamination of sandwich panels was prevented due to theuse of the fiber insertions. The effects of fiber insertion density,face sheet thickness and panel thickness on the strength and stiff-ness of the panels were studied. However, although the interfacedelamination issue can be relieved, the initial bending stiffness ofa sandwich panel was hardly improved. In practice, the commonsolutions to improve the initial bending stiffness are to use thehigher density foam core and the thicker face sheets, which resultin an sharply increase in engineering costs and dead loads. Hence,under the premise of keeping the minimum construction costs andthe minimum weight, how to improve the ultimate bendingstrength and initial bending stiffness of sandwich panels is a criti-cal issue. This is the motivation of this study.

Authors have developed a kind of foam-filled lattice compositesandwich panel consisted of GFRP face sheets and a foam-webcore. The connection details and manufacture process were intro-duced in our companion paper [21]. As shown in Fig. 1, the facesheets, webs and foam cores are combined by vacuum infusingresin. The axial compression tests have been carried out by theauthors. The test results indicated that the ultimate compressivestrength, initial stiffness and energy absorbing of GFFW panelswere improved significantly. The reason was that the compressivestrength of foam was improved due to the confinement effects pro-vided by GFRP lattice webs, and the foam cores can also restrict thelocal buckling of the lattice webs.

In order to thoroughly understand the bending behavior of theGFFW panels, the four-point bending test was conducted to inves-tigate the ultimate bending strength, initial bending stiffness andfailure mode of this type of panels in this study. An analyticalmodel was developed to predict the mid-span deflection of GFFWpanels under four-point bending. The accuracy of the model wasverified through a comparison of the model with experimentalresults. Meanwhile, a comprehensive conclusion of four-pointbending behavior was summarized, which can be used to aid engi-neers in designing GFFW panels and to ensure proper panel detail-ing for desirable performance.

Face sheet

Foam

GFRP Web

Fig. 1. The sandwich panel with GFRP face sheets and a foam-web core.

2. Experimental program

2.1. Description of test specimens and parameters

In this study, ten panels were manufactured by means of vac-uum assisted resin infusion process in the Advanced CompositeStructures Research Center at Nanjing Tech University. The GFRPand HS-2101-G100 unsaturated polyester resin were used for facesheets and webs. The polyurethane foam (PU foam) with 60 kg/m3

density was used for filled core. Table 1 shows a summary of thetest matrix and details of specimens. All the specimens had theidentical length (L = 1000 mm), width (d = 225 mm) and face sheetthickness (ts = 3.2 mm). Specimen FPB50-CON was a controlledsandwich panel with GFRP face sheets and a foam core, whichwas used to investigate the bending performance of normal sand-wich panels. Specimens FPB50-16, FPB50-32 and FPB50-48 andSpecimens FPB75-16, FPB75-32 and FPB75-48 were fabricatedwith 50-mm-web height and 75-mm-web height, respectively,which were used to investigate the influence of web thickness(tw). Specimens FPB50-16, FPB75-16 and FPB100-16 and Speci-mens FPB50-32, FPB75-32 and FPB100-32 were fabricated with1.6-mm-web thickness and 3.2-mm-web thickness, respectively,which were used to investigate the influence of web height (h).Specimens FPB100-32 and FPB100-32-II were fabricated with3.2-mm-web thickness and 100-mm-web height, which were usedto investigate the influence of web spacing (s).

2.2. Material properties

The face sheet were fabricated using E-glass mat, and HS-2101-G100 unsaturated polyester resin, and had an average thickness of3.2 mm of the cured GFRP laminate. Five tension coupons weretested by the authors according to ASTM D3039/D 3039M-08[22]. The tensile strength ranged from 290.9 MPa to 351.3 MPa,with an average of 322.9 MPa, and the tensile modulus rangedfrom 19.9 GPa to 23.3 GPa, with an average of 20.9 GPa. Mean-while, five compression coupons were tested by the authorsaccording to ASTM D695-10 [23]. The compressive strength rangedfrom 50.2 MPa to 59.4 MPa, with an average of 55.3 MPa, and thecompressive modulus ranged from 5.6 GPa to 7.1 GPa, with anaverage of 6.7 GPa. Table 2 summarizes the material propertiesof the GFRP face sheet.

Totally fifteen cubic foam coupons of 50 mm thick were testedby the authors in tension according to ASTM C297/C297M-04 [24],in compression according to ASTM C365-03 [25], and in shearaccording to ASTM C273/273M-07 [26], using five cubes for eachcase. The measured ultimate tensile strength and tensile modulusof foam were 150 and 340 kPa, respectively. The measured ulti-mate compressive strength and compressive modulus were0.36 MPa and 17 MPa, respectively. Also, the measured ultimateshear strength and shear modulus were 0.36 MPa and 50 MPa,respectively. The material properties are summarized in Table 3.

Table 1Details of specimens.

Specimen L (mm) d (mm) h (mm) s (mm) tw (mm) ts (mm)

FPB50-CON 1000 225 50 – – 3.2FPB50-16 1000 225 50 75 1.6 3.2FPB50-32 1000 225 50 75 3.2 3.2FPB50-48 1000 225 50 75 4.8 3.2FPB75-16 1000 225 75 75 1.6 3.2FPB75-32 1000 225 75 75 3.2 3.2FPB75-48 1000 225 75 75 4.8 3.2FPB100-16 1000 225 100 75 1.6 3.2FPB100-32 1000 225 100 75 3.2 3.2FPB100-32-II 1000 225 100 100 3.2 3.2

Table 2Material properties of face sheet.

Face sheet

Compression Yield strength (MPa) 55.3Young’s modulus (GPa) 6.7

Tension Yield strength (MPa) 322.9Young’s modulus (GPa 20.9

272 L. Wang et al. / Composites: Part B 67 (2014) 270–279

2.3. Test set-up and instrumentation

For the four-point bending tests, the clear span (L) between thetwo roller supports was 750 mm. A monotonic load was providedby a 200 kN capacity hydraulic actuator, which was equally dividedinto two concentrated loads by a steel transfer beam and loaded atthe two trisection points of the panel. Then a 250 mm-length purebending zone was formed in the middle part of the panel, as shownin Fig. 2(a) and (b). The loading was applied under displacementcontrol with 2 mm per min displacement rate.

To measure the deflections of the panel, three linear variable dis-placement transducers (LVDTs) with a stroke of 50 mm, installed atmiddle span and support locations. Fig. 3(a) shows the arrangementof the LVDTs. Ten electric resistance strain gauges, pasted on the topand bottom face sheets, were adopted in the four-point bendingtests. The readings of strain gauges were used to judge the failuremodes. Fig. 3(a) shows the location of the strain gauges.

3. Experimental results and discussion

3.1. Failure mode

The macroscopic failure modes of specimens can be categorizedas three primary types: (1) top face sheet delamination, whichoccurred in control specimen; (2) top face sheet compressive fail-ure (see Fig. 4a), which is common in specimens with 3.2 mm(FPB50-32, FPB75-32, FPB100-32 and FPB100-32-II) and 4.8 mmweb thickness (FPB50-48 and FPB75-48); (3) core shear failure(see Fig. 4b), which occurs in specimen FPB50-16, FPB75-16 andFPB100-16. The microscopic phenomena that result in the corre-sponding macroscopic failure modes can be described, respec-tively, as follows: (1) the shear stress in the interface was largerthan adhesive strength, the delamination phenomenon betweentop face sheet and foam core can be observed; (2) the compressivestrain of the top face sheet reaches its ultimate strain; (3) the max-imum shear strain of the core exceeds its crushing strain. Unlikethe normal sandwich panels (Specimen FPB50-CON), the delami-nation failure did not occur in the GFFW panels due to the presenceof the webs, which can improve adhesive strength between facesheets and foam cores. In the meantime, the indentation failurewas not observed during the tests because the GFRP webs can pro-vide resistance to the shear force and improve the bending stiffnessof the panels. For the local wrinkling and buckling of face sheets,according to the readings of the strain gauges attached to the topface sheet, the compressive strain was less than the critical buck-ling strain before reaching the ultimate bending strength. Hence,it can be concluded that the local wrinkling and microbuckling oftop face sheet did not occur.

Table 3Material properties of foam.

Foam

Compression Yield strength ffy (MPa) 0.36Young’s modulus Ef (MPa 17

Shear Yield strength (MPa) 0.37Young’s modulus (MPa) 50

3.2. Influence of web thickness

The test results are presented along with a discussion on theinfluence of various parameters on the bending behavior of speci-mens. The yield load (Py), ultimate load (Pu), yield displacement(Dy), ultimate displacement (Du), initial bending stiffness (Ke)and the observed failure modes are summarized in Table 4. The ini-tial bending stiffness of a panel is defined as the ratio of the yieldload to the yield displacement,

Ke ¼PyDy

ð1Þ

Fig. 5 shows the influence of web thickness (tw) on the ultimatebending strength under the same web spacing (s = 75 mm) andface sheet thickness (ts = 3.2 mm). Despite the difference in theweb height (h = 50 mm and 75 mm for the results shown inFig. 5(a) and (b), respectively), similar findings can be observedin two figures. Among all the specimens with the 56.4 mm panelheight, Specimen FPB50-CON had the minimum ultimate bendingstrength (Pu = 7.3 kN), which was due to lack of the GFRP webs.Compared to Specimens FPB50-16 and FPB75-16, the ultimatebending strengths of Specimens FPB50-32 and FPB75-32 with3.2-mm-thick web increased by 9.1% and 15.4%, respectively, theultimate bending strengths of Specimens FPB50-48 and FPB75-48with 4.8-mm-thick web increased by 34.8% and 47.2%, respec-tively. The thicker webs can improve the shear capacity of theGFFW panels and meanwhile the foam core shear failure can beavoided, thus the ultimate bending strength can be enhanced.

The initial bending stiffness of specimens can be obtained by Eq.(1), as listed in Table 4. It can be concluded that the initial bendingstiffness of specimens increased with the increase in the webthickness. The values of Ke of Specimen FPB50-16 and SpecimenFPB75-16 were minimum with the thinnest web, which were equalto 2.09 kN/mm and 3.39 kN/mm, respectively. While the values ofKe of Specimen FPB50-48 and Specimen FPB75-48 were maximumwith the thickest web, which were equal to 3.09 kN/mm and4.96 kN/mm, respectively. Hence, using thicker GFRP webs canincrease the initial bending stiffness of GFFW panels.

3.3. Influence of web height

In the tests, three web heights (50 mm, 75 mm and 100 mm)were adopted to investigate the influence of web height on ulti-mate bending strength and initial bending stiffness. As shown inFig. 6(a) and (b), it can be found that the ultimate bending strengthof specimens increased with the increase in the web height. Whenthe web height was 100 mm, the ultimate bending strength ofSpecimen FPB100-16 and Specimen FPB100-32 were equal to39.2 kN and 45.1 kN, respectively, which were 42.0% and 49.8%greater than those of Specimen FPB50-16 and Specimen FPB50-32 (h = 50 mm), respectively, and 37.1% and 36.7% greater thanthose of Specimens FPB75-16 and FPB75-32 (h = 75 mm), respec-tively. Moreover, increasing the web height also can significantlyimprove the initial bending stiffness of GFFW panels. Accordingto the values calculated by Eq. (1), the initial bending stiffness ofSpecimens FPB100-16 and FPB100-32 were nearly three times ofFPB50-16 and FPB50-32, respectively. It can be concluded thatincreasing the web height can obtained a larger moment of inertia,then the bending stiffness of a panel can be enhanced.

3.4. Influence of web spacing

Fig. 7 shows the comparison of the load–mid-span deflectioncurve of Specimens FPB100-32 and FPB100-32-II, which were usedto evaluate the influence of web spacing on ultimate bending

(a)

(b)

GFFW panel

Loading cell

Steel transfer

beam

Fig. 2. Test set-up (a) schematic diagram and (b) photo of test set-up.

(a)

(b)

LVDT

Strain

gauge

Fig. 3. Instrumentation of Specimen FPB50-32 (a) LVDT and (b) strain gauge arrangements.

L. Wang et al. / Composites: Part B 67 (2014) 270–279 273

strength and initial bending stiffness. It is shown in Table 4 that theyielding strength and ultimate bending strength of SpecimenFPB100-32 was 41.2 kN and 45.1 kN, respectively, which wereapproximately the same as those of Specimen FPB100-32-II(Py = 42.5 kN, Pu = 43.5 kN). Similarly, the difference of initial bend-ing stiffness between Specimen FPB100-32 and Specimen FPB100-32-II was negligible. The initial bending stiffness of SpecimenFPB100-32 was 98.5% of that of FPB100-32-II. The reason of thisphenomenon was that although the web spacing of SpecimenFPB100-32-II was larger than that of Specimen FPB100-32, thethickness, height, length and number of web was not changed, in

other words, the volume ratio of GFRP web to the panel was fixed.Hence, the ultimate bending strength and initial bending stiffnesswere hardly affected by the web spacing.

4. Analytical model

4.1. Equivalent Young’s modulus of the web-foam core

Consider a GFRP web-foam core (WFC) element cut out of thepanel, as shown in Fig. 8(a), the length, width and height are 2a,2b and h, respectively. When the element subjected to

Fig. 4. Failure modes (a) top face sheet compressive failure of Specimen FPB75-48 and (b) core shear failure of Specimen FPB100-16.

Table 4Test results.

Specimen Py (kN) Pu (kN) Dy (mm) Du (mm) Ke (kN/mm) Failure mode

FPB50-CON 5.9 7.3 4.5 5.1 1.31 DelaminationFPB50-16 24.3 27.6 11.6 13.9 2.09 ShearFPB50-32 25.8 30.1 11.8 14.5 2.17 CompressionFPB50-48 34.6 37.2 11.2 15.2 3.09 CompressionFPB75-16 27.8 28.6 8.2 10.0 3.39 ShearFPB75-32 29.7 33.0 7.6 10.3 3.91 CompressionFPB75-48 35.2 42.1 7.1 9.8 4.96 CompressionFPB100-16 37.3 39.2 5.6 7.2 6.61 ShearFPB100-32 41.2 45.1 6.1 8.0 6.75 CompressionFPB100-32-II 42.5 43.5 6.2 7.9 6.85 Compression

Fig. 5. The influence of web thickness (a) h = 50 mm, s = 75 mm, ts = 3.2 mm and (b)h = 75 mm, s = 75 mm, ts = 3.2 mm.

Fig. 6. The influence of web height (a) s = 75 mm, tw = 1.6 mm, ts = 3.2 mm and (b)s = 75 mm, tw = 3.2 mm, ts = 3.2 mm.

274 L. Wang et al. / Composites: Part B 67 (2014) 270–279

Fig. 7. The influence of web spacing.

L. Wang et al. / Composites: Part B 67 (2014) 270–279 275

compression (Px) in the x-direction, by considering force equilib-rium (see Fig. 8b), the Px can be expressed as

2Pfx þ Pwx ¼ Px ð2Þ

where Pfx and Pwx are the resistance of the foam and GFRP web,respectively.

Then the compression Px can be re-written as

Px ¼ rxð2bþ twÞh ð3Þ

where rx is the stress in the x-direction.According to the compatibility of deformation in the x-

direction,

dfx ¼ dwx ð4Þ

where dfx and dwx are the deformation of foam and web in the x-direction, respectively, which can be calculated by

dfx ¼PfxaEf bh

ð5Þ

dwx ¼Pwxa

Ewtwhð6Þ

where Ef and Ew are the Young’s modulus of foam and GFRP web,respectively.

Substituting Eqs. (5) and (6) into Eq. (4) gives

Pfx ¼Ef b

EwtwPwx ð7Þ

Substituting Eq. (7) into Eq. (2) gives

Pfx ¼rxð2bþ twÞEf hb

Ewtw þ 2Ef bð8Þ

Fig. 8. Analytical model (a) the element of the foam-

Pwx ¼rxð2bþ twÞEwtwb

Ewtw þ 2Ef bð9Þ

Then the energy associated with the WFC element deforming(U0)

U0 ¼ r2x ð2aþ twÞð2bþ twÞh

2Ecxð10Þ

The energy associated with the web deforming (Uw) and theenergy associated with the foam deforming (Uf) are respectivelygiven by

Uw ¼r2x 2bþ twð Þ

2ahEwtw2 Ewtw þ 2Ef b� �2 ð11Þ

Uf ¼r2x 2bþ twð Þ

2ahEf tw2 Ewtw þ 2Ef b� �2 ð12Þ

Because U0 = 2Uw + 4Uf, the equivalent Young’s modulus of theweb-foam core in the x-direction (Ecx)can be expressed as

Ecx ¼ð2aþ twÞðEwtw þ 2aEf Þ

2að2bþ twÞð13Þ

Similarly, equivalent Young’s modulus of the web-foam core inthe y-direction (Ecy) is given by Eq. (14).

Ecy ¼ð2bþ twÞðEwtw þ 2bEf Þ

2bð2aþ twÞð14Þ

4.2. Equivalent shear modulus of the web-foam core

The main function of GFRP web in the y-direction is to improvethe adhesive strength of the interfaces and provide the elastic sup-ports to the face sheet to avoid the occurrence of indentation andlocal wrinkling failure. Hence, we assume that the equivalent shearmodulus of the web-foam core is not affected by the GFRP web inthe y-direction.

The overall shear deflection of web-foam core is the sum of theweb and foam shear deflections. Based on the static relationship:

sxy ¼ swVw þ sf Vf ð15Þ

where sxy, sw and sf are the shearing stress of web-foam core, weband foam, respectively, and Vw and Vf are the volume ratio of weband foam, respectively, which can be obtained by

The geometrical relationship:

cxy ¼ cw ¼ cf ð16Þ

where cxy, cW and cF are the shear strain of web-foam core, web andfoam, respectively.

Using Hooke’s law, the corresponding stresses are

sxy ¼ cxyGxy ð17Þ

web core and (b) force equilibrium of Section I-I.

Table 5Comparison of analytical and experimental bending strength and stiffness.

Specimen Kbs (kN/mm) Ke (kN/mm) Kbs/Ke Ppre (kN) Pu (kN) Ppre/Pu

FPB50-CON 1.46 1.31 1.11 – 7.3 –FPB50-16 2.01 2.09 0.96 28.7 27.6 1.04FPB50-32 2.21 2.17 1.02 27.6 30.1 0.92FPB50-48 2.86 3.09 0.93 35.7 37.2 0.96FPB75-16 3.33 3.39 0.98 29.5 28.6 1.03FPB75-32 3.77 3.91 0.96 32.6 33 0.99FPB75-48 4.56 4.96 0.92 39.4 42.1 0.94FPB100-16 6.57 6.61 0.99 41.5 39.2 1.06FPB100-32 6.72 6.75 1.00 44.5 45.1 0.99FPB100-32-II 6.23 6.85 0.91 41.2 43.5 0.95

Ave. – – 0.98 – – 0.98St. DEV – – 0.06 – – 0.05

Table 6Comparison of analytical and experimental mid-span deflections.

Specimen Db,pre (mm) Ds,pre (mm) Dpre (mm) Du (mm) Dpre/Du

FPB50-CON 3.57 1.79 5.36 5.1 1.05FPB50-16 9.32 5.66 14.98 13.9 1.08FPB50-32 10.03 6.13 16.16 14.5 1.11FPB50-48 10.14 7.02 17.16 15.2 1.13FPB75-16 5.57 3.99 9.66 10.0 0.97FPB75-32 5.71 4.51 10.22 10.3 0.99FPB75-48 6.17 4.63 10.80 9.8 1.10FPB100-16 3.53 4.09 7.62 7.2 1.06FPB100-32 3.95 4.72 8.67 8.0 1.08FPB100-32-II 3.86 4.55 8.41 7.9 1.06

Ave. – – – – 1.06St. DEV – – – – 0.05

276 L. Wang et al. / Composites: Part B 67 (2014) 270–279

sw ¼ cwGw ð18Þ

sf ¼ cf Gf ð19Þ

where Gxy, Gw and Gf are the shear modulus of web-foam core, weband foam, respectively.

Substituting Eqs. (17)–(19) into Eq. (15) gives

Gxy ¼ GwVw þ Gf Vf ð20Þ

Similarly, the shear modulus of web-foam core Gxz and Gyz canbe obtained by Eqs. (21) and (22), respectively.

Gxz ¼ 1Vw

Gxz;wþ Vf

Gf

� ��ð21Þ

Gyz ¼ 1Vw

Gyz;wþ Vf

Gf

� ��ð22Þ

4.3. Equivalent bending stiffness of the GFFW panel

In accordance with the sandwich beam theory, the overallbending stiffness of GFFW panel (Kbs) can be expressed as [21]

Kbs ¼ Esdt3s6þ Es

dts hþ tsð Þ2

2þ Ec

dh3

12ð23Þ

where Es is the Young’s modulus of face sheet, and Ec is the equiv-alent Young’s modulus of foam-web core.

In Eq. (24), the first term can be neglected if 3 dtf

� �2> 100. Then

the overall bending stiffness can be expressed as

Kbs ¼Es

dts hþtsð Þ22 ; if

6Ests hþtsð Þ2

Ech3 > 100

Esdts hþtsð Þ2

2 þ Ec dh3

12 ; if6Ests hþtsð Þ2

Ech3 6 100

8<: ð24Þ

4.4. Analytical ultimate bending strength

For the face sheet compressive failure, if the bending stressreaches the compressive strength (fcy) of face sheet, the ultimatebending strength (Ppre) can be obtained by Eq. (25) [27].

Ppre ¼fcyKbs

Esl h2þ ts� � ð25Þ

where l is the span of the panel.For the core shear failure, Manalo et al. [28] developed a theo-

retical model considered the contribution of bending created bythe top and bottom face sheets in the shear force calculation. Thefailure load can be calculated by

Ppre ¼ 2scb 2tsGcGsþ h

� �ð26Þ

4.5. Prediction of mid-span deflection

For the GFFW panel under four-point bending, the mid-spandeflection of GFFW panel (Dpre) is the sum of the bending (Db)and shear (Ds) deflections of the panel,

Dpre ¼ Db þ Ds ð27Þ

Db ¼23Pl3

1296Kbsð28Þ

Ds ¼Pl

6AGcð29Þ

where l is the span of the panel, and AGc is the equivalent shearmodulus of foam-web core.

AGc ¼dGxzðhþ 2tsÞ

hð30Þ

4.6. Comparison between experimental and analytical results

The predicted bending strength, initial bending stiffness, bend-ing deflection, shear deflection and total mid-span deflection ofGFFW panel can be calculated by Eqs. (24)–(30), as presented inTables 5 and 6. In general, the proposed analytical model is ableto conservatively estimate the actual bending strength of theGFFW panels in four-point bending with an average underestima-tion of 2%, and standard deviation is 0.05. The largest variationbetween analytical and experimental results in the bendingstrength was 2.7 kN, which occurred in Specimen FPB75-48. Forthe prediction of mid-span deflections of the GFFW panels in

Fig. 9. The comparison of load–mid-span deflection curves obtained from tests and analytical model.

L. Wang et al. / Composites: Part B 67 (2014) 270–279 277

four-point bending, the average error and standard deviation are6% and 0.05, respectively. The largest variation and the maximumdeviation between analytical and experimental results in the mid-span deflection was 1.96 mm and 13%, respectively, whichoccurred in Specimen FPB50-48.

Fig. 9 shows the comparison of load–mid-span deflection curvesobtained from tests and analytical model. It can be found that thepredicted initial bending stiffness (Kpre) of panels were slightly less

than experimental results. The maximum deviation between ana-lytical and experimental results in the initial bending stiffnesswas 9%, which occurred in Specimen FPB100-32-II. Comparingthe analytical and experimental results reveals that the proposedanalytical model is generally able to conservatively estimate theinitial bending stiffness of the GFFW panels under four-point bend-ing with an average underestimation of 2.0%, and standard devia-tion is 0.06.

Fig. 9 (continued)

278 L. Wang et al. / Composites: Part B 67 (2014) 270–279

5. Conclusions

This paper presents the experimental and analytical studies onthe sandwich panels with GFRP face sheets and a foam-web coreloaded in four-point bending. The main findings of this study aresummarized as follows:

(1) The mechanical performance of sandwich panels with GFRPface sheets and a foam-web core loaded in four-point bend-ing was studied. These panels had the characteristics of highbending strength and stiffness, simple construction, and costeffectiveness.

(2) The experimental results show that compared to the normalsandwich panels, a maximum of an approximately 410%increase in the ultimate bending strength of GFFW panelscan be achieved due to the presence of webs.

(3) The thicker web and the larger web height can significantlyenhance the ultimate bending strength and initial bendingstiffness of GFFW panels.

(4) When the volume ratio of GFRP web was fixed, the ultimatebending strength and initial bending stiffness of GFFW pan-els were hardly affected by the web spacing.

(5) An analytical model was proposed to predict the bendingstrength, initial bending stiffness and mid-span deflectionof GFFW panels. The formulae to calculate the equivalentYoung’s mdulus and shear modulus of foam-web core werederived.

(6) Very good agreements between the experimental and ana-lytical results are found. The analytical model has beenshown to be able to accurately predict the strength, stiffnessand deflection of GFFW panels.

(7) This new type of sandwich panels with GFRP face sheetsand a foam-web core is still under development; the cor-responding finite element model will be established toinvestigate the performance of GFRP webs, and the mini-mum weight design procedure will also be provided afterconducting more experimental or numerical testing ofspecimens. In the meantime, although the anti-corrosionability of GFFW panels can be enhanced because the foamcore are confined by GFRP webs and face sheets, theflammability of panels should be researched in futurebecause the mechanical performance of GFFW panelsare affected significantly by the high temperature. More-over, no matter GFFW panels acting as the bridge decksor slabs, the fatigue issue cannot be ignored in futurestudy.

Acknowledgement

The research described here was supported by the Key Programof National Natural Science Foundation of China (Grant No.51238003).

L. Wang et al. / Composites: Part B 67 (2014) 270–279 279

References

[1] Romanoff J, Varsta P. Bending response of web-core sandwich beams. ComposStruct 2006;73:478–87.

[2] Romanoff J, Varsta P. Bending response of web-core sandwich plates. ComposStruct 2007;81:292–302.

[3] Flores-Johnson EA, Li QM. Experimental study of the indentation of sandwichpanels with carbon fibre-reinforced polymer face sheets and polymeric foamcore. Compos B Eng 2011;42:1212–9.

[4] Roberts JC, Boyle MP, Wienhold PD, White GJ. Buckling, collapse and failureanalysis of FRP sandwich panels. Compos B Eng 2002;33:315–24.

[5] Sokolinsky VS, Shen H, Vaikhanski L, Nutt SR. Experimental and analyticalstudy of nonlinear bending response of sandwich beams. Compos Struct2003;60:219–29.

[6] Borsellino C, Calabrese L, Valenza A. Experimental and numerical evaluation ofsandwich composite structures. Compos Sci Technol 2004;64:1709–15.

[7] Russo A, Zuccarello B. Experimental and numerical evaluation of themechanical behaviour of GFRP sandwich panels. Compos Struct 2007;81:575–86.

[8] Chen Z, Yan N. Investigation of elastic moduli of Kraft paper honeycomb coresandwich panels. Compos B Eng 2012;43:2107–14.

[9] Koh TM, Isaa MD, Feiha S, Mouritz AP. Experimental assessment of the damagetolerance of z-pinned T-stiffened composite panels. Compos B Eng2013;44:620–7.

[10] Rejaba MRM, Cantwell WJ. The mechanical behaviour of corrugated-coresandwich panels. Compos B Eng 2013;47:267–77.

[11] Petronea G, Raob S, De Rosa S, Maceb BR, Francoa F, Bhattacharyya D. Initialexperimental investigations on natural fibre reinforced honeycomb corepanels. Compos B Eng 2013;55:400–6.

[12] Roy R, Nguyen KH, Park YB, Kweon JH, Choi JH. Testing and modeling ofNomex™ honeycomb sandwich panels with bolt insert. Compos B Eng2014;56:762–9.

[13] Steeves CA, Fleck NA. Collapse mechanisms of sandwich beams withcomposite faces and a foam core, loaded in three-point bending. Part I:analytical models and minimum weight design. Int J Mech Sci 2004;46:561–83.

[14] Steeves CA, Fleck NA. Collapse mechanisms of sandwich beams with compositefaces and a foam core, loaded in three-point bending. Part II: experimentalinvestigation and numerical modeling. Int J Mech Sci 2004;46:585–608.

[15] Tagarielli VL, Fleck NA, Deshpande VS. Collapse of clamped and simplysupported composite sandwich beams in three-point bending. Compos B Eng2004;35:523–34.

[16] Sharaf T, Shawkat W, Fam A. Structural performance of sandwich wall panelswith different foam core densities in one-way bending. J Compos Mater2010;44:2249–63.

[17] Wang ZX, Shen HS. Nonlinear vibration and bending of sandwich plates withnanotube-reinforced composite face sheets. Compos B Eng 2012;43:411–21.

[18] Dawood M, Taylor E, Rizkalla S. Two-way bending behavior of 3-D GFRPsandwich panels with through-thickness fiber insertions. Compos Struct2010;92:950–63.

[19] Reis EM. Characteristics of innovative 3-D FRP sandwich panels. Doctoraldissertation, North Carolina State University; 2005.

[20] Reis EM, Rizkalla SH. Material characteristics of 3-D FRP sandwich panels.Constr Build Mater 2008;22:1009–18.

[21] Wu Z, Liu W, Wang L, Fang H, Hui D. Theoretical and experimental study offoam-filled lattice composite panels under quasi-static compression loading.Compos B Eng 2014;60:329–40.

[22] ASTM D3039/D3039M-08. Standard test method for tensile properties ofpolymer matrix composite materials, ASTM, PA, USA; 2008.

[23] ASTM D695-10. Standard test method for compressive properties of rigidplastics, ASTM, PA, USA; 2010.

[24] ASTM C297-04. Standard test method for flatwise tensile strength of sandwichconstructions, ASTM, PA, USA; 2004.

[25] ASTM C365-03. Standard test method for flatwise compressive strength ofsandwich cores, ASTM, PA, USA; 2004.

[26] ASTM C273/273M-07. Standard test method for shear properties for sandwichcores materials, ASTM, PA, USA; 2007.

[27] Allen HG. Analysis and design of structural sandwich panels. New York,USA: Pergamon; 1969.

[28] Manalo AC, Aravinthan T, Karunasena W. In-plane shear behaviour of fibrecomposite sandwich beams using asymmetrical beam shear test. Constr BuildMater 2010;24:1952–60.

http://refhub.elsevier.com/S1359-8368(14)00283-2/h0005http://refhub.elsevier.com/S1359-8368(14)00283-2/h0005http://refhub.elsevier.com/S1359-8368(14)00283-2/h0010http://refhub.elsevier.com/S1359-8368(14)00283-2/h0010http://refhub.elsevier.com/S1359-8368(14)00283-2/h0015http://refhub.elsevier.com/S1359-8368(14)00283-2/h0015http://refhub.elsevier.com/S1359-8368(14)00283-2/h0015http://refhub.elsevier.com/S1359-8368(14)00283-2/h0020http://refhub.elsevier.com/S1359-8368(14)00283-2/h0020http://refhub.elsevier.com/S1359-8368(14)00283-2/h0025http://refhub.elsevier.com/S1359-8368(14)00283-2/h0025http://refhub.elsevier.com/S1359-8368(14)00283-2/h0025http://refhub.elsevier.com/S1359-8368(14)00283-2/h0030http://refhub.elsevier.com/S1359-8368(14)00283-2/h0030http://refhub.elsevier.com/S1359-8368(14)00283-2/h0035http://refhub.elsevier.com/S1359-8368(14)00283-2/h0035http://refhub.elsevier.com/S1359-8368(14)00283-2/h0035http://refhub.elsevier.com/S1359-8368(14)00283-2/h0040http://refhub.elsevier.com/S1359-8368(14)00283-2/h0040http://refhub.elsevier.com/S1359-8368(14)00283-2/h0045http://refhub.elsevier.com/S1359-8368(14)00283-2/h0045http://refhub.elsevier.com/S1359-8368(14)00283-2/h0045http://refhub.elsevier.com/S1359-8368(14)00283-2/h0050http://refhub.elsevier.com/S1359-8368(14)00283-2/h0050http://refhub.elsevier.com/S1359-8368(14)00283-2/h0055http://refhub.elsevier.com/S1359-8368(14)00283-2/h0055http://refhub.elsevier.com/S1359-8368(14)00283-2/h0055http://refhub.elsevier.com/S1359-8368(14)00283-2/h0060http://refhub.elsevier.com/S1359-8368(14)00283-2/h0060http://refhub.elsevier.com/S1359-8368(14)00283-2/h0060http://refhub.elsevier.com/S1359-8368(14)00283-2/h0060http://refhub.elsevier.com/S1359-8368(14)00283-2/h0065http://refhub.elsevier.com/S1359-8368(14)00283-2/h0065http://refhub.elsevier.com/S1359-8368(14)00283-2/h0065http://refhub.elsevier.com/S1359-8368(14)00283-2/h0065http://refhub.elsevier.com/S1359-8368(14)00283-2/h0070http://refhub.elsevier.com/S1359-8368(14)00283-2/h0070http://refhub.elsevier.com/S1359-8368(14)00283-2/h0070http://refhub.elsevier.com/S1359-8368(14)00283-2/h0075http://refhub.elsevier.com/S1359-8368(14)00283-2/h0075http://refhub.elsevier.com/S1359-8368(14)00283-2/h0075http://refhub.elsevier.com/S1359-8368(14)00283-2/h0080http://refhub.elsevier.com/S1359-8368(14)00283-2/h0080http://refhub.elsevier.com/S1359-8368(14)00283-2/h0080http://refhub.elsevier.com/S1359-8368(14)00283-2/h0085http://refhub.elsevier.com/S1359-8368(14)00283-2/h0085http://refhub.elsevier.com/S1359-8368(14)00283-2/h0090http://refhub.elsevier.com/S1359-8368(14)00283-2/h0090http://refhub.elsevier.com/S1359-8368(14)00283-2/h0090http://refhub.elsevier.com/S1359-8368(14)00283-2/h0100http://refhub.elsevier.com/S1359-8368(14)00283-2/h0100http://refhub.elsevier.com/S1359-8368(14)00283-2/h0105http://refhub.elsevier.com/S1359-8368(14)00283-2/h0105http://refhub.elsevier.com/S1359-8368(14)00283-2/h0105http://refhub.elsevier.com/S1359-8368(14)00283-2/h0135http://refhub.elsevier.com/S1359-8368(14)00283-2/h0135http://refhub.elsevier.com/S1359-8368(14)00283-2/h0140http://refhub.elsevier.com/S1359-8368(14)00283-2/h0140http://refhub.elsevier.com/S1359-8368(14)00283-2/h0140

Mechanical performance of foam-filled lattice composite panels in four-point bending: Experimental investigation and analytical modeling1 Introduction2 Experimental program2.1 Description of test specimens and parameters2.2 Material properties2.3 Test set-up and instrumentation

3 Experimental results and discussion3.1 Failure mode3.2 Influence of web thickness3.3 Influence of web height3.4 Influence of web spacing

4 Analytical model4.1 Equivalent Young’s modulus of the web-foam core4.2 Equivalent shear modulus of the web-foam core4.3 Equivalent bending stiffness of the GFFW panel4.4 Analytical ultimate bending strength4.5 Prediction of mid-span deflection4.6 Comparison between experimental and analytical results

5 ConclusionsAcknowledgementReferences