Accepted Manuscript

Theoretical and experimental study of foam-filled lattice composite panels un-

der quasi-static compression loading

Zhimin Wu, Weiqing Liu, Lu Wang, Hai Fang, David Hui

PII: S1359-8368(14)00002-X

DOI: http://dx.doi.org/10.1016/j.compositesb.2013.12.078

Reference: JCOMB 2870

To appear in: Composites: Part B

Received Date: 7 September 2013

Revised Date: 11 November 2013

Accepted Date: 30 December 2013

Please cite this article as: Wu, Z., Liu, W., Wang, L., Fang, H., Hui, D., Theoretical and experimental study of foam-

filled lattice composite panels under quasi-static compression loading, Composites: Part B (2014), doi: http://

dx.doi.org/10.1016/j.compositesb.2013.12.078

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Theoretical and experimental study of foam-filled lattice composite panels

under quasi-static compression loading

Zhimin Wua, Weiqing Liua*, Lu Wangb**, Hai Fanga, David Huic

a College of Civil Engineering, Nanjing University of Technology, Nanjing, China b Advanced Engineering Composites Research Center, Nanjing University of Technology, Nanjing, China

c Dept. of Mechanical Engineering, University of New Orleans, New Orleans, LA 70124, USA

Abstract

In this paper, a simple and innovative foam-filled lattice composite panel is proposed to upgrade

the peak load and energy absorption capacity. Unlike other foam core sandwich panels, this kind

of panels is manufactured through vacuum assisted resin infusion process rather than adhesive

bonding. An experimental study was conducted to validate the effectiveness of this panel for

increasing the peak strength. The effects of lattice web thickness, lattice web spacing and foam

density on initial stiffness, deformability and energy absorbing capacity were also investigated.

Test results show that compared to the foam-core composite panels, a maximum of an

approximately 1600% increase in the peak strength can be achieved due to the use of lattice webs.

Meanwhile, the energy absorption can be enhanced by increasing lattice web thickness and foam

density. Furthermore, by using lattice webs, the specimens had higher initial stiffness. A

theoretical model was also developed to predict the ultimate peak strength of panels.

Keywords: A. Glass fibres; A. Foams; B. Strength; D. Mechanical testing.

*Corresponding Author: Weiqing Liu, Tel: +86-25-58139862, Fax: +86-25-58139863, Email: wqliu@njut.edu.cn **Corresponding Author: Lu Wang, Tel: +86-25-58139871, Fax: +86-25-58139877, Email: kevinlwang@hotmail.com

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1. Introduction

Sandwich panels have been widely used for constructing bridge decks, temporary landing

mats and thermal insulation wall boards due to better performance in comparison to other

structural materials in terms of enhanced stability, higher strength to weight ratios, better energy

absorbing capacity and ease of manufacture and repair. In sandwich panels, low density material,

known as core, is usually adopted in combination with high stiffness face sheets to resist high

loads [1]. The most common types of core 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 provide resistance to face sheets to avoid

local buckling.

Extensive experimental studies of composite sandwich panels with balsa wood core have been

conducted in the past two decades [2-5]. Osei-Antwi et al.[6] investigated the shear mechanical

characterization of composite sandwich panels with balsa wood core. Six specimens, cut from

the panels in accordance with the three principal shear planes, were tested. The test results

indicated that shear stiffness and strength increased with increasing density of the 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 method for the balsa

sandwich cores by vacuum assisted resin infusion, and conducted the experimental study on

these cores under shear force. The test results revealed that the new manufacturing method can

increase stiffness and strength of the balsa sandwich cores. However, the compressive and shear

stiffness and strength of balsa wood have very large variations due to the natural and anisotropic

characteristics of the material. Hence, a lot of material tests have to be carried out to obtain

reliable values for practical design. Furthermore, appropriate fire and corrosion protections

should be provided due to the use of wood.

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Up to now, many investigations of geometric configurations have been conducted to find more

effective lightweight energy absorbing structures [8-21]. Cartie and Fleck [22] studied the

compressive strength of foam-cored sandwich panels with pin-reinforcements. The test results

showed the compressive strength and energy absorption capacity of the sandwich panels were

increased. In the buckling analysis of pin- reinforcements, the foam core was considered as an

elastic Winkler foundation in supporting the pins. The compressive strength was governed by

elastic buckling of the pins. Furthermore, the relationship between the compressive strength and

loading rate was studied. Fan et al. [23] tested a series of multi-layered glass fiber reinforced

composite woven textile sandwich panels under quasi-static compression loading. Their test

results revealed that energy absorption of the multi-layered panel was greatly improved and far

exceeded that of the monolayer panel of the same thickness, and the failure mode was

progressively monolayer collapses. The authors also conducted the bending tests of multi-layered

glass fiber reinforced composite woven textile sandwich panels [24]. The failure mode was

associated with the crippling and shear failure within the face sheets, and the load capacity was

dictated by the fracture strength of the face sheets. Meanwhile, the authors pointed that the

plastic hinge mechanism made the panels to possess a long deflection plateau after the peak

strength. As an effectively kind of energy absorbing structures, the egg-box shape has also

extensively been investigated [25-27]. Yoo et al. [28] carried out the compressive tests on foam-

filled composite egg-box panels to evaluate the energy absorbing capacity. The crack initiation

and propagation of composite egg-box cores without foam were observed and analyzed.

Furthermore, the possible use of foam-filled composite egg-box panels as a thermal insulation

wall board for membrane type liquefied natural gas ships was also evaluated. Although a lot of

geometric configurations for energy absorbing structures have been developed in recent years,

the majority of them have been applied to various protective packaging and crashworthiness

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structures for automobiles, ships and aero planes rather than civil engineering structures, because

the compressive, shear and bending stiffness of these composite panels are low, the

manufacturing process of these geometric configurations is complicated, and the cost of

production may stay at a relative high level. Choy et al. [29] developed two types of sandwich

panels, namely the fiber inserted foam panels and the aluminum foil covered panels. Their test

results proved that the bending stiffness of these panels was increased. However, these panels

were used to reduce the noise and isolate the vibration in the air conditioning. Hence, the

composite panels with these geometric configurations are hardly extended to civil engineering

field.

Chen and Davalos have investigated the strength and stiffness properties of composite

sandwich deck panels with sinusoidal core geometry in the past few years. The compressive and

shear tests of FRP sandwich deck panels with sinusoidal core geometry have been conducted

[30]. Chopped Strand Mat, composed of E-glass fibers and polyester resin, was used for the core

material. The test results showed that the typical shear failure mode was delamination at the

core-face sheet bonding interface, and the maximum strength of these panels was determined by

the number of bonding layers and core thickness. An analytical model for the buckling capacity

of FRP panels with two loaded edges partially constrained was proposed by Davalos and Chen

[31]. By considering the skin effect, Chen and Davalos [32] obtained an accurate solution of the

transverse shear modulus and the interfacial stress distribution for sandwich structures with

sinusoidal core. However, in their studies, the critical buckling stress of sinusoidal core is usually

low, which is obviously caused by the absence of restriction from foam core. Hence the

compressive strength of panels cannot be improved. Meanwhile, the energy absorbing capacity

of panels was not evaluated.

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To address the aforementioned shortcoming, a simple and innovative foam-filled lattice

composite panel, manufactured through vacuum assisted resin infusion process [33], is

developed in this study, as shown in Fig. 1. The face sheets, lattice webs and foam cores are

combined by vacuum infusing resin, which can enhance the peel resistance between face sheets

and foam cores. Unlike other foam-core sandwich composite panels, the compressive strength of

foam is improved due to the confinement effects provided by lattice webs, and the foam cores

can also restrict the local buckling of the lattice webs. Hence, the compressive strength of foam-

filled lattice composite panels can be improved significantly. An experimental study was

conducted to validate the effectiveness of this new type of panel. The peak strength, initial

stiffness, deformability and energy absorbing capacity were investigated. A theoretical model

was also developed to predict the ultimate peak strength of panels.

2. Manufacture process

The manufacture process can be divided into the following six steps: (i) four GFRP mats are

placed on a large flat board as shown in Fig. 2(a), and the fiber orientation angle is 0/900 to the

panel horizontal axis; (ii) the foams are cut into cubes according to the design dimensions, and

then wrapped using GFRP with ±450 fiber orientation angle see Fig. 2(b); (iii) to place four

GFRP mats on the foam cores, and the fiber orientation angle is also 0/900 to the panel horizontal

axis; (iv) before vacuum infusing UPR, the stripping cloth, diversion cloth and a thicker cover

plate which is used to make the face board flat are installed, respectively, as shown in Fig. 2(d);

(v) the unsaturated polyester resin is infused into the vacuum bag due to the effect of

atmospheric pressure (see Fig. 2(e)); (vi) After UPR curing, the manufacture of foam-filled

lattice composite panels is completed, and then the panels are cut in accordance with special

requirements, as shown in Fig. 2(f).

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3. Theoretical model

3.1. Local buckling of the GFRP web

The local buckling of the GFRP web can be analyzed using elastic foundation model, as

shown in Fig. 3(a). The foam is represented by the spring with a stiffness of k (per unit width and

length). In accordance with classical theory of elastic stability [34], the governing differential

equation for the stability analysis of web is expressed as

where D is the bending stiffness of the web, which can be determined by

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

The energy associated with the web deforming (U1) and the energy associated with the applied

loading (U2) are respectively given by

The loaded edges of web are fixed supports, and unloaded edges are simply supports. The

web is only subjected to a uniform axial compression 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 in the x-direction,

the boundary conditions of web at the loaded and unloaded edges are

when x = 0 or x = h, w = 0 and dw/dx = 0

when y = 0 or y = b, w = 0 and d2w/dx2 = 0

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Assuming that the deflection functions in the x and y directions are the cosine and sine

functions, respectively, the deformed shape can be expressed as

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

where U3 is the energy associated with elastic foundation, defined as

According to the principle of minimum potential energy,

The critical buckling stress (fcr) can be calculated by

3.2. Ultimate axial load capacity

The panel can be considered as consisting of closed web-foam core (CWFC) element (Part I)

and unclosed web-foam core (UWFC) element (Part II), as shown in Fig. 3(c). For the CWFC

element, the depth and width are a and b, respectively. The thickness of web is t/2. By

considering force equilibrium, the theoretical peak strength of the CWFC element (Pc,pre) can be

expressed as

where AW and AF are cross-sectional areas of the web and foam, respectively, fW is the axial

compressive strength of web, and fF ’ is the axial compression strength of the confined foam,

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which can be calculated by

where fF is the compressive strength of the unconfined foam, k1 is the effectiveness coefficient of

confinement, which is equal to 2.98 [35], fl is the lateral confining pressure, and ks is the shape

factor, which can be calculated by

where Ae is the effective confinement area, and RF is the corner radius.

Teng et al. [35] proposed the following formula to calculate the lateral confining pressure fl of

confined foam:

where fWt is the tension strength of web.

For the UWFC element, because the GFRP web can not provide the effective lateral confining

pressure to the foam, the effect of compressive strength of foam on the ultimate peak strength

can be ignored. Hence, the theoretical peak strength of the UWFC element (Pu,pre) can be

expressed as

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

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

4. Experimental program

4.1. Test specimens

The specimens were manufactured using a vacuum assisted resin 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 sheets and webs. The panels were

filled urethane foams (UF) with variation density (40 kg/m3, 60 kg/m3 and 80 kg/m3). During

vacuum infusion 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. The specimen was cut from the

panels, and it was representative of a symmetric volume element of the structure when subjected

to compression loading, as shown in Fig. 1(a). All specimens had the same width (w=200 mm)

and length (d=200 mm). Specimens H5D4, H5D6, H7D6 and H5D8 were control specimens

without webs to demonstrate the mechanical performance of the normal foam core GFRP

sandwich panels. The other specimens were strengthened by webs with varying foam density (ρ),

thickness of the lattice web (t) and spacing of the lattice web (s). The details of specimens are

given in Table 1.

(1) Webs with either 50 mm, 75 mm or 100 mm height, designated as H5, H7 and H1,

respectively.

(2) Webs with either 2.4 mm, 4.8 mm or 7.2 mm thickness, designated as T2, T4 and T7,

respectively.

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(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 cubic foam samples of 50 mm thick were made and tested in

accordance with ASTM D1621-10 [36] to obtain the compressive strength and the Young’s

modulus. Table 2 shows the cube compressive strength and the Young’s modulus for each foam.

Tensile and compressive tests, based on ASTM D3039/D3039M-08 [37] and ASTM D695-10

[38] respectively, were carried out to determine the tensile strength, the tension Young’s

modulus, the compressive strength and the compression Young’s modulus of web. The material

tension and compression properties of web are summarized in Table 3.

4.3. Test set-up and Instrumentation

Fig. 4 shows the test set-up. The support system consisted of a steel framed structure. The base

of the frame was bolted to the strong floor of the Structural Engineering Laboratory at Nanjing

University of Technology. Loading was applied by a hydraulic actuator with an axial capacity of

500 kN. Prior to the compressive test, two surfaces of the specimen were connected to 20-mm-

thick steel plates, and the specimens were placed at the center of the loading system. The load

was applied under displacement control with a displacement rate at 0.015 mm/s.

Vertical loading data was collected via a five-channel load cell which was mounted directly

beneath the panels. Axial shortening was measured by four linear variable displacement

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transducers (LVDTs) which were internal to the vertical actuator. The displacement data

reflected the total displacement of the top surface of the panel 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)

where Py and Δy are yield load and corresponding yield displacement, respectively. According to

the load-displacement curves as shown in Figs. 5 to 7, it should be noted that the specimens

exhibited an approximate linear behavior until failure occurs, hence, the yield load (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 energy absorption (Se), are summarized in Table 4. Fig. 5 and

Fig. 8(a) show the 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 H5T7S7D6 increased by 447.8%, 1317.3% and 2377.3%, respectively, and the

K1 of Specimens H5T2S7D6, H5T4S7D6 and H5T7S7D6 increased by 2051.8%, 4535.1% and

6416.4%, respectively. Compared to Specimen H7D6 (Pu = 20.15 kN, K1 = 4.01 kN/mm), the Pu

of Specimens H7T2S7D6, H7T4S7D6 and H7T7S7D6 increased by 698.9%, 1523.7% and

1581.3%, respectively, and the K1 of Specimens H5T2S7D6, H5T4S7D6 and H5T7S7D6

increased by 1375.8%, 3062.3% and 4700.2%, respectively. Compared to Specimen H5D4 (Pu =

4.66 kN) and H5D8 (Pu = 35.23 kN), the Pu of Specimens H5T2S5D4 and H5T2S5D8 increased

by 5314.4% and 807.2%, respectively. This may be due to the fact that thicker web can provide

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higher lateral confining pressure to the foam as presented in Eq. (14), then the compressive

strength of the confined foam can be enhanced. Meanwhile, the thicker web can lead to a larger

axial stiffness. Hence, the use of thicker web can improve the strength and initial stiffness of

panels significantly.

Fig. 6 and Fig. 8(b) illustrate the effects of lattice web spacing on the Pu and K1 of panels.

According to Fig. 6(a) and Fig. 8(b), for the specimens with 70mm web height, 2.4mm web

thickness and 60 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 Specimen H7T2S7D6 (s = 70 mm) and H7T2S1D6 (s = 100 mm), respectively, and 73.5%

and 84.4% larger than the K1 of Specimen H7T2S7D6 and H7T2S1D6, respectively. According

to Fig. 6(b) and Fig. 8(b), for the specimens with 70mm web height, 6.8mm web thickness and

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 Specimen

H7T7S7D6 (s = 70 mm) and H7T7S1D6 (s = 100 mm), respectively, and 13.8% and 91.8%

larger than the K1 of Specimen H7T2S7D6 and H7T2S1D6, respectively. According to Eq. (14),

the smaller web spacing can result in a larger lateral confining pressure to the foam, which can

improve the compressive strength of the confined foam. Therefore, decreasing the web spacing

can increase the peak strength of panels.

Fig. 7 and Fig. 8(c) illustrate the effects of foam density on the Pu and K1 of the panels.

Compared to Specimen H5T2S5D4 (Pu = 252.31 kN, K1 = 162.78 kN/mm), the Pu of Specimens

H5T2S5D6 and H5T2S5D8 increased by 5.1% and 26.7%, respectively, and the K1 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 Specimens H1T2S1D6

and H1T2S1D8 increased by 6.4% and 15.9%, respectively, and the K1 of Specimens H1T2S1D6

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and H1T2S1D8 increased by 8.2% and 22.1%, respectively. The foam with higher density also

behaves stiffer. Hence higher density foam can provide much more resistance to the applied

loads. Therefore, a larger foam density can give a higher peak strength and initial stiffness.

5.2. Compressive behavior and failure modes

According to the load-displacement curves, the deformation of specimens can be divided into

three stages: linear-elastic stage, post-yield stage and foam densification stage. All specimens

exhibited a linear-elastic response up to failure at the elastic stage. In the post-yield stage, the

compressive load capacity decreased sharply, which was associated with buckling of lattice webs,

as shown in Fig. 9(b). The compressive load capacity of lattice composite panels roughly stayed

at a half of peak strength level, while the compressive load capacity of control specimens kept

peak load level. In the foam densification stage, the compressive load capacity of panels

increased, but the deformation of panels was very large. With an increasing applied load, the

buckled webs violently extruded the foam, which resulted in crushing of the foam, as shown in

Fig. 9(c).

For the sandwich members, there are usually five failure modes including 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 core shear and

indentation failure usually occurred when the sandwich panels subjected to the concentrated

compression loading. In this study, the failure mode of all the specimens was quite similar.

However, the mentioned failure modes were not observed in this study because sandwich panels

were tested under uniform distributed 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 buckling failure. The microscopic phenomena which originate

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the corresponding failure modes can be summarized, respectively, as follows: (1) the

compressive stress of the web reaches its yield stress before the occurance of the local buckling,

and (2) the critical buckling stress of the web is less than its yield stress. According to the critical

buckling stress obtained from Eq. (9), the failure mode of panels can be judged.

5.3. Stroke efficiency

The stroke efficiency (Ste) is introduced to evaluate the deformability of a panel. The load-

displacement responses of the specimens as shown in Figs.4-6 can be idealized as a quadri-linear

curve (Fig. 10). Because specimens exhibited an approximate linear response up to failure, a line

OA can be considered as a tangent line to the load-displacement curve before reaching the peak

strength. The line BC can be drawn according to the average value of the compressive strength in

the post-yield part. A tangent line CD to the load-displacement curve in the region of

densification of foam can be drawn and its intersection point with line BC is point C. The

horizontal coordinate value corresponding to point C is the stroke length (Δst). The stroke

efficiency [39] is defined as the ratio of the stroke length to the height of a panel (H), thus

Fig. 11(a) shows a distinct decrease of the measured stroke efficiencies with increasing web

thickness. The Ste of Specimens H5D6 and H7D6 (without web) were largest compared to the

corresponding lattice web composite panels. The Ste of Specimens H5T2S7D6 and H7T2S7D6

with 2.4 mm lattice web thickness reduced to 62.6% and 67.9%, respectively. The panels with

the thickest lattice webs had the lowest values of Ste (57.9% for H5T7S7D6, and 59.8% for

H7T7S7D6). The reason of this phenomenon was that the thicker webs can lead to the larger

axial stiffness of the panel, hence, the stroke length become small for a given compressive load.

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Fig. 11(b) shows a slight increase of the measured stroke efficiencies with increasing lattice

web spacing. Compared to Specimen H7T2S5D6 (s = 50 mm), the Ste of Specimens H7T2S7D6

(s = 70 mm) and H7T2S1D6 (s = 100 mm) increased by 4.3% and 12.1%, respectively.

Compared to Specimen H7T7S5D6 (s = 50 mm), the Ste of Specimens H7T7S7D6 (s = 70 mm)

and H7T7S1D6 (s = 100 mm) increased by 6.9% and 14.9%, respectively. Because the larger

web spacing can give a smaller volume ratio of the web to the whole panel, hence the axial

stiffness of the panel decrease, which lead to an increase in the stroke length.

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

For Specimen H5T2S5D4 with 40 kg/m3 foam density, the measured stroke efficiency was

56.1%, while for Specimen H5T2S5D8, the Ste reduced to value of 44.7% due to the higher foam

density (ρ = 80 kg/m3). Although the difference in the web height and spacing, both curves in Fig.

10(c) show a similar trend. The Ste of Specimen H1T2S1D4 with 40 kg/m3 foam density was

28.0%, which was 12.4% and 15.1% larger than that of Specimen H1T2S1D6 (ρ = 60 kg/m3 )

and Specimen H1T2S1D6 (ρ = 60 kg/m3), respectively. Seitzberger et al. [39] proposed that the

reduction of the stroke efficiency is related to the foam behavior. With increasing foam density,

the region of densification, where the compressive force starts to increase steeply, was shifted to

lower values of the compressive strain. The foam suffered very large compressive 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]

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

where P is the applied compressive force, and Δ is the displacement of specimen (with

integration variable ). Assuming that the contribution due to elastic deformations is negligible,

W can approximately be regarded as the energy dissipated by plastic deformation.

Fig. 12(a) shows the effects of lattice web thickness on the specific energy absorption of the

panels. For the specimens with 70 mm web height, 70 mm web spacing and 60 kg/m3 foam

density, the Se of Specimen H7T7S7D6 (t = 7.2 mm) was 4.3, which was 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 web height, 70 mm web

spacing and 60 kg/m3 foam density, the Se of Specimen H5T7S7D6 (t = 7.2 mm) was 4.1, which

was 485.7%, 141.2% and 17.1% larger than the Se of Specimen H5D6 (without lattice webs),

H5T2S7D6 (t = 2.4 mm) and H5T4S7D6 (t = 4.8 mm), respectively. Hence, the lattice web

thickness can play an important role in increasing the energy absorption of the panels.

Fig. 12(b) shows the effects of lattice web spacing on the specific energy absorption of the

panels. For the specimens with 70 mm web height, 2.4 mm web thickness and 60 kg/m3 foam

density, the Se of Specimen H7T2S5D6 (s = 50 mm) was largest, which was equal to 3.9, the Se

of Specimens H7T2S7D6 (s = 70 mm) and H7T2S1D6 (s = 100 mm) were 3.3 and 2.4,

respectively. For the specimens with 70 mm web height, 7.2 mm web thickness and 60 kg/m3

foam density, the Se of Specimen H7T7S5D6 (s = 50 mm) was largest, which was equal to 5.2,

the Se of Specimens H7T7S7D6 (s = 70 mm) and H7T7S1D6 (s = 100 mm) were 4.3 and 3.6,

respectively. The test results indicated that the smaller lattice web spacing of the panels can

achieve the larger energy absorption.

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Fig. 12(c) shows the effects of foam density on the specific energy absorption of the panels.

For the specimens with 50 mm web height, 2.4 mm web thickness and 50 mm web spacing, the

Se of Specimen H5T2S5D4 (ρ = 40 kg/m3) was 2.6, which was 19.2% and 34.6% smaller than

that of Specimen H5T2S5D6 (ρ = 60 kg/m3) and H5T2S5D8 (ρ = 80 kg/m3), respectively. For

the specimens with 100 mm web height, 2.4 mm web thickness and 100 mm web spacing, the Se

of Specimen H1T2S1D4 (ρ = 40 kg/m3) was 3.7, which was 8.1% and 18.9% smaller than that of

Specimen H1T2S1D6 (ρ = 60 kg/m3) and H1T2S1D8 (ρ = 80 kg/m3), respectively. Thus, the

energy absorption of the panels 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 panels with sinusoidal core geometry

under compression loading. The face sheets and cores consisted of chopped strand mat. For each

specimen, the volume ratio of the core respect to the whole panel (η) was calculated. Table 5

compares the peak strength and initial stiffness presented in Chen and Davalos [30] with those of

Specimen H5T7S7D6 because the value of η of Specimen H5T7S7D6 is similar with their

specimens. Compared to Specimen H5T7S7D6, 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 buckling stress of web can be increased due to the restriction

from foam cores, and the compressive strength of the foam is also improved because of the

confinement provided by webs. Hence, even the value of η of Specimen H5T7S7D6 is slightly

smaller, larger peak strength and initial stiffness can be achieved.

7. Comparison with available experimental results

18

Table 4 summarized the theoretical ultimate peak strength of panels. During the calculation,

Specimens H5T2S5D4, H5T2S5D6, H5T2S5D8 and H7T2S5D6 failed by local buckling of web.

The critical buckling stresses of them were 36 MPa, 40 MPa, 54 MPa and 51 MPa, respectively.

For the foam-filled lattice composite panels, the largest variation between theoretical and

experimental results in the ultimate peak strength was 18%, which occurred in Specimen

H5T2S5D8. In general, comparing the theoretical and experimental ultimate peak strengths

reveals that the proposed theoretical model is able to conservatively estimate the actual ultimate

peak strength of panels under quasi-static compression loading 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 compression loading. The main findings of this study are summarized as

follows:

(1) A kind of foam-filled lattice composite panels applied to civil engineering field was

developed through vacuum assisted resin infusion process. The comparison between the

available test results of Chen and Davalos [30] and the test results was presented. These

panels had the characteristics of high compressive stiffness and strength, and strong energy

absorbing capacity.

(2) The experimental results show that compared to the foam-filled composite panels, a

maximum of an approximately 1600% increase in the peak load of panels can be achieved

due to the use of lattice webs.

(3) The thicker lattice web and smaller lattice web spacing can enhance the peak load of panels

significantly, but the effects of foam density on the peak load of panels are small.

19

(4) A quadri-linear curve was proposed to idealize the load-displacement responses of panels.

The stroke length can be determined according to the quadri-linear curve.

(5) The thiner lattice web and larger lattice web spacing can the improve stroke efficiency of

panels, while the larger foam density can decrease the stroke efficiency of panels because the

larger density foam, suffered larger compressive strain, can provide much more resistance to

prevent the folds from touching each other.

(6) The energy absorption of panels is affected by lattice web thickness, lattice web spacing and

foam density. Larger energy absorption can be achieved by increasing the lattice web

thickness and foam density and decreasing the web spacing.

(7) Overall, it has been demonstrated that the foam-filled lattice composite panels exhibited

better performance than the normal foam-core sandwich panels. It is expected that the foam-

filled lattice composite panels can be widely used as bridge decks, formworks and wall

boards.

Acknowledgements

The research described here was supported by the Key Program of National Natural Science

Foundation of China (Grant No. 51238003), Natural Natural Science Foundation for the Youth

(Grant No. 51008157) and Key University Science Research Project of Jiangsu Province (Grant

No. 12KJA580002).

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20

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24

(a) (b)

Fig. 1. The foam-filled lattice composite panels (a) photo of Specimen H5T2S5D6 and (b) schematic diagram

Face sheet

Foam

Lattice web

25

(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 v and (f)

manufacturing step vi

Stripping cloth

Diversion cloth

GFRP mat

26

(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)

GFRP Web

a

b

27

Fig. 4. Test set-up

Specimen

Load cell

28

(a) (b)

(c) (d)

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

mm, ρ =80 kg/m3

29

(a) (b)

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

30

(a) (b)

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

31

(a) (b)

(c) 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

32

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

stage and (c) foam densification stage

(a)

(b)

(c)

Local buckling Local

buckling

33

Fig. 10. The idealized load-displacement curve

(a) (b)

(c)

Fig. 11. The stroke efficiency of the panels (a) the effects of lattice web thickness; (b) the effects of lattice web spacing and (c) the effects of foam density

Quatri-linear approx.

Actural Behavior

A

B C

D

34

(a) (b)

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

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

35

Table 1. Details of specimens.

Specimen H (mm)

s (mm)

h (mm)

t (mm)

ρ (kg/m3)

H5D4 54.8 - 50 - 40

H5D6 54.8 - 50 - 60

H7D6 74.8 - 70 - 60

H5D8 54.8 - 50 - 80

H5T2S5D4 54.8 50 50 2.4 40

H5T2S5D6 54.8 50 50 2.4 60

H5T2S5D8 54.8 50 50 2.4 80

H5T2S7D6 54.8 75 50 2.4 60

H5T4S7D6 54.8 75 50 4.8 80

H5T7S7D6 54.8 75 50 7.2 80

H1T2S1D4 104.8 100 100 2.4 40

H1T2S1D6 104.8 100 100 2.4 60

H1T2S1D8 104.8 100 100 2.4 80

H7T2S5D6 74.8 50 70 2.4 60

H7T2S7D6 74.8 75 70 2.4 60

H7T2S1D6 74.8 100 70 2.4 60

H7T7S5D6 74.8 50 70 7.2 60

H7T4S7D6 74.8 75 70 4.8 60

H7T7S7D6 74.8 75 70 7.2 60

H7T7S1D6 74.8 100 70 7.2 60

36

Table 2. Material properties of Foams. Foam density D (kg/m3)

Yield strength ffy (MPa)

Young’s modulus Ef (MPa)

40 0.163 4.83

60 0.358 9.38

80 0.609 14.70

Table 3. Material properties of lattice webs. Compression Yield strength fcy (MPa) Young’s modulus Ec (GPa) 59.76 5.66

Tension Yield strength fty (MPa) Young’s modulus Et (GPa) 296.31 6.41

Table 4. Experimental and theoretical results of specimens. Specimen Pu (kN) K1

(kN/mm) Ste (%)

m ( g )

W(Δst) (kJ)

Se (kJ/kg)

Ppre (kN)

Ppre / Pu

H5D4 4.66 1.86 68.5 771 0.13 0.2 6.52 1.40

H5D6 18.09 2.99 67.2 811 0.57 0.7 14.32 0.79

H7D6 20.15 4.01 73.5 859 1.23 1.4 14.32 0.71

H5D8 35.23 7.03 64.3 851 1.07 1.3 24.36 0.69

H5T2S5D4 252.31 162.78 56.1 1109 2.88 2.6 229.84 0.91

H5T2S5D6 265.11 186.7 49.3 1147 3.55 3.1 240.33 0.91

H5T2S5D8 319.61 202.28 44.7 1191 4.16 3.5 261.10 0.82

H5T2S7D6 99.09 64.34 62.6 1062 1.77 1.7 113.65 1.15

H5T4S7D6 56.39 138.59 60.2 1312 4.58 3.5 284.33 1.11

H5T7S7D6 448.14 194.84 57.9 1563 6.34 4.1 489.69 1.09

H1T2S1D4 308.1 174.07 28 1109 4.12 3.7 260.34 0.84

H1T2S1D6 27.84 188.41 24.9 1134 4.55 4.0 272.36 0.83

H1T2S1D8 357.13 212.58 24.3 1195 5.29 4.4 299.32 0.84

H7T2S5D6 278.23 102.67 65.1 1327 5.15 3.9 230.97 0.83

H7T2S7D6 160.97 59.18 67.9 1102 3.65 3.3 175.56 1.09

37

H7T2S1D6 103.03 55.69 73 1093 2.64 2.4 117.89 1.14

H7T7S5D6 624.31 219.06 56 2267 11.73 5.2 689.82 1.10

H7T4S7D6 327.18 126.81 65.8 1687 6.52 3.9 347.63 1.06

H7T7S7D6 338.79 192.49 59.8 1912 8.19 4.3 325.41 0.96

H7T7S1D6 285.55 114.22 64.3 1560 5.66 3.6 310.63 1.09

Mean - - - - - - - 0.97

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

Specimens Pu,chen (kN)

K1,chen (kN/mm)

η (%) Pu,chen /Pu,H5T7S7D6 (%)

K1,chen /K1,H5T7S7D6 (%)

B1C2 155.54 86.41 24.4 34.7 44.3

B2C2 163.07 148.25 23.1 36.4 76.1

B3C2 177.22 136.32 22.1 39.5 70.0

H5T7S7D6 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].