A Comparison of Bending Properties for Cellular Core Sandwich Panels

doi:10.4236/msa.2013.48057

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Materials Sciences and Applications, 2013, 4, 471-477

http://dx.doi.org/10.4236/msa.2013.48057 Published Online August 2013 (http://www.scirp.org/journal/msa)

471

A Comparison of Bending Properties for Cellular Core

Sandwich Panels

Li Yang1, Ola Harrysson2, Harvey West2, Denis Cormier3

1Department of Industrial Engineering, University of Louisville, Louisville, USA; 2Department of Industrial & Systems Engineering,

North Carolina State University, Raleigh, USA; 3Department of Industrial & Systems Engineering, Rochester Institute of Technology,

Rochester, USA.

Email: [email protected]

Received May 15th, 2013; revised June 21st, 2013; accepted July 2nd, 2013

permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

ABSTRACT

In this study, various sandwich panel structures with different reticulate lattice core geometries were designed and then

fabricated in titanium via the electron beam melting (EBM) process. Bending tests were performed on the titanium sam-

ples, and mechanical properties such as modulus, bending strength, and energy absorption were evaluated. Different

failure mechanisms were observed, and it was found that sandwich structures with auxetic cores exhibited more homo-

geneous deflection and bending compliance compared with other structures. It was also demonstrated that properties of

auxetic sandwich structures can be tailored using different cell structure geometries to suit the needs of a given design

application. Furthermore, it was found that other 3D cellular sandwich structures can also exhibit high stiffness and

strength, which is desirable in potential applications.

Keywords: Auxetic Structure; Cellular Structure; Sandwich Panels; Electron Beam Melting; Bending Properties

1. Introduction

3D cellular structures possess unique advantages with

respect to specific strength, specific modulus, and energy

absorption at low densities. They are therefore promising

for applications that require light weight (e.g. aerospace,

automotive, etc.). Two-dimensional cellular structures

and foams are frequently used as sandwich structure

cores in order to provide increased bending and shearing

stiffness as well as energy absorption ability [1].

Among the range of possible cellular geometries, aux-

etic structures are of specific interest to researchers. Aux-

etic structures exhibit negative Poisson’s ratio in one or

more directions. These structures have been shown to

exhibit significantly improved shear performance com-

pared with regular structures [2-4]. According to the the-

ory of elasticity, the shear modulus of negative Poisson’s

ratio structures could become even larger than the bulk

moduli, making the structures ideal for use in sandwich

panel cores [5-7]. Furthermore, auxetic structures exhibit

synclastic bending [8-9], which also favors their potential

applications in curved sandwich panels and sandwich

skins for various applications.

Traditionally, auxetic structures have been fabricated

through multi-step processes in which specific control

over the cell geometry (i.e. strut sizes and angles) is quite

difficult. The relatively recent emergence of polymer and

metal additive manufacturing processes has given engi-

neers the ability to fabricate parts with precise cellular

geometries directly from the CAD models. It therefore

has become possible to fabricate these structures and to

compare their experimentally determined material prop-

erties with predicted values.

In the current study, sandwich structures with re-en-

trant auxetic cores as well as several other 3D reticulate

cellular core geometries were designed in CAD and then

fabricated via Arcam’s electron beam melting (EBM)

process. Mechanical properties pertinent to sandwich

structure performance were measured, including stiffness,

strength and energy absorption. A comparison of the

bending properties between different auxetic core de-

signs is provided to evaluate their potential in structural

applications.

2. Structural Designs

The unit cell of the 3D re-entrant lattice auxetic structure

used in this study is shown in Figure 1(a) [10,11]. This

auxetic structure is an orthotropic structure with direc-

tions x and y exhibiting identical properties due to the

A Comparison of Bending Properties for Cellular Core Sandwich Panels

472

(a) (b)

Figure 1. Design of the 3D re-entrant lattice structure.

symmetry. Therefore, the design of the structure could be

represented by the simplified 2D geometry shown in

Figure 1(b), which includes the length of the vertical (H)

and re-entrant (L) struts, the re-entrant angle θ, and the

thickness (t) of the strut (not shown in the figure). Li et al.

[12] showed that compressive properties of this auxetic

structure could be estimated as a function of design pa-

rameters H, L, θ, and t. The relationship between the

Poisson’s ratio values and the design parameters could be

written as:



22 2

12 34

6cos cos

sin 6sin4

Gt t

Et t

Gt tEtt

Et t



















(1)



sin

cos cos





  (2)

where νz and νx are Poisson’s ratios of the structure under

compression in the z and x directions respectively. Pois-

son’s ratios along the x and y axes are identical due to

symmetry of the structure (i.e. νx = νy). E and G are

Young’s modulus and shear modulus, α = H/L, t1 and t2

are dimensions of the re-entrant struts, and t3 and t4 are

dimensions of the vertical struts. The cross section of the

struts is taken as rectangular for this analysis, although

similar analysis’ can be performed for other cross sections.

The Poisson’s ratio values are expected to have a sig-

nificant effect on the mechanical properties of the re-en-

trant auxetic structures. With greater negative Poisson’s

ratio values, the modulus and strength of the structures

will also become greater [11,12]. In the current study,

two configurations were designed for the re-entrant au-

xetic structure with significantly different Poisson’s ra-

tios, as shown in Table 1. In Table 1, tV and tR stand for

the thickness of the square shaped vertical struts and re-

entrant struts, respectively.

The sandwich panels for bending tests were designed

as illustrated in Figure 2 using the two different auxetic-

core designs (A1 and A2). The dimensions of the sand-

wich panel cores were kept at approximately 17 mm × 20

mm × 150 mm while maintaining structural symmetry in

each direction. In addition, the thickness of the sandwich

skins was fixed at 0.75 mm. The resulting structures had 1 ×

2 × 14 auxetic unit cell repetitions for design A1, and 1.5 ×

2 × 20 auxetic unit cell repetitions for design A2.

From the unit cell orientation as shown in Figure 2, it

was known that under a bending load, the auxetic struc-

tures would be subject to compressive stress normal to

the bending load direction. According to Equation (2),

design A2 will have a higher νx value and would therefore

be expected to exhibit higher strength and higher mo-

dulus than design A1.

In order to compare the auxetic geometries with other

reticulate cellular geometries, octahedral, rhombic, and

hexagonal cellular structures were designed in CAD.

These geometries have been demonstrated elsewhere and

fabricated by electron beam melting [13-15]. The unit

cells of these structures are shown in Figure 3. Parame-

ter values for each structure are shown in Table 2. The

resulting sandwich panels had unit cell array counts of 2 ×

2 × 19 for the octahedral panel, 2 × 2 × 18 for the rhom-

bic panel, and 3 × 3 × 28 for the hexagonal panel. The

sandwich skin thickness for each design was fixed at 1

mm.

All of the cellular structure designs except for A1 pos-

sess similar relative densities as shown in Ta ble s 1 and 2.

According to the cellular theory, the relative density of a

structure has a significant influence on its mechanical

properties [16]. The selected geometries therefore permit

a high level comparison of material properties between

the different cellular geometries.

3. Experimental Procedures

Three titanium (Ti-6Al-4V) samples for each sandwich

panel design were fabricated using an Arcam A2 EBM

system using +325/−100 spherical powder. The powder

was made via the plasma rotating electrode (PREP)

process. Identical default process settings for electron

Table 1. Design parameter values for the re-entrant auxetic structure.

Design H (mm) L (mm) θ (Deg.) tV (mm) tR (mm) νx νz Relative Density (%)

A1 15 7.5 45 1 0.707 −1.704 −0.547 6.3

A2 7.595 4 70 1 0.940 −0.445 −1.658 11.6

A Comparison of Bending Properties for Cellular Core Sandwich Panels

473

Figure 2. The sandwich panel with auxetic core.

(a) (b) (c)

Figure 3. Unit cell designs for (a) octahedral; (b) rhombic;

and (c) hexagonal structures.

Table 2. Designs of various cellular structures.

Design L (mm) θ (Deg.) t (mm) Relative

Density (%)

O (Octahedral) 8 - 1 11.98

R (Rhombic) 4.65 60 1 11.00

H (Hexagonal) 3.19 120 1 11.72

beam melting of lattice geometries were used to produce

all samples. All samples were oriented in the build

chamber such that the two face skins were normal to the

build direction. Due to build chamber size limitations,

the 18 samples (total) were fabricated in two batches.

After the samples were cleaned, their dimensions were

measured using digital calipers, and their masses were

measured using a digital balance having a resolution of

0.0001 g.

Bending tests were carried out using an Applied Test

System 1620 C at a constant strain rate of 1.27 mm/min.

Three point bending tests were carried out with a support

span of L = 114.3 mm as shown in Figure 4. The support

rollers had a diameter of 12.7 mm, and the load roller had

a diameter of 25.4 mm. The displacement and load (F) of

the loading roller were recorded through the crosshead.

The test was automatically stopped when the loading

level of the roller dropped below 70% of the maximum

recorded loading level. The actual experimental setup is

further illustrated in Figure 5. An FEA analysis for each

model was also performed in order to compare predicted

material properties with actual measured properties. As

shown in Figure 6, each model was fixed at two strips on

Figure 4. Experimental setup for the three point bending

test.

Figure 5. Actual setup for the bending test.

Figure 6. FEA of the bending of the sandwich panel.

the bottom face, and then loaded at the strip on the center

of the top face. The width of each strip was 1 mm. Dur-

ing the FEA studies, loadings ranging from 1000 - 5000

N were simulated for each structure. The strength values

were obtained by determining the minimum loading level

for which the stress across the entire cross section of any

strut exceeded the yield strength of Ti-6Al-4V (1050

MPa).

4. Results and Discussion

The measured dimensions of fabricated titanium sam-

ples are listed in Tab le 3. In Table 3, D1 and D2 are the

A Comparison of Bending Properties for Cellular Core Sandwich Panels

474

Table 3. Actual parameters of the samples made by EBM.

Design D1 (mm) D2 (mm) L (mm) Mass (g) Relative Density (%)

A1 20.405 ± 0.259 22.538 ± 0.125 148.675 ± 0.155 45.063 ± 2.688 14.87 ± 0.81

A2 19.829 ± 0.153 16.222 ± 0.029 150.334 ± 0.140 45.852 ± 1.504 21.40 ± 0.60

O 23.292 ± 0.116 17.052 ± 0.029 151.875 ± 0.125 48.646 ± 0.616 18.20 ± 0.22

R 19.668 ± 0.205 17.230 ± 0.039 144.848 ± 0.073 41.647 ± 1.965 19.15 ± 0.73

H 20.616 ± 0.106 17.729 ± 0.000 160.274 ± 0.076 52.112 ± 1.242 20.08 ± 0.38

overall thickness and width of the sandwich panels, and

L is the total length. It could be seen that the dimensions

of the samples were quite consistent, indicating stable

process quality. The relative densities of the samples

were significantly larger than 0.1 due to the existence of

the surface skins. All the designs, except for A1, had

measured relative densities close to 0.2.

The thickness of the sandwich skins for auxetic de-

signs A1 and A2 were around 0.75 mm, while the thick-

ness of the skins for the other sandwich structures were

very close to 1 mm. According to the classic theory of

sandwich panels, skin thickness is the dominant factor

for the performance of the structure. However, prelimi-

nary FEA results with the designed structures showed

that the skin thickness hada minimal effect on the bend-

ing modulus of the sandwich panels. It is hypothesized

that this is due to the very low relative density of the core

structure which leads to large compliance that accom-

modates local deflections of the two skin panels. Fur-

thermore, preliminary study showed that for auxetic sand-

wich structures, the dominant failure mode during bending

was core shear, which is in turn determined by the geome-

tries of individual struts rather than the surface skin.

During bending, the upper region of the sandwich

panel is subject to compressive stress, while the lower

region is subject to tensile stress. For regular core struc-

tures, compressive stresses result in lateral expansion. As

a consequence, localized stress concentrations and poten-

tial wrinkling on the face skins can be expected. Con-

versely, auxetic structures with negative Poisson’s ratios

exhibit lateral shrinkage (or inward movement) under

compression and will therefore better accommodate ma-

croscopic structural deformation.

Figure 7(a) shows the auxetic sandwich panel defor-

mation during testing, whereas Figure 7(b) shows the

corresponding FEA simulation result. Figures 7(a) and

(b) both show very little localized deformation during

bending. Instead, the deflection is distributed along the

length of the sandwich panel homogeneously. Whereas

sandwich panels with foam cores typically fail via face

yield, core shear, indentation, delamination and face

wrinkle [5], the auxetic sandwich panels failed by frac-

ture of vertical struts under the combination of bending

and tension. Failure occurred at the vertical struts located

roughly at the middle section between the loading roller

and the support roller where the local deformation was at

its maximum as seen in Figure 7(a). Because of the

highly homogeneous distribution of deflection and stress,

this auxetic sandwich structure could potentially be use-

ful for applications such as structural beams. Since the

vertical struts are subject to critical failure, new designs

involving non-uniform strut sizes could be applied to fur-

ther improve the structural performance.

Figure 8 shows the deflection of the other sandwich

structures in FEA simulation. Again, the tested titanium

structures exhibited similar behavior as that predicted

from the FEA studies. It is apparent that for octahedral,

rhombic and hexagonal sandwiches, the stress distribu-

tions, and therefore the deformation of the structures,

was largely concentrated at the surface area where the

structure was loaded. Upon failure, face yield was observ-

ed for all three of these geometries.

Table 4 shows the bending strength and modulus re-

sults, as well as the total energy absorption for each type

of structure. The results for rhombic and octahedral sam-

ples showed an unusually high variation in maximum

force and therefore, the strength and the total energy ab-

sorption. It is noted that in order to produce comparable

relative densities between sample geometries, the rhom-

bic and octahedral samples had fewer unit cell repetitions

through the thickness of the samples. It is surmised that

the small number of unit cell repetitions through the

thickness of the samples contributed to this elevated de-

gree of variance. All the other type of structures showed

relatively consistent properties.

Comparing A1 and A2, it is apparent that A2 exhibited

significantly higher strength and modulus, as predicted.

With higher νz value, the modulus of A2 is about 7 times

that of A1, while the strength of A2 had an approximately

200% increase compared with A1. On the other hand,

design A1 exhibited significantly higher resilience com-

pared with A2. The maximum deflection for A1 was al-

most twice as much as that of A2. Although design A1

could withstand much greater deflection than A2, design

A2absorbed a considerable amount of energy during the

bending, as also shown in Table 4.

The octahedral, rhombic, and hexagonal sandwich

panels showed relatively high strength and modulus val-

A Comparison of Bending Properties for Cellular Core Sandwich Panels

475

(a)

(b)

Figure 7. The shape of (a) titanium auxetic sandwich and (b)

FEA model under bending.

ues compared with the auxetic sandwiches. However, the

maximum deflections of these structures were signifi-

cantly lower, indicated that these structures had rather

low overall structural ductility.

From the comparison, it was apparent that the auxetic

structures showed significantly superior performance in

terms of maximum deflection that can be tolerated. Al-

though design A1 exhibited lower strength and modulus

compared to the other designs, it absorbed a significant

amount of energy. Design A2 showed higher modulus

and strength compared to A1. Furthermore, the total en-

ergy absorption of A2 was about 100% higher than that

of A1. The octahedral, rhombic and hexagonal structures

showed significantly lower ductility compared to the au-

xetic sandwich structures, while possessing higher modu-

lus and potentially strength values. As a result, these

structures could exhibit energy absorption abilities com-

parable to the auxetic sandwich with larger negative

Poisson’s ratio values in the thickness direction.

It is known that for many applications, the energy ab-

sorption of the sandwich panels during bending is of

great interest. For energy absorption purposes, it is de-

sired that the structure exhibit low peak response force,

and high total energy absorption. Comparing the struc-

tures in Table 4, it is apparent that the auxetic structures

possess significant advantages over the other unit cell

geometries. At a similar peak response force level

(around 3000 N), the auxetic sandwich designs absorbed

about 100% more energy than the other designs. At the

same energy absorption level (about 9 J), the auxetic

structures had a response force of about 1200 N, which

(a)

(b)

(c)

Figure 8. FEA of the bending of various sandwich struc-

tures. (a) Octahedral; (b) Rhombic; (c) Hexagonal.

was significantly lower than the others. The other struc-

tures do not seem to be ideal candidates for energy ab-

sorption applications due to their significantly higher

response force level. However, their higher modulus and

strength properties make them potential candidates for

applications where high specific stiffness and static

strength of the sandwich panels are required.

A comparison between the FEA and the average ex-

perimental results is shown in Table 5 . The strength val-

ues of the FEA agree quite well with the experimental

results, while the modulus values from the FEA study are

uniformly higher than experimental results, especially for

the octahedral and hexagonal structures. Given that the

crosshead displacement was used to monitor the deflec-

tion of the beam, the compliance of the load cell, when

testing stiffer structures would reduce the measured

modulus.

It is worth noting that the ability of additive manufac-

turing processes such as EBM to fabricate engineered

cellular structures with any desired strut sizes and angles

opens up tremendous possibilities for further design op-

A Comparison of Bending Properties for Cellular Core Sandwich Panels

476

Table 4. Bending properties of various struc tures.

Design Max. Force (N) Max. Deflection (mm) Strength (MPa) Modulus (GPa) Energy Abs. (J)

A1 1206.43 ± 37.35 9.20 ± 0.77 22.04 ± 0.21 0.39 ± 0.02 8.73 ± 0.50

A2 3432.23 ± 58.58 5.96 ± 0.27 92.26 ± 1.62 2.98 ± 0.04 16.54 ± 1.61

O 5714.50 ± 977.40 2.61 ± 0.48 105.99 ± 18.83 5.23 ± 0.78 9.08 ± 0.17

R 3163.86 ± 966.96 2.92 ± 0.76 81.06 ± 23.39 4.65 ± 0.51 6.21 ± 4.39

H 5261.75 ± 199.04 3.13 ± 0.26 119.70 ± 3.48 6.20 ± 0.45 16.78 ± 2.68

Table 5. Comparison of FEA and experiments.

Design Measured Strength (MPa) FEA Strength (MPa) Measured Modulus (GPa) FEA Modulus (GPa)

A1 22.04 26.56 0.39 0.47

A2 92.26 75.00 2.98 3.26

O 105.99 103.12 5.23 10.85

R 81.06 82.50 4.65 6.46

H 119.70 111.94 6.20 9.06

timization of all of the cellular geometries examined in

this paper. For instance, critically loaded struts can be

fabricated with slightly larger diameters than other struts.

5. Conclusions

In the current work, sandwich panels with different cellu-

lar cores were designed and compared. Although the 3D

reticulate cellular core structures were not optimized for

bending, their overall performance showed promising

potential as future sandwich cores. During bending, the

auxetic sandwich panels exhibited homogeneous distri-

bution of stress and deformation. Failure by fracture of

the vertical struts located roughly at the middle section

between the loading and support rollers was seen in all

cases. Future studies should therefore focus on optimiza-

tion of the cellular structure based on the expected load-

ing patterns. Thickening of the critical vertical struts

would potentially lead to significant enhancements in

material properties with relatively little increase in mass.

The other sandwich structures showed significant stress

concentration at the loading area, and failed by face

yield.

The bending tests revealed that with different Pois-

son’s ratio values, the mechanical properties of the aux-

etic sandwich panels could be tailored over a wide range.

In addition, the auxetic sandwich panels also exhibited

extraordinary resilience under bending compared with all

the other structures. As a result, the auxetic sandwich

panels generally possess considerable potential specifi-

cally for energy absorption applications.

While the non-auxetic cellular geometries studied here

had relatively low ductility and arbitrarily chosen geo-

metrical parameters, they exhibited relatively high strength

and modulus. In addition, some of these designs also

exhibited high energy absorption during bending due to

the high modulus. In conclusion, these structures have

potential in applications where stiff and strong structural

beams are employed, and where high toughness is needed.

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