Flexural behavior of sandwich beams fabricatedby vacuum-assisted resin transfer molding

Jin Dai *, H. Thomas Hahn

Mechanical & Aerospace Engineering Department, University of California, Los Angeles, 48-121 Engineering IV, PO Box 951597, Los Angeles,

CA 90095-1597, USA

Abstract

The static and fatigue behavior of vacuum-assisted resin transfer molded sandwich panels has been experimentally investigated

under flexural loading. Two core materials, D-100 balsa wood and H 250 PVC foam, were used to study the effect of core material

on static failure in 3-point and 4-point bending. The face consisted of a quasi-isotropic E-glass non-woven fabric cured in Derakane

441-400 epoxy vinyl ester resin. The stresses in the face and core at failure were calculated from failure loads using the simple beam

theory and compared with their respective strength values to identify underlying failure mechanisms. For short beams, core failure

led to failure of the beam as a whole. In long beams, however, failure of the wood core could be contained until the face failed. Only

D-100 end grain balsa wood was used as core for fatigue tests. A good similarity was seen between the static and fatigue failure

modes for both short span and long span specimens.

� 2003 Published by Elsevier Science Ltd.

Keywords: Sandwich; Flexural; Fatigue; VARTM

1. Introduction

Sandwich structures consist of two thin faces with

high stiffness and high strength, and a core with low

density and low stiffness. In vacuum-assisted resin

transfer molded (VARTM) sandwich structures, the

faces are usually made of a carbon fiber or a glass fiber

composite, and the core is typically made of end grainbalsa wood or closed-cell polymer foams such as

polyvinyl chloride (PVC) or polyurethane. Sandwich

structures are used in many applications ranging from

buildings to aerospace systems because of their high

specific bending stiffness and strength, and good acous-

tical insulation [1]. Their good shock resistance com-

bined with reasonable affordability, furthermore, makes

them ideal for large ship hulls as well [2].Durability is one of the key design parameters for any

structure where a safe life must be guaranteed before the

initiation of observable damage [3]. When used in ship

hulls, the sandwich structures are mostly subjected to

flexural loading [2,4–7]. Although much experimental

work has been done on the fatigue of sandwich beams

[8–15], it is rather limited to the shear fatigue of foam

cores using short beams while neglecting the face fatigue

failure. Furthermore, there is little data on the fatigue of

sandwich beams with balsa wood cores. It is to be noted

that results from short beams are more applicable to

bulkheads and joints where shear stresses in the core

tend to be high.

The present paper reports on the static and fatiguebehavior of sandwich panels under flexure. Two types of

core materials were used for the study of static behavior:

D-100 balsa wood and H 250 PVC foam. For the fatigue

behavior, however, only D-100 balsa wood was used in

light of the preponderance of literature data on foam

cores. The face consisted of a quasi-isotropic E-glass

non-woven fabric in Derakane 441-400 epoxy vinyl ester

resin, and the sandwich panels were fabricated using aVARTM process. The main objective was to study the

static and fatigue failure mechanisms of VARTM

sandwich beams.

2. Static behavior

A number of researchers have studied the failure

modes of sandwich structures in flexure [4–7]. Trianta-

fillou [4] studied failure modes of sandwich beams with

*Corresponding author.

E-mail address: Hahn@ime.ucla.edu (J. Dai).

0263-8223/03/$ - see front matter � 2003 Published by Elsevier Science Ltd.

doi:10.1016/S0263-8223(03)00040-0

Composite Structures 61 (2003) 247–253

www.elsevier.com/locate/compstruct

aluminum face sheets and a rigid polyurethane foam

core. Failure maps for various core densities and span-

to-depth ratios were constructed for face yielding, face

wrinkling, core yield in shear, and core yield in tensionand compression. Based on similar failure equations, a

weight optimum design of composite sandwich struc-

tures was proposed by Yoshii [5]. A summary of design

approaches to sandwich construction may be found in

[1] while information on cellular solids is available in

[16].

This section describes the results of a study on failure

of sandwich beams in 3-point bending. A limitedamount of results are presented on 4-point bending also.

Particular emphasis is on the effect of core material on

failure mode.

2.1. Failure modes of sandwich beams in flexure

Under flexure a sandwich beam (Fig. 1) exhibitsvarious failure modes depending on the state of stress

and the materials used. The potential failure modes to-

gether with the corresponding simplistic failure criteria

are summarized below:

1. Face failure in tension or compression: �rfc 6 rf 6rft

2. Face wrinkling due to compression: rf 6 0:5ðEfEcGcÞ1=3

3. Core failure in shear: sc 6 scs4. Core failure in tension or compression: �rcc 6 rc 6

rct

5. Face/core interface failure: si 6 sis

In the above equations r ¼ in-plane normal stress,

s ¼ out-of-plane shear stress, E ¼ Young’s modulus,

G ¼ shear modulus, sub f ¼ face, sub c ¼ core, sub i ¼interface, sub fc ¼ face compressive strength, sub ft ¼face tensile strength, sub cs ¼ core shear strength, and

sub is ¼ interface shear strength. In case of localized

loading, face/core indentation is an additional failure

mode.

For a symmetric beam with thin face sheets shown in

Fig. 1, the maximum face stress is given by

rf ¼ CL

btfðtc þ tfÞP ð1Þ

where C is 1/4 for 3-point bending and 1/8 for 4-point

bending. In the core the shear and normal stresses are

respectively give by

sc ¼1

2bðtc þ tfÞP ð2Þ

rc ¼Ec

Ef

rf ð3Þ

The interface shear stress is taken equal to the core shear

stress, si ¼ sc.

2.2. Experimental procedure

The sandwich panels were fabricated by the VARTM

process, as described in [17]. The top and bottom faces

consisted of two layers of EQX5300 quasi-isotropic E-glass non-woven fabric with the final [0/45/90/)45/45/90/)45/0] lay-up cured in Derekane 441–400 epoxy vinyl

ester resin. The nominal face thickness was 2.8 mm. The

specimens were divided into two groups: one group of

specimens with a D-100 end grain balsa wood core and

the other with a H-250 PVC foam core. Both types of

cores were 25.4 mm thick. The normalized beam spans

(normalized with respect to the core thickness) werevaried from 6 to 38 to change the state of stress while the

width was held at 63 mm. Another group of wood-core

specimens had a normalized span of six and a width of

76.2 mm. Properties of the face and core materials ob-

tained from various sources are shown in Tables 1 and 2,

respectively.

Bending tests were conducted on an Instron machine

in accordance with the ASTM C-393 flexure test stan-dard.

2.3. Results and discussion

Due to their different properties, the wood and foam

cores exhibited significantly different failure modes

under 3-point bending. To identify dominant stresses

responsible for failure, face and core stresses given in

Eqs. (1)–(3) were normalized by their respective strength

Fig. 1. Specimen geometry.

Table 1

Properties of face laminate

Properties E-glass/epoxy

In-plane Young�s modulus (GPa) 22

Poisson�s ratio 0.3

In-plane shear modulus (GPa) 8.2

In-plane tensile strength (Mpa) 241

In-plane compressive strength (MPa) 372

In-plane shear strength (MPa) 124

248 J. Dai, H. Thomas Hahn / Composite Structures 61 (2003) 247–253

values. These normalized stresses at failure were then

used to study the effect of each stress component on

failure.

2.3.1. D-100 balsa wood core

As the beam span increases, the normalized face

tensile stress rf=rft increases also, exceeding the nor-

malized core shear stress sc=ss. The critical span Lfc,which renders these two normalized stresses equal to

each other, is given by

Lfc ¼tfC

rfc

scsð4Þ

For the wood-core beam under 3-point bending, the

critical span is calculated to be 18 from the properties in

Tables 1 and 2.The normalized stresses at failure are shown at vari-

ous beam spans in Fig. 2. The core shear stress is much

less than its strength value even at the shortest span

tested, L=tc ¼ 6, whereas the face tensile stress reaches its

strength value as the span becomes much longer than

the critical span. The reason for the lower than expected

core shear stress is not clear. However, what is inter-

esting is that the normalized core tensile stress rc=rct isvery high. In fact, this stress increases in proportion to

the face tensile stress.

To account for the coupling effect of tensile and shear

stresses in the core, one may use one of the following

two failure functions:

f1 ¼rc

rct

þ scscs

ð5Þ

f2 ¼1

rct

�� 1

rcc

�rc þ

1

rctrcc

r2c þ

1

s2css2s ð6Þ

Failure is then assumed to occur when f1 or f2 reachesunity.

The calculated values of f1 and f2 at failure are shownin Fig. 3. For the shortest span, f1 is around unity in-

dicating core failure. However, it becomes greater than

unity as the span increases. For shorter spans, f2 is lowerthan f1 while the reverse is observed for longer spans.

Overall, the linear failure (5) criterion appears better

than the quadratic failure criterion (6) as the formerstays closer to unity.

It is puzzling how f1 or the normalized core shear

stress can be much greater than unity for large spans.

The reason for this observation may be the progressive

nature of the core failure. Although the core shear stress

remains fairly constant through the depth of the beam,

the core bending stress changes from tensile at the bot-

tom to compressive at the top. When the core fails at thebottom as the failure criterion f1 ¼ 1 is satisfied, a crack

Fig. 2. Normalized stresses in wood-core beams in 3-point bending.

Fig. 3. Values of failure functions in wood-core beams in 3-point

bending.

Table 2

Properties of core materials

Properties D-100 end grain balsa wood H-250 PVC foam

In-plane tensile modulus (GPa) 0.1 0.2898

Transverse tensile modulus (GPa) 3.56 0.2898

In-plane tensile strength (MPa) 0.69 6.1824

Transverse tensile strength (MPa) 13 8.5008

In-plane compressive modulus (GPa) 0.13 0.1449

Transverse compressive modulus (GPa) 3.98 0.3864

In-plane compressive strength (MPa) 0.7 5.1198

Transverse compressive strength (MPa) 12.9 5.6028

Transverse shear modulus (GPa) 0.16 0.104328

Transverse shear strength (MPa) 2.96 4.347

Density (kg/m3) 154 252.8842

Poisson�s ratio N/A 0.32

J. Dai, H. Thomas Hahn / Composite Structures 61 (2003) 247–253 249

will appear in the thickness direction at the bottom.

There can be two different scenarios for subsequent

failure depending on the beam span. If the span is short,

the core shear stress is high throughout the core.Therefore, the crack can grow further in shear. How-

ever, if the span is long, the resulting shear stress is not

high enough, and as load is increased, additional cracks

will appear while the original crack remains stationary.

Since the initial core cracking does not lead to a beam

failure, the calculated value of the failure function would

be greater than unity.

The normalized core stresses at failure are used inFig. 4 to compare 3-point and 4-point bending test re-

sults. These stresses are ranked in the increasing order.

All but two specimens had a normalized span of 6. The

two remaining specimens were twice as long as the

majority of specimens.

The normalized shear stress is seen to be lower in 3-

point bending where the core tensile stress is higher.

However, the sum of normalized core stresses, Eq. (5),yields the same values for both types of bending. Fur-

thermore, the average value is close to unity. This may

offer some credence to the linear failure criterion.

For short beams with a normalized span between 6

and 12, the core usually fails somewhere between theload introduction point and one of the supports al-

though the maximum core tensile stress occurs at the

center of the beam, Fig. 5(a). This may indicate the

dominant effect of shear stress on failure. However, it

should be pointed out that the core is not homogenous

as it consists of many smaller pieces bonded together.

When the normalized span is between 12 and 30, many

cracks appear in the core before final failure, Fig. 5(b).The cracking of the core leads to debonding between the

core and the face laminates. When the normalized span

is longer than 30, the bottom face laminate fails in

tension, leading to core failure, Fig. 5(c).

2.3.2. H-250 PVC foam core

The H-250 PVC foam core is much stronger in in-

plane tension and shear although it is weaker in the

thickness direction, Table 2. Further, it is much less

anisotropic than the wood core. Fig. 6 shows the

Fig. 4. A comparison of normalized stresses between 3-point bending

and 4-point bending.

Fig. 5. Failure modes of wood-core sandwich beams in 3-point bending: (a) normalized span ¼ 6, (b) normalized span ¼ 28, (c) normalized

span ¼ 38.

Fig. 6. Normalized stresses in foam-core beams in 3-point bending.

250 J. Dai, H. Thomas Hahn / Composite Structures 61 (2003) 247–253

normalized stresses in the face and core, respectively, at

failure. Since the foam has a rather low modulus in the

thickness direction, there is the possibility of face wrin-

kling. Therefore, the figure includes the face compressivestress normalized with respect to the calculated face

wrinkling strength.

As in wood-core beams, the core shear stress domi-

nates when the span is short. As the beam gets longer,

the face tensile stress begins to dominate. Unlike in

wood-core beams, the core tensile stress remains fairly

low relative to its strength value regardless of the span.

For normalized spans longer than 12, the dominantfailure mode is predicted to be face wrinkling. However,

the observed failure mode was in fact tensile failure of

bottom face. Therefore, the equation for face wrinkling

is not applicable to the sandwich beams studied.

To investigate the stress coupling effect on core fail-

ure, the quadratic failure function was used both with

the tensile stress and with the compressive stress, in the

core. The linear failure criterion was not used since thefoam did not have a clearly defined plane of weakness.

Fig. 7 shows that the values of f2 on the compression

side of the core are higher than on the tension side be-

cause the core in the thickness direction is weaker in

compression. Nevertheless, f2 remains less than unity.

Fig. 8 shows typical failure modes observed for short

beams and long beams, respectively. Short beams fail

because of the yielding in the core whereas long beamsfail when the face fails in tension.

2.3.3. Comparison between wood core and foam core

The effect of core material on the load carrying ca-

pability of sandwich beams is shown in Fig. 9 in terms of

the measured failure loads per unit width. The higher

shear strength of the foam core leads to a higher load

carrying capability for shorter beams. However, this

advantage disappears as the span becomes longer so that

the beam failure is the result of the face failure. It should

be noted that the H-250 PVC foam core is heavier thanthe D-100 balsa wood core.

3. Fatigue behavior

A number of researchers have studied the fatigue

behavior of sandwich structures in flexure experimen-

tally and theoretically [8–15]. Burman and Zenkert [8,9]

studied the shear fatigue of foam cores using short

sandwich beams under 4-point bending. He found that

the shear fatigue of foam cores was similar to the fatigue

of metals. Initial defects such as butt joint and skin/coredebonding were found to have a great effect on fatigue

life. Using sandwich beams with FRP (fiber reinforced

plastic) skins and foam core subjected to 10-point flex-

ural fatigue, Shenoi et al. [10–13] found that the loading

frequency had no significant effect on the fatigue be-

havior below 1 Hz. However, the stress ratio R had a

great influence on the fatigue life. The simple beam

Fig. 7. Values of failure functions in foam-core beams in 3-point

bending. Fig. 9. Effect of core type on failure loads per unit width.

Fig. 8. Failure modes of foam-core sandwich beams under 3-point

bending: (a) normalized span ¼ 6, (b) normalized span ¼ 38.

J. Dai, H. Thomas Hahn / Composite Structures 61 (2003) 247–253 251

theory was used to analyze the stresses in the beam.

They showed that different core and face materials re-

sulted in different failure modes. While the core mate-

rials in the sandwich beams discussed above were eithera polymer foam or a balsa wood, a metal alloy foam

core was also studied in [14].

In the present study, two different beam spans were

used under 3-point bending: a short span (152 mm

yielding a span-to-depth ratio of six) and a long span

(965 mm with a span-to-depth ratio of 38. The core was

a D-100 balsa wood.

Fatigue tests were run on a hydraulic Instron ma-chine at a frequency of 0.5 Hz and a stress ratio R of 0.1.

Load control was used for the short beams, and dis-

placement control for the long beams. Failure modes

were monitored visually and through a long-distance

microscope.

The S-N (stress vs number of cycles to failure) rela-

tions for short beams are shown in Fig. 10(a). In the

figure, the core shear stress calculated from the fatigueload using Eq. (2) was divided by the average static core

strength (2.26 MPa) measured earlier to yield the nor-

malized fatigue stress. The fatigue strength at 106 cycles

is seen to be about 45% of the static strength, which is

comparable to the values reported in the literature. The

reason for using the core shear stress is that only core

shear failure was observed in all the tests on short beams.

The long beams show a similar S-N relationship whenthe face tensile stress is used to plot the data, Fig. 10(b).

The static tensile strength used was 236 MPa. As with

the short beams, the fatigue strength at 106 cycles is

about 45% of the static strength, indicating both the

core and the laminate have almost the same rate of fa-

tigue degradation.As in static testing, all short beams failed in core.

Typical fatigue failure modes included a large crack

starting in the center of the core and propagating into

the top and bottom interfaces at the same time. The top

and bottom laminates remained undamaged until final

failure. For long beams, however, most damage was

contained in an area under the loading pin in the bottom

laminate. The laminate failed in a typical mode involv-ing ply cracking, fiber breaks, delamination and de-

bonding. As the fatigue load was increased, fewer cracks

were observed before final failure. As expected, some

reduction in bending stiffness was observed with the

appearance of damage. The first sign of damage was in

the bottom laminate followed by debonding in the

bottom face-core interface. Eventually, debonding oc-

curred in the top face-core interface as well and the finalfailure was the result of crushing of the core.

4. Conclusions

The failure behavior of sandwich beams in static

3-point and in 4-point bending has been studied using

two different core materials: D-100 balsa wood and H-

250 PVC foam. The faces were quasi-isotropic E-glass

non-woven fabric and the sandwich panels were fabri-

cated using Derakane 441-400 epoxy vinyl ester resin in

a VARTM process. Failure of short beams was seen to

be initiated in the core mostly due to the relatively highshear stress. The wood-core fractured in the thickness

direction along the wood grains and led to face/core

debonding. The foam core, however, yielded without

cracking. The normalized shear stress in the core de-

creased with increasing span in both types of beams. The

core failure was difficult to predict because of the lack of

reliable property data and the non-linear behavior of

core materials. Long beams failed in the face on thetension side when the tensile strength of the face was

exceeded. The wood core was predicted to fail along the

thickness direction before the face failure because of the

relatively high tensile stress in the core. However, such

core failure was not deleterious enough to induce the

face failure. Compared with the wood core, the foam

core was better for short beams because its higher shear

strength resulted in a higher load carrying capability.Such advantage, however, disappeared as the span be-

comes longer.

Sandwich beams having a D-100 balsa wood were

studied in 3-point flexural fatigue as well. As in the static

case, the short beams failed as a result of the fatigue

failure of the core in shear, and the long beams because

of the fatigue failure of the bottom laminate. Both theFig. 10. S-N relations for short and long beams under 3-point bending

fatigue: (a) short beams, (b) long beams.

252 J. Dai, H. Thomas Hahn / Composite Structures 61 (2003) 247–253

core and the laminate appeared to have the same rate of

fatigue degradation.

Acknowledgements

This paper is based on work supported by the Office

of Naval Research under Grant N00014-99-4-0798.

Sincere appreciation is extended to Yapa D.S. Raja-

pakse, Scientific Officer for his support.

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