Composites: Part A 54 (2013) 88–97
Contents lists available at ScienceDirect
Composites: Part A
journal homepage: www.elsevier.com/locate/compositesa
Compressive response of glass fiber composite sandwich structures
A.J. Malcom a,⇑, M.T. Aronson b, V.S. Deshpande c, H.N.G. Wadley d
a
Department of Mechanical Engineering, University of Virginia, 122 Engineers Way, PO Box 400746, Charlottesville, VA 22904-4745, USA
DuPont Spruance Plant, New Fibers Group, Richmond, VA 23234, USA
c
Department of Engineering, University of Cambridge, Cambridge, UK
d
Department of Materials Science and Engineering, University of Virginia, Charlottesville, VA 22903-4745, USA
b
a r t i c l e
i n f o
Article history:
Received 15 March 2013
Received in revised form 17 May 2013
Accepted 12 July 2013
Available online 20 July 2013
Keywords:
A. Glass fibers
A. Foams
A. 3-Dimensional reinforcement
B. Mechanical properties
a b s t r a c t
Sandwich panels with crushable foam cores have attracted significant interest for impulsive load mitigation. We describe a method for making a lightweight, energy absorbing, glass fiber composite sandwich
structure and explore it is through thickness (out-of-plane) compressive response. The sandwich structure utilized corrugated composite cores constructed from delamination resistant 3D woven E-glass fiber
textiles folded over triangular cross section prismatic closed cell, PVC foam inserts. The corrugated structure was stitched to 3D woven S2-glass fiber face sheets and infiltrated with a rubber toughened, impact
resistant epoxy. The quasi-static compressive stress–strain response of the panels was experimentally
investigated as a function of the strut width to length ratio and compared to micromechanical predictions. Slender struts failed by elastic (Euler) buckling which transitioned to plastic microbuckling as
the strut aspect ratio increased. Good agreement was observed between experimental results and micromechanical predictions over the wide range of core densities investigated in the study.
Published by Elsevier Ltd.
1. Introduction
Analysis of the response of metallic, edge clamped plates to
localized impulsive loads has led to a recognition that the out-ofplane deflection of the plate varies inversely with a material property index (ry/q)1/2 where ry is the yield strength of the material
and q its density [1]. Some fiber reinforced composites have a
specific tensile strength (parallel to the fiber direction) significantly above that of metallic alloys, providing a potentially superior solution to localized impulsive load mitigation. Recent
theoretical [2] and experimental [3,4] studies of impulsively
loaded; edge clamped metallic panels have shown that sandwich
panel concepts with cellular cores suffer even smaller deflections
than equivalent (same mass per unit area) solid plates, provided
the cellular core is sufficiently strong to maintain face sheet separation (and sandwich panel action) during loading.
Cellular solids are micro-architectured materials consisting of
cells bounded by interconnected networks of solid ligaments or
plates [5]. Those with random cell sizes and shapes are widely
found in natural materials such as wood, bones, shells and sponges.
Honeycombs with hexagonal shaped cells are an example of a
⇑ Corresponding author at: Department of Mechanical Engineering, University of
Virginia, 122 Engineers Way, PO Box 400746, Charlottesville, VA 22904-4745, USA.
Cell: +1 419 350 7764, tel.: +1 434 982 5837, home: +1 434 296 2231; fax: +1 434
982 5677.
E-mail address: [email protected] (A.J. Malcom).
1359-835X/$ - see front matter Published by Elsevier Ltd.
http://dx.doi.org/10.1016/j.compositesa.2013.07.007
periodic cellular structure also found in nature. The first synthetic
analogues of random cellular materials were made by adding
foaming agents to polymers [6]. Since then, foaming and other
space holding concepts have been used to make cellular structures
from metals [7] including aluminum [8], titanium [9,10] and from
ceramics [11]. Polymeric cellular materials are widely used for
packaging to provide impact load mitigation [12] and energy
absorption [13]. The more recent development of much stronger
metallic cellular materials with periodic (lattice) cell topologies
[14] made from high strength alloys [15,16] has led to considerable
interest in their use for mitigating impulsive loads created by impacts [17] and interactions with shock fronts resulting from nearby
explosions in water [18–20], air [19,21], and buried under soil
[22,23]. These later applications motivate the composite structure
investigated here.
Zenkert and his collaborators developed a carbon fiber composite sandwich panel with a foam core and investigated its impact
damage mechanisms [24]. In their design; T 700 carbon composite
laminates were used for the faces and Divinycell foam (a PVC
closed cell foam) for the core. The compressive strength of their
foam cores was low (4–8 MPa), and the laminated carbon fiber
composite faces were susceptible to delamination. Nevertheless,
the system showed significant promise. Here we explore an alternative glass fiber composite sandwich panel concept intended for
impulsively loaded situations. The concept incorporates (i) Divinycell foam cores reinforced by the corrugated glass fiber composite
webs, (ii) the use of 3D woven fabrics to inhibit delamination, (iii)
A.J. Malcom et al. / Composites: Part A 54 (2013) 88–97
control of matrix cracking by the use of (rubber toughened) impact
resistant polymer matrices, (iv) the application of higher strength
(but more costly) fibers in regions subjected to the highest tensile
stress (the face sheets) and (v) the use of a stitching method to increase the core web-face sheet node bond strength. We discuss the
factors governing materials selection and panel design, propose a
method for sandwich panel manufacture and use a combination
of experiments and micromechanical modeling to explore the
factors governing the panel’s compressive stiffness, strength, and
energy absorption.
2. Panel materials selection, design and fabrication
2.1. Materials selection and panel design
A schematic illustration of the panel concept is shown in
Fig. 1(a). A glass fiber composite sandwich structure integrating a
corrugated composite/polymer foam core was chosen for study
because; (i) it is relatively simple to manufacture over a wide range
of length scales, (ii) the high in-plane stretch and shear resistance
and through thickness (out-of-plane) compressive strength of the
structure enhances the performance of heavily loaded edge
clamped sandwich beams, and (iii) the closed cell foam confines
resin infiltration within the glass fiber struts/faces. A rigid polyvinyl chloride (PVC) closed cell foam, Divinycell H130 was used for
the core. The foam has a compressive strength of 3 MPa and a
density of 130 kg/m3, and has frequently been used in sandwich
structure applications [25]. During edgewise compression of conventional composite laminates, failure occurs by interplay delamination [26]. To avoid this, inexpensive 3D woven E-glass fibers
were used for reinforcement of the foam core. The E-glass fiber is
a high strength fiber, commonly used in transportation applications [27]. Similarly woven S2-glass was used in the face sheets because of its higher strength [27]. The fiber architecture of both 3D
woven textiles consists of alternating layers of originally straight
warp and weft fiber tows held in place by a smaller fraction of
Fig. 1. Schematic illustration of (a) the composite hybrid panel design with the
materials selected for its fabrication and (b) the assembly of the composite
sandwich panel. (For interpretation of the references to colour in this figure legend,
the reader is referred to the web version of this article.)
89
z-yarns that loop over and under the weft tows in the warp tow
direction. The 3D laminates used here consisted of a [0°/90°/0°/
90°/0°] layup of weft and warp tows. The z-yarn extended to the
outermost weft tows, binding the entire structure and thereby
increasing the delamination strength [28] but at the cost of increased warp and weft tow fiber waviness.
The relative density of the E-glass composite in the panel core
(the ratio of volume occupied by struts to the core volume) was
varied from 15% to 40% by changing the composite strut thickness,
t, to length, l, ratio. Four cores were made with t/l ratios ranging
from 0.07 to 0.25 by laminating 1, 2 or 3 layers of the E-glass fabric
resulting in webs with dry thicknesses of 1.49, 2.98, and 4.47 mm.
Samples were made with strut lengths of 14 ± 1 mm and
25 ± 1.5 mm. The strut thickness (t), core height (H), node thickness (c), strut length (l), and strut orientation angle (x) define a
core design, Fig. 1, and the values for the four designs are summarized in Table 1. The face sheet thickness (hf) was held constant for
all designs at 2.8 ± 0.2 mm.
2.2. Panel manufacture
The test panels were assembled as illustrated in Fig. 1(b). The
Divinycell foam was cut into triangular prismatic bars and each
bar was inserted into the fabric structure to form the corrugated
core. Kevlar thread with approximately 6 straight stitches per cm
was used to join the corrugated core and the fabric face sheets.
The core webs were constructed from a 3WeaveÒ fabric (grade
P3W-GE045) made by 3Tex (Cary, NC) using Hybon 2022 silane
sized, E-glass fibers approximately 18 lm in diameter. The faces
used S2-glass 3WeaveÒ (grade P3W-GS025) also obtained from
the same company. The first foam core prism was placed on a
3WeaveÒ S2-glass layer with the longitudinal axis of the prism
aligned with the warp tow direction of the S2 fabric. The 3WeaveÒ
E-glass laminate was then folded over the foam with the E-glass
fabric warp tows aligned with the prism axis, and stitched to the
S2-glass face sheets. An inverted foam insert was then added,
and the folding and stitching process repeated until the full, dry
panel was completely assembled. A SC-11 epoxy (Applied Poleramic Inc., Benicia, California) was used for the polymer matrix. It is a
two component, two-phase, rubber toughened, epoxy system
developed for ballistic shock loading applications, and is intended
for use with vacuum assisted resin transfer molding processes. The
fiber volume fraction, vf, in the struts of the corrugated core structure varied between 30% and 40%.
Manufactured samples exhibited slight imperfections from the
as-designed glass fiber core sandwich panel, Fig. 2(a). The applied
vacuum pressure provided sufficient loading to the structure to
slightly compress the foam core inserts resulting in non-flat face
sheets. Additionally, there was a ±1 mm variation in the stitch
placement such that the node height and internode separation varied slightly, Fig. 2(b). Combined, these two factors created slight
variations between strut lengths. The strut lengths were measured
to be 14 ± 1 mm for Design 1 and 25 ± 1.5 mm for designs 2–4. Initial testing revealed these imperfections resulted in unequal strut
loading at small strains. A series of single unit cell samples were
therefore fabricated with equal length trusses and extra epoxy
added to troughs in the wavy face sheets. This epoxy uniformly distributed the load to the entire sample surface and resulted in more
parallel face sheet surfaces. The mechanical response of both the
‘‘as manufactured’’ 3 cell core and the smooth face sheet single unit
cell structures are both presented in this study.
2.3. Relative density
In order to independently determine the role of the E-glass
composite trusses and the foam inserts used in the hybrid core,
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A.J. Malcom et al. / Composites: Part A 54 (2013) 88–97
Table 1
Design parameters of the E-glass fiber corrugated core along with the measured panel core density and relative density of the test structures with measured and predicted values
for the open corrugated core.
t (mm)
Design
Design
Design
Design
1
2
3
4
3.5
1.75
3.5
5.25
l (mm)
14.1
23.8
24.9
24.8
H (mm)
14.1
21.6
23.8
24.3
x (°)
c (mm)
1.8
1.0
1.9
3.15
60.6
59.6
61.3
58.4
Core density (kg/m3)
Open core relative density (%)
Open
Filled
Measured
Predicted
758
282
440
580
774
355
518
650
45.1
16.8
26.2
34.6
40.4
15.0
26.7
35.8
measured and predicted relative densities (from Eq. (2)) of the four
core designs are given in Table 1. The measured values are slightly
higher than predications due to the accumulation of resin at the
foam-web interface (resulting from gaps between the foam prisms
created during the panel assembly process).
3. Material characterization and properties
3.1. Core components
Fig. 2. (a) Photograph of an as-manufactured panel (Design 3). (b) Schematic
illustration of node height variations resulting from stitch offset during manufacture. This resulted in small variations of strut length, l and strut orientation angle,
x. (c) Unit cell with epoxy filler on face sheets to uniformly distribute pressure. (For
interpretation of the references to colour in this figure legend, the reader is referred
to the web version of this article.)
the foam was removed from some of the samples. The measured
densities of the (foam) filled and unfilled core structures are sum , of the open core strucmarized in Table 1. The relative density, q
ture is determined by the volume occupied by the corrugated core
in a unit cell of the core divided by the unit cell volume shown in
Fig. 1 and is given by:
The composite core structure is comprised of an E-glass weave,
SC-11 epoxy matrix, and Divinycell H130 PVC foam core inserts.
The measured elastic modulus of the E-glass fibers was 74 GPa,
in good agreement with literature values of 72 GPa [29]. However,
the measured tensile strength of tows extracted from the woven
fabric was 1.0 GPa which was less than the expected strength
(3.45 GPa29) and is attributed to fiber damage during fabric weaving. The shear yield strength of the SC-11 rubber toughened epoxy
measured at (25 °C) was 22 MPa. Its compressive yield strength
measured at the same temperature was 45 MPa and its Young’s
modulus was 1.35 GPa. Micrographs of the E-glass 3Weave composite revealed that both the warp and weft fiber tows have significant waviness resulting from the tension applied by the z-yarn
during fabric manufacture. This waviness significantly affects compressive strength in the fiber loading direction [30]. The warp tows
had the largest average fiber misalignment angle of 5.9° (averaged across both warp tows) and a maximum fiber tow misalignment angle of 12° (single tow observation). The fiber waviness
in the weft tows was smaller with an average misalignment of
2.5° (averaged across all weft tows) with a localized maximum
fiber tow misalignment of 8° (single tow observation). The
straighter weft tows were therefore oriented parallel with the
eventual axis of compressive loading of the struts in the corrugated
core to improve the compressive strength.
The compressive stress–strain response of the Divinycell H130
foam is shown in Fig. 3(a). The yield strength of the foam was
3.0 MPa at a yield strain of 3.5%. It has an elastic modulus of
100 MPa. The measured density of this foam was 130 kg/m3.
These values are all in agreement with manufacturer reported values. We note that the Divinycell foam exhibits a Calladine and English [31] type I (plateau) stress–strain response and has been found
to exhibit a strength that is less sensitive with loading rate [31].
3.2. Composite strut mechanical response
2
q¼
tH c cos x
Hðt þ H cos x 2c cos xÞ
ð1Þ
We note that for cases where tH c2 cos x, Eq. (1) can be simplified to give:
q ¼
t
t þ H cos x 2c cos x
ð2Þ
The structural parameters are defined in Fig. 1(a) and the
measured values used for the four designs given in Table 1. The
In principle, the compressive failure of E-glass fiber reinforced
composite laminates can occur by either plastic fiber micro-buckling, Euler-elastic buckling, or delamination failure [26]. The selection of a 3D woven fabric was intended to preclude the low
strength delamination mechanism and failure by delamination
was never observed during testing. To investigate the effect of
the strut aspect ratio on failure mode and determine the effective
failure strengths of these struts, single, double and triple laminate
E-glass composite test panels were fabricated to simulate the core
A.J. Malcom et al. / Composites: Part A 54 (2013) 88–97
91
of the core and equivalent test coupons where relatively low, ranging from 31% to 38%. Additionally, coupons with high fiber
fractions, approximately 55%, were manufactured to evaluate the
effect of fiber fraction on strength, modulus, and failure mode
and used to validate the micromechanical model. Tested in compression with the weft tows parallel to the load direction, strength
and modulus values were obtained following the procedure set
forth in ASTM D6641. Photographs and stress–strain responses
for the three struts are shown in Fig. 3(b) and (c) respectively.
The stubby struts, Fig. 3(b)i and 3(b)ii, failed by fiber microbuckling while the most slender one, Fig. 3(b)iii, failed by Euler-elastic
buckling.
Struts tested with a low aspect ratio, t/l = 0.07 (1 laminate
thick), exhibited failure by Euler-elastic buckling while the struts
with a higher aspect ratio, 0.107 < t/l < 0.248 (2 or 3 laminates
thick) exhibited failure by plastic microbuckling. Observed failure
modes, based on aspect ratio, in the both the simulated struts
and the actual struts within the open core structure were identical.
The experimentally measured critical strengths for struts with low
fiber fractions (mf 35%) ranged from 88 MPa for elastic failure to
122 MPa for plastic microbuckling failure. Strut strengths for high
fiber fractions (mf 55%) ranged from 106 MPa for elastic failure to
228 MPa for plastic microbuckling failure. Strut strength data is
presented in Table 2. The struts exhibit a consistent Young’s Modulus around 12 GPa for low fiber fractions, mf, 35%, and approach
25 GPA for higher fiber fractions, mf 55%.
The elastic failure mode is a geometrically driven buckling
failure with a strength prediction consistent with Euler’s elastic
buckling mode failure prediction. The Euler-elastic buckling
strength, Eq. (3), is dependent on the cross sectional geometry,
Young’s modulus of the strut, Ec, and the clamping condition coefficient, K (where K = 0.5 for fully clamped end constraints and K = 1
for pin-jointed end constraints). The geometric constraint on failure is an important observation in core design. In the plastic microbuckling regime, increasing the fiber fraction is one method to
increase the modulus of the strut and thereby effectively increase
the strut strength. However, increasing the fiber fraction of a fixed
areal density fabric is equivalent to reducing the through thickness
and, at low aspect ratios, significantly affects the critical Eulerelastic failure point. Therefore a twofold effect on strength occurs
between increasing the modulus and decreasing the aspect ratio
under higher fiber fractions. Due to this twofold effect, the low aspect ratio struts (t/l 0.07) provided only a 18 MPa increase in
strength when increasing the fiber fraction from 33% to 54%. Higher aspect ratio struts failing by plastic microbuckling exhibited an
increase in strength ranging from 106 to 136 MPa when fiber fractions were increased.
rEuler ¼
Fig. 3. (a) Compressive stress versus engineering strain response of H130 Divinycell
foam. (b) Compressive microbuckling (i and ii) and Euler elastic buckling (iii) failure
of E-glass struts tested in the weft direction with thicknesses of (i) 5.25 mm, (ii)
3.5 mm, and (iii) 1.75 mm. (c) Shows the compressive stress–strain response of the
three struts with vf 55%. The 1 laminate (thin) strut failed by Euler elastic
buckling while the 2 and 3 laminate struts fail by microbuckling. (For interpretation
of the references to colour in this figure legend, the reader is referred to the web
version of this article.)
struts within the corrugated structures. Test coupons with lengths
ranging from 141 to 152.4 mm were cut from the E-glass test panel
to form samples with gauge lengths of 14–25.4 mm, corresponding
to the strut lengths measured within the corrugated core structure.
The remaining 127 mm was utilized for gripping purposes within
the test fixture. Sample coupons were created to match the strut
thicknesses and fiber fractions within the core. The fiber fractions
2
p2 Ec t
12K 2 l
ð3Þ
Plastic microbuckling was the predominant failure mode observed during strut failure. While the failure strength of the core
presented in the paper is purely based on experimental measurements of strut failure, Malcom et al. [32] have shown that plastic
microbuckling failure strength can be predicted from a modified
version of Argon’s expression for composites in compression.
Argon’s unidirectional composite prediction, Eq. (4), predicts that
plastic microbuckling is controlled by the fiber misalignment
angle, u, and the shear strength, sm, of the matrix [33].
s
rf ¼ m
/
ð4Þ
Optical microscopy [32] indicates that 3D woven composites
can have rather large initial average fiber misalignment angles
due to the binding z-yarn impinging the warp and weft tows
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A.J. Malcom et al. / Composites: Part A 54 (2013) 88–97
Table 2
Parameters for the independently manufactured E-glass struts with low and high fiber fractions. The low fiber fraction struts are representative of the struts found in the
corrugated core structures. The high fiber fraction struts illustrate effect of minimized resin content with improved manufacture processing techniques.
Number of laminates
1
2
3
Low fiber fraction struts
High fiber fraction struts
Core design
vf (%)
t/l
rstrut (MPa)
Core design
vf (%)
t/l
rstrut (MPa)
Design
Design
Design
Design
33%
31%
38%
35%
0.074
0.141
0.248
0.212
88
92
122
113
N/A
N/A
54%
55%
0.066
0.107
106
228
N/A
56%
0.171
225
2
3
1
4
causing fiber misalignment. The initial average fiber misalignment
angle among the three weft fiber tow laminates in the loading
direction was experimentally measured as 2.5° along weft fiber
tows of the 3D woven E-glass composite struts and was responsible for the low axial compressive strength.
4. Core response and predictions
4.1. Stress–strain response
Three cell wide corrugated core specimens with 1, 2, or 3 laminate thick struts were tested to determine both the modulus and
strength of the structure. Variation in the number of laminations
per web allowed the thickness to length (t/l) ratio to be varied from
0.07 to 0.25 (enabling the empty core relative density to be varied
from 15% to 40%). The specimens were tested in compression at an
ambient temperature of 25 °C and a strain rate of 103 s1. Measurements were made using a screw-driven universal test machine
utilizing a 300 kN load cell for nominal stress measurements and a
laser extensometer to measure strain between the two face-sheets.
The tests used lateral confinement to inhibit lateral shear failure.
Unloading–reloading curves (not shown) were used to determine
the modulus.
The compressive stress–strain responses of the four core
designs (with empty core relative densities ranging from 15% to
40%) are shown in Fig. 4 for both the foam filled core and empty
(open) core structures. During initial loading, the sample cores
Fig. 4. Compressive stress–strain response for the glass fiber corrugated core structures. (a) Multi-cell structure with H130 foam inserts, (b) single unit cell structure with
H130 foam inserts, (c) open core multi-cell structure, and (d) the open core single unit cell structure.
A.J. Malcom et al. / Composites: Part A 54 (2013) 88–97
93
deformed linearly elastically, reaching a peak yield strength at
strain levels, e < 10%. They then began to inelastically collapse by
either Euler buckling or plastic micro-buckling of the struts. The
samples exhibited a reduced plateau strength (50–80% of the initial
peak strength) during core compression until a densification strain
limit, eD, was reached. At the onset of densification, material consolidation changed the approximately flat stress–strain response
to rapid strain hardening. Fig. 4 shows that the peak strength
increased and the densification strain decreased with relative density. The drop in strength after the initial peak was reduced in the
foam filled cores, a result with significant implications for impact
energy absorption applications.
The compressive stress–strain responses of the single, unit-cell
core designs exhibit a similar trend to their multi-cell counterparts
with one main difference. The single, unit cell cores exhibited a
significantly increased stiffness during the linear elastic loading.
The yield strengths and densification strains were identical to
those of the multi-cell experiments (for both foam filled and open
unit cell core structures).
4.2. Modulus
The unloading modulus of the 3-cell wide samples varied linearly with core relative density, Fig. 5, but was anomalously low
compared to the single unit cell samples whose unloading modulus
results are overlaid on the same picture. The compressive, elastic
modulus of an open corrugated core sandwich panel can be predicted by assuming that all the struts are equal in length and uniformly loaded. Utilizing a free body diagram, in which the applied
load is parallel to the vertical axis [34], enables the force in each
strut can be determined. Assuming the strain is small, the struts
are pin-jointed and inclined at an angle x to the applied force,
the core elastic modulus, Ecore depends upon the measured modulus of the strut material, Estrut, and the strut geometry.
4
Ecore ¼
tEstrut sin x
ðt þ H cos x 2c cos xÞ
ð5Þ
Substituting for the simplified form of the open core relative
density (Eq. (2)), the compressive modulus is predicted to have a
linear dependence upon core relative density and strut material
modulus.
4
Estrut sin x
Ecore ¼ q
ð6Þ
Fig. 6. Peak compressive strength measurements and predictions for the corrugated composite core. (a) Divinycell H130 foam filled core and (b) the open core.
Data is shown as a function of the relative density (strut volume fraction) of the
open composite core. The predicted strengths of the corrugated structures are based
on the experimentally measured critical strengths of the strut.
To determine the effective modulus of the foam filled core
structures, the rule of mixtures is utilized to combine the open core
modulus (Eq. (6)) with the measured modulus of the foam, Efoam
based upon the assumption that all volume not occupied by struts
is filled with foam.
ÞEfoam
Efoamfilledcore ¼ Ecore þ ð1 q
Fig. 5. Elastic modulus data and micromechanical predictions for the foam filled
and open core geometries. Imperfections in multi-cell samples resulted in nonuniform strut loading and a measured modulus significantly lower than model
predictions. The measured modulus of single unit-cell samples are in good agree
with the micromechanical model predictions.
ð7Þ
The predicted moduli for the open (Eq. (6)) and foam filled/hybrid cores (Eq. (7)) for measured strut fiber volume fractions, vf, of
30–40% are plotted in Fig. 5. They are in good agreement with the
single unit cell measurements.
We note that increasing the fiber volume fraction of the struts
enables the strut material modulus to be increased and thus that
of the core. Small variations in the length and inclination angle
of the core struts combined with slight waviness in the face sheets
(resulting from variations in the heights of the nodes and sagging
of the face sheet during resin infusion) were an inherent feature
of the pressure assisted resin infusion approach used here. This
led to much lower measured moduli for the multi-cell samples. If
sandwich structures of the type investigated here were intended
for stiffness limited design, these sources of variation would need
to be eliminated.
An empirical relationship for the dependence of the compressive modulus of foams, Efoam on the relative density has been proposed by Maiti et al. [35].
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A.J. Malcom et al. / Composites: Part A 54 (2013) 88–97
Efoam
Þn1
¼ C 1 ðq
Es
ð8Þ
where Efoam is the compressive modulus of the foam/core structure,
is
Es is the modulus of the solid material that forms the cell walls, q
the foam relative density and C1 and n1 are constants. For DIAB-H
grade closed cell Divinycell foams, we find C1 = 0.40 and n1 = 1 best
fit the foam modulus data. We also note that the modulus data for
both the empty and foam filled single unit cell structures can be well
fitted by the empirical Eq. (8) using n1 = 1.1 and C1 = 2. The wavy
face sheets and strut length variability of the multi-cell structures,
resulted in uneven load distribution between the struts. In this case
the multi-cell modulus that was well fitted by Eq. (8), with constants n1 = 1.1 and C1 = 0.6. This approximately linear dependence
of modulus upon density for the hybrid core is typical of stretch
dominated cellular materials [35].
4.3. Strength
Multiple tests (at least five at each core density) were used to
determine the average strength for each structure. A histogram
of initial (peak) strength for the open core samples of various relative densities is shown in Fig. 6. The strength clearly rose rapidly
with relative density. The peak strengths for the filled core varied
from 12 to 37 MPa as the cores composite volume fraction (relative
density) increased from 15% to 40%. The strength of the open core
samples was less, varying from 5 to 33 MPa over the same core relative density range. By comparing Fig. 6(a) and (b) it can be seen
that the peak strength of the foam filled cores was 3–7 MPa higher
than that of the open core structure.
The composite strut exhibits a linear elastic response prior to
compressive failure at a critical stress, rcritical, defined either by Euler or plastic fiber micro-buckling. Using a free body diagram in
conjunction with the experimentally measured critical strut
strength, Table 2, the compressive core strength is:
2
rcore ¼
t rcritical sin x
ðt þ H cos x 2c cos xÞ
ð9Þ
Substituting for the relative density of an empty core (Eq. (2)),
gives a relation between the compressive strength of the core,
the core relative density and the struts compressive strength
rcritical:
rcore ¼ q rcritical sin2 x
ð10Þ
The predicted strength for each core, using the strut orientation
angles from Table 1 and critical strut strength presented in Table 2,
is compared with the experimental data in Fig. 6(b) At the lowest
relative density tested, the core failed by Euler buckling, and the
struts aspect ratio and the fiber volume fraction control the strut
modulus. At higher relative densities the strut was predicted to fail
by plastic micro-buckling as observed in the experiments. It can be
seen from Eq. (10) that the core strength is predicted to rise
approximately linearly with relative density and the critical (buckling) strength of the strut.
The strength of the foam filled structures can be estimated by
again using a rule-of-mixtures approach to give a predicted strength.
rfoam filled core ¼ q rcritical sin2 x þ ð1 q Þrfoam
ð11Þ
Fig. 6 shows that in most cases the measured foam filled core
strength was well predicted by Eq. (11). Examination of the experimental strength data for the lowest density open and foam filled
structures reveals that the strength of the foam filled structure
(12 MPa) exceeded the sum of the foam strength (3 MPa) and the
open cell core (5 MPa). The strength of struts with a thickness to
length ratio (t/l) of 0.07 or less was governed by Euler buckling,
and it is possible that the foam stabilized the strut by providing lateral pressure to the strut wall during buckling leading to an increase in the critical buckling strength. All structures with t/
l > 0.07 failed by microbuckling (at a critical stress much higher
than the compressive strength of the foam), and it is unlikely that
the foam used here could significantly impede this failure mode.
During plastic microbuckling the fiber misalignment angle and
the shear strength of the epoxy matrix controlled the strength. In
this regime, the compressive strengths of these structures were
approximately linearly dependent upon the strength of the struts,
the relative density of the core and the strength of the foam. The
use of z-yarns to increase resistance to delamination of the struts
was the primary reason for the large misalignment angle in these
materials. The fiber waviness might be decreased by reducing the
tension of the z-yarn during 3D weaving since this reduces the inward forces on the warp and weft yarns of the fabric and the average fiber misalignment angle. However, this also reduces the fiber
volume fraction within a strut. It is also possible to weave a more
unbalanced 3D laminate in which a larger fraction of the fibers in a
strut are in the direction of compression loading. This adversely affects the shear and stretching resistance of the strut, but might
provide a better compromise for some loading scenarios. Since it
Fig. 7. Photographs taken during compression of (a) the foam filled ‘‘Design 3’’ sandwich structure and (b) the open core ‘‘Design 3’’ structure. Initial failure of the trusses
occurred by micro-buckling. Parts a-f correspond to the multi-core structure and parts g-l correspond to the single, unit-cell structure for strains of 0%, 10%, 20%, 30%, 40%, and
50% respectively. The ‘‘white’’ regions correspond to matrix crazing. (For interpretation of the references to colour in this figure legend, the reader is referred to the web
version of this article.)
A.J. Malcom et al. / Composites: Part A 54 (2013) 88–97
is difficult to reduce the fiber misalignment angle in 3D woven
laminates that utilize z-clamping fibers, increases in matrix shear
strength may be a more promising route for achieving increased
core strength, but at the potential expense of a more brittle-like response that would adversely affect behavior under impact loading.
4.4. Densification regime
Photographs taken during the testing of core Design 3 (t/
l = 0.14) are shown in Fig. 7 for the foam filled and open core systems as the structure was compressed to a strain of 50%. Initial failure in both cases was due to strut microbuckling where the peak
failure strength occurred at a strain between 6% and 8% for the
multi-cell samples and between 3% and 5% in the single, unit cell
sample. Variability in strut length and inclination angle contributed to the reduced modulus observed in the multi-cell samples.
The rise in stress towards the end of the test resulted from
impingement of the buckled core struts with the face sheets, the
compressed/densified foam inserts, and with neighboring struts
giving rise to the densification of the foam.
95
We define a densification strain, eD as the strain at which the
compressed material reaches the initial peak strength of the structure. Densification strain values for the samples studied here were
determined from the stress–strain curves shown in Fig. 4, and are
presented in Fig. 8(a). Data for the densification of H130 (Fig. 3(a))
and other Divinycell foams [36] is also shown in Fig. 8(a). The densification strain of the single and multi-celled corrugated structures depended weakly upon the relative density of the empty
core for the relative density ranges tested here. The open core
and foam filled structures had densification strains of approximately 60% and 48% respectively for open cell relative densities
in the 15–40% range. The densification strain relationships for
the corrugated cores were markedly different to those of the
Divinycell foam, Fig. 8(a).
A simple linear densification strain dependence upon relative
density has been proposed for closed cell foams by Gibson and
Ashby [5] and by Maiti et al. [35]:
eD ¼ 1 C 3 q
ð12Þ
For the range of Divinycell foams tested, as shown in Fig. 8(a),
the data is well predicted with C3 = 6.However, it is expected that
tends to
that the densification strain will converge to zero as q
unity. Eq. (12), therefore, poorly predicts the behavior of the higher
relative density composite cores.
Since knowledge of the densification strain dependence upon
relative density is essential for predicting the energy absorbed during crushing of the strut reinforced core, an alternative model to
predict the densification strains is developed. After initial microbuckling failure occurs during compression, Fig. 7, the strut develops a hinge that expands laterally along a face sheet. The hinge
motion allows the face sheet separation to decrease, the effective
strut length (supporting the stress) to decrease, and the strut inclination angle to gradually rise. Eventually, a geometry is reached
where the fractional strut length, x, that has undergone bending
reaches a value of 0.70 ± 0.03 of the strut length, l. This is experimentally observed to coincide with the strain at which continued
compression occurs at a stress equal to the initial peak in strength.
We can predict the densification strain from the model by noting that the definition of compressive strain, e, is:
e ¼ d=l sin x
ð13Þ
where d is the out-of-plane unit cell displacement.
By summing vertical distances in Fig. 9 we see that
d + t + l(1 x) sin (h + x) = l sin x
and
d = l sin x t l(1 x)
sin (h + x). By substituting these expressions into Eq. (13) we find
the compressive strain is given by:
Fig. 8. (a) Densification strain measurements are shown for the unit cell structures
(open and foam filled) and the various grades of Divinycell foam. The densification
strain data for the foams is well approximated by a linear model proposed by Maiti
et al. [35]. Core predictions are based on the developed strut hinge model using
specific parameters unique to each core geometry (green markers). The strut hinge
densification model is simplified using fixed constants x = 0.70 and x = 60° (solid
black line) with anticipated trends illustrated to the bounding limits (dotted lines)
(b) the energy absorbed per unit volume during compression to the densification
strain. Data is shown for the empty and foam filled corrugated core composite
structures investigated here and compared to Divinycell foams. Energy absorption
predictions based on the micromechanical models developed in this study and are
shown for comparison. (For interpretation of the references to colour in this figure
legend, the reader is referred to the web version of this article.)
Fig. 9. The strut collapse model used to predict densification strain. The densification strain is reached when the deformed strut aspect ratio and inclination angle
result in a cell strength sufficient to support the structures initial peak strength.
(For interpretation of the references to colour in this figure legend, the reader is
referred to the web version of this article.)
96
A.J. Malcom et al. / Composites: Part A 54 (2013) 88–97
e¼1
t
ð1 xÞ sin ðh þ xÞ
l sin x
sin x
structures tested here and for Divinycell foams [36] in Fig. 8(b).
The composite cellular structures extend the energy absorption
of H130 foam from 1.1 MJ/m3 to about 13 MJ/m3 while increasing
the density from 130 to 800 kg/m3. Composite strut reinforcement
of foams therefore provides an interesting approach for creating
high energy absorbing structures.
The volumetric energy absorption efficiency, f, of a structure
can be defined as the ratio of the actual energy absorbed during
compression of the structure to its densification strain divided by
that of an ideal material with a flat stress plateau to the densification strain.
ð14Þ
By summing the horizontal distances within the cell, it can be
qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
xx2
. Substituting this in Eq.
shown that sin ðh þ xÞ ¼ 1 cos1x
(15) gives an expression for the compressive strain:
t
1x
e¼1
l sin x sin x
rffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
cos x x2
1
1x
ð15Þ
The densification strain, eD, predicted by Eq. (15) is given by
substitution of the measured hinge position, x, at densification.
Parameters of the core geometry, t, l, and x (Table 1) along with
the experimental measured hinge position, x (Table 3), provide
the densification strain, eD, prediction shown in Table 3. The measured and predicted densification strains are compared in Fig. 8(a)
and seem to be in good agreement.
We note that the densification strain was smaller for foam filled
core structures because strut collapse reduced the available volume within which the foam resided. This causes the foam to compress beyond its own densification strain, and the stress it can
support to rises rapidly. If we assume the stress in the foam is
the same as that supported by the struts, the strain in the H130
foam at densification of the structure, efoam, varies from 72% to
87%. The predicted densification strain of the foam filled corrugation is simply the product of the densification limit of the foam
at the equivalent stress levels during densification of the corrugated structure with the densification strain of the open cell corrugated structure.
eD ¼ efoam
t
1x
1
l sin x sin x
rffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi!
cos x x2
1
1x
1¼
U actual
U ideal
ð17Þ
This efficiency parameter, f, was 0.46 for the open core and 0.82
for the foam filled structure, while the Divinycell foam had a nearly
ideal efficiency of 0.99. The lower efficiencies of the corrugated
structures was a result of the unstable buckling response of their
struts. Given an efficiency parameter, the energy absorption (per
unit volume), U, of a core can be predicted from the product of
the compressive strength, r, of the core (predicted by Eqs. (10)
and (11)), and the densification strain (given by Eqs. (15) and
(16)) of the core.
U ¼ n eD r
ð18Þ
The energy predictions for each of the four open and foam filled
core designs is overlaid on the data in Fig. 8(b), and predicts the
general trends of the experimental results quite well. Table 3 lists
the predicted volumetric energy absorptions for each core design.
We note that Divinycell H130 has a volumetric energy absorption
of 1.1 MJ/m3 when compressed to its densification strain. The energy absorption of the hybrid structure was higher slightly than
that of the sum of the foam and empty core components due to
compression of the foam beyond its densification strain and stabilization of slender struts that failed by Euler (elastic) buckling.
ð16Þ
The predicted densification-relative density relation (curve) and
specific predictions for each structure (open green triangles) agree
well with the experimental data, Fig. 8(a).
The densification strain models for the open core (Eq. (15)) and
foam filled core (Eq. (16)) can be simplified using the observed
average hinge value of x = 0.7 and intended design orientation angle of x = 60° for all specimens. Simplified predictions are compared to the comprehensive densification models along with data
measurements and shown in Fig. 8(a). It can be seen that the simplified predictions agree well with the experimental data regardless of the small variation in the geometric parameters x and x,
providing a useful predictive tool in design when t and l are the
only primary variables.
5. Concluding remarks
We have developed a method for making robust composite
sandwich panel structures that appear well suited for impact loading applications. By combining three dimensional woven glass
fiber fabrics that utilize z-yarn fibers to inhibit delamination,
prismatic polymer foam inserts, and vacuum infusion of a rubber
toughened epoxy, we have made a variety of corrugated core
sandwich structures. The combination of Kevlar stitching of a corrugated E-glass core to higher strength S2 glass fiber face sheets,
together with the large foam area of contact with the core webs
and face sheets resulted in robust core-face sheet attachment
and reliable load transfer. The quasi-static experiments reported
here, and others conducted in the impact loading regime [12],
4.5. Energy absorption
The energy absorbed per unit volume during the compression of
a cellular structure is obtained by integrating the stress–strain
response up to the densification strain, eD, and is shown for the
Table 3
Predicted densification strain, core strength, and energy absorption from the developed micromechanical models. Average dimensional parameters for each core geometry were
used in the prediction. The hinge position (position of strut hinge at time of densification), x, was experimentally measured for each core geometry and utilized as an empirical fit
in the hinge model.
Core type
Predicted open core
relative density (%)
Hinge position, x
Strength,
r (MPa)
Densification strain, eD
Efficiency parameter, n
Energy absorbed
(MJ/m3)
Design 1
Open core
Foam filled core
40.4
0.72
0.69
37.4
39.2
0.53
0.38
0.46
0.82
9.1
12.4
Design 2
Open core
Foam filled core
15.0
0.69
0.66
9.8
12.4
0.62
0.42
0.46
0.82
2.8
4.2
Design 3
Open core
Foam filled core
26.7
0.70
0.70
18.9
21.1
0.61
0.44
0.46
0.82
5.3
7.6
Design 4
Open core
Foam filled core
35.8
0.73
0.69
29.3
31.2
0.56
0.41
0.46
0.82
7.6
10.6
A.J. Malcom et al. / Composites: Part A 54 (2013) 88–97
indicate that neither the struts, face sheets nor the bond between
them are susceptible to the delamination failure encountered in
normal 2D laminates.
The out-of-plane compressive elastic modulus of the corrugated
structures varied linearly with the composite corrugation volume
fraction for volume fractions of 15–40%, and was well predicted
by a small strain, straight strut, pin jointed model. The effect of
the foam on the elastic modulus could be approximated with a
rule-of-mixtures, and was small because the modulus of the foam
was much less than that of the composite core. Further increases in
elastic modulus of the core were more effectively achieved by
increasing the fiber fraction in the strut loading direction or by
substituting the mass of the foam core with additional composite
material.
The compressive strength of the foam filled composite core increased from 12 to 37 MPa as the volume fraction of the corrugated
material was increased from 15% to 40%. The strength of both the
empty and foam filled structures exhibit an approximately linear
dependence upon the volume fraction (or relative density) of the
composite corrugation. The compressive strengths of the slenderest struts (t/l = 0.07) was controlled by Euler buckling, and otherwise by plastic microbuckling of the struts. Removal of the 3 MPa
plateau strength foam after fabrication of the composite reduced
the strength of the core by 3–6 MPa consistent with a small synergistic influence of the foam linked to a delayed Euler buckling of
the slenderest strut structure and local densification of the foam
beyond its densification strain.
Micromechanical models were developed to relate the corrugated structures modulus and strength to the geometry and properties of the materials that made up cores. In general, good
agreement was observed between the measurements, and the
micromechanical predictions. The micromechanical model indicates that stronger, and more energy absorbing cellular structures
could be fabricated by increasing the composite matrix shear
strength, increasing the fiber volume fraction in the direction of
loading, and reducing the misalignment angle of the fibers within
the struts.
The energy absorbed per volume during core compression to
the onset of densification (defined here as the strain at which the
stress reached the initial peak strength) varied from 1.1 to 13 MJ/
m3 as the relative density of the core (and its strength) was increased. The energy absorption of the hybrid structure was higher,
on average, than that of the sum of the foam and empty core due to
compression of the foam beyond its densification strain and stabilization of slender struts that failed by Euler (elastic) buckling.
Acknowledgements
We are grateful to T. George for use of his Divinycell foam
mechanical property data and to the Office of Naval Research
(ONR) for funding this Project under Grant number N00014-071-0764 (Program manager, Dr. David Shifler).
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