Mechanical behavior and failure of sandwich structures
The failure behavior of composite sandwich beams under three- and four-point bending was studied. The beams were made of unidirectional carbon/epoxy facings and various core materials including PVC closed-cell foams, a polyurethane foam and an aluminum honeycomb. Various failure modes including fa...
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Інститут електрозварювання ім. Є.О. Патона НАН України
2013
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| Цитувати: | Mechanical behavior and failure of sandwich structures / Е. Gdoutos // Автоматическая сварка. — 2013. — № 10-11 (726). — С. 107-111. — Бібліогр.: 11 назв. — англ. |
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irk-123456789-1032362016-06-16T03:03:08Z Mechanical behavior and failure of sandwich structures Gdoutos, Е. Пленарные доклады Международной конференции The failure behavior of composite sandwich beams under three- and four-point bending was studied. The beams were made of unidirectional carbon/epoxy facings and various core materials including PVC closed-cell foams, a polyurethane foam and an aluminum honeycomb. Various failure modes including facing wrinkling, indentation failure and core failure were observed and compared with analytical predictions. It was established that the initiation, propagation and interaction of failure modes depend on the type of loading, constituent material properties and geometrical dimensions. 2013 Article Mechanical behavior and failure of sandwich structures / Е. Gdoutos // Автоматическая сварка. — 2013. — № 10-11 (726). — С. 107-111. — Бібліогр.: 11 назв. — англ. http://dspace.nbuv.gov.ua/handle/123456789/103236 620.192.7:62-112.81 en Автоматическая сварка Інститут електрозварювання ім. Є.О. Патона НАН України |
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Пленарные доклады Международной конференции Пленарные доклады Международной конференции |
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Пленарные доклады Международной конференции Пленарные доклады Международной конференции Gdoutos, Е. Mechanical behavior and failure of sandwich structures Автоматическая сварка |
| description |
The failure behavior of composite sandwich beams under three- and four-point bending was studied. The beams were
made of unidirectional carbon/epoxy facings and various core materials including PVC closed-cell foams, a polyurethane
foam and an aluminum honeycomb. Various failure modes including facing wrinkling, indentation failure and core
failure were observed and compared with analytical predictions. It was established that the initiation, propagation and
interaction of failure modes depend on the type of loading, constituent material properties and geometrical dimensions. |
| format |
Article |
| author |
Gdoutos, Е. |
| author_facet |
Gdoutos, Е. |
| author_sort |
Gdoutos, Е. |
| title |
Mechanical behavior and failure of sandwich structures |
| title_short |
Mechanical behavior and failure of sandwich structures |
| title_full |
Mechanical behavior and failure of sandwich structures |
| title_fullStr |
Mechanical behavior and failure of sandwich structures |
| title_full_unstemmed |
Mechanical behavior and failure of sandwich structures |
| title_sort |
mechanical behavior and failure of sandwich structures |
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Інститут електрозварювання ім. Є.О. Патона НАН України |
| publishDate |
2013 |
| topic_facet |
Пленарные доклады Международной конференции |
| url |
http://dspace.nbuv.gov.ua/handle/123456789/103236 |
| citation_txt |
Mechanical behavior and failure of sandwich structures / Е. Gdoutos // Автоматическая сварка. — 2013. — № 10-11 (726). — С. 107-111. — Бібліогр.: 11 назв. — англ. |
| series |
Автоматическая сварка |
| work_keys_str_mv |
AT gdoutose mechanicalbehaviorandfailureofsandwichstructures |
| first_indexed |
2025-07-07T13:30:09Z |
| last_indexed |
2025-07-07T13:30:09Z |
| _version_ |
1836995062135783424 |
| fulltext |
10710-11/2013
UDC 620.192.7:62-112.81
MECHANICAL BEHAVIOR AND fAILURE
Of SANDWICH STRUCTURES
E. GDOUTOS
School of Engineering, Democritus University of Thrace, GR-671 00 Xanthi, Greece. E-mail: egdoutos@civil.duth.gr
The failure behavior of composite sandwich beams under three- and four-point bending was studied. The beams were
made of unidirectional carbon/epoxy facings and various core materials including PVC closed-cell foams, a polyure-
thane foam and an aluminum honeycomb. Various failure modes including facing wrinkling, indentation failure and core
failure were observed and compared with analytical predictions. It was established that the initiation, propagation and
interaction of failure modes depend on the type of loading, constituent material properties and geometrical dimensions.
11 Ref., 2 Tabls, 4 figures.
K e y w o r d s : investigation of failure behavior, three-point bending, sandwich beams, carbon-epoxy facing, various core
materials, strength-to-weight ratio
1. Introduction
Sandwich structures consisting of strong and stiff
facings and light weight cores offer improved stiffness
and strength to weight ratios compared to monolithic
materials. Under flexural loading the facings carry al-
most all of the bending, while the core takes the shear
loading and helps to stabilize the facings. facing ma-
terials include metals and fiber reinforced composites.
The latter are being used in advanced applications due
to the large strength-to-weight ratio. The core mate-
rials mainly include honeycombs, foams and wood.
Possible failure modes of sandwich structures in-
clude tensile or compressive failure of the facings,
debonding at the core/facing interface, indentation
failure under concentrated loads, shear core failure,
wrinkling of the compression face and global buck-
ling. Recently, the authors have performed a thorough
investigation of the failure behavior of sandwich
beams with facings made of carbon/epoxy composite
material and core made of foam materials [1-6].
In the present work, failure modes were investi-
gated experimentally in sandwich beams under four-
point and three-point bending. failure modes ob-
served and studied include core failure, face sheet
wrinkling and indentation failure.
2. Materials and Specimens
The sandwich beams were fabricated from 8-ply
unidirectional carbon/epoxy (AS4/3501-6) facings
and various core materials. The facings were bonded
to the core with an epoxy adhesive (Hysol EA 9430).
The assembly was cured at room temperature. The
facings and core had a thickness of 1 and 25.4 mm,
respectively. Beam specimens 25.4 mm wide and of
various lengths were cut from the sandwich plates.
Tables 1 and 2 give some characteristic properties of
the sandwich constituent materials.
3. Experimental Procedure
Special test fixtures were fabricated to provide
three- and four-point bending for beams of various
lengths. five span lengths of 10.2, 20.3, 25.4, 40.6
Ta b l e 1 . Properties of balsa wood, aluminum and foam-filled honeycomb, and polyurethane materials
Property Balsa Wood CK57
Aluminum
Honeycomb
PAMG 5052
foam filled
Honeycomb
Style 20
Polyurethane
fR-3708
Density, r kg/m3 (lb/ft3) 150 (9.4) 130 (8.1) 128.3 (8) 128.3 (8)
In-plane long. comp. elast. mod., E1c MPa (ksi) 129.5 (18.8) 9.5 (1.38) 24.1 (3.5) 38.5 (5.6)
In-plane long. tens. elast. mod., E1t MPa (ksi) 93.6 (13.6) 4.5 (0.65) 1.3 (0.19) 416.6 (60.4)
In-plane trans. comp. elast. mod., E2c MPa (ksi) 129.5 (18.7) 6 (0.87) 7.6 (1.1) 38.5 (5.6)
Out of plane comp. elast. mod., E3c, MPa (ksi) 5394 (782.3) 2125 (308) 269.1 (39) 108.7 (15.8)
Transverse shear elast. mod., G13, MPa (ksi) 58.7 (8.5) 579 (84) 8.5 (1.23) 10.3 (1.49)
In-plane long. comp. strength, f1c MPa (ksi) 0.78 (0.11) 0.2 (0.03) 0.4 (0.06) 1.15 (0.17)
In-plane long. tensile strength, f1t MPa (ksi) 1.13 (0.16) 1.63 (0.24) 0.48 (0.07) 1.1 (0.16)
In-plane trans. comp. strength, f2c MPa (ksi) 0.78 (0.11) 0.17 (0.03) 0.32 (0.05) 1.15 (0.17)
Out of plane comp. strength, f3c MPa (ksi) 9.6 (1.39) 11.8 (1.7) 1.35 (0.2) 1.74 (0.25)
Transverse shear strength, f13 MPa (ksi) 3.75 (0.54) 3.45 (0.5) 0.75 (0.11) 1.4 (0.2)
© E. Gdoutos, 2013
108 10-11/2013
and 76.2 cm were tested. In studying the effects of
pure bending, special reinforcement was provided for
the core at the outer sections of the beam to prevent
premature core failures. Also, under three-point bend-
ing, the faces directly under concentrated loads were
reinforced with additional layers of carbon/epoxy to
suppress and prevent indentation failure. Only in the
case when the indentation failure mode was studied,
there was no face reinforcement. The concentrated
load was applied to the specimens with a cylinder of
diameter of 25.4 mm (1 in.).
Strains on the outer and inner (interface between
facing and core) surfaces of the facings were record-
ed with strain gages. Most gages were oriented along
the axis of the beam, but some were mounted in the
transverse direction to record transverse strains. Beam
deflections were measured with a displacement trans-
ducer (LVDT) and by monitoring the crosshead mo-
tion. The deflection was also monitored with a course
moiré grating (31 lines/cm). Longitudinal and trans-
verse strains in the core were measured with finer
moiré gratings of 118 and 200 lines/cm. The deforma-
tion of the core was also monitored with birefringent
coatings using reflection photoelasticity.
4. Failure Modes
A number of failure modes were recorded and
studied in the composite sandwich beams subjected
to three- and four-point bending. They include wrin-
kling of the compression facing, core failure and in-
dentation of the loaded face. These failure modes are
discussed in the following sections.
4.1. Compression Facing Wrinkling
Compression facing wrinkling failures were ob-
served in sandwich beams under both four-point
and three-point bending. fig. 1 shows moment ver-
sus strain results for two different tests of sandwich
beams with Divinycell H100 cores under four-point
bending. Evidence of wrinkling is shown by the sharp
change in recorded strain on the compression facing,
indicating inward and outward wrinkling in the two
tests. In both cases the critical wrinkling stress was
σcr = 673 MPa.
Wrinkling is a localized short-wave buckling of
the compression facing. Wrinkling may be viewed
as buckling of the compression facing supported by
an elastic continuum, the core. The critical wrinkling
stress according to Heath [7] is given by
( )cr
12
3 1
12 21
2
3 1
f
c
fcE Eh
h
s =
- ν ν
(1)
where , cfh h : facing and core thicknesses, respec-
tively; 31,f cE E : facing and core moduli, respective-
ly; ijν : Poisson’s ratio associated with loading in the
i-direction and strain in the j-directio and the indices
1 and 3 refer to the in-plane and through-the-thickness
directions, respectively.
Equation (1) predicts the following value of the
wrinkling stress
cr 687MPa.s =
This value is close to the experimental value of
673 MPa.
In the case when shear is present in addition to
bending, the influence of the transverse shear mod-
ulus of the core, 13cG , must be taken into account.
An expression given by Hoff and Mautner [8] has the
form
( )cr
1/3
3 131 c cfc E E Gs =
(2)
where c is a constant usually taken as equal to 0.5, 0.6,
or 0.65. Note that the critical stress in this expression
depends only on the elastic moduli of the facing and
core materials. In the relation above the core mod-
uli are the initial elastic moduli if wrinkling occurs figure 1. facing wrinkling in sandwich beam under four-point bending
(Divinycell H100 foam core; dimensions are in cm)
Ta b l e 2 . Properties of carbon/epoxy facings, adhesive, and H100 and H250 PVC foams
Property facing fM-73 Adhesive foam Core (H100) foam Core (H250)
Density, r, kg/m3 1,620 1,180 100 250
Thickness, h, mm 1.01 0.05 25.4 25.4
Longitudinal Modulus, E1, MPa 147,000 1,700 120 228
Transverse Modulus, E3, MPa 10,350 139 403
Transverse Shear Modulus, G13, MPa 7,600 110 48 117
Longitudinal Compressive Strength, f1c, MPa 1,930 1.7 4.5
Transverse Compressive Strength, f3c, MPa 240 1.9 6.3
Transverse Shear Strength, f13, MPa 71 33 1.6 5.0
10910-11/2013
while the core is still in the linear elastic range. This
requires that the shear force at the time of wrinkling
be low enough or, at least,
c csV A F< (3)
where Ac is core cross sectional area and fcs the shear
strength of the core. This is the case for long span
beams under three-point bending.
4.2. Core Failure
Core failures were observed in sandwich beams
under three-point bending. The core carries primar-
ily the applied shear loading. In short beams under
three-point bending the core is mainly subjected to
shear and failure occurs when the maximum shear
stress reaches the critical value (shear strength) of the
core material. In long-span beams the normal stresses
in the core become of the same order of magnitude
or even higher than the shear stresses. In this case,
the core is subjected to a biaxial state of stress and
fails according to an appropriate failure criterion. It
was shown that failure of the core materials can be
described by the Tsai-Wu failure criterion [9]. for a
beam loaded under combined bending and shear, the
foam is subjected to longitudinal normal stress, s1,
and in-plane shear stress, t5 (t13). The Tsai-Wu crite-
rion for this case takes the form
2 2
1 1 11 1 1f f ks + s = - (4)
where
5
1 11 55 2
1 1 1 1 5 5
1 1 1 1, , ,
t c t c
f f f k
F F F F F F
t
= - = = =
f1t, f1c = tensile and compressive strengths in the in-
plane (1, 2) direction. f5 = shear strength on the 1-3
plane.
In the above equations σ1, σ3 and τ5 are the normal
and shear stresses referred to the principal material
directions (in-plane is direction 1 and through-the-
thickness is direction 3), f1c and f1t are the com-
pressive and tensile strengths along the in-plane di-
rection, f3c and f3t are the compressive and tensile
strengths along the through-the-thickness direction
and f5 (= f13) is the shear strength on the 1-3 plane.
The state of deformation and failure mechanisms
in the core were studied by means of moiré method.
fig. 2 shows moiré fringe patterns in the core of a
sandwich beam with Divinycell H250 core under
three-point bending. The moiré fringe patterns corre-
sponding to the horizontal and vertical displacements
away from the applied load consist of nearly parallel
and equidistant fringes from which it follows that the
normal strains are zero, while the shear strain is nearly
constant across the core thickness. This is valid only
in the linear range.
4.3. Indentation Failure
Indentation failure was observed in beams under
three-point bending when no special reinforcement of
the facing or the core was provided in the area un-
der the load. fig. 3 shows the variation of the applied
load with the displacement of the indenting roller for
a 36 cm long beam under three-point bending. The
displacement represents the sum of the global beam
deflection and the local indentation, but it is more sen-
sitive to the local indentation. Therefore, the propor-
tional limit of the load-displacement curve is a good
indication of initiation of indentation. In the present
case the beam was made with a Divinycell H100 core.
The load at initiation of indentation is 735 N. The
peak load measured was Pmax = 1080 N.
The indentation failure of the sandwich beam can
be predicted by treating the loaded face as a beam
resting on a foundation. for linear elastic behavior,
the core is modeled as continuous distributed linear
tension/compression springs. The stress s at the in-
terface between core and facing is proportional to the
figure 2. Moire fringe patterns corresponding to horizontal and vertical
displacements in sandwich beam under three-point bending (12 lines/
mm; Divinycell H250 core)
figure 3. Load versus deflection under load of sandwich beam under
three-point bending (carbon/epoxy facings, Divinycell H100 core)
110 10-11/2013
local deflection, w
kws = (5)
where k is the foundation modulus given by [10]
3
1
3 30.64 .c c
f f
E E
k
h E
= (6)
for a long (assumed infinite) facing the deflection
Pw under the load P is [10]
2P
Pw
kb
λ
= (7)
where
1
3
1.18 c
f f
E
h E
λ = (8)
and b is the width of the facing.
Yield of the core under the load occurs when the
interfacial stress s reaches the yield stress of the foam
core. The critical load at initiation of core yield is cal-
culated from Eqs. (5) to (8) and the yield condition as
1
31.70 f
cy ys f
c
E
P bh
E
= s (9)
where yss is the yield stress of the core.
As the load increases beyond the yield value, plas-
tic deformation propagates through the core from the
center to the ends of the facing. for a rigid-perfectly
plastic foundation the local bending stress at the upper
surface of the facing is given by [11]
2
2 2
9 .
16fl
f ys
P
b h
s =
s
(10)
for a beam in three-point bending the global stress
in the facing is
( )4fb
f f c
PL
bh h h
s =
+
(11)
where ch is the thickness of the facing.
Indentation failure occurs when the sum of the lo-
cal and global bending stresses, andfl fbs s , reaches
the compressive strength of the facing material. The
load at initiation of indentation in fig. 3 is 735 N and
agrees with the calculated value of 800 N from Eq.
(9). The peak load measured is max 1080,P = while the
calculated value is max 1310 .P N= The difference in
the results may be attributed in the simplifying as-
sumption of a rigid-perfectly plastic foundation.
5. Failure Mode Transition
from the above discussion it is obvious that in-
itiation of a particular failure mode depends on the
geometrical characteristics, the material properties
and the loading conditions of the beam. In the case
of beams under three-point bending when reinforce-
ment of the facings or the core is provided to sup-
press indentation failure, the prevalent failure modes
are facing wrinkling and core failure. for short spans,
core failure occurs first and then it triggers facing
wrinkling. for long spans, facing wrinkling can occur
before any core failure. Thus, a curve for the critical
load for core failure initiation versus span length is
obtained. On the other hand, the critical load for fac-
ing wrinkling as a function of span length can be pre-
dicted from Eq. (2). fig. 4 shows curves of the critical
load versus span length for initiation of failure by core
failure and facing wrinkling for a sandwich beam with
various core materials.
The intersection of the curves defines the transition
from core failure initiation to facing wrinkling initia-
tion. Note that for core materials H250, balsa wood
and aluminum honeycomb with increased through-
the-thickness Young’s modulus the compressive fac-
ing wrinkling failure curve is displaced, according to
Eq. (2) to the right, and therefore, the critical length
for failure mode transition from core failure to wrin-
kling increases. Thus, as the through-the-thickness
Young’s modulus of the foam increases, the critical
length of the beam for failure mode transition from
core failure to wrinkling, also increases.
6. Conclusions
failure modes of composite sandwich beams de-
pend on the type of loading, constituent material
properties and geometrical dimensions. for sandwich
beams made of unidirectional carbon/epoxy facings
and PVC closed-cell foam cores failure modes ob-
served and studied include core failure, compressive
facing wrinkling and indentation failure. Experimen-
tal results were compared with theoretical predictions
whenever they were available.
following initiation, interaction of failure modes
takes place leading to catastrophic fracture. Thus,
failure initiation by plastic deformation of the core
degrades the supporting role of the core and precip-
itates other failure modes, such as facing wrinkling.
When core failure and stiffness degradation occur
first, the critical wrinkling stress is substantially re-
duced. Thus, catastrophic failure of a sandwich beam
appears to be the result of initiation propagation and
interaction of failure modes, as influenced by type of
loading, constituent material properties and geometri-
cal dimensions.
figure 4. Critical load versus span length for failure initiation in sand-
wich beams under three-point bending. Horizontal lines indicate core
shear failure and curved lines indicate failure by compressive facing
wrinkling
11110-11/2013
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Received 08.04.2013
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