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Experimental characterization and numerical simulations of asyntactic-foam/glass-bre composite sandwich
Alberto Corigliano a,*, Egidio Rizzi b, Enrico Papa a
aDipartimento di Ingegneria Strutturale, Facolta di Ingegneria Leonardo, Politecnico di Milano, piazza Leonardo da Vinci 32, 20133 Milan, ItalybDipartimento di Ingegneria Strutturale, Facolta di Ingegneria di Taranto, Politecnico di Bari, via Orabona 4, 70125 Bari, Italy
Received 7 February 2000; accepted 11 May 2000
Abstract
This note presents the main results of an experimental and numerical investigation on the mechanical behaviour of a composite
sandwich primarily designed for naval engineering applications. The skins of the sandwich are made of glass-bre/polymer-matrix
composites; their interior layers are connected with interwoven threads called piles which cross the sandwich core. Such core consists
of a syntactic foam made by hollow glass microspheres embedded in an epoxy matrix. Experimental tests and numerical nite ele-
ment (FE) simulations on both the sandwich composite and its separate components have been performed in order to characterise
fully the complex mechanical behaviour of such a highly heterogeneous material. # 2000 Elsevier Science Ltd. All rights reserved.
Keywords: A. Glass bre; Composite sandwich; Syntactic foam; Mechanical tests; Numerical simulations (FE)
1. Introduction
Composite sandwiches are commonly adopted inmarine and aeronautical engineering for structures or
structural elements requiring high stiness and strength,
mainly to exural loads, together with low specic
weight (see e.g. [15]). Frequently, the weakest point of
such composite elements consists in the possible
debonding (delamination) of the external facings of the
sandwich (skins), which must possess considerable
rigidity and strength, from the central part of the sand-
wich (core), which is required to possess a low specic
weight and an adequate shear stiness.
This note presents the salient results of an experi-
mental and numerical study on the mechanical beha-
viour of a syntactic-foam/glass-bre composite sandwich
primarily designed as a lightweight material for naval
engineering applications (Fig. 1). The sandwich core
material is a syntactic foam consisting of hollow glass
microspheres embedded in an epoxy resin matrix, whereas
the sandwich skins are glass-bre/polymer-matrix com-
posites. To reduce the risk of possible delamination
damage, the interior layers of the skins are interconnected
to each other by glass bre piles which cross the syn-
tactic foam core. Actually, the sandwich under study is
in practice a monolithic element made by a sandwich-fabric in which the syntactic foam core is inated until
the proper sandwich thickness is obtained.
The mechanical characterization of this highly hetero-
geneous material (or rather, structural element) has
been carried out at the Department of Structural Engi-
neering, Politecnico di Milano, through the following
sequence of steps: (a) experimental characterization of
the syntactic foam material adopted for the core; (b)
development and numerical exploitation of engineering-
oriented constitutive models for the foam behaviour; (c)
experimental testing of the sandwich panels and their
single components; (d) numerical FE simulation of the
sandwich panels under three- and four-point bending
tests. The present paper focusses on the results obtained
through phases (c) and (d) of the above program;
whereas the mechanical characterization of the syntactic
foam emerging from phases (a) and (b) is described in
detail in a companion paper [6]. A separate, compre-
hensive presentation and discussion exclusively on the
experimental results and techniques employed on both
syntactic foam and sandwich materials is further avail-
able to the interested reader in [7].
The paper is organised as follows. In Section 2, the
sandwich under study is fully described. The experimental
0266-3538/00/$ - see front matter # 2000 Elsevier Science Ltd. All rights reserved.
P I I : S 0 2 6 6 - 3 5 3 8 ( 0 0 ) 0 0 1 1 8 - 4
Composites Science and Technology 60 (2000) 21692180
www.elsevier.com/locate/compscitech
* Corresponding author. Tel.: +39-2-2399-4244; fax: +39-2-2399-
4220.
E-mail address: [email protected] (A. Corigliano).
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results concerning the uniaxial tension/compression
behaviour of the syntactic foam, the tensile response of
the composite external skins and the mechanical char-
acterization of the entire sandwich structure are pre-
sented in Section 3. Section 4 is dedicated to the
numerical simulations of both three and four pointbending (TPB, FPB) tests carried out on the sandwich
specimens. Closing remarks and future perspectives are
briey outlined in Section 5.
2. The sandwich under study
The syntactic-foam/glass-bre composite sandwich
under study was manufactured by a former branch of
Intermarine S.p.A. (Italy). The sandwich structure is
depicted schematically in Fig. 1a.
The sandwich skeleton is made by a sandwich-fabric,
produced by Parabeam (The Netherlands), studied in depthin the framework of a BRITE EURAM project (AFICOSS
Advanced Fabrics for Integrally-woven Composite
Sandwich Structures [8]). It is constituted by two plain-
wave fabrics maintained, through pre-impregnation, at
a xed distance by interwoven threads called piles [8]. A
side view of the sandwich-fabric is shown in Fig. 1b.
The syntactic foam core to be injected in the sandwich-
fabric was manufactured by the same industry which
furnished the whole sandwich, under the trademark
Tencara 2000TM. The foam is assembled with an epoxy
resin matrix which embeds hollow air-lled glass micro-
spheres. The matrix is made with SP Ampreg 20TM
epoxy resin treated with SP AmpregTM UltraSlow hard-
ener. The air-lled hollow glass microspheres, named 3M
ScotchliteTM Glass Bubbles, type K1, are manufactured
with a water-resistant, chemically stable, borosilicate
glass. Bubbles have an average diameter of 70 mm and an
average wall thickness of 0.58 mm. The syntactic foam isprepared by mixing resin and hardener under vacuum
and by adding microspheres repeatedly until full homo-
genization. The density of the resulting syntactic foam
averages 0.55 g/cm3 (see [6,9] for all the details).
To increase the stiness of the 3D fabric facings, two
additional layers of bi-dimensional fabrics were simply
laminated on them: a non-directional glass reinforced
plastic (GRP) fabric, called MAT 300TM (manufactured
by Vetrotex, Italy) and a plain-weave GRP fabric, called
ROVING 900TM (manufactured by Chomarat, France);
the ensemble of the fabrics constitutes the so-called
ROVIMAT 1200TM tissue (thickness 2.5 mm). These
additional layers will be called extra skins in the fol-lowing. The global thickness of the sandwich is t 15
mm; a side view is shown in Fig. 1c.
As can be observed from Fig. 1, in the nal sandwich
supplied by the producer for testing, the piles were not
completely stretched as they should be after a correct
manufacturing procedure, but they were inclined at
about 45. This fact has important consequences on the
mechanical behaviour of the tested sandwich, as will be
discussed later in Section 3.
Table 1 collects some nominal mechanical properties
of the single sandwich components as given by the
manufacturers. The data in Table 1 refer to uniaxialtension or compression tests. Due to the fact that the
ROVING 900TM is a plain weave directional fabric,
data are given for both loading in the weft and in the
warp directions.
3. Experimental results on the sandwich and its components
All the mechanical tests on the sandwich and its
components described in this Section have been per-
formed on an MTS 329.10 S testing machine, with axial
and torsional actuators. The axial jack has a static
capacity of 100 kN, with a maximum stroke of 150 mmand incorporates a linear variable dierential transfor-
mer (LVDT). The torsional jack is mounted in line with
respect to the axial jack. It has a static capacity of 1100
Nm, with a maximum stroke of 50 and with an angular
dierential transformer (ADT) mounted on it.
3.1. Uniaxial tension/compression tests on the syntactic
foam
This section concerns the uniaxial tests performed on
the syntactic foam Tencara 2000TM which constitutes
Fig. 1. The sandwich under study: (a) schematic representation; (b)
side picture of the three-dimensional fabric; (c) side view of a piece of
the nal sandwich after foam ination.
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the core of the sandwich. The material specimens were
prepared directly by the manufacturer.
For the compression tests, specimen shapes and sizes
were determined according to UNI 6132-72 for concrete
and to ASTM D 695 M-91 for composites (Fig. 2a).
Guideline for tensile specimens geometry was the
ASTM D 638 for composites (Fig. 2b). The stress/strain
curves from the uniaxial tests are reported in Fig. 2c.The compression behaviour is rather ductile, with a
softening post-peak branch which tends to stabilize on
an horizontal plateau at residual strength. Loading/
unloading paths performed in some of the compression
tests showed that the elastic stiness degradation is not
particularly signicant [7]. The collapse mechanism is
preceded by strain localization along a shear band
inclined to an angle of about 45 with respect to the
loading axis: interlocking and friction govern the beha-
vior after the onset of strain localization and are
responsible for the residual strength that can beobserved in the stress/strain curves (Fig. 2c). The
response under tension is instead perfectly brittle with
rupture on a section perpendicular to the loading axis;
only one test displayed fracture in the central part of the
specimen; the other two tests exhibited breakage in
zones near the tapered sections and showed slightly
lower tensile strength.
The values of experimental elastic stinesses and
strengths are reported in Table 2, together with the
nominal values furnished by the manufacturer, repeated
from Table 1 for the sake of comparison. Tensile
strength, 't
mx 15X6 MPa, is about 55% of the com-pressive strength, 'c
mx 28X4 MPa; Young's modulus
in tension, Et 2X2 GPa, is about 38% larger than
Young's modulus in compression, E 1X6 GPa. The
phenomenological feature of bimodularity Et T E is
not pointed out in the available literature on syntactic
foams (see the references quoted in [6]). Part of the dif-
ference should be attributed to the fact that the speci-
mens tested in tension belonged to a second set of
syntactic foam specimens which displayed lower degree
of porosity and compressive stiness about 15% higher
with respect to the set tested in compression. The
remaining 20% dierence should be mainly explained in
terms of the presence of air bubbles between matrix andller. In fact, further experimental tests on foams pre-
pared with more careful manufacturing techniques did
not show appreciable dierences in elastic stinesses [7].
Poisson's ratio was instead rather unaected by the sign
of the applied stress: the average value of # 0X34 was
recorded. In the following no consideration will be further
taken of the syntactic foam bimodularity. Moreover, as
explained in Sections 3.3 and 4, the elastic modulus
attributed to the core for numerical simulations has
been chosen equal to that obtained in atwise compression
tests on the sandwich.
Table 1
Mechanical nominal data on the single sandwich components as provided by the manufacturera
Tension Compression
'tmx
w 4tfil
7 Etw 'tmx
w 4tfil
7 Etw
Syntactic foam 16 0.92 1812 32 8.9 1414
Roving Weft 175 1.7 14 200 215 17 000
900/53/300TM Warp 210 1.5 17 000 235 18 100
MAT300TM 98 8050
a Data for ROVING fabric are given for loading in both weft and warp directions.
Fig. 2. Uniaxial tension/compression tests on the syntactic foam (ten-
sion positive): (a) shape and size of the specimen used for compression
(dimensions in mm); (b) shape and size of the specimen used for ten-
sion (dimensions in mm); (c) stress/strain curves.
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Beside the uniaxial tests, biaxial compression tests
and TPB tests on notched specimens were also per-
formed on the syntactic foam. The rst suggest an egg-
shaped failure domain typical of frictional geomaterials;the second showed a quasi-brittle response during frac-
ture (see [6, 7]).
3.2. Tension tests on the composite extra-skins
Uniaxial tension tests were performed on specimens
of 1 mm thickness made with the same material of the
extra skins (ROVIMAT). The ASTM D 3039 was fol-
lowed, which provides specimen shape and size (Fig.
3a), suggestions on loading xtures and a way to classify
the dierent failure modes.
The specimens, which were directly provided by themanufacturer, were instrumented with glued electric
strain gauges: because of the size of the fabric repeated
unit cell (10 mm), large grid strain gauges were choosen
and only few specimens were equipped with an addi-
tional transverse device to detect the transversal strain.
Because of marked anisotropy, seven specimens were
cut parallel to each of the two main warp and weft
directions and were tested under displacement control at
a 1 mm/mm loading rate.
As shown in Fig. 3b, where the results of a typical test
are reported, the composite skin shows an almost linear-
elastic brittle behaviour with a slight deviation near
failure, caused by the successive partialization of thecross-section; just before the complete rupture of the
fabric the threads fail one after another causing a rapid
decreasing of strength. The failure is sudden and brittle
and displays the typical pattern shown in Fig. 4.
The elastic stinesses and strengths of the composite
skins as measured through the tests are compared in
Table 3 with the nominal values given by the producer.
The composite tested shows a less marked anisotropy in
the elastic moduli and a more marked one in the values
of strength with respect to the nominal data (see also
Fig. 3b).
3.3. Flatwise compression tests on the sandwich
The C365-94 ASTM [10] was followed to perform
atwise compression (FC) tests on the sandwich. The
norm covers the determination of the compressive
strength and of the elastic modulus of sandwich cores in
the direction normal to the plane of the structure.According to the norm, the specimens, of square geometry
with sides of 25 mm (Fig. 5a), were loaded under displace-
ment control at a rate of 0.5 mm/min. The displacement
Table 2
Experimental mean values and nominal values of the syntactic foam
properties in uniaxial tension/compression
Nominal value
provided by the
manufacture
Experimental
mean
value
Tension 't
mx w 16 15.64tfil
7 0.92 0.7
Etw 1812 2200
#t 0.34
Compression 'mx
w 32 28.4
4fil
7 8.9 3.5
Ew 1414 1600
# 0.34
Fig. 3. Composite extra-skin tested under tension: (a) shape and size
of the specimen used (dimensions in mm); (b) axial and transverse
stress/strain responses under tension in both weft and warp directions.
Fig. 4. Composite extra-skin tested under tension. Picture of a speci-
men after rupture.
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was measured by four LVDTs applied to the loading
plate (Fig. 5b). Fig. 5c shows a side and a top view of a
specimen after the compression test.
Fig. 6 shows the stress/strain experimental curves
corresponding to eight dierent tests. The rst seven
plots are named FC1-FC7; the last one, labeled FCC, has
been obtained by prolonging the test until the maximumavailable limits for the loading device: only part of the
total response is shown in the gure. The values of the
stresses corresponding to a 2% strain (as prescribed by
the norm) and of the elastic moduli are given in Table 4.
At dierence with the plain syntactic foam (Section
3.1), the sandwich core under atwise compression
shows a ductile behaviour. Moreover, after a plastic
plateau, a strong locking is shown due to the following
the complete compactness reached and to the three-dimensional containment eect created by the stier
skins and by the piles. Another eect which can justify
the increased ductility of the core compared with that of
the simple foam is represented by the piles inclination.
During loading, the sandwich may in fact undergo a
shear deformation with relative sliding of the external
skins which is contrasted by the piles. It is interesting to
remark that syntactic foams loaded in triaxial compres-
sion show similar qualitative locking behaviours (see,
e.g. [11]).
Comparing the values in Table 4 with the compressive
elastic properties of the foam (Table 2), it can be noticed
that the mean value of the stiness of the syntactic foamcore (with the sandwich-fabric piles) is about 21% lower
than that of the plain foam. This reduction in stiness is
again to be attributed to the presence of the piles, which
preclude full monoliticity of the foam: the epoxy resin,
mixed with the glass bubbles, is in practice a viscous
uid which is not easy to inject in the narrow empty
space inside the sandwich-fabric. In [7], the estimated
values of the voids percentages in the core as a result of
the presence of piles are reported and it is shown that
the mechanical properties of the sandwich decrease at
increasing void percentage; i.e. the responses in Fig. 6
vary from FC1 with a void percentage of about 22% toFC7 with a void percentage of about 30%.
Table 3
Experimental mean values and nominal values of the extra-skins in
uniaxial tension for loading in the weft and warp direction
Nominal value
provided by the
manufacture
Experimental
mean
value
Warp 'tmx
w 210 267
4tfil
7 1.5 2.3
Etw 17 000 14 707
#t 0.20
Weft 'tmx
w 175 187
4tfil
7 1.7 2.0
Etw 14 200 13 153
#t 0.21
Fig. 5. Flatwise compression (FC) tests on the sandwich: (a) shape
and size of the specimen used (dimensions in mm); (b) the specimen
mounted on the testing device; (c) side and top views of a specimen
after the test.
Fig. 6. Stress/strain response of the sandwich under atwise compres-
sion (eight tests, one carried out until maximum stroke is reached).
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3.4. Flatwise tension tests on the sandwich
The atwise tension (FT) tests were performed
according to the ASTM C 297-94 [12], on square speci-
mens with 25 mm side, hence the same specimens used
for the atwise compression tests (Fig. 7a). The test
method covers the evaluation of the bond resistance
between core and skins in a sandwich structure. As
suggested by the norm, the tests were carried out by
using self-aligning loading xtures, composed by a couple
of sti loading blocks bonded to the skins by a suitable
adhesive (Fig. 7b). All the specimens failed due to dela-mination of the weakest interface in the series arrange-
ment, namely the ROVIMAT/sandwich-fabric interface
(Fig. 7c).
The values of stress at debonding 'tmx
are given in
Table 5 for ve tests (FT1FT5). The data of Table 5
show the weakness of the bond between the sandwich-
fabric and the ROVIMAT. The failure of the skin/core
bond was also investigated by edgewise compression tests,
which are separately described in [7], and by exural tests
as discussed below in Section 3.5. The weakness of the
ROVIMAT/sandwich-fabric bond can be mainly
attributed to the production technology which consisted
in a simple lamination. On the light of the experimental
observations, this manufacturing technique appears to
be rather inadequate and should be improved or sub-stituted by a more ecient one.
3.5. Three- and four-point bending tests on the sandwich
Three- and four-point bending (TPB and FPB) tests
on at sandwich panels were conducted according to the
ASTM C 393-94 [13], in view to determine the sandwich
exural stiness, the core shear modulus G and the core
shear strength (mx. Rectangular plates 110 mm long
and 30 mm wide were cut from the 16 mm thick sandwich
panel. Fig. 8 displays specimens and testing devices.
The sandwich panels were prepared by cutting themout of a larger panel in two dierent ways with respect
to the piles orientations in the core. A rst group of
specimens was prepared so that the piles were inclined
along the specimen length, and a second group so that
the piles were inclined along the specimen width. From
the dierence in the recorded mechanical properties of
the two groups, it can be inferred that the piles inuence
the core mechanical properties.
In Table 6 are given values of G and (mx, as derived
from the tests. The core shear modulus G was calculated
from the measured deections of the specimens on the
three-point bending tests as suggested by the ASTM
standard. The core shear strength (mx was determinedfrom both TPB and FPB tests.
The data collected in Table 6 show that the specimens
under FPB display an higher shear resistance of the
core; this can be partially explained by observing that
Table 4
Experimental data of the sandwich in atwise compression (FC) tests
FC1 FC2 FC3 FC4 FC5 FC6 FC7 Average value
'27w 22.72 21.31 21.4 16.98 26.42 15.57 15.88 20.04
Ew 1148 1054 1290 1053 1765 845 687 1120
Table 5
Experimental data of the sandwich in atwise tension (FT) tests
FT1 FT2 FT3 FT4 FT5 Average value
'tmx
w 6.34 4.11 8.03 4.32 6.47 5.85
Fig. 7. Flatwise tension (FT) test on the sandwich: (a) shape and size
of the specimen used (dimensions in mm); (b) the specimen mounted
on the testing device; (c) three specimens after testing showing dela-
mination failure.
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the risk of local core crushing under the load points is
lower when the load is applied through two points
rather than one.
Dierent kinds of load/displacement responses are
shown in Figs. 9 and 10 for TPB and FPB, respectively.
The dierence in the responses is a result of the various
failure mechanisms that may separately appear in thesandwich panel and lead to its nal collapse. The main
characteristic mechanisms reported for the specimen are
(Fig. 11ad): (a) unsymmetric collapse with the forma-
tion of a single 45 inclined crack in the core; (b) sym-
metric collapse with development of two 45 inclined
cracks in the core; (c) extra skin collapse in tension; (d)
extra skin delamination.
The kind of rupture mechanism is strongly inuenced
by the piles inclination. The single crack follows the
piles slope when the piles are inclined along the length
of the specimen (Fig. 11a); some specimens with piles
inclined along the specimen width showed the samebehaviour, whereas other specimens loaded on FPB
conguration failed with double symmetric crack opening
(Fig. 11b).
As shown in Figs. 10 and 11, the sandwich structure
can be loaded after the core failure: at higher loads the
failure extends to the skin under tension or, in some
cases, to the skin/core bond under shear.
Table 6
Experimental data of the sandwich in TPB and FPB tests
Piles inclined along
the specimen length
Piles inclined along
the specimen length
TPB G (MPa) 229 167
(mx (MPa) 12.6 12.8
FPB (mx (MPa) 13.7 15.8
Fig. 8. Flexural tests on the sandwich: (a) shape and size of the speci-
men used (dimensions in mm); (b) testing device for three-point-bend-ing (TPB); (c) testing device for four-point-bending (FPB).
Fig. 9. Load/displacement curves of TPB tests. Failure mechanisms ofcore rupture and lower skin rupture appear subsequently during the
test.
Fig. 10. Load/displacement curves of FPB tests. Dierent failure
mechanisms characterise the single test.
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4. Numerical FE simulations of the three- and four-point-bending tests
The purpose of this section is to present the numerical
FE simulations of the TPB and FPB tests on the sand-
wich. The numerical model adopted, described in Section
4.1, is based on rather simplifying assumptions. Such
choice has been made in order to check the possibility to
simulate the main rupture mechanisms observed in the
tests by making use of a commercial code, with the
addition of few, ad-hoc developed, procedures. Indeed,
the industrial-oriented simulations presented in Section
4.2 show the potentiality of the simplied procedure
adopted here. All the numerical simulations have beenperformed with the commercial nite element code
ABAQUS [14].
4.1. Numerical nite-element strategy and material
modelling
From the experimental results of Section 3.5 it can be
deduced that the main rupture mechanisms which may
develop in the TPB and FPB tests are the formation of
macroscopic cracks in the core or at the interface core/
extra-skins (delamination) and the extra-skin collapse in
tension (see Fig. 11). The purpose of the numericalsimulations was therefore to correctly capture those
single collapse mechanisms (and the corresponding failure
loads) when considered as independent and occurring
separately in the specimen.
The dierent materials in the sandwich thickness were
reproduced by the superposition of three strips of ele-
ments with dierent mechanical properties: two external
strips representing the skins and the extra skins (3 mm
thick) and a central layer for the core (9 mm thick).
In order to simulate, respectively, core collapse, skin
collapse or delamination, the numerical simulations
were done by activating separately a simplied proce-
dure for the simulation of the progressive damage in thecore, in the skins or in the line of elements near the
interface between the extra-skin and the core.
The simplied procedure consists in a local stiness
release at the Gauss point level, implemented through a
user subroutine. When a threshold value of a scalar
failure index is reached in a single Gauss point, the tensile
elastic modulus Et is annihilated locally; the contribu-
tion of that Gauss point to the element stiness matrix
is then brought to zero. Dierent failure indexes may be
considered, either based on local strain or stress states.
In the numerical calculations, a Rankine criterion was
Fig. 11. Recorded rupture mechanisms in TPB and FPB tests.
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assumed for the simulation of damage in the core and
the skins, while a control on the maximum shear stress
was adopted for the strip of elements at the boundary
core/lower skin for the simulation of skin debonding.
The above procedure implies that the mechanical
behaviour of the single constituents was assumed to be
elastic/perfectly brittle as depicted schematically in Fig.12. Moreover, in the simulations, the core was con-
sidered as homogeneous and isotropic, the presence of
piles was neglected, and the skins were also considered
as homogeneous and isotropic.
The critical value of shear stress for the simulation of
skin debonding was assumed equal to the ILSS (inter-
laminar shear stress) for the glass/epoxy-resin fabric:
(mx 16X4 MPa, since the delamination occurred
between the ROVIMATTM extra-skin and the sand-
wich-fabric external surface. This value of (mx was
derived from previous experimental tests on laminate
specimens similar to the sandwich skins considered here
[15,16]).The skin and core model parameters used for the
numerical simulations are collected in Table 7. The values
of the elastic modulus and failure stress of the external
skins were obtained from the tensile tests of the skin
alone (Section 3.2 and Table 3) by averaging the
experimental values obtained for loading in the warp
and weft directions.
The average critical-stress threshold and Poisson's
ratio for the core were obtained from the uniaxial ten-
sion tests on the foam (Section 3.1 and Table 2). The
elastic stiness of the core was instead taken from the
FC tests on sandwich specimens (Section 3.3 and Table
4), since it has been observed that the presence of piles
modies the Young's modulus with respect to the value
of the pure syntactic foam: the recorded ratio
EoreaEfom is in fact about 0.63.
The numerical analyses were conducted under theassumption of plane strain, since the specimen width to
span ratio is equal to 0.5 (Fig. 8a). Although the speci-
men geometry and loading congurations were symme-
trical, since the behaviour at rupture was unsymmetrical
in some cases, the whole cross-section was modelled. To
simulate single, unsymmetric, crack propagation, half of
the section was considered indenitely elastic, while in
the other half the local stiness release procedure was
applied.
The mesh adopted in the simulations are shown in
Fig. 13a and b for a symmetric TPB case and an
unsymmetric FPB one, respectively. The meshes are
composed of four node plane strain elements. Theloading and support rollers are simulated as rigid bodies.
4.2. Comparison between numerical and experimental
results for the three- and four-point bending tests.
In Fig. 13a and b the numerically computed crack
patterns at the end of the analyses in the numerically
simulated TPB and FPB are shown. More precisely, in
Fig. 13 the elements which were concerned in the stiness
release procedure are marked in black. Crack patterns
in Fig. 13 can be compared with the experimental ones
in Fig. 11; from the comparison it can be observed thatthe crack pattern is correctly reproduced, at least quali-
tatively. As in the experiments, during the numerical
simulations the rst elements which fail are near the
edge of the loading cylinders and the crack proceeds
from top to bottom and is inclined towards the lower
cylindrical support.
A numerical load/displacement plot obtained for the
TPB test by activating the rupture criterion in the core
only is compared in Fig. 14 with two experimental plots
concerning TPB tests which registered unsymmetric
failure in the core. The elastic stiness and the fracture
load are adequately captured considering the great sim-
plicity of the adopted model.Fig. 15 shows the comparison between experimental
and numerical load/displacement plots for the FPB
tests. In this case the control on the failure index is also
applied only in the core elements and the specimen tested
failed for unsymmetric crack propagation in the core.
The results of Fig. 15 show again that the numerical
analyses are in good qualitative and quantitative agree-
ment with the experiments.
Finally, in Fig. 16, two experimental load-displace-
ment plots concerning specimen failed for extra-skin
delamination are compared with a numerically simu-
Fig. 12. Schematic representation of the elastic/brittle behaviour
assumed for the numerical simulations.
Table 7
Mechanical data adopted for the numerical simulations of the TPB
and FPB tests
E (MPa) # 'tmx
w
Skin 14 000 0.20 225
Core 1100 0.34 15
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lated response. The numerical analysis was carried out
by activating the simplied procedure for progressive
damage simulation in the strip of elements at the
boundary core/lower skin.
In this case, the agreement between the numerical and
the experimental failure loads is particularly good.
As shown by the results displayed in Figs. 1316, the
simplied procedure devised in the present analyses
Fig. 13. Finite-element meshes adopted for numerical simulations of TPB and FPB tests. Marked elements represent the numerically simulated
crack pattern.
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leads to results which are overall in good qualitative
agreement with the experimental tests. As a matter of
fact, it can be noticed that the stiness release procedure
was already attempted in [6] with reference to the simu-
lation of the plain syntactic foam behaviour in notched
TPB specimens; however, in that case, the numerical
results were not completely satisfactory as a result of theconsiderable brittleness of the numerical responses
which did not take advantage of the extra structural
resources available here from the sandwich geometry. In
the simulations of the plain foam behaviour, an alter-
native, more rened procedure, based on the discrete
crack approach (see, e.g. [1721]) was also adopted,
leading to a considerable improvement of the numerical
results. Such computational procedure could also be
employed here for a further renement of the present
results, but this falls beyond the scope of the present
simulations and comparisons to the experimental tests.
5. Closing remarks
The present paper focussed on the mechanical experi-
mental characterization and numerical simulation of a
syntactic foam/glass bre composite sandwich con-
ceived as a light-weight material for naval engineering
applications.
The experimental campaign conrmed the remarkable
potentialities of the innovative sandwich structure with
syntactic foam core and skins interconnected by trans-
verse piles. The structured material studied appears to
be well suited for naval engineering and, more generally,for advanced transportation related technologies.
The use of a syntactic foam to ll the sandwich core
appears to increase the sandwich stiness and strength
quite remarkably with respect to lighter but weaker
solutions; at the same time it furnishes a drastic weight
saving with respect to a fully laminated glass-bre-rein-
forced plate.
As a main point of remark, from the experimental
study, it emerges the considerable weakness of the
sandwich/extra-skins bonding. The risk of delamination
of the extra skins in real engineering applications could
then be quite relevant; this should be, at least partially,
eliminated or reduced by improving the productiontechnology on this specic aspect.
The models chosen for the numerical simulations
represent a good compromise between the conicting
requirements of correctly describing the real material
behaviour and of oering a cost-eective analysis tool for
numerical simulations in a real industrial environment.
A better agreement between experimental results and
numerical simulations could be obtained by adopting
more sophisticated constitutive modelling and relevant
computational techniques. In particular, for the simula-
tion of damage processes and strain localization in the
Fig. 14. Comparison between experimental and numerical load/dis-
placement plots for the TPB tests with core rupture. Marked lines:
experiments.
Fig. 15. Comparison between experimental and numerical load/dis-
placement plots for the FPB tests with core rupture. Marked lines:
experiments.
Fig. 16. Comparison between experimental and numerical load/dis-
placement plots for the FPB tests with skin delamination. Marked
lines: experiments.
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core, use could be made of ad-hoc formulated damage
models (see, e.g. [2225]), while the phenomenon of
extra-skin delamination could be captured by making
use of suitable interface models (see, e.g. [2629]). Also
the possible rate dependency of the sandwich mechanical
behaviour should be checked and possibly simulated by
means of suitable models.
Acknowledgements
The present paper originated from a research project
between Intermarine S.p.A. and Politecnico di Milano
headed by Professor Giulio Maier at the Department
of Structural Engineering. At that time, author E.R.
was an employee of Politecnico di Milano. The authors
wish to thank Intermarine SpA for providing reference
material on composites for naval engineering applica-
tions and for granting permission to publish the pre-
sent results. We are grateful to Professor Giulio Maierfor involving us in this research topic and for fruitful
discussions on selected related subjects. We acknowl-
edge the contributions of our former students Mara
Savioli and Ilaria Schiavi who were involved in the pre-
sent research during the preparation of their Laurea
theses.
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