experimental characterization and numerical simulations

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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.

2170 A. Corigliano et al. / Composites Science and Technology 60 (2000) 21692180


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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.

A. Corigliano et al. / Composites Science and Technology 60 (2000) 21692180 2171


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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



10/12

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.



11/12

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.


placement plots for the FPB tests with core rupture. Marked lines:

experiments.


placement plots for the FPB tests with skin delamination. Marked

lines: experiments.



12/12

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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