Structural behaviour of composite sandwich panels
for applications in the construction industry
Maria Inês Avó de Almeida
M.Sc. Thesis Extended Abstract
October 2009
Structural behaviour of composite sandwich panels
for applications in the construction industry
1
Introduction
The recent need for structures with low self-weight, high stiffness and durability has increased the demand for
composite materials, from which sandwich structures are an example [1]. And, in fact, the use of composite
materials in general and glass fiber reinforced polymers (GFRP) in particular has increased significantly in the
past few years due to their low self-weight, high strength, good insulation properties and improved durability
even in harsh environments. However, due to the low Young’s modulus their design is often influenced by
instability phenomena and deformability. In addition, in alkaline environments and when submitted to high
temperatures, an appropriate special design is required [2].
Sandwich panels are applied in situations that require high mechanical strength and low weight and, in
addition, when adequate levels of sound and thermal insulation are needed. Sandwich panels are composite
materials with a three layer structure: two thin, stiff and resistant composite material skins (such as GFRP),
separated by a layer of a low density material that can be much less stiff, resistant and durable than the skins
[3]. The proper combination of different core and skin materials allows merging the most advantageous
properties of each constituent material, and even eliminating some of their negative properties. The
combination of GFRP skins with appropriate cores allows obtaining high stiffness-to-weight and strength-toweight ratios.
The durability of GFRP skins allows increasing the service life of built structures with relatively lower life cycle
costs and fewer load restrictions [4]. The development of new production techniques has made sandwich
panels affordable and their pre-fabrication allows an easier mounting, with greatly reduced construction times.
When protected by the skins, the core material may confer excellent thermal insulation properties [5], good
stress dissipative characteristics and energy absorption [6]. However, the low resistance to high temperatures,
the potential excessive deflections for relatively high loads, the poor acoustic insulation (comparing to
structural solutions with higher mass, such as concrete and masonry), a wide variety of failure modes and,
above all, the lack of information for engineers and designers, make the acceptance of sandwich panels by the
construction industry more difficult [7].
Marine and aerospace industries had an important role in the development of composite materials and were
responsible for the first applications of sandwich panels. Subsequently, their field of application was extended
to the automobile and shipbuilding industries and, more recently, to the transportation industry [8], to
geotextil infrastructures, to the stabilization and drainage of soils [4], to offshore oil structures [9], to the wind
industry and sports [7]. In construction, sandwich panels have been applied as structural elements in vehicular
bridges, in footbridges, in the rehabilitation or replacement of concrete bridges, in cladding, roofing and also as
partition wall elements [8], sometimes with translucent properties [10].
In order to improve the performance of sandwich panels with standard geometry, different types of
reinforcements have been studied. Stitches have been one of the most studied ones. Potluri et al. [11]
concluded that the mechanical properties of the skins, including their strength, stiffness and fatigue behaviour
1
can vary according to the type of composite material and sewing technique. Lascoup et al. [12] studied the
effect of introducing stitches crossing the two skins and the core and concluded that stitching increases
significantly the stiffness and the ultimate strength, in terms of bending, shear in the core and flatwise
compression. Hassan and Reis [1] studied the effect of introducing fiber elements with a three-dimensional
architecture that join the GFRP skins and the foam core and concluded that this strengthening technique
increases the stiffness of the sandwich panel and that the uncracked foam used as a filling material confines
the fibers and contributes to increase significantly the core shear modulus. Sharaf and Fam [13] studied
different configurations of ribs and their influence on the mechanical properties of panels made of GFRP skins
and polyurethane foam core. They concluded that the ribs significantly increase the strength and stiffness of
the panel.
In this paper the possible use of GFRP sandwich panels as structural elements in construction is investigated. In
particular, their possible use in floors of buildings or decks of pedestrian bridges is envisaged. An experimental
campaign was performed in order to study two types of composite sandwich panels with GFRP skins and a core
made of either (i) rigid polyurethane foam or (ii) honeycomb polypropylene core material. In addition to the
evaluation of the effect of the core material on the service and ultimate behaviour of the GFRP sandwich
panels, the objective of this research project was to investigate the effect of adding GFRP reinforcements to
the longitudinal lateral edges of these two types of panels. Dynamic tests were also performed to determine
and compare the dynamic behaviour of these panels. The study was complemented by the numerical modelling
of rigid polyurethane foam core sandwich panels. The objective was to develop simple numerical models
capable of simulating the mechanical behaviour of sandwich panels at service and ultimate limit states,
calibrated with the experimental results, therefore avoiding the need to carry out further experimental tests on
different geometries.
2
Analytical study of sandwich panels behaviour
In order to predict the service and ultimate behaviour of sandwich panels, a survey of analytical equations that
describe their behaviour was first undertaken. The behaviour of a panel or a sandwich beam can be compared
to an I beam, where the skins act as flanges, supporting the tensile and compressive axial stresses, and the core
functions as the web of the profile, setting the distance between the skins and resisting to shear stresses. The
skins are connected to the core by means of an adhesive material that transfers the stresses between the two
elements. The maximum deflections of sandwich panels are an important design criterion for the service limit
state. The vertical displacement of a sandwich panel is the sum of two parts: (i) the bending deflection and
(ii) the shear deflection. The maximum deflection at mid-span of a sandwich panel (w) subjected to a
concentrated load (P) or a uniformly distributed load (p) along the span (L) may be estimated by equations (2.1)
and (2.2), respectively, where b is the width, ec is the core thickness, eL is the skin thickness, D is the flexural
stiffness and Gc is the core shear modulus. The values of the constants Kg and Ks are presented in table 2.1 for
different supporting and loading conditions [13]. Certain materials, such as some foams and GFRP skins,
present a considerable creep, which should be considered in service limit states design.
2
w
w
3
K g PL

K s PL
D
b ( e c  e L )Gc
4
K g pL
2
K s pL

D
(2.1)
(2.2)
b ( e c  e L )G c
Table 2.1 Values of Kg e Ks for different supporting and loading conditions (adapted from [15]).
Support conditions and load type
Kg
Ks
1/48
Support conditions and load type
Kg
Ks
1/4
1/8
1/2
1/192
1/4
5/384
1/8
1/3
1
1/384
1/8
A sandwich panel has several different failure modes, which may condition its load-bearing capacity. Such loadbearing capacity depends on the sandwich materials, the panel dimensions and the structural geometry itself.
Table 2.2 presents the most common failure modes and their corresponding design equations.
Table 2.2 Most frequent failure modes of sandwich panels and corresponding design equations.
Tensile failure of the skins [16]
Compressive stress
Buckling failure [16]
Shear crimping failure [16]
P  2e b L,u
u
L
2
 D
Pb 
2
2  D
L 
G c db
Pb,c  ec Gc b
Intra-cellular buckling
failure [17]
2EL  eL
 cr,cel. 
2 
(1   L )  s
Wrinkling failure [16]
 cr,w  0.50 E C GC E L

Core shear failure [9]
V  bd Cv
u
Crushing failure of the skins and the
core [9]
F  L  Cc
u
s
d - distance between center-lines of
opposite skins;
s - cellular core dimension;
Ec - core Young’s moduli;
EL - skin Young’s moduli;
νL- skin Poisson’s ratio;



3
Vu - ultimate shear force
Pu - ultimate tensile force;
Pb - ultimate compressive force
(buckling);
Pb,c - ultimate compressive force
(shear crimping);
3
2
1
σL,u - skin tensile strength;
σcr,cel. - intra-cellular buckling compressive
strength;
σcr,w - wrinkling compressive strength;
σCc - compressive strength;
τCv - shear strength.
3
Experimental investigations
3.1
Experimental programme
The objective of the experimental programme was to study and to compare the behaviour of four composite
sandwich panels: (i) two standard sandwich panels with GFRP skins, and different core materials - one of them
with polyurethane (PU) rigid plastic foam core and the other one with polypropylene (PP) honeycomb core
(designated by PU-U and PP-U, respectively); and (ii) two sandwich panels with GFRP skins, comprising GFRP
ribs on the longitudinal edges, each one with the referred core materials (designated by PU-R and PP-R,
respectively). The sandwich panels were produced with the hand lay-up technique (figure 3.1) by the
Portuguese company ALTO, Perfis Pultrudidos, Lda. The GFRP skins were made of three different types of mats
(bride veil mats, chopped strand mats and woven fabric mats), embedded in a polymer matrix of polyester
resin. The lateral reinforcements (ribs) were made by folding the skin mats (the upper one) through the border
of the other skin (the lower one).
Figure 3.1 Hand lay-up technique.
The experimental programme included different types of mechanical tests. Initially, the material of the
sandwich panels was characterized by means of (i) flatwise tensile tests of the GFRP laminates and (ii) edgewise
and (iii) flatwise compressive tests of GFRP sandwich specimens (figure 3.2). Subsequently, the structural
behaviour and some of the most relevant mechanical properties of the sandwich panels, such as their elastic
constants and strength, were evaluated by means of full-scale flexural tests, that included static tests to
determine the service and ultimate behaviour and dynamic tests to investigate the dynamic behaviour.
Figure 3.2 Flatwise tensile test of a GFRP skin (left) and flatwise (centre) and edgewise (right) compressive tests of sandwich specimens.
4
3.2
3.2.1
Tests on sandwich panels coupons
Flatwise tensile tests of GFRP laminates
A total of 6 GFRP laminates identical to those used in the skins of the panels were tested with the following
nominal dimensions: height of 300 mm, width of 25 mm, thickness of 6 mm and distance between grips of
150 mm. The tensile force was applied in the laminate longitudinal axis with an Instron universal hydraulic
testing machine (with a load capacity of 250 kN). Load was applied at a speed of 0.18 mm/s with a grip
pressure of 40 bar. The load and displacement of the machine during the tests were registered on a PC using a
HBM data acquisition system with 8 channels, model Spider8. The axial strains were measured in the
longitudinal direction of 3 specimens with TML electrical strain gauges. The GFRP laminates showed a linear
elastic behaviour until failure and a Young's modulus (EGFRP) of 20.5 GPa was measured. A brittle tensile failure
occurred for a maximum average load (Fmax) of 32.6 kN. The average values of the tensile strength (u) and
strain at failure (u) were also experimentally determined (see table 3.1).
Table 3.1 Properties of GFRP laminates.
Test
Flatwise tensile
(ISO 527-1,4) [18, 19]
3.2.2
Material
Fmax [kN]
u [MPa]
u [µstrain]
EGFRP [GPa]
GFRP
32.60 ± 1.98
202.39 ± 15.35
1128 ± 84
20.47 ± 0.916
Flatwise compressive tests
In these tests the flatwise compressive behaviour of the different core materials was evaluated. The tests were
performed on sandwich specimens (6 for the PP core and 5 for the PU core) with 5 mm thick GFRP skins and
2
90 mm thick core materials, and with a square cross section of 100 × 100 mm . To ensure a uniform transfer of
loads from the testing machine to the specimen surfaces, a layer of polyester resin was applied in the skins in
order to level out their surface, thereby guaranteeing that the specimen surface was fully in contact with the
plate of the testing machine. The load was applied with the same machine used in tensile tests and the values
of the load and machine displacement were registered on a PC using a HBM data acquisition unit of 8 channels,
model Spider8. Specimens made of both core materials showed an approximately linear initial behaviour up to
the maximum load (Fmax), whose average value was 24.1 kN for the PP honeycomb and 3.01 kN for the rigid PU
foam. After the occurrence of a load reduction (which was less pronounced in the rigid polyurethane foam
specimens), the load-deflection curves of both materials showed a plateau with an increase of the
displacement values for approximately constant loads of about 10-12 kN and 2.75 kN for the PP and PU foam
cores, respectively. High residual deflections were observed after unloading (see figure 3.3). Average
compressive strengths (u) and stiffnesses (K) were estimated, together with the apparent Young’s modulus
(Eapparent) of both materials, which were estimated based on the assumption that the GFRP skins did not deform
(table 3.2). The results obtained allowed concluding that in the flatwise direction the PP honeycombs were
stiffer than the PU foam - the Young’s modulus of the PP honeycomb core (52.9 MPa) were significantly higher
than that of the PU foam core (5.6 MPa) - and, at the same time, they were considerably stronger (2.40 MPa vs.
0.29 MPa).
5
Figure 3.3 Load-displacement curve for (i) PP honeycomb core (left) and (ii) PU foam core (right) specimens.
Table 3.2 Flatwise and edgewise compressive properties of PP honeycomb core and PU foam core sandwich specimens.
3.2.3
Test
Material
Fmax [kN]
u [MPa]
E [MPa]
K [kN/mm]
Flatwise compressive
(ASTM C365-03) [20]
PP
24.09 ± 1.41
2.40 ± 0.16
52.90 ± 5.21
10.43 ± 1.54
PU
3.01 ± 0.06
0.29 ± 0.01
5.60 ± 0.45
1.02 ± 0.10
Edgewise compressive
(ASTM C364-99) [21]
PP
212.90 ± 28.70
3.31 ± 0.43
-
65.49 ± 10.76
PU
122.28 ± 19.56
2.01 ± 0.29
-
67.95 ± 9.62
Edgewise compressive tests
The egdewise compressive tests allowed evaluating the in-plane behaviour of the sandwich panels specimens.
The specimens used in these tests (6 for each type of core) had a thickness of 101 mm and presented a square
2
section of 250 × 250 mm . The surfaces of the specimens in contact with the plates of the testing machine were
also levelled. For the PP specimens, this was accomplished by adding a layer of polyester resin as the surface of
this core is discontinuous due to the geometry of the honeycombs. In about half of the tests (specimens
Ct.PU5, Ct.PU6, Ct.PP4, Ct.PP5 and Ct.PP6) two transducers were placed on each side of the specimens to
measure the horizontal displacements at their centre. The same hydraulic machine used in the tensile tests was
used to apply the load. Both types of specimens showed a non-linear initial behaviour most likely due to the
loading system, namely due to the adjustment of the plates to the specimen. The load increased up to a value
of about 110 kN and, approximately for this load, the load-vertical displacement curves exhibited a small
section with increased displacements for an approximately constant load. After this small section, the load
increased again until failure (see figure 3.4). The average ultimate strength (Fmax) of the PP honeycomb core
specimens (212.9 kN) was approximately twice of that of the PU foam core specimens (122.3 kN) (table 3.2).
Failure of PP honeycomb core specimens occurred (i) by buckling instability of the skins, sometimes followed by
delamination, and (ii) by crushing of the skins near the hydraulic machine’s plates. Failure of PU foam core
specimens occurred (i) by buckling instability of the skins, followed by delamination, or (ii) by shear failure of
the PU foam and/or by crushing of the skins next to the metal plates of the testing machine. The higher
flexibility in the out-of-plane direction of the PU foam (compared to that of the PP honeycombs) allowed it to
follow the skins deformation. The axial stiffness of the two types of sandwich panels is similar as it depends
essentially on the skins. Based on simple calculations, it was concluded that the axial stiffness of the tested
6
panels is considerably lower than the axial stiffness of current concrete or timber floors - this is a disadvantage
when the use of sandwich panels in building floors is planned and it may be necessary to adopt thicker skins. In
this case, a similar stiffness to that of timber floors may be obtained by doubling the skins thickness.
Figure 3.4 Load-displacement curves for (i) PP honeycomb core (left) and (ii) PU foam core (right) specimens.
3.2.4
Flexural test of a PP honeycomb core panel
To determine the bending and shear stiffness of the PP honeycomb core, a panel of this material was tested
(without skins) according to ASTM C393-00 standard [22] with the following dimensions: length of 2.50 m,
width of 0.50 m and thickness of 0.09 m. The mid-span point load was applied by successively placing metal
plates, within 1 minute intervals. A TML displacement transducer, model CDP100, with a stroke of 100 mm and
a precision of 0.01 mm, was used to measure deflections at mid-span. The elastic constants were tentatively
estimated by performing a linear regression analysis of the slope values obtained from the load-deflection
curves (δ/PL) concerning panels with different lengths: (i) 1.5 m, (ii) 2.0 m and (iii) 2.4 m. The slope corresponds
to 1/48D and the intercept to 1/4U. This method is only valid for linear elastic behaviour materials and, in this
case, for all spans and load levels, a significant creep was observed. Therefore, it was not possible to estimate
the apparent elastic constants of the core material with this technique.
3.3
Full-scale static flexural tests on sandwich panels
Two types of static flexural tests were performed: tests for the characterization of (i) service and (ii) ultimate
behaviour. In the first type of tests the panels were loaded in a 3 point bending configuration up to a 10 mm
displacement at mid-span. In the second type of tests the panels were loaded in a 4 point bending scheme up
to failure (figure 3.5). The panels, with a length of 2.50 m, a width of 0.50 m and a thickness of 0.10 m (5 mm
skins and 90 mm core) were tested according to ASTM C393 [22] in a 2.3 m span supported by cylindrical
2
bearings contacting with the lower surface of the panels in an area of 0.06 × 0.5 m . Load was applied with an
Enerpac hydraulic jack (with a load capacity of 300 kN) and measured with a Novatech load cell (with a load
capacity of 200 kN), placed between the jack and the sandwich panels. In order to guarantee a uniform load
distribution along the width of the panel, in the 3 point bending tests, a metallic tubular spreader plate (with a
0.04 m × 0.08 m section) was placed between the sandwich panel and the hydraulic jack; in the 4 point bending
tests, the loads were applied at a distance of 0.38 m from the mid-span section - two spreader beam plates
(with a width of 0.10 m) were used and a metallic beam was interposed between the hydraulic jack and the
7
spreader plates. Three TML, APEK and M = M electrical transducers with a stroke of 100 mm were placed under
the panel at mid-span and at a distance of 0.38 m from the mid-span section, coinciding with the two load
application points in the 4 point bending tests. For the failure tests, 4 strain gauges were placed in the midspan section, at a distance of 7.5 cm from the center of the width of the panel, in order to measure the
longitudinal strains in this section.
3.3.1
Tests for the characterization of the sandwich panels service behaviour
Three loading-unloading tests were performed in order to allow characterizing the mechanical behaviour of the
sandwich panels. In the second and third tests, the maximum load was applied for 10 minutes before
unloading. All panels showed a linear elastic behaviour for displacements up to about 10 mm, with the residual
displacements after unloading being lower than 1 mm. The bending and shear stiffness parameters and the
apparent elastic constants of the sandwich panels were determined using the equations that allow obtaining
the mid-span displacement in 3 point and 4 point bending. Knowing the values of the span, the applied load
and the corresponding displacement, the bending, D, and shear, U, stiffness values were determined. Based on
the equations presented in standard C393 [22], the apparent Young’s modulus of the skins, EGFRP, and the
apparent core shear modulus, Gc, were also estimated. The results obtained using this method were not always
congruent, particularly in what concerns the determination of the bending stiffness. Therefore, it was
concluded that somehow the method was not suitable to estimate the elastic constants of sandwich panels –
this issue should be addressed in future investigations.
3.3.2
Tests for the characterization of the sandwich panels ultimate behavior
Before applying the load up to failure, two loading-unloading tests were conducted up to a 10 mm
displacement at mid-span in order to guarantee the necessary adjustment of the test system. The ultimate load
(Fu) was significantly higher in the reinforced sandwich panels than in the panels without reinforcements (with
an increase of 158% and 171% in the panels with PP and PU cores, respectively). All panels presented a linear
behaviour up to failure, with a slight loss of stiffness occurring for loads close to the collapse load (figure 3.6).
The PP-U panel was slightly stiffer (Kp) than the PU-U panel (about 24%), which is in accordance with the
compressive tests that revealed the PP honeycombs to be stiffer than the PU foam. The stiffness of the
reinforced panels was very similar for the two different core materials and significantly higher than that of the
unreinforced panels – this can be easily perceived by the higher slope of the load-deflection curves. This higher
stiffness is provided by the lateral GFRP ribs.
Figure 3.5 4 point bending test setup.
8
The failure of PP-U panel occurred due to shear of the core material in a vertical surface of the honeycomb
cells, at about 60 cm from the left extremity of the panel. Delamination between the skins and the core also
occurred but it did not reach the support section of the panel. The failure of PU-U panel occurred also due to
shear of the PU foam, with a 45° angle failure surface at a distance of about 20 cm from the left extremity of
the panel. Delamination between the bottom skin and the core occurred up to the left extremity of the panel.
In the PP-R panel, the compressive force on the upper skin led to a local separation from the core material in
the mid-span section, forming a kind of bubble, and failure occurred by crushing/delamination on the top of
the bubble. The cracks spread through the side ribs, reaching its lower part but without reaching the bottom
skin. The failure of the PU-R panel was similar to that of the PP-R panel, also occurring in the area between the
application of the load but in a section near the left load application point. Unlike the panel PP-R, the cracks
spread through the side ribs and reached one side of the bottom skin.
Figure 3.6 Load-mid-span deflection curves of sandwich panels (left) and failure modes (right) in ultimate behaviour tests.
The load-strain curves of the unreinforced panels presented a linear evolution and the positive (ut) and
negative (uc) strains were similar, in absolute value. The reinforced panels showed a non-linear progress,
influenced by the bubble in the mid-span section which may have caused errors in the readings of the strain
gauges. In fact, in the panels without ribs, the neutral axis was exactly at mid-height of the cross section and
the increase of the strains was directly proportional to the bending moment increase. The PU-R panel axial
strain-section height curves show a significant increase of negative strains on the upper skin. The delamination
caused by the bubble led to a loss in stiffness in the failure section and therefore to an increase of the neutral
axis depth. The readings of the gauges in the PP-R panel were not valid – here, the strains data may contain
some errors due to the possibility of a deficient bonding of the gauges because of the skin surface excessive
irregularity/roughness.
Although no equations are available for the shear stresses of reinforced panels, it is reasonable to note that the
stresses at the core of the reinforced panels shall be lower than those of the unreinforced panels because most
of these stresses are taken by the ribs. Thus, shear stresses shall be approximately uniform across the width of
the core in unreinforced panels and they are expected to vary in reinforced panels (this was confirmed in the
numerical investigations). The properties in failure of each panel are presented on table 3.3.
9
Table 3.3 Properties of PP-U, PU-U, PP-R and PU-R sandwich panels.
1
2
3
4
5
Fu
[kN]
δmax
[mm]
Kp
[kN/mm]
σmax
[MPa]
τmax
[MPa]
εu,c
[µstrain]
εu,t
[µstrain]
Ec
[GPa]
Et
[GPa]
PP-U
28.26
51.57
0.665
43.58
0.30
-2015
2007
21.77
21.81
PU-U
31.74
72.54
0.536
48.94
0.33
-2751
2565
18.06
19.33
PP-R
72.83
72.30
1.084
78.09
-
-
3498
-
-
PU-R
86.13
89.16
1.246
85.81
-
-2509
4572
-
-
3.4
Full-scale dynamic flexural static tests on sandwich panels
In these tests centered and eccentric strikes were manually applied approximately at mid-span section of the
panels and their corresponding vertical vibration was measured with two accelerometers, A1 and A2,
symmetrically positioned at midspan at a distance of 5 cm from the lateral border of the panel. The
accelerometers (one from Bruel & Kjaer, model 4379, and the another one, equivalent, from Endevco), with a
precision of 0.01 mm, were connected to amplifiers (also Bruel & Kjaer, model 2635). The signal readings were
performed at a rate of 400 scans per second. The recording of the measuring apparatus was performed in PC
through an acquisition unit with 8 channels from HBM, model Spider8. In these tests, steel weights were placed
over the top skin of the panels in the support area to prevent them from lifting during the application of the strikes.
Although the strikes may have not been applied exactly with the same intensity in the different tests, maximum
values of vertical vibrations showed that the displacements in the unreinforced panels were higher than those
of the reinforced panels. Fast Fourier Transform (FFT) analysis allowed determining the natural frequencies and
their spectral values (see table 3.4). The highest spectral values corresponded to frequencies of about 1.0 to
1.5 Hz. However, they may not correspond to any natural vibration mode of the panels and may be influenced
by any other element of the testing system. For this reason, the scale of spectral values was reduced in order to
obtain the frequencies corresponding to the vibration modes of each panel. The introduction of lateral ribs
increased the flexural frequency and reduced the torsion frequency. Thus, the increase in torsional stiffness
6
was not sufficient to offset the extra weight of the panel .
Table 3.4 Flexural and torsional frequencies of the sandwich panels.
Panel type
PP-U
PU-U
PP-R
PU-R
Flexural frequencies [Hz]
1.07 (from 1.07 to 1.17);
29.84 (from 29.79 to 29.88)
1.11 (from 0.88 to 1.27);
24.37 (from 23.93 to 25.39)
1.09 (from0.98 to 1.47);
31.54 (from 30.76 to 33.30)
11.46 (from 1.95 to 30.18);
31.18 (between 30.18 to 32.71)
1
Torsional frequencies [Hz]
0.98 (from 0.88 to 1.07);
14.16
1.07 (from 0.93 to 1.27);
13.26 (from 12.99 to 13.38)
0.88 (from 0.78 to 0.98);
13.20 (from 13.09 to 13.28)
1.03 (from 0.88 to 1.17);
12.68 (between 12.40 to 13.09)
Stiffness of the panel: determined by the slope of loads and respective displacements.
Maximum axial stress: determined by the quotient between the maximum bending moment and the flexural
moduli.
3
Maximum shear stress: determined by beam theory (τ=V/bd).
4
Compressive Young’s modulus: determined by the slope of skin compressive tension and respective skin strains.
5
Tensile Young’s modulus: determined by the slope of skin tensile tension and respective skin strains.
6
Concerning the numerical results, as for the flexural frequencies between 1.0 and 1.5 Hz, it is believed that this
value may not correspond the first vibration torsional mode being associated to another element of the experimental
system.
2
10
4
Numerical investigations
4.1
Description of the finite element models
The three-dimensional finite element models were developed with the commercial software SAP2000 (version
11.07). Due to the higher difficulty in modeling the PP honeycombs (because of both their geometry and
anisotropic behavior) and due to time constraints, only the PU foam core sandwich panels (PU-U and PU-R)
were modeled. In order to reproduce as faithfully as possible the conditions of the experimental tests, the
panels were modeled with the same dimensions of the sandwich panels used in the flexural tests. The skins
were modeled with thin shell finite elements (thickness of 6 mm), the core material with solid finite elements
(4 layers with a thickness of 22.5 mm) and the lateral ribs of the PU-R panel with thin shell finite elements with
the same thickness of the top and bottom skins. The panels supports were modeled with solid finite elements
with the same width and thickness of the metallic plates of the cylindrical bearings in contact with the bottom
skin of the panels and the support restraints were set by the central nodes of the lower surface of those plates.
One support (the left one) was fixed and the other (the right one) also allowed to slide. The total load was
applied with uniform loads on the upper surface area corresponding to the metal plates used in the
experimental tests. For the dynamic analyses, masses were applied in the upper skin nodes at each support
-5
area (4.55 × 10 kg per node) – these masses correspond to the weight of the metal plates placed on the
supports to prevent the lifting of the panels. All materials were modeled assuming linear-elastic behaviour
(table 4.1). In the reinforced panel, only the numerical model and experimental values were compared due to
the absence of equations describing the reinforced panels behaviour.
Table 4.1 Properties of modeled materials.
Material
GFRP
PU
3
Density [kg/m ]
1582
69.67
2
Ex; Ey [kN/m ]
6
20 × 10
16900
2
Ez [kN/m ]
6
7.5 × 10 *
16900
2
Gxy; Gxz; Gyz [kN/m ]
6
3.5 × 10 *
6500
νxy
0.3*
0.3
νxz = νyz
0.1*
0.3
*[15]
4.2
Service behaviour
2
The panels were loaded with a 100 kN/m uniformly distributed load, equivalent to a total load of 10 kN, which
falls into the linear section of the load-displacement curve of the panels (see figure 3.6).
The calculated displacements at mid-span of both PU-U and PU-R panels were similar to those obtained
experimentally - the stiffness obtained with the numerical models of both panels (and also that of the
theoretical model stiffness, in PU-U panel) was slightly lower than the experimentally measured stiffness. The
error in the PU-U panel was about 15.5%, and in the PU-R panel it was about 26.2%, which is considered to be
acceptable taking into account the uncertainty on some materials properties, especially the rigid PU foam, and
the thickness of the skins and ribs (which, according to the experimental measurements, presented some
variability). In the PU-U panel, an increase of the Young’s modulus of the PU foam led to a better agreement
between the numerical model and the experimental values of mid-span displacement; the effect of varying the
GFRP skins Young’s modulus on such displacement was significantly lower. In the PU-R panel, the variation of
the Young’s modulus of the PU foam had a little effect, which shows that in those reinforced panels the
deformability is mainly driven by the ribs. The variation of the GFRP skins Young’s modulus reveals an
11
important effect on the behaviour of the panel - the variation in the mid-span displacement of panel PU-R was
about twice of that of panel PU-U, as in the former panel such variation affects both the skins and the ribs. The
variation of the shear modulus of the GFRP in the reinforced panel (PU-R) had some effect on the deformability
of the panel (although reduced), in opposition to the PU-U panel, where no influence was perceived (as
7
expected ). This shows that the lateral ribs contribute considerably to the stiffness of the panel and have an
important role in the serviceability behaviour of the panel. The variation of the thickness of the skins (and the
ribs, in the PU-R panel) has a significant influence in the mid-span displacement. Thus, the uncertainty of such
thickness in the tested panels may be one of the causes for the difference between experimental results and
numerical and theoretical (analytical) calculations.
8
In the PU-U panel, both calculated tensile (lower skin) and compressive (upper skin) strains were relatively
close to the experimental results - the numerical values were lower in absolute value, with errors of 7.7% and
11.1% concerning the negative and positive strains, respectively. The theoretical values were the highest, in
absolute value, with errors of 4.1% and 14.6% concerning the negative and positive strains, respectively. In the
PU-R panel, the numerical strains deviated significantly from those obtained experimentally, which may be due
to the already referred deficient bonding of the gauges on the test that certainly influenced the experimental
readings.
4.3
Ultimate behaviour
The theoretical and numerical stiffness of the PU-U panel were very similar but, as already mentioned, were
both lower than the experimental one for load levels corresponding to the linear-elastic behaviour. Regarding
the mid-span deflection at failure, the difference between numerical and experimental values was only about
6%. This reduction in the difference between calculated and measured deflections is mainly due to the fact that
the PU-U panel had a non-linear behaviour for load values higher than about 20 kN, with a significant increase
in deformability – therefore, measured deflections prior to failure tended to approach the corresponding
numerical values.
In the PU-R panel, the numerical load-deflection curve is below the experimental one in the path
corresponding to the linear behaviour and the deflection corresponding to the experimental failure load is
about 10% higher than the numerical deflection value. In what concerns maximum displacements, the model
reproduces with acceptable accuracy the behaviour in the vicinity of failure. In general, the model reasonably
reproduces the behaviour of the reinforced panel, although it provides higher displacements than those
observed in the experiments.
In the numerical model, the shear stresses on the core of the PU-R panel are approximately uniform along the
height but vary across the width, presenting lower values near the edges (figure 4.1). In fact, the lateral ribs
absorb a significant portion of shear force and, in the PU-U panel, the numerical shear stress determined for
7
Note that the skins were modeled with thin shell finite element-type and, thus, could not present any shear
deformation.
8
Determined by the quotient between the numerical stress value of each skin and the skin Young’s modulus.
12
the ultimate load was twice the stress in the PU-R panel, which justifies the non-occurrence of core shear
failure in the reinforced panel.
Figure 4.1 Shear stresses in the PU-U (on the left) and PU-R (on the right) sandwich panels.
4.4
Dynamic behavior
The calculated flexural frequencies are similar to those obtained in the experimental tests with a very low error
of 0.5% in the PU-U panel, and an acceptable error of 17.4% in the PU-R panel (table 4.2). It was not possible to
compare the torsional frequencies because these were not detected in the experimental tests.
Table 4.2 Vibration modes and respective flexural and torsional frequencies.
Vibration mode
Numerical
PU-U
Experimental
Numerical
PU-R
Experimental
5
Flexural mode [Hz]
24.20
24.07
35.50
30.18
Torsional mode [Hz]
52.60
(not detected)
102.56
(not detected)
Conclusions
This paper has demonstrated that composite sandwich panels using either PU foam core or PP honeycomb core
between two GFRP skins have a great potential for structural applications, with a considerable strength and
stiffness, particularly when reinforced with lateral GFRP ribs. The following main conclusions can be addressed
based on the analytical, experimental and numerical investigations:
1. Sandwich panels tested in bending showed a linear-elastic behaviour with a slight loss of stiffness for
load levels relatively close to the collapse load;
2.
Unreinforced sandwich panels with PP honeycomb core are stiffer than those made with PU foam core;
3. The mid-span deflections of sandwich panels submitted to bending can be estimated with simple
equations that have to take into account the shear contribution to overall deformability;
4. The ultimate strength of unreinforced sandwich panels was governed by the shear strength of the core
material; in opposition, the ultimate strength of the reinforced sandwich panels was governed by the
instability of the top skins under compressive forces;
5. The adding of longitudinal ribs had an important effect on the behaviour of the panel: (i) the stiffness
increased significantly and therefore caused mid-span deflections to decrease; (ii) the ultimate
strength increased considerably, with the ribs absorbing a great part of the shear stresses, originally
taken by the core; (iii) the vibration frequencies were modified;
13
6. The numerical models developed, which were calibrated with the experimental results, in general, are
able to simulate the static and dynamic mechanical behaviour of the PU sandwich panels, for both
service and failure conditions.
6
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14