Experimental Investigation of Stress Concentrations
Caused by Inserts in Sandwich Panels
N.G. Tsouvalis1 and M.J. Kollarini2
Associate Professor, 2Undergraduate Student
Shipbuilding Technology Laboratory, School of Naval Architecture and Marine Engineering
National Technical University of Athens
Heroon Polytechniou 9, GR-15773 Zografos, Athens, Greece, [email protected]
1
ABSTRACT
This paper presents an experimental study of the stress concentrations developing across the insert-core junctions in a
sandwich beam with an implanted stiff insert into its core. Strain measurements were carried out at several positions on the
skins and across the insert-core junction, for several sandwich beam specimens loaded in 3-points bending and having inserts
with various geometries. The materials used were typical marine glass/polyester composite and PVC foams and the
specimens were manufactured with the vacuum infusion method. A full material characterization was performed for the
composite skins. The experimental results demonstrated a pure linear bending response of the specimens, as well as
significant strain concentration factors across the insert-core junction, reaching values up to 3.3. Concentrated factors
measured for butt inserts were lower than those measured on the tension side of the specimens with scarf inserts. Transverse
strains measurements verified that all specimens were in a plane stress state.
Introduction
The high stiffness-to-weight and strength-to-weight ratios which are the basic advantages of composite sandwich materials,
are continuously improving during the last years, allowing the use of these materials in an always broadening range of
engineering applications. Thus, joining and functional requirements for these materials are becoming much more demanding.
Among the most difficult loading conditions a sandwich structure can carry, is the action of transverse concentrated loads,
against which sandwich materials are by default sensitive. These concentrated loads can be the result of either direct external
forces or support reactions and lead to the development of high local bending stresses and, consecutively, early failure. The
local implantation of small high stiffness reinforcing inserts (i.e. wooden, metallic, high density foams, etc.) in the core of the
sandwich during manufacture is a quite common solution to the above problem, distributing the applied concentrated load in a
larger area. These inserts, however, have as a result an abrupt change in the material stiffness at the insert-core junction,
thus leading to high local bending stresses in the sandwich skins near the junction, as well as to high local normal and shear
stresses in the core of the sandwich.
Several efforts to calculate these stress concentrations have relatively recently been presented in the literature, being both
analytical and numerical and including comparisons to relevant experimental measurements. Analytical solutions and
parametric studies are given in [1-4], including closed form solutions for the local skin and core stresses across the insert-core
junction which are also experimentally verified. These analytical estimates may be used directly for preliminary design
considerations. A major conclusion of these works is that the stress concentrations at the insert-core junction may be reduced
by reinforcing the skins across the junctions or, even better, by incorporating a gradual transition of the core stiffness from the
stiff insert to the softer normal core. The use of anisotropic inserts is, in addition, a very effective way for reducing local
stresses near the junctions. Numerical modelling of the problem is also investigated in several studies [4-9], using either selfdeveloped or commercially available finite element codes. In all cases, a 2-D modelling of the problem was carried out, using
either plane strain or plane stress conditions. The element size near the insert-core junction was, in all cases, very small.
Numerical results compare very well to the experimental ones, whereas it was shown that scarf inserts result in superior
performance compared to the conventional butt inserts, since local stresses can even almost vanish in some cases. A number
of experimental studies was also carried out [3,5-7,10], incorporating in all cases aluminum skins that are adhesively bonded
to PVC foams to form the sandwich specimens, which are loaded in 3-points bending. It is reported that experimental
measurements indicated no significant difference in the stiffness and, thus, in the overall deformation behaviour, between
sandwich beams with butt and scarf inserts. In all the above works, significant values of stress concentration factors at the
insert-core junctions are reported, reaching values up to 4 with respect to the globally induced bending stress at the same
point. Moreover, it comes up that the local effects occur within a certain small length around the junction.
The aim of this study is to experimentally measure the magnitude that the stress concentrations can reach across the insertcore junctions, as well as to test and evaluate different inserts’ geometries, thus comparing various insert design concepts. In
an effort to broaden the existing experimental measurements data base with sandwich materials incorporating other than
aluminum skins and wooden or very stiff PVC foam inserts, this experimental study is done for common marine composite
materials. Skins are typical glass/polyester laminates incorporating commonly used Chopped Strand Mat (CSM) and Woven
Roving (WR) fiber reinforcements, whereas both the normal core and the inserts are made of typical marine PVC foams with
different densities. Inserts have either an orthogonal geometry (butt inserts) or a trapezoidal one (scarf inserts) with varying
angle. The sandwich test specimens were manufactured using the Vacuum Infusion (VI) method, in an effort to achieve high
quality products and high glass content in the skins. The specimens were tested in 3-poins bending and strains were
measured at various positions and compared between each other.
Experimental Study
The experimental program was carried out at the Shipbuilding Technology Laboratory of the School of Naval Architecture and
Marine Engineering of the National Technical University of Athens (NTUA). Eight sandwich beam specimens were tested in 3points bending, corresponding to four different specimen configurations (2 specimens per configuration). Six of the beam
specimens had a variable geometry central insert in their core, the other two had no insert and served as reference
specimens.
®
Typical marine composite materials were used for manufacturing the test specimens. Hence, the normal core is Klegecell R
3
®
45 from DIAB [11], a PVC foam having a density of 45 kg/m . The stiffer insert is made of Airex C70.130 from ALCAN
Composites [12], also a closed cell, cross-linked PVC foam having density equal to 130 kg/m3. Both cores were available in
the form of 25 mm thick plates. Their material properties are given in Table 1. The sandwich skins are symmetric between
each other and consist of four layers of a typical marine glass/polyester composite system. More specifically, the resin used is
®
the low viscosity isophthalic polyester NORSODYNE G 703 from CRAY VALLEY, whereas all fiber reinforcements are made
of E-glass. The first layer next to the core is a typical 450 g/m2 CSM, followed by three identical layers of OC® AGIMAT
2
600.300 fabric from OWENS CORNING, which is a combined reinforcement having 600 g/m WR stitch-bonded together with
2
300 g/m of CSM into one fabric. The three AGIMATs were placed in such a way so that the 300 g/m2 CSM side of each layer
was facing the external surface of the sandwich skin.
Table 1. Nominal properties of core materials
Property
Nominal Density (kg/m3)
Compressive Strength (MPa)
Compressive Modulus (MPa)
Tensile Strength (MPa)
Tensile Modulus (MPa)
Shear Strength (MPa)
Shear Modulus (MPa)
®
Klegecell R45
Airex® C70.130
45
0.54
25
0.86
32
0.55
19
130
2.6
160
3.8
110
2.3
47
The material characterization of the glass/polyester skins was done by performing tensile and bending tests in coupons cut
from a test plate, specially manufactured for this purpose. As it is already mentioned, it was decided to manufacture the final
sandwich specimens using the VI method. Thus, the same method was also applied for manufacturing the test plate, trying to
keep the infusion conditions same to those followed for the sandwich specimens. The glass reinforcements were placed with
their warp direction parallel to the resin infusion direction, whereas the average vacuum applied during infusion was equal to
0.97 bar. Thus, it took only 7 s to fully infuse the resin into the 500x315 mm test plate. The test plate was left to cure in room
temperature for two days and then standard coupons were cut, in order to perform the tensile and bending tests. Tensile tests
were carried out according to standards ISO 527-1 and ISO 527-4 in 255x25 mm coupons [13,14], whereas bending tests
were performed according to standard ISO 14125 in 90x15 mm coupons [15]. The measured modulus of elasticity in tension,
ET, maximum stress in tension, σuT, modulus of elasticity in bending (flexure), EF and maximum stress in bending, σuF, are
presented in Table 2, where CoV denotes the coefficient of variation (ratio of standard deviation over average). Tests for the
determination of the fiber ratio by weight (glass content), Wf, were performed according to method A of standard ISO 1172
(burn off test) [16] in two coupons. The values measured were rather high, 64.7% and 64.9%, thus resulting in an average Wf
of 64.8%.
The geometry of the sandwich specimens is schematically shown in Figure 1. This figure shows a top, a side and a bottom
view of a specimen, together with the locations and numbering of the strain gauges mounted on it. All specimens have a total
length of 340 mm and an unsupported span of 290 mm, resting on rollers which provide simply supported boundary conditions.
Their width is 62 mm, the core thickness is 25 mm and the thickness of each identical skin is approximately 2.8 mm. The
length and width of the sandwich specimens were selected in accordance with the 3-points bending standard for sandwich
structures ASTM C 393-00 [17]. As mentioned before, each skin comprises of one CSM and three AGIMAT glass/polyester
layers. The parameter investigated throughout the experimental study is the geometry of the central insert. Its basic midthickness length is 100 mm (see Figure 1), with angle θ varying and taking the values of 90° (butt insert), 60° and 45° (scarf
inserts). Figure 2 presents a photo of one specimen of each type.
Table 2. Results of the skin material characterization tensile and bending tests
Tension
Coupon
Bending
ET (MPa)
σuT (MPa)
EF (MPa)
σuF (MPa)
1
−
−
15819
286.1
2
17445
334.5
12788
231.4
3
14098
−
16225
287.6
4
16721
326.2
15051
317.8
5
15680
309.3
15994
323.4
6
16246
346.3
14138
225.3
7
15716
347.7
12845
291.5
Average
15984
332.8
14694
280.4
CoV (%)
7.1
4.8
9.9
13.7
85
Top view
62
SG-6
SG-7
SG-5,4,3,2,1
340
2.8
SG-5,4,3,2,1
SG-6,7
25
Side view
θ
2.8
SG-8,9
SG-10
25
SG-15,14,13,12,11
100
290
25
Bottom view
SG-8
SG-9
SG-15,14,13,12,11
SG-10
55
85
Figure 1. Geometry of the sandwich specimens
All specimens were manufactured using the VI method. To keep the same infusion conditions for all specimens, sandwich
plates with all core geometries taken into account were infused together as one plate, with total dimensions 800x400 mm. As
a first step, the normal core pieces and the inserts were cut in the appropriate shape and were bonded together using a typical
polyester putty, forming four panels with dimensions 200x400 mm each (see Figure 3a). These four panels correspond to the
three insert angles investigated, plus one reference core panel without any insert. Each one panel was then grooved in an
orthogonal grid pattern (Figure 3b), in order to facilitate resin flow during infusion. The grooves’ grid spacing was equal to 20
Figure 2. Sandwich specimens with insert angle equal to 90°, 60° and 45°, respectively
mm in both directions, whereas their cross section was 1 mm wide by 2 mm deep. In the sequence, the four different panels
were placed one beside the other, thus forming a greater panel to be infused in one-piece (Figure 3c). This great core panel
was covered with the fiber reinforcements, the peel-ply, the infusion mesh and the vacuum bag and the vent and injection lines
are then put in place (Figure 3d). In this particular application, apart from the plane mould below the sandwich panel, we also
used an additional Plexiglas transparent plate above the sandwich panel, in order to obtain a smooth external surface of the
upper skin. Photos (e) and (f) in Figure 3 show two different steps of the infusion procedure, where the orthogonal grid
followed by the resin channels is obvious. Infusion procedure lasted for 50 min and the average infusion vacuum applied was
0.98 bar.
(a)
(d)
(b)
(c)
(e)
Figure 3. Manufacturing procedure of sandwich specimens
(f)
The finished sandwich panel was left in room temperature and cured for two days, before the final sandwich specimens were
cut from it. Eight specimens were cut, two from each sub-panel with different insert geometry and two without insert for
reference. These specimens have the dimensions of Figure 1 and the nomenclature of Table 3. This table presents also the
skin thickness measurements performed for each sandwich specimen. Four rectangular small coupon were additionally cut
from each one of the two sandwich skins, for measuring their glass content. These measurements resulted in a glass content
of 59.9% for the upper skin and in a glass content of 55.9% for the lower skin. Hence, the glass content achieved for the skins
Table 3. Sandwich specimens’ nomenclature and skin thickness
Specimen
1
2
3
4
5
6
7
8
Insert Angle, θ
No insert
90°
60°
45°
Skin thickness (mm)
2.7
2.7
2.8
2.8
2.8
3.0
2.8
2.9
Figure 4. Failure mode of sandwich specimens
of the sandwich panel is somewhat lower than the glass content of the material characterization plate (64.8%), and, therefore,
the mechanical properties of the skins are expected to be also somewhat lower than those measured from the test plate.
In specimens 3 to 8 with inserts, strains were measured at 15 locations, shown in Figure 1. More specifically, strains were
measured at 7 locations on the upper face (SG-1 to SG-7) and 8 locations on the lower face (SG-8 to SG-15). Strain gauges 1
to 5 and 11 to 15 constitute two chain-gauges, having five separate small gauges each, with 2 mm gauge length and 3 mm
spacing. These chain-gauges were placed exactly at the junction between the normal core and the insert, in order to measure
the longitudinal strain concentrations expected to develop in this area. Apart from these chain-gauges, longitudinal strains
were also measured in three other places (SG-6 on the upper face and SG-8 and SG-10 on the lower), together with
transverse strains on both faces (SG-7 and SG-9), far away from the zones where local effects occur. All strain gauges except
from the chain ones had a gauge length of 10 mm.
In specimens 1 and 2 without insert, strains were measured in the same way only at locations 6, 7, 8, 9 and 10. In these two
specimens, strains were also measured at locations 3 and 13, where these two latter locations are at a distance of 50 mm from
the center of the specimen, that is they coincide with locations 3 and 13 for specimens 3 and 4 with the butt insert. The center
deflection was also measured for all sandwich specimens, at the point on the upper face where the actuator loads the
specimen. All tests were displacement controlled, with an applied loading rate of 2 mm/s.
Results and Discussion
In all cases, first failure appeared in the normal core due to shear, as it is indicatively shown in Figure 4 for specimens 1, 3 and
7. As expected, position of failure moved towards the side support for specimens with insert, in comparison to those without
insert. The variation of center deflection versus the applied load is shown in Figure 5 for all specimens tested. This figure
indicates that specimens 5 and 6 (60° scarf insert) were the strongest ones failing at approx. 1800 N, whereas specimens 1
and 2 without insert were the weakest ones failing at approx. 1550 N. These values indicate that differences in failure loads
were not quite significant (16% maximum difference). Figure 5 shows also that stiffness of all specimens with insert is similar
between each other, an observation which is in accordance with what has already been reported in the literature [3,7,10].
Moreover, stiffness of specimens with insert is about 25% greater than the stiffness of specimens without insert. It can also be
seen in the same figure that the load-deflection response of specimens with insert is linear up to a load of approx. 800 N,
whereas the linear response region of specimens without insert is slightly smaller, up to a load of approx. 600 N.
Figures 6 to 8 present the variation of longitudinal strains versus the applied load, indicatively for specimens 1, 3 and 5.
Strains measured in other specimens present a similar behaviour. Compressive strains on the left side of each plot are
measured on the upper surface of the specimen, whereas tensile strains, on the right side of each plot, are measured on the
lower surface. Same color has been used for corresponding strain gauges which are located at the same position on the
upper and on the lower surface (i.e. yellow color is used for both SG-6 and SG-8). The first observation that can be made is
that the response is linear, at least up to a load of 800 N. Moreover, strain measurements are consistent between each other,
in the sense that strains measured at positions closer to the specimen center are higher (i.e. SG-13 readings are higher than
SG-8 readings, which in turn are higher than SG-10 readings). An observation that farther verifies strain readings consistency
is that strain gauges at corresponding positions on the upper and on the lower surface give similar readings with opposite sign,
that is their response curves are symmetric with respect to the zero strain axis; see for example SG-3 and SG-13 curves in
Figure 6 and SG-6 and SG-8 curves in Figures 6 and 7. SG-6 and SG-8 curves in Figure 8 slightly deviate from symmetry,
since strains at these two positions are affected differently from the 60° scarf insert.
Studying strains measured by the two chain-gauges (SG-1 to 5 on the upper surface and SG-11 to 15 on the lower one),
Figure 7 presents a perfectly symmetric behaviour, which is expected since the specific geometry of the butt insert results in
the same distance of both chain-gauges from the specimen center. Comparing the chain-gauges measurements in Figure 7 to
the SG-3 and SG-13 readings in Figure 6, it is evident that the presence of the butt insert causes significant strain, and thus
stress, concentrations. These stress concentrations are similar on the upper and on the lower surface of specimen 3. Chain-
2000
1800
1600
1400
Load (N)
1200
1000
800
600
Spec. 1,2 (no insert)
400
Spec. 3,4 (butt insert)
Spec. 5,6 (scarf insert 60 deg)
200
Spec. 7,8 (scarf insert 45 deg)
0
0
1
2
3
4
5
6
7
8
Center deflection (mm)
Figure 5. Center deflection versus applied load
Specimen 1
1800
1600
1400
Load (N)
1200
1000
800
600
400
Upper Surface
Lower Surface
200
SG-3
SG-6
SG-8
SG-10
SG-13
0
-2500
-2000
-1500
-1000
-500
0
500
1000
1500
2000
2500
Strains εx (με)
Figure 6. Variation of longitudinal strains versus applied load for specimen 1 (no insert)
gauges readings in Figure 8 for the 60° scarf insert specimen 5 do not present a symmetric behaviour, since they are not
located at the same distance from the specimen center. In this case, the chain-gauge on the tension side gives clearly higher
readings that that on the compression side, although the former is farther away from the specimen center than the latter.
Therefore, it can be concluded that, in this case, the level of stress concentrations is higher on the tension than on the
compression side.
In order to present more clearly the measured strain concentration levels and include measurements from all specimens,
Figures 9 to 11 present the variation of the measured longitudinal strains as a function of the distance of the measuring
position from the center of the specimen, for the three types of insert geometry, respectively. These measurements
correspond to an applied load of 600 N, that is they are inside the linear response phase of the specimens. The first
conclusion that can be drawn out from these three figures is that all strain measurements present a very good repeatability of
Specimen 3
1800
1600
1400
Load (N)
1200
SG-1
SG-2
SG-3
SG-4
SG-5
SG-6
SG-8
SG-10
SG-11
SG-12
SG-13
SG-14
SG-15
1000
800
600
400
Upper Surface
Lower Surface
200
0
-2500
-2000
-1500
-1000
-500
0
500
1000
1500
2000
2500
Strains εx (με)
Figure 7. Variation of longitudinal strains versus applied load for specimen 3 (butt insert)
Specimen 5
1800
1600
1400
Load (N)
1200
SG-1
SG-2
SG-3
SG-4
SG-5
SG-6
SG-8
SG-10
SG-11
SG-12
SG-13
SG-14
SG-15
1000
800
600
400
Upper Surface
Lower Surface
200
0
-2500
-2000
-1500
-1000
-500
0
500
1000
1500
2000
2500
Strains εx (με)
Figure 8. Variation of longitudinal strains versus applied load for specimen 5 (60° scarf insert)
the results between the two identical specimens per case. In addition, strains measured at the reference specimens without
insert (Sp-1 and Sp-2) present a very consistent behaviour, linearly increasing towards the specimen center and being
symmetric on the tension and on the compression side.
Strain concentrations measured across the insert-core junction for the butt insert (Figure 9) are similar on the tension and on
the compression side. If we define as strain concentration factor, k, the ratio of the maximum strain measured at the insertcore junction over the strain at the same point when no insert exists, then, in the case of the butt insert, k factor values around
2.5 were measured. Strains away from the insert are not significantly affected (see for example strains at locations 8 and 10).
The behaviour of strains at the insert-core junction is somewhat different in the case of the two scarf inserts (Figures 10 and
11). In these cases, strain concentrations occur only on the tension side of the specimens, giving strain concentration factors
equal to approx. 3.3 for both cases, that is higher than in the case of the butt insert. This observation is in contrast to other
Butt Insert
1000
Sp-1
Sp-2
Sp-3
Sp-4
Lower Surface
800
600
200
0
0
10
20
30
40
50
60
70
80
90
100
110
120
-200
Upper Surface
Strain εx (με)
400
-400
-600
-800
-1000
Distance from center (mm)
Figure 9. Variation of longitudinal strains versus distance from specimen center,
for reference and butt insert specimens
60 deg Insert
1000
Sp-1
Sp-2
Sp-5
Sp-6
Lower Surface
800
600
200
0
0
10
20
30
40
50
60
70
80
90
100
110
120
-200
-400
-600
Upper Surface
Strain εx (με)
400
-800
-1000
Distance from center (mm)
Figure 10. Variation of longitudinal strains versus distance from specimen center,
for reference and 60° scarf insert specimens
experimental measurements reported in the literature, where scarf inserts resulted in smoother stress transitions than butt
inserts [5,7], although materials in these case were significantly different than the present ones (much stiffer insert and/or
much stiffer and much thinner skins). Again, strains away from the insert are not significantly affected from its presence. On
the compression side of the four specimens with the scarf inserts, strains away from the insert are in general higher than those
measured on the reference specimens. Strains present a minimum at the insert-core junction and they rise up again towards
the specimen center. Thus, on the compression side of the scarf insert specimens, we did not measure any strain
concentration at all at the insert-core junction. On the contrary, strains present a minimum at this location. Such a behaviour
has already been reported in the literature [7].
45 deg Insert
1000
Sp-1
Sp-2
Sp-7
Sp-8
Lower Surface
800
600
200
0
0
10
20
30
40
50
60
70
80
90
100
110
120
-200
-400
-600
Upper Surface
Strain εx (με)
400
-800
-1000
Distance from center (mm)
Figure 11. Variation of longitudinal strains versus distance from specimen center,
for reference and 45° scarf insert specimens
Transverse strains at positions 7 and 9 were measured in an effort to evaluate the stress state in the sandwich beam
specimens during testing. Transverse strains readings in the linear response phase for all specimens resulted in an
experimental Poisson ratio ν = −(εtrans/εlong) equal to 0.25 (CoV=22%), which is very close to the Poisson’s ratio of the
glass/polyester skins, and, therefore, it can be concluded that the beam specimens are in a plane stress state.
Conclusions
The experimental study performed investigated the stress concentrations that can appear across the insert-core junctions in a
sandwich beam with an implanted stiff insert into its core. Actual strains were measured in several positions on the sandwich
skins and across the junctions, for several specimens with various insert geometries. Typical marine composite materials
were used, in combination with the vacuum infusion method for manufacturing the test specimens. The resulting sandwich
can be described by the following material and geometric parameters: skin modulus over normal (soft) core modulus, Ef/Ecs =
588; insert modulus over normal core modulus, Ech/Ecs = 6.4; insert width over core thickness, w/tc = 4; and skin thickness over
core thickness, tf/tc = 1/9.
The experimental results indicated first failure due to shear in the core, for all cases. Response was linear up to a certain load
and it was once more verified that insert geometry does not affect the stiffness of the sandwich beam. On the contrary,
specimens with insert were approx. 25% stiffer than those without insert. Strains measurements were perfectly consistent to
those expected from simple beam theory, with respect to measurement position. Strain concentration factors of the order of
2.5 were measured across the insert-core junction for the case of butt insert, being the same on both the tension and the
compression skin. In the case of scarf inserts, higher concentration factors equal to 3.3 were measured, but only on the
tension skin. No stress concentrations were measured across the insert-core junction on the compression side of the scarf
insert specimens.
Acknowledgments
The authors acknowledge the contribution of Messrs A. Markoulis, H. Xanthis and L. Mirisiotis in the experimental activities.
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®
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