THERMOELASTIC STRESS ANALYSIS OF
SANDWICH STRUCTURES WITH CORE JUNCTIONS
M. Johannes1, J.M. Dulieu-Barton2, E. Bozhevolnaya1 and O.T. Thomsen1
Department of Mechanical Engineering, Aalborg University, Aalborg, Denmark
2
School of Engineering Sciences, University of Southampton, Highfield, Southampton UK
1
ABSTRACT
The paper concerns local effects occurring in the vicinity of junctions between different cores in sandwich beams subjected to
cyclic tensile in-plane or transverse bending loading. It is known from analytical and numerical modelling that these effects
display themselves by an increase of the bending stresses in the faces as well as the core shear and transverse normal
stresses at the junction. In the present paper the local effects have been studied experimentally by means of Thermoelastic
Stress Analysis (TSA) for two types of sandwich beams with aluminium and GFRP face sheets and core junctions with
polymer foams of different densities and aluminium edge stiffeners. Calibration tests on the constituent materials have been
used to obtain the calibration constants necessary for calculating stress data from the thermal data. Reference data obtained
from Finite Element Modelling (FEM) were used for comparison with the experimentally obtained results. In tests examining
the sandwich face surface stresses looking on the top or bottom side of the sandwich beam, the TSA was able to predict
confidently the overall nominal surface stresses in the regions that were undisturbed by the discontinuities. A local variation of
face surface stresses in the vicinity of the core junctions was qualitatively captured by the TSA, but of different magnitudes
than predicted by the FEM. In tests examining the stresses at the sandwich’s longitudinal edge, the quality of the data was
significantly affected by motion effects in the bending tests, even when employing motion compensation software. For the
tensile in-plane loading case, the effects of motion were less pronounced and stress data could be obtained without the motion
compensation. The local variation of face stresses was not resolved properly by the TSA, whereas in the aluminium core the
local stress patterns from TSA were similar to the ones predicted by the FEM. In the foam core materials, no reliable stress
data was obtained.
Introduction
A sandwich structure is a layered composite element with two relatively thin and strong outer layers, known as the face sheets,
and a relatively thick and lightweight inner layer, known as the core. The sandwich assembly is formed by adhesive bonding of
the face sheets to the core. A sandwich structure has favourable specific strength and stiffness properties and outperforms
mass-equivalent monolithic structures for most load cases. Sandwich constructions have thus gained an important role in
lightweight construction and are being used in many applications such as ship and aircraft structures. Difficulties arise when
local effects disturb the uniform distribution of stresses in the sandwich structural components. These local effects occur due to
discontinuities in the structure such as changes of geometry or material properties, or when localised external loads are
applied. It is well-known that in the vicinity of sandwich sub-structures, e.g. joints, stiffeners or inserts, stress concentrations
are inevitably present. These may initiate local failure processes which lead to global failure of the whole structure [1]. The
local effects that are caused by the mismatch of the elastic properties of the adjoining materials at core junctions have been
analytically and numerically modelled for the linear elastic range and the sandwich face deformations accompanying these
effects have been verified experimentally using strain gauges [2-5]. However, this technique does not give a full-field strain
representation and the spatial resolution is limited due to the physical size of the strain gauges. Additionally, the relatively high
stiffness of the strain gauges reduces their applicability for the measurements of strains in soft polymer foam cores. The actual
peak stresses often remain unknown and can be difficult to predict for the whole stress range of the chosen constituent
sandwich materials. In the present paper, Thermoelastic Stress Analysis (TSA) is used to identify global and local stresses in
the components of sandwich beams with core junctions subjected to cyclic tensile in-plane or transverse bending loading. Two
types of sandwich beams with aluminium and GFRP face sheets and core junctions with polymer foams of different densities
and aluminium edge stiffeners are considered and two types of tests have been carried out. One test series focuses on
examining the sandwich face surface stresses on the top or bottom sides/faces of the sandwich. In the second test series, an
attempt is made to obtain data from the edge of the sandwich and in this case a zoom lens is also used to obtain data of
higher spatial resolution for this test type. The thermoelastic response of the constituent materials of the sandwich structure is
also evaluated experimentally and used to obtain calibration constants necessary for determining stress data from thermal
image data. The results from the TSA are compared with reference data from linear and nonlinear FEM.
Local Effects in Sandwich Structures
In general sandwich structures are designed so that the face sheets are loaded in a membrane stress state and the core
carries the shear stresses. However, in the vicinity of material or geometrical discontinuities, the nominal stress field is
disturbed by local effects. Although there are many forms of sub-structures in sandwich panels, the phenomenon of stress
concentrations at discontinuities is fundamental and can be represented by the special case of junctions of sandwich cores
with different stiffness. Here, local bending of the face sheets is induced, along with local tension or compression of the
adjacent cores. This is accompanied by a rise of the in-plane stresses in the sandwich faces and a variation of the shear and
through-the-thickness stresses in the adjacent cores. The effect of such a discontinuity on the stress distribution has been
subject to previous research [2-5], and analytical and numerical models are available for the linear elastic range. The local
deformation patterns at core junctions are shown schematically in Figure 1 for the case of both axial in-plane and transverse
loading.
Figure 1: Loading conditions, deformation pattern and a schematic representation of the resulting stresses at a core junction
Although it has been shown in [2-5] that it is possible to capture the local effects with respect to the local bending of the face
sheets by taking local strain measurements with strain gauges, this method has a number of disadvantages. As mentioned
before it has a rather limited spatial resolution due to the physical size of strain gauges, the applicability for the measurements
of strains in the soft foam cores is very limited, and the actual peak stresses resulting from the local deformation often remain
unknown and can be difficult to predict for the whole stress range of the chosen constituent sandwich materials. Thus, full-field
stress/strain measurement techniques offer many potential advantages in analysing this problem, as they are high resolution,
non-contact and non-destructive.
Thermoelastic Stress Analysis
Thermoelastic stress analysis is based on the measurement of the thermal response from a structure resulting from the
application of a cyclic load within the elastic range of the material [6]. It is a non-contact technique that provides full-field stress
data from the surface of a component. In practice, a structure or component is cyclically loaded and the resulting temperature
change is measured with a highly sensitive infrared (IR) detector. Originally, the area of interest had to be scanned by the
detector in order to take full-field data, but the more recent systems employ detector arrays that can instantly capture full-field
data using high frame rates and measurement times of a few seconds. The system used in the work described in this paper is
the Silver 480M manufactured by Cedip Infrared Systems. It employs a 320 x 256 pixel InSb sensor array that is radiometrically calibrated by the manufacturer. This pre-calibration has the advantage that the absolute surface temperature can be
measured directly, if the surface emissivity is known. Thus, it is possible to apply the basic equation describing the
thermoelastic effect for a linear elastic, homogeneous and isotropic material:
ΔT = - K T Δ(σ 1 + σ 2 )
(1)
where ΔT is the measured surface temperature change, K is the thermoelastic constant, T is the absolute surface temperature
and Δ(σ1 + σ2) are the changes in the sum of principal stresses. The thermoelastic constant is a material property with
K = α/ρCp, where α is the linear coefficient of thermal expansion, ρ the density of the material and Cp the specific heat at
constant pressure. Equation (1) presumes that there is no heat conduction, and this assumption of adiabatic conditions is valid
if the material is loaded at a sufficiently high frequency, in practice ranging from about 2 to 5 Hz for polymer materials to 20 Hz
for steel [7]. For specially orthotropic materials the small temperature change described above is not simply related to the
stress changes, Δσ, but to a combination of these and the coefficients of thermal expansion in the principal material directions
as follows [8]:
T
(2)
ΔT =
Δ(αpσp + α t σ t )
ρCp
Very often it is difficult to obtain reliable data for the thermoelastic constants, especially for non-homogeneous materials. To
derive quantitative stress data from the recorded thermal data a calibration is recommended. There are various approaches to
calibration, e.g. as described in [9]. The most accurate approach is considered to be the so-called indirect calibration, i.e. a
calibration against a calculated stress. For the Cedip system this means that the change in the IR detector output signal
defined in units of digital level DL, known as the thermoelastic signal, S, is related to a known stress in the standard manner to
give the calibration factor A for homogeneous material as follows:
(3)
Δ(σ1 + σ2 ) = A S
where A can for example be determined directly in a test in uniaxial tension with σ2 = 0. For specially orthotropic materials the
principal coefficients of thermal expansion αp and αt have to be included in the calibration. Here the calibration consists of two
tests performed parallel and transverse to the principal material directions; a detailed description of a typical calibration
procedure on an orthotropic material can e.g. be found in [8].
Sandwich Test Specimens
Two sandwich specimen configurations have been considered in the experimental investigation. Configuration 1 was a
sandwich beam with aluminium face sheets and configuration 2 used GFRP face sheets. Both configurations of sandwich
beams contained three core sections, as specified in Table 1. The face thickness, hf, varied depending on the face sheet
material; the thickness of the core, hc, was 25 mm and the width, w, of the beams was 45 mm for both configurations.
Table 1: Considered sandwich configurations
Sandwich config.
Face Material
Core Material 1
Core Material 2
Core Material 3
hf [mm]
1
Aluminium 7075-T6
Aluminium
Rohacell 51WF
Rohacell 200WF
1.0
2
GFRP, quasi-isotropic
Aluminium
Rohacell 51WF
Rohacell 200WF
2.8
The Rohacell 51WF and 200WF are polymer foams of different densities and thus different mechanical properties and together
with the aluminium edge stiffener they form two core junctions, as can be seen in Figure 2.
Core 1: Aluminium
Junction 1
Core 3: Rohacell 200 WF
Core 2: Rohacell 51 WF
Junction 2
lc1 = 90 mm
lc2 = 100 mm
lc3/2 = 60 mm
Figure 2: Photographs of the sandwich test specimens 1 (left) and 2 (right) – only half specimens are shown due to symmetry
Two techniques were employed to manufacture the sandwich specimens. For configuration 1, aluminium strips were bonded to
previously manufactured core layers consisting of the three core sections as described in Table 1. For all bonds, an
Araldite® 2011 epoxy adhesive was used. To bond the face sheet strips to the core layer, the specimens were stacked and a
uniform pressure applied to all specimens simultaneously. After curing of the resin, the specimens were brought to their final
shape by machining them along the edges to their final width. The specimens of configuration 2 were produced by vacuum
infusion. The lay-up of each face sheet consisted of 4 layers of a quadric-directional quasi-isotropic stitched non-crimp fabric
2
with an areal weight of 850 g/m . A previously manufactured core plate was placed on the lay-up of the lower face, and the layup of the upper face was placed on top of the core layer. The core plate consisted of the three core sections stated in Table 1.
The whole lay-up was bagged and by a consecutive one-step vacuum infusion process a sandwich plate was produced, from
which sandwich beams were cut and then machined to their final shape.
To facilitate the TSA measurements, the surface emissivity of the test specimens was enhanced in the regions of interest by
coating them with RS matt-black paint. On the edges of the sandwich specimens the foam cores were left unpainted, as it is
very difficult to achieve a uniform layer of paint without filling the cells. Finally, the specimens were marked with a pencil to
define the measurement fields and provide a scale for later analysis.
Calibration Test Specimens
In addition to the sandwich test specimens a set of calibration test specimens was used for obtaining the calibration constant
of each sandwich test specimens constituent materials. For the aluminium and the GFRP rectangular plane coupons
(500 mm x 30 mm) were used and rectangular blocks (150 mm x 100 mm x 25 mm) for the foam materials. As with the
sandwich test specimens the aluminium and GFRP specimens were coated with RS matt-black paint and the foam cores were
left unpainted. Table 2 lists the constituent materials with their properties that are used in the FEM described later in the paper.
Table 2: Material properties of the sandwich constituents
Material
Aluminium 7075-T6
GFRP, NCF, [0/+45/90/-45 / +45/90/-45/0]2
Rohacell 51WF
Rohacell 200WF
[a] Measured
[b] Material supplier’s data
3
E-Modulus [MPa]
Poisson’s ratio
ρ [g/cm ]
Yield stress [MPa]
Tensile strength [MPa]
71700 [a]
19280 [c]
0.320 [b]
0.280 [c]
7.600 [b]
3.400 [b]
480 [a]
-
550 [a]
n.a.
75 [b]
350 [b]
0.343 [b]
0.459 [b]
0.051 [b]
0.200 [b]
-
1.6 [b]
7.0 [b]
[c] Classical laminate theory
Experimental work
The TSA measurement set-up consisted of an Instron servo-hydraulic test machine, set-up to accommodate the different test
configurations for calibration and the sandwich tension and bending tests, the IR-camera and a PC for signal processing. The
test configurations are shown in Figure 3.
(a)
(b)
(c)
(d)
Figure 3: Test set-ups for the TSA measurements:
(a) sandwich tensile test, (b) sandwich bending test, (c) calibration test for face materials, (d) calibration test for foam cores
For the sandwich beams two test set-ups were used: in-plane tensile tests and 3-point bending. TSA readings were taken from
the sandwich face surface and the sandwich edge. In the bending tests, a mirror was employed for examining the sandwich
face surface. For the calibration tests the specimens were loaded in uniaxial tension. The calibration test for the aluminium
face sheet was done both with and without the mirror, as the mirror used in the sandwich bending tests has certain IR signal
attenuation. For the foam cores an ‘Arcan’ type rig specially designed for mixed-mode testing of foam materials was used in
the mode-1 configuration.
In TSA, a cyclic load is applied and the load signal from the test machine is used as a reference signal that is correlated with
the IR-signal. This allows signal inputs at frequencies other than that of the loading signal to be removed in the signal
processing. The TSA data were taken in the Cedip software module Altair in form of a continuous thermal data stream. The
data were recorded at the maximum possible frame rate of 269 Hz when using the cameras standard lens and 285 Hz when
using a zoom lens (resulting from different integration times). Each data set contained 1000 frames. For the tests with the
zoom lens, the Cedip software module Random Motion was used to conduct motion compensation if necessary. Motion
compensation becomes important in order to avoid “edge effects” and blurring of the signal when data are collected at higher
spatial resolutions. Edge effects occur at the specimens’ outer edges, at discontinuities with respect to thermoelastic
properties or in a wider sense also when a thermal gradient is present [10]. The thermal data (both with and without motion
compensation) were subsequently “stress-analysed” in the Cedip software module AltairLI. The process is called stress
analysis, because it is possible to calculate the stress range field from the thermal data sets for a component manufactured
from a single material. To do this it is necessary to know the thermoelastic constant K of the material (Equation (1)).
Alternatively, without a knowledge of K, the “stress analysis” calculates the thermoelastic signal S (Equation (3)), and by
applying the calibration factor A to the data the range of the sum of the principal stresses can be determined.
Table 3 and Table 4 give the test matrices for the sandwich tests and the calibration tests, respectively. The bold entries are
the reference values of the test parameters, around which the parameters were varied. Table 4 also gives the obtained
calibration constants, where A and AM denote the calibration constant without and with the mirror, respectively. The value AM
has experimentally been obtained only for the aluminium coupons and the calculated signal attenuation caused by the mirror
has been applied to the calibration constant A of the GFRP to obtain AM. Two specimens of each set were used for the
calibration and as no significant mean stress, stress amplitude or frequency dependence could be observed for the given
parameter range, the overall mean values were used for A and AM. The associated standard deviations are given in brackets.
It should also be noted that the stresses obtained from the TSA for the GFRP are the overall average stresses in the specimen
and not the surface layer stress; this complies with the FEM, as the face sheets were modelled as a homogeneous material.
Table 3: Test matrix of the TSA sandwich tests
Sandwich config. Test type
1
2
Mean load [N] Load range [N]
Tension
2250
Bending
200
Tension
Bending
1800, 900
200
4900, 6500
400
Frequency [Hz]
4900, 7350, 9800
300
Viewing direction Measurement fields
Lens
4, 6, 8, 16, 24, 32 Surface / Edge
Junction 1 and 2
Scanning 4 fields
Standard
6
Surface / Edge
Junction 1 and 2
Std. / Zoom
8
Surface / Edge
Junction 1 and 2
Scanning 6 fields
Standard
8
Edge
Junction 1 and 2
Standard
Table 4: Test matrix of the TSA calibration tests
Material
A [MPa/DL]
AM [MPa/DL]
Aluminium 7075-T6
25.0, 40.0
GFRP, NCF, [0/+45/90/-45 / +45/90/-45/0]2 26.8
Mean stress [MPa] Stress range [MPa] Frequency [Hz]
20.0, 40.0, 60.0
17.9, 35.8
6, 8, 10
4, 6, 8
7.38 (0.07)
6.74 (0.09)
8.17 (0.18)
7.48
Rohacell 51WF
Rohacell 200WF
0.2, 0.3
0.2, 0.3, 0.5
4, 6, 8, 16
4, 6, 8, 16
0.142 (0.003)
0.647 (0.040)
0.15, 0.2
0.15, 0.2, 0.3
-
Finite Element Modelling
A two dimensional finite element (FE) model of a sandwich beam with core junctions was used to calculate global and local
stresses numerically. The model was made using the commercially available FE program ANSYS. The material combinations
and face and core thicknesses were chosen in accordance with the sandwich configurations used in the experiments (see
Table 1). Isoparametric two-dimensional 8-node PLANE 183 elements were used for the finite element mesh. A sequential
refinement of the mesh was used at the core junctions to obtain sufficiently small element edge lengths (1/32 mm) that ensure
convergence of the results. The bond between the face sheets and the core and between the two core materials at the
junction was assumed to be perfect and relatively thin, and hence no additional layer of adhesive was considered in the
analysis. Figure 4 shows the sandwich section with a core junction and the corresponding finite element mesh at the trimaterial corner of face sheets and cores.
y’
x’
Face sheet
Tri-material corner
Compliant core
Stiff core
Figure 4: Sandwich core junction and the FE mesh at the tri-material corner
Only half of the beam was modelled, as the beam is symmetrical about its centre, so that symmetry boundary conditions were
applied to the y-axis located at the centre of the beam. For the tensile in-plane loading case, pressure loads in accordance
with the nominal stresses were applied on the face and the core at the left end of the sandwich beam (see Figure 4, left). For
the 3-point bending loading case, the forces were applied on the nodes at the positions of the loading point and supports.
Some material properties were available from data sheets, and some were obtained by materials testing. All materials were
assumed to be isotropic and linear elastic. For the range of loading used in the TSA experiments, linear elasticity is a valid
assumption. The assumption of isotropy is fully valid for the aluminium and approximately valid for the polymer foams. It is a
simplification for the GFRP face sheets, but considered as reasonable with respect to the nominal membrane stress state in
the sandwich face sheets and the quasi-isotropic lay-up of the composite. In the area of the local face bending a layered
model of the composite may be more appropriate, but this has not been done in the present study. An overview of the material
input data used for the FEM is given in Table 2. The finite element calculations were based on the assumption of plane stress.
They were run both as a linear and a geometrically nonlinear analysis to check the linearity of the local effects, and no
significant geometrical nonlinearity was found. Thus for simplicity the linear analysis mode was used. The load was set as the
load range used in the cyclic TSA tests, but the results can be scaled as it is a linear analysis.
The results from the FEM are presented in two ways. For comparison with the TSA data from the face surface scans the face
stresses calculated by the FEM were obtained from paths along the face outer surface and along the face/core interface
parallel to the x-axis of the beams. For comparison with the TSA data from the sandwich edge scans, contour plots of element
table data for the first stress invariant (σ1 + σ2) were used, so that the results correspond directly with the calibrated TSA data.
As the tri-material corner possesses a stress singularity within the framework of linear elasticity [11], the stresses are infinitely
high at the tri-material corner. Based on ideas of Ribeiro-Ayeh, Hallström and Grenestedt [12-13] and following previous work
by Bozhevolnaya et al. [5], the elements within a characteristic distance of d = 0.6 mm from the singularity were excluded in
the contour plots.
Results
The calibration constants obtained above were applied to the TSA data and compared with the FEM data. The experimentally
derived calibration constants are provided in Table 4. TSA data sets were obtained for the face surface and the sandwich
edge, according to the test configurations as given in Table 3. Typical sets of data obtained from the sandwich face surface
are shown in Figure 5; the scale is in digital level DL and is equivalent to the thermoelastic signal, S, in Equation (3).
(a)
(b)
(c)
Junction 1
Junction 1
Junction 1
Analysis tools
Pencil marks
Mirror frame
Figure 5: TSA readings from the sandwich face surface at junction 1 with line and area tools for analysis
(a) tensile test - configuration 1, (b) tensile test - configuration 1, (c) bending test - configuration 1
The readings are taken at junction 1 and it can be seen that due to the different core stiffnesses different stress levels are
present in the two sandwich sections. Also, a stress variation can be seen in the transition from one section to the other. The
full-field data were interrogated to provide line plots along the beams’ longitudinal axes. Data from individual lines proved to be
very noisy and thus area data were used instead, where the data were averaged in the beam’s transverse direction and then
plotted over the beams’ longitudinal axes. The averaging is valid because of the plane stress condition. Moreover, the data are
practically uniform across the beam width. The stress data obtained from the TSA are plotted together with FEM data in Figure
6. These data were collected using the reference test parameters given in bold in Table 4.
Face stresses σ 1+σ 2 [MPa]
22
22
(a)
20
20
18
18
16
14
16
14
12
12
10
10
8
8
6
6
FEM - face surface
FEM - face/core interface
TSA - face surface
4
2
0
50
70
90
110 130 150 170 190 210 230
x-coordinate [mm]
25
(b)
15
10
5
0
FEM - face surface
FEM - face/core interface
TSA - face surface
4
2
0
50
(c)
20
70
90
110 130 150 170 190 210 230
x-coordinate [mm]
-5
FEM - face surface
FEM - face/core interface
TSA - face surface
-10
-15
50
70
90
110 130 150 170 190 210 230
x-coordinate [mm]
Figure 6: Analysed and calibrated TSA area data from the sandwich face surface in comparison with FEM data
(a) tensile test - configuration 1, (b) tensile test - configuration 1, (c) bending test - configuration 1
In Figure 6 the FEM for all three configurations clearly exhibits distinct departures in the uniform stress field that is expected in
the face sheet as a result of the discontinuities in the core material. For the tensile test with specimen configuration 1 with the
aluminium face sheets (Figure 6a) it can be seen that the TSA and the FEM show reasonably good correspondence in the
areas away from the discontinuities. However, there is a significant difference in the section of the face sheet attached to the
aluminium core. This may be attributable to the very low stresses and thus temperature changes in this region. The different
nominal stresses in the foam core sections are captured by the TSA. However, the local effects predicted by the FEM for the
face surface are not apparent in TSA. There is a peak in the stresses from TSA of the same magnitude as for the FEM, but the
stress variation is of a shape that follows the stress variation in the face core interface rather than that of the face surface. As
the face sheets are very thin and therefore subject to a large stress gradient in this region an explanation for this could be a
non-adiabatic response; this will be discussed below. The results for specimen configuration 2 (i.e. with the GFRP face sheets)
are shown in Figure 6b. Here there is a very poor correspondence between the values produced by the FEM and the TSA,
even in the areas away from discontinuities in the core. However, the TSA data appears to follow the FEM much better in the
region of the discontinuity than the results from configuration 1. It should be noted that non-adiabatic behaviour is less likely in
the GFRP as the material has a thermal conductivity of two orders of magnitude less than that of the aluminium. The scatter in
the TSA data for this configuration is very high and could be attributed in part, to inhomogeneities in the surface of the material
(apparent in Figure 5b) and variations in the material properties. In Figure 6c the results from the bending configuration are
shown. As with configuration 1 there is reasonable agreement between the FEM and TSA data away from the discontinuities.
Once again, there is poor agreement at the discontinuities and the TSA shows an increase in stress at the discontinuity
whereas the FEM shows a decrease. This concurs with the findings from configuration 1 of non-adiabatic response. The stress
gradient in the face sheet is much larger in this configuration and this could lead to the reduced response at the discontinuity.
In order to establish if the response was adiabatic, tests were undertaken at a range of frequencies as indicated in Table 3.
These tests produced results that provided practically identical stress distributions as those given in Figure 6. Therefore a
conclusion of this initial work is that the maximum frequency of 32 Hz that could be obtained with the test set-up is not
sufficient to eliminate non-adiabatic behaviour or that non-adiabatic behaviour is not the cause of the discrepancy between the
FEM and TSA results. It should be noted that the FEM results were compared with similar previous experimental data [2-5]
from strain gauges, and generally the FEM results given here correspond with the early work. Therefore the conclusion is that
the TSA cannot respond to the high stress gradients that occur in the face sheets at the discontinuities. To investigate if using
higher spatial resolutions improved matters up to six overlapping measurement fields (see Figure 6b) were “scanned” along
the beam; these did not change the overall trends but merely increased the noise. Thus, the deviations from the FEM cannot
be resolved by increasing the spatial resolution.
Figure 7 shows typical sets of TSA data obtained from the sandwich edge in the tensile tests and the corresponding FEM data
using the reference parameters given in Table 2. The TSA data were converted into stresses using the calibration data for
aluminium. This calibration has been applied to the whole contour plot, but it should be noted that the stresses can only be
correct for the aluminium core and not for the GFRP face sheets. The FEM data are given in terms of Δ(σ1 + σ2) in MPa as
well, and a colour map was created with the same scale as for the TSA data to be directly comparable.
(a)
13.5
GFRP face
Edge effects
Aluminium
Rohacell 51 WF
(b)
13.5
Compr.
zone
Compression zone
0.35
(c)
Aluminium
0.0
Figure 7: TSA readings and FEM results from the sandwich edge at junction 1 in the tensile test of specimen configuration 2
(a) Calibrated TSA data in MPa, (b) TSA phase data in degrees, (c) FEM data corresponding to Δ(σ1 + σ2) in MPa
It can be seen that TSA and FEM correspond reasonably well qualitatively. The FEM shows small compressive stresses in the
zone indicated by the arrow. TSA data like that shown in Figure 7a are always of positive sign, but when taking into account
the phase plot shown in Figure 7c, it can be seen that there is a change in phase indicating a compressive stress with the
magnitude as shown in Figure 7a. Similar results were obtained for specimen configuration 2, but despite the good qualitative
agreement between TSA and FEM for both specimen configurations, it was difficult to obtain reliable quantitative stress data in
the region of interest close to the tri-material corner. When examining junction 2, i.e. between the foam cores, the data quality
was poor and not even the nominal stresses in the core could be detected.
Figure 8 shows the results from the bending tests, where the data quality was severely affected by motion effects; the use of
motion compensation software did not improve matters. This was because the motion compensation routine works most
effectively for cases with large displacements compared to the size of regions of homogeneous temperature or thermoelastic
properties and with pure translation/rotation and no distortion of the measurement field. A good example is shown in Figure 8c
where the zoom lens is used.
(b)
(a)
(c)
Figure 8: TSA readings taken in the bending tests from the sandwich edge of specimen configuration 1
(a) without motion compensation, (b) with motion compensation, (c) with zoom lens and motion compensation
Closure
The work in this paper has shown that TSA can be applied in a quantitative manner to sandwich structures. The focus of the
work was to examine the effect of discontinuities in the stress field using the technique. The paper has presented initial work in
this area and highlights a number of issues that warrant further investigation. From a physical viewpoint these include an
analysis of non-adiabatic effects that may occur as a result of the large stress gradient in the face sheets at the discontinuities,
the implications of the surface structure of cellular core materials and the magnitude of the stiffness changes at the
discontinuities. From an equipment point of view, the over sampling that is required to obtain the necessary resolution to detect
the departures in the stresses in the face sheets resulting from the discontinuities appears to introduce significant ‘noise’ in the
data. Also, the motion compensation routine requires improvements for a quantitative analysis.
Acknowledgments
The work presented was associated with the Innovation Consortium “Integrated Design and Processing of Lightweight
Composite and Sandwich Structures” (KOMPOSAND), funded by the Danish Ministry of Science, Technology and Innovation.
The polymer foam core materials used in the experimental work were provided by Röhm GmbH & Co. KG. The support
received is gratefully acknowledged. The work presented herein was conducted during the period of a 6 month stay of the first
author with the Fluid Structure Interactions Group at the School of Engineering Sciences, University of Southampton. The kind
hospitality of the School of Engineering Sciences and access to its experimental facilities is gratefully acknowledged.
References
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
13.
Zenkert, D., An Introduction to Sandwich Construction, EMAS, London (1997).
Bozhevolnaya, E., Thomsen, O.T., Kildegaard, A. and Skvortsov, V., “Local effects across core junctions in sandwich
panels”, Composites. Part B: Engineering, 34, 509-517 (2003).
Bozhevolnaya, E. and Thomsen, O.T., “Structurally graded core junctions in sandwich beams: quasi static loading
conditions”. Composite Structures, 70, 1-11 (2005).
Bozhevolnaya, E. and Thomsen, O.T., “Structurally graded core junctions in sandwich beams: fatigue loading conditions”.
Composite Structures, 70, 12-23 (2005).
Bozhevolnaya, E. and Lyckegaard, A., “Local effects at core junctions of sandwich structures under different types of
loads”, Journal of Composite Structures, 73(1), 24-32 (2006).
Dulieu-Barton, J. and Stanley, P., “Development and applications of thermoelastic stress analysis”, Journal of Strain
Analysis for Engineering Design, 33, 93-104 (1998).
Sathon N. and Dulieu-Barton, J.M., “Internal crack detection and analysis using thermoelastic stress analysis”,
In Proceedings of 16th European Conference of Fracture (ECF-16), 2006, 557-558 and 8 pages on CD.
Dulieu-Smith, J., Quinn, S., Shenoi, R., Read, P. and Moy, S., “Thermoelastic Stress Analysis of a GRP Tee Joint”,
Applied Composite Materials, 4, 283-303 (1997).
Dulieu-Smith, J., “Alternative calibration techniques for quantitative thermoelastic stress analysis”, Strain, 31, 9-16 (1995).
Hemelrijck, D., Schillemans, L. and Cardon, A.H., “The Effects of Motion on Thermoelastic Stress Analysis”, Composite
Structures, 18, 221-238 (1991).
Pageau, S.S., Joseph, P.F. and Biggers, Jr., S.B., “The Order of Stress Singularities for Bonded and Disbonded ThreeMaterial Junctions”, International Journal of Solids and Structures, 31(21), 2979-2997 (1994).
Ribeiro-Ayeh, S. and Hallström, S., “Strength Prediction of Beams with Bimaterial Butt-Joints”, Engineering Fracture
Mechanics, 70, 1491-1507 (2003).
Hallström, S. and Grenestedt, J.L., “Mixed Mode Fracture of Cracks and Wedge Shaped Notches in Expanded PVC
foam”, International Journal of Fracture, 88, 343-358 (1997).