STRAIN MEASUREMENT IN THE ADHESIVE LAYER OF BONDED JOINTS
USING HIGH MAGNIFICATION MOIRE INTERFEROMETRY
a
P. D. Ruiza, F. Jumboa, J. M. Huntleya, I. A. Ashcrofta and G. M. Swalloweb
Wolfson School of Mechanical and Manufacturing Engineering, Loughborough University,
Loughborough, LE11 3TU, UK, [email protected]
b
Physics Department, Loughborough University, Loughborough, LE11 3TU, UK,
ABSTRACT
The behaviour of Aluminium-aluminium (Al-Al) and Aluminium-Carbon Fibre Reinforced Polymer (Al-CFRP) bonded double-lap
shear joints under tensile load has been investigated both experimentally and numerically. High resolution maps of the inplane strain distribution in the region of the adhesive line and fillet were obtained experimentally using high magnification Moiré
Interferometry. These were used to evaluate the shear strain distribution, which was compared with 3-D Finite Element (FE)
predictions. Regions of strain concentration predicted by the FE models within the adhesive layer were experimentally verified.
Introduction
Adhesive bonding is acknowledged as superior to riveting in terms of structural efficiency because of the weight penalty of
introducing a mechanical fastener and the improved stress distribution and rigidity of the bonded joint. However, the adoption
of adhesively bonded joints in structural applications has been inhibited by the lack of trusted design codes. The complexity of
the stress distributions in bonded joints has led to their analysis using FE [1,2], the predictions of which have to be
experimentally validated.
Several authors have used Moiré Interferometry in the past to study strains within the adhesive layer in bonded joints [3-9].
Tsai and Morton [4-6] investigated single-lap aluminium specimens using strain gauges and Moiré Interferometry, and
compared the resulting data with numerical and theoretical analyses. Even though they could only resolve around one fringe
within the adhesive layer, they obtained a reasonable agreement between the experimentally determined adhesive average
shear stresses with those determined from numerical and theoretical analyses, showing that the maximum values were very
sensitive to the presence of a spew fillet. Post [7] has used fringe counting methods to measure strain fields within the
adhesive layer of single lap joints with no spew fillet, without reporting regions of strain concentration. Wood [8] detected and
measured delaminations in Carbon-epoxy composite laminates by looking at the top/bottom surface of the adherends rather
than the side faces. Ruiz et. al [9] have studied strain distributions in steel-steel, Al-Al and CFRP-Al double lap joints both
numerically and experimentally using neutron diffraction and low magnification Moiré Interferometry. No strain concentration
regions were found in the adherends for the loads used, which were within the elastic limits of the adherends, however this
may be attributable to the relatively low spatial resolution of the strain measurements.
In the current paper we use high magnification Moiré Interferometry to measure surface strains within the narrow (~ 200µm)
adhesive layer in the fillet region of both Al-Al and CFRP-Al double lap joints, and compare the experimental measurements
with FE simulations. Fringe processing is performed by evaluating the optical phase change due to tensile loading of the joints
using temporal phase shifting [10] and phase unwrapping [11]. This allows the evaluation of displacement fields in both
horizontal and vertical sensitivities that are then numerically differentiated to obtain strain distributions.
Double lap joint sample preparation
Al/Al and Al/CFRP double-lap joints (DLJ) were manufactured by QinetiQ using unclad 7075 T6 aluminium alloy adherends
and unidirectional IM7/8552 carbon fibre epoxy composite. In the CFRP/Al DLJ, the outer adherends are Al and the central
one is made of CFRP. The aluminium adherends were prepared for bonding by degreasing in acetone and then etching in
chromic/sulphuric acid before a final rinse in distilled water followed by drying in an oven. After assembly, the specimen was
cured under a pressure of 0.28MPa taking 30 minutes to heat to 120ºC and then holding for 60 minutes at 120ºC. The
adhesive used in both joints was FM73, which is manufactured by Cytec Ltd. This is a single part, toughened epoxy based
adhesive which was supplied as a nominally 0.25mm film with a polyester mat carrier. The thickness of the cured adhesive
layer in the Al-Al and Al-CFRP joints was 0.19±0.01mm, the scatter being due to variations in the thickness of the adhesive in
individual joints. The Young’s Modulus of FM73 has been determined from tensile tests at 23°C with a loading rate of
0.1mm/minute to be 2.35 GPa. Figure 1 shows the geometry and main dimensions of the bonded joints.
FOV
middle adherend
B
side view
Adhesive
x
bottom adherend
y
C
fillet
A
x
y
E
top view
D
z
x
RG
DLJ
Al-Al
CFRP-Al
A (mm)
3.0
4.2
B (mm)
3.0
2.0
(0,0,0)
C (mm)
25.0
12.5
D (mm)
25.0
25.0
E (mm)
250.0
150.0
Figure 1. Adhesively bonded joints. FOV indicates the field of view in which moiré interferometry measurements and FE
predictions have been performed. Only a part of the fillet is visible on the FOV around the upper right corner of the bottom
adherend.
Moiré interferometer
In the interferometer, an optical fibre delivers a collimated light beam that is diffracted by a crossed-lines transmission grating
-1
beam splitter G (1200 lines mm ). This produces a pair of collimated beams in the vertical plane and another pair in the
horizontal plane. Four mirrors steer the beams coming from the grating beam splitter towards the sample, which has a
-1
reflection crossed-lines diffraction grating (600 lines mm ) replicated onto its surface. The sample grating is imaged with a
high-speed camera and a long working distance microscope objective lens that sit along the optical axis of the input fibre and
between the steering mirrors. Quantitative displacement fields were obtained across the replicated grating from the optical
phase change measured between the reference and loaded states of the sample. Temporal phase shifting was implemented
by translating the grating beam splitter with a PZT transducer on its plane and along an axis at 45 degrees to the horizontal
plane, and in a plane perpendicular to the input fibre optical axis. A π/2 phase shift between the +1 and -1 diffracted orders in
the horizontal or vertical planes is introduced when the grating beam splitter moves a distance g(√2)/8 (with g the grating
pitch). In this way, the system is insensitive to vibrations affecting the input fibre. Wrapped phase maps representing the inplane displacement components u and v were unwrapped and then differentiated to give the engineering shear strain
ε xy = ∂u / ∂y + ∂v / ∂x
.
Incidence angles of 18.6° were used to illuminate gratings of 600 lines mm-1 replicated onto one side of the joints. The light
source consisted of a Lightwave® laser with a wavelength λ= 532 nm and an output power of 200mW. The magnification of
the system and the sensor size and pixel number lead to recorded interferograms with a spatial resolution of 2µm per pixel.
Comments on experimental errors
Molimard et al [12] recently studied longitudinal strains in the adherends of a steel/composite double lap joint by means of low
magnification electronic speckle pattern shearing interferometry. They compared the experimental results with analytical
predictions from a Volkersen model, and found a 20% error in their results. There are a number of sources of error due to rigid
body motion of the sample when using a moiré interferometer with collimated illumination: 1) in-plane rotation around the
loading axis (x axis) introduces horizontal moiré fringes which do not contribute error terms to the longitudinal strain
ε xx . 2)
Out-of-plane translation along the axis perpendicular to the virtual grating planes (z axis) and out-of-plane rotation about the x
axis (elevation angle on plane yz) do not introduce spurious strains because the projection of the sample grating onto the xy
plane remains unchanged [13]. 3) In the case of out-of-plane rotation around the y axis (azimuth angle Ψ on plane xz), the
projection of the specimen grating pitch onto the plane xy becomes shorter, which introduces a spurious uniform compressive
strain that adds to ε xx . By solving the grating equation for both illumination beams and letting the grating normal rotate an
angle Ψ around the y axis, it can be shown that for a small azimuth angle Ψ the associated fictitious strain is
ε xx ' ≈ − Ψ 2 ( 2 + Ψ 2 ) .
In order to reduce these sources of error in our experiments we used collimated illumination and repositioned the sample after
the load was applied to correct for deformations of the loading rig. Collimation was achieved by checking the cross section of
the beam with a screen at different distances from the source. Divergence/convergence errors of less than 0.001 rad are
achievable in this simple way. During the acquisition of the moiré interferograms, rotations around the y and z axes were kept
below 0.00013 rad by using dial gauge displacement sensors to monitor sample rotation and adjusting screws in the loading
rig to bring the sample back into alignment after the load was applied. This small rotation around the y axis introduces a
fictitious compressive strain ε xx ' = −8 × 10 −9 , well below the strain error due to phase ripples from the phase shifting algorithm of
~2×10-5. Rotations around the x axis were not monitored nor corrected as they do not contribute to fictitious strains for
collimated illumination. The results shown in Figures 3 and 4 have been obtained taking all these considerations into account.
Finite element analysis
Finite element modelling was carried out using the commercial FEA package MSC.Marc. In order to reduce the complexity of
the model and computational demands, the model was simplified without compromising the results. The adhesive fillets and
offsets are included in the model geometry and only a quarter of the joint was modelled due to symmetry. The joint was
modelled using 8 node full brick 3D elements with assumed strain formulation for the adhesive and aluminium adherends and
8 node 3D composite brick elements for the CFRP adherends. Owing to the high resolution of strains required over a small
area, the structural zooming function in MSC.Marc was used to improve the strain results. This structural zooming analysis
typically involves a global model containing global results and a local model to obtain refined results in the region of interest.
Figure 2(a) shows the global mesh used and figure 2(b) shows the local mesh refinement in the fillet area for the local model.
For each joint, a 7kN load was applied along the x-axis and the material properties used are presented in table 1.
(a)
(b)
Figure 2. FEA mesh for the double lap joint showing (a) global model and (b) local model refinement of the fillet area.
Results
Figures 3(a) and 3(b) show the wrapped phase obtained using temporal phase shifting for horizontal and vertical sensitivity
respectively, when a tensile load of 7kN is applied to the Al/Al DLJ. Phase unwrapping was performed by means of a minimum
cost matching algorithm from Phase Vision Ltd [10], whilst the u and v displacement fields were obtained by multiplying the
unwrapped phase by the sensitivity of the system of 0.83µm per 2π phase change. To obtain the various strain components,
the displacement distributions were differentiated by locally fitting a plane by least squares analysis over square kernels and
finding the gradient of the plane at the kernel centre in both horizontal and vertical directions. A 21x21 pixel kernel, at ~2mm
per pixel, determines a “gauge length” in the strain evaluation of ~40µm, similar to the average spacing of the nodes in the
mesh used in the FE model. Figure 3(c) shows the engineering shear strain obtained in this way in the fillet region of the
adhesive layer, in the field of view indicated as “FOV” in Fig. 1. A region of strain concentration is clearly visible on the positive
side of the horizontal axis close to the (0,0) position. Figure 2(d) shows the engineering shear strain FE prediction when the
model described in previous section is used.
Table 1. Material properties for joint constituents at 23°C
E11 (GPa)
IM7/8552
Unidirectional CFRP
165
E22 (GPa)
11.38
72.4
2.35
E33 (GPa)
11.38
72.4
2.35
G12 (GPa)
5.12
27.2
0.83
G13 (GPa)
5.12
G32 (GPa)
3.92
27.2
27.2
0.83
0.83
υ12
0.30
0.33
0.40
υ23
0.487
0.33
0.40
0.021
0.33
0.40
υ31
7075-T6
Aluminium
72.4
FM73M
2.35
(a)
(b)
(c)
(d)
Figure 3. High magnification Moiré Interferometry measurements in the adhesive layer for an Al/Al DLJ under 7kN tensile
load: a) wrapped phase change obtained for horizontal sensitivity; b) wrapped phase change obtained for vertical sensitivity; c)
engineering shear strain; e) FE prediction of the engineering shear strain.
Profile plots across the strain fields in Figs. 3(c) and (d) reveal absolute discrepancies of only around 10%. The spatial
distribution of strain predicted by the FE model compares well with the measured strains, especially with regard to localization
of strain concentration regions, shape and absolute values of the strain near the region of maximum values, and also in the
spew fillet region.
Similarly, Figures 4(a) and 4(b) show the wrapped phase change obtained in the same way as explained above when a tensile
load of 7kN is applied to the CFRP/Al DLJ. Figure 4(c) shows the engineering shear strain obtained within the adhesive layer
in the spew fillet region of the joint in the field of view denoted FOV on Fig. 1. The predicted FE shear strain distribution is
shown in Fig. 4(d). The black regions in Figs. 4(a)-(c) correspond to a digital mask that was used to exclude pixels with low
intensity modulation in the original interferograms. Those pixels were not taken into account for phase evaluation or strain
calculation.
A region of strain concentration is not clearly visible in Fig. 4(c) close to the (0,0) position, as it is in the case of the Al-Al joint.
In part this is due to the fact that smaller strains occur, which are within the noise level of the system. This noise comes from
imperfections in the surface of the grating replicated onto the joint and also from ripples due to the phase shifting algorithm,
which lead to spatial phase fluctuations that are further amplified by differentiation when the strains are evaluated. A
comparison of profiles across the adhesive layer show absolute differences that range from 30% to 80% for different distances
from (0,0).
(a)
(b)
(c)
(d)
Figure 4. High magnification Moiré Interferometry measurements in the adhesive layer for a CFRP/Al DLJ under 7kN tensile
load: a) wrapped phase change obtained for horizontal sensitivity; b) wrapped phase change obtained for vertical sensitivity; c)
engineering shear strain; d) FE prediction of the engineering shear strain.
Conclusions
This paper describes how FE predictions of shear strain distributions within the adhesive layer in Al-Al bonded double lap
joints have been validated to within 10% by using high magnification moiré interferometry. However, it should be noted that in
this case the joints were produced under laboratory conditions and deviations from the idealized geometry may be more
severe in practical applications, especially at the scales we have studied. As the adhesive layer thickness is only ~200µm,
small variations in the radius of curvature of the adherends could result in large variations in the relative thickness of the
adhesive layer, and hence have an important influence on the strain distributions.
Also, care must be taken when interpreting the experimental strains in that the values obtained on the adhesive/adherend
interface are not true values of strain within the gauge length used, because the gauge length overlaps two different materials
with different elastic modulus.
Measurements in CFRP-Al samples should be performed with higher sensitivity, taking special care of the tolerances during
manufacturing, in particular of the radius of curvature of the adherends in the plane xy in the fillet region. This can be done by
increasing the frequency of the grating replicated on the sample, and by using more robust phase shifting algorithms,.
Although the use of a longer gauge length would also reduce the rms phase noise that leads to strain errors the consequent
reduction in spatial resolution is not considered desirable in this application.
Acknowledgments
We acknowledge funding of this project by the Engineering and Physical Sciences Research Council under contract
GR/R72525/01 with additional support provided by QinetiQ. J M Huntley is also grateful to the Royal Society and Wolfson
Foundation for a Royal Society-Wolfson Research Merit Award.
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