WSEAS International Conference on ENGINEERING MECHANICS, STRUCTURES, ENGINEERING GEOLOGY (EMESEG '08),
Heraklion, Crete Island, Greece, July 22-24, 2008
The power of Digital Image Correlation for
detailed elastic-plastic strain measurements
H.J.K. Lemmen, R.C. Alderliesten, R. Benedictus, J.C.J. Hofstede, R. Rodi
Faculty of Aerospace Engineering
Delft University of Technology
P.O. box 5058, 2600 GB Delft
The Netherlands
Abstract: - Digital image correlation is more and more applied in test environments where material behavior is
investigated. The advantages of using images for analyzing the deformations in a specimen are enumerable.
Besides making it easier to perform some tests, digital image correlation enables it to make detailed material
behavior visible which previously could only be shown by modeling. At Delft University of Technology, a
tool was developed to use digital image correlation for tensile tests on weld. However, within a short period of
time different test applications were found for which the digital image correlation tool could be used. This
paper describes the details of the digital image correlation tool and some examples in which the tool was
applied in different test.
Key-Words: - Digital Image Correlation, Friction Stir Welding, Thick Adherend, Static Crack Extension
demands the user requires to perform a test in which
2D deformations have to be measured. Because no
special paint pattern and no contact with the
specimen are required, this correlation tool has a
large freedom and a broad area of applications.
1 Introduction
In an experimental environment a trade off is
always made between the detail of the information
from the test and the complexity of the test. In
general, a lot of different measurement systems are
available
to
measure
displacements
and
deformations like strain gauges, extensometers,
photo elastic paper, linear variable differential
transformers, etc. However, it is not possible to get
detailed local information of the strain field, because
the nature of these measurement systems. Besides,
those measurement systems need to have physical
contact with the test specimen which limits the
freedom of testing.
This paper describes the outline of the correlation
tool and the solutions used to overcome typical
problems found in the practical environment of a
test setup. To demonstrate the success of the
correlation tool, different examples of tests in which
the correlation tool was used are described. The tests
described in this paper include tensile tests on
Friction Stir (FS) welded specimens, thick adherend
tests and static crack growth tests in Fiber Metal
Laminates (FML). Besides showing how the
correlation tool was used, it is discussed how the
correlation tool contributed to the different
researches.
The development of sophisticated digital cameras
and image processing software enables new noncontact measurement technologies, called “digital
image correlation” [1]. Digital image correlation
(DIC) is the analysis of images taken from a test
specimen during the test, to measure the
displacements on the test specimen. Once the
displacements of different points in the specimen are
known, it is possible to calculate the strains,
rotations, shear or any deformation related property
in which the user is interested.
2 Digital Image Correlation
2.1 Outline of the DIC tool
To use DIC in different tests, a correlation tool was
developed based on a Matlab code. The outline of
the correlation tool is such that the DIC is not
dependent on the type of test, the amount of images
per test or the size and shape of the grid. This
At Delft University of Technology a correlation tool
was developed using a Matlab code, which performs
the DIC. This correlation tool is written such that the
input and output can be altered to meet the specific
ISBN: 978-960-6766-88-6
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the same as the area in the target image, 0 means
that no correlation exists and -1 means that the
analysed area in the target image is a negative of the
source image. Because DIC is an image based
technology, a pixel based coordinate system is used.
In this correlation tool the X and Y coordinate
within an image are defined as shown in Fig. 1. The
correlation square is always uneven with the pixel of
interest exactly in the centre of this square. The size
of the square must be such that enough detail of the
specimen surface is included such that the square is
unique. For instance if only one pixel is taken in the
example, many locations exist in the target image
which are the same. In the correlation tool the size
of this square can be adapted.
freedom was obtained by separating the DIC process
in three modules.
The first module is the definition of the grid based
on the strain level required for the analyses. Two
standard types of grid, for the tensile test and for the
thick adherend test, are available in the correlation
tool. The user has to define the size and the location
of these two types of grids. A third option is
available using an excel file in which a grid can be
defined by the user in any shape or size that is
required.
ISBN: 978-960-6766-88-6
y2 = 4
y1 = 5
The second module is the core of the correlation
tool, where the correlation is performed. Basically,
this module uses the predefined grid and starts to
find each individual grid point
Correlation
Target image
Source image
in each image in the series.
x1 = 3
x2 = 5
square
The result of this module are
four files, two with the x and y
coordinates of all the grid
points in each image, one
containing all the correlation
values from each grid point
Correlation with all
and one contains the check
pixels in target image
values of each grid point. The
structures of these files are
Location/pixel with highest
equally sized 3D matrices in
Location/pixel of interest
correlation value = new location
which each value corresponds
dx = x 2 – x1 = 2 pixels
Movement of specimen:
to one grid point in one of the
dy = y 2 – y1 = -1 pixels
images in the series. For
Fig. 1, Schematic overview of the correlation process for one pixel
example a correlation of a grid
of 3 rows and 2 columns in 5
images will result in a 3D
The correlation square is compared with all the
matrix of 2 by 3 by 5 (x by y by z).
pixels in the target image, returning a correlation
value for each pixel, resulting in a data set as
The third module is the post processing in which the
illustrated by Fig. 2. The location in the target image
output of the second module is used to calculate the
that corresponds best to the correlation square is
properties in which the user is interested. Again this
clearly recognised by the peak with the highest
module is test dependent and can be defined by the
correlation value. However, the new coordinate has
user. It is also possible to import test data from a test
an accuracy of 1 pixel which is not accurate enough
machine to synchronize the deformation data from
for strain measurements. To get higher accuracy a
the DIC with data measured by the test machine like
method was developed which uses the correlation
force, stress or other data.
values around the peak to get sub pixel level
accuracy. To obtain that a 6th degree polynomial
surface is fitted through the correlation values of the
pixels around the pixel with the highest correlation
2.2 Single pixel recognition
value, using a least squares approach. By filling a
The core of the correlation tool is based upon a
grid of sub pixel coordinates into the function of the
Matlab routine which uses a normalized cross
fitted polynomial surface, a new maximum can be
correlation to correlate a part of the source image
obtained at sub pixel level. In the correlation tool the
with the target image (Fig. 1). This routine uses the
resolution in which the coordinates are given is
grey scale levels of the pixels in the area of interest.
0.01 pixels. It was found that a higher resolution did
The routine returns for each pixel in the target image
not further contribute to the accuracy of the
a correlation value between -1 and 1. The value 1
measurement.
means that the part of the source image is exactly
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in the series (Fig. 3). For clarity, each grid point is a
user defined digital location, so no special pattern is
present at the surface of the test specimen. The only
requirement for the specimen surface is that it must
be irregular such that each location is unique.
Sometimes this requires paint to produce a speckle
pattern, but in many cases the surface of the
specimen is irregular enough from itself.
Pixel with highest
correlation value
Correlation value
Surrounding pixels contain
information for sub-pixel
level analyses
x [p
ixe
ls]
For the correlation of one grid point, the correlation
routine analyses each pixel in the target image. If the
target image is 1600 times 1200 pixels, this can take
a minute or more, depending on the processor. If, for
example, a grid of 22 columns and 12 rows has to be
correlated in multiple images, it takes too much time
to perform the correlation of a tensile test for which
100 to 500 images were required. To solve this
problem, each grid point is not correlated with the
whole target image, but only with a small part of it.
The size of this target area is kept as small as
possible to decrease the calculation time as much as
possible. Therefore it is required to know where the
grid point will go in the target image. Because the
camera is not fixed to the specimen during a test, it
does not automatically follow the deformation of the
specimen. Especially if a high magnification is used,
like for the thick adherend test, small movements of
the specimen result in large movements in the
image.
els]
y [pix
Fig. 2, Correlation values for an
area in a target image
2.3 Grid recognition
In the previous paragraph, it is described how a
single location (pixel) in a source image is traced in
a target image. However, to calculate local strains at
different locations in the specimen, multiple grid
points are required. To correlate a large grid with
multiple rows and columns of grid points in the
source image with a target image somewhat more
work is required. First, a grid must be defined which
suits the purpose of the test. In the correlation tool
several routines are present to define different
distributions of grids. One routine uses Excel to
define a grid such that any distribution and shape of
the grid is possible.
Source image
Target image 1
Target image 2
Target image n
Time [s]
Grid points
Base
grid point
…
…
Correlation
process
Correlation
squares
X - Y coordinates
grid in image 1
X - Y coordinates
grid in image 2
X - Y coordinates
grid in image n
Calculation of
deformations
To solve this problem and decrease
the search area for each grid point,
first the overall offset of the target
image with the source image is
obtained (Fig. 4). Therefore one grid
point, called the ‘base grid point’, is
correlated at first in a larger part of
the target image. The base grid point
is defined by the user together with
the definition of the grid. The user
also defines the area in the target
image in which the base grid point
must be located in all the images of
the test.
To evaluate the accuracy of the
coordinate of the base grid point, the
correlation tool defines two control
points close to the base grid point which are
correlated with the same area as the base grid point.
These three independent points result in three values
for the offset of the target image. If the difference
between the three offset values is too large, the
image is out of focus or the base grid point is not
Fig. 3, Schematic overview of DIC process for multiple
grid points and multiple images
In general, each test contains more than one image,
sometimes up to several hundreds of images,
depending on the nature of the test. As default, the
first image in a series is taken as source image, but
the user can define another image if required. The
grid in the source image is correlated to each image
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Step 1:
Find the location of the base
points and the two control points
target image n
Step 2:
Offset base
point and
control points
Yes:
= equal?
No:
Skip target image n
and continue with
target image n+1
Search area to find base
point and control points
Use x - y coordinates of grid in
target image n-1 to determine
target areas relative to base point
target image n
2 control
points
Source image:
Step 4:
Grid squares
Step 3:
Save the new x-y coordinates of
the grid points in target image n
and proceed to target image n+1
Correlation of the grid squares
within the target areas:
target image n
target image n
Base grid point
Fig. 4, Schematic overview of the four steps in the correlation process of one image in the
series
single grid point or image was not successful.
present in the target image. In both cases the DIC
Alongside the x and y coordinates, also the
tool automatically skips the current image and
correlation value and a so called check value is
proceeds to the next image in the series. When the
saved for each grid point. The correlation value
three offset values are approximately the same, this
provides information on the quality of the
offset value is superposed on the coordinates of the
correlation, while the check value gives information
grid found for the previous image in the series.
about different errors or situations which can occur
These coordinates can be used to define small target
during the correlation. The check value is used in
areas in which the grid points must be situated. The
the post processing phase to ignore the values which
sizes of the target areas are larger than the size of the
are not representative (Table 1).
grid squares. Again the size of the target areas can
be defined by the user when the grid is defined.
However, the target areas must be large enough to
In the case of a good correlation, the check value is
keep the grid points situated in the target areas,
1, which means that the correlation value was higher
despite the deformation of the specimen between
than the threshold correlation value given by the
two images.
user. The threshold correlation value represents a
criterion for the correlation value. When the
When the coordinates of all the grid points are
correlation value is lower than the threshold value,
obtained in the target areas, the x-y coordinates of
the correlation is considered to be unsuccessful and
the grid belonging to the target image are known and
the check value will be 0. In general a threshold
are saved in two 3D matrices. One matrix contains
correlation value of 0.7 is used because a good
the y-coordinate values and the other the
correlation value is in general between 0.8 and 1.0.
x-coordinate values.
Increasing the threshold value results in less grid
points which are accepted, but the quality of the
points left over is higher. The check value will also
2.4 Fault tracking
be 0 when the small target area in the target image is
Within the image correlation tool a fault tracking
situated partly or complete outside the image.
system is implemented which enables to continue
the correlation process after the correlation of a
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Check
value:
0
1
2
3
Table 1: Explanation of the check values in the check matrix
description:
Correlation values < threshold correlation value
Small target area (step 3) is outside image
Correlation value >= threshold correlation value
Difference in offset value of base point and control points > expected deformation
Image does not exist in directory
If the base grid point cannot be determined
accurately, i.e. the three offset values differ too
much, the target image is not analysed and all the
check values for the grid points in that image get the
value 2. If one image is missing in the series, the
check values for the grid points belonging to this
image get the value 3.
In all the cases that the check value is not 1 for any
of the grid points, the x-y coordinates from the
previous target image is filled in and saved for these
grid points. This is necessary because the
x-y coordinates are required for the correlation
process of the next target image.
2.5 Post processing
In the post processing phase the x and y coordinates
of all the grid points are translated into
deformations. At first the post processing must load
the files containing the x and y coordinates and the
check values. The check values are used to exclude
the grid points which were not correlated properly
from the analyses. What is calculated afterwards
depends completely on the test. It is possible to load
other test data into the post processing, this enables
to use test data from a test machine. In the
experiments chapter three examples are presented in
which different post processing codes were
developed and used successfully.
Table 2: Explanation of the check values after
an image or a grid point is skipped
Check Check values after skipping:
value: image grid point Both image and
(+4):
(+10):
grid point (+4+10):
0
4
10
14
1
5
11
15
2
6
12
16
3
7
13
17
3 Experiments
3.1 Tensile tests on welded specimens
The DIC tool is initially developed to measure the
local 0.2 % yield strength of Friction Stir (FS)
welded aluminium in tensile test specimens [2,3].
DIC is the only solution to determine quantitatively
the local material properties in the weld [4,5]. An
extensometer can only measure the average strain
over a larger gauge length and is not able to measure
the local strains at a resolution of, for instance, a
millimetre while strain gauges can only measure the
strain in a single spot and photo elastic techniques
give only qualitative information.
Sometimes it can happen that some images are out
of focus but still give (inaccurate) results. In that
case it is possible in the correlation tool to skip that
image afterwards from the analyses. The correlation
tool skips an image by adding a value 4 to the check
values of the grid points belonging to this image
(Table 2). This method preserves the information
such that it can be restored by subtracting a value of
4 from the check values. In some cases, the
correlation of one grid point is wrong and deviates
from the location where it should be. Because the
target area in the next image is determined using the
wrong coordinate, the coordinates of the grid point
will also be wrong in the subsequent images. It is
possible to skip a single grid point from the analyses
and in this case, the correlation tool ads a value of
10 to the check value representing this grid point in
all the images. The removal of a grid point is
reversed by subtracting a value of 10 from the check
values belonging to that grid point.
ISBN: 978-960-6766-88-6
The illustration of the test setup in Fig. 5 shows a
few important characteristics of this test setup. For
these tests standard tensile test specimen were
designed according to the standard ASTM E8M 04.
Test specimens were produced from the alloys
AA2024-T3, AA7075-T6 and AA6013-T4 in both
FS welded and un-welded (parent material tests)
condition. The tensile test specimen had a width of
12.5 mm and a gauge length of 50 mm. The
thickness varied per specimen because the upper and
lower surfaces of the welds were machined to avoid
any influence of the surface roughness. The
dimensions of each specimen were measured using a
vernier calliper (accuracy: 0.01 mm). The tensile test
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Applied load
1600 pixels
x
12.5mm
Weld
a < 5°
y
CCD
camera
e- x
1200 pixels
50mm
e- y
70 pixels
Weld
Tensile test specimen
Digital applied
grid points
extensometer
Note: image is rotated 90°
Fig. 5, Illustration of tensile test setup to obtain the material properties of FS welded
material
and black paint was applied to create a speckle
machine used for
these tests
was
a
pattern and to get rid of the reflection of the
Zwick 1455 20kN tensile testing machine equipped
aluminium. Both colour layers existed of small
with Zwick TesteXpert V11 software. The
droplets applied by a paint brush, such that it just
specimens were tested with a constant deformation
covered the aluminium. The result was a wide range
rate of 6 mm/min. The images of 1600 by
of black, white and grey intensities which is
1200 pixels (width x height) were taken by the CCD
favourable for the correlation.
camera with a frequency of 3.75 Hz.
In these tests, the camera was aligned perpendicular
to the specimen. During the test the camera setting
was not changed, because that would influence the
strain measurements. Only the height of the camera
was adjusted during the test to keep the area of
interest in the image. The camera was aligned such
that the angle between the specimen surface and the
image was less than 5º, because in the post
processing analyses the orientation of the strains are
defined relative to the image and not to the
specimen.
The size of the area captured by the camera was
approximately 22 by 18 mm which was not
sufficient to capture the whole width of the weld
which is approximately 30 mm. This was solved by
pointing the camera at different locations of the
weld in the different tests. Afterwards, the data of
the different tests were combined to assemble the
yield strength profile for the whole weld. Another
solution is to zoom out, but that means loss of detail
in the measurements. 70 Pixels were taken as the
distance between the grid points which is basically
the strain gauge distance. If the maximum error in
the location of these grid points is 0.1 pixels, this
gives an uncertainty in strain of 0.14 %. However,
experience learned that a distance smaller than
60 pixels between the grid points lead to too large
scatter in the strain data, while for 70 pixels the
inaccuracy was small enough to get good quality
stress-strain curves. In this case a distance of
70 pixels is comparable with approximately 1 mm in
the specimen.
The strain between each pair of grid points was
calculated using the distance between the grid points
in the source image as reference. To extract the local
yield strength, the strain must be coupled to the
force data measured by the Zwick tensile test
machine. A button was pressed together with the
start of the camera which sends a trigger signal to
the tensile test machine. The signal left a mark in the
test data which corresponds to the first image taken
by the camera. The data from the zwick test machine
was saved in a text file and imported by the post
processing code to couple each image to a force
measurement. To capture the trigger signal it is
required that the tensile test machine has started the
test and is measuring, therefore the camera was not
Apparently the accuracy of the correlation was
better than 0.1 pixels, because the scatter found in
the stress-strain curves was smaller than 0.14 %, but
this depends completely on the quality of the
specimen surface. In these test a thin layer of white
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linear part of the curve to adjust
the strain such that the linear part
is aligned with the origin.
Fig. 6 shows an example of
stress-strain curves obtained
from a FS weld in AA2024-T3.
The stress-strain curves exhibit
small variations in strain as a
result of small vibrations of the
camera, either due to camera
movements to keep it aligned
with the specimen during the test
or by other equipment in the
laboratory. However, it is easy to
eliminate the images which are
out of focus from the analyses as
is described in the paragraph
“fault tracking”. For these tests,
Fig. 6, Typical local stress-strain curves, plotted with an offset of
the errors were only eliminated
0.5 %, representing the material behavior at different locations
in the first part of the test
across a FS weld in AA2024-T3 with the calculated yield strength
because only the yield strength
indicated in each curve
was of interest. The errors in the
last part of the curves were not
started when the specimen was unloaded. Besides, at
removed because they do not influence the
the beginning of a tensile test, some stiffness
calculation of the yield strength.
influence of the test machine itself is measured.
Therefore, the camera was always started at a point
When the yield strengths are calculated for the
where the stress-strain curve became linear to
whole specimen area, the profile is visualized by a
eliminate the influence of the test machine at the
colour scale plotted over one of the images from the
beginning of the test. The stress strain curves created
test (Fig. 7). Such visualisation enables to locate the
in the post processing were corrected using the
Local yield strength [MPa]
HAZ
TMAZ
Weld Nugget
TMAZ
HAZ
Fig. 7, Image of a tensile test specimen with a overlay representing a typical
local yield strength distribution for FS welded AA2024-T3
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Table 3 Overview of the differences in yield strength found between the standard method using
an extensometer and the DIC tool
Alloy:
Yield strength
Maximum difference
Maximum scatter found for
Extensometer:
between extensometer and
individual specimen:
image correlation:
AA2024-T3
L
353 MPa
6 MPa
28 MPa
AA2024-T3
LT
336 MPa
10 MPa
33 MPa
AA7075-T6
L
527 MPa
2 MPa
19 MPa
AA6013-T4
L
221 MPa
2 MPa
9 MPa
AA6013-T4
LT
202 MPa
4 MPa
10 MPa
the extensometer data and the DIC technique. The
standard technique calculates one yield strength
value whereas the DIC calculates several local yield
strength values for each specimen. For each alloy
the average yield strength from the different test
specimens are given in the first column in Table 3.
From the local yield strength values calculated by
DIC, the average value is obtained and compared
with the value obtained by the standard method. The
largest difference observed for a specimen is given
per alloy in the second column of Table 3. In the
third column, the largest difference between the
maximum and minimum local yield strength value
found in one test is given. The AA2024-T3
specimens included the specimens which were used
to find out what the best test setup; therefore, the
differences found for these tests are largest. On these
specimens different types and colours of paint were
used and the light was changed to see which gives
the best result. For the other alloys the differences
obtained are exceptionally good because a scatter of
19 MPa is less than 4 % and the average value from
the correlation tool differed less than 2 % with the
value obtained by the standard method.
FS weld and the different weld zones, i.e. the Heat
Affected Zone (HAZ), the Thermo Mechanically
Affected Zone (TMAZ) and the weld nugget, in the
specimen.
In the yield strength profiles small differences
between the left and right (upper and lowed sides in
image) sides of the specimens were observed. This
is caused by in-plane bending due to intentionally
misalignment of the specimen with the centre line of
the test machine (2 mm at maximum). The reason
for the misalignment is that it was difficult to align
the camera both perpendicular to the specimen and
pointed at the correct location on the specimen. This
was solved by first aligning the camera
perpendicular to the specimen, and than adjust the
specimen a few millimetres to get the right location
in the centre of the image.
The accuracy of the DIC tool was determined in two
ways. One method compared two images from a
specimen which was unloaded but moved before
taking the second images. Because the specimen is
unloaded in both images, the strain is zero and thus
the distance between the grid points should be
unchanged. The differences found in the distance
between the grid points are a measure for the
accuracy of the DIC tool. The maximum error
observed was 0.02 pixels. However, this error is
obtained in optimal conditions because the images
were taken in a rack in which the alignment and the
distance of the camera were unchanged, resulting in
high quality images.
3.2 Thick adherend test
The thick adherend test is used for the determination
of adhesive mechanical properties under shear. The
shear stress (τ) is plotted versus shear strain (tan(γ))
(Fig. 8). From this curve the following typical
properties can be derived:
•
Shear Modulus of Elasticity (G): the tangent of
the linear elastic part of the curve;
•
Knee point: the point of intersection between
an extrapolation of the linear elastic part and
the non-linear part of the curve;
•
Maximum shear stress: the highest value of the
shear stress;
•
Maximum tan(γ): the highest value of the shear
angle prior to failure.
Knowing these properties in shear of an adhesive
bonded joint is necessary for design purpose and
strength prediction.
Another method to obtain the accuracy is
performing a test on an un-welded tensile test
specimen using an extensometer and the DIC tool to
measure the yield strength. This method validates
both the DIC method and the test setup. For this
purpose tensile tests were performed on
AA2024-T3, AA7075-T6 and AA6013-T4 for
which afterwards the yield strength was determined
using two techniques, the standard technique using
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The accompanying shear deformation expressed as
tan(γ) is calculated by dividing the relative
displacement of the two substrates with respect to
each other by the bond line thickness. In this the
shear deformation over the thickness is considered
to be constant, which is a first order approximation.
40
max. shear stress
"knee" point
35
shear stress (MPa)
30
25
max. tan(gamma)
20
Shear Modulus
of Elasticity
15
tan(γ ) =
EA 9696
RT-dry
10
tan(γ) = adhesive shear strain
ds = displacement of one adherend
to the other adherend
t = bond line thickness
In the test the relative displacement of both
substrates needs to be measured. For long the
standard method used is based on the work by
Krieger [7]. A specially developed type of
mechanical extensometer is used attached to both
sides of the specimen to measure the relative
displacements of the substrates. Pins are positioned
on the substrates as close as possible to the bond
line. The accuracy of this method is about 1 micron.
0
0,2
0,4
0,6
0,8
1
tan(gam m a) (-/-)
Fig. 8, Example of shear stress-strain curve
The thick adherend specimen, as depicted in Fig. 9,
is made from two 6 mm thick aluminium plates
bonded together and milled to a width of 25 mm. A
bonded overlap of 5 mm is created by milling two
grooves in parallel, one in each plate. The specimen
dimensions are according to test specification
EN 2243-6 [6]. Special attention is paid to the
overlap area: the grooves are milled to halfway the
bond line thickness.
The difficulties encountered by using this kind of
extensometer are threefold [8]:
•
Rotation of the bond line due to secondary
bending requires a 3 or 4 pins attachment
•
Pins are located some distance away from the
substrate-adhesive interface, so the shear
deformation of the aluminium adherend needs
to be filtered out
•
Slippage of the pins makes the device reading
incorrect
These difficulties reduce the accuracy of the
measurements.
By using an optical method the above given
drawbacks are automatically eliminated, as the bond
line deformation is measured directly. Slippage of
course is not possible and adherend deformation and
rotation do not affect the measurement.
Fig. 9, Thick Adherend specimen according EN
2243-6 [6] (left), principle of shear deformation
in Thick Adherend specimen (right)
By making the substrates thick and the overlap small
the shear stress distribution in the overlap can be
considered constant over the overlap. Subsequently
the shear stress can be calculated by dividing the
applied force by the overlap area:
τ=
F
w.l
with:
Theoretically the specimen can be analysed by
determining the image coordinates of four points,
two on each adhesive-substrate interface (Fig. 10).
From a comparison of corresponding points between
two images the actual bond line deformation, and
from that the shear angle, can be calculated for the
given load. In practice five points on each substrateadhesive interface were selected to improve
accuracy and eliminate errors. Those ten points were
located in each consecutive image on pixel level.
(1)
τ = average shear stress in the adhesive
F = applied load
w = specimen width at overlap location
l = overlap length (average of left and right
side)
ISBN: 978-960-6766-88-6
(2)
with:
5
0
ds
t
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Shear angle
+
substrate rotation
Substrate
rotation
Fig. 10, Determination of bond line shear deformation from CCD images
failure at a cross-head displacement rate of
1.0 mm/min. The applied load and cross-head
displacement were recorded by the test machine
software.
In the calculation of the shear angle the rotation of
the substrate interface (due to secondary bending)
needs to be taken into account. It was actually found
that for the linear region of the τ-γ curve, the
rotation of the substrate is of the same order of
magnitude as is the shear angle.
The images were captured real time using a
KAPPA DX 2 N-FW 1380 x 1028 CCD camera
mounted on a tripod. The camera movements
(XYZ translations) were driven by three small
electromotors, controlled using a joystick for
focussing and positioning in the middle of the
overlap. During the test small adjustments to the
camera position were necessary to compensate for
the downward movement of the specimen and for
losing focus. The camera has a fixed focal distance
and a narrow focal depth, therefore the distance
between the specimen and the camera is
The thick adherend tests were performed on a
Zwick 1455 20kN tensile test machine equipped
with Zwick TesteXpert V11 software (Fig. 11). The
specimen was placed in a cardanic suspension to
obtain a moment-free application of the load and
carefully aligned with the loading axis of the test
machine. A pre-load of 50 N, e.g. adhesive shear
stress of 0.4 MPa, was shortly maintained to enable
accurate positioning and focussing of the CCD
camera. After that, the specimen was tested to
Cardanic suspension
Lights
Lens
Camera
Specimen
Fig. 11, Thick Adherend test setup at the Adhesion Institute (from left to right): XYZ
tripod, KAPPA CCD camera, Zwick 1455 tensile machine with cardanic suspension and
specimen (detail on the right)
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microscopic images.
A special grid definition module was written to
facilitate this test. On each of the substrates in the
source image a grid of points is defined consisting of
at least 5 rows and 3 columns (Fig. 13). After the
correlation of the grid, in the post processing
module, the output of the correlation is used to
calculate the average displacement of the substrate
at the location of the interface with the adhesive.
Besides, the rotation of each substrate is calculated,
resulting in the shear angle deformation in the
direction of the bond line belonging to each image.
To link the force data from the Zwick test machine
to the deformation data, measured by DIC, the user
has to enter the force given in one of the images.
When each force level is unique during the test, this
together with the frame rate is enough to couple both
data sets. Once both data sets are coupled, the
τ-γ curve can be obtained and all the required
mechanical properties can be calculated.
approximately the same for all the images which are
in focus. Images were captured at a frame rate of
1 Hz containing besides the bond line deformation
also the actual applied load, the specimen ID and the
actual time, as shown in Fig. 12.
For the manual analyses small markers, in the form
Fig. 12, Example image of bond line deformation of scratches made using a scalpel, were applied on
with the actual applied load, specimen ID and
the substrates to facilitate the measurements. Other
actual time at the bottom side
means are diamond shaped markers made with miniVickers equipment or application of paint using
The accuracy of this manual method is at best
brushes. However, for the DIC tool none of the
limited to 1 pixel which means an accuracy of about
above markers are necessary because the DIC tool is
1 micron. Next to that the method is very time-and
capable of finding positions based on the groove
user-consuming and error prone. Yet, due to the
pattern created by the milling operation. This pattern
implicit benefits of using an optical method, the
was found sufficient for the required accuracy.
method is already as good as the mechanical
Besides, the images used for the manual method
methods. However, once the DIC tool was
were without any problems analysed by the DIC
developed for the welded tensile tests, it became
tool.
clear that the analyses of the images could be
automated to save time. Therefore an application
Fig. 14 shows excellent agreement between the
was written to use the DIC tool to determining the
shear stress strain curve calculated with the DIC and
relative adherend displacement from the recorded
with the manual method. The analysis is based on
Fig. 13, Images of un-deformed (left) and deformed (right) adhesive layer with grid points
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loss of focus during testing
caused
by
specimen
movement.
The
accompanying images are
somewhat blurred making
the DIC more difficult. In the
manual method these images
were excluded, but in the
DIC tool it is possible to
eliminate those images too.
40
35
shear stress (MPa)
30
25
20
15
DIC method
Manual method
The use of DIC greatly
enhances the possibilities of
the optical method for
determination of shear angle
in the bond line. For one it
facilitates
within
pixel
accuracy (0.1 micron) and
secondly
it
saved
a
tremendous amount of time.
10
5
0
0
0,1
0,2
0,3
0,4
0,5
0,6
tan(gamma) (-/-)
Fig. 14, The shear stress strain curve obtained using the DIC
compared to the manual method
the same images. Note that the DIC curve contains
more points: the computer evaluation allows for
more images to be analysed, where this would be
too time consuming for the manual method.
Two small deviations should be noted here. In the
linear part both curves are parallel, yet slightly offset
with respect to each other. This is caused by the post
processing module which automatically shifts the
curve such that the linear part of the curve crosses
the origin. In the manual method this correction is
not performed. Further some of the DIC points
evidently deviate from the trend, which relates to
3.3 Static crack extension test
Another application for which the DIC approach has
given good results is the static crack extension test
on fibre metal laminates. For the purpose of this test,
simple modifications in the existing post processing
code of the tensile test have been made, in order to
calculate the strain field ahead of a crack tip. The
followed approach has been twofold: first, the area
in front of the crack tip has been divided in 9 sectors
with a size of 13 by 18 mm, as shown in Fig. 15.
This was necessary because the accuracy of the DIC
1
4
7
2
5
8
3
6
9
y
Digital
camera
x
13
mm
18 mm
Half specimen width = 70 mm
X-Y-Z axes
electronically
controlled rack
Fig. 15, Static crack extension test approach
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Fig. 16, Development of the strain field ahead the crack tip due to a static load
interpolating the strain data into the known stress
strain curve of the tested material.
Basically, the DIC approach allows to calculate the
entire strain and stress fields ahead of a generic
crack tip, or an open hole. The results presented in
this paper refer to tests performed on panels of
Glare 3-2/1-0.3 and Glare 3-2/1-0.5 [9].
tool, which is 0.02 to 0.1 pixels, determines the
gauge length between the grid points, and thus the
resolution of the measurements on the specimen. To
capture the whole influenced strain field, and keep a
high resolution of measurements, multiple images
were required.
In order to collect the source images a photo shot
was taken at zero force in each of the nine sectors.
The same procedure was followed at different load
increments keeping the same focal distance. The
movement of the camera system along the specimen
area was controlled by using an x-y-z axes
electronically controlled rack.
Fig. 16 shows an example of the strain distribution
ahead of a crack tip in a statically loaded
Glare 3-2/1-0.5 panel. The image is a collage of the
results obtained after the DIC was performed in the
sectors 1, 2 and 3. The colours in the image indicate
the level of the local strain, red is high strain and
blue is low strain. The so called “butterfly shape
strain field” typical for isotropic materials is evident.
After all the images for each sector and at each load
level were stored, the DIC was performed for each
sector individually. The stress field was obtained by
Since DIC does not give only the qualitative results,
but also the quantitative values,
it is possible to plot the strain
Load = 28 KN
distributions in figures to analyse
the data. Fig. 17 represents the
Load = 40 KN
strain distribution ahead of the
crack tip for different load levels.
Load = 44 KN
0,18
0,16
0,14
Strain [-]
0,12
0,1
Load = 48 KN
Also in Fig. 18 the strain fields
in front of the crack tip are
0,06
visualised for different load
0,04
levels. It is clearly visible that
0,02
the magnitude of the load
0
determines the size of the
0
2
4
6
8
10
12
14
16
18
butterfly shape. These results can
Position ahead of the crack tip [mm]
be used to determine the size of
Fig. 17, Example of strain field for different load levels calculated the plastic zone in front of the
crack tip, which is important
along the crack line (sector 2); Glare 3-2/1-0.5 panel
0,08
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Fig. 18, Example of strain field visualization for different load level (sector 2)
scatter found in the data is a typical result of the
error in the coordinates of the grid points,
determined by the DIC itself. It was stated before
that the error is in the order of 0.02 to 0.1 pixels,
depending on the quality of the image and surface of
the specimen. The influence of this error on the
strain can be affected by changing the distance
between the grid points, and thus the gauge length.
The other error found, is the negative strain values
in Fig. 20. Physically, a lower strain than zero is
only possible when the specimen was loaded in
compression, but that was not the case. Probably, the
reason for these negative values is a small change in
the distance of the camera, which results in an error
in strain measurement in the whole image, and a
shift down or upwards of the curves in Fig. 20.
Movement of the camera is inherent to this test
approach because for each sector the camera has to
be moved. Besides, for this test a lens with a large
focal depth was used, which makes it impossible to
use the focal distance to maintain the same distance
between the camera and the specimen.
information for the analyses of the static crack
growth. Previously it was only possible to obtain
this information by means of Finite Element (FE)
analyses. This test enables it to validate these
FE analyses with real test data.
In Fig. 19 the comparison between the experimental
results and a FE analyses for the same
Glare 3-2/1-0.5 panel is shown. The trend is the
same for both the FE analyses and the test results;
however small variations in the measurements are
observed. Especially for small strain values, like
those typical of the elastic field, the variations are of
the same order as the magnitude of the local strain
values. This implies that the error strongly affects
the results for small strain value (e.g. ε ≤ 0.4 %).
This behaviour is even more evident in Fig. 20,
which represents the same curves as Fig. 19 but with
a different scale of the strain axes.
A more focused analysis of the data of Fig. 20
reveals that the DIC results are affected by two
different errors, resulting from different origins. The
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0,07
DIC; load = 41 kN
0,06
FE analyses; load = 41 kN
0,05
DIC; load = 25 kN
Strain [-]
FE analyses; load = 25 kN
0,04
0,03
0,02
0,01
0
-0,01
9
11
13
15
17
19
21
23
25
29
27
Position ahead of the crack tip [mm]
Fig. 19, Comparison between DIC and FEM results; Glare 3-2/1-0.3 panel (sector 2)
0,005
DIC; load = 41 kN
Strain [-]
DIC; load = 25 kN
0
Scatter bandwidth,
approximately 0.002
Negative strain
-0,005
9
11
13
15
17
19
21
23
25
27
29
Position ahead of the crack tip [mm]
Fig. 20, Example of scatter in strain due to correlation errors and negative strain values
due to error in the test setup
test. Besides, the required changes to use the DIC
method in test setups which already existed were
small and involved only the imaging system itself.
Only for the tensile tests the specimen surface had to
be prepared because the aluminium surface reflected
too much light resulting in overexposed images. The
other two tests were performed with the same
equipment and the same test setup as was used
previously without the DIC tool.
4 Discussion
In the previous sections different examples of
experiments were presented for which the DIC tool
to obtain the required test results has been used.
Although for all three tests the grid module and the
post processing module had to be changed, the basic
principle of the DIC tool could be used for all the
three tests. This proves how flexible this method is
and how easy it is to adapt this method to a different
ISBN: 978-960-6766-88-6
Different setups of the CCD camera were used, from
a simple tripod to an electrically controlled
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The contribution of the DIC methodology to the
thick adherent test is the possibility for direct
measurement of bond line deformation, thereby
eliminating the problems encountered with indirect
methods like mechanical extensometers. Further the
accuracy is higher due to the use of high resolution
CCD cameras and DIC software. The manual
analysis of the images was time consuming
compared to the use of extensometers. The use of
the DIC tool reduced the time for the analysis
tremendously. The loss of focus during testing due
to specimen movement is a cause for reduced
accuracy, which can easily be solved by using an
autofocus mechanism. The test setup is build–up
with several different pieces of equipment, so it
requires a lot of time for set-up. So far the DIC tool
is only used to measure the shear angle between
thick substrates assuming it is constant over the
bond line thickness. However, in a “real” adhesive
bonded joint adherends are not so thick and overlaps
are not so short which means that there will be strain
variation over the thickness. Using the DIC enables
to actually measure this strain variation and makes a
detailed comparison with, for instance, FE analyses,
which was not possible up until now. Moreover, the
DIC tool can be applied to measure strain variation
along the length of the bond line and even measure
the high strain gradients at the edges of bonded
joints. Besides the DIC method can be used to
investigate failure initiation and fracture propagation
in “real-life” bonded joints.
X-Y-Z axes controlled rack. In practice, the
X-Y-Z axes controlled rack is preferred because it is
much easier to align the camera with the specimen.
Besides, if the camera must be moved to follow the
specimen, or to capture a different area, an
X-Y-Z axes controlled rack gives less vibrations and
a higher accuracy of the positioning. If the high
magnification is used with a fixed focal distance,
like for the thick adherend tests, this rack is the only
option to align and focus the camera during the test.
For both the tensile tests on FS welded specimens
and the static crack extension test, the DIC tool
revealed material behaviour which has never been
shown before in such detail. For the tensile tests the
yield strength profiles of the welds are a large
contribution to the knowledge about these welds.
Moreover, the correlation tool has proven that it is
possible to calculate the yield strength accurate
enough to measure the same yield strength values as
was obtained by using an extensometer. A
difference of 4 MPa at 200 MPa is small enough,
especially when the scatter between the individual
tests is higher. It must be noted that the accuracy is
directly related to the quality of the images and the
pattern of the paint and amount of light used in the
test. Besides, from the local stress-strain curves
much more material data than the required local
yield strength could be obtained, for instance, the
modulus of elasticity, the strain hardening
coefficient, etc. Besides, this correlation tool enables
to analyse typical material or structural local
behaviour like necking just before failure, or the
Portevin Le Chatelier effect [4].
For all three tests it was found that using the DIC
tool has advantages above the standard strain
measurements systems like strain gauges, Moire’
pattern, extensometers etc., simply because it is the
only strain measuring method which can obtain local
qualitative and quantitative strain data at a large
surface area of the specimen.
For the static crack extension test, the DIC approach
allows the user to follow the strain field variation
during the crack propagation phase in detail.
Moreover, DIC showed to be powerful for the crack
tip behaviour analysis because it is possible to
extract information regarding the elastic-plastic
strain distribution, and the size and shape of the
plastic zone.
With regards to Fibre Metal Laminates, it is
expected that the DIC methodology is able to reveal
information about features like stresses repartition,
static delamination and plasticity induced
delamination onset which are not measurable in any
other way. For all the mentioned mechanisms
mainly qualitative descriptions have been provided
so far by several authors [9-13]. DIC finally enables
it to obtain a quantitative description of all those
strain related mechanisms in a fibre metal laminate.
ISBN: 978-960-6766-88-6
The only drawbacks at the moment are that the DIC
tool can only evaluate 2D deformations, for 3D
analyses at least two cameras are required, or
systems which uses laser scanning to measure the
shape of the specimen. Besides, DIC can only
measure the strain at the surface, what happens at
subsurface level is unknown.
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5 Conclusion
In the previous sections different experiments for
which the DIC tool is used, were evaluated and the
advantages and disadvantages discussed. For these
tests the DIC tool was successful, but there is always
a trade of required whether the use of the DIC tool
ads something or not. Besides, the user must
carefully design the experiment, before the DIC can
be applied, because a lot of errors can be made.
However, once the method is optimised and
validated for the test, it is possible to obtain
magnificent results. The following conclusions were
drawn from experience gained during the successful
application of the DIC tool in the three presented
experiments:
• DIC is a measurement methodology with a high
flexibility because of its independence of the test
article and the test method.
• DIC is able to visualize and measure detailed
material behaviour which were never shown
before.
• The use of DIC makes faster and more accurate
determination possible of bond line deformation in
thick adherend tests and drawbacks related to
mechanical means of displacement measurement
are eliminated.
• DIC is the only method to measure quantitatively
the local strain in a test article, which can directly
be used to validate FE analyses.
• The DIC method not only allows for a more
accurate determination of bond line shear angle,
but in future may also allow for the determination
of strain gradients near edges of bonded joints and
capture actual failure initiation and propagation.
• The DIC approach used in this paper is only
applicable to 2D strain fields; no 3D measurements
can be performed.
Science and Engineering, vol. 50, p. 1-78.
[4] L. G. Hector, Y.-L. Chen, S. Agarwal, C.
L. Briant, (2007), Journal of Materials
Engineering and Performance, vol. 16, n.
4, p. 404-417.
[5] C. Genevois, A. Deschamps, P. Vacher,
(2006),
Materials
Science
and
Engineering, vol. A 415, p. 162-170.
[6] (2005), Aerospace series – Non metallic
materials – Structural adhesives – Test
method – Part 6: Determination of shear
stress and shear strain, Report, EN 22436.
[7] R. B. Krieger, Stress Analyses Concepts
for Adhesive Bonding of Aircraft Primary
Structure - in: Adhesive Bonded Joints;
Testing, analysis and Design, in: W. S.
Johnson (Ed.) American Society for
Testing and Materials, Philidelphia, 1988,
pp. 264-275.
[8] C. Yang, H. Huang, J. S. Tomblin, D. W.
Oplinger, Evaluation and Adjustments for
ASTM D 5656 Standard Test Method for
Thick-Adherend Metal Lap-Shear Joints
for determination of the Stress-Strain
Behavior of Adhesives in Shear by Tension
Loading, Report.
[9] A. Vlot, J. W. Gunnink, (2001), Fibre
Metal Laminates an Introduction, Kluwer
Academic Publishers.
[10] C. A. J. R. Vermeeren, (1991), The
application of carbon fibres in ARALL
laminates, Report, LR-658.
[11] T. J. d. Vries, Blunt and sharp notch
behaviour of Glare laminates, Ph.D. thesis,
Delft University of Technology, 2001.
[12] C. A. J. R. Vermeeren, (1990), The blunt
notch behaviour of Metal Laminates: Arall
and Glare, Report, LR-617.
[13] C. A. J. R. Vermeeren, The Residual
Strenght of Fibre Metal Laminates, Ph.D.
thesis, Delft University of Technology,
1995.
References:
[1] P.-C. Hung, A. S. Voloshin, (2003), J. of
the Braz. Soc. of Mech. Sci. & Eng., vol.
XXV, n. 3, p. 215-221.
[2] H. J. K. Lemmen, R. C. Alderliesten, R. R.
G. M. Pieters, R. Benedictus, (2008),
Influence of Local Yield Strength and
Residual Stress on Fatigue in Friction Stir
Welding,
in:
49th
AIAA/ASME/ASCE/AHS/ASC
Structures, Structures dynamics, and
Materials Conference, AIAA, Schaumburg
IL, p. 22.
[3] R. S. Mishra, Z. Y. Ma, (2005), Materials
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