Two Dimensional Image Correlation (2D DIC) is now broadly recognised and applied
in the most experimental fields as a practical and capable instrument for in-plane
deformation measurement of a planar object surface. The full-field displacements
and strains to sub-pixel accuracy are calculated directly by comparing the digital
images of a test object acquired before and after deformation (Pan
et al., 2009a). On the other side, the importance of the material
as reinforced concrete in the structures is known to everyone who is involved
in construction. So, it seems that every property of this material will have
a great importance to study extensively by the new techniques in order to discover
precise behaviour of that material perfectly. One of the most important feature
in the reinforced concrete is the bond between bars and concrete that was studied
in this project. The joint performance of steel and concrete in a reinforced
concrete element is based on the fact that a bond is maintained between two
materials after concrete hardens. The bond strength depends on three major factors,
as friction between steel and concrete, interlocking and chemical adhesion (Nadim
Hasson and Al-Manaseer, 2008).
Theoretically, the calculated bond strength depends on several effective factors
and it has not completely equaled with practical results (Vandewalle
and Mortelmans, 1988). In order to have a useful step and dependable criteria
to judge theoretical results, realistic bond stress distribution based on experimental
sample seems to be helpful to great extent. Furthermore, such approaches can
help us to gain enhanced understanding of bond behavior that may lead to appropriate
usage of bars in concrete structures. Accordingly, it may change some related
conception or may help in discoveries innovative ideas in the bond field.
As shown in Fig. 1, the reactions of subjected tensile force
to the reinforcement in concrete block are inclined reaction forces (Fig.
1a) that can be presented with two components (Fig. 1b),
parallel and normal to the bar axes (Nadim Hasson and Al-Manaseer,
2008). The main purposes of this investigation were calculation of the bond
stress components and mapping the distribution of them on the concrete.
|| (a) Subjected tensile force and inclined reaction forces
and (b) Subjected tensile force and two components of reaction forces
TWO DIMENSIONAL DIGITAL IMAGE CORRELATION
Overview: One of the important tasks of experimental solid mechanics
is the measurement of the surface deformation and motion of material which is
subjected to various loadings. Apart from the commonly used conventional tool
for test measurement; such as LVDT, strain gauges, extensometer and etc., several
full-field non-contact optical methods have been developed and applied for this
purpose. The method of 2D DIC, developed at the University of South Carolina
in 1980s, is one of the non-contact optical technique that is widely accepted
and used as a powerful tool for the surface measurement (Peter
and Ranson, 1982). This method uses a single fix camera and is limited to
in-plane deformation measurement of the planar object surface. In this technique,
the full-field displacement and strain are measured by comparing grey intensity
changes of digital images of the specimen surface in un-deformed and deformed
states respectively (Sutton et al., 1986).
The advantage of the DIC method is that the experimental setup and specimen
preparation are quite simple (Schreier, 2003). For recording
the digital images of specimen before and after deformation, only one fixed
CCD camera is needed. A white light source or natural light can be used for
illumination during loading. On the weakness side, the object surface to be
measured must be planar and must have a random grey intensity. Besides, the
use of high quality imaging system is very important because the image quality
has a considerable effect on reliability of measurement. Some developments in
DIC; such as reduction of computation complexity and accomplishing high accuracy
deformation measurement, has been widely explored and considerably improved
in recent years (Sutton et al., 2008).
Fundamentals of 2D DIC: In this experimental a typical digital image
camera (Nikon D80) for acquiring images of test specimen is applied as shown
in Fig. 2. A computer is connected to this CCD camera in order
to control and take images automatically on regular bases. The camera is adjusted
with normal optical axis to the specimen surface. This surface which is illuminated
by white light sources, must have a random gray intensity distribution (i.e.,
speckle pattern). This feature deforms together with the object surface as a
carrier of deformation information. The speckle pattern can be the natural texture
of the surface or artificially made by spraying black and white paints.
The actual physical motion of one point on the specimen surface is calculated
by the estimated motion of image point multiplying the magnification of the
imaging system (in units of mm/pixel).
|| 2D DIC experimental system in the research
In order to obtain good result, the object surface must be flat and remain
in the same plane parallel to the CCD sensor camera during the loading. Any
out-of-plane motion will change the magnification of the recorded images and
this will lead to some error in calculation of displacement. Minimizing this
error effect, use of telecentric imaging system or placing the camera far from
the specimen is proposed (Sutton et al., 2008).
Secondly, geometric distortion in imaging system could produce some errors in
calculation of displacement. It is important that this error is reduced to minimal
level. However, techniques for correction of the geometric distortion are available
(Pan et al., 2009b).
The motion of each point at image is calculated by comparing the digital images
taken during test, using DIC software. Generally, several software are available
for correlation in market as RapidCorrelator, Vic 2D, Opticist and MATLAB toolbox.
At the first step of 2D DIC method, the Region of Interest (ROI) should be defined
on the reference image. This area will be divided into evenly spaced virtual
grids. Calculation of full-field deformation will be done based on the obtained
displacement of each grid points. For this purpose, small equal square area
as subsets are assigned to every grid point in some way that the point locates
in the centre of square (Fig. 3). The subsets have specific
number of points and their value in grey level, so for every subset in estimated
deformed shape, a criterion as Cross-correlation (CC) or Sum-squared Difference
(SSD) can be calculated. Having the distribution of these criterions and choosing
the peak value can yield to the desire deformed subset. Therefore, with this
method each subset could be traced in the next image. These related subset and
its centre, leads to the new location of the correlated points in the deformed
|| Schematic illustration of a reference square subset (a) Before
and (b) After deformation (Pan et al., 2009b)
The differences in centres of reference and target subsets yield in-plane displacement
vector at two centre points. This process will be continued till all the grid
points displacements are obtained.
Then, the new location of the rest points in the deformed subset can be computed
by using a math formula termed as shape function. This function is obtained
easily by using the data of the primary achieved displacement vector of subsets
center. A zero-order function can be used when the subsets displacement in reference
and deformed images is occurred because of only the rigid body translation.
A first-order shape function can be applied when translation, rotation and their
combination exist in deformed subset.
In calculation of the other points coordinate in the subset by using the shape
function, there is a probability that the coordinate of new point would be located
between two points. Solving this issue, a certain sub-pixel interpolation scheme
should be employed to provide the location of these points with the intensity,
before using correlation criterion or evaluating the similarity of subsets.
Miscellaneous interpolation schemes are used in literature and their detailed
algorithms can be found in numerical computing books (William,
2003). Nevertheless, bicubic and biquintic spline interpolation as a higher-order
interpolation scheme is greatly suggested by Knauss et
Displacement and strain field measurement: The integer displacements
with one pixel accuracy are computed easily because of the distinct nature of
digital images. Certain sub-pixel registration algorithms should be applied
for having more accuracy in this measurement (Bing et
al., 2006). Therefore, to achieve this level of accuracy two following
steps, namely initial deformation estimation and sub-pixel displacement measurement
should have been considered in the implementation of 2D DIC. This means that
for having sub-pixel accuracy in 2D DIC method, an accurate initial guess of
the deformation should be employed primarily. Strain distribution is more desirable
in most measurement area in the theory and practice. The strain is calculated
from the results of displacement. Pan and Xie (2009)
discussed the methods for calculating strain.
Errors in 2D DIC measurement: 2D DIC is heavily depending on the quality
of loading system, the perfection of imaging system and the accuracy of correlation
algorithms. The measurement in higher level of accuracy relies directly to the
estimation of the errors and their sources (Haddadi and
Belhabib, 2008). Entirely, the error sources can be divided into two discrete
categories, namely errors during test and errors after the test. The first group
which is related to the specimen, loading and imaging consists of four major
elements, specifically speckles pattern, test object position, image distortions
and noises. The second group is related to the correlation algorithm composed
of fours features, called subset size, correlation criteria, interpolation scheme
and shape function (Pan and Xie, 2009).
Application of 2D DIC: A large number of applications of 2D DIC are
available in the literature. Some of the important ones can be listed as, determining
the deformation field of various materials subjected to loading, determining
the different mechanical parameters of a material including Youngs modulus,
Poissons ratio, stress intensity factor, residual stress and thermal expansion
coefficient and the elastic properties of materials. Numerous other interesting
applications can be found in the experimental works based on measurement using
DIC. Valenca et al. (2012) has introduced an
innovative method named MCRACK to characterise cracks automatically using processing
of digital images. This interesting method, in spite of reducing working time
significantly, gives a considerable increase of data, with higher reliability
in cracks. Rouchier (2012) proposed digital image correlation
as a suitable method to obtain complete mapping of the deformations at the surface
of the samples and the use of non-destructive fracture characterization for
the purpose of moisture transfer modelling. In the field of damage assessment
in the Reinforced Concrete (RC), the combination of DIC method and acoustic
emission technique have used to provide the state of damage in RC structures
(Vidya Sagar and Raghu Prasad, 2012). Gardner has showed
DIC can be suitable for measuring the deflections of the masonry wall panels
in an experiment (Herbert et al., 2011).
The experiment is done with image acquiring of the concrete block surface during
the pull out test. A concrete block (400x100x55 mm) with embedded steel bar
(ø12) was prepared with the mix proportion of cement, water, fine and
coarse aggregate of 410, 250, 997 and 693 kg for producing one cubic meter of
concrete. The specimen was cured in room temperature for 28 days before conducting
the pull out test. The concrete compressive strength tested at 28 days was 31
MPa. Before conducting the pull out test, the specimen surface was coated with
white and black paint in order to have proper speckle pattern with high contrast.
Once the specimen was secured on the test bed, a CCD digital camera was setup
on a leveled tripod. The camera was located and adjusted such that the lens
axes was directed perpendicular to the side surface of the concrete block to
be recorded. The camera was connected to a computer and the snapping was controlled
and done automatically by software. An LVDT was installed next to the specimen
to record the displacement of a point that is shown in Fig. 4.
Pull out load was applied to the bar using Universal Machine at the speed of
0.05 kN sec-1 until failure. The images of the concrete block surface
were taken at every two seconds during loading. The LVDT reading was taken at
every 10 sec during loading. The pull out specimen set up is shown in Fig.
4. The obtained digital images were used as input data for correlation software
to analyze the displacement and strain of the concrete surface.
RESULTS AND DISCUSSION
Controlling the correctness of DIC result: Displacements of a specific
point on the specimen (Fig. 4), calculated by two different
correlation software, are compared with LVDT recorded results in Fig.
|| Specimen set up in pullout test
|| Load versus displacement of the certain point
The trends of two displacement curves obtained from DIC software are almost
same. However, there is a little difference in quantities of displacements.
which, the reason can be the use of dissimilar algorithm or correlation criterion.
In the following, the results of Vic-2D are used for further analysis and discussion.
Strain distribution: Having detailed assessment for better investigation,
the numerical results of correlation software are used for mapping full-field
distribution of three principal components of bond strain on the surface of
the specimen by Excel in Fig. 6a, when the tensile force is
In Fig. 6b, the major principal strain distribution, the
effect of bond action between concrete and reinforcement on the strain distribution
is observed clearly. The sharp increase of strain on the top of the bar is because
of the existence of the bond between concrete and reinforcement. The minor principal
strain distribution, Fig. 6c, manifests that the bond has
influence around the bar but with less intensity in comparison with the principal
strain distribution. As a remarkable point, it is obviously seen that this component
of strain has negative quantities in the most part of the specimen surface.
Last chart, Fig. 6d which illustrates the principal strain
angel distribution, exhibits that this strain in the specimen sides, is more
than top of the bar on the surface of the specimen.
|| (a) Pull-out specimen subjected to 67 kN, (b) Full-field
major principal strain distribution, e1, (c) Full-field minor
principal strain distribution, e2 and (d) Full-field principal
strain angle (in radians)
|| Plain stress descriptions
In other words, these two mentioned area have opposite rotation angle on the
plane of specimen due to subjected tensile force.
Stress distribution: One step further, after obtaining the result of
correlation analysis, is calculation of the related bond stress. Considering
the face of specimen as plane stress (σiz = 0), we can simplify
the components as shown in Fig. 7.
From advanced mechanics of material we have Eq. 1 for calculating
stresses in plain stress based on strains (e), young module (E) and Poisson
Substitution of (E) and (v) by their values the above Eq. 1
simplified as in Eq. 2:
With having this equation and the strains from DIC analysis, three components
of stress can be calculated for every point of specimen. Thanks to Excel that
eases these considerable operations along remarkable plots just by doing some
table work. Three full-field stress distributions are calculated and drawn for
normal stresses and shear stress on the face of specimen in Fig.
Considering the drawn full-field stress distribution plots, the trace of the
bar is observed clearly on the surface of specimen, due to existence of the
||Normal full-field stress distribution of specimen in 67 kN,
(a) Normal stress σx (N mm-2), (b) Normal stress
σy (N mm-2) and (c) Shear stress τxy
Ferguson et al. (1988) also presented the stress
distribution in 1988 as shown in Fig. 9 by different method.
Comparing this figure with the calculated stress distribution in Fig.
8a, the high similarity can be found easily in the shape and trend of stress
changes at the both figures.
However, the full-field stress distribution obtained by DIC results (Fig.
8a) gives more detail information about the bond behavior and it seems more
suitable than the other methods for investigation on the bond field.
In order to have accurate evaluation of stress growth throughout loading process
two perpendicular lines on critical area of specimen are selected and the variations
of stress is mapped versus tensile load rising. Figure 10
illustrates the changes of normal stress in x direction on a line (y = 100 mm)
in the width of the specimen, by growing tensile load till failure. The first
curve of this figure shows the changes of σx, when load is 12
kN. As it can be seen, the whole stresses have minus amount which shows the
area is on pressure in this stage. By load increasing, the line shape of curve
converts to polynomial because of the bond effect. In other words, the bond
changes the surface elements behavior in the vicinity of the bar by changing
their stress sign from negative to positive or from compression to tension.
The following chart, Fig. 11, illustrates the changes of
normal stress in x direction on a line (x = 0) in the length of the specimen
by growing tensile load till failure.
|| Normal stress (σx) on the transversal surface
line (y = 10) in various tensile forces
|| Normal stress (σx) on the longitudinal surface
line (x = 0) in various tensile forces
In this chart, at two initial loads, there is uniform increasing in σx
at entire line except in the top that is related to reaction of the support.
The σx of the bottom part has a high decrease in stress that
it may connect to unwilling out of plane motion of the end of specimen. The
shape of increasing of the stresses in top of the specimen shows the effect
of the bond in stresses on the surface. These stresses have positive sign in
the last loads and can be considered as tension stresses. It seems that this
bond stress component cause extensive tension on elements more than strength
of concrete and can be known as a generating factor of crack and failure of
specimen in the end.
Moreover from Fig. 11, the distribution of bar tension is
predictable in the length of specimen. Since, this tension magnitude in each
unit length of the bar is equal to sum of the related bond stress in around
of the bar in concrete, so the shape of tension distribution follows the shape
of bond stress in concrete. This claim is supported by the result of the experimental
work that was carried out by Feldman and Michael Bartlett
(2007) about bond stress along bar in pullout specimen. The other outcome
of that investigation is about the peak bond stress shifting from loaded end
to unloaded end of specimen during the increase of applied load, the behavior
which is clearly observed from figures in Fig. 11. Likewise,
the development of bond stress distribution under load increment conforms to
the result of finite element analysis for bonding simulation in the research
work with similar condition which was accomplished by Chen
and Pan (2006).
A full-field measuring system based on digital image correlation was successfully
applied to measure non-uniform strain of bond on the surface of concrete pull-out
specimen, subjected to tensile force. It was presented that this method is a
robust tool that has many benefits regarding to the testing conditions. Moreover,
it was showed that the bond stress can be calculated numerically by using the
results of 2D DIC. The development of non-uniform bond strain and stress in
concrete was depicted with full-field distribution maps, plus the growth of
bond stress at various loading stages. Considering the presented figures, it
is deduced that the proposed numerical method for calculation of bond stress
in concrete using 2D DIC results has adequate capability to investigate bond
stress in concrete precisely.
The author thanks the Universiti Teknologi Malaysia (UTM) and its Structural
and Material Lab for supporting of this research work. Also, the author is grateful
to Dr. Redzuan Abdullah for the valuable guidelines and useful comments to complete