Digital Image Correlation Technique for Detailed … · 1 Digital Image Correlation Technique for...
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Digital Image Correlation Technique for Detailed CFRP Plate1
Debonding Fracture Investigation2
G.X. Guan; C.J. Burgoyne3
Abstract4
Carbon fibre reinforced polymer (CFRP) plate is now commonly used in reinforced concrete5
beam retrofitting, and a common premature failure mode is the plate debonding, which is6
inherently the fracture of concrete close to the concrete-plate interface and very difficult to7
investigate. This paper presents a low cost digital image correlation technique specifically8
designed for the plate debonding fracture investigation, using widely available digital cameras.9
The technique provides detailed fracture and strain field images associated with debonding10
fracture, from which the fracture process zone can be found. It can suitable for use in ordinary11
structural laboratories since it does not require specialist equipment. The technique adopts the12
common searching process used in conventional digital image correlation, but with special13
features developed to meet the needs of debonding fracture investigation. It uses 16-bit14
images and sub-pixel tracing techniques with cubic spline interpolation on the correlation15
space. Methods to cater for the narrow inspection region in debonding, and to evaluate and16
adjust the errors due to in-plane rotation and out-of-plane tilting are developed. The technical17
details are first discussed, followed by validation and debonding investigation results.18
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Keywords20
Digital Image correlation (DIC); Debonding fracture; Strain field; Fracture process zone21
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Note for Reviewers1
This paper is one of three that have been submitted to different journals and which cross-refer.2For the benefit of reviewers only, copies of all three papers, as submitted, can be downloaded.3
Guan X.G. and Burgoyne C.J., Digital Image Correlation Technique for Detailed CFRP4Plate Debonding Fracture Investigation. Submitted to Experimental Mechanics. (This paper).5Available at http://www-civ.eng.cam.ac.uk/cjb/papers/dic.pdf6
Guan X.G. and Burgoyne C.J., Determination of debonding fracture energy using a wedge-7split peel-off test. Submitted to Engineering Fracture Mechanics. Available at http://www-8civ.eng.cam.ac.uk/cjb/papers/wedge.pdf9
Guan X.G. and Burgoyne C.J., Fracture process in CFRP Plate Debonding Fracture,10submitted to Engineering Fracture Mechanics. Available at http://www-11civ.eng.cam.ac.uk/cjb/papers/process.pdf12
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Introduction14
It is common to strengthen concrete structures by gluing carbon fibre reinforced polymer15
(CFRP) plates on the tensile surface of the concrete. These have been observed to fail16
prematurely by fracture in the concrete, and as part of a fracture mechanics study of this17
phenomenon, it is necessary to determine the strain field in a narrow strip, typically about 1018
mm wide, on the side of a specimen that may extend for only 50 mm.19
The study of concrete fracture, even in relatively large specimens, is very difficult because the20
fracture propagates on a scale smaller than the size of the aggregate. This means that concrete21
is not homogeneous, but the precise nature of the heterogeneity cannot be predicted before the22
test. It is thus necessary to determine the strain over a large area within which the crack23
might propagate.24
The region affected by the crack is called the fracture process zone (FPZ) and contains all the25
information needed for the crack study. However, detection of the FPZ has been difficult and26
there exist very limited sound experimental results. Since cracks in concrete are localised,27
with small opening displacements, of the order of a fewm, detection techniques with high28
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resolution are required. Various techniques have been used since 1980s, including electronic-1
speckle-pattern interferometry (ESPI), digital image correlation (DIC), scanning electron2
microscopy (SEM), photoelastic techniques, X-Ray microscopy, acoustic emission and3
holographic Moire interferometry. There exist very limited direct observations of the4
concrete fracture process, and these usually show poor quality: a review can be found in5
Mindess (1991) in RILEM Report 1991. There has been little improvement since then despite6
development in technique.7
Scanning electron microscopy, X-Ray techniques, and holographic interferometry are8
considered to have the highest resolution. However the accuracy depends on the quality of9
the set-up, which is very complicated. SEM and X-Ray techniques usually give a direct10
picture of the micro crack patterns but do not clearly indentify a FPZ (Otsuka & Date 2000,11
Bascoul et al. 1989, Mindess & Diamond 1982). The FPZ, if found, usually has a size of12
several mm (e.g. 1 – 4 mm in Tait & Garrett 1986), while the SEM and X-Ray results may13
also be influenced by shrinkage-induced cracks (Stroeven 1990). As well as being14
complicated to set up, holographic interferometry needs a relatively large gauge length (of the15
order of tens of mm) to work, which is comparable to the size of the concrete cover layer16
where debonding occurs. Photoelastic techniques, strain/displacement measurement with17
gauges, acoustic emission techniques, and digital image crack morphology techniques have18
also been used for concrete crack identification due to their relatively simple setup but they19
give only a qualitative geometrical description of the damage zone, and no clear information20
for the size of the FPZ (Reinhardt & Hordijk 1988).21
What remains are the ESPI and DIC techniques. ESPI, also known as TV holography,22
measures deformation by comparing the change of speckle patterns generated from laser23
illumination. ESPI produces results similar to those of holographic interferometry when used24
properly (e.g. Chen & Su 2010, Su et al. 2012) and the gauge length needed can be smaller25
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than that of holographic interferometry due to the use of lasers. However, in order to avoid1
the complicated setup and to ensure accuracy, ESPI is usually integrated into a commercial2
device similar to a digital camera. Although convenient to use, with its commercial nature,3
ESPI is expensive and comes as a black-box with binding licensed software for data4
processing that cannot be altered, which makes it difficult to apply to novel problems. Such a5
case is the debonding crack, which is likely to occur in a narrow interface region, requiring6
modification of the data processing software. Thus ESPI was considered unsuitable.7
DIC techniques need only a relatively good digital camera and a computer program for post-8
processing, and have been used increasingly for strain detection in recent years. Specific9
features needed for the debonding fracture investigation can be built into the process program.10
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Digital Image Correlation Techniques for strain measurement12
In DIC techniques, deformation is measured by comparing the digital photos taken of an13
object at different times. As with holography and ESPI, the digital photo of an object is the14
reflection of the light from that object, except that the source of this light is not carefully15
controlled. In DIC techniques it is the intensity rather than the frequency of the light16
reflection that is used for the comparison, and correspondingly, it is a correlation of intensities,17
rather than interference of phases, that is needed. Through correlation, the appearance of an18
object in the later stages can be compared with its original state to identify deformations.19
An image is taken of a planar surface of an object, on which is superimposed a sampling grid20
with the nodes being taken as the sample points. If the locations of the sample points can be21
determined in two images, before and after the formation of a crack, the changes of the22
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sample point location coordinates can be used to construct the strain field and identify the1
FPZ.2
A black and white digital image is essentially a collection of the voltages across a charged3
couple device (CCD) that depend on the light intensity, with the brightest and darkest4
noticeable light displayed as “white” and “black” respectively. Two typical digital images are5
shown in Fig. 1, which are taken for the same object with a small in-plane rigid body6
movement.7
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Figure 1 Two images taken for the same object10
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A region of the matrix consisting of a certain number of pixels is defined as a feature that can12
be distinguished from the rest of the image, which is known as a template (Template RA in13
Fig. 1). The template has dimensions of m×n and its centre is defined as the sample point (i,14
j). The same feature should also appear in Image B (Template RB), but at a different location15
(r,s) which is not yet known. The sample point is taken as the centre of the template, whose16
original location is known on the reference image (e.g. Image A). The objective of DIC17
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technique is to locate the sample point in later images (e.g. Image B). In searching for the1
later sample point location, the differences in the intensities (I) of each pixel in the template in2
the two images are compared using normalised correlation coefficient:3
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( , ) = ∑ ( ( , ) ̅ )∙( ( , ) ̅ )( , )∑ ( ( , ) ̅ )( , ) . ∙ ∑ ( ( , ) ̅ )( , ) . (1)5
where ̅ = ∙ ∑ ( + , + )( , ) , and ̅ = ∙ ∑ ( + , + )( , ) are the average6
intensities of Template RA and RB respectively, and K is the number of pixels on the template.7
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C(r,s) gives the degree of match and has a value in the range of [-1,1], where 1 and 0 indicates9
an exact match and no relationship respectively, and -1 corresponds to a negative image.10
C(r,s) is computed for the templates whose centre is aligned at (r+m/2, s+n/2), and the11
normalising makes the process insensitive to the overall exposure. A typical C(r,s) plot for12
aligning the template centre at different locations is as shown in Fig. 2.13
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Figure 2 The variation of correlation coefficient with locations (r,s).2
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The location of the best match (r,s) is now an integer coordinate in units of pixels. However,4
the movement may not be a whole pixel number. Many interpolation techniques have been5
developed to determine the intermediate correlation coefficient values including the6
interpolation on intensity values, Newton-Raphson iteration and curve-fitting interpolation on7
correlation coefficients (Bruck et al. 1989, Cary & Lu 2000, Wattisse et al. 2001, Hung &8
Voloshin 2003, Pan et al. 2009). Interpolation on correlation coefficient using 2D cubic9
splines is adopted here to determine the sub-pixel correspondence.10
A cubic spline is obtained by using third-order polynomials to smoothly join the discrete data11
such that it passes through all the data points and has continuous first and second derivatives12
at interior data points. In the one-dimensional case, in order to fit a third-order polynomial13
between the nodes i and i+1, the data from the nodes i-1 to i+2 are needed. In the two-14
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dimensional case, the nodes in both directions from i-2 to i+2 are needed, where the one1
additional node is used to determine the region for the peak of the 2D spline surface, that is, in2
the range from i-1 to i, or from i to i+1. The built-in 2D cubic spline interpolation code in3
MATLAB is used for this interpolation to improve the code efficiency. After this 2D4
interpolation, a smooth variation of the correlation coefficient can be achieved. The5
interpolation result around the peak region of C(r,s) in Fig. 2 is shown in Fig. 3, based on the6
nodal correlation C(r,s) data. The interpolated C(r,s) surface is smooth, and the location7
corresponding to the maximum interpolated C(r,s) value is taken as the location of the8
template in the second image.9
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Figure 3 C(r,s) after the 2D cubic spline interpolation12
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The precision of the sub-pixel tracing depends on the template size, and the larger the14
template size the better. It has been claimed that if a template of a proper size is used, the15
precision of the interpolation can be as high as 0.01 – 0.05 sub-pixel using 8-bit images, such16
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as Schreier et al. (2000), Hung & Voloshin (2003), Pan et al. (2006). However, a rigorous1
demonstration is rarely presented, since such a proof needs very advanced devices with even2
higher precision, for example electron microscopes, which are not easily accessible.3
The influence of template size on correlation precision is illustrated in Fig. 4, which shows4
correlations computed using different sized templates.5
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(a) (b)8
Figure 4 Influence of template size on correlation peak (16-bit): (a) 50 pixel templates; (b) 209
pixel templates.10
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The peak of the correlation values is more obvious compared with the noise using a larger1
template, Fig 4(a). However, since the purpose of the DIC here is to inspect the detailed2
fracture related to concrete with localised cracks, a larger size is not necessarily better. There3
are two main drawbacks: (i) the total number of independent templates in an image becomes4
smaller, as does the number of independent sample points; (ii) The time required for5
searching a large template is much longer than a small template, which may become6
impractical.7
In order to demonstrate the importance of using small and non-overlapping templates, Fig. 58
shows an image with a crack, which will be compared with the reference image. The grids9
show the template size; two different-sized independent templates are used.10
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Figure 5 Crack investigation with different template sizes12
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The reference image is taken before loading so does not contain a crack. The second image14
does contain a crack. It is convenient to reverse the correlation process, searching for15
templates from the cracked image in the uncracked image. When templates from the later16
image contain a crack, the correlation coefficient is low. Below some threshold (say 0.5) the17
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template is considered to be unfound and it is assumed that this area is cracked, so no further1
information can be obtained. If a large template is used, the discontinuous region along a2
crack-line appears magnified, so using a template larger than the real FPZ size would give3
results that depend on the template size. A series of overlapping large templates could be4
used to trace the crack, but the shifting intervals would need to be small, which leads to a high5
computational demand. Furthermore, overlapping templates give a man-made smooth change6
of the correlation coefficient from the uncracked to the cracked region. This would lead to the7
problem of defining the correlation level at which a region is denoted “unfound” (i.e. cracked),8
which again affects the determination of FPZ size. Thus there exists an optimum template9
size, and small independent templates are preferred providing that they give sufficient10
precision. In addition, if a crack is close to the edge of a specimen, as happens when a11
debonding crack is considered, a relatively small template has to be used.12
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Image enlargement to make use of the deeper images14
In the previous discussion about template size, the dimensions were measured in pixel units15
rather than physical length. When calculating strain, the change in position over a gauge16
length has to be calculated, and the selection of a suitable gauge length relative to the size of17
the template and the size of the crack is important. Since the concrete crack is a localised18
phenomenon, a large gauge length would enlarge the area that appears to be influenced by the19
crack, lowering the apparent strain, and affecting the determination of the FPZ size. Thus, a20
small gauge length should be used. In this DIC technique, the shortest possible gauge length21
is the physical distance between sample points which are at the template centres. Since22
independent templates are preferred and a certain template size is required for the DIC23
precision, there exists a lower limit for the number of pixels that should be zoomed into the24
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region being studied. This can be ensured in two ways: (i) using a large pixel CCD together1
with a long zooming lens and (ii) using deeper images (e.g. 16-bit instead of 8-bit images).2
When zooming closer the viewing area becomes smaller and the lens distortion becomes3
higher. For a commercial camera, the increment of pixel density obtained from lens zooming4
is limited. Before zooming close enough to make the effect of lens distortion significant, the5
best ordinary commercial CCD-lens system commonly gives around 50 – 100 pixels per mm6
while providing a viewing window around 40 50 mm. If a template of 50×50 pixels is used,7
the smallest grid interval to allow independent template is around 1 mm, which is barely8
enough for interface crack investigation. Most of the existing DIC techniques focus on9
improving the CCD-lens capacity, which can easily make the device very expensive and hard10
to generalise.11
Many commercial cameras can now save 16-bit raw images instead of the compacted and12
lossy 8-bit JPEG images. A 16-bit image has pixel values ranging from 0 – 65535 and13
provides a much better texture then an 8-bit image with pixel values from 0 – 255. As shown14
in Fig. 6, the “white dot” texture in the template consists of three pixels. If 8-bit data is used,15
they all have the same pixel value “255”, however, if 16-bit data is used, more detail can be16
distinguished.17
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Figure 6 Pixel value of the same object in 8-bit and 16-bit images2
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The sub-pixel precision is a strong function of template size and a weak function of the4
surface texture (White 2002). The debonding cracks are in a narrow band as small as 2 – 55
mm wide. It usually has good texture, but it is difficult to provide space for large templates.6
Since the template size dominates the correlation precision, the better-textured image is used7
to construct a more refined image with a smoother texture by enlargement. The 16-bit raw8
image is linearly interpolated and new pixels are generated at intermediate positions to9
enlarge the original image. This enlargement would be beneficial for getting finer details10
provided the image is not over-interpolated and no texture is lost. The average of the absolute11
pixel intensity difference (APD) of adjacent pixels across a template can be used as the12
indicator of texture. APD depends on the object texture and the depth of the image (8-bit or13
16-bit). APD of different surfaces are shown in Fig. 7 (the sandy surface is made by adhering14
thin layer of fine sands on a surface), where the APD number is greater than the maximum15
depth of the 8-bit image, that is, 256. Typically, even after a 5-times enlargement, the 16-bit16
images still have much better texture than unrefined 8-bit images.17
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Figure 6 Pixel value of the same object in 8-bit and 16-bit images3
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The sub-pixel precision is a strong function of template size and a weak function of the18
surface texture (White 2002). The debonding cracks are in a narrow band as small as 2 – 519
mm wide. It usually has good texture, but it is difficult to provide space for large templates.20
Since the template size dominates the correlation precision, the better-textured image is used21
to construct a more refined image with a smoother texture by enlargement. The 16-bit raw22
image is linearly interpolated and new pixels are generated at intermediate positions to23
enlarge the original image. This enlargement would be beneficial for getting finer details24
provided the image is not over-interpolated and no texture is lost. The average of the absolute25
pixel intensity difference (APD) of adjacent pixels across a template can be used as the26
indicator of texture. APD depends on the object texture and the depth of the image (8-bit or27
16-bit). APD of different surfaces are shown in Fig. 7 (the sandy surface is made by adhering28
thin layer of fine sands on a surface), where the APD number is greater than the maximum29
depth of the 8-bit image, that is, 256. Typically, even after a 5-times enlargement, the 16-bit30
images still have much better texture than unrefined 8-bit images.31
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Figure 6 Pixel value of the same object in 8-bit and 16-bit images4
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The sub-pixel precision is a strong function of template size and a weak function of the32
surface texture (White 2002). The debonding cracks are in a narrow band as small as 2 – 533
mm wide. It usually has good texture, but it is difficult to provide space for large templates.34
Since the template size dominates the correlation precision, the better-textured image is used35
to construct a more refined image with a smoother texture by enlargement. The 16-bit raw36
image is linearly interpolated and new pixels are generated at intermediate positions to37
enlarge the original image. This enlargement would be beneficial for getting finer details38
provided the image is not over-interpolated and no texture is lost. The average of the absolute39
pixel intensity difference (APD) of adjacent pixels across a template can be used as the40
indicator of texture. APD depends on the object texture and the depth of the image (8-bit or41
16-bit). APD of different surfaces are shown in Fig. 7 (the sandy surface is made by adhering42
thin layer of fine sands on a surface), where the APD number is greater than the maximum43
depth of the 8-bit image, that is, 256. Typically, even after a 5-times enlargement, the 16-bit44
images still have much better texture than unrefined 8-bit images.45
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Figure 7 Appearance of different surfaces (16-bit)2
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DIC Procedures and strain field construction4
Figure 8 summarises the overall DIC sample point tracing procedures, where the hatched5
square is the template and the dashed rectangle is the region in which the template is sought.6
The search process is divided into three stages: (i) Pre-search: To determine the rough7
location of correspondence in a later image by searching the image before enlargement; (ii)8
Search: To determine the accurate location for a sample point around the rough location using9
enlarged images; (iii) Final determination: To determine the final location of the sample point10
using sub-pixel interpolation.11
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Figure 8 Procedures of the DIC techniques2
3
(i) A template in the reference image is constructed with the sample point at the centre in the4
original image. Then it is sought in a large search region in a later image to determine the5
rough position. A relatively small template and large search region is used to quickly locate6
the region for more accurate searching later. It is impractical to search a large template in a7
large region due to the computer time required. The purpose of this step is to narrow down8
the search region.9
(ii) The template and the region around the rough position obtained from (i) are enlarged. A10
new template with larger size on the enlarged image is constructed, and it is sought in a small11
accurate search region in a later image. The outcome of the step is a surface of correlation12
coefficient C(r,s) across the accurate search region.13
(iii) 2D cubic spline interpolation is used to obtain the intermediate correlation coefficient14
values for positions with sub-pixel accuracy. The sub-pixel position corresponding to the15
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peak of the interpolated correlation coefficient is taken as the position of the sample point in1
the later image.2
Once the sample points have been found, the strains can be computed. The sample point in3
two different images are determined as at C1(x1,y1) and C2(x2,y2), as shown in Fig. 9.4
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Figure 9 Determination of strain7
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The displacements of point (i,j) can be obtained by searching a template centred at that9
location, and are given by10
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, = ( ) , − ( ) , , = ( ) , − ( ) , (2)12
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When the displacements of the four adjacent grid nodes are determined, the strain at their14
centre position (C1 in Fig. 9) is given by15
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= , ,∆ − , ,∆ (3)1
= , ,∆ − , ,∆2
= , ,∆ − , ,∆ + , ,∆ − , ,∆3
4
where and are the strains along x and y directions; is the shear strain, and;5 ∆ = , − , and ∆ = , − , are the gauge length for strain. The principal strains6
( and ) and their directions can then be determined using Mohr's Circle.7
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Dealing with In-plane rigid body movement9
Strain should be independent of in-plane rigid body movement, but rotation would affect the10
value of the correlation coefficient, since a square template is used and can only be traced11
along the columns and rows in an image. As an example, consider the specimen in the12
wedge-split test for debonding fracture investigation (for details see Guan & Burgoyne13
2014b). At late stages of loading, the displaced part in the top left of the image can rotate14
significantly, Fig. 10 (a).15
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1Figure 10 Local registration for the displacing part2
3
The region in the rectangle in Fig. 10(b) needs to be investigated, which includes an area that4
rotates. In order to get a good match, the displacing part is registered to the reference image5
before searching to cancel the rigid-body rotation. Two points in the displacing part, remote6
from the crack, are identified in both the reference and the later images. The relative7
orientation of these is used to determine the rigid body rotation of the displaced region, which8
is then applied to the target image. When searching the displacing region, templates would9
be constructed from the rotated image. Near the inclined crack at the base of the displaced10
region, templates would be matched in both the rotated and unrotated reference images and11
the search result with a higher correlation used. This local registration is a general way to12
deal with rigid-body rotations, and in a real test only the cases with large rotation need13
registration.14
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Dealing with out-of-plane rigid body movement1
Another difficulty that arises in non-destructive strain measurement techniques lies in the2
relative movement between the camera and the specimen rather than in the resolution of the3
imaging device. The DIC technique discussed above assumes the surface to be imaged is4
planar but there are likely be out-of-plane rigid body movement in real tests. Although the5
absolute out-of-plane movement is small, its influence on the strain field can be significant.6
Depending on the exact structure and the materials used, the real strain to be measured has an7
absolute value ranging from 100 to 10,000 µε, with a gauge length around 1 mm. It has also8
been identified that the out-of-plane movement-induced error is significant in interferometry9
(Chen & Su 2010). This relative movement is impossible to avoid since the specimen moves10
when it is loaded. It may be mitigated by attaching the camera to the specimen and reducing11
the relative deformation, but it is not always clear to what the camera should be attached, and12
it is difficult to achieve a rigid connection that does not itself cause distortions of the13
specimen. Instead, a simple model is used here to investigate and adjust the influence of the14
out-of-plane rigid body movement.15
Figure 11 shows the surface being imaged as P, with the viewing angle of the camera (2αc)16
outlined by the dashed line. P0 is the ideal case where the surface is perpendicular to the17
centre axis CO of the camera, while P1 and P2 are two imperfect cases: (i) where the surface P18
tilts by angle θ, pivoted at O, and (ii) with an additional eccentricity |OM|.19
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Figure 11 Effect of out-of-plane movement on apparent strain2
3
In the three cases P0, P1 and P2, the regions where the image is taken are QR, Q1R1 and Q2R24
respectively. Since the number of pixels on an image is fixed, the number of pixels assigned5
to unit length in the three cases is different. It is assumed that the number of pixels across an6
image is N and they are evenly distributed, which is ensured by the lens optical properties (e.g.7
no lens distortion). In the P0 case, a unit pixel represents the real length of |QR|/N. For P1 a8
unit pixel represents an average length of 2|Q1O|/N and 2|OR1|/N on the left and right of the9
centre axis CO respectively. If P0 is taken as the reference, P1 would have a false strain.10
Note that it is the change of the tilting angle rather than its absolute value that causes this false11
strain. The real strain can be calculated in the real object coordinate or the image coordinate12
in units of pixel, and here the latter is used.13
Case P1 is compared with case P0 to determine the effect of out of plane tilting. Since Point O14
is at the same place in cases P1 and P0, where there is no false strain, the lengths in P1 and P015
cases are calculated from Point O. If the apparent tilting-induced strain of an arbitrary Point16
A is considered, the length |OA| and |OA1| are assigned the same pixels, so a unit pixel in the17
two cases represents an average length of:18
21
1
| |/ = | | / (4)2
| |/ = | | ( ( − ) + )/ (5)3
where NOA is the number of pixels assigned to the length |OA| and |OA1|.4
Thus the tilting induced strain at point A is given by:5
= | |/ | |/| |/ = ( ( ) )(6)6
The tilting-induced strain varies as the position of Point A changes, both from side-to-side in7
the image and towards or away-from the camera. In real tests, in order to get a high8
resolution image, pixels are zoomed to the object surface as densely as possible. As a result,9
the overall viewing angle αc is commonly small and around 2 − 3 . If the viewing angle for10
A (φ) is taken as 2.5 and the tilting angle is taken as 0.2 , is -150 με. Such a small11
change in tilting angle (<< 1 ) is considered to be inevitable during structural tests, and strain12
errors of the order of 100 με are comparable with the conventional ultimate tensile strain of13
concrete. Thus, it is necessary to adjust this tilting-induced-strain in the post-processing stage.14
If the multiplication factor ( ( ) ) is applied to the measurement of |OA1| in the15
P1 case before it is compared with the P0 case, the tilting-induced strain is cancelled.16
However, the tilting angle θ is not normally measured directly and has to be found by trial and17
error with a reference point having a strain value known. An example of the adjustment for Al18
plate specimen is presented in the validation section later, where a point with the strain19
measured by strain gauge is taken as a reference for the adjustment. When in debonding20
fracture, a location far from the fracture affecting region, having zero strain, can be taken as21
the reference point.22
22
For a more general case (P2), the object plane pivots at a general Point M, which is the same1
point in the tilted and perfect planes. Point M may be at any point; in the adjusting code2
written here, lengths are measured from M if it is within the image, otherwise the lengths are3
measured from the image edge closest to M. The expressions for Point M out of the viewing4
angle to the left, as shown in Fig. 11, are given by:5
6
| | = | |( − ) (7)7
| | = (| | + | |) ( ( − ) − ( − )) (8)8
9
In this case, Point A tilts away from the camera. Thus if is taken as 3 , as 0.2 , φ as10 2.5 , |OM| as 100 mm and |CO| as 600 mm (which are typical values for the image close to11
the edge in a wedge-split test), the adjusting factor for Point A in P2 case is |QA|/|Q2A2| =12
0.9997 which is equivalent to a false strain of about 300 με.13
Generally, if the unit for length in DIC is taken as one pixel on the perfect plane (P0), the14
same length in the imperfect planes (P1 or P2) should be converted back to the perfect plane.15
If an object is closer to the camera than it was in the perfect case (P0), more pixels are needed16
to represent the same length. Thus a multiplication factor greater than one should be used.17
The final strain is constructed using the ‘image length’ (i.e. pixels) after adjusting onto the18
perfect plane. This tilting-induced strain is fixed for each pixel on an image provided the19
tilting angle and the eccentricity are known. Different points on an image are subject to20
different adjusting factors (due to different values in Fig. 11).21
In practice, of course, the plane can tilt about two axes but the tilting rotations are small, so22
the adjusting factors in the two directions can be multiplied to approximate the final adjusting23
23
factor for each location. An example of this effect is shown in Fig. 12. The adjusting factor1
deviates most from unity at about 0.9996 on this plot at the image edge, which corresponds to2
a strain error of about 400 με.3
4
5
Figure 12 Variation of adjusting factor across an image, corresponding to the eccentricities of6
10 mm (in x) and 20 mm (in y), and tilting angle of 0.2o in both directions. (50 pixels7
correspond to around 1 mm on the object.)8
9
The adjusting factor for a given point on the image also varies against the tilting angle θ and10
the eccentricity |OM|, which is illustrated in Fig. 13 for one particular point. When the tilting11
angle is zero, the adjusting factor is exactly one, which is the case of in-plane rigid body12
movement. The contour lines are obtained from interpolation.13
24
1
Figure 13 Variation of adjusting factor against tilting angle and eccentricity for a point taken2
from an image in a real DIC test corresponding to = ~3 , |CO| = 600 mm, and the point is3
about 30 mm from the lens axis CO. The positive sign for the tilting angle and the4
eccentricity refer to the anticlockwise angle and the Point M to the left of the camera axis.5
6
The rectangular region covers the area of normal interest with the eccentricity less than 1157
mm and the tilting angle within 0.5o. The adjusting factor is within 1 ± 1×10-3, except at the8
corners of the rectangle. Note that the region of interest is normally in the centre of an image,9
and the adjustment does not use the extreme values of the tilting angle and the eccentricity,10
the tilting error is considered to be within ± 500 με. This error is large compared with the11
conventional understanding of concrete tensile strain under a gauge length common over 1012
mm, but it can be insignificant when a much smaller gauge length is used, for example 1 mm13
here for debonding fracture investigation.14
The tilting effect has a limit that depends on the focus sensitivity of the lens. For example if15
the distance between P2 and P0 surfaces |OO’| is large, P2 surface would be out of focus, and16
the auto focus would be readjusted. Hence, the combination of the tilting angle and the17
eccentricity should not lead to a large |OO’|. Since| | = | | , if the lens focus18
25
sensitivity is assumed to be 1 mm, and is taken as 0.5 , the maximum eccentricity |OM| is1
115 mm, and if an eccentricity is given the maximum undetectable tilting angle can be2
calculated as well. Thus the eccentricity and tilting angle are interdependent. If the strains on3
three locations forming a triangle is known, the strains given by the DIC technique can be4
compared with them to determine the necessary adjustment.5
6
Validation of DIC technique7
Strain fields for aluminium plate under tension8
In this test, the strains obtained with the DIC technique are compared with strain gauge9
records and the theoretical results from elastic analysis. A slender aluminium plate 4.2 mm10
thick, and 35 mm wide was tested under tension in the vertical direction. The region of11
inspection was remote from the loaded ends as shown in Fig. 14.12
13
14
Figure 14 Inspected region of aluminium plate under direction tension. The surface has been15
coated with sand.16
17
26
The relatively coarse sand (up to 1 mm size) would move as a rigid body and would generate1
shadows under lights. Three 45-degree strain gauge rosettes were attached on the rear surface2
at the locations indicated in the figure. The reference image was taken when the plates were3
under 0.5 kN preload. The strain fields of the inspected region for the two plates under4
different loading states are shown in Fig. 15.5
6
7
Figure 15 The strain fields for aluminium plate under direct tension: (a) and (b) are under 5.58
kN and 8 kN tension respectively; “before” refers to the results without adjustment for out-of-9
plane rigid body movement; “after” takes account of the adjustment.10
11
27
The gauge length is 1.5 mm, and xx & yy represent the horizontal (transverse) and the vertical1
(axial) directions respectively. Some obvious strain pattern due to the rigid body tilting effect2
could be seen from the “before” figures, appearing as large tensile and compressive strains on3
the top left and bottom right. The reading from the strain gauges and the fact that the plate4
was loaded symmetrically were used as the adjusting reference for removing the tilting effect.5
The adjusted strain fields are as shown in the “after” figures.6
7
Figure 16 Axial strains across horizontal cross-sections of the specimen8
9
After the adjustment, the average axial strains over each horizontal section of the specimen10
are shown in Fig. 16 with the ±1.64 standard deviation (s) values which give information11
about the noise in the process. A noise level of about 40 με is observed, which is thus taken12
as the limit of precision of the DIC technique as implemented here.13
The comparison between the DIC and the strain gauge results is shown in Table 1.14
28
Table 1 Comparison of the DIC and strain gauge results1
Load
(reference
image taken
at 0.5 kN)
yy (Strain
gauge)
()
yy (DIC)
()
xx (Strain
gauge)
()
xx (DIC)
()
Young’s
modulus E
(DIC) (GPa)
Poisson’s
Ratio (DIC)
5.5 kN 473 481 -149 -153 70.7 -0.318
8 kN 749 728 -233 -224 70.0 -0.308
2
The strains obtained from both techniques are similar, while the Young’s modulus and3
Possion’s ratio obtained from the DIC techniques are close to the standard values for4
aluminium. The local variation of the strain is assumed to be due to the randomness of the5
sandy surface and the small gauge length (1.5 mm) used. It can be concluded that the DIC6
technique gives reasonable strain results down to about 100 with a 1.5 mm gauge length.7
8
Strain fields for concrete cube test9
A concrete cube test was used to examine the capacity of the DIC technique for both strain10
and concrete fracture detection. 100 mm concrete cubes with 10 mm maximum aggregate11
size where tested in a conventional cube testing machine with a loading rate of 0.3 MPa/s till12
the peak load. Images were taken during the testing process every 5 MPa, from which the13
DIC technique was used to construct the strain fields.14
The results are presented for three cubes, which were cast from the same batch of concrete.15
The strengths for cubes 1 to 3 were 42.4 MPa, 44.2 MPa, and 43.7 MPa respectively. The16
axial stress-strain relationships are shown in Fig. 17. Since the cube testing machine has load17
control, the post-peak behaviour cannot be followed.18
29
1
2
Figure 17 Stress-strain relationship for the cubes3
4
The stresses in the figure were read from the testing machine, and the strains were obtained5
using both the DIC technique and elastic theory. Using the formula = 4733 ′ in the6
ACI 318-08 code, and taking the cylindrical strength (fc’) as 80% of the cube strength, their7
expected elastic moduli are 27.6 GPa, 28.3 GPa and 28 GPa respectively. For stresses less8
than 25 MPa (about half the strength), the three cubes responded linearly elastically, which is9
consistent with the conventional understanding of concrete compressive response. The10
“theoretical” data in Fig. 17 are obtained from linear-elastic stress-strain relationship using11
the Ec value above.12
Fig. 18 shows the DIC inspection region, and the axial compressive strain fields on the13
surface corresponding to the linear-elastic region with loads less than 25 MPa. The surface of14
Cube 1 was made sandy by attaching a thin layer of fine sand, while the surfaces for Cube 215
and 3 were as-cast. The range for the strain is ± 1500 , with contour interval of 200 .16
30
Since the cubes were under compression in the test, and the contacting surface between the1
specimen and the loading plate was large, the possibility for the specimen to tilt was much2
less than the direct tensile test for the aluminium plate. No tilting patterns were noted from3
the strain fields and no adjustment was applied. It can be observed that the surface strain is of4
similar magnitude for the three cubes. A slightly uneven distribution is found for each cube,5
which is assumed to be due to the heterogeneity of concrete.6
7
89
Figure 18 Compressive strains for the three cubes under low loads (Reference images taken10
at the compressive stress of 2 MPa)11
12
31
The principal tensile strains for the three cubes are shown in Fig. 19. The compression cone1
can be observed; crushing starts from cracks at the edges and corners and then develops into2
the centre. When the diagonal crack goes far enough into the centre, the amount of effective3
material taking the load reduces and the cube loses its capacity. All the strain field4
observations of cubes with the DIC technique agree well with the conventional wisdom about5
concrete cube tests, and therefore the technique is considered to be reliable for concrete6
fracture investigation.7
8
9
Figure 19 Principal tensile strains for the three cubes close to failure (Reference images taken10
at the compressive stress of 2 MPa)11
12
Strain fields for timber split test13
To provide a contrast with the concrete specimens, timber specimens were also tested.14
Timber splitting under the wedge-split test setup (Guan & Burgoyne 2014b) was used to15
examine the suitability of the DIC technique for FPZ inspection, and the strain fields are16
shown in Fig. 20; the strain fields around the crack tip are overlaid on the timber image.17
32
Timber is a well-known quasi-brittle fibre reinforced material with a large FPZ, and the1
consistent of the DIC result and the understanding prove that the DIC technique is capable of2
detecting a large FPZ if it exists.3
4
Figure 20 Strain fields for timber DCB specimen under split (gauge length: 1 mm)5
6
DIC results for CFRP plate debonding fracture7
Fig. 20 shows typical strain fields for the plate debonding of a concrete specimen plated with8
CFRP plates on both sides in a wedge-split test; the loading stages corresponding to different9
strain fields are marked by “dots” on the split load vs. wedge displacement curve. The test10
details can be found in Guan & Burgoyne (2014b). The strain fields shown are the principal11
tensile strains; a small gauge length of around 1 mm was used to ensure that the determination12
of the crack-influencing region would not be magnified by gauge length effect. The red13
region on the strain field represents strains over 0.01, while the clear regions arefeatures that14
cannot be traced back to the original image. They thus indicate regions severely influenced15
by cracks. Some of the inconsistent developing small strains are considered as noise, likely16
to be due to the small gauge length used, but they can also be due to increasing heterogeneity17
in the concrete as the stresses increase. However, this noise has little effect in identifying the18
region influenced by the crack.19
33
1
Figure 20 Principal tensile strain fields for specimen DCB12
3
It is clear that the cross-crack formed first, followed by the debonding crack. There exists no4
large FPZ and the crack influence is in a narrow band a few mm wide. The first strain figure5
corresponds to 63% of the peak load, and no strain concentration was recorded, which6
indicates the specimen was mainly elastic. The second and third strain field are for the stages7
33
2
Figure 20 Principal tensile strain fields for specimen DCB13
4
It is clear that the cross-crack formed first, followed by the debonding crack. There exists no8
large FPZ and the crack influence is in a narrow band a few mm wide. The first strain figure9
corresponds to 63% of the peak load, and no strain concentration was recorded, which10
indicates the specimen was mainly elastic. The second and third strain field are for the stages11
33
3
Figure 20 Principal tensile strain fields for specimen DCB14
5
It is clear that the cross-crack formed first, followed by the debonding crack. There exists no12
large FPZ and the crack influence is in a narrow band a few mm wide. The first strain figure13
corresponds to 63% of the peak load, and no strain concentration was recorded, which14
indicates the specimen was mainly elastic. The second and third strain field are for the stages15
34
just before (97%) and after (89%) the peak load. The strain grows rapidly from around1
4,000 με to over 10,000 με, and mainly in the cross-crack region, which indicates that a region2
with strain of 4,000 – 7,000 με can still take some load but a region with strain over 10,000 με3
is likely to be traction-free. The region on the left, just ahead of the pre-notch, is damaged4
(with a strain around 2,000 – 3,000 με) in the formation of the cross-crack, but does not open5
further in the later stages. This debonding strain field is extremely important for the6
understanding of debonding fracture and the determination of fracture energy for debonding7
analysis use (Guan & Burgoyne 2014b). The strain field around the crack tip is similar in8
different debonding crack propagating stages, so the debonding fracture resistance should9
remain effectively constant. It is the ability given by the DIC technique that allows this level10
of detail to be studied.11
12
Conclusion13
The debonding strain fields have shown the applicability of the image correlation technique14
that were specially developed for plate debonding fracture investigation. The technique is15
able to provide strain fields with a gauge length down to 1 mm with a precision around 40 με,16
and it has been demonstrated to be accurate for strain measurement and capable of capturing17
large fracture process zones for quasi-brittle materials. Since plate debonding is inherently18
the fracture in concrete around a narrow region close to the interface, 16-bit image with the19
image enlargement technique is used to deal with the difficulty of constrained inspection20
space. Local image registration is used to eliminate the effect of in-plane rotation, and an21
adjusting technique has been proposed to evaluate and correct the out-of-plane tilting effects.22
The resulting debonding strain fields indicate that the fracture process zone associated with23
35
plate debonding is small and does not vary as debonding propagates. Furthermore, this1
technique makes use of commonly available camera and lens.2
3
References4
1. Achintha, M. and Burgoyne, C.J. (2008). “Fracture mechanics of plate debonding”,5
Journal of Composite for construction, ASCE, 12(4), 396-404.6
2. ACI Committee 318 (2008). Building code requirements for structural concrete and7
commentary. American Concrete Institute, Farmington Hills, Mich, US.8
3. Bruck, H.A., McNeill, S.R., Sutton, M.A. and Petters, W.H. (1989). “Digital image9
correlation using Newton-Raphson method of partial differential correction”,10
Experimental Mechanics, 29(3), 261-267.11
4. Buyukozturk, O., Gunes, O. and Karaca, E. (2004). “Progress on understanding12
debonding problems in reinforced concrete and steel members strengthened with FRP13
composites”, Construction and Building Materials, 18(1):9–19.14
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40(4), 393-400.17
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electronic speckle pattern interferometry and finite element method”, ICCES, 15(3), 91-19
101.20
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Structural Journal, 111(1), 27 – 36.23
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using wedge-split peel-off test”, Submitted to Engineering Fracture Mechanics.25
Available at http://www-civ.eng.cam.ac.uk/cjb/papers/wedge.pdf26
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Using Image Correlation Techniques”, First International Conference on Performance-28
based and Life-cycle Structural Engineering (PLSE 2012).29
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36
11. Hung, P.C. and Voloshin, A.S. (2003). “In-plane strain measurement by digital image1
correlation”, Journal of the Brazil Society of Mechanics, Science and Engineering, 25,2
215-221.3
12. Mindess, S. (1991). “Fracture process zone detection”, In: Shah, S.P. and Carpinteri, A.4
editors, Fracture mechanics test methods for concrete, Chapman and Hall, London,5
231-262.6
13. Pan, B., Xie, H.M., Xu, B.Q. and Dai, F.L. (2006). “Performance of sub-pixel7
registration algorithms in digital image correlation”, Measurement Science and8
Technology, 17, 1615-1621.9
14. Schreier, H.W., Braasch, J.R., Sutton, M.A. (2000). “Systematic errors in digital image10
correlation caused by intensity interpolation”, Optical Engineering, 39(11), 2915-2921.11
15. Smith, S.T. and Teng, J.G. (2002). “FRP-strengthened RC beams. I: Review of12
debonding strength models”, Engineering Structures, 24(4), 385–395.13
16. Su, R.K.L., Chen, H.H.N. and Kwan, A.K.H. (2012). “Incremental displacement14
collocation method for the evaluation of tension softening curve of mortar”,15
Engineering Fracture Mechanics, 88, 49-62.16
17. Wattisse, B., Chrysochoos, A., Muracciole, J.M. and Nemoz-Gaillard, M. (2001).17
“Analysis of strain localization during tensile tests by digital image correlation”,18
Experimental Mechanics, 41, 29-39.19
18. White, D.J. (2002). “An investigation into the behaviour of pressed-in piles”. PhD20
dissertation, Dept. of Engineering, University of Cambridge, UK.21
22