Digital Image Correlation Technique for Detailed … · 1 Digital Image Correlation Technique for ... 17 prematurely by fracture in the concrete, and as part of a fracture mechanics

$Page 1: Digital Image Correlation Technique for Detailed … · 1 Digital Image Correlation Technique for ... 17 prematurely by fracture in the concrete, and as part of a fracture mechanics$
1

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

19

Keywords20

Digital Image correlation (DIC); Debonding fracture; Strain field; Fracture process zone21

22

2

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

13

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

3

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

4

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

11

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

5

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

8

9

Figure 1 Two images taken for the same object10

11

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

6

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

4

( , ) = ∑ ( ( , ) ̅ )∙( ( , ) ̅ )( , )∑ ( ( , ) ̅ )( , ) . ∙ ∑ ( ( , ) ̅ )( , ) . (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

8

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

7

1

Figure 2 The variation of correlation coefficient with locations (r,s).2

3

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

8

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

10

11

Figure 3 C(r,s) after the 2D cubic spline interpolation12

13

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

9

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

6

7

(a) (b)8

Figure 4 Influence of template size on correlation peak (16-bit): (a) 50 pixel templates; (b) 209

pixel templates.10

11

10

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

11

Figure 5 Crack investigation with different template sizes12

13

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

11

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

13

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

12

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

18

19

13

1

Figure 6 Pixel value of the same object in 8-bit and 16-bit images2

3

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

18

13

2


4















19

13

3


5















20

14

1

Figure 7 Appearance of different surfaces (16-bit)2

3

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

12

15

1

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

16

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

5

6

Figure 9 Determination of strain7

8

The displacements of point (i,j) can be obtained by searching a template centred at that9

location, and are given by10

11

, = ( ) , − ( ) , , = ( ) , − ( ) , (2)12

13

When the displacements of the four adjacent grid nodes are determined, the strain at their14

centre position (C1 in Fig. 9) is given by15

16

17

= , ,∆ − , ,∆ (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

8

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

18

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

15

19

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

20

20

1

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


4





33

3


5





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

5. Cary, P.D. and Lu, H. (2000). “Deformation measurement by digital image correlation:15

implementation of a second-order displacement gradient”, Experimental Mechanics,16

40(4), 393-400.17

6. Chen, H.H. and Su, R.K.L. (2010). “Study on fracture behaviours of concrete using18

electronic speckle pattern interferometry and finite element method”, ICCES, 15(3), 91-19

101.20

7. Guan, G.X. and Burgoyne, C.J. (2014a). “Comparison of FRP plate debonding analysis21

using global energy balance approach with different moment-curvature models”, ACI22

Structural Journal, 111(1), 27 – 36.23

8. Guan, G.X. and Burgoyne, C.J. (2014b). “Determination of debonding fracture energy24

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

9. Guan, G.X. and Burgoyne, C.J. (2012). “Fracture Investigation in FRP Plate Debonding27

Using Image Correlation Techniques”, First International Conference on Performance-28

based and Life-cycle Structural Engineering (PLSE 2012).29

10. Gunes, O., Buyukozturk, O. and Karaca, E. (2009). “A fracture-based model for FRP30

debonding in strengthened beams”, Engineering Fracture Mechanics, 76, 1897-1909.31

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

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Digital Image Correlation Technique for Detailed … · 1 Digital Image Correlation Technique for ... 17 prematurely by fracture in the concrete, and as part of a fracture mechanics