determination of debonding fracture energy using … determination of debonding fracture energy...

$: Determination of debonding fracture energy using … Determination of debonding fracture energy using wedge-split 2 peel-off test 3 G.X. Guan*; C.J. Burgoyne; 4 *Email: garfieldkwan@gmail.com;$
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Determination of debonding fracture energy using wedge-split1

peel-off test2

G.X. Guan*; C.J. Burgoyne;3

*Email: [email protected]; Mobile: +852 914090594

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Abstract6

Debonding is a common premature failure of CFRP plated RC structures. In this paper a7

wedge-split peel-off test is used to investigate the detailed debonding fractures and to obtain8

the peel-off debonding fracture energy values that have rarely been reported before. Digital9

image correlation techniques are used for the fracture observation, and a simple fixed-end10

cantilever beam model is proposed for the fracture energy determination. The results from11

two types of plated specimens are presented together with the strain fields obtained using a12

special digital image correlation technique developed for plate debonding fracture13

investigation.14

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Keywords16

Peel-off fracture; debonding fracture energy; fixed-end cantilever beam model17

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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. Available at5http://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. (This paper). Available at8http://www-civ.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

Reinforced concrete structures are now being enhanced by gluing carbon fibre reinforced15

polymer (CFRP) plates on the tension face. This application suffers from premature16

debonding that has proved difficult to analyse [1,2]. Plate debonding is clearly a fracture17

event that is initiated from the inevitable flaws in the concrete cover layer between the FRP18

plate and the steel level. Various fracture analyses based on global energy balance have been19

proposed to predict debonding [3-5], and these analyses indicate that debonding fracture is20

inherently a peel-off fracture in concrete. If the “Mode I” concrete fracture energy value from21

conventional fracture tests is used as the fracture criterion, these fracture analyses give22

accurate debonding predictions. However, there have been debates about which of the23

debonding fracture modes is applicable and as a result, slip-off tests rather than peel-off tests24

have usually been conducted to investigate debonding. The much higher fracture energy25

values obtained from slip-off tests are recognised to be unsuitable for analyses of fracture26

debonding.27

3

In plate end (PE) debonding, the FRP plate end or the root of the hanging debonded layer is1

under zero stress, while the concrete in a beam just next to it undergoes bending. Thus there2

is a stress and strain discontinuity that is bridged by the adhesive layer which allows a gradual3

variation. Fig. 1 shows a magnified picture of this mismatch at the plate end.4

5

Figure 1 Plate end debonding failure6

So a debate has arisen between those who believe that the peel-off stress is crucial in7

debonding and cannot be neglected [1, 6-8] and others who have tried to develop more8

complicated models, such as the two parameter model, the 2D continuum model and various9

finite element models. These models have tried to study the stress concentration in the10

normal direction [9-15] and effectively model debonding as a mixed-mode fracture. However,11

there exist very few tests for mixed debonding fracture studies, and no well-recognised values12

of the corresponding fracture energy.13

The objective of the current paper is to present a controllable test to determine the fracture14

energy of CFRP peeling away from a concrete substrate. The method uses digital Image15

Correlation (DIC) techniques developed by the authors and described in detail elsewhere [16]16

to determine the amount of cracking, the debonding length and to investigate the extent of the17

4

Fracture Process Zone (FPZ). The methods described in this paper are then used extended to1

study give detailed insights into the debonding fracture of concrete [17].2

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Existing Peel-off Tests4

Only a small number of peel-off debonding tests have been reported; the most relevant are5

shown in Fig. 2.6

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8

Figure 2 Typical peel-off tests for FRP-concrete interface fracture energy: (a) taken9

from [18]; (b) taken from [19]; (c) taken from [20]; LVL in the figure stands for laminated10

veneer lumber.11

12

5

Fig. 2(a) is modified from the conventional centre-notched TPB test to simulate the peel-off1

for the determination of the Mode I fracture energy [18, 21]. The preparation and setup for2

the specimen is complicated and the computation of the fracture energy is not straightforward3

since it needs the exact fracture or crack tip locations to be identified. Furthermore, this test4

only allows for a relatively short debonding fracture propagation. Fig. 2(b) is a direct peel-off5

test used by several researchers with different modifications in the way in which the tensile6

load P is applied to the composite plate [19, 22-24]. The specimen preparation and setup in7

this test is straightforward, but the control of the tensile load can be complicated, and again8

the exact fracture or crack tip location is needed for the fracture energy calculation. Fig. 2(c)9

is based on the tapered double-cantilever beam specimen tests for conventional concrete10

fracture energy [20]. The top substrate is a piece of tapered timber, while the bottom11

substrate is concrete. The piece of timber is cut, via trial and error (as reported in [20]), into a12

shape that would give a constant compliance as the bi-beam system splits. There is no need to13

locate the exact crack tip for the energy calculation in this test setup, but it requires much14

preparatory work to determine the tapered shape of the upper substrate.15

Since concrete is considered to lose tensile strength at a very small crack opening, which is16

smaller than the resolution of the naked eye and impossible to inspect with crack microscopes17

during the test process, the extent of crack propagation and the area of the newly fractured18

surface are difficult to determine. The same problem makes it difficult to determine the19

elastic strain energy stored in the bent debonded composite plate.20

The problem of determining the extent of the crack can be overcome by the use of digital21

image correlation techniques that allow detailed observation of the crack propagation, and22

hence the determination of the proportion of the external work done by the loads that ends up23

as strain energy, and how much goes into fracturing the concrete. Such tests are described24

here.25

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1

Wedge-split Peel-off Test2

Concrete is usually found attached to the debonded plate, so debonding is inherently the3

failure of concrete substrate in the cover layer. A double-cantilever beam (DCB) specimen4

was thus designed to simulate the concrete cover layer in size and shape, as shown in Fig. 3.5

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Figure 3 Plated DCB specimen under wedge load (dimensions in mm)8

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CFRP plates were attached to both sides of the specimen and a pre-notch was made in the10

concrete to simulate the inevitable flaws. The cantilever arms were shaped to provide space11

for the installation of the loading clamp, and 4 mm steel bars were placed inside the arms to12

prevent arm failure. The specimen was loaded with a wedge as for the conventional wedge-13

split concrete fracture test. With this setup, the specimen was easy to prepare, and the peel-14

off load was exerted via compression, which is easier to control than tension. The wedge-15

split test setup is shown in Fig. 4.16

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1(a) (b) (c)2

Figure 4 Wedge-split test setup with DIC techniques.3

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A roller bearing system was used to transfer the wedge compression into splitting loads which5

were then transferred to the specimen via a steel clamp head. The far end was supported on6

rollers that allowed the specimen to slide horizontally during splitting. The region below the7

tip of the pre-notch was inspected using a digital image correlation (DIC) technique.8

Photographs taken under load are compared with those taken before loading to determine the9

displacement field, from which cracks and strains can then be found. The DIC technique used10

here was developed by the authors [16] with special features for interface crack investigation,11

using a common commercial digital camera system (Nikon D40 having 3872 2592 pixels,12

and Sigma 150 mm 2.8f macro lens).13

Concrete specimens with 10 mm and 20 mm maximum aggregate size were tested, and two14

types of adhesive were used: the material properties are given in Table 1.15

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Table 1 Material properties for the test1

Concrete (kg/m3) With 10

mm Max.

Aggregate

With 20

mm Max.

Aggregate

Adhesive Plate

Aggregate (10 mm) 840 208 1. Araldite

(soft, thin and

tough)

2. Sikadur 30

(cement-like,

thick and

hard)

Sika CarboDur

S1012 (CFRP plate,

1.2 mm thick, Ef =

165 GPa)

Aggregate (20 mm) – 764

Fine sand 746 617

Cement 485 425

Water 228 185

Cube Strength (MPa) 50.9 52.1

Cylinder Strength (MPa) 38.7 37.7

Cylinder Split Strength

(MPa)

3.63 3.52

2

The specimens with Sikadur adhesive and Araldite were used to compare the influence of the3

adhesive. Since the concrete fracture process is commonly recognised to be influenced by the4

aggregate size, specimens with maximum aggregate size of 10 and 20 mm were tested.5

Although 20 mm aggregates are large compared with the specimen thickness (= 50 mm), in6

reality 20 mm aggregates are more commonly used for beams and will be present in the beam7

cover layer.8

9

Typical Test Results10

Six CFRP-plated DCB specimens were tested, with the results listed in Table 2. The details11

of the loads and fracture energy will be explained later.12

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Table 2 Test results14

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Specimen Adhesive Aggregate Size Peak Load Debonding

Load

Average

Gf

DCB-CS-10-1 Sikadur 10 355.5 72.3 0.141

DCB-CS-10-2 Sikadur 10 463.9 79.6 0.115

DCB-CS-20-1 Sikadur 20 260.6 60.0 0.113

DCB-CS-20-2 Sikadur 20 182.9 62.9 0.130

DCB-CA-10-1 Araldite 10 383.9 45.5 0.128

DCB-CA-10-2 Araldite 10 406.8 45.8 0.134

(i) The peak load is the peak exhibited during the whole test(ii) The debonding load is the average loading value at the plateau during debonding.

1

A typical failure of the DCB specimens is shown in Fig. 5: During the test a cross-crack in2

the transverse direction occurs first, starting from the pre-crack tip; after the cross-crack3

reaches the edge, a debonding crack propagates in the longitudinal direction along the4

concrete-plate interface. A thin layer of concrete (0.5 – 2 mm thick) is commonly found5

attached to the debonded plate, indicating that failure is in the concrete. This is similar to the6

behaviour in a real RC beam, where debonding initiates from shear-flexural cracks7

(equivalent to the cross-cracks here); a layer of concrete normally remains attached to the8

debonded plate.9

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Figure 5 (a) Typical failure of DCB specimens; (b) Concrete attached on debonded plates2

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Notably, the debonding crack did not propagate within the adhesive layer, nor did a thick4

layer of concrete remain attached to the CFRP. On a close inspection it was observed that5

some adhesive had penetrated up to 1 mm into the concrete. Thus the debonding crack6

effectively propagates along the interface, predominantly in the concrete, the properties of7

which may have been affected by the adhesive. The tests described here show that plate8

debonding does not occur in the intact bulk concrete away from the interface, which differs9

from debonding in real retrofitted beam, where a thick layer of attached concrete is sometimes10

found. This is probably because the concrete in the cover layer often contains flaws, either11

from frost, shrinkage or loading, which are not present in laboratory specimens.12

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Detailed Debonding Fracture Investigation14

Fig. 6 shows the vertical wedge load against displacement (W-D) curve for Specimen DCB-15

CS-20-1. The left hand photograph was taken at the end of the test, while the photo to the16

right shows the region ahead of the pre-notch tip, before the tests, that was inspected using17

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DIC techniques. The inspection region is across the whole width of the specimen and the grid1

nodes for DIC tracing are at intervals of 1 mm, shown by the dots on the photo; this gauge2

length of 1 mm was used strain determination for all specimens, unless otherwise specified.3

The loading stages at which the strain fields are constructed are marked by the points on the4

W-D curve.5

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Figure 6 W-D curve for Specimen DCB-CS-20-18

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The vertical wedge load Pv can be converted to the horizontal split force Ph by simple10

equilibrium (adapted from [25]):11

= ( )( ) (1)12

11





W-D curve.10

7

8


10



= ( )( ) (1)13

11





W-D curve.15

8

9


11



= ( )( ) (1)14

12

where is the wedge angle (here 15o) and is the overall friction coefficient of the wedge-1

roller system.2

3

The friction coefficient depends on both the friction from the roller and the contacting4

surface between the wedge and the roller, so it may vary from test to test depending on the5

exact alignment of a specimen. The friction from the roller was found to be small, about6

0.05%. Even if the overall friction coefficient is assumed to be 10 times higher (0.5%) the7

influence of friction on Ph is only 1.9%, so the friction effect is neglected, giving:8

= = 1.87 (2)9

For the test shown in Fig. 6 the peak split load for the specimen is thus around 500 N, which10

is similar to the values for all the DCB specimens. The area under the W-D curve gives the11

external work done by the wedge, which is shared between the energy released during the12

specimen fracture and the strain energy stored in the elastic portion of the specimen.13

Before peak load the specimen responds almost linearly, except for a small initial increase of14

stiffness as the system aligns. Just after the peak load, the strength reduces suddenly, which15

corresponds to the development of the cross-crack. In the post-peak stage, corresponding to16

the debonding crack propagation, the specimen strength is virtually constant. The test was17

stopped when the wedge reached its travel limit, and slow unloading (around 1 – 3 mm per18

minute in Dw-v) was then carried out. For this specimen, after a little strength reduction, the19

strength remained constant in the initial unloading, and then dropped quickly to zero. The20

constant-strength unloading stage is probably due to aggregate interlock.21

Fig. 7 shows the field of principal tensile strain corresponding to the loading stages in Fig. 6;22

the strain field is drawn on the undeformed specimen. A gauge length of 1 mm was used for23

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this strain field construction. The red region on the strain field represents all strains over 0.01,1

and the blank region indicates the presence of a crack. The colours on the plot are banded at2

intervals of 0.001. Some of the inconsistent small strains are considered to be noise, and are3

likely to be due to the small gauge length used and small test disturbances such as change of4

lighting levels, but may also be due to heterogeneity in the concrete since the magnitude5

increases as the load increases. The noise has little effect on identifying the crack-influenced6

region.7

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Figure 7 Principal tensile strain for Specimen DCB-CS-20-12

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4

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3


5

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Since most of the previous studies of concrete tensile constitutive relationships use a much1

larger gauge length, commonly several tens of times larger, the peak strain values obtained2

here are larger than those reported elsewhere. If converted back to elongation, the results3

obtained here are of the same order of magnitude as the previous findings, such as Raiss et al.4

[26] where the Moire interferometry was used to determine the strains in a direct tensile test5

with a gauge length of 20 mm, giving crack strains ranging from 100 – 1000 . The small6

strain patterns on the peeled-away corner (top right in Fig 7) are less reliable, especially in the7

later loading stages, since this block was subjected to large rotation and disturbance, and may8

also be influenced by the shadows from the wedge during imaging.9

Strain Field (a) was measured while the load was still increasing at 63% of the peak load, and10

no strain concentration was recorded, which indicates the specimen was mainly elastic under11

small strain. Strain fields (b) and (c) correspond to the stages just before (97% Pv) and after12

(89% Pv) the peak load. After stage (c), the strength of the specimen drops suddenly, and the13

strain grows rapidly from around 0.004 – 0.007 to over 0.01, mainly in the cross-crack region,14

which indicates that a region with strain of 0.004 – 0.007 can still take some load but a region15

with strains over 0.01 is likely to be traction-free. The region to the left, and just ahead of the16

pre-notch, is damaged (with a strain around 0.002 – 0.003) during the formation of the cross-17

crack, but does not open further in the later stages. Clearly, both cantilevers were undergoing18

bending but the weakest of them failed first. This kind of cross-crack development is usually19

seen for the specimens using 20 mm maximum aggregate. A strain of about 0.00320

(corresponding to 3 m crack opening) can be considered as the threshold for permanent21

damage in concrete but this damaged zone should still be able to take some stress. The22

debonding crack propagates from Strain Field (d) onwards, both upwards and downwards,23

while the wedge load Pv remains virtually constant. Most of the debonding cracking region24

has a strain over 0.01, and the strain at the crack tip falls rapidly from a high value to virtually25

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zero in a small transition length of a few mm. The location of the crack tip visible to the eye1

was usually over 30 mm behind the high strain tip revealed by the DIC, so is an unreliable2

measure of the crack length.3

Figure 8 plots the same results as Fig. 7 showing the principal tensile strain in the third4

dimension to give a better visualisation of the strain concentration around cracks; strains over5

0.01 are set to 0.01 and the colour scale is the same as that in Fig. 7. These plots allow the6

strain concentration around the tip of the crack to be visualised, but it is necessary to7

eliminate the variations caused by noise or general heterogeneity in the plots. The8

background level is found by considering a “region remote from cracks” in Fig. 7(j) which9

gives an average noise strain v = 0.00083, with a standard deviation s = 0.00013. The10

contours of = v + 1.64s, and 2 are shown in the 3D plots; the area enclosed by 211

provides a good indication of the cracking region, and the influence of the noise in this region12

is negligible. It is also clear that the strain drops very suddenly at the tip of the crack with a13

rapid transition from high strain in a very a short distance. There is little evidence of an14

extensive fracture process zone extending beyond the end of the crack.15

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Figure 8 3D view of the principal tensile strain3

4

Fixed-end Cantilever-beam Model5

In a wedge-split test, the work (Wext) done by the wedge is shared between the recoverable6

strain energy (Estrain) stored in the elastic deformation of the beam and the unrecoverable7

energy released during fracture propagation. Since the objective of the present study is to8

18

determine the fracture energy using a measurement of the work done by the load, it is1

necessary to determine the stored strain energy, which is mainly stored in the CFRP plate that2

remains elastic during the test, while being bent as a beam. If the tractions and the3

displacement along the bent CFRP plate can be obtained, the stored strain energy can be4

determined.5

It would be ideal if the stress-strain relationship in the cracked region could be measured, so6

that the strain energy and thus the fracture energy could be determined. Although the strains7

in the concrete next to a debonding crack can be measured, there is no way to measure8

directly the stress. Rather than measuring directly, various methods have been proposed to9

calculate the stress based on the direct strain measured. The majority of these are based on10

beam-foundation models where a stress-strain relationship of the debonding interface is11

assumed which allows the stress to be calculated from the strain. In turn this allows the stored12

strain energy to be calculated and finally the fracture energy to be determined. A number of13

beam-foundation models with different complexity have been proposed, where various14

interface constitutive laws and finite element models were used to describe the behaviour of15

the interface [8, 10, 14, 27-28]. They usually have a large number of parameters that can be16

tuned to match their validation target, which is the global structural response (e.g. load vs.17

deflection). To the knowledge of the authors, none of these models has had their individual18

parameters validated against crack information at a local scale. Instead, a simple fixed-end19

cantilever beam model is used that assumes that no recoverable strain energy is stored in the20

cracked concrete (or interface); only the elastic CFRP plate can store strain energy. The21

difference between the external work done and the strain energy stored in the fixed-end22

cantilever beam should be the energy dissipated by the debonding fracture.23

It was shown earlier that a region in the concrete that has once experienced a strain over 0.00424

would show permanent strain even after stress release. The region with strain over 0.01 can25

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be carrying very little stress, so the region with continuous development of such a strain is1

taken as the debonded region. It is impossible to know whether the region is completely2

traction-free, but the energy released in developing the debonded region cannot be recovered.3

This debonded region, even if it is not traction-free, is considered unable to resist load as a4

part of a competent beam. The debonded length is needed for two purposes: (i) to calculate5

the elastic strain energy stored in the CFRP plate, and (ii) to determine the extent of the6

fracture.7

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Figure 9 Fixed-end cantilever beam model for debonding process10

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Figure 9 shows the idealised fixed-end cantilever beam model for the CFRP with a typical12

debonding strain field of Specimen DCB-CS-20-1. Fig. 9 (a) shows the region of interest.13

The moving part of the specimen above the cross-crack displaces and rotates, allowing the14

loading point D to move. The CFRP is rigidly attached to this displacing part above B, and15

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also to the specimen below A. The CFRP between A and B acts as an elastic cantilever, with a1

rigid extension from B to D.2

The length of the cantilever |AB| can be determined in two ways. The load applied at D and3

the displacement of D are both known, as is the stiffness of the CFRP. It is then relatively4

simple to determine the length of the cantilever Ld that shows the same response from simple5

beam theory. However, in order to determine Ld, it is necessary to determine the location of B6

and hence the length of the rigid extension Le.7

The CFRP is regarded as debonded from the concrete if the principal tensile strain in the8

concrete near the interface is over 0.01. The location of B can be found by plotting the strain9

against position, as in Fig. 9 (b). The two points where the principal tensile strain is over 0.0110

can then be identified, as in Fig. 9(c). The top one is taken as the point B; the lower one is11

called E. Once B is identified, Ld can be determined as one estimate of the debonding length12

using simple beam theory, while the distance |BE| provides a second estimate (Ld-sf). The13

method adopted is thus to find B and E from the DIC strain field, which gives Le and Ld-sf14

directly. The length of the calculated Ld is found from the stiffness of the cantilever. In a15

perfect world, Ld should equal Ld-sf and the difference between them (i.e. the distance |AE|)16

can be taken as the discrepancy between the fixed-end cantilever model and reality.17

The horizontal displacement of the loading point D can be calculated from the recorded18

vertical wedge displacement (Dw-v):19

20

= (3)21

where is the wedge angle (15o).22

23

21

can also be calculated from the end deflection of the cantilever beam with a length of Ld1

and a rigid extension Le, using simple beam theory.2

3

= 0.5 + (4)4

5

The deflection of the fixed-end cantilever beam is equal to twice the horizontal split on6

one side, so there is a coefficient of 0.5. Combining Eqs. 3 and 4, Ld can be determined.7

Since the cantilever is elastic, the strain energy stored in the cantilever at a given load is8

9

= + (5)10

11

The debonding fracture energy corresponding to a certain debonding crack length increment12

is then given by13

14

= ∆∆ (6)15

16

Here Wext is the external work done by the wedge; ∆ is the change of the strain energy17

between the stages before and after the input of Wext ; b is the specimen width (here 100 mm)18

22

and Ld-sf is the difference in debond length (i.e. strain > 0.01) measured from the DIC strain1

fields before and after the input of Wext.2

3

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Figure 10 The comparison of Ld and Ld-sf for DCB specimens5

6

Fig. 10 shows comparisons of Ld obtained from the fixed-end cantilever beam model, and Ld-sf7

from strain field measurement for the DCB specimens. The difference between Ld and Ld-sf is8

usually less than 10 mm and often much smaller, which demonstrates that the fixed-end9

cantilever beam model is sufficiently accurate to describe the specimen response. The Ld and10

Ld-sf curves are close to a straight line and have a similar trend, which indicates a static11

propagation of debonding cracks proportional to the wedge downward displacement. Thus it12

is reasonable to use the wedge displacement (Dw-v) to study the variation of Gf for different13

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crack lengths. In most cases Ld is slightly greater than Ld-sf when the wedge displacement is1

small, while Ld is slightly less than Ld-sf when the wedge displacement gets large. The main2

error comes from the misfit in the specimen-to-wedge setup, which leads to errors in Dw-v and3

Dw-h values at the initial stage. Furthermore, the interactions of the materials on both sides of4

the debonding crack are also more complicated at the initial stage, which would lead to5

relatively larger errors when applying the fixed-end cantilever beam model.6

7

Determination of Debonding Fracture Energy8

9

Figure 12 Debonding fracture energy obtained for DCB specimens10

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The debonding fracture energy for the DCB specimens is obtained using Eqs. 3 – 6, as shown12

in Fig.12. The fracture energy Gf associated with debonding is found to be in the range from13

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12



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13



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0.03 – 0.28 N/mm, which is in consistent with the conventional Mode 1 fracture energy of1

concrete. The average (Gf-avg) is found to be 0.142 N/mm and the standard deviation (s) is2

0.077 N/mm, which indicates large variations and which is assumed to be due to concrete3

heterogeneity. The Gf values for specimens with 10 mm and 20 mm aggregates are similar,4

probably because the relatively large variation of Gf is at least as big as the effects of the5

aggregate size. There is no evidence of consistent variation with the crack extent, so there is6

no R-curve phenomenon. Thus, it is reasonable to assume that the average fracture energy is7

constant during debonding crack propagation, although a relatively large variation may occur8

at a small scale.9

Unlike conventional concrete fracture, debonding cracks do not go around the aggregates but10

through the weakest locations at the interface on the concrete side. Since the concrete where11

this interface was formed was against the mould during the original casting, when using larger12

aggregate there will be a large surface zone that is likely to have worse grading and be looser.13

This provides more opportunities for interface flaws to weaken the fracture resistance, while14

the additional interlocking provided by larger aggregates inside the bulk concrete is irrelevant15

to debonding resistance.16

17

Conclusions18

The results from the double-cantilever beam specimens have shown that the peel-off19

debonding fracture energy is in the range of 0.05 – 0.33 N/mm, which is in the same range as20

the conventional “Mode I” concrete fracture energy, but much lower than the fracture energy21

obtained from bond-slip tests. A relatively large random variation has been noted in the22

fracture energy during propagation of debonding but no clear trend has been observed that23

relates fracture energy to crack length. Concrete heterogeneity almost certainly plays an24

25

important role in the debonding fracture variation, but the size of the aggregate particles had1

almost no effect on the fracture energy. In the absence of any detailed fracture energy test in2

a particular case, it is recommended that a fracture energy value of 0.14 – 0.15 N/mm is used3

in analyses to determine whether premature debonding is likely to occur.4

5

References6

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determination of debonding fracture energy using … determination of debonding fracture energy...

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