Effective bond length of FRP-to-concrete adhesively-bonded joints: Experimental evaluation of existing models

International Journal of Adhesion & Adhesives 48 (2014) 150–158

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Effective bond length of FRP-to-concrete adhesively-bonded joints: Experimental evaluation of existing models Ardalan Hosseini n, Davood Mostofinejad Department of Civil Engineering, Isfahan University of Technology (IUT), Isfahan 84156-83111, Iran

art ic l e i nf o

a b s t r a c t

Article history: Accepted 3 September 2013 Available online 25 September 2013

Bond behavior of adhesively-bonded fiber reinforced polymers (FRPs) to concrete substrate has been investigated by many researchers worldwide. An interesting aspect of FRP-to-concrete bond behavior is that there exists an effective bond length beyond which an extension of the bond length cannot increase the ultimate capacity of the joint. Effective bond length of FRP composites, in fact, is an important part of all strengthening calculations, and conservative design guideline predictions can lead to waste of composite materials in strengthening projects. Consequently, the main intention of the current study is to evaluate the accuracy of existing guideline models of effective bond length by means of single-shear bond tests. To do so, carbon FRP (CFRP) sheets with a wide range of bond length from 20 to 250 mm, were adhered to 22 concrete prisms using externally bonded reinforcement (EBR) technique. The specimens were then subjected to single-shear test and debonding loads as well as the effective bond length of the CFRP sheets were determined. Moreover, an image based technique, i.e. particle image velocimetry (PIV) was used to verify the estimated effective bond length by analyzing strain distribution along the CFRP strips during loading process. Experimental results of the current study show that fib Bulletin 14 model overestimates debonding loads and effective bond length. The model adopted by ACI 440.2R-08 also overestimates effective bond length while accurately predicts debonding loads. Appropriate calibration factors were introduced to modify the existing models for CFRP sheets. & 2013 Elsevier Ltd. All rights reserved.

Keywords: Fiber reinforced polymer (FRP) Externally bonded reinforcement (EBR) Bond strength model Effective bond length Single-shear test Particle image velocimetry (PIV)

1. Introduction Certain advantages of FRP composites including high tensile strength, light weight and ease of application, have led engineers all over the world to utilize FRPs as an easy-to-use alternative to conventional materials for strengthening of reinforced concrete (RC) structures [1]. Almost all shear/flexural strengthening techniques with FRP are relying on bonding of the composite onto the concrete substrate. EBR is the most common technique for strengthening of existing RC members; however, despite ease of use, the efficiency of EBR technique could be seriously affected by various types of debonding of FRP composite from concrete substrate [2]. In this case, FRP-to-concrete bond strength is a key factor that controls debonding failures in FRP-strengthened members. As a result, substantial experimental and theoretical investigations have been conducted on FRP-toconcrete bond strength and numerous models have been proposed to predict FRP-to-concrete bond capacity [3,4]. Initial models were mostly proposed based on the average bond shear stress at failure, τu, (Tanaka [5], Sato et al. [6], and Hiroyuki and Wu [7]). Soon it emerged that there exists an effective bond length, Le, beyond which an extension of the bond length cannot

n

Corresponding author. Tel.: þ 98 311 391 3818; fax: þ98 311 391 2700. E-mail addresses: [email protected], [email protected] (A. Hosseini).

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increase debonding load. In other words, unlike reinforcing steel bars, it is not possible to increase the bond length of the adhesively bonded plate in order to ensure that the maximum capacity is attained by rupture of FRP plates/sheets or yield of steel plates [8]. Consequently, modified bond strength models were proposed based on effective bond length concept (Maeda et al. [9], Neubar and Rostásy [10], Khalifa et al. [11], and Sato et al. [12]). Bond strength models can be classified into three distinct categories as follows [3,4]: 1. Empirical relations directly based on the regression of test data such as the models proposed by Tanaka [5], Hiroyuki and Wu [7], and Maeda et al. [9]. 2. Fracture mechanics based models, including Holzenkämpfer [13], Täljsten [14], Niedermeier [15], Neubauer and Rostásy [10], Blaschko et al. [16], Yuan and Wu [17], Yuan et al. [18], Wu et al. [19], Yuan et al. [20], Toutanji et al. [21]. 3. Design models generally proposed by adopting simple assumptions such as Van Gemert [22], Khalifa et al. [11], Sato et al. [12], Chen and Teng [3], Dai et al. [23] and, Seracino et al. [24]. Despite primitive models, almost all recently developed models have been proposed based on effective bond length. Many experimental studies have shown that only a limited zone of the bonded joint, called active bond zone, plays the key role in load bearing

A. Hosseini, D. Mostofinejad / International Journal of Adhesion & Adhesives 48 (2014) 150–158

[9,25,26]. Furthermore, some fracture mechanics analyses confirmed that extension of bond length beyond effective bond length has no effect on debonding capacity [13,17–20]. Due to importance of the issue, considerable research has been conducted to investigate steel/FRP-to-concrete bond behavior up to now. However, almost all the aforementioned investigations generally focused on evaluating the accuracy of existing debonding models, or in some cases, calibrating existing models or rarely developing new expressions. Hence, less attention has been paid to effective bond length of FRP composites used through EBR method. Consequently, the main intention of the current study is to experimentally evaluate the accuracy of the effective bond length models presented in well-known existing guidelines, i.e. fib Bulletin 14 [27], ACI 440.2R [1], and HB 305 [8] by means of single-shear bond tests on externally bonded (EB) CFRP systems.

2. Theoretical debonding and effective bond length models As it was mentioned earlier, substantial experimental and theoretical research works exist on FRP-to-concrete bond strength and numerous models have been proposed in the literature. However, only a few of them have been accepted by design guidelines such as fib Bulletin 14 [27], ACI 440.2R [1], and HB 305 [8]. Consequently, well-known expressions of the fib Bulletin 14 [27], Chen and Teng's [3] model presented in both ACI 440.2R [1] and HB 305 [8], and also Seracino et al. [24] model presented in HB 305 [8] are briefly discussed here and experimental results of the current study are compared with these models.

Debonding load of FRP composites, P, and effective bond length, Le, in fib Bulletin 14 [27] are evaluated based on the following expressions. qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi P ¼ αc1 kc kb bf Ef t f f ctm ð1aÞ

sffiffiffiffiffiffiffiffiffiffiffiffiffi Ef t f Le ¼ c2 f ctm 

P ðLf o Le Þ ¼

(

βL ¼

sin π2 1:0

Lf o Le Lf Z Le

sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2 bf =bc βw ¼ 1 þbf =bc

Le ¼

ð2dÞ

2.3. Seracino et al. [24] Debonding load and effective length of FRP composites based on Seracino et al. [24] model can be calculated from the following expressions.

Le ¼

π

2

qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ðτf Lper =δf Ef Af Þ



τf ¼ 0:802 þ 0:078 δf ¼

where P, Lf and Le are debonding load, FRP bond length, and effective bond length, respectively. Moreover, bf, tf, and Ef are width, thickness and elasticity modulus of the FRP reinforcement, respectively; bc is width of the concrete element; fctm is mean tensile strength of concrete, and α is a reduction factor, approximately equal to 0.9, to account for the influence of inclined cracks on the bond strength [10]; kc is a factor accounting for the state of compaction of concrete (generally can be assumed to be equal to 1.0); and kb is a geometry factor presented by Eq. (1b). Note that c1 and c2 in Eqs. (1a) and (1c) may be obtained through calibration with test results; however, for CFRP strips they are equal to 0.64 and 2.0, respectively [27]. Moreover, for bond lengths Lf o Le, the ultimate debonding load can be calculated by Eq. (1d) [13,27]. 2.2. Chen and Teng [3] Debonding load and effective bond length of FRP composites based on Chen and Teng's [3] model can be calculated from the

 df ðf c Þ0:6 bf

 0:5 0:73 df ðf c Þ0:67 τf bf

P ðLf o Le Þ ¼ ð1dÞ

ð2bÞ

where fc is mean cylindrical compressive strength of concrete; α ¼0.427 to obtain a mean prediction; and βw is a geometry factor presented by Eq. (2c). It should be noted that, in the case of Lf o Le, Chen and Teng's [3] expression is capable of predicting the ultimate debonding load by considering reduction factor, βL, calculated by Eq. (2b).

ð1bÞ



ð2aÞ

ð2cÞ

sffiffiffiffiffiffiffiffiffi Ef t f pffiffiffiffi fc

ð1cÞ

Lf Lf P 2 Le Le

Lf Le

 0:25 qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi df P ¼ 0:85 ðf c Þ0:33 Lper Ef Af bf

2.1. fib Bulletin 14 [27]

sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2  ðbf =bc Þ Z 1:0 kb ¼ 1:06 1 þ ðbf =400Þ

following expressions. qffiffiffiffi P ¼ αβ w βL bf Le f c

151

Lf P Le

ð3aÞ

ð3bÞ

ð3cÞ

ð3dÞ

ð3eÞ

where Af is transversal area of FRP reinforcement; df is thickness of the failure plane perpendicular to the concrete surface (suggested value for EB systems¼ 1 mm) and Lper is length of the debonding failure plane which can be assumed as 2df þ bf for EB systems. Moreover, τf and δf are peak interface shear stress and slip beyond which bond stress is zero, respectively. Although τf and δf may be experimentally evaluated, however, they can be calculated by Eqs. (3c) and (3d) [24]. It should be noted that for bond lengths Lf o Le, debonding load may be determined using a linear variation from zero to P, at Lf ¼Le (Eq. (3e)) [24]. To the best knowledge of the authors, to date no research can be found in the literature experimentally evaluate the accuracy of the existing models in predicting the effective bond length of externally bonded FRP composites. Hence, in the current study 22 concrete prism specimens having CFRP bond length from 20 to 250 mm were subjected to single-shear test. Consequently, the effective bond length of CFRP sheets was experimentally evaluated by comparing debonding loads of tested specimens, and the accuracy of effective bond length models in existing guidelines was evaluated based on the experimental results.

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Table 1 Properties of FRP materials. Type

Fibers

SikaWrap 230 C Adhesive Sikadur 330

Thickness (mm)

0.131 0.5–0.9

P Tensile strength (MPa)

Elastic modulus (GPa)

Elongation at break (%)

4300

238

1.8

30

4.5

P CFRP

Support Support Unbonded zone (35 mm)

0.9

Lf 350 mm

3. Experimental procedure

bf =48 mm

Concrete prism

3.1. Specimens detail and material characteristics Support

In order to carry out the experimental program on single-shear tests, 22 concrete prisms with dimensions of 150  150  350 mm were cast using steel molds. To obtain a compressive strength of about 30 MPa, 425 kg/m3 of normal Portland cement, 892 kg/m3 sand, 736 kg/m3 coarse aggregate and, 221 kg/m3 water were used. The molds were removed after 24 h and all the specimens were cured in water for 28 days at standard conditions [28]. CFRP composite sheets were made up of SikaWrap 230C carbon fibers and two-component epoxy adhesive, Sikadur 330, and were fabricated through wet lay-up process. Mechanical properties of carbon fibers and epoxy resin utilized in the current study are presented in Table 1 according to the manufacturer's catalog.

bc=150 mm

hc=150 mm

Fig. 1. Specimen dimensions and loading arrangement.

3.2. Test layout and specimens preparation The notation of all tested specimens is EBR-x-n, where EBR is the strengthening technique; x identifies CFRP bond length in mm (Lf), and n distinguishes the ordinal number of each test (1 or 2). Since it was observed that in some studies concerning on FRP-toconcrete bond behavior only one specimen per case was used in experimental phase [24], in the current study two specimens were assumed to be sufficient in each case. Carbon fibers were adhered to the prism specimens using conventional EBR technique. To do so, first the weak layer of the concrete surface was removed using a grinding machine. Then the concrete surface was properly cleaned with air jet to remove dust. Finally, carbon fiber sheets were cut into selected sizes and were adhered to concrete surface using epoxy resin through wet lay-up procedure. Lf was considered to vary in a wide range from 20 to 250 mm, while all other experimental parameters such as CFRP width and thickness remained constant and equal to bf ¼48 mm and tf ¼0.131 mm. 3.3. Test setup According to the manufacturer's suggestion, i.e. Sika group catalog, all prepared specimens were cured in laboratory condition for 7 days before testing in order to ensure strength development in epoxy resin. After 7 days of curing, all the specimens were subjected to single-shear test by means of a 300 kN tension machine specially designed for single-shear bond tests in structural laboratory of Isfahan University of Technology (IUT). All tests were performed under displacement control with a speed of 2.0 mm/min according to ASTM D3039 recommendation [29]. Specimen dimensions and loading arrangement are presented in Fig. 1. Since the compression reaction of the support may cause stress concentration at the loaded end of the concrete specimens [30], the first 35 mm of the CFRP composite was left unbonded to eliminate any probable stress concentration (Fig. 1). Note that similar setups for eliminating stress concentration at the loaded edge of CFRP composites, in single-shear bond tests, have been utilized by other researchers [31,32].

Fig. 2. Test setup (camera and projectors positions and testing machine).

In order to provide full field deformation measurements, an image-based technique was used. One CCD (charge couple device) digital camera, i.e. Nikon D80 with resolution of 10.0 megapixels (3872  2592 pixels) having a Nikkor 18–135 mm lens was placed perpendicular to the specimens' face at a distance equal to 1.0 m. Digital images were automatically taken from each specimen undergoing deformation using a remote control at regular intervals. A digital data logger was used to monitor the load cell and image numbers simultaneously. Moreover, the specimens were illuminated using two white light projectors to eliminate any probable parasitic lights. Test setup including specimen, camera and projectors positions and testing machine is presented in Fig. 2.

4. Image analysis using particle image velocimetry (PIV) Particle image velocimetry (PIV) was used to obtain accurate deformation measurements during test process by analyzing successive digital images. PIV is originally a velocity-measuring technique which was first developed by Adrian [33] in the field of experimental fluid mechanics. As detailed review on PIV method is beyond the scope of the current paper, the readers are referred to White et al. [34] and Slominski et al. [35] for further details of the technique. Moreover, the ability of the technique to accurately

A. Hosseini, D. Mostofinejad / International Journal of Adhesion & Adhesives 48 (2014) 150–158

investigate the bond behavior of CFRP sheets attached to concrete substrate has been previously discussed by the authors [36]. In the current study, successive digital images were taken from each tested specimen during the test process. It is necessary for the images to have a proper texture to create features upon which image processing can operate. Since CFRP sheets originally does not show suitable texture, natural colored sand between sieve Nos. 50 and 100, obtained from mixing equal proportions of five different colors was embedded to all specimens' face at the end of adhering CFRP sheets to the concrete surface and before epoxy hardening. Obviously, embedded sand has no effect on CFRP-toconcrete bond behavior. Images were then analyzed using GeoPIV8 software developed by White and Take at Cambridge University [37]. All PIV analyses due to displacement measurements were undertaken using 128  128 pixel patches. A search area of 5  5 pixels for each pair of successive images was considered in all PIV analyses, which provides sufficient area to give good tracking of the patches.

5. Results and discussions 5.1. Failure mode As it is illustrated in Fig. 3 all tested specimens failed due to debonding of the CFRP sheet from concrete substrate. Note that a thin layer of concrete including crushed aggregates was adhered to all debonded CFRP strips (Fig. 3). It means that the failure plane occurred in concrete near to the interface, not in the adhesive

153

layer. Depth of concrete failure plane (df) was approximately equal to 1 mm as suggested by Seracino et al. [24]. However, such a parameter is not easy to be accurately determined since the failure plane passes through the crushed aggregates (Fig. 3). 5.2. Experimental results versus theoretical predictions Experimental debonding loads (Ptest) for all tested specimens are presented in Table 2. The table also contains the theoretical debonding loads (Pmodel) based on fib Bulletin 14 [27], Chen and Teng [3], and Seracino et al. [24] expressions which were calculated from Eqs. (1a), (2a), and (3a), respectively. The percentage differences between the experimental and theoretical debonding loads, computed as Δ ¼(Ptest,avg ˗ Pmodel)/Ptest,avg are also reported in the table in parentheses. Obviously, positive values correspond to underestimated predictions while negative values report overestimated predictions of theoretical models. It can be observed in Table 2 that fib Bulletin 14 [27] and Chen and Teng's [3] models generally overestimate debonding loads, while Seracino et al. [24] model safely underestimates failure loads. Experimental versus calculated debonding loads for tested specimens are also plotted in Fig. 4. Note that the points which are located above line y¼x represent conservative predictions. Fig. 4 shows the capability of both Chen and Teng [3] and Seracino et al. [24] models to predict almost accurate debonding loads while fib Bulletin 14 [27] predictions are mostly overestimated. Theoretical effective bond lengths for tested specimens predicted by fib Bulletin 14 [27], Chen and Teng [3], and Seracino et al. [24] expressions are presented in Table 3. The table shows that

Fig. 3. Debonding of CFRP sheets from concrete substrate.

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A. Hosseini, D. Mostofinejad / International Journal of Adhesion & Adhesives 48 (2014) 150–158

Table 2 Experimental and theoretical debonding loads. Test specimen

fc (MPa)

Lf (mm)

Ptest (kN)

Ptest,avg (kN)

Pmodel (kN) (Δ

(%))

fib Bulletin 14 [27] EBR-20-1 EBR-20-2 EBR-35-1 EBR-35-2 EBR-50-1 EBR-50-2 EBR-75-1 EBR-75-2 EBR-100-1 EBR-100-2 EBR-125-1 EBR-125-2 EBR-150-1 EBR-150-2 EBR-175-1 EBR-175-2 EBR-200-1 EBR-200-2 EBR-225-1 EBR-225-2 EBR-250-1 EBR-250-2

36.8

20

36.8

35

36.8

50

36.5

75

36.5

100

39.1

125

39.1

150

41.1

175

41.1

200

40.6

225

40.6

250

7.94 7.58 9.24 9.88 9.74 9.85 9.52 9.80 9.89 9.95 9.45 10.09 9.42 9.60 9.86 10.12 9.62 9.95 9.81 9.35 9.39 9.67

Chen and Teng [3]

7.76

5.69

(26.7%)

4.27

(45.0%)

4.35

(43.9%)

9.56

8.69

(9.1%)

6.98

(27.0%)

7.61

(20.4%)

9.80

10.60

(  8.2%)

8.94

(8.7%)

9.18

(6.3%)

9.66

11.45

(  18.5%)

10.03

(  3.8%)

9.16

(5.2%)

9.92

11.45

(  15.4%)

10.03

(  1.1%)

9.16

(7.7%)

9.77

11.64

(  19.1%)

10.21

(  4.5%)

9.37

(4.1%)

9.51

11.64

(  22.4%)

10.21

(  7.4%)

9.37

(1.5%)

9.99

11.79

(  18.0%)

10.34

(  3.5%)

9.52

(4.7%)

9.79

11.79

(  20.5%)

10.34

(  5.7%)

9.52

(2.7%)

9.58

11.75

(  22.7%)

10.30

(  7.5%)

9.48

(1.0%)

9.53

11.75

(  23.3%)

10.30

(  8.1%)

9.48

(0.5%)

Table 3 Effective bond lengths predicted by theoretical models.

12 11

Test specimen

fc (MPa)

Lf (mm)

10 9 Ptest (kN)

Seracino et al. [24]

EBR-20-1(2) EBR-35-1(2) EBR-50-1(2) EBR-75-1(2) EBR-100-1(2) EBR-125-1(2) EBR-150-1(2) EBR-175-1(2) EBR-200-1(2) EBR-225-1(2) EBR-250-1(2)

8 7 6 fib Bulletin 14 [27]

5

36.8 36.8 36.8 36.5 36.5 39.1 39.1 41.1 41.1 40.6 40.6

20 35 50 75 100 125 150 175 200 225 250

Le (mm) fib Bulletin 14 [27]

Chen and Teng [3]

Seracino et al. [24]

69.0 69.0 69.0 69.1 69.1 67.9 67.9 67.1 67.1 67.3 67.3

71.7 71.7 71.7 71.8 71.8 70.6 70.6 69.7 69.7 70.0 70.0

42.2 42.2 42.2 42.3 42.3 41.5 41.5 41.0 41.0 41.1 41.1

Chen and Teng [3] 4 Seracino et al. [24] 3 3

4

5

6

7 8 Pmodel (kN)

9

10

11

12

Table 4 Average discrepancies between experimental and theoretical debonding loads. Model

Average discrepancy (%)

Fig. 4. Experimental versus calculated debonding loads.

calculated Le based on fib Bulletin 14 [27] and Chen and Teng [3] expressions (Eqs. (1c) and (2d) which are basically identical) is about 70 mm, while predicted Le based on Seracino et al. [24] (Eq. (3b)) is about 40 mm. Note that slight differences in predicted Le for tested specimens in Table 3 are due to the small variation of compressive strengths of different concrete batches. Table 2 shows that increasing the bond length (Lf) beyond 35 mm has no significant effect on debonding capacity, and ultimate loads are approximately constant when Lf increases beyond 35 mm. Consequently, it can be concluded that the experimentally evaluated Le for the CFRP strips of the current study is approximately equal to 35 mm. Comparing the experimentally evaluated Le with the theoretically calculated values in Table 3 shows that fib Bulletin 14 [27] and Chen and Teng's [3] models overestimate Le up to 100 percent, while Seracino et al. [24] model predicts more realistic values for Le. Note that in

fib Bulletin 14 [27] Chen and Teng [3] Seracino et al. [24]

Lf 40

Lf 4Le

Lf oLe

18.5 11.1 8.9

 20.0  5.2 3.7

14.7 26.9 32.2

externally strengthened flexural members, it is recommended [8,38] that the bond length beyond the inflection point be extended at least two times of Le specified by theoretical models to appropriately anchor the tension force developed in external strengthening plate/sheet. Consequently, fib Bulletin 14 [27] and Chen and Teng [3] Le predictions lead to waste of composite materials in practical projects. Average discrepancies between experimental and theoretical debonding loads are presented in Table 4. The average discrepancies between experimental and theoretical debonding loads are estimated in three distinct categories: Lf 4Le, Lf oLe, and an overall

A. Hosseini, D. Mostofinejad / International Journal of Adhesion & Adhesives 48 (2014) 150–158

estimation for all data which is indicated as Lf 40; where Lf is FRP bond length and Le is the effective bond length predicted by theoretical models. In the case Lf 40, all 22 experimental results of the current study are considered and errors of theoretical models are computed as (Σ|Δ|)/n, where Δ ¼(Ptest,avg ˗ Pmodel)/Ptest,avg and n is number of tests. The main intention of considering this category is to evaluate the accuracy of theoretical models through absolute errors, regardless of under/overestimated predictions. Unlike the first category, errors of theoretical models in two other categories were computed as (ΣΔ)/n; where n here is the number of only a part of data in which Lf 4Le or Lf oLe. Consequently, negative values indicate overestimated unsafe predictions. 12 11 10

8 7 6 5 4

Current study (exp.)

3

fib Bulletin 14 [27]

2

Chen and Teng [3]

1

Seracino et al. [24] 0

20

40

60

It is expected that when Lf 4Le, theoretical models conservatively predict debonding loads; however, as it is presented in Table 4, fib Bulletin 14 [27] generally overestimates debonding loads up to 20 percent. Chen and Teng [3] and Seracino et al. [24] models, by contrast, very well predict debonding loads of FRP sheets when Lf 4Le, with average discrepancies of 5.2 and 3.4, respectively. In case Lf oLe, all three models conservatively predict debonding loads, since theoretical models overestimate effective bond lengths. In order to better describe the effect of Lf on debonding load, experimental debonding load versus bond length (Lf), are plotted in Fig. 5. The figure also shows the corresponding predicted loads of fib Bulletin 14 [27], Chen and Teng [3] and Seracino et al. [24] models for comparison. It is observed in Fig. 5 that when Lf 4Le, the experimental curve (solid line with circles) is limited to Seracino et al. [24] predictions (as lower bound), and Chen and Teng [3] predictions (as upper bound); which means that the performance of both Seracino et al. [24] and Chen and Teng's [3] models is acceptable. The model of fib Bulletin 14 [27], however, overestimates debonding loads. Although Seracino et al. [24] model predicts more accurate values for both Le and P when Lf 4Le, the predictions of Seracino et al. [24] diverged from experimental results in case Lf oLe (Fig. 5). An accurate inspection of Fig. 5 reveals that assumption of linear variation of debonding load in case of Lf oLe is too conservative.

5.3. Evaluation of effective bond length using PIV

0 80 100 120 140 160 180 200 220 240 260 Bonded length, Lf (mm) Fig. 5. Debonding loads versus bond length.

Effective bond length of the utilized CFRP composite can be also evaluated by monitoring strain distribution along the strip at different stages of loading. In other words, when the FRP-toconcrete bonded joint reaches its ultimate capacity, the length of the effective bond zone can be evaluated using longitudinal strain field of the strip, obtained from PIV analysis. To do so, successive

Longitudinal strain (%)

0.1

0.2

0.3

0.4

0.5

0.6

0

0

10

10

z (mm)

z (mm)

0.0

20 30 40

0.8

0.9

1.0

20 30 50

0.65 P

0.71 P

0

0

10

10

20

20

z (mm)

z (mm)

0.7

40

50

30 40 50

30 40 50

0.91 P

0.86 P 0

0

10

10

z (mm)

z (mm)

Debonding load (kN)

9

155

20 30

20 30 40

40

50

50

0.95 P

P

Fig. 6. Evolution of longitudinal strain field of specimen EBR-50-1 during loading process (dash lines indicate 48 mm width of CFRP strip, P ¼9.74 kN).

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digital images were taken and analyzed using PIV method, and longitudinal strain field corresponding to each load level was derived. To perform PIV analysis, 128  128 pixel patches, spaced at 32 pixels center-to-center were generated and displacement fields were calculated; then triangular elements were generated and strain fields were evaluated using nodal displacements. Evolution of longitudinal strain field in the CFRP sheet during the loading process for specimen EBR-50-1 is presented in Fig. 6. Note that vertical axis, z, represents the distance from loaded end of CFRP strip. Fig. 6 obviously shows the fact that, at each stage of loading, only a limited zone of the CFRP strip experiences deformation and, subsequently strain values. As it is illustrated in Fig. 6, by increasing the applied load, the strain further distributes along the CFRP strip. At ultimate load level (P), however, only a limited zone of the bond length (not the whole Lf ¼ 50 mm), which is approximately equal to 35 mm, is

affected by the applied load (Fig. 6f). Therefore, it can be concluded from Fig. 6 that the effective bond length, Le, for the tested specimen is approximately equal to 35 mm. In order to better describe the concept of effective bond length and effect of bond length (Lf) on debonding phenomenon in FRP-toconcrete adhesively-bonded joints, longitudinal strain fields corresponding to different load levels for specimen EBR-250-2 are plotted in Fig. 7. Careful inspection of Fig. 7 reveals that at ultimate load level, P, only the first 35 mm of the bonded zone is affected by the applied load (Fig. 7a). Consequently, the effective bond zone is approximately equal to 35 mm. Immediately after reaching the ultimate capacity of the joint, however, the FRP in close zones to loading point detaches from the concrete substrate and the effective bond zone shifts further to new areas, while the load is fluctuating close to the ultimate load (Fig. 7b–f). In fact, debonding rapidly propagates toward the free end

Longitudinal strain (%)

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0

0

50

50

50

100

100

100

z (mm)

z (mm)

z (mm)

0

150

150

150

200

200

200

250

250 P

0.94 P 0

50

50

50

100

100

100

z (mm)

z (mm)

z (mm)

0

150

150

150

200

200

200

250

250 0.95 P

1.0

250 0.97 P

0

250

0.9

P

0.99 P

Fig. 7. Evolution of longitudinal strain field of specimen EBR-250-2 during loading process (dash lines indicate 48 mm width of CFRP strip, P¼ 9.67 kN).

A. Hosseini, D. Mostofinejad / International Journal of Adhesion & Adhesives 48 (2014) 150–158

of CFRP strip causing strain redistribution along the strip, as previously discussed by the authors [36]. Finally the whole length of the CFRP strip detaches from the concrete substrate. As it was discussed earlier, the effective bond length (Le) of the CFRP sheets used in the current study was experimentally determined equal to 35 mm based on debonding loads. PIV results presented in Figs. 6 and 7 strongly verify the experimentally determined value of the Le; since the length of the effective bond zone obtained from the PIV analysis is equal to 35 mm for both specimens EBR-50-1 (Fig. 6f) and EBR-250-2 (Fig. 7a). Furthermore, comparing the PIV results of specimen EBR-50-1 (having Lf ¼50 mm) with those of specimen EBR-250-2 (having Lf ¼250 mm) verifies that effective bond length is independent of bonded length, Lf. This is due to the fact that Le is a function of material characteristics.

6. Calibration of theoretical models As discussed earlier, fib Bulletin 14 [27] considers constant values c1 and c2 for calibrating debonding load and effective bond length as expressed in Eqs. (1a) and (1c), respectively. Since fib Bulletin 14 [27] overestimates debonding loads and effective bond length, the values of c1 ¼0.53 and c2 ¼7.7 are suggested for calibrating Eqs. (1a) and (1c) for CFRP sheets based on the current experimental results, instead of former values of c1 ¼0.64 and c2 ¼ 2.0. On the other hand, Chen and Teng's [3] model only considers calibration factor α, suggested to be 0.427 by Yao et al. [38] using 72 single-shear tests. As previously discussed, Chen and Teng's [3] model overestimates effective bond length, though the model clearly provides accurate debonding loads. Consequently, based on experimental results of the current study, the reduction factor c¼0.5 can be introduced to Eq. (2d) in order to reduce Le values predicted by Chen and Teng's [3] model. As a result, α in Eq. (2a) can be modified as 0.854 (0.427/0.5), since Le is directly used in Eq. (2a). It was mentioned earlier that Seracino et al. [24] model more accurately predicts both Le and debonding loads. The model is slightly conservative, however, its calibrating is not easily applicable since the model operates based on df (thickness of the failure plane) and such a parameter is not easy to be determined based on limited experimental results. Nevertheless linear variation assumption of debonding loads is too conservative in case Lf oLe and using a non-linear reduction factor such that presented by Chen and Teng [3] (Eq. 2b) can increase the capability of Seracino 11 10

Debonding load (kN)

9 8 7 6 5 4

Current study (exp.)

3

fib Bulletin 14 [27] (calibrated)

2

Chen and Teng [3] (calibrated)

1

Seracino et al. [24] (calibrated)

0 0

20

40

60

80 100 120 140 160 180 200 220 240 260 Bonded length, Lf (mm)

Fig. 8. Modified debonding loads versus bond length (based on the suggested factors).

157

et al. [24] model in predicting debonding loads of FRP strips with Lf oLe. Calculated debonding loads based on the suggested factors for calibrated models of fib Bulletin 14 [27], Chen and Teng [3] and Seracino et al. [24] are plotted in Fig. 8. Modified predictions of fib Bulletin 14 [27] very well match the experimental results, since both bond strength and effective bond length models were calibrated based on experimental results of the current study. The modified Chen and Teng's [3] effective bond length model also results in an agreement between the predicted debonding loads and the experimental results. Furthermore, Fig. 8 illustrates that the non-linear reduction factor calculated from Eq. (2b) can improve the capability of Seracino et al. [24] model in predicting more accurate debonding loads in case of Lf oLe. It should be noted that the presented calibration factors in this section can be surely improved when more experimental results, focused on the effective bond lengths, become available. It is also important to notice that the modified theoretical models using the suggested factors predict nominal values of debonding loads and effective bond lengths; therefore, appropriate safety factors are definitely needed to be incorporated in existing guidelines such as fib Bulletin 14 [27], ACI 440.2R [1] and HB 305 [8].

7. Summary and conclusions In this study, performance of well-known FRP-to-concrete bond strength models in fib Bulletin 14 [27], ACI 440.2R [1] and HB 305 [8] was evaluated by means of experimental tests. To do so, CFRP sheets having a wide range of bond length from 20 to 250 mm were adhered to 22 concrete prisms. The specimens were then subjected to single-shear test and the effective bond length of the utilized CFRP composite was evaluated based on debonding loads. Furthermore, a full field image-based deformation measurement technique, i.e. particle image velocimetry (PIV) was used to investigate strain distribution along CFRP strips during loading process. Based on the experimental results of the current study in comparison with debonding loads and effective bond length calculated from code expressions, the following concluding remarks can be drawn. 1. The expressions of fib Bulletin 14 [27], overestimate both debonding loads and effective bond lengths up to 20% and 100%, respectively. Based on the experimental results of the current study, constant values of c1 ¼0.53 and c2 ¼ 7.7 are suggested for calibrating bond strength and effective bond length expressions for CFRP sheets, respectively; instead of former values of c1 ¼0.64 and c2 ¼2.0. 2. Chen and Teng's [3] model utilized in both ACI 440.2R [1] and HB 305 [8], slightly overestimates debonding loads, where the mean error of the model is 5.2% compared with the experimental results. The model, however, overestimates the effective bond length up to 100%. Consequently, reduction factor c ¼0.5 can be introduced to Chen and Teng's [3] effective bond length model. 3. Seracino et al. [24] model more accurately predicts effective bond length of externally bonded (EB) CFRP sheets compared with other code expressions. Furthermore, the model conservatively predicts debonding loads with an average discrepancy of 3.7% compared with experimental results in case of Lf 4 Le; however, when Lf o Le the model is too conservative which is due to assuming linear variation of debonding load in this case. Hence, using non-linear reduction factor presented by Chen and Teng [3] can improve the capability of Seracino et al. [24] model in predicting debonding loads of EB FRP systems with Lf oLe.

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