LOCAL BOND-SLIP BEHAVIOR OF DEFORMED REINFORCINGBAR UNDER CYCLIC LOADING
Shuai HAO
Graduate Student, University of Tsukuba, Japan
s1420947@u.tsukuba.ac.jp

Toshiyuki KANAKUBOAssociate Professor, University of Tsukuba, Japankanakubo@kz.tsukuba.ac.jp

Hitomi OKAZAKI
Graduate Student, University of Tsukuba, Japan
s1420872@u.tsukuba.ac.jp

ABSTRACT: In this study, pullout bond test both for monotonic and cyclic loading is conducted forseveral types of deformed bars with different dimensions of lugs. The test variables are the ratio of lugheight to spacing, loading history and concrete strength. The specimens are subjected to splitting test
after pullout loading to observe the interface between the bars and concrete. As a result, deformation of
concrete at the front of the lug is recognized. For the cyclic loading specimens, the relationship between
bond stress and cumulative slip, that considers the returnable limit slip, shows a similar tendency to bondstress - slip curve of monotonic loading specimens regardless of the type of deformed bars. It is feasible
to use the monotonic loading results to evaluate the bond strength under cyclic loading.

1. Introduction
Researches on bond behavior of deformed reinforcing bars have been studied so far (Sato et al., 2012).
However, there are few studies on local bond behavior under cyclic loading. For example, although Morita
and Kaku (1975) proposed a hysteretic model for the relationship between bond stress and slip undercyclic loading and reported the bond deterioration in the range of experienced slippage, there is no further
discussion when the slippage exceeds the experienced slippage. Suzuki et al., (1985) also proposed ahysteretic model. However, bond behavior after the experienced slippage is not mentioned.
On the other hand, when the reinforcing bars in beam, column or beam-column joint are under anantisymmetric loading, they are subjected to a cyclic load with large slippage. The authors focus on bondbehavior of deformed bars under cyclic loading in the case of large deformation (Okazaki and Kanakubo,2014). As a result, the hysteretic curve can return to the one under monotonic loading even the slippage
exceed the experienced slippage in a certain region. However, when it exceeds that region, bonddeterioration appears remarkably. For some rib dimensions, bond stress decrease rapidly at the slip of
1/20 bar diameter. The designed capacity and ductility of reinforced concrete members may beoverestimated if the bond deterioration under cyclic loading is unknown.
In this study, focusing on the local bond behavior of deformed reinforcing bars, bond test is conducted.
The bond length is 4 times bar diameter and the deformed bars are originally manufactured for various
type (different ratio of lug height to spacing).It can be used to investigate the influence of ratio of lugheight to spacing on the bond behavior. In addition, the specimen is restricted by a steel tube to avoid
splitting failure. The purpose of this study is to investigate the influence of loading history and dimensionsof lugs on local bond behavior.

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2. Experimental Program
2.1. Tested Deformed Bars
Table 1 and Fig.1 shows the list of deformed bars and the dimensions, respectively. The tested bar was
manufactured by machining a round steel bar. Variation factors are the height of lug and lug spacing. The
ratio of lug height to spacing varies from 0.05, 0.075 to 0.25 (called F050，F075 and F250, respectively).
The lug dimension of F075 is similar to the normal deformed bar specified in Japanese Industrial
Standard. Sectional area of those bars is defined as the equivalent area calculated by volume divided by
the length. Yield strength of the bar before machining is 570MPa, and the elastic modulus is 207GPa.
Table 1 –Tested reinforcing bar
ID

Height of lug(mm)Lug spacing(mm)

Ratio of lug height tospacing

Sectional area
2(mm )Perimeter
(mm)

F050

1.2

24.0

0.05

201

50.2

F075

1.2

16.0

0.075

204

50.6

F250

2.4

9.6

0.25

194

49.4

Fig. 1 – Dimensions of tested bar

2.2. Specimen
Fig.2 shows the details of the specimen. One deformed bar was set at the center of the concrete cylinder.
The cylinder was confined by steel tube to avoid concrete splitting. External diameter of the steel tube is
216mm, the thickness is 5.8mm and the width is 112mm. The bond region was set as 4 times the referred
deformed bar (φ16), so bond length is 64 mm. Unbond regions were set in both two sides with 24mm
length.

Fig. 2 – Details of specimen

2.3. Loading Method and Measurement
Loading apparatus is shown in Fig.3. The Teflon sheet and reaction steel plates with a hole of 112mm
were set beside two sides of specimen. Load cells and center-hole jacks were set at both left and right

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sides of the specimen. Using the jack in each side alternately applied a cyclic loading. Monotonic loading
was also carried out by only use one side of jack.
The measurement items are pullout load measured by load cell and the relative displacement between
lateral side of specimen and the tested bar end. The slippage at free end is defined as the relative
displacement measured by LVDT, which is set at the opposite side of loading direction. The loaded end
slip is calculated as that the elongation of reinforcement is added to the free end slip under theassumption that bond stress distributes uniformly among bonded region.

Fig. 3 – Loading apparatus

C3

C2

Bond stress(MPa)C1

Loaded end slip(mm)Loaded end slip(mm)Fig.4 shows the loading history, which is the main experimental factor. It includes a monotonic loading
and three types of cyclic loading called C1, C2 and C3. C1 loading was a reversed cyclic loading and it
increases gradually. Each cycle corresponds to the loaded end slip at 0.2, 0.4, 0.6, 0.8, 1.0, 1.5, 2.0, 3.0,
4.0, 5.0, 6.0, 7.0 and 8.0mm. C2 loading was a cyclic loading in only positive direction, the target slip ofeach cycle is same as C1 loading. The pullout load in negative direction was applied after unloading until
the slip returns to 0mm. In C3 loading, bond stress was set as a target value at when the target slip
reached to 0.1, 0.3, 0.5, 1.0 and 2.0mm at first time. Five cycle loadings were applied for each bondstress. Upper side of the specimen in concrete pouring was set as the reaction surface for the positive
loading and the monotonic loading.

τ2.0
τ1.0
τ0.5
τ0.3
τ0.1
τ-0.1
τ-0.3
τ-0.5
τ-1.0
τ-2.0

Fig. 4 – Loading history

2.4. Observation of the Interface between Bars and Concrete
Half of the specimens (concrete target strength of 13MPa and 36MPa, explained after) were subjected to
splitting test to observe the interface between the bars and concrete after the loading of the target slip
cycle. Fig.5 shows the photo of the splitting test.

Fig. 5 – Splitting test

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2.5. Experimental Factor
The experimental factors are dimensions of rib of deformed bars, loading history and concrete target
strength (13MPa, 21MPa and 36MPa). Table 2 shows the mechanical properties of concrete. Fig.6 gives
the definition of ID of specimens. Specimens are listed in Table 3.
Table 2 – Mechanical properties of concrete
ID Compressive strength (MPa) Tensile strength (MPa) Elastic modulus (GPa)
C13
C21
C36

13.3
20.9
37.3

1.48
1.97
2.58

20.7
24.9
27.8

Fig. 6 – Specimen ID
Table 3 – List of specimens and test results
At maximum load
Bond stress Slip
(MPa)
(mm)
C21-F050-M
24.6*
6.32*
C21-F075-M
25.1*
2.05*
C21-F250-M
18.7*
0.58*
C13-F050-M-20(6.27)(2.0)
C13-F050-M-40(8.16)(4.0)
C13-F050-M-80
8.91
5.09
C13-F075-M-08(7.44)(0.8)
C13-F075-M-20
8.44
1.42
C13-F075-M-40
8.44
1.74
C13-F250-M-04(6.16)(0.4)
C13-F250-M-08(6.31)(0.8)
C13-F250-M-20
6.05
0.54
C36-F050-M-20 (19.62)(2.0)
C36-F050-M-40 (24.21)(4.0)
C36-F050-M-80
24.71
5.50
C36-F075-M-08 (22.49)(0.8)
C36-F075-M-20
24.41
1.62
C36-F075-M-40
28.57
1.82
C36-F250-M-04
20.30
0.21
C36-F250-M-08
21.24
0.31
C36-F250-M-20
20.78
0.27
ID

At maximum load
Bond stress (MPa) Slip (mm)
Cycle
+
+
C21-F050-C1
8
23.1
17.2
3.0 3.0
C21-F050-C2
9
22.5
4.0
C21-F050-C3
20
16.9
15.6
2.0 2.0
C21-F075-C1
4
16.7
13.6
0.8 0.8
C21-F075-C2
6
26.2
1.5
C21-F075-C3
16
19.1
20.4
1.0 1.0
C21-F250-C1
1
20.0
14.2
0.2 0.2
C21-F250-C2
2
21.4
0.4
C21-F250-C3
7
13.8
9.8
0.5 0.5
C13-F050-C1-20
7(6.73)(5.58)(2.0) (2.0)
C13-F050-C1-40
8
7.02
5.50
3.0 3.0
C13-F050-C1-80
8
7.81
6.71
3.0 3.0
C13-F075-C1-08
4(8.16)(4.63)(0.8) (0.8)
C13-F075-C1-20
6
7.60
4.88
1.5 1.5
C13-F075-C1-40
6
7.48
5.66
1.5 1.5
C13-F250-C1-04
2(7.49)(5.08)(0.4) (0.4)
C13-F250-C1-08
2
7.30
4.77
0.4 0.4
C13-F250-C1-20
2
7.00
5.30
0.4 0.4
ID( ): For observing interface, the load terminated before maximum load appears.
*: Average value of three specimens.
Three same specimens (C13 series and C36 series) for each parameter were tested. They were
subjected to splitting test to observe the interface between the bars and concrete after the loading of the

Page 4 of 9

target slip cycle. The target slip cycle was set as 3 stages (load increase region, just before or after the
maximum load, and after the maximum load). For C13 series specimens, the loading was carried out only
for monotonic and C1 loading. C36 series specimens were only subjected to monotonic loading. For C21
series specimens, three same specimens for each parameter were subjected to monotonic loading. Total
number of specimens is 45.

3. Test Result
3.1. Observation of the Interface between Bars and Concrete
The photos of interface between bars and concrete after loading for C13 and C36 series specimens areshown in Fig.7 and Fig.8, respectively. For F050 and F075 deformed bars, when it reached to the target
slip, the lug moved from its original position with the concave of concrete. The damage of the concretearound the front of the lug was unapparent. Some cracks took place in perpendicular to the axis direction
in C13 series specimens. The crashed powder of concrete was not remarkably. The lug shape on
concrete collapsed after maximum load in cyclic loading specimens. For the F250 deformed bars, there
was almost no damage to the concrete before the maximum load. However, local shear failure ofconcrete between lugs was recognized after maximum load.
Target slip

2.0mm

4.0mm

8.0mm

0.8mm

2.0mm

4.0mm

0.4mm

0.8mm

2.0mm

-M(monotonic)
F050-C1(cyclic)
Target slip-M(monotonic)
F075-C1(cyclic)
Target slip-M(monotonic)
F250-C1(cyclic)

Fig. 7 – Interface between bars and concrete after loading (C13 series)

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Target slip

2.0mm

4.0mm

8.0mm

0.8mm

2.0mm

4.0mm

0.4mm

0.8mm

2.0mm

F050-M(monotonic)
Target slip
F075-M(monotonic)
Target slip
F250-M(monotonic)

Fig. 8 – Interface between bars and concrete after loading (C36 series)

3.2. Bond Stress‐Slip Relation

C13-F050-M
C21-F050-M
C36-F050-M

20

10

0

5

10

15

20

30

C13-F075-M
C21-F075-M
C36-F075-M

20

10

0

5

10

15

Slip(mm)Slip(mm)Bond stress(MPa)30

Bond stress(MPa)

Bond stress(MPa)

Relationships between bond stress and slip of monotonic loading specimens are shown in Fig.9. Although
the bond stress has a large difference among the C13, C21 and C36 series of specimens, slip at
maximum bond stress are almost the same. The lug spacing affects the shape of bond stress - slip curves
and the slip at maximum bond stress.

30

C13-F250-M
C21-F250-M
C36-F250-M

20

10

0

5

Slip(mm)Fig. 9 – Bond stress - slip curve (monotonic loading)Fig.10 shows the relationships between bond stress and slip by C1 cyclic loading. It can be found that thehysteretic curve can return to that by monotonic loading until slip reaches to a certain value (hereafter
called “returnable limit slip”). When the slip exceeds the returnable limit slip, the bond stress drops
remarkably. The returnable limit slip is not depended on concrete strength but lug spacing.

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10

-5

0

-5

0

5

30
20
10
0

5

-10
-20
-30

-5

0

5

-10

20
10
0

-20
-30

5

Slip(mm)

30
20
10

-5

5
Slip(mm)-10

C21F050-M
F050-C1

10

30

-5

Slip(mm)

C13F250-M
F250-C1

Slip(mm)-10

Bond stress(MPa)

Bond stress(MPa)10Slip(mm)-10-5

C13F075-M
F075-C1

Bond stress(MPa)C13F050-M
F050-C1

0

5

Slip(mm)-10-20

C21F075-M
F075-C1-30

C21F250-M
F250-C1

Fig. 10 – Bond stress - slip curve (C1 cyclic loading)

-5

20
10

0
-10
-20

5
Slip(mm)
C21F050-M
F050-C1
F050-C2
F050-C3-5

Bond stress(MPa)

Bond stress(MPa)

Bond stress(MPa)Fig.11 shows the envelope curves of bond stress - slip relations for C21 series specimens. The loading
history affects the returnable limit slip. In addition, the bond deterioration tendency after the returnable
limit slip also changes by differences of loading history. Basically, the returnable limit slip decreases with
the number of reversed cycles increasing.

20
10

0
-10
-20

5
Slip(mm)
C21F075-M
F075-C1
F075-C2
F075-C3

-5

20
10

0
-10
-20

5
Slip(mm)
C21F250-M
F250-C1
F250-C2
F250-C3

Fig. 11 – Envelope bond stress - slip curve (C21 series)

4. Evaluation by Cumulative Slip
Cumulative values are generally used to evaluate the fracture and response of materials. For thosevalues, cumulative energy and cumulative strain are often used. As mentioned before, observing theinterface between bars and concrete can find out that the lug moves from its original position with theconcave of concrete. It is considered that bond deterioration occurs due to the cumulative deformation of
concrete under cyclic loading.
Fig.12 shows the relationship between the cumulative slip (each peak slip is summed as the absolutevalue) and bond stress.

Page 7 of 9

20

10

0

10

20

30

40

30

20

10

0

Cumulative slip(mm)C21F075-C1
F075-C2
F075-C3

10

20

30

Bond stress(MPa)C21F050-C1
F050-C2
F050-C3

Bond stress(MPa)

Bond stress(MPa)

30

40

30

20

10

0

Cumulative slip(mm)C21F250-C1
F250-C2
F250-C3

10

20

30

40

Cumulative slip(mm)Fig. 12 – Bond stress - cumulative slip relation (C21 series)

C21F050-M
F050-C1
F050-C2
F050-C3

20

10

0

5

10

15

20

Cumulative slip(mm)30C21F075-M
F075-C1
F075-C2
F075-C3

20

10

0

5

10

15

20

Cumulative slip(mm)Bond stress(MPa)30

Bond stress(MPa)

Bond stress(MPa)

Although the curves show a large difference among three specimens reinforced with different bars, for
one bar, the curves show a similar tendency despite of difference of loading history. It is possible to use
cumulative slip to evaluate bond deterioration under cyclic loading. From the result of discussion in
Section 3.2, bond stress can return to that under monotonic loading until slip reaches to the returnable
limit slip. It is considered that this phenomenon can be employed into the cumulative slip. The cumulative
slip is calculated by sum of peak step subtracting the returnable limit slip when the peak step exceeds thereturnable limit slip. Considering the effect of dimension of lug spacing, the returnable limit slip is to beequal as two thirds of the lug spacing, as the results of try-and-error. The results are shown in Fig.13.
Fig.13 also includes the results of monotonic loading specimens.

30

C21F250-M
F250-C1
F250-C2
F250-C3

20

10

0

5

10

15

20

Cumulative slip(mm)Fig. 13 – Bond stress - cumulative slip relation (returnable limit slip considered, C21 series)

The relationship between bond stress and cumulative slip, in which the returnable limit slip is considered,is similar to the one of monotonic loading specimens. It is feasible to use the monotonic loading results toevaluate the bond strength under cyclic loading.

5. Conclusion(1) For the deformed bar with the ratio of lug height to spacing of 0.05 and 0.075, lug moved from its
original position with the concave of concrete from the interface observation. For the deformed bar
with the ratio of lug height to spacing of 0.25, local shear failure of concrete between lugs wasrecognized after maximum load.
(2) Lug spacing has a large influence on the bond stress - slip curves and the slip at maximum load.
(3) For the cyclic loading specimens, the hysteretic curve can return to the one under monotonic loading
until slip reached to the returnable limit slip. Bond stress drops remarkably after the returnable limit
slip and it cannot return to the curve of monotonic loading.

Page 8 of 9

(4) For the cyclic loading, the relationship between bond stress and cumulative slip, that considers thereturnable limit slip, shows a similar tendency to bond stress - slip curve of monotonic loading
specimens. It is feasible to use the monotonic loading results to evaluate the bond strength undercyclic loading.

References
MORITA, Shiro, KAKU, Tetsuzo, “Bond-Slip Relationship under Repeated Loading”, Transactions of theArchitectural Institute of Japan, (229), March 1975, pp.15-24 (in Japanese).
OKAZAKI, Hitomi, KANAKUBO, Toshiyuki, “Influence of Rib Dimensions to Bond Behavior under Cyclic
Loading”, Summaries of technical papers of annual meeting Architectural Institute of Japan, Structures IV,
2014, pp.15-16 (in Japanese).
SATO, Yuichi, SHIMA, Hiroshi, KANAKUBO, Toshiyuki, “Japan Concrete TC Activities on Bond Behavior
and Constitutive Laws in RC (Part 1: Research Survey on Bond Problems)”, Bond in Concrete 2012,
Volume 1. General Aspects of Bond, 2012, pp.89-96.
SUZUKI, Kazuo, OHNO, Yoshiteru, MIYAMARU, Takashi, YAMAMUKAI, Masaru, “Bond of Deformed Bar
under High Cycle Repeated Loads”, Summaries of technical papers of annual meeting Architectural
Institute of Japan, Structures II, September 1985, pp.527-528 (in Japanese).

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