Composite materials term paper

ACI MATERIALS JOURNAL TECHNICAL PAPER Title no. 92-M30

Tensile and Bond Properties of GFRP Reinforcing Bars

by L. Javier Malvar

The bond characteristics of four different types of glass fiber reinforced plastic (GFRP) reinforcing bars with different suiface deformations were analyzed experimentally. Local bond stress-slip data. as well as bond stress-radial deformation data. needed for constitutive modeling of the inteiface mechanics, were obtained for varying levels of confining pres- sure. In addition to bond stress and slip, radial stress and radial deforma- tion were considered fundamental variables needed to provide for configuration-independent relationships. Each test specimen consisted of a #6 GFRP reinforcing bar embedded in a 3-in.-(76-mm)-diameter, 4-in.- ( 102-mm)-long cracked concrete cylinder subjected to a controlled, con- stant amount of confining axisymmetric radial pressure. Only 2.625 in. (67 mm, i.e., the equivalent of five steel bar lugs) of contact was allowed between the bar and concrete. For each reinforcing bar type, bond stress- slip and bond stress-radial deformation relationships were obtained for five levels of confining axisymmetric radial pressure. It was found that small suiface indentations were sufficient to yield bond strengths compara- ble to that of steel bars. Effects of deformations on tensile properties were addressed. It was also shown that radial pressure is an important parame- ter that can increase the bond strength threefold.

Keywords: bond (concrete to reinforcement); concretes; fibers; plastics, polymers and resins.

Extensive and costly condition assessment, repair, andre- habilitation programs are under way to extend the service life of reinforced concrete structures. The main cause of de- terioration is corrosion of the steel reinforcement exposed to marine environment and aggressive agents such as deicing salts for bridges and pavements. To prevent this corrosion, the galvanized and epoxy coated bars in use have been inves- tigated, 1-4 with mixed results. 2 A more recent alternative is use of fiber reinforced plastic (FRP) bars, which have excel- lent corrosion resistance and mechanical properties similar to steel. 5·6 FRP reinforcing bars, tendons, and grating have already been used in waterfront structures and bridges. 6- 11

A concern with FRP, as well as epoxy-coated, reinforcing bars, is the behavior of the interface between the reinforcing bar and concrete.3,1 2- 19 The objectives of the present study are to investigate mechanical properties and bond-slip be- havior of four commercially available FRP reinforcing bars. For each FRP reinforcing bar type, up to eight tensile tests are carried out and bond stress-slip constitutive relationships are experimentally determined. These latter data are ob-

276

tained as a family of bond stress-slip curves for five levels of constant radial confining stress. In addition, bond stress-ra- dial deformation curves are obtained that characterize the ra- dial expansion at the interface.

RESEARCH SIGNIFICANCE Acceptance of FRP reinforcing bars in structural engineer-

ing has been inhibited partly due to lack of design criteria, particularly with regard to bond. 20•21 One reason for the lack of design criteria for bond is lack of standards for bar defor- mation geometry and bar composition. Comparison of bond properties of various types of deformation is a first step in determination of optimum deformation geometry.

Determination of constitutive bond stress-slip relation- ships is useful for mathematical or numerical modeling of re- inforced concrete structural behavior. In particular, these models can be used to determine anchorage requirements without extensive testing for reinforcing bars.

TENSILE AND BOND TESTS FOR FRP REINFORCING BARS

Reinforcing bar types Four commercially available FRP reinforcing bar types

with different deformations are considered (Fig. 1). All are 3/ 4-in.-(19-mm)-diameter bars composed of pultruded E- glass fibers with a fiber volume fraction of 45 percent (60 percent by weight) or more, embedded in a vinyl ester or polyester resin matrix. Table 1 reports deformation spacing in inches and as a fraction of the nominal diameter 0, and the coefficient of variation. For steel bars, the maximum defor- mation spacing is 0.70, i.e., 0.525 in. (13 mm) for a #6 bar. 22 Table 1 also indicates deformation height (or indentation depth) in inches and as a fraction of the diameter. The defor- mation height (or indentation depth) is measured as the dif- ference between the bar radius at a deformation and the

ACT Materials Journal, V. 92, No. 3 May-June 1995. Received Nov. 8, 1993, and reviewed under Institute publication policies. Copy-

right © 1995, American Concrete Institute. All rights reserved, including the making of copies unless permission is obtained from the copyright proprietors. Pertinent dis- cussion will be published in the March-April 1995 ACI Materials Journal if received by Dec. I, 1995.

ACI Materials Journal I May-June 1995

AC! member L. Javier Malvar is an assistant research engineer in the Civil Engineer- ing Department, the University of California at Davis. He has conducted research on fracture mechanics, finite element modeling, and experimental analysis of concrete and reinforced concrete structures at the Naval Facilities Engineering Service Center, Port Hueneme, California.

radius at midpoint between that deformation and the next In addition, each reinforcing bar type presents the following characteristics:

L Type A-These bars have an external helicoidal tow which both provides a protruding deformation and small in- dentation of the bar surface. An outer layer consisting exclu- sively of matrix material is provided around the fibers for additional protection. The deformation width was about 0.125 in. (3.2 mm), yielding a clear deformation spacing of 0.595 in. (15 mm).

2. Type B-During fabrication of these bars, the surface tow is stressed so that indentations are obtained rather than deformations. These bars showed a large variation of cross section, which was expected to yield variation in mechanical properties. Large variations in surface indentations were ap- parent as well.

3. Type C-These bars have the surface tow glued to the exterior of the bar to provide only surface deformations. Fi-

Table 1-Geometrical properties

bers in the bar itself are perfectly straight 4. TypeD-Here, an indentation similar to the one in Type

B is provided. These bars appear to have an outer veil to pro- tect the glass fibers.

Tensile tests For each bar type, five tensile tests following ASTM D

3916-8423 were first conducted to determine secant modulus of elasticity at 24 ksi (165 MPa), ultimate stress, and ultimate strain. The secant modulus was measured, since it is expect- ed that a working stress approach would be used in design, with allowable stresses between 18 and 30 ksi (124 and 207 MPa). Elongation measurements were taken using two L VDTs on either side of each bar, attached via two clamps spaced an average of 13 in. (330 mm). Total specimen length was 42 in. (1.07 m) with a clear spacing between grips of about 28 in. (0.7 m).

It was decided that these tests, which use an actual bar specimen, would be more representative than those under ASTM D 638-90,24 which requires a machined-down speci- men. Shortcomings of using a machined specimen are that effects of indentations and specimen size on tensile strength cannot be evaluated, and bar cross-sectional area may not be easily determined. Shortcomings of using an undisturbed bar

Deformation or indentation spacing, Deformation height or indentation Bar type, 3/ 4 -in. diameter in. * depth, in. *

A 0.72 (0.96 0) ± 13.8 percent 0.041 (0.054 0) ± 7.5 percent B 0.94 (1.25 0) ± 1.9 percent 0.063 (0.084 0) ± 51.8 percent

c 0.78 (1.03 0) ± 2.3 percent 0.047 (0.067 0) ± 2.8 percent D 1.35 (1.80 0) ± 7.6 percent 0.069 (0.092 0) ± 13.7 percent

Steel < 0.525 (0.70 0) > 0.038 (0.0507 0) * 1 in.= 25.4 mm.

Fig. 1-Bar types

ACI Materials Journal I May-June 1995 277

specimen are related to grip effects. To alleviate these grip effects, three additional tensile tests were conducted for Types A and C. In these tests, specially designed grips con- sisting of four aluminum blocks bolted together were used and new values for the ultimate stresses were obtained.

Bond tests The objective of these tests was to determine configura-

tion-independent, local bond stress-slip data for use in con- stitutive material models. Typically, bond stress-slip curves are derived from pullout tests, or other more complex setups, without regard for the lateral confinement exerted by a par- ticular setup. As a result, very disparate curves have been ob- tained, representative only of the particular setup. If lateral confinement is taken into account, a family of curves can be obtained, which could be used with any other configuration. Similar tests have already been carried out for steel bars,25 -27

yielding general bond stress-slip relationships that were suc- cessfully used in predicting a variety of well-known re- sults.28·29* For FRP bars, bond strength is more affected by low transverse stiffness, which is itself dependent mostly on the matrix material.

The specimen used is shown in Fig. 2. It consists of a 3- in.-(76-mm)-diameter, 4-in.-(102-mm)-long concrete cylin- der surrounding an FRP bar. Only 2.625 in. (67 mm) of the bar is actually in contact with the concrete, contact being prevented in the rest of the specimen via silicone rubber spacers. The outer concrete surface is surrounded by a split, threaded steel pipe, which carries the pullout force via shear stresses (Fig. 3). The pipe is split into eight strips to offer no lateral resistance. The concrete cylinder is actually cast in place against the pipe threads. Casting was carried out with the specimen placed vertically.

Radial confining pressure on the specimen is applied via a thin ring surrounding the portion of pipe containing the con- crete cylinder. A hydraulic jack with an adjustable relief valve closed the ring with a constant force during the test. In

* Cox, J. V., "Development of a Plasticity Bond Model for Reinforced Con- crete~ Theory and Validation for Monotonic Applications," PhD thesis, University of California, Davis, Sept. 1994.

this way, the longitudinal reaction and radial confinement can be both controlled and measured independently of each other.

Concrete mix proportions were 1:3.02:1.35 for cement, sand, and 3/,-in. gravel, respectively. The water-cement ratio was 0.55. Three uniaxial unconfined compressive tests at 28 days on three 6-in.-tall, 3-in.-diameter cylinders yielded a compressive strength of 4220 psi (29 MPa). Three tensile splitting tests on the same specimen size yielded a tensile strength of 405 psi (2.8 MPa).

On the loaded end, two L VDTs were clamped to the bar and measured relative displacement of the outer concrete surface, i.e., the pipe. They were diametrically opposed to compensate for any rotation. A third L VDT was located in- side the pipe and measured relative displacement (slip) be- tween the pipe and unloaded end of the bar. Finally, a fourth L VDT measured the opening of the confining ring. This was later translated into a radial deformation. The apparatus was installed in an MTS testing machine. The MTS load cell pro- vided pullout load measurements. Bond stresses were calcu- lated by dividing pullout loads by the contact area between bar and concrete.

Prior to each test, the concrete cylinder was precracked by setting a bar surface pressure of 500 psi (3.4 MPa) and pull- ing on the bar until longitudinal splitting occurred. The spec- imen was then unloaded. After cracking, confining pressure at the bar surface was set at 500, 1500, 2500, 3500, or 4500 psi (3.4, 10.3, 17.2, 24.1, or 31 MPa) and kept constant dur- ing the remainder of the test (these E-glass composites have transverse compressive strengths around 20 ksi, or 138 MPa). After cracking (and assuming that cracks are open), all pressure from the confining ring was transferred to the bar. Tests were performed in displacement control.

EXPERIMENTAL RESULTS Tensile test results

For each bar type, Table 2 shows the average properties obtained. The modulus of elasticity indicated is the secant modulus at a stress of24 ksi (166 MPa). Ultimate stresses are obtained by dividing ultimate loads by the nominal cross

RADIAL STRESS APPLIED

VIA CONFINING RING

278

DISPLA;:~~~~ l_ ~ ~ ~ ~ ~ ~ ~ ~ ~ SH[AR STRESSES APPLIED - /'v"V'v'v'VV'v'VV\/VVV''.. VIA SPU T PIPE

314'

:3 in

t t t t t t t t t ~---- 4 in ----~

Fig. 2--Test specimen ( 1 in = 25.4 mm)

CONCRETE PULL-OUT

FORCE __..

ACI Materials Journal I May-June 1995

3/4' FRP REBAR t -.....~

/ CONCRETE SPECIMEN

""

H/0 OPPOSITE L VlJTs (SLJP)

L v'DT

(I~!NI~ OPENINCi) I

1 ===Jol (~ft- \ --=_j

,/~--- \ / RI~JG

INTERNAL L VDT liB' suns

3' EXTRP1 STRDNC:i l STE:EL f'IPE

Fig. 3-Bond test setup ( 1 in. = 25.4 mm)

ACI Materials Journal I May-June 1995

HYDRAULIC ,H1CK

CLAHF'ING

DEVICE

------~ CONFINING PIN!~

PLMJ VIE'..' -------

279

Table 2-Mechanical properties Number Modulus of Ultimate strain,

Bar type Test procedure of tests elasticity, msi* Ultimate stress, ksi t percent

A ASTM D 3916-84 5 6.74 (±1.3 percent) 86.7 (±2.2 percent) 1.41 (±3.4 percent)

A Special grips 3 - 89.5 (±2.7 percent) -

B ASTM D 3916-84 5 4.10 (±22.6 percent) 65.1 (±20.7 percent) 1.73 (±11.2 percent)

c ASTM D 3916-84 5 6.88 (±2.4 percent) 81.4 (±5.1 percent) 1.23 (±6.5 percent) c Special grips 3 - 103.0 (±5.1 percent) - D ASTM D 3916-84 5 5.77 (±2.2 percent) 81.3 (±2.2 percent) 1.79 (±3.8 percent)

* I ms1 = 6.9 GPa. t I ksi = 6.9 MPa.

section. Coefficients of variation are also included. The fol- lowing observations are pertinent for each bar type:

1. Type A-These bars have an additional layer consisting exclusively of matrix material around the fibers. This layer would tend to separate and initiate bar failure, usually close to the grips. Subsequent to this separation (which resulted in a sudden stress drop), the bars could be reloaded to loads close to the ultimate. In all five tests, longitudinal bar split- ting was observed, which could be caused by a weak fiber- matrix interface. 30 Additional tests using the special grips showed reduced grip effects and yielded higher ultimate stress values.

2. Type B-The indentations produced sharp kinks in the longitudinal bar fibers. Bar failure was initiated by cracking at the kinks.

3. Type C-During the tests, it was observed that defor- mations would break and separate from the bar surface. In two cases, failure initiated at the grips. In all tests, longitudi- nal bar splitting was observed. Successive tests with the spe- cial grips showed a significant increase in ultimate stress, to 103 ksi (710 MPa). Previous tests on these bars following

ASTM D 638 yielded an average ultimate stress of 100 ksi (690 MPa) and elastic modulus of 6.1 msi ( 42 GPa). 17

4. Type D-As in Type B, bar failure usually initiated at the indentations. Previous tests on two 3/4-in. (19-mm) cou- pons following ASTM D 638 were reported to yield ultimate stresses of 77.6 and 84.6 ksi (535 and 583 MPa), similar to the current average value. 31

Bond test results: Complete bond stress-slip curves

Tests 1 through 5 for each bar type correspond to confin- ing pressures at the bar surface of 500 to 4500 psi (3 .4 to 31 MPa) in 1000-psi (6.9-MPa) increments, as mentioned earli- er. The slip specified in this section is the average measure- ment of the two L VDTs located on the loaded end of the bar. This measurement was corrected for the unbonded length of the reinforcing bar and the gage offset. Fig. 4 shows longitu- dinal cracks for all four types under a confining stress of 500 psi (3.4 MPa). Fig. 5 shows the complete bond stress-versus- loaded-end slip response. If the slip at the unloaded end was included in Fig. 5, it could scarcely be differentiated from the

500 psi

Fig. 4-Longitudinal cracks

280 ACI Materials Journal I May-June 1995

2.0

n 0.8 z D rQ

0.4

2.0

~

~ 1,6 (/) (/)

w 1.2 C>: f- (/)

n 0.8 z 0

"'

SLIP C\1M) s 10 15

,-----,----,--,--,.-----~~,- -----,--

TYPE A TEST

No

~ ~ ~~ 32500

-~ 4 3:100

PAlliAL STRESS

CPSD 500

1500

~~ 5 4500

2-------- -~----- ---~

~---~-

0.2 04

sur ON) a)

SLIP CM\1)

0.6

20 15

bj

D z

10 tj

"' __, A; rc: V1 V1

5 "' 0 0

0.8

5 10 15 20 ,-----,---,-----,----,---,-~-- ,----,---~ 15

0.2 0.4 SLIP (IN)

c)

TYPE C TEST

No 1 2 3 4 5

0.6

RADJAL STRESS

(''SD 500

1500 2500 3500 4500

bj

0 z

10 t1 V1 - I AJ n V1 V1

5 :s: u 0

0.8

0

0.4

0

20

~ :.6

(/) v, w :.2 "" f- (/)

n 0.8 z CJ rQ

0.4

02

5

0.2

SLIP CMM) 10

0.4

SLIP c[~!)

b)

SLIP <M~IJ

15

TYPE 3 TEST

Nc 1 2 3 4

0.6

10 15

04 SLIP (]N)

d)

0.6

RADIAL STRESS

CPSD 500

1500 2500 3500 4500

20

bj

D z

10 0 V1 -j

;Q Cl V1 (/)

5 :;2

0.8

20 15

u 0

bj

D z

10 0

0.8

(/) -; ;Q n (/)

vo

Fig. 5-Complete bond stress-slip curves: (a) Type A; (b) Type B; (c) Type C; (d) TypeD

loaded-end slip (both slips only differ initially, as explained in the next section).

1. Type A-In Test 5 of Type A [missing from Fig. 5(a)], the concrete cylinder appeared weaker and those results were discarded. Although the concrete specimen was subjected to a confining pressure of 4500 psi (31 MPa) at the bar surface in excess of the uniaxial compressive strength, in most cases this did not result in crushing (due to the multiaxial confine- ment). The response is qualitatively similar to that of steel reinforcing bars25 -27 in that the bond stress peaks rapidly, then decays smoothly up to a slip approximately equal to the clear deformation spacing, and finally remains constant thereafter. Bond strength increased threefold with confine- ment. The concrete in front of the deformations was crushed and sheared, but the bar surface was damaged as well, re- flecting the relatively low shear strength of the composite.

2. Type B-Bond strength also increased threefold with confining pressure. A large scatter was present: for Test 5, the bar exhibited much greater indentations yielding an un- expectedly high bond strength, and peak slips varied signifi- cantly

3. Type C-In these tests, the concrete cylinder never split, so most of the confining pressure was carried by the concrete cylinder as hoop stress. Consequently, the response

ACI Materials Journal I May-June 1995

was almost unaffected by confinement. The response exhib- its a high initial adhesion followed by a constant bond stress for all five tests. For this type, it was observed that the defor- mations initially glued to the bar would break and separate from the bar during the test. 32 Subsequently, bond resistance was only provided by friction between the bar itself and the concrete. Since the adhesion between bar and deformations can be variable and is not easily determined, this type of de- formation is not recommended.

4. Type D-In two of these specimens, the protective veil was sheared off the bar surface. Bond strength increased smoothly up to fourfold with increasing confinement. Bond stresses peaked at relatively high slips and remained high thereafter. This is an advantage, since it allows for more stress redistribution in the structure and more energy dissipa- tion. This indentation geometry appeared most efficient in terms of bond response.

5. Confinement effects on bond strength-Fig. 6 compares these results with previous data obtained for steel reinforcing bars.25 -27 It is seen that the maximum normalized bond strengths (bond strength/tensile strength) obtained are simi- lar in magnitude (between 4 and 5), although they are ob- tained for higher confinement values (confining stress/ tensile strength). For a given confinement, the bond strength

281

developed by a steel bar is between 1.2 and 1.5 times higher than that of the equivalent FRP bar.

6. Effect of indentation depth-Two additional tests for Types B and D were performed to evaluate effects of inden- tation depth on the results.

For Type B, a bar was chosen with a low indentation depth of 0.022 in. (0.56 mm). This test (3a) was carried out at a confinement of 2500 psi (17 .2 MPa) to compare with Test 3, where the bar had an average indentation depth of 0.057 in. (1.45 mm)[Test 5 indentation depth was 0.088 in. or (2.24 mm)]. Test 3a showed a bond strength decrease of about 18 percent when compared to Test 3. 32

Similarly, for TypeD, a second test (2a) was carried out at a confinement of 1500 psi (10.3 MPa). The bar in Test 2a had an indentation depth of 0.051 in. ( 1.3 mm) versus 0.071 in. (1.8 mm) for Test 2. Test 2a showed a corresponding de- crease in bond strength of 16 percent.

Although deeper indentations may yield higher bond strengths, they also promote lower tensile strengths due to the resulting kinks in the fibers. An outer, helicoidal layer of fibers (as in a cable) could yield deformations without sharp kinks.

Bond tests results: Initial bond stress-slip curves On loading, the two L VDTs on the loaded end of the rein-

forcing bar begin to measure displacement; however, the in- ternal L VDT on the unloaded end does not record any movement for some time. During this initial phase, the slip is nonuniform within the five-lug test section of the reinforc- ing bar. This contrasts with the end of the test, where all three L VDTs record practically equal slips. Reference 29 docu- ments evolution of the slip distribution along the test length. For the beginning of loading, it indicates that the average slip within the test length is approximately equal to

where s 1 = average slip from two loaded-end L VDTs s2 = slip from unloaded-end (internal) L VDT

In all cases, initial bond stress-average slip curves showed some adhesion, i.e., a bond stress at zero average slip, be- tween 100 and 300 psi (0.7 and 2.1 MPa). Beyond this adhe- sion, the slope of the curve appears to increase with higher confinement. 32

Bond test results: Bond stress-radial displacement curves

On first loading, the reinforcing bar deformations exert ra- dial pressures against the surrounding concrete until the lat- ter splits longitudinally. If external confinement is provided (as in the present case), the reinforcing bar tends to slowly open the concrete cracks until enough space is created for de- formations to advance, via a combination of sliding, concrete crushing, and superficial bar damage. Eventually, after enough combined damage has taken place, a radial contrac- tion may occur. 25 -27 To capture this dilation/contraction, the ring opening was measured, which is converted to a radial displacement at the outer surface of the concrete cylinder specimen. The bond stress-versus-radial displacement curves obtained are shown in Fig. 7.

282

The following was observed for each reinforcing bar type: 1. Type A-A response qualitatively similar to that of

steel reinforcing bars25· 27 is obtained, where radial dilation takes place, mainly past the peak stress, then a fairly constant maximum opening is reached, usually followed by a contrac- tion. The contraction is most visible in Test 1, whereas the constant maximum opening is more obvious in Tests 2 and 3. The maximum dilation reached decreases rapidly with in- creasing confining pressure. In Test 4, external pressure is high enough to prevent any dilation and allows only for some contraction at the end of the test. For this, and higher, exter- nal pressures, longitudinal cracks do not open and some of the confinement is carried via hoop stresses. Bond failure oc- curs via lateral contraction of the bar and superficial bar damage, in addition to crushing/shearing of the concrete in front of the deformations. It is expected that it will not be possible to significantly exceed the bond strength attained by further increasing the external confinement.

2. Type B-A similar response is obtained. Larger dila- tions are obtained due to the presence of large indentation depths.

3. Type C-No dilation is apparent, due to the fact that the concrete cylinders never split.

4. Type D-No contraction is apparent at the end of the tests, possibly due to the limited slip attained (relative to the indentation spacing). Some scatter is present, as evidenced by the fact that Test 3 has a greater maximum dilation than Test 2. No dilation is present for higher confining pressures.

ANALYTICAL MONOTONIC ENVELOPE An analytical expression for the monotonic bond stress-

slip curve would be useful to extend the present results to sit- uations with generic confinement and different concrete strength. This expression is derived in a two-step procedure. First, the peak on the bond stress-slip curve is defined as a function of confinement as follows

where

'tm

~ 68

-t- 90

-*- A

-4- B

.......... c -lf- D

( -Ccrlf,) 'tml j 1 = A + B 1 - e

= bond strength (peak bond stress)

:r !;s z w a: :0" Q z 03 m Q

~2 ~ .. ~~----------------------~ < :::1!1 ~ z 0~~~~--~~~~~--L-~~~

o 1 2 3 4 s 6 r 8 9 ~ n n NORMALIZED CONFINEMENT STRESS

Fig. 6-Bond strength: Comparison to previous steel results

ACI Materials Journal I May-June 1 995

\ l 1

Fig. 7-Bond stress-radial displacement curves: (a) Type A; (b) Type B; (c) Type C; (d) TypeD

cr = confining axisymmetric radial pressure ft = tensile strength Om slip at peak bond stress 0 nominal bar diameter A,B,C,D,E = nondimensional empirical constants for each bar type.

Second, the complete normalized bond stress-slip curve can be expressed as

where F,G =nondimensional empirical constants for each bar type.

The constants were evaluated for bar types A and D (Types B and C were not considered, B due to scatter, and C due to constant response), and also for the two types of steel bar from References 25 through 27 (with lugs inclined at 68 and 90 deg, respectively, with the longitudinal axis), and are reported in Table 3. These analytical fits are compared to the actual data for Type A in Fig. 8.

The proposed empirical formulas are limited to the ranges of pressures tested. They are useful for calibration of simple numerical models that can compute the bond stress-slip re- sponse as a function of radial stress. This may be accom-

ACI Materials Journal I May-June 1995

plished via bond-link, or node-tie elements, which can be viewed as two orthogonal springs connecting two nodes with identical coordinates. 33 However, a more complete represen- tation of bond phenomena should also be able to reproduce the radial dilation which accompanies slip, e.g., using inter- face elements.28 •29·*

CONCLUSIONS Tensile and bond properties for four types of FRP rein-

forcing bar with different deformation patterns were ana- lyzed experimentally. Local bond stress-slip and bond stress-radial displacement curves were obtained for various levels of axisymmetric radial confining pressure. The fol- lowing were observed:

1. Tensile tests using actual bar specimens (following ASTM D 3916) instead of coupons showed that deep inden- tations and resulting kinks in the longitudinal fibers will re- duce bar strength. Grip effects were found using the ASTM D 3916 setup, which were mitigated by using special grips. Significant variations in dimensions and properties were ap- parent for some reinforcing bars.

2. For the 3/ 4-in.-(19-mm)-diameter bars tested, ultimate strengths varied from 65 to 103 ksi ( 448 to 710 MPa) and the

Cox, J. V., "Development of a Plasticity Bond Model for Reinforced Concrete- Theory and Validation for Monotonic Applications," PhD thesis. University of Cali- fornia, Davis, Sept. 1994.

283

5

4 ~ T tJ) tJ) UJ a: Iii 3 0 z 0 CD 0 UJ N 2 :::::; <C ::::;: a: 0 z

oa--------L--------~-------L--------~----- 0 0.2 0.4 0.6 0.8

NORMALIZED SLIP

Fig. 8-Fit of Type A bond stress-slip data

Table 3-Analytical fit parameters

Bar type A B c Type A 1.00 9.04 0.05

TypeD 0.266 5.63 0.15

Steel 68-deg lugs 0.9 3.5 0.35

Steel 90-deg lugs 0.9 4.4 0.35

moduli of elasticity ranged from 4.1 to 6.9 msi (28 to 48 MPa).

3. Small surface deformations, about 5.4 percent of the nominal rebar diameter (i.e., similar to that of steel), are suf- ficient to yield maximum bond stresses up to five times the concrete tensile strength, similar to that obtained with steel reinforcing bars. Both surface deformations and indentations obtained by stressing an external helicoidal strand are ac- ceptable for bond purposes. Deformations merely glued to the surface are not recommended, since they may become unbonded and thereafter fail to provide any bond per se.

4. For an identical amount of confinement, bond strength for a steel bar is, on average, 1.2 to 1.5 times greater than that for an FRP bar (for the cases studied).

5. Large variations in indentation depths resulted in large variations in bond strength.

6. Bond strength can usually be increased threefold by in- creasing confining pressure.

ACKNOWLEDGMENT Funding and facilities for the present study were provided by the Naval

Facilities Engineering Service Center (formerly Naval Civil Engineering Laboratory), Port Hueneme, California. Support provided by Dr. T. A. Shugar and Mr. Gary Neal is gratefully acknowledged.

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2. Gustafson, D. P., "Epoxy Update," Civil Engineering, ASCE, V. 58, No. 10, Oct. 1988, pp. 38-41.

3. Darwin, D.; McCabe, S. L.; Hadje-Ghaffari, H.; and Choi, 0. C., "Bond Strength of Epoxy Coated Reinforcement to Concrete--An Update,"

284

D E F G

0.0270 0.00317 11.0 1.1

0.0633 0.02824 13.0 0.5

0.0279 0.00508 9.0 0.65

0.0071 0.00770 5.5 1.1

Serviceability and Durability in Construction Materials, Proceedings of the First Materials Engineering Congress, Denver, Aug. 1990, pp. 115-124.

4. Hadje-Ghaffari, H.; Darwin, D.; and McCabe, S., "Effects of Epoxy- Coating on the Bond of Reinforcing Steel to Concrete," SM Report No. 28, University of Kansas Center for Research, July 1991.

5. Ballinger, C. A., "Development of Composites for Civil Engineering," Proceedings of the Conference on Advanced Composite Materials in Civil Engineering Structures, ASCE, Las Vegas, 1991, pp. 288-301.

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