Effects of FRP-Concrete Interface Bond Properties on the Performance of RC Beams Strengthened in Flexure with Externally Bonded FRP Sheets

Transcription

1 Effects of FRP-Concrete Interface Bond Properties on the Performance of RC Beams Strengthened in Flexure with Externally Bonded FRP Sheets Hedong Niu 1 and Zhishen Wu 2 Abstract: Fiber reinforced polymer FRP sheets have been increasingly used as externally bonded reinforcements in the rehabilitation of concrete structures. The efficacy of the FRP bonding technology highly depends on the bond integrity between the FRP sheets and the concrete. The bond performance may directly influence the cracking of the concrete, whereas the presence of concrete cracks would impair the bond between the FRP sheets and the concrete. This paper aims to clarify the effect of interface bond properties on the performance of FRP-strengthened reinforced concrete RC beams in terms of concrete cracking, interface stress transfer, and failure mechanisms using nonlinear fracture mechanics based finite element analyses. To represent the typical crack patterns and capture the local interaction between FRP debonding and concrete cracking, a specially designed structural model with uniformly distributed cracking is used within the frame of the discrete crack approach. A detailed parametric study is performed to investigate the effects of interface bond properties in terms of stiffness, strength, fracture energy or toughness, and bond curve shape. It is concluded that bond fracture energy or toughness is the main parameter influencing the structural strength and ductility. This study may serve as a valuable reference for optimization of the FRP-concrete bond interface in practical applications. DOI: / ASCE :5 723 CE Database subject headings: Fiber reinforced polymers; Rehabilitation; Retrofitting; Concrete beams; Bonding; Cracking; Adhesives; Numerical analysis. Introduction In recent years, fiber reinforced polymer FRP composites, which have been widely and successfully used in aerospace, sports, and recreation industries, have seen a steadily increasing use as externally bonded reinforcement in the rehabilitation of concrete structures. Central to the FRP bonding technology is to ensure the integrity of the bond between the FRP and the concrete through which stresses can be appropriately transferred from the concrete to the FRP. Any failure in this stress transmission zone would invalidate such composite action and lead to a brittle, catastrophic failure prior to the expected gains. The bond performance between the FRP and the concrete may directly influence the stress transfer and the concrete cracking behavior, whereas the presence of concrete cracks would cause high stress concentrations or debonding between the FRP and the concrete and, in turn, 1 Postdoctoral Scholar, Dept. of Structural Engineering, Univ. of California, San Diego, La Jolla, CA ; formerly, JSPS Research Fellow, Dept. of Urban and Civil Engineering, Ibaraki Univ., Nakanarusawa , Hitachi , Japan corresponding author. hniu@ucsd.edu or hdniu@yahoo.com 2 Professor, Dept. of Urban and Civil Engineering, Ibaraki Univ., Nakanarusawa , Hitachi , Japan. Note. Associate Editor: Laura De Lorenzis. Discussion open until March 1, Separate discussions must be submitted for individual papers. To extend the closing date by one month, a written request must be filed with the ASCE Managing Editor. The manuscript for this paper was submitted for review and possible publication on October 11, 2004; approved on January 9, This paper is part of the Journal of Materials in Civil Engineering, Vol. 18, No. 5, October 1, ASCE, ISSN /2006/ /$ influence the bond performance. The interaction between the bond properties and the concrete cracking behavior is very complicated and directly influences the efficacy of the FRP strengthening. Therefore, the investigation of bond behavior and its effect is extremely important for the efficient application of FRP bonding technology. As far as the bond behavior of FRP sheets in concrete beams strengthened in flexure is concerned, it is generally accepted that debonding propagation resembles Mode II in-plane shear/ sliding fracture behavior in that FRP sheets are primarily loaded in tension and the adhesive layer is mainly in shear transferring stresses from the concrete to the FRP composites. Even for the case of diagonal flexural-shear or shear cracks, the induced debonding propagation is still mainly governed by the Mode II fracture behavior due to a small peel angle as shown by Niu and Wu In a strict sense, the debonding within the cover concrete may be associated with concrete Mode I tension/opening fracture and the shearing fracture behaviors. But it can still be considered as Mode II fracture behavior along the FRP-concrete interface Wu et al. 2002a. So considerable investigations into the Mode II bond behavior between FRP sheets and concrete have been done using simple shear tests Kamiharako et al. 1999; Yoshizawa et al. 2000; Nakaba et al or modified beam tests De Lorenzis et al as shown in Fig. 1. The detailed classification and review of the bond test methods can be seen in Chen et al and Ueda and Dai It is worth mentioning that different bond test methods and numerical modeling approaches were reviewed in detail by Ueda and Dai 2005 to characterize the bond behavior of the FRP-concrete interface under shear, tension, and a combination of shear and tension. Local bond-slip curves were identified from the experiments and schematically JOURNAL OF MATERIALS IN CIVIL ENGINEERING ASCE / SEPTEMBER/OCTOBER 2006 / 723

2 Fig. 3. Details of the studied FRP-strengthened RC beam Fig. 1. Bond test methods: a single-lap shear bond test; b doublelap shear bond test; and c bending-type shear bond test shown in Fig. 2. These curves are characterized by an ascending branch before reaching the local bond strength, followed by plastic debonding within the adhesive from the flexural bond test by De Lorenzis et al or softening behavior debonding within the concrete from shear bond tests by Kamiharako et al ; Yoshizawa et al ; Nakaba et al ; and Ueda and Dai 2005 up to an ultimate slip. Kamiharako et al and De Lorenzis et al did not find any effect from the concrete strength on the bond performance. But Nakaba et al and Ueda and Dai 2005 presented that local bond strength increases with the concrete strength. No matter what kind of interfacial constitutive law is adopted, the ultimate loadcarrying capacity of FRP-bonded joints can be predicted by the same simple equation Täljsten 1996; Wu et al. 2002b, which is only related to the FRP stiffness defined by multiplication of the elastic modulus and the thickness and interfacial fracture energy Fig. 2. Local bond-slip relationships result from different test methods defined by the area below the bond-slip curve. Yoshizawa et al found that local shear stress distribution, effective bond transfer length beyond which nearly no stress is transferred, and initiation and propagation of debonding could be well represented by the simplified model with three parameters: interfacial stiffness, k s, local bond strength, f, and interfacial fracture energy, G f b, as shown in Fig. 2. Little literature can be found concerning the interaction between concrete cracking and the FRP-concrete interface bond fracture behavior. Bizindavyi and Neale 1999 found that a crack in the concrete block at the loaded end may increase the stress transfer length in single-lap shear bond tests. Ueda et al identified that cracks may deteriorate the nearby bond properties in reinforced concrete RC tension members and pointed out that more data are needed to verify this phenomenon. Yang et al presented a linear elastic fracture mechanics based discrete crack finite element model to only simulate the concrete cover separation failure. They adopted a very complicated remeshing scheme to simulate the concrete cracking with no consideration of the tension softening behavior in the fracture process zone. In addition, no discussions were made on the effect of FRP-concrete interface bond properties. Kishi et al used threedimensional finite element model consisting of both discrete crack and smeared crack approaches to simulate the debonding behavior in the FRP-strengthened RC beams. Major cracks observed in the tests were simulated by the discrete crack model to capture the corresponding effects on the FRP-concrete interface bond behavior and such simulation was only aimed to represent the experimental phenomena. Some experimental attempts were made to use a flexible adhesive layer with a low shear modulus and high rupture strain to improve the flexural strengthening performance of FRP sheets Maeda et al. 2001; Gao et al However, not all the Table 1. Summary of Material Properties Materials Mechanical properties Values Concrete Young s modulus GPa 35.1 Compressive strength MPa 49.3 Tensile strength MPa 3.0 Tensile fracture energy N/mm 0.12 Poisson s ratio 0.13 Steel reinforcement Young s modulus GPa 210 D16 Yield strength MPa 364 D13 Yield strength MPa 358 CFRP sheets Young s modulus GPa 230 Tensile strength GPa Thickness mm Epoxy Young s modulus GPa 3.43 Poisson s ratio / JOURNAL OF MATERIALS IN CIVIL ENGINEERING ASCE / SEPTEMBER/OCTOBER 2006

3 Fig. 6. FEM model of the FRP-strengthened RC beam Finite Element Modeling Fig. 4. Constitutive relationships of concrete material: a linear tension softening model; b compressive response beams strengthened with modified adhesive exhibited improved performances and the improvement did not increase with the thickness of flexible adhesive. In this study, a nonlinear fracture mechanics-based discrete crack finite element analysis is performed on a carbon FRP CFRP -strengthened RC beam to gain a clear understanding of the influencing mechanisms of the FRPconcrete interface bond properties on the performance of RC beams strengthened in flexure with bonded FRP sheets. A CFRP-strengthened RC beam subjected to three-point bending Wu and Kurokawa 2002 is analyzed using the commercial finite element program DIANA TNO The beam was 150 mm wide, 200 mm deep, and 2,100 mm long, with 1,700 mm long axially oriented unidirectional CFRP sheets bonded to its full width. Deformed reinforcing bars were used in tension and compression. The geometric and reinforcement details of the beam are shown in Fig. 3. The mechanical properties of the materials are given in Table 1. The beam was observed to fail in debonding failure from intermediate flexural cracks. For simplicity, stirrups used to prevent the shear failure are not considered in the following simulations. To simulate the real response of the composite beam and to investigate the failure mechanisms caused by flexural cracks, it is important to accurately model the crack propagation behavior in the concrete, the local bond-slip behavior between reinforcing steel bar and the Fig. 5. Interfacial bond behaviors: a FRP-concrete interface; b steel-concrete interface Fig. 7. Mesh sensitivity study: a single localized crack pattern; b distributed crack pattern JOURNAL OF MATERIALS IN CIVIL ENGINEERING ASCE / SEPTEMBER/OCTOBER 2006 / 725

4 Table 2. FRP-Concrete Interfacial Parameters Used in Numerical Simulations Cases Initial stiffness, k s MPa/mm Interface bond parameters Bond strength, f MPa Fracture energy, G f b M/mm Interfacial stiffness ,000 Bond strength Interfacial fracture energy concrete, and the interfacial bond behavior of the FRP-concrete interface in addition to the constitutive behavior of the concrete, the steel and FRP sheets. Generally, there are two different approaches describing the concrete cracking behavior: The discrete crack and the smeared crack approach. In view of the fact that the smeared crack approach is incapable of modeling individual macrocracks and the interaction between concrete cracking and interfacial debonding, the discrete crack approach is used in this study. Possible flexural crack locations are predefined to be vertical along the depth of the beam with interface elements, which describe concrete cracking behavior in terms of a relation between the normal and shear tractions and the normal and shear relative displacements across the cracking plane. A very large initial penalty stiffness is assigned to interface elements to ensure inner continuity of the concrete prior to cracking. Under loading, a linear softening curve Fig. 4 a was employed to model Mode I cracking behavior of concrete, where f t =concrete tensile strength and G f c =Mode I fracture energy of the concrete. Unloading and reloading behaviors are modeled by a secant path. After cracking, no shear stress is assumed to be transferred along the crack surface. In order for the prevention of computational problems, the compressive response of concrete is assumed to follow the curve Fig. 4 b specified by JSCE 1996 but without the limitation of strain capacity. As reviewed previously, the simplified linear softening bond curve can be used to simulate the real FRP-concrete interface bond behavior Fig. 5 a. Macrodebonding is considered to occur when no stress can be transferred, or the energy required to create a unit area of debonding is met. The area under the curve is defined as the interfacial fracture energy G f b. The scheme of unloading and reloading is represented by the secant path. This model is capable of simulating the bond behavior regardless of whether debonding occurs within the concrete substrate or through the adhesive. The difference only lies in the choice of the parameters: local bond strength f, initial stiffness k s, and the fracture energy G f b. It should be noted that concrete flexural cracking near the extreme tensile fibers of the beam can damage the bond to FRP composites. Due to the scarcity of data, the deterioration of bond properties caused by cracking in the concrete was not considered here. Reinforcing steel is treated as a linear elastic-perfectly plastic material. And the bond behavior between the concrete and the deformed steel rebar is assumed to follow the experimental data from Morita et al. 1967, as shown in Fig. 5 b. Unidirectional FRP sheets generally behave in a linear elastic fashion until rupture. Fig. 8. Effect of interfacial stiffness in the case of a single crack: a load-deflection response; b midspan steel stress versus deflection; c midspan FRP stress versus deflection; d FRP stress distributions at the debonding initiation; and e FRP stress development k s =160 MPa/mm 726 / JOURNAL OF MATERIALS IN CIVIL ENGINEERING ASCE / SEPTEMBER/OCTOBER 2006

5 play a role in transferring stresses from the concrete to FRP sheets by shear, which can be modeled using zero-thickness interface elements. Similarly, the bond between the reinforcing steel and the concrete is modeled with zero-thickness interface elements. The flexural cracks represented by thick lines are modeled by zero-thickness interface elements at a spacing of L c with predefined cracks observed in the experiment. Based on experimental observations, uniformly distributed cracks with a crack spacing of L c =56.3 mm are assigned to the beam in this study. Although flexural cracks are predefined at a spacing of L c =56.3 mm, different crack patterns may be produced depending on the FRPconcrete interface bond properties. As a comparison, a single crack pattern is also presented to give a clear understanding of effects of FRP-concrete interface bond properties on the debonding behavior without the consideration of cracking interaction. In order to obtain the postpeak behavior of the strengthened beam, the line search algorithm, which is proved to be very robust and efficient as compared to Newton or quasi-newton method in the incremental-iterative solution for the structures with strong nonlinearities, is used in the present investigation. A sensitivity study was performed to determine the appropriate mesh density by using the average bond parameters identified by Yoshizawa et al : f =8.0 MPa, k s =160 MPa/mm, and G f b =1.2 N/mm. As shown in Fig. 7, the structural performance is overestimated with the use of a coarse mesh. The medium mesh can provide a satisfactory result as compared to the refined mesh or the experimental result Wu and Kurokawa So the medium mesh is used for the following analyses. A significant difference between the experimental data and the prediction lies in the ductility of the structure. This may be due to two factors: 1 elastic-perfectly plastic behavior is assumed for the concrete compressive behavior and 2 the impact resulted from the debonding, which may fail the structure, is not accounted for in the analyses. However, this should not be a problem for investigating the effects of the bond properties on the strengthening performance under the same assumption. Results and Discussions Fig. 9. Effect of interfacial stiffness in the case of the distributed crack pattern: a load-deflection response; b steel stress distributions; and c FRP stress distributions Due to symmetry only half of the beam is modeled with appropriate boundary conditions. The load is applied in displacement control. As shown in Fig. 6, the concrete is modeled with four-node quadrilateral plane stress elements, whereas reinforcing bars and FRP sheets are modeled using two-node linear truss elements connected to the concrete through zero-thickness line interface elements. Herein, the adhesive is assumed to mainly As discussed previously, the simplified bond model bilinear relationship may be used to characterize the bond behavior between the FRP sheets and the concrete. According to test data Kamiharako et al. 1999; Yoshizawa et al. 2000; De Lorenzis et al. 2001; Nakaba et al. 2001, initial interfacial stiffness was found to be over 30 MPa/ mm, local bond strength was from 3 to 12 MPa and interfacial fracture energy was in the range of N/mm depending on some factors such as surface preparation condition, adhesive type, failure path, and test method. In this study, a series of bond parameters are chosen in Table 2 to overlap the realistic bond performance with an aim to investigate the complicated interaction between interfacial bond failure and cracking in the concrete. In addition, the effect of the choice of bond curve for the realistic behavior is also studied on the overall strengthening performance. Effect of Interfacial Stiffness, k s Interfacial stiffness has a direct effect on the stress transfer rate from the concrete to the FRP sheets. After concrete cracking, low interfacial stiffness may result in a slow stress flow into FRP sheets causing the early yielding of the tension steel and a JOURNAL OF MATERIALS IN CIVIL ENGINEERING ASCE / SEPTEMBER/OCTOBER 2006 / 727

6 Fig. 10. Effect of interfacial bond strength on the structural response: a load-deflection response single crack pattern ; b load-deflection response distributed crack pattern ; c midspan shear stress versus deflection single crack pattern ; d FRP stress distributions at the debonding initiation single crack pattern ; e steel stress development for the of f =0.5 MPa distributed crack pattern ; and f steel stress development for the case of f =16.0 MPa distributed crack pattern little reduction in the overall structural stiffness. To clearly demonstrate the effect of FRP-concrete interfacial stiffness, overall structural response and stress transfer in the tension steel and FRP sheets are presented for the case of a single crack. Although interfacial stiffness may have a localized effect on the steel yielding Figs. 8 b and c, it has no effect on the overall structural behavior Fig. 8 a in terms of stiffness and ultimate load-carrying capacity if keeping other parameters constant. The yield load may be enhanced to a lesser extent with the increase of interfacial stiffness but the debonding point remains almost the same. Fig. 8 d shows the same ultimate FRP stress obtained at the initiation of debonding at midspan despite the variation in interfacial stiffness, after which debonding propagates from the midspan to the end of the FRP without the change of the FRP stress Fig. 8 e. This means that interfacial stiffness does not influence the ultimate load. But it should be noted that low stiffness may result in a longer stress transfer length Fig. 8 d, which may be helpful to relieve stress concentrations in the FRP sheets or steel. In practice, RC structures strengthened with FRP sheets exhibit distributed cracks. The interaction between concrete cracking and interfacial debonding may complicate the effect of interfacial stiffness. However, it is similarly concluded that interfacial stiffness has a very slight effect on the yield load but has no effect on the ultimate load-carrying capacity Fig. 9 a. If considering that the variation of the adhesive thickness corresponds to changing the interfacial stiffness, this finding agrees well with the experimental observations that adhesive thickness had no effect on the structural behavior Hollaway and Leming As shown in Figs. 9 b and c, it is confirmed that low interfacial stiffness may result in a more uniform distribution in both steel and FRP sheets, which may relieve stress concentrations at cracks. As noted previously, quantitative evaluation of the detrimental effect of cracking or stress concentrations on the bond is still unavailable and no deterioration of the bond properties is considered in this study due to concrete cracking. However, stress concentrations together with the bond deterioration by cracking might fail the structure in practice. So it may be helpful to use more flexible adhesive for the effective and efficient applications of FRP bonding technology. Effect of Interfacial Bond Strength, f As seen in Figs. 10 a and b, high interfacial bond strength may present a high yield load and a high ultimate load. Low interfacial bond strength has a low stress transfer limit thus resulting in the early yielding of the tension steel. If keeping other parameters constant, high bond strength presents more brittle stress transfer behavior, which results in almost no shear stress at the yielding of steel in the case of f =16 MPa, and thus high bond strength may result in early local debonding Fig. 10 c. In addition, high bond strength presents a short stress transfer length as shown in Fig. 10 d. With the interaction of concrete cracking, high bond strength shows high load-carrying capacity without any reduction in the structural ductility. As shown in Figs. 10 e and f, high bond strength 16.0 MPa yields a close crack spacing as compared to low bond strength 0.5 MPa. This suggests that high bond strength be used for distributing cracks and making full use of FRP sheets in the strengthening of concrete structures. Effect of Interfacial Fracture Energy, G f b The larger interfacial fracture energy the harder debonding becomes. With the increase of interfacial fracture energy, the ultimate load-carrying capacity and the structural ductility can be enhanced, as shown in Figs. 11 a and b. Low interfacial fracture energy may result in early debonding at midspan Fig. 11 c and limit the transferable load to the FRP sheets leading to the early yielding of the tension steel Fig. 11 d. Seen from Figs. 11 e and f, it is demonstrated that high interfacial fracture energy yields a large stress transfer length and a high ultimate FRP stress. With 728 / JOURNAL OF MATERIALS IN CIVIL ENGINEERING ASCE / SEPTEMBER/OCTOBER 2006

7 Fig. 11. Effect of interfacial fracture energy on the structural response: a load-deflection response single crack pattern ; b load-deflection response distributed crack pattern ; c midspan interface shear stress versus deflection single crack pattern ; d midspan steel stress versus deflection single crack pattern ; e interfacial shear stress distributions at the debonding initiation single crack pattern ; f FRP stress distributions at the debonding initiation single crack pattern ; g G f b =0.2 N/mm distributed crack pattern ; and h G f b =2.0 N/mm distributed crack pattern JOURNAL OF MATERIALS IN CIVIL ENGINEERING ASCE / SEPTEMBER/OCTOBER 2006 / 729

8 Conclusions Fig. 12. Different bond curves with the same fracture energy of 1.2 N/mm consideration of the interaction of multiple cracks, high interfacial fracture energy distributes concrete cracks more effectively and results in a more uniform stress distribution in the tension steel Figs. 11 g and h, which is very similar to the case of high interfacial bond strength. Effect of Bond Curve Shape As reviewed previously, two typical curves are observed in either simple shear tests or flexural tests: A linear softening curve within the cover concrete or a plastic curve in the adhesive Fig. 2. Herein four different bond curves with the same interfacial fracture energy Fig. 12 are used to investigate the effect of bond curve shapes on the structural performance. As shown in Fig. 13, it can be concluded that the bond curve shape has nearly no effect on the yield load and the ultimate load if the same fracture energy is given. This also confirms that real bond behavior can be simplified using the linear softening curve or other simple models in structural design and analysis. Actually, the change of bond shape may be equivalent to the change of interfacial stiffness. In the present study, a specially designed finite element model based on the discrete crack approach is used to clarify the effects of the adhesive bond properties on the strengthening performance of FRP sheets, which is intrigued by experimental attempts made Maeda et al. 2001; Gao et al with the use of a flexible adhesive to improve the FRP strengthening performance. The adhesive layer is mechanically represented by a medium for transferring stresses from the concrete to the FRP sheets, which is characterized by interfacial stiffness, bond strength, fracture energy, and curve shape. Through performing a parametric study on the beam having the capability to reproduce different crack patterns and simulate the interaction between concrete cracking and interface debonding, the following conclusions can be drawn and may be used as a reference for the choice of the adhesive in practical application: 1. Interfacial stiffness might have insignificant effect on the structural stiffness, yield load, and ultimate load-carrying capacity. Relatively low stiffness may be helpful to distribute more uniform stresses in both steel and FRP sheets, which may help to relieve local stress concentrations and reduce the likelihood of debonding in practice. 2. Interfacial bond strength influences the yield load and to a less extent, the ultimate load-carrying capacity. Though high bond strength may produce the early local debonding in the case of a single crack, no such adverse effect can be found in practice due to interaction between cracks. High bond strength may be helpful to distribute cracks and thus increase the effectiveness of FRP strengthening. 3. Interfacial fracture energy is the main parameter influencing the strengthening performance in terms of the yield load, ultimate load-carrying capacity, and ductility. High interfacial fracture energy can be used to better distribute cracks and enhance the yield and ultimate loads. 4. Local bond shape has nearly no effect on the overall strengthening performance. Any simplified bond model with the same fracture energy may make no difference in the design or assessment of the FRP strengthened structural system. Acknowledgments The partial financial supports from the National High Technology Research and Development Program of China 863 Program under Grant No. 2001AA and the Joint Research Fund for Overseas Chinese Young Scholars of National Natural Science Foundation of China Grant No are gratefully acknowledged. References Fig. 13. Effect of bond curve shape on the load-deflection response: a single crack pattern; b distributed crack pattern Bizindavyi, L., and Neale, K. W Transfer lengths and bond strengths for composites bonded to concrete. J. Compos. Constr., 3 4, Chen, J. F., Yang, Z. J., and Holt, G. D FRP or steel plate-toconcrete bonded joints: Effect of test methods on experimental bond strength. Steel Compos. Struct., 1 2, De Lorenzis, L., Miller, B., and Nanni, A Bond of FRP laminates to concrete. ACI Mater. J., 98 3, Gao, B., Leung, W. H., Cheung, C. M., Kim, J.-K., and Leung, C. K. Y. 730 / JOURNAL OF MATERIALS IN CIVIL ENGINEERING ASCE / SEPTEMBER/OCTOBER 2006

9 2001. Effects of adhesive properties on strengthening of concrete beams with composite strips. Proc., Int. Conf. on FRP Composites in Civil Engineering, Hong Kong, Hollaway, L. C., and Leming, M. B Strengthening of reinforced concrete structures using externally-bonded FRP composites in structural and civil engineering, Woodhead Publishing Limited, Cambridge, U.K. Japan Society of Civil Engineers JSCE standard specification for design and construction of concrete structures. Tokyo. Kamiharako, A., Shimomura, T., Maruyama, K., and Nishida, H Stress transfer and peeling-off behavior of continuous fiber reinforced sheet-concrete system. Proc., 7th East Asia Pacific Conf. on Structural Engineering and Construction, Kochi, Japan, Kishi, N., Mikami, H., and Zhang, G Numerical analysis of debonding behavior of FRP sheet for flexural strengthening RC beams. JSCE Journal of Material, Concrete Structures and Pavements, , Maeda, T., Komaki, H., Tsubouchi, K., and Murakami, K Strengthening behavior of carbon fiber sheet using flexible layer. Trans. Jpn. Concr. Inst., Sapporo, Japan, 23 1, Morita, S., Muguruma, H., and Tomita, K Fundamental study on bond between steel and concrete. Transaction of the Architectural Institute of Japan, 131 1, 1 8. Nakaba, K., Kanakubo, T., Furuta, T., and Yoshizawa, H Bond behavior between fiber-reinforced polymer laminates and concrete. ACI Struct. J., 98 3, Niu, H. D., and Wu, Z. S Peeling-off criterion for FRPstrengthened R/C flexural members. Proc. Int. Conf. on FRP Composites in Civil Engineering, Hong Kong, Täljsten, B Strengthening of concrete prisms using the platebonding technique. Int. J. Fract., 82, TNO Building and Construction Research DIANA-8 user s manual, TNO DIANA BV, Delft, The Netherlands. Ueda, T., and Dai, J Interface bond between FRP sheets and concrete substrates: Properties, numerical modeling and roles in member behavior. Prog. Struct. Eng. Mater., 7 1, Ueda, T., Yamaguchi, R., Shoji, K., and Sato, Y Study on behavior in tension of reinforced concrete members strengthened by carbon fiber sheet. J. Compos. Constr., 6 3, Wu, Z. S., and Kurokawa, T Strengthening effects and effective anchorage method for flexural members with externally bonded CFRP plates. Japan Society of Civil Engineers, J. Materials, Concrete Structures and Pavements, , Wu, Z. S., Yin, J., Ishikawa, T., and Iizuka, M. 2002a. Interfacial fracturing and debonding failure modes in FRP-strengthened concrete structures. Proc. 4th Joint Canada-Japan Workshop on Composites, Vancouver, Canada, Wu, Z. S., Yuan, H., and Niu, H. D. 2002b. Stress transfer and fracture propagation in different kinds of adhesive joints. J. Eng. Mech., 128 5, Yang, Z. J., Chen, J. F., and Proverbs, D Finite element modelling of concrete cover separation failure in FRP plated RC beams. Constr. Build. Mater., 17, Yoshizawa, H., Wu, Z. S., Yuan, H., and Kanakubo, T Study on FRP-concrete interface bond performance. Japan Society of Civil Engineers, J. Material, Concrete Structures and Pavements, , JOURNAL OF MATERIALS IN CIVIL ENGINEERING ASCE / SEPTEMBER/OCTOBER 2006 / 731