LOCAL BOND STRESS SLIP RELATIONS FOR FRP SHEETS-CONCRETE INTERFACES

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1 See discussions, stats, and author profiles for this publication at: LOCAL BOND STRESS SLIP RELATIONS FOR FRP SHEETS-CONCRETE INTERFACES Conference Paper June 3 DOI:.4/ _ CITATIONS 4 READS 347 authors: Jian-Guo Dai The Hong Kong Polytechnic University 34 PUBLICATIONS,45 CITATIONS SEE PROFILE Tamon Ueda Hokkaido University 37 PUBLICATIONS,59 CITATIONS SEE PROFILE Some of the authors of this publication are also working on these related projects: Concrete-PCM interface preformance View project Bond mechanics of FRP-to-concrete interfaces View project All content following this page was uploaded by Jian-Guo Dai on 3 May 6. The user has requested enhancement of the downloaded file.

2 FRPRCS-6, Singapore, 8- July 3 Edited by Kiang Hwee Tan C World Scientific Publishing Company LOCAL BOND STRESS SLIP RELATIONS FOR FRP SHEETS-CONCRETE INTERFACES J.G. DAI AND T. UEDA Division of Structural and Geotechnical Engineering, Hokkaido University Kita 8 Nishi 5, Kita-ku, Sapporo 6-88, Japan Both increasing FRP stiffness and decreasing adhesive s shear stiffness can enhance the interfacial performance of FRP sheets bonded to concrete. However, in comparison with the former way, the latter one can improve the interfacial fracture energy due to the good toughness and nonlinearity of low shear stiffness adhesives. As a result, the high strength of FRP material can be utilized more efficiently. Depending on the fracture energy and the experimentally obtained strain distributions of FRP, this paper applied an optimum back-calculation method to propose a nonlinear interfacial bond stress-slip model, in which the effects of all interfacial components can be included. All the necessary parameters serving for the model are the fracture energy and two other empirical constants α and β, which govern the ascending and descending parts of the interfacial bond-stress slip curves respectively. Analytical results based on the proposed model show good agreement with the experimental ones. Keywords: bond stress-slip model, interfacial fracture energy, FRP stiffness, shear stiffness of adhesive INTRODUCTION The interfacial bond between FRP and concrete plays a critical role on maintaining the mechanical performances and durability of FRP strengthened concrete structures. Epoxy adhesive bonding system has proven to be an efficient way to transfer the stresses durably between FRP and concrete. However, unexpected premature interfacial fracture always happens inevitably due to the local shear stress concentration. In addition, a lot of past studies (see Ref.) indicate that the existence of effective bond length makes the interfacial load be transferred only in a limited distance. All these factors lead to the wasteful way of utilizing FRP materials in consideration of their advantages but high cost. Especially, when the amount of FRP material is increased in use, the strength of FRP materials available for design decreases significantly. Therefore, to improve the bonding performances between FRP and concrete is an important task facing to the FRP strengthening technology. Plenty of research work related to evaluating the interfacial performances,

3 44 FRPRC-6: Bond Behaviour which are affected by concrete strength, concrete surface processing, FRP stiffness, bond length, freezing and thawing and so on, has been carried out. Comparatively, how to optimize the using of adhesives was seldom studied. And in general, the high rather than low stiffness adhesives were selected in the past studies probably due to the lack of commercial offers and the criteria of ensuring non-adhesive failure. Different from the previous studies, one of the objectives in this study is to observe the effects of lower shear stiffness epoxy adhesives on the interfacial fracture mechanisms. Correspondingly, in order to simulate and predict the interfacial bond behaviors between FRP sheets and concrete precisely, to propose a reasonable interfacial constitutive model is another target. EXPERIMENTAL PROCEDURES A common single-lap pullout test setup as described in the previous studies was applied in this study. Three types of FRP materials (CFRP, AFRP and GFRP) and four types of epoxy adhesives (FR-E3P, SX-35, CN- and primer FP-NS) were used. The mechanical properties of FRP are shown in Table. To evaluate the properties of adhesives and get the detailed geometrical information of all adhesive components, tensile coupon tests for adhesives were carried out according to the test specification JIS K (the section area of adhesive specimens is 6 mm and the marked distance for measuring the deformation is 8 mm). Meanwhile, the FRP sheets attached with a thin layer of failed concrete were processed after the pullout tests. From their photos taken under microscope as shown in Fig., the thickness of every bonding layer (primer layer, adhesive layer and first resin matrix layer) can be measured. Fiber layer Resin matrix Adhesive layer P(N) FR-E3P and FP-NS SX-35 Primer layer Interlocking layer CN- δ (mm) Attached concrete Fig. Microscopic observations of FRP sheets after test 5 5 Fig. Load~deformation curves of adhesives

4 Bond Stress Slip Relationship for FRP-Concrete Interfaces 45 The obtained load-deformation curves of adhesives and the mechanical properties are described in Fig. and the Table. respectively. To keep same concrete strength for all specimens, ready-mixed early strength concrete with the compressive strength of 35MPa was prepared. The sheet bonding system was applied in the present study. However, the resins used in the adhesive layer (see Fig.) and in the matrix of FRP materials are different. Adhesive FR-E3P, which is commercially used as the resin matrix and the bonding adhesive for carbon fiber sheets, acted as the resin matrixes in all specimens. To observe the whole peeling-off process, the bond length of 3 mm was applied in all specimens. Table Mechanical properties of FRP materials Tensile Elasticity strength modulus (MPa) (GPa) (mm) Fiber Type Density of Fiber (g/m 3 ) Design thickness Elongation (%) Carbon FTS-C Aramid AT AT Glass FTS-GE Table Mechanical properties of adhesives Types of adhesives CN- SX-35 FR-E3P FP-NS (Primer) Mixing ratio (resins/hardener by weight) : : : : Elastic modulus (GPa) Tensile strength (MPa) Flexural strength (MPa) EXPERIMENTAL RESULTS All observed imum loads and imum slips at loading points of FRP sheets-concrete interfaces are shown in Table.3. The slips at the loading points of bond areas are obtained through integrating the strains measured continuously along the FRP sheets. The shear stiffness of adhesive (shear modulus thickness) is related to the shear force and deformation in adhesive and can be calculated as follows 3 : G G p G a r =, E p G p t a G p t r + G r t =, E r G r = () p ( + γ p ) ( + γ r ) Where: E P, E r ; t p, t r and γ p, γ r are the elasticity modulus, thickness and Poisson ratio of primer and resin layer respectively. Fig.3 and Fig.4 show the experimental load ~ loaded end slip relations. The points circled are considered to be correspondent to initial peeling, because after that the overall interfacial stiffness changes significantly. But for specimen CR3L with the softest adhesive (in Fig.4), no obvious change to overall stiffness was observed. The reason will be explained later.

5 46 FRPRC-6: Bond Behaviour Table3 Details of specimens and test results Codes of specimens E r t E r p t p G a / t Failure a f f s P G u f type * (GPa) (mm) (GPa) (mm) (GPa/mm) (GPa-mm) (mm) (kn) (N/mm) CRL CF CRL CF CRL CF CRL CF CR3L >3 >.8 FF CRL CF CRL CF CRL CF CRL CF CRL CF CR3L FF CR3L FF CRL CF CRL CF CRL CF CRL CF CR3L CF CRL CF GRL FF GRL CF GRL CF GRL CF GRL CF GR3L >3.4 >. FF ARL CF ARL CF ARL CF ARL CF AR3L CF R L The number of the FRP sheets plies Adhesive type;, and 3 mean FR-E3P, SX-35 and CN- respectively FRP type, C, G and A mean carbon, glass and aramid respectively. Failure type: CF: Concrete failure; FF: FRP fracture Load(kN) Concrete crack propagation Initial peeling CRL CRL CRL Slip(mm) Fig.3 Interfacial load-slip relationships and effect of FRP stiffness Load(kN) FRP fracture Initial peeling CRL CRL CR3L Slip(mm) Fig.4 Interfacial load-slip relationship and effect of adhesive stiffness

6 Bond Stress Slip Relationship for FRP-Concrete Interfaces 47 It is indicated that both initial peeling and ultimate interfacial loads increase with the FRP stiffness (elasticity modulus thickness). The initial peeling happens at almost the same slip values (see Fig.3). This fact can be understood as follows: higher FRP stiffness leads to lower local strain level but longer load transfer length at initial peeling. Comparatively, lower FRP stiffness leads to higher local strain but shorter load transfer length 4. So the overall slip value, which is the integration of the FRP strains along the load transfer length, may be similar in both cases. From the initial peeling off points to the macro interfacial crack propagation points or the imum interfacial load points (marked with ellipses), the overall interfacial stiffness decreases more slowly when the stiffness of FRP stiffness is lower. Many experimental studies show that the imum local bond stress increases but the strain of FRP sheets at peeling decreases with increasing the FRP stiffness,3,5. In other words, concrete prefers fracture at higher stress but lower strain level when the high stiffness FRP is used in the interfaces. This higher bond stress is accompanied by less interfacial softening ductility. (And vice versa.) The whole interfacial fracture energy hardly changes irrespective of FRP stiffness as shown later. The effects of adhesive layers on the load-slip curves are shown in Fig.4. It can be seen that low shear stiffness adhesives can lead to higher initial peeling and ultimate interfacial loads. The overall interfacial stiffness is greater if the adhesive is stiffer before the initial peeling off. After that, the overall interfacial stiffness decreases significantly in the case of using stiffer adhesive. However, it does not decrease obviously when the softer adhesive is used. And finally, the progressive interfacial softening is interrupted by the FRP fracture (see CR3L in Fig.4). As the authors reported previously, the lower shear stiffness adhesives increase the effective bond length significantly. As a result, the local peeling does not affect the overall interfacial stiffness obviously in comparison with the cases when higher shear stiffness adhesives are used. These different interfacial fracture mechanisms affected by different adhesive shear stiffness indicate that the overall structural performances of FRP strengthened RC elements can be optimized through appropriate adhesives. Meanwhile, these differences necessitate to develop a reasonable interfacial constitutive model, upon which the observed different bond mechanisms can be clarified precisely. INTERFACIAL FRACTURE ENERGY G f Based on the nonlinear fracture mechanics, the interfacial energy G f is defined as the area under the bond stress slip curve. In a single lap pullout

7 48 FRPRC-6: Bond Behaviour P u x = E f, A f E c, A c G a, t a Fig.5 Single lap shear test x = l P u (kn) experimental data regressing line y = 4.94x.54 R = E f t f (GPa-mm) Fig.6 P u ~E f t f relation case shown as in Fig.5, at any interfacial location: E f A f ε f ( x) + Ec Acε c ( x) = () If the interfacial slip is defined as the strain difference between FRP sheets and concrete, for the case of long bond length (end slip s(x)= at x=l), with Eq., G f can be written as follows: l l E f A f G f = τds = E f t f ( ε f ( x) ε c ( x)) dε f ( x) = E f t f ( + ) ε f ( x) dε f ( x) E A E f A f = ( + ) E f t f ε f ( x) (3) E c Ac x = At the imum interfacial load P u, the boundary conditions ε(x)=p u /E f t f b f at x= and ε(x)= at x=l can be substituted into Eq.3, so that ( + α )( Pu / b f ) E f t f G f G f = or P u = b (4) E t + α f f Where: α=e f A f /E c A c, in general, α can be approximated as. Based on energy or force equilibrium method and the assumptions of some bilinear τ~s relations, Eq.4 was proved by previous researchers 6,7. It is clearly shown that Eq.4 is not only applicable for bilinear but also for any unknown τ~s relation. Fig.6 shows the experimental ultimate loads of the interfaces with different FRP types and different FRP stiffness but the same adhesive. It can be seen that the ultimate load is nearly proportional to the square root of FRP stiffness. Through the comparison between the regressed expression in Fig.6 and Eq.4, it can be known that the interfacial fracture energy is almost a constant value regardless of FRP type or FRP stiffness. Fig.7 shows the relation between the calculated interfacial fracture energy based on Eq.4 and the shear stiffness of adhesive layer. It is obviously seen that G f increases with decreasing the shear stiffness of adhesive layers. To have a further view of the adhesive s effects on the G f, the whole interfacial x = l c c

8 Bond Stress Slip Relationship for FRP-Concrete Interfaces 49 slip can be separated into two parts: the adhesive s shear displacement s a and slippage s ac between adhesive and concrete. Therefore, ( s a + s ac ) = τ ds a + τds ac = G f G f G f = τ ds = τd + (5) In fact, the adhesive layer undertakes a loading and unloading process before and after initial peeling. As shown in Fig.8, when the shear stress in hard adhesive reaches the interfacial peeling stress τ, the adhesive layer lies in elastic period. So the shear displacement of adhesive layer before and after the interfacial softening can be written as: s a =τ t a /G a, therefore: G f (N/mm) G l t a f = = G a a 3.5 experimental data regressing line.5.5 y =.79x R = G a/t a (GPa/m m ) Fig.7 Effects of adhesive on G f t x = l a τ dτ = τ (6) G x = τ τ Hard adhesive Soft adhesive However, when the shear stress in the soft adhesive layer reaches the interfacial peeling stress τ, the adhesive lies in nonlinear period. If the interfacial crack surface propagates a unit area, an extra interfacial G f is consumed (see Fig.8). It can be known as well that the thickness of bond layer affects the interfacial performance more in soft adhesive cases due to its larger plastic shear deformation capacity. While when stiff adhesive is used, the thickness almost has no affect as reported previously 8. τ G f sa Fig.8 Shear stress~displacement of adhesive LOCAL BOND STRESS~SLIP RELATION An important task of pullout bond tests for FRP sheets-concrete interfaces is to propose a precise interfacial bond stress-slip model. Though a lot of interfacial bond tests have been carried out, no reasonable model has been proposed probably mainly due to the observed random scattering of τ~s curves at different locations 5,9. As a result it is not convincing to pick up one of those different τ~s curves as the overall interfacial model. And also it is difficult to discuss the effects of interfacial components on the τ~s relations.

9 5 FRPRC-6: Bond Behaviour Therefore, it is necessary to build up a rule, upon which a reasonable interfacial bond stress-slip model can be proposed. In order to obtain the local interfacial bond behaviors, strain gages with a small interval are usually required to be arranged along the FRP sheets to record strain distributions of FRP during the whole test procedure. Strain(-6) Corresponding to each step of load (P i ) or slip (s i ), the experimental strain of FRP sheets at every interfacial location ε(i,j) exp (j=,n; n is the number of continuously arranged gages) can be obtained. On the other hand, if a local bond stress-slip model is given, the interfacial strain distribution ε(i,j) ana (j=,n) can be obtained analytically as well 5. The criterion, upon which the most suitable τ~s relation is determined, is to find an optimum solutions to minimize the differences between ε(i,j) exp and ε(i,j) ana for every specimen. In this study a multi-dimensional nonlinear optimum program is made to calibrate the unknown parameters needed for a nonlinear τ~s relation, which is assumed as follows: s λ τ = τ ( ) s s (7a) s τ = τ exp( β ( s s )) s > s (7b) The objective function is: J =Min 3 m ( i= 6 n j s=.mm exp s=.43mm exp s=.3mm exp s=.8mm exp s=.35mm exp s=.mm ana s=.43mm ana s=.3mm ana s=.8mm ana s=.35mm ana 9 5 Location(cm) Fig.9 comparison between experimental Fig. Proposed τ ~ s relations and analytical interfacial strain distribution ana exp i, j ε i, j ) ana i, j f f ε ε = f ( τ ( s), E t ) Meanwhile, the following constraint conditions for the optimum calculation are given according to the definition of the G f : τ s τ G f = + ; λ (,) ; τ ( τ, τ ) ; s ( s, s ) ; + λ β Where: τ,τ and s,s are the possible ranges of τ and s, which are Bond stress(mpa) RL RL RL3 RL R3L Slip(mm)

10 Bond Stress Slip Relationship for FRP-Concrete Interfaces 5 determined based on pullout test results of every specimen. Fig.9 shows an example of comparison between the experimental and analytical strain distribution. It can be said that reasonable agreement is reached. Through the optimum back calculation analysis on all specimens with different FRP stiffness and adhesives, finally the parameters for Eq.7a and Eq.7b can be determined as follows:.575αk +.48α K + 6.3αβ KG f τ = β (8) s = τ /( αk) (9) α =.8 ( E.54 ) () f t f β = K ( E f t f ) () λ =.575 () Where: K=G a /t a (MPa/mm) and E f t f (GPa-mm) are the stiffness of adhesive and FRP respectively. Based on the present study and with the consideration of the effects of concrete strength f c (MPa) 3,9, G f (N/mm) can be obtained as follows:.449 '.343 G f = K ( f c ) (3) According to Eq.7~Eq.3, Fig. gives different bond stress~slip curves of FRP sheets-concrete interfaces with different adhesives and number of FRP layers. The experimentally observed imum bond stress and interfacial ductility,3,5,9, which are affected by FRP stiffness and adhesives, can be predicted by these models appropriately. Through these bond stress slip curves, the above-mentioned load-slip relations can be predicted as well (see Fig. and Fig.). Load(kN) CRL EXP CRL ANA CRL EXP CRL ANA CRL3 EXP CRL3 ANA Slip(mm) Load(kN) CRL EXP CRL ANA 3 CRL EXP CRL ANA CR3L EXP CR3L ANA Slip(mm) Fig. Comparison of experimental and analytical results (FRP stiffness effects) Fig. Comparison of experimental and analytical results (adhesives effects)

11 5 FRPRC-6: Bond Behaviour CONCLUDING REMARKS Using moderately low shear stiffness adhesive may become a selectable way to improve the interfacial performances of FRP sheets bonded to concrete and to utilize the high strength of FRP materials in more efficient way. The good toughness and the nonlinearity of low stiffness adhesive contribute to longer effective bond length, more ductile interfacial deformation and higher interfacial fracture energy. Increasing the FRP stiffness can increase the imum bond stress and the ultimate bond force. However, the interfacial fracture energy and the strength efficiency of FRP cannot be improved. To describe the different interfacial bond mechanisms caused by different interfacial components, a local nonlinear interfacial bond stress~slip model is developed based on the interfacial fracture energy and an optimum method. The proposed model can be taken as a reference for selecting suitable interfacial bonding materials and optimizing the design of FRP strengthened RC elements. REFERENCES. Chen. J.F., and Teng. J.G., Anchorage Strength Model for FRP and Steel Plates Bonded to Concrete, Journal of Structural Engineering, ASCE, Vol.7, No.7, July, pp T. Ueda et al., New Approach for Usage of Continuous Fiber as Non-Metallic Reinforcement of Concrete, Structural Engineering International,., pp Laura De Lorenzis et al, Bond of Fiber-Reinforced Polymer Laminates to Concrete, ACI Material Journal, V.98, No.3,, pp L.Bizindavyi and K.W.Neale, Transfer Length and Bond Strength for Sheets Bonded to Concrete, Journal of Sheets for Construction, Vol. 3., No. 4,999, pp Yasuhiko Sato et al., Fundamental Study on Bond Mechanism of Carbon Fiber Sheet, Translation from Proceedings of JSCE, No.648/V-47, 6. Bjőrn Täljsten, Strengthening of Concrete Prisms Using the Plate-bonding Technique, International Journal of Fracture, Vl.8; 996, pp Hong YUAN et al., Theoretical Solutions on Interfacial Stress Transfer of Externally Bonded Steel/Composite Plates, J. Structural. Mech. Earthquake Eng. JSCE, Vol.8, No.,, pp Swamy, R.N. et al., Shear Adhesion Properties of Epoxy Resin Adhesives, Proceedings of an International Symposium on Adhesion between Polymer and Concrete, Sept. 986, pp K., Nakaba et al., Bond Behavior between Fiber-Reinforced Polymer Laminates and Concrete, ACI Structural Journal, V.98, No.3,, pp View publication stats