FATIGUE DURABILITY OF CONCRETE EXTERNALLY STRENGTHENED WITH FRP SHEETS

Transcription

1 FATIGUE DURABILITY OF CONCRETE EXTERNALLY STRENGTHENED WITH FRP SHEETS H. Diab () and Zhishen Wu () () Department o Urban and Civil Engineering, Ibaraki University, Japan Abstract A primary concern o the FRP-strengthened structures is local debonding o FRP-concrete interace, which aects negatively the structural integrity and long-term durability o strengthened members. This paper concerns the development o a nonlinear hybrid model or studying the FRP-concrete interace behavior under atigue loading. Based on the creepatigue interaction, the proposed model describes the behavior o the FRP-concrete interace beore debonding initiation. The atigue debond process is governed by the sotening model that depends on the strain racture energy o the FRP-concrete interace and a damage accumulation actor. A series o double lap shear specimens subjected to variable maximum atigue loading has been carried out to calibrate and validate the proposed model. The results show the ability o the proposed model not only to predict the atigue lie o double-lap shear specimens, but also to provide useul insight into the ailure mechanism o the FRP-concrete interace due to atigue loading. This model can also be used to understand the atigue deormation and FRP sheet strain distributions due to atigue loading. This model allows or the numerical study o the atigue perormance o structures that are externally strengthened with FRP sheets. Keywords: Fatigue; FRP-concrete interace; Numerical analysis. INTRODUCTION External bonding o Fiber Reinorced Polymer (FRP) plates or sheets has recently emerged as a popular method or strengthening o Reinorced Concrete (RC) structures. In this strengthening method, the perormance o the FRP-concrete interace in providing an eective stress transer is o crucial importance. Indeed, extensive research has been directed to investigate the stress transer at the FRP-concrete interace and to develop constitutive models or the static behavior o this type o strengthening [-2]. Comparatively, there have been increasing but still limited numbers o studies directed to investigate the atigue perormance o the FRP-concrete interace [3-5]. Because many structures, in particular road and railway bridges, are subjected to dynamic loading, it is important to understand the bond characteristics o the FRP-concrete interace under cyclic loading. Fatigue loading tests on FRP/concrete bonded joints have shown that 507

2 FRP-concrete interace debonding propagates progressively with the increase o atigue cycles [3, 5]. A FRP-concrete interace with a suicient anchorage length, may keep its interace bonding capacity ater some expected number o atigue cycles [6, 7]. Nevertheless, the progressive local interace deiciency aects adversely the serviceability o FRP strengthened structures. In all these studies, the most common way to represent the atigue lie o FRP/concrete bonded joints was by means o Whöler curve, where atigue strength o structure (S) is plotted against the number o cycles to ailure (N ). This paper presents a inite element model to assess bonding and debonding atigue process o the FRP-concrete interace. The proposed model is expected to provide useul insight into the ailure mechanism o the FRP-concrete interaces. Moreover, this model is essential or a better understanding o atigue perormance o structures externally strengthened with FRP sheets or plates, K 0 τ K K 2 η η 2 K n η n e S c S S τ Local Bond Stress e βs p τ = τ Figure : A hybrid viscoelastic model and (b) a bond-slip model 2. CONSITITUTIVE MODEL During a atigue test, the behavior o the FRP-concrete interace can be divided into two stages: a crack initiation period and a debonding propagation period. The ormer relies on the creep-atigue interaction behavior through the viscoelastic model, while the latter is controlled by the exponential bond-slip model and a damage accumulation actor. The damage accumulation actor and parameters o the viscoelastic model must be determined rom experiment results. The atigue load is kept at a constant value equal to the maximum load, while the constitutive model describes the evolution o permanent deormations with increasing atigue cycles (N). 2. Beore initiation o debonding The constitutive model describing the nonlinear behavior o FRP-concrete interaces can be represented through a series o analogical models as shown in Fig.. A system o Maxwell s chains, which describe the creep-atigue interaction phenomenon beore debonding, is placed in series with an element that schematizes the sotening model. The cycle-dependent stiness and the increment in creep atigue slip at the irst stage can be obtained rom Eqs. () and (3). K n λ ( ) λ t + Δ t = e K () t () = 0 Δ t τ Δ t S p G a S d G s Slip s 508

3 Δ S c K ( t + Δ t ) ( t + Δ t ) = n = 0 Δ t λ τ ( t ) e (2) while the shear stress increment due to the cycle increment is obtained rom Eq. (3) Δ n ( t ) λ τ = e Δs τ () t (3) = 0 Δt K Δt λ where n is the number o terms o the series, K ( t ) are elastic aging coeicients to be determined, λ = ( t ) K ( ) are the relaxation cycles, η ( ) are the viscosities o the η 0 / t 0 dampers, Δ s is the total slip increment at the FRP-concrete interace element, Δτ is the shear stress increment to be updated at every time step or each chain, and Δ t is the time increment. The time increment represents the number o atigue cycle increments divided by the atigue load requency, Hz ( Δ t = ΔN / ν ). Further details regarding these equations may be ound in [8]. The parameters o the viscoelastic model must be determined rom experimental tests or atigue loads beore debonding initiation. 2.2 Ater debonding initiation With the increase o atigue cycles, the shear stress along the FRP-concrete interace decreases due to the stress relaxation unction which means the debonding will not occur ater the instantaneous loading based on the bond strength criteria. Thereore, micro-crack will be e c assumed to initiate i the total slip o the intact FRP-concrete interace, s + s, increases more than the micro-slip deormation, s d ( sd = τ / K(0) ), which is determined rom the short-time interacial model. The exponential sotening slip relationship shown in Fig..b is employed in the present study. The constitutive equations o the cycle-dependent shear stress are expressed as τ τ ( + Δt) = τ ( t) + Δτ t d p ( β s ) ( t + Δt) = τ t exp d t 0 s s (4) s > s (5) where τ t is the bonding strength which depends on the debonding initiation time, s p is the sotening slip, and β is a coeicient depending on the racture energy o the FRP-interace element and the atigue damage accumulation. The value o τ t, obtained and stored by the computational program when the element is beginning to soten, represents the cycle-dependent shear strength. This value is not constant or all elements but depends on the time at which element debonding initiates and on the relaxation parameters o the viscoelastic model. The interacial racture energy, G, which corresponds to the energy per unit bond area required or complete debonding, is represented by the area below the τ s curve and can be divided into two parts as ollows: G = G + G (6) a s 509

4 where G a and G s are the racture energy or the ascending branch and the sotening branch o the τ s curve, respectively. G a depends on the initial interacial stiness (K(0)) and the maximum shear strength, while G s is equal to the area below the exponential curve and can be expressed as s p = τ p p t p τ t G s = τ t exp ( βs ) ds = exp( βs ) = (7-a) s p = 0 β β p β = τ / (7-b) t G s Damage accumulation actor The atigue lie or the FRP-concrete interace ater debonding initiation is controlled by three parameters: Maxwell parameters, the racture energy and a damage accumulation actor. A simple logarithmic degradation unction or the damage accumulation actor was previously introduced by the authors [5] is given by: ζ = B log ( N t N ) 0 ζ. 0 (8) 0 i where ζ is a damage accumulation actor, B is an experimental coeicient, and N t and N i are total atigue cycles and debonding initiation atigue cycles o the element. The atigue cycles and debonding initiation atigue cycles is deined by the ollowing Equation: N N = 60 ν (9-a) t t t = 60 ν (9-b) i t i where t t, t i are total time and debonding initiation time in minutes and ν is the load requency. This damage accumulation actor has the ability to predict the atigue lie o the experimental results, however it had a less accuracy to simulate the atigue slip deormation and timedependent FRP sheet strain distribution as will be discuss later. The experimental results, conducted specially or calibration o this model, have shown that the rate o atigue debonding along FRP concrete interace is time-dependent and diminish with time. Thereore a new relation to imitate the experimental behavior is developed as ollows: K ζ = log0 ( 60 ν ( t )) 0. t ti 0 ζ. 0 (0) ( + t ) i where K is an experimental coeicient obtained by regression analysis. This relation shows that the atigue lie o the element not only depends on the subjected atigue cycle but also on the time o debonding initiation. This damage accumulation actor is incorporated into the racture energy, G s, which essentially governs the sotening behavior o the model by calculating actor β at each increment o atigue cycles according to the ollowing Equation: β = τ ζ G ) () t /( s p s = s = 0 50

5 As the atigue load is kept at a constant value equal to the maximum load value, the proposed model based on actor β and the viscoelastic parameters will describe the evolution o permanent deormations ater debonding. It is worth to note that the debonding propagation rate along the FRP-concrete interaces may depend on many actors such as the mean load, the load requency, the concrete strength, and the type o the adhesive. Thereore, all these actors should be considered in the determination o the K coeicient based on the experimental results. The present study establishes the eectiveness o the proposed model through a series o double-lap specimens. 3. EXPERIMENTAL PROGRAM 3. Test procedure and specimens details Details o the test specimen are shown in Fig. 2. The compressive strength o concrete was 30 MPa whereas the tensile strength and tensile modulus o FRP iber were 3500 MPa and 240GPa, respectively. One layer o CFRP sheet with (dimension 430x50x0.67 mm 3 ) was bonded with an epoxy adhesive (FR-E3P) to both sides o the concrete block along the axial direction. The tensile strength and modulus o elasticity o the epoxy resin (FR-E3P) are 5.9 MPa, and 3.43 GPa, respectively. A 20 mm pre-cracked length was set between CFRP sheet and concrete near the loaded end o CFRP sheet. The cyclic tensile load is applied by pulling both ends o the steel bolt using Instron 8502 series testing machine. In order to monitor debonding propagation along the FRP-concrete interace, thirteen strain gauges with length 6 mm were attached on the CFRP sheet at each side, two strain gauges at unbonded area o the CFRP sheet and eleven strain gauges to monitor debonding growth along the FRP-concrete interace. Moreover, our clip-strain gauges were attached to each specimen to monitor the relative slip under atigue loading. Fiteen specimens were used in this study; three specimens were used to determine the static bond capacity (28 kn) which was identiied as the minimum value among the load carrying capacities, and twelve subjected to sinusoidal wave load between a minimum value 0% and a maximum Load varied rom 30% to 80% o the static capacity and the load requencies were 5.0 Hz. The test temperature was about o C and humidity was about 30%-40%. The speciications o specimens are as ollows (F-80-2): 80 represent the maximum atigue load percent, and 2 indicate the specimen number. 3.2 Experimental results No ailure occurred or specimens subject to maximum atigue loading less than 60%, and the post-atigue static bond capacity was not less than static bond capacity. This implies that the bond capacity o the FRP-concrete interace does not aect adversely by atigue loading i the remain bonded length is long enough. Furthermore, and based on the experiments o this paper, S max =60% can be considered as the threshold value o the atigue loading. Most o specimens ailed by debonding o CFRP sheet which initiated by shear ailure in the concrete near the precrack location. 5

6 Mechanical Anchoring Pre-existing crack FRP sheets Steel bolt Fiber direction Clip Strain gauges, Bond length 200mm 250 (a) Side View Steel bolt Concrete block Clip strain gauge 3,4 Interval: 0mm 20mm Interval: Clip strain gage, 2 20 mm unbonded length (b) Side A or Side B View Figure 2: Details o the FRP sheet-concrete specimens (Double-lap shear test) 4. NUMERICAL SIMULATION A two-dimensional FE analysis is carried out to simulate the experimental specimens using a commercially available FE code DIANA (2004). The FRP-concrete interaces are represented by an interace element (L8IF) o zero thickness. The bond-slip sotening model shown previously in Fig..b is adopted to simulate the bond behavior o the FRP-concrete interaces. The properties o material used or numerical simulation were the same that mentioned previously and sd = 0. 05mm, τ 0 =6.0 MPa, and G =0.97 N/mm were adopted or the bond slip model to represent the maximum static capacity o the FRP-concrete interace (28 kn). The slope o the ascending branch represents the initial interacial stiness K(0). Using a supplied subroutine mechanism oered by DIANA, the atigue behavior o the FRPconcrete interaces is represented by the proposed model outlined above. Since the ailure occurred or all specimens at the FRP-concrete interace, linear behavior is assumed or the concrete and the CFRP sheet. 4. Determination o linear-viscoelastic- model s parameters Cyclic loading on the FRP-concrete interace produces an eect that is similar to creep, i.e. increase slip (or strain at speciic place) with increase in cycles. Specimen F-30-, where no debonding was observed due to cyclic loading, was employed to ind the degradation o the interacial stiness o FRP-concrete interace. This degradation is represented by the viscoelastic model. The material parameters o the viscoelastic model represented by Eq. () ( k and the various k and λ ) were obtained base on cyclic-dependent slip. Identiication o viscoelastic model parameters was ully explained by the authors elsewhere [8]. The relaxation cycles ( λ, minutes) were chosen to be λ 0 =, λ =0, λ 2 =00, and λ 3 =000 (where one minute=300 cycles or a requency o 5.0 Hz). The values o the stiness ratios 52

7 ( α n = K n / K(0), where K(0)=20 MPa ) were ound to be α 0 =0.43, α =0.0, α 2 =0.9, α 3 =0.22, andα 4 =0.06 to match the experimental curve as shown in Fig. 3. Also this Figure shows a comparison between normalized slip resulted due to sustained loading and atigue loading accompanied by the predicted results rom the viscoelastic model. The creep deormation or the same epoxy and CFRP sheet and its predicted value are introduced by the authors [8]. It is clearly comes out that the increase o compliance due to sustained loading is higher than that due to atigue loading. Norm alized Slip Proposed Model -Fatigue Experimental- Fatigue.2 Proposed model- Wu & Diab 2007 Experimental- Wu & Diab 2007] Time (min) Figure 3: Experimental and numerical normalized maximum FRP sheet slip versus time or sustained and atigue loading Stress level (%) Number o cycles Experimental Proposed model K=0.2 Endurance Limit No ailure Figure 4: A comparison between the theoretical S-N diagram and experimental results 4.2 Fatigue lie analysis o FRP-concrete interace Cycle-dependent degradation o the interacial stiness, the damage accumulation actor, and the bond-slip model are the governing actors o the debonding propagation along the FRP-concrete interaces. Using the above viscoelastic parameters and the bond-slip model mentioned previously the value o the damage accumulation actor (ζ ) is determined using regression analysis to it the experimental results. As the damage accumulation actor depends on the experimental actor K, K=0.2 is ound to give a good itting to the experimental results. It is worth to note that this coeicient also depends on many experimental actors as mentioned previously. Fig. 4 shows the relationship between the maximum atigue load percent and atigue lie, the so-called S-N curves or experimental and theoretical results. It can be seen that the theoretical S-N diagram alls within the range o the experimental results.. A central point o the proposed model is not only the prediction o the theoretical S-N diagram but also the reproducing o the characteristic eatures o the experimental results with good accuracy as will discuss in the ollowing sections. 4.3 Failure process o the FRP-concrete interace due to atigue loading Fatigue deormation characteristics Fig. 5 shows a comparison between the predicted and experimental atigue displacements. Fig. 5.a reports displacement o specimens subjected to 70% atigue loading versus the normalized atigue lie. The predicted displacements represent the displacement obtained by 53

8 the proposed model and that ormally introduced by the authors [5]. The rate o displacement increase is high in the early stage, and thereater become lower in stable manner. Fig. 5.a clearly shows that the proposed model has the ability to simulate the real behavior o experimental displacements. The modiication o the damage accumulation actor gives a good accuracy or the atigue displacement prediction, while the previous model shows a steady displacement increase until ailure. It is worth to notice that the cycle-dependent displacement can be considered as a ailure criterion o the FRP-concrete interace. Fig. 5.b shows, respectively, the predicted and experimental cycle-dependent displacements or the specimens that did not ail under atigue loading. In this igure, it can be observed that the proposed model correctly predicts the atigue displacement and the rate o its development or dierent atigue loading levels. The dierence in experimental cycledependent displacement, or the same stress level, resulted rom the change o debonding length or each specimen, however the predicted value alls within these results. Displ. mm Exp. N=95,000 Cycles 0.4 Exp. N=27,000 Cycles Exp. N=4,000 Cycles 0.2 Proposed Model Fatigue Model Normalized Fatigue lie Displ. (mm) Proposed Model 60% Exp. S Exp. S-50-2 Proposed Model 50% 0. Exp. S-60- Exp. S E E+05.0E+06.5E E E E E E+06 Number o Cycles (a) Displ. o specimens S-70 versus the normalized atigue lie (b) Displ. o specimens S-60 and S-50 versus the number o cycles Figure 5: A comparison between experimental and predicted atigue displacement CFRP sheet strain Distribution The local interace debonding is caused by gradual increase o the local slip resulted rom repetitive load eect, even the tensile stress in CFRP sheet is kept at a certain value that is smaller than the static bond capacity. The local interace debonding propagates toward the ree end with the increase in atigue cycles. Once the remaining bonded length can no longer sustain the maximum atigue loading, atigue ailure will occur. Fig. 6 shows a comparison between experimental and analytical cycle-dependent CFRP sheet strain distributions or specimens S-70-(27000) and specimen S-60-. The propagation speed o debonding is high at early stages, and thereater becomes lower. This behavior can be observed rom the experimental and the predicted CFRP sheet strain distributions. Thereore, it is expected that increasing the bonding length may lead to increase the atigue lie o the specimen. The atigue test o specimens S-60- was stopped at,630,000 cycles since the debonding progress was very small ater 33,000 cycles. Obviously, Fig. 6.b was analogous or specimens S-60, and S-50, where the debonding rate decrease with atigue cycles. Results notated by FEM in Fig. 6 are in acceptable agreement with the experimental results not only or ailure specimen but also or un-ailure specimen. 54

9 FRP sheet strain (µε) Distance (mm) Normalized Fatigue lie 4.E-05 4.E Proposed Model FRP sheet strain (µε) Distance (mm) Number o Cycles 00,000 0,000 33,000 45, ,500,630,000 Proposed Model (a) Specimen S-70- (b) Specimen S-60- Figure 6: A comparison between experimental and predicted cycle-dependent CFRP sheet strain distribution due to atigue loading 5. A COMPARISON BETWEEN SUSTAINED AND FATIGUE LOADING EFFECT A comparison between experimental results o sustained loading reported by the authors [0] and those o atigue loading or the same epoxy resin is reported in Fig. 7. Such a igure reports loading periods o specimens under atigue and under sustained loading compared with predicted results. Fatigue specimens are represented by the maximum atigue loading and the number o specimens or each maximum stress, S, S2, S3. By comparing experimental results o creep and atigue or the same maximum load, it clearly comes out that specimens ail higher at high atigue loading while creep specimens have shorter loading period at low sustained loading. It is worth pointing out that hysteric heating at the crack tip may occur, particularly at high atigue loading. However, viscoelastic properties o the FRPconcrete interace are believed to be the dominant actor at sustained loading. Exp. Fatigue S 80 Max. Applied Load percent No Failure Exp. Fatigue S2 Exp. Fatigue S3 Proposed Model atigue Exp. Creep Creep Model [0] Loading Period (min.) Figure 7: Loading periods o specimens under atigue and sustained loadings 6. CONCLUSION 55

10 A hybrid viscoelastic inite element model has been proposed or the simulation o bonding and debonding atigue process in the FRP-concrete interaces. The proposed model depends on the creep-atigue interaction beore debonding initiation, while the bond-slip model based on the racture energy and a damage accumulation actor govern debonding process along the FRP-concrete interaces. The validity o the proposed model has been veriied against experimental results o double-lap shear specimens. By using this model, not only a theoretical S-N diagram can be generated but also, the ailure mechanism o the FRPconcrete interace can be explored in details. Furthermore, this model gives the opportunity to numerically study the atigue perormance o structures externally strengthened with FRP sheets. REFERENCES [] Kamiharako, A., Shimomura, T., Maruyrama, K., and Nishida, H. Stress Transer and Peeling-o Behavior o Continuous Fiber Reinorced Sheet-Concrete System, Proceedings o 7 th East Asia- Paciic Con. on Structural Engineering and Construction, EASEC-7, Kochi University o Technology, Kochi, Japan, 999, [2] Wu, Z. S., Yuan, H., and Niu H. D. Stress transer and racture propagation in dierent kinds o adhesive joints, J. Eng. Mech., ASCE, 28(5)(2002) [3] Bizindavyi, L., Neale, K.W., and Erki, M. A. Experimental Investigation o Bonded Fiber Reinorced Polymer-Concrete Joints under Cyclic Loading, ASCE Journal o Composites or Construction, 7(2)(2003) [4] Ferrier, E., Bigaud, D., Hamelin, P., Bizindavyi, L., and Neale, K. W. Fatigue o CFRPs externally bonded to concrete, Materials and Structures, 38() (2005) [5] Diab, H., Wu, Z., and Iwashita, K. Experimental and Numerical Investigation on the Fatigue Behavior o FRP-Concrete Interace, Proceeding o FRPRCS-8, Greece, [6] Tan, K. H. Eect o Cyclic Loading on FRP-Concrete Interace Bond Strength, Proceeding o the International Symposium on Latest Achievement o Technology and Research on Retroitting Concrete structures, Japan Concrete institute, [7] Dai, J. G., Saito, Y., Ueda, T., and Sato, Y. Static and Fatigue Bond Characteristics o Interaces Between CFRP Sheets and Frost Damage Experienced Concrete, proceeding o 7th International Symposium on Fiber-Reinorced Polymer (FRP) Reinorcement or Concrete Structures, SP-230, Vol.2, November, ACI, 2005, pp [8] Wu, Z.S., and Diab, H.M. Constitutive model or time-dependent behavior o FRP-concrete interace, Journal o Composites or Construction, ASCE, (5) (2007) [9] DIANA-8. User's Manual (2004). TNO Building and Construction Research. Lakerveld b.v., The Hague. [0] Diab, H.M. and Wu, Z.S. Nonlinear Constitutive Model or Time-Dependent Behavior o FRP-Concrete Interace, Journal o Composite science and Technology, 67(/2) (2007)