conceptual model for prediction of frp-concrete bond

Conceptual Model for Prediction of FRP-ConcreteBond Strength under Moisture Cycles

C. Tuakta1 and O. Büyüköztürk, M.ASCE2

Abstract: Fiber-reinforced polymer (FRP) retrofit systems for concrete structural members such as beams, columns, slabs, and bridge deckshave become increasingly popular as a result of extensive studies on short-term debonding behavior. Nevertheless, long-term performanceand durability issues regarding debonding behavior in such strengthening systems still remain largely uncertain and unanswered. Becauseof its composite nature, the effectiveness of the strengthening system depends on the properties of the interfaces between the three constituentmaterials; namely, concrete, epoxy, and FRP. Certain factors, including those related to environmental exposures, can cause degradationof the interface properties during service life. This is particularly critical when predicting service life and planning maintenance ofFRP-strengthened concrete structures. In this study, effect of moisture on an FRP-concrete bond system is characterized by means of thetri-layer fracture toughness, which can be obtained experimentally from peel and shear fracture tests. Fracture specimens were conditionedunder various durations and numbers of wet-dry cycles at room temperature and 50°C. An irreversible weakening in bond strength wasobserved in fracture specimens under moisture cyclic condition. A conceptual model is developed based on the experimental results ofthe fracture specimens under variable cyclic moisture conditions for the bond strength prediction of the FRP-concrete bond system. A numeri-cal study of a precracked FRP-strengthened reinforced concrete beam is then performed to show potential application of the proposed pre-dictive model. DOI: 10.1061/(ASCE)CC.1943-5614.0000210. © 2011 American Society of Civil Engineers.

CE Database subject headings: Fiber reinforced polymer; Concrete; Rehabilitation; Moisture; Cyclic tests; Predictions; Bonding.

Author keywords: Fiber reinforced polymer; Concrete; Rehabilitation; Moisture; Cyclic test; Predictions.

Introduction

In recent years, the use of fiber-reinforced polymer (FRP) materialsfor repair and strengthening has become a widely accepted practiceas a result of design code revision, physical aging, environmentaldeterioration, and catastrophic events. Advantages of FRP overother conventional repair materials include its higher strength-to-weight ratio, additional corrosion resistance, and ease of appli-cation. Several strengthening techniques, including FRP platebonding and column wrapping, have been widely applied duringthe past decades as a result of extensive studies and availabilityof ample experimental results on the mechanical behavior of theretrofit systems (Antonopoulos and Triantafillou 2003; Lin andLiao 2004; Meier 1995; Parvin and Wu 2008; Saadatmanesh1997; Teng et al. 2001). For flexural strengthening of reinforcedconcrete (RC) elements such as beams and slabs, FRP laminatesin the form of rigid plates or flexible sheets are externally bondedto the tension faces of the elements using epoxy adhesive throughdry or wet lay-up processes. American Concrete Institute (ACI)Committee 440 (2008) provides design guidelines, employing de-sign principles similar to that of typical steel reinforced concrete

beams. Nonetheless, premature failure by debonding of theconcrete-epoxy interface may occur, which can significantly affectthe load capacity of the retrofitted systems (Au and Büyüköztürk2005; Büyüköztürk et al. 2004; Büyüköztürk and Hearing 1998;Gunes 2004; Hearing 2000; Meier and Kaiser 1991; Oehlers2006; Teng et al. 2001). This failure behavior is undesirableowing to its lack of prior indication and brittle nature. In manysituations, it is critical to consider this issue, especially when anFRP-strengthened beam is subjected to variable environmental con-ditions during its service life, causing deterioration of the bondstrength.

In real-life applications, FRP-strengthened structural membersare exposed to humidity fluctuations owing to seasonal rainfallor snowfall. This kind of environmental fatigue can affect anFRP-retrofit system in a number of ways, as shown by various stud-ies on the durability of FRP-plated RC beams and FRP-confinedRC columns. In particular, cyclic moisture effect was identifiedas an important environmental deterioration mechanism that pro-motes reduction in the overall stiffness and ultimate strength, lead-ing to premature system failures. Toutanji (1999) found that theextent of deterioration in FRP-confined RC columns dependedon both the types of epoxy and FRP. Under 300 wet-dry cycles,the strength and ductility of glass FRP-confined column specimensdecreased, although no significant detrimental effects were ob-served in carbon FRP-confined column specimens. These observa-tions are in good agreement with recent findings reported by Baeand Belarbi (2008). As for FRP-plated RC beams, reductions inultimate strength and stiffness owing to accelerated wet-dry cyclingwere generally observed. Chajes et al. (1995) reported 20 to 30%reduction in ultimate strength for glass FRP (GFRP) and carbonFRP (CFRP) retrofitted specimens that were subjected to 100wet/dry cycles. In one study (Toutanji and Gomez 1997), the ob-served strength reductions could be as much as 33% in FRP-plated

1Ph.D. candidate, Dept. of Civil and Environmental Engineering, MIT,Room 5-336, 77 Massachusetts Ave., Cambridge, MA 02139. E-mail:[email protected]

2Professor, Dept. of Civil and Environmental Engineering, MIT, Room1-281, 77 Massachusetts Ave., Cambridge, MA 02139 (correspondingauthor). E-mail: [email protected]

Note. This manuscript was submitted on July 30, 2010; approved onFebruary 9, 2011; published online on February 11, 2011. Discussion per-iod open until March 1, 2012; separate discussions must be submitted forindividual papers. This paper is part of the Journal of Composites for Con-struction, Vol. 15, No. 5, October 1, 2011. ©ASCE, ISSN 1090-0268/2011/5-743–756/$25.00.

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concrete beams subjected to 300 wet-dry cycles in salt water.Ultimate load also depreciated at various degrees, depending onthe number of wet-dry cycles (Soudki et al. 2007). Similar to thecase of FRP-confined RC columns, the stiffness of FRP-plated con-crete beams deteriorates under cyclic moisture condition. In onestudy (Myers et al. 2001), it was experimentally determined thatGFRP-plated specimens could lose up to 85% of their originalflexural stiffness after only 20 wet-dry cycles, compared to 55%in the case of CFRP-plated specimens. Aramid FRP-plated spec-imens in the same test series appeared somewhere in between.In general, failure mode was reported as a debonding that tookplace near the FRP-concrete interface.

It is clear from the experimental investigations that the strengthand the stiffness of FRP-strengthened and FRP-retrofitted concretestructural elements are affected by moisture cycles. The overallintegrity of a structure through its service life will in turn dependon the performance of each retrofitted structural component. As aresult, the ability to predict the service-life of an FRP-concretebond system under the effect of moisture is crucial to improvingthe safety of civil structures strengthened by this technique. Despitethe need, a model for prediction of FRP-concrete bond strengthunder moisture cycles has not yet been proposed. In this research,a fracture-based predictive model has been developed from adatabase of degradation in FRP-concrete bond caused by variablemoisture cycles.

Research Objective and Approach

The objective of this research is to use the concept of fracture me-chanics to develop a conceptual model for predicting the strength ofan FRP-concrete bonded joint subjected to moisture cycling, and toextend its application to FRP-retrofitted concrete structures. Deg-radation of bond strength under cyclic moisture condition is quan-tified by the tri-layer fracture toughness in Au (2009) and Au andBüyüköztürk (2006b). This paper is organized as follows. First,the effects of continuous and cyclic exposure to moisture on theFRP-concrete bond system are briefly discussed. The developmentof the predictive model based on the experimental results of thepeel and shear fracture specimens is then described. Based on thispredictive model and the concept of fracture mechanics, a schemefor predicting the debonding failure in an FRP-retrofitted structuralelement is presented through an example of its application to aprecracked FRP-strengthened RC beam.

Service Life Prediction

In a civil infrastructure, each of the structural components is ini-tially designed according to the design guidelines to meet itsown strength and serviceability criteria. For example, an RC beamgirder in a bridge needs to be checked during the design processfor flexural and shear capacity, acceptable crack opening, andmaximum deflection. Similar criteria will need to be establishedfor the durability and life cycle performance of the structure. Owingto physical changes in the structure during its service life, and pos-sible chemical changes in the surrounding, the performance ofthe structural components may decrease in various ways, whichin turn affects the overall structural integrity of the infrastructurein service. Knowing when the performance of a structural compo-nent will fall below an acceptable limit could be helpful in oper-ation and maintenance planning. There are three aspects to beidentified when determining the service life: limit state, damagingfactors that affect material properties, and deterioration mechanism(Cheung and Kyle 1996; Hong and Hastak 2006). In the case of

FRP-strengthened RC beam members, the limit state may be theflexural capacity before any premature debonding, which can becaused by weakening of the concrete-epoxy-FRP interface. Thecorresponding deterioration process may be driven by moisturediffusion. For example, rain or melting snow can seep throughexisting cracks or deck joints to retrofitted RC girders and diffuseinto the FRP-concrete bond region, causing bond strength todeteriorate. Hence, to predict the service life, a model is requiredto describe the extent of deterioration with respect to the moisturecontent.

In this study, the bond strength of the FRP-concrete interfaceunder the effect of cyclic moisture condition is characterized byfracture toughness. This approach is more suitable to the debondingproblem because debonding can be considered as a local failure.During failure initiation at an existing defect, such as an unbondedregion at the concrete-epoxy interface, both mode I (opening) andmode II (shearing) driving forces may exist, depending on locationof the defect. In this situation, the tri-layer fracture toughness modelspecialized for opening and shearing modes is a suitable tool forquantification of the bond strength of the interface. The relationshipcan be derived between the extent of bond strength degradation andmoisture content in the bond line obtained from a finite-element(FE) simulation of moisture diffusion.

Quantification of Bond Strength by Tri-Layer FractureToughness Model

In FRP-strengthened concrete structural members, FRP-concretebond joints can be idealized as a three-layered material system con-sisting of concrete, epoxy, and FRP. In such a system, cracks canpropagate in five regions, as shown in Fig. 1. Using energy con-siderations, the energy release rate can be computed from the differ-ence in the strain energy of the cracked body (far behind the cracktip) and that of the intact body (far ahead of the crack tip). Thedetailed derivation of the tri-layer fracture toughness is given inAu (2009) and Au and Büyüköztürk (2006a). The expression ofthe energy release rate contains geometric and material informationfrom all three material layers. To obtain the fracture toughness ofthe system from the experiment, configurations of the peel andshear fracture specimens are chosen such that they represent pos-sible loading cases found in a full-sized FRP-strengthened concretebeam, as shown in Figs. 2(a) and 2(b). To compute the interfacefracture toughness of the FRP-concrete bond system, critical loadsobtained from the debonding tests and material properties obtainedfrom the material characterization were used.

Peel and Shear Fracture Specimens and Test Setup

The effect of continuous moisture ingress and its reversibility wasinvestigated quantitatively and qualitatively by means of peel andshear fracture tests. Figs. 3(a) and 3(b) show the dimensions of thepeel and shear specimens, respectively. The CFRP plate in bothspecimens is 1.28 mm thick and made of unidirectional carbon fi-bers. The thickness of the adhesive layer is uniformly kept at 1 mm

Fig. 1. A three-layered system consisting of concrete, epoxy, and FRP

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over the bond region. In each specimen, an initial crack of 75 mmwas introduced at the epoxy-concrete interface next to the CFRPcantilever arm by Teflon tape. For the peel fracture test, the spec-imens were placed horizontally in a loading frame and constrainedfrom any movement by alignment screws and an end plate[Fig. 4(a)]. Load was applied by vertically pulling the tip of theCFRP plate. Shear specimens were placed vertically in the loading

frame and pulled upward [Fig. 4(b)]. Detailed discussion on instru-mentation and test procedure can be found in Au and Büyüköztürk(2006b). Specimens were conditioned in a moisture environmentat 23°C using water tanks, and at 50°C using an environmentalchamber before testing. The load-displacement behavior and de-bonding modes were observed and correlated with the moisturelevel obtained from the finite-element diffusion simulation.

Fig. 2. (a) Idealization of loading state in FRP near crack; (b) peel and shear fracture specimens

Fig. 3. Geometry of specimens: (a) peel fracture; (b) shear fracture

Fig. 4. Test setups: (a) peel fracture; (b) shear fracture



Predicting the Interface Moisture Content

Because it is difficult to directly measure the moisture content at theinterface in peel and shear fracture specimens during the test, anumerical simulation of moisture diffusion was performed. In thiscase, the governing equation for mass diffusion is basically anextension of Fick’s equation, which allows nonuniform valuesof diffusivity and solubility in multiple constituent materials ofthe fracture specimens (Crank 1975). In finite-element analysis,moisture diffusion is driven by a concentration gradient with con-centration normalized by solubility being the nodal variable ofan element. Three-dimensional models of the peel and shear frac-ture specimens (Fig. 5) were created with exactly the same dimen-sions for the analysis by a general purpose finite-element program(ABAQUS 2006). Eight-node three-dimensional mass diffusionelements were used throughout the models, with temperature-dependent diffusion coefficients for room temperature and 50°C,as shown in Table 1 (Au 2009). Because the models involve threematerials, elements were constructed such that nodes were shared atthe concrete-epoxy and CFRP-epoxy interfaces. The epoxy layerand the CFRP plate were modeled using one layer of diffusionelements with thicknesses of 1 and 1.28 mm, respectively. Forconcrete block, the 5 × 5 × 4:7 mm3 diffusion elements were usedthroughout. The boundary condition was specified as 100% mois-ture concentration on the outer surface of concrete, epoxy, andCFRP plate to represent the total submersion of the specimensunder water. Time integration of the transient diffusion analysiswas conducted with backward Euler method (also known as themodified Crank-Nicholson operator) because it is unconditionallystable for this type of linear problem (Butcher 2008). The temper-ature and mass diffusion are not coupled in solving the differentialequation for mass diffusion because moisture diffusion took placeat a constant temperature during moisture conditioning. The aver-age moisture content in terms of weight percentage (C) or thetransient moisture content corresponding to various conditioning

durations are shown in Table 2 for the tri-layer fracture specimens.These values were used to obtain the corresponding mechanicalproperties (from the tensile and compression tests) of the epoxyand concrete in the interface fracture toughness calculation. As pre-dicted, under higher temperature, moisture diffuses more into thebond line of the fracture specimens. This simulation method will beused later in this study to determine moisture content in the bondline of other FRP-concrete structures, such as a precracked FRP-strengthened RC beam.

Effect of Continuous Moisture Ingress

The objective of continuous moisture ingress is to investigate theextent of bond strength degradation caused by prolonged exposureto moisture. Peel and shear fracture specimens were subjected tomoisture condition for durations ranging between two andeight weeks at room temperature and 50°C. They were then testedwhile they were still in a wet condition. The relationship betweenmoisture content in the bond line and bond degradation were ob-tained. Figs. 6(a) and 6(b) show the effect of moisture on the peeland shear fracture toughness, respectively. The values of fracturetoughness are the average of three specimens in each conditiongroup. Significant reduction in facture toughness after moistureconditioning in both peel and shear fracture specimens indicatedthat moisture had a detrimental effect on the strength of theFRP-concrete bond system. More than 50% of the initial bondstrength is reduced by the exposure to moisture, even after an initialduration of two weeks. For both peel and shear fracture specimens,there was a shift in the failure mode from concrete delamination indry specimens to concrete-epoxy interface separation in wet spec-imens, at both room and high temperatures. This indicates theweakening of the interface owing to the presence of moisture. Itwas observed that the fracture toughness approximately reaches

Fig. 5. (a) FE model for diffusion simulation in fracture specimen; (b) moisture content in the adhesive bond line as predicted by FEM for a timeperiod of 2 to 10 weeks (only peel fracture specimen at room temperature shown)

Table 1. Diffusion Coefficients of Concrete, CFRP, and Epoxy

MaterialTemperature

(°C)Diffusivity

(10�11 m2=s)Solubility(wt%)

Concrete 23 3.24 7.71

50 3.24 7.76

CFRP 23 0.068 0.34

50 0.081 0.9

Epoxy 23 0.023 2.58

50 0.048 5.42

Table 2. Moisture Content (Weight %) at the Interface in Peel and ShearFracture Specimens from Finite-Element Simulation of Moisture Diffusion

Duration (weeks)

Moisture content (%)

23°C 50°C

2 0.41 0.87

4 0.77 1.63

6 1.01 2.14

8 1.29 2.71

10 1.41 3.26



an asymptotic value after eight weeks for both peel and shear frac-ture specimens. Hence, Table 2 shows that the threshold moisturecontents (Cth), beyond which no additional degradation is regis-tered, are 1.29 at room temperature and 2.71 at high temperature.The extent of strength degradation and its correlation with interfacemoisture content in terms of the ratio of transient and thresholdmoisture contents (C=Cth) is shown in Figs. 7(a) and 7(b). The frac-ture toughness values corresponding to these moisture contentswere later used in the analysis of the effect of moisture reversaland moisture cyclic conditioning on the bond strength of theFRP-concrete bonded joint.

Effect of Cyclic Moisture Condition

The difference between continuous moisture ingress and cyclicmoisture condition is that in the former, specimens are tested aftercontinuous exposure to moisture as they are still wet, whereas in thelatter, specimens are allowed to dry after a series of wet-dry cyclesbefore being tested. A wet-dry cycle involves submersing a speci-men for a period of time, followed by drying the specimen. Thedrying duration has been determined by observing the weightchange during drying of bulk epoxy coupons and separate groupof the peel and shear fracture specimens that were conditioned forvarious periods of time. For this part of the study, dry condition isdefined as the duration after which small change in weight is reg-istered in such specimens. It has been found that at least four daysare required for the specimens to attain a small weight change (lessthan 0.05%). Therefore, drying duration is four days in this study.Any irreversible effect will be shown by comparing the residualfracture toughness from the cyclic moisture condition tests withthat from the continuous moisture ingress tests.

Peel and Shear Fracture Toughness under MoistureReversal

Peel and shear fracture specimens were conditioned under themoisture environment for one, two, three, four, six, and eight weeksat 23 and 50°C. They were then left to dry for four days beforetesting. Characterization of plain concrete and the epoxy undermoisture reversal were also conducted by means of compressiveand tensile tests, respectively (Tuakta and Büyüköztürk 2011).The epoxy was unable to regain its initial mechanical propertyin spite of drying. This may be attributed to the loss of cross-linkingdensity and permanent swelling damage owing the presence ofwater. On the other hand, the residual Young’s modulus of concreteafter moisture reversal did not show any significant change, imply-ing that concrete can regain its initial properties after drying.

Correlation between the residual fracture toughness and theintermediate moisture content is shown in Fig. 8. In this case,the intermediate moisture content is defined as the amount of waterin the bond line at the end of each wet interval. Longer intermediateconditioning durations result in higher permanent deterioration ofthe interface. Irreversible effect of moisture conditioning was evi-dent in both peel and shear specimens conditioned at both roomand high temperatures, as shown in Figs. 9 and 10, respectively. Itwas found that although the specimens were dried before testing,deterioration in bond strength owing to prior continuous exposureto moisture could still be captured during the fracture tests. Thespecimens could not fully regain their initial bond strength, andthe residual strength decreased for increasing intermediate condi-tioning durations. In general, the specimens could regain somebond strength from drying, when compared to those tested inwet condition. Nonetheless, sharp loss in the ability to regainbond strength is apparent at conditioning durations longer thanthree weeks. At high temperature, however, bond strength regain

Fig. 6. Effect of continuous moisture condition on: (a) peel fracture toughness; (b) shear fracture toughness

Fig. 7. Empirical relationship between moisture content and the effect of continuous moisture condition on: (a) peel fracture toughness; (b) shearfracture toughness



was observed only in specimens conditioned for less than sixweeks. The peel and shear fracture specimens conditioned forlonger periods at this temperature seemed to have even lowerstrength than the wet specimens. With respect to the failure surface,more concrete debris was found on the debonded epoxy layer inspecimens that had higher residual bond strength.

Peel and Shear Fracture Toughness under MoistureCyclic Condition

To determine the effect of conditioning duration and the number ofwet-dry cycles on the residual strength of the adhesive bond, peeland shear specimens were subjected to a conditioning programshown in Fig. 11, with three weeks being the longest continuous

Fig. 8. Residual fracture toughness of specimens obtained from moisture reversal tests: (a) peel fracture specimens; (b) shear fracture specimens

Fig. 9. Comparison between moisture-affected fracture toughness and residual fracture toughness for peel fracture tests at: (a) room temperature;(b) 50°C

Fig. 10. Comparison between moisture-affected fracture toughness and residual fracture toughness for shear fracture tests at: (a) room temperature;(b) 50°C

Fig. 11. Condition groups in moisture cyclic condition test



conditioning duration. Similar to continuous moisture condition,three specimens were tested for each condition group. After eachbrief continuous moisture ingress, the specimens were left to dryfor four days in the laboratory at room temperature and approxi-mately 60% relative humidity. For example, each fracture specimenin the two-weeks-two-cycles group underwent conditioning se-quence as follows: two weeks under water, followed by four daysin dry condition, followed by two weeks under water, and finallyfour days in dry condition. At the end of the conditioning program,the specimens were tested in dry condition using the same configu-rations as in Fig. 4. Corresponding material characterization wasalso conducted for plain concrete and the epoxy to obtain mechani-cal properties as functions of durations and cycles by curve-fitting,which were used in calculating the tri-layer fracture toughness. Theproperties of the concrete are not affected significantly by the wet-dry cycles. On the other hand, Young’s modulus of the epoxy atboth temperatures decreased for longer period of intermediate con-ditioning (and hence higher intermediate moisture content). Thiseffect is shown by the plots in Fig. 12.

Figs. 13 and 14 show the effect of wet-dry cycles on the residualinterface fracture toughness in the peel and shear fracture speci-mens. Both the number of wet-dry cycles and the intermediate con-ditioning duration affect the residual bond strength. Reduction inresidual interface fracture toughness with the increase in number ofwet-dry cycles is observable in both peel and shear fracture spec-imens. Longer intermediate conditioning duration results in smallerresidual strength. In most cases, higher temperature seems to accel-erate the deterioration process, resulting in further reduction inresidual bond strength. This is possibly attributable to higher mois-ture uptake between each wet-dry cycle. Similar to moisture rever-sal, higher residual strength is associated with more concrete debrisleft on the fracture surface of the peel and shear fracture specimens.Specimens that were conditioned for shorter duration and fewer

wet-dry cycles appeared to have more concrete debris left onthe epoxy. This suggests that strength degradation can take placein the CFRP-concrete interface as the FRP-strengthened concreteelement is exposed to wet-dry cycles during its service-life.

Application: Prediction of Debonding in aPrecracked FRP-Strengthened RC Beam underMoisture Cycles

Conceptual Predictive Model for FRP-Concrete BondStrength under Moisture Cycles

Considering the results of the peel and shear fracture tests, the re-duction in the FRP-concrete bond strength under continuous mois-ture exposure can be expressed in the form of an exponential decaywith respect to interface moisture content:

Γ ¼ Ae�bðC=CthÞ ð1Þ

where the coefficients A and b are obtained from the continuousmoisture condition tests (Fig. 7). As discussed earlier, reductionin the residual bond strength was found to increase with increasednumber of wet-dry cycles. For simplicity, it is assumed here that therate of this deterioration remains constant for any wet-dry cycle,while it is dependent only on the intermediate moisture content.Figs. 13 and 14 show that the rate of deterioration is generally highduring the first few wet-dry cycles, but will decrease to an almostconstant value as the number of wet-dry cycles increases beyondthree cycles. Because civil structures are designed to withstandmuch more wet-dry cycles during service life, this assumption isdeemed reasonable for this analysis. Therefore, owing to the cyclicnature of the problem, a general form of the moisture cyclic deg-radation model is proposed as follows:

Fig. 12. Effect of cyclic moisture condition on Young’s modulus of epoxy at: (a) room temperature; (b) 50°C

Fig. 13. Effect of number of wet-dry cycles on the residual fracturetoughness of peel fracture specimens

Fig. 14. Effect of number of wet-dry cycles on the residual fracturetoughness of shear fracture specimens



dΓdN

¼ qðC=CthÞn ð2Þ

where Γ = interface fracture toughness obtained from Eq. (1);N = number of wet-dry cycles. The coefficients q and n are deter-mined from fracture tests on peel and shear specimens underseveral sets of moisture cyclic duration, the results of which werediscussed earlier. Their values at room temperature and 50°C wereobtained by statistically curve-fitting the relationship between thedeterioration rate of the bond strength (dΓ=dN) and the intermedi-ate moisture content in the bond line obtained from the cyclic mois-ture condition tests (Fig. 15). Eq. (2) implies that as the moistureconcentration approaches the threshold value, a fewer number ofwet-dry cycles will be required for the fracture toughness to reachan asymptotic value.

To determine the number of cycles, Nth, that cause the fracturetoughness to reach the asymptotic value, Eq. (2) is to be integrated:

ZNth

0dN ¼ Nth ¼

ZΓ0

Γth

1qðC=CthÞn

dΓ ð3Þ

where Γ0 and Γth = initial fracture toughness of the control spec-imens (dry) and the asymptotic fracture toughness (wet), respec-tively. The coefficients in Eq. (1) and (2) are shown in Table 3.These coefficients are specific to the certain type of adhesive usedin this study. Nonetheless, the methodology presented here is gen-erally applicable to other commercially available structural adhe-sives, and further studies are needed to establish the variation ofthe coefficients based on the variety of epoxy types used in practice.The integration of Eq. (3) results in a function of C, which is thelevel of intermediate moisture content between each wet-dry cycle:

Nth ¼Γ0 � Γth

qðC=CthÞnð4Þ

Substituting various values of C=Cth into Eq. (4), the number ofcycles at which the residual bond strength reaches an asymptoticvalue is plotted in Fig. 16 for the peel and shear fracture specimensat room and high temperatures. It is predicted that higher intermedi-ate moisture content and higher temperature will require slightlyfewer wet-dry cycles for the fracture toughness to reach the asymp-totic value.

Predicting Debonding Failure in an FRP-StrengthenedRC Beam Exposed to Moisture Cycles

In real-life applications, existing RC beams are designed such thatthe service load should not cause any structural failure during theservice life. This design philosophy also applies to the case of anFRP-strengthened RC beam. Given a loading history during thedesign service life of an RC beam, the driving force that can causepremature debonding may be characterized by the energy releaserate (ERR) of an existing interfacial crack at a given time. Accord-ing to ACI (2008), the stress in steel reinforcement is limited to0.8 times its yield strength to avoid any inelastic deformation. Thislimitation implies the maximum load a beam will carry during itsservice life. However, this design principle is not conservative, inthat a premature failure by debonding may occur at a lower level ofthe load. The ERR corresponding to the maximum load can indi-cate potential premature debonding failure when compared toavailable fracture toughness of the interfaces and the bulk materials(i.e., concrete and epoxy). A schematic is given in Fig. 17 forpredicting debonding under moisture cycles in a precrackedFRP-strengthened RC beam based on the proposed predictivemodel and the finite-element method. The two input parametersof the proposed predictive model are the ERR and the interfacemoisture content, both of which are calculated from FEM.

Fig. 15. Relationship between the rate of deterioration and the ratio of intermediate and threshold moisture contents for specimens under cyclicmoisture condition: (a) peel fracture specimens; (b) shear fracture specimens

Table 3. Coefficients Obtained from the Moisture Reversal and MoistureCyclic Condition Tests

Coefficients

Peel Shear

Room 50°C Room 50°C

A 647.97 587.09 1,040.40 1,013.50

b 1.24 1.30 0.49 0.73

Cth 1.29 2.71 1.29 2.71

q 223.73 190.85 218.29 406.42

n 0.83 0.78 0.48 0.63

Fig. 16. Number of wet-dry cycles required to reach the asymptoticvalue of the bond strength



Calculation of the Interface Energy Release Rate

To demonstrate the use of the proposed predictive model [Eq. (2)],a CFRP-strengthened concrete beam with a preexisting interfacecrack was investigated. The beam has a span length of 7.2 m, andits geometry and reinforcement are given in Fig. 18. An interfacecrack 5 cm in length was initially placed at the interface betweenconcrete and the epoxy layer to simulate a possible initially

debonded region, which may occur during or after applicationof the CFRP plate owing to poor workmanship or environmentalexposure. This value of crack length was selected based on its criti-cality compared to the asymptotic value of the bond strength aftera number of crack lengths were investigated using FEM. A set offinite-element models of the beam was built using a commercialfinite-element program (ABAQUS 2006). Each model, represent-ing half of an actual beam, had a preexisting diagonal crack in con-crete connected to the interface crack (Fig. 19). This diagonal crackrepresents existing intermediate shear-flexural cracks in a pre-loaded RC beam before FRP strengthening is applied. A pair ofa diagonal crack and an interface crack is positioned at differentlocations in each model to investigate its criticality on the ERR.Except for the case of plate-end debonding, which has no diagonalcrack, the interface crack is located at 5, 35, 65, 95, 125, and155 cm from the loading point.

Constitutive Model of Materials, Finite Elements, andLoading Scheme

In finite-element implementation of the FRP-strengthened RCbeam, concrete was modeled by 4-node plane-strain elements. Aconcrete damage plasticity model was used to describe the com-pression and tension behavior of concrete, using properties frommaterial characterization. In both regimes, a linear elastic behavioris assumed up to the yield stress of concrete, with Young’s modulusbeing 35 GPa from material characterization. In the compressionzone, the concrete is assumed to deform in a nonlinear manner(Fig. 20) with yield and ultimate stresses of 15 and 36 MPa, respec-tively. With this model, the stiffness of the concrete elements isreduced to zero when cracking is determined to have occurredat an element integration point. The effect of biaxial loading(i.e., biaxial failure of concrete) is taken into account by specifying

Fig. 17. Schematic of service life prediction under moist conditions

Fig. 18. Geometry of precracked FRP-strengthened RC beam

Fig. 19. FE model of precracked FRP-strengthened RC beam and submodel of the vicinity of the interface crack



failure ratios. Interaction between the concrete and the steelreinforcement in the tension zone is governed by a tension stiffen-ing model, in which the stiffness of concrete in the vicinity of thereinforcement decreases linearly as the crack opening increases.Cracking in the concrete is initiated when the tensile stress exceeds3.72 MPa. The area under this softening curve is controlled by themode I fracture energy of concrete, which is 124 N=m (Meyer et al.1994). These values were chosen to ensure convergence of the sol-ution for the purpose of demonstrating the application of the pro-posed model.

Modeled using 2-node truss elements, the steel reinforcement isassigned a bilinear material behavior with specified Young’s modu-lus of 200 GPa and yield stress of 552 MPa, and the CFRP plate andadhesive were modeled by 4-node plane-strain elements with linearelastic behavior (Fig. 20). The Young’s moduli of CFRP plate andthe adhesive are 148 and 1.5 GPa, respectively. By assuming a per-fect bond between the steel reinforcement and the concrete, thetruss elements are embedded at the edges of concrete elements,meaning that the nodal displacements of the two element typesare the same at the contact. Regarding boundary conditions, a dis-placement was applied at the top of the beam to simulate loading ofthe beam under displacement control. The model is allowed tomove only in the y-direction on the left side to create symmetry,but allowed to move in both x-and y-directions at the bottom sup-port (Fig. 19). Reaction forces at the support, nodal displacements,stresses, and strains were recorded as the results of the simulation.Yielding of the steel reinforcement was determined from the con-tour plot of the principal stresses in the model. The load level cor-responding to the first occurrence of steel reinforcement yieldingwas then used as the maximum allowable load for the beam in thenext step of the analysis when calculating the maximum ERR.Owing to the nonlinear behavior of concrete in the tension regionafter cracking, a quasi-Newton technique (ABAQUS 2006) calledthe Broyden-Fletcher-Goldfarb-Shanno (BFGS) method was usedto improve the convergence rate in the analysis. In cases whenthe BFGS method led to a difficulty to converge to a solution, anenergy dissipation scheme was implemented to overcome rapid

change in the kinetic energy of the elements owing to softeningbehavior of the material.

Energy Release Rate Calculation

Prenotch in the concrete beam and initial interface crack at theconcrete-epoxy interface were modeled by having the regeneratednodes on the opposite surfaces of the cracks sharing initial coor-dinates. This allows an initially closed surface to separate as a resultof the external load. To calculate the stress intensity factors, KI andKII , at the interfacial crack tip, the interaction integral method (Shihand Asaro 1988) was implemented together with 8-node singularelements at the crack tip in a separate submodel (Fig. 19). The no-dal displacements of all the elements in the submodel are governedby the displacement field from the half-beam model described pre-viously. Knowing KI and KII , the driving force for crack propaga-tion can be calculated in terms of the corresponding ERRs. Unlikefracture in a homogenous material, KI and KII are complex stressintensity factors in interface fracture (He and Hutchinson 1989;Rice 1988). Assuming plane-strain condition, the energy releaserates in mode I and mode II (GI and GII ) are given by

GI ¼1� β2

E� ðK2I Þ and GII ¼

1� β2

E� ðK2IIÞ ð5Þ

where

1E� ¼

12

�1�E1

þ 1�E2

�; β ¼ μ1ðκ2 � 1Þ � μ2ðκ1 � 1Þ

μ1ðκ2 þ 1Þ þ μ2ðκ1 þ 1Þ

and κi ¼ 3� 4vi; �Ei ¼ Ei=ð1� ν2i Þ; μi = shear modulus; vi =Poisson ratio; Ei = Young’s modulus, with i denoting the individualconstituents. Switching the materials changes the sign of β, but willnot affect the value of the ERR. In this case, material 1 is defined asconcrete, and material 2 is the epoxy.

Interface Moisture Content during Service Life

Because the predictive model is derived from the relationship be-tween the rate of bond strength deterioration and the intermediate

Fig. 20. Material constitutive models of concrete, steel reinforcement, CFRP, and epoxy



moisture content, a finite-element simulation of moisture diffusionin the FRP-strengthened RC beam has to be performed. The relativehumidity (RH) in the United States is generally in the range of 30and 80 during a year. At some point, RH may become as high as100%, for example, in Florida and Louisiana during a rainy season.An FRP-strengthened beam would be exposed to high moistureconditions during a rainfall. Using this as the boundary conditionin a moisture diffusion simulation and the solution method dis-cussed earlier, the predicted moisture content present in the bondline of the full-scale FRP-strengthened RC beam after various du-rations is calculated, as shown in Fig. 21. According to precipita-tion frequency information published by the National Oceanic andAtmospheric Administration National Weather Service (Hershfield1961), the typical rainfall durations range from 30 min to 24 h. Forthis rainfall durations, the predicted interface moisture contentwould be as large as 0.02 weight%; or C=Cth is 1.55%.

Prediction of Debonding Failure under MoistureCondition

For a beam model of the same configuration and reinforcementwithout any interface crack, the maximum allowable service loadunder four-point bending is 368 kN to avoid inelastic deformationof the reinforcement. This value is close to the one obtained ana-lytically using elasticity and strain compatibility (ACI 2008). Inpractice, a beam with the same configuration as the model wouldhave the maximum value of the driving force for interface crackpropagation limited by this load level. The criticality of the cracklocation on the ERR is shown in Fig. 22. When the interfacecrack is located further from the loading point toward the support,

GI will increase [Fig. 22(a)]. On the other hand, GI will reachits maximum value in the early stage of loading, and will decreasewhen the interface crack is closer to the loading point (i.e., whenthe interface crack mouth is closing). For mode II, GII increasesas the load increases in most cases, except for the case whenthe interface crack is located 35 cm from the loading point[Fig. 22(b)]. Both energy release rates are very much negligiblewhen the location of the interface crack is at the plate-end. Themaximum energy release rates attainable within the limit of theservice load for all cases are listed in Table 4.

Table 4 shows that GI for all cases are smaller than the thresholdvalue of the peel fracture toughness obtained from the continuousmoisture condition test. This implies that interface debondingowing to the moisture effect is unlikely to occur by mode I fracture.The same conclusion can also be made forGII in most cases, exceptfor the location of interface crack at 35 cm. The value of GII atthis location is higher than the threshold value of shear fracturetoughness, implying that premature failure by debonding in anFRP-strengthened RC beam is most likely governed by the modeII fracture. Therefore, an existing interface crack at this locationmay be considered critical and most likely to cause extensivedebonding after extended period of exposure to cyclic moisturecondition. Solving Eq. (2) with the original fracture toughnessand the corresponding ERR from the FE analysis as the upperand lower bounds of the integration on the right side of the equa-tion, the number of wet-dry cycles required for the concrete-epoxybond strength to reach that particular value of fracture toughness,GII is given as

Fig. 21. Normalized moisture content in the adhesive bond line as predicted by FEM for a time period from 2 to 10 weeks (viewed from the beamsoffit)

Fig. 22. ERRs in FRP-strengthened RC beams with an interface crack at various locations: (a) mode I; (b) mode II



Nf ¼Γ0 � GII

qðCint=CthÞnð6Þ

where Cint = intermediate moisture content (from diffusion simu-lation); and GII = maximum ERR of the FRP-strengthened beam inconsideration. The number of wet-dry cycles to cause permanentdeterioration in the bond, resulting in residual shear fracture tough-ness of GII ¼ 455:70 N=m, is shown in Fig. 23 for various inter-face moisture contents. For typical rainfall durations, 30-min, 1, 6,and 24-h, the ratio of threshold moisture contents are 3 × 10�4,6 × 10�4, 3:7 × 10�4, and 0.015, respectively. Correspondingly,the number of wet-dry cycles required to reach the residual fracturetoughness of 455:7 N=m are 129, 94, 41, and 21 cycles. Nonethe-less, the probability of having a rainfall of longer duration, 24-h forexample, in a year is quite small. Therefore, the service life is likelyto be much more than 21 cycles. To obtain the service life in termsof the expected number of years, an in-depth statistical analysis onrainfall data similar to that of Hershfield (1961) should be per-formed. The effect of mode-mixity on the interface bond strengthis neglected in this analysis because only one mode of fracture isdeemed critical when considering the maximum energy release ratein conjunction with the minimum bond strength, resulting in a more

conservative approximation. Nonetheless, mode-mixity should betaken into account when such data is available.

Potential Effect of Sustained Load on InterfaceFracture Toughness

In a real service condition, strengthened concrete structures areunder both mechanical and environmental stresses at the sametime. To simulate this condition and as a preliminary investigation,fracture tests on peel specimens under coupled moisture diffusionand stress were conducted. The shear fracture specimen was notstudied here because the load required to fail in this mode is afew orders of magnitude larger than the case of peel fracture, whichrenders conditioning process impractical under regular laboratoryconditions. Stress in the interface was created by applying loadscorresponding to 10, 20, and 30% of the initial bond strengthon the cantilever tip of peel fracture specimens. The loading frameswere left in water containers at 23 and 50°C (Fig. 24). The level ofsustained load was a fraction of the threshold value obtained innormal continuous moisture condition testing (i.e., 10, 20, and30 N). Vertical displacement of the tip of the CFRP cantileverwas recorded.

In all levels of sustained load, there was a brief jump in deflec-tion during the first few hours, which could be attributed to instan-taneous microcracking in the epoxy. The deflection then increasedin small magnitudes owing to the creep effect in the bond line. Thiseffect is significantly pronounced in specimen under 30 N sustainedload at high temperature. It was found that specimens undersustained load of 30 N at 50°C failed after only five days of con-ditioning time, with the last CFRP tip deflection measured atapproximately 7 mm before a jump in deflection owing to creepcrack propagation. Recall that peel specimen under continuousmoisture ingress failed at a tip deflection in the range of 5 to10 mm. This corresponds to maximum load between 45 and 60 N,depending on the duration of moisture conditioning. On the otherhand, specimens under sustained loads of 10 and 20 N did not failby creep fracture. Instead, they were tested in peel fracture afterfour and six weeks. Comparing the maximum force at crack initia-tion, it was found that the effect of coupled stress-diffusion on bondstrength is not obvious for these specimens under 10 and 20 N. Thisimplies that the interface fracture toughness could be affectedby an existing sustained load, if the load level was higher thana certain lower bound value, which is 30 N in this case. Such effectof sustained stress coupled with moisture diffusion can furtherdegrade the strength of FRP-concrete interface leading to prema-ture failure at load levels much lower than predicted by the model.The effect of sustained load on interface fracture toughness in aspecimen under moisture effects needs to be further studied forthe modification of the proposed model to take into account theeffect of stress-diffusion coupling.

Fig. 24. Loading frame for coupled stress-diffusion test (photo by C. Tuakta)

Table 4. Maximum Mode I and II Energy Release Rates Limited by theService Load

Location ofinterface crack

Maximum ERR (N=m)

Mode I Mode II

5 35.87 297.29

35 30.07 455.70

65 32.33 261.14

95 40.04 263.93

125 48.13 234.17

155 76.21 120.40

Plate-end 0.000622 0.08

Fig. 23. Number of wet-dry cycles to reach residual shear fracturetoughness equal to GII ¼ 455:7 N=m



Conclusion

In this study, the effects of moisture cyclic conditions on thefracture toughness of a CFRP-concrete bond system have beendetermined considering the peel and shear fracture toughness.The findings from this study can be summarized as follows:1. Cyclic moisture conditioning tests have shown that the adhe-

sive bond cannot regain its original bond strength after succes-sive wet-dry cycles at both room and high temperatures.Significant loss in the ability to regain original bond strengthwas observed after three weeks of exposure to moisture. Theresidual bond strength decreases as the number of wet-drycycles and the intermediate conditioning duration increases.

2. Based on this deterioration behavior, a predictive model hasbeen developed for predicting the service-life of FRP-concretebond systems.

3. Based on the concept of fracture mechanics, application of theproposed conceptual model to a precracked FRP-strengthenedRC beam was demonstrated for the prediction of debondingfailure under moisture cycles.

4. Possible effect of sustained stress is noted; this effect should befurther investigated.Areas of further research includes conducting a comprehensive

experimental program considering both controlled laboratory andfield conditions for further validation and refinement of the pro-posed model. In addition, integration of debonding failure undercyclic moisture condition to other deterioration mechanisms, suchas chloride ion attack on steel reinforcement or carbonation of con-crete, needs to be developed for a more complete framework as abasis for service life prediction.

Acknowledgments

This research was supported by the National Science Foundation(NSF) CMS Grant No. 0510797. The authors are grateful to theformer program manger, Dr. Lawrence C. Bank, for his interest andsupport of this work.

Notation

The following symbols are used in this paper:C = transient moisture content (weight percentage);

Cint = intermediate moisture content;Cth = threshold moisture content;E = Young’s modulus of material;GI = mode I energy release rate;GII = mode II energy release rate;KI = mode I stress intensity factor;KII = mode II stress intensity factor;N = number of wet-dry cycles;Γ = fracture toughness;μ = shear modulus of material; andν = Poisson ratio of material.

References

ABAQUS. (2006). “ABAQUS 6.6 documentation.” SIMULIA, Providence,RI.

American Concrete Institute (ACI). (2008). “Guide for the design andconstruction of externally bonded FRP systems for strengtheningconcrete structures.” ACI 440.2R-08, Detroit.

Antonopoulos, C. P., and Triantafillou, T. C. (2003). “Experimental inves-tigation of FRP-strengthened RC beam-column joints.” J. Compos.

Constr., 7(1), 39–49.Au, C. (2009). Hygrothermal effects on interface fracture of FRP bonded

concrete: Theory, experiment, and simulation, LAMBERT AcademicPublishing, Saarbrücken, Germany.

Au, C., and Büyüköztürk, O. (2005). “Effect of fiber orientation and plymix on fiber reinforced polymer-confined concrete.” J. Compos.Constr., 9(5), 397–407.

Au, C., and Büyüköztürk, O. (2006a). “Debonding of FRP platedconcrete: A tri-layer fracture treatment.” Eng. Fract. Mech., 73(3),348–365.

Au, C., and Büyüköztürk, O. (2006b). “Peel and shear fracture characteri-zation of debonding in FRP plated concrete affected by moisture.”J. Compos. Constr., 10(1), 35–47.

Bae, S. W., and Belarbi, A. (2008). “Effects of various environmentalconditions on RC columns wrapped with FRP sheets.” J. Reinf. Plast.Compos., 29(2), 290–309.

Butcher, J. C. (2008). Numerical methods for ordinary differentialequations, Wiley, West Sussex, England.

Büyüköztürk, O., Gunes, O., and Karaca, E. (2004). “Progress on under-standing debonding problems in reinforced concrete and steel membersstrengthened using FRP composites.” Constr. Build. Mater., 18(1),9–19.

Büyüköztürk, O., and Hearing, B. (1998). “Failure behavior of precrackedconcrete beams retrofitted with FRP.” J. Compos. Constr., 2(3),138–144.

Chajes, M. J., Thomson, T. A. J., and Farschman, C. A. (1995). “Durabilityof concrete beams externally reinforced with composite fabrics.”Constr. Build. Mater., 9(3), 141–148.

Cheung, M. S., and Kyle, B. R. (1996). “Service life prediction of con-crete structures by reliability analysis.” Constr. Build. Mater., 10(1),45–55.

Crank, J. (1975). The mathematics of diffusion, Oxford Science Publica-tions, Oxford, UK.

Gunes, O. (2004). “A fracture based approach to understanding debondingin FRP bonded structural members.” Ph.D. thesis, Massachusetts Insti-tute of Technology, Cambridge, MA.

He, M. Y., and Hutchinson, J. W. (1989). “Kinking of a crack out of aninterface.” J. Appl. Mech., 56, 270–278.

Hearing, B. (2000). “Delamination in reinforced concrete retrofittedwith fiber reinforced plastics.” Ph.D. thesis, Massachusetts Instituteof Technology, Cambridge, MA.

Hershfield, D. M. (1961). “Rainfall frequency atlas of the United Statesfor durations from 30 minutes to 24 hours and return periods from1 to 100 years.” Technical Paper No. 40, Weather Bureau, Washington,DC.

Hong, T. H., and Hastak, M. (2006). “Life-cycle performance modelfor FRP bridge deck panels.” Civ. Eng. Environ. Syst., 23(1),35–56.

Lin, H. J., and Liao, C. I. (2004). “Compressive strength of reinforcedconcrete column confined by composite material.” Compos. Struct.,65(2), 239–250.

Meier, U. (1995). “Strengthening of structures using carbon fibre epoxycomposites.” Constr. Build. Mater., 9(6), 341–351.

Meier, U., and Kaiser, H. (1991). “Strengthening of structures with CFRP.”Advanced composite materials in civil engineering structures, S. L. Iyerand R. Sen, eds., ASCE, Reston, VA, 224–232.

Meyer, R., Ahrens, H., and Duddeck, H. (1994). “Material model forconcrete in cracked and uncracked states.” J. Eng. Mech., 120(9),1877–1895.

Myers, J. J., Murphy, S. S., and Micelli, F. (2001). “Effect of combinedenvironmental cycles on the bond of FRP sheets to concrete.” Compo-sites in Construction, International Conf.

Oehlers, D. J. (2006). “FRP plates adhesively bonded to reinforced concretebeams: Generic debonding mechanisms.” Adv. Struct. Eng., 9(6),737–750.

Parvin, A., and Wu, S. H. (2008). “Ply angle effect on fiber compositewrapped reinforced concrete beam-column connections under com-bined axial and cyclic loads.” Compos. Struct., 82(4), 532–538.

Rice, J. R. (1988). “Elastic fracture-mechanics concepts for interfacialcracks.” J. Appl. Mech., 55(1), 98–103.



Saadatmanesh, H. (1997). “Extending service life of concrete and masonrystructures with fiber composites.” Constr. Build. Mater., 11(5-6),327–335.

Shih, C. F., and Asaro, R. J. (1988). “Elastic-plastic analyis of crackson bimaterial interfaces: Part I—Small scale yielding.” J. Appl. Mech.,55(2), 299–316.

Soudki, K., El-Salakawy, E., and Craig, B. (2007). “Behavior of CFRPstrenghtened reinforce concrete beams in corrosive environment.”J. Compos. Constr., 11(3), 291–298.

Teng, J. G., Chen, J. F., Smith, S. T., and Lam, L. (2001). FRP-strengthened

RC structures, John Wiley & Sons, West Sussex, England.Toutanji, H. A. (1999). “Durability characteristics of concrete columns con-

fined with advanced composite materials.” Compos. Struct., 44(2-3),155–161.

Toutanji, H. A., and Gomez, W. (1997). “Durability characteristics of con-crete beams externally bonded with FRP composite sheets.” Cem.Concr. Compos., 19, 351–358.

Tuakta, C., and Büyüköztürk, O. (2011). “Deterioration of FRP/concretebond system under variable moisture conditions quantified by fracturemechanics.” Composites, Part B, 42(2), 145–154.



conceptual model for prediction of frp-concrete bond

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