Conceptual Model for Prediction of FRP-Concrete Bond 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 decks have become increasingly popular as a result of extensive studies on short-term debonding behavior. Nevertheless, long-term performance and durability issues regarding debonding behavior in such strengthening systems still remain largely uncertain and unanswered. Because of its composite nature, the effectiveness of the strengthening system depends on the properties of the interfaces between the three constituent materials; namely, concrete, epoxy, and FRP. Certain factors, including those related to environmental exposures, can cause degradation of the interface properties during service life. This is particularly critical when predicting service life and planning maintenance of FRP-strengthened concrete structures. In this study, effect of moisture on an FRP-concrete bond system is characterized by means of the tri-layer fracture toughness, which can be obtained experimentally from peel and shear fracture tests. Fracture specimens were conditioned under various durations and numbers of wet-dry cycles at room temperature and 50°C. An irreversible weakening in bond strength was observed in fracture specimens under moisture cyclic condition. A conceptual model is developed based on the experimental results of the fracture specimens under variable cyclic moisture conditions for the bond strength prediction of the FRP-concrete bond system. A numerical study of a precracked FRP-strengthened reinforced concrete beam is then performed to show potential application of the proposed predictive 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) materials for repair and strengthening has become a widely accepted practice as a result of design code revision, physical aging, environmental deterioration, and catastrophic events. Advantages of FRP over other conventional repair materials include its higher strengthto-weight ratio, additional corrosion resistance, and ease of application. Several strengthening techniques, including FRP plate bonding and column wrapping, have been widely applied during the past decades as a result of extensive studies and availability of ample experimental results on the mechanical behavior of the retrofit systems (Antonopoulos and Triantafillou 2003; Lin and Liao 2004; Meier 1995; Parvin and Wu 2008; Saadatmanesh 1997; Teng et al. 2001). For flexural strengthening of reinforced concrete (RC) elements such as beams and slabs, FRP laminates in the form of rigid plates or flexible sheets are externally bonded to the tension faces of the elements using epoxy adhesive through dry or wet lay-up processes. American Concrete Institute (ACI) Committee 440 (2008) provides design guidelines, employing design principles similar to that of typical steel reinforced concrete 1
Ph.D. candidate, Dept. of Civil and Environmental Engineering, MIT, Room 5-336, 77 Massachusetts Ave., Cambridge, MA 02139. E-mail:
[email protected] 2 Professor, Dept. of Civil and Environmental Engineering, MIT, Room 1-281, 77 Massachusetts Ave., Cambridge, MA 02139 (corresponding author). E-mail:
[email protected] Note. This manuscript was submitted on July 30, 2010; approved on February 9, 2011; published online on February 11, 2011. Discussion period open until March 1, 2012; separate discussions must be submitted for individual papers. This paper is part of the Journal of Composites for Construction, Vol. 15, No. 5, October 1, 2011. ©ASCE, ISSN 1090-0268/ 2011/5-743–756/$25.00.
beams. Nonetheless, premature failure by debonding of the concrete-epoxy interface may occur, which can significantly affect the load capacity of the retrofitted systems (Au and Büyüköztürk 2005; Büyüköztürk et al. 2004; Büyüköztürk and Hearing 1998; Gunes 2004; Hearing 2000; Meier and Kaiser 1991; Oehlers 2006; Teng et al. 2001). This failure behavior is undesirable owing to its lack of prior indication and brittle nature. In many situations, it is critical to consider this issue, especially when an FRP-strengthened beam is subjected to variable environmental conditions during its service life, causing deterioration of the bond strength. In real-life applications, FRP-strengthened structural members are exposed to humidity fluctuations owing to seasonal rainfall or snowfall. This kind of environmental fatigue can affect an FRP-retrofit system in a number of ways, as shown by various studies on the durability of FRP-plated RC beams and FRP-confined RC columns. In particular, cyclic moisture effect was identified as an important environmental deterioration mechanism that promotes reduction in the overall stiffness and ultimate strength, leading to premature system failures. Toutanji (1999) found that the extent of deterioration in FRP-confined RC columns depended on both the types of epoxy and FRP. Under 300 wet-dry cycles, the strength and ductility of glass FRP-confined column specimens decreased, although no significant detrimental effects were observed in carbon FRP-confined column specimens. These observations are in good agreement with recent findings reported by Bae and Belarbi (2008). As for FRP-plated RC beams, reductions in ultimate strength and stiffness owing to accelerated wet-dry cycling were generally observed. Chajes et al. (1995) reported 20 to 30% reduction in ultimate strength for glass FRP (GFRP) and carbon FRP (CFRP) retrofitted specimens that were subjected to 100 wet/dry cycles. In one study (Toutanji and Gomez 1997), the observed strength reductions could be as much as 33% in FRP-plated
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concrete beams subjected to 300 wet-dry cycles in salt water. Ultimate load also depreciated at various degrees, depending on the number of wet-dry cycles (Soudki et al. 2007). Similar to the case of FRP-confined RC columns, the stiffness of FRP-plated concrete beams deteriorates under cyclic moisture condition. In one study (Myers et al. 2001), it was experimentally determined that GFRP-plated specimens could lose up to 85% of their original flexural stiffness after only 20 wet-dry cycles, compared to 55% in the case of CFRP-plated specimens. Aramid FRP-plated specimens in the same test series appeared somewhere in between. In general, failure mode was reported as a debonding that took place near the FRP-concrete interface. It is clear from the experimental investigations that the strength and the stiffness of FRP-strengthened and FRP-retrofitted concrete structural elements are affected by moisture cycles. The overall integrity of a structure through its service life will in turn depend on the performance of each retrofitted structural component. As a result, the ability to predict the service-life of an FRP-concrete bond system under the effect of moisture is crucial to improving the safety of civil structures strengthened by this technique. Despite the need, a model for prediction of FRP-concrete bond strength under moisture cycles has not yet been proposed. In this research, a fracture-based predictive model has been developed from a database of degradation in FRP-concrete bond caused by variable moisture cycles.
FRP-strengthened RC beam members, the limit state may be the flexural capacity before any premature debonding, which can be caused by weakening of the concrete-epoxy-FRP interface. The corresponding deterioration process may be driven by moisture diffusion. For example, rain or melting snow can seep through existing cracks or deck joints to retrofitted RC girders and diffuse into the FRP-concrete bond region, causing bond strength to deteriorate. Hence, to predict the service life, a model is required to describe the extent of deterioration with respect to the moisture content. In this study, the bond strength of the FRP-concrete interface under the effect of cyclic moisture condition is characterized by fracture toughness. This approach is more suitable to the debonding problem because debonding can be considered as a local failure. During failure initiation at an existing defect, such as an unbonded region at the concrete-epoxy interface, both mode I (opening) and mode II (shearing) driving forces may exist, depending on location of the defect. In this situation, the tri-layer fracture toughness model specialized for opening and shearing modes is a suitable tool for quantification of the bond strength of the interface. The relationship can be derived between the extent of bond strength degradation and moisture content in the bond line obtained from a finite-element (FE) simulation of moisture diffusion.
Research Objective and Approach
In FRP-strengthened concrete structural members, FRP-concrete bond joints can be idealized as a three-layered material system consisting of concrete, epoxy, and FRP. In such a system, cracks can propagate in five regions, as shown in Fig. 1. Using energy considerations, the energy release rate can be computed from the difference in the strain energy of the cracked body (far behind the crack tip) and that of the intact body (far ahead of the crack tip). The detailed derivation of the tri-layer fracture toughness is given in Au (2009) and Au and Büyüköztürk (2006a). The expression of the energy release rate contains geometric and material information from all three material layers. To obtain the fracture toughness of the system from the experiment, configurations of the peel and shear fracture specimens are chosen such that they represent possible loading cases found in a full-sized FRP-strengthened concrete beam, as shown in Figs. 2(a) and 2(b). To compute the interface fracture toughness of the FRP-concrete bond system, critical loads obtained from the debonding tests and material properties obtained from the material characterization were used.
The objective of this research is to use the concept of fracture mechanics to develop a conceptual model for predicting the strength of an FRP-concrete bonded joint subjected to moisture cycling, and to extend its application to FRP-retrofitted concrete structures. Degradation of bond strength under cyclic moisture condition is quantified by the tri-layer fracture toughness in Au (2009) and Au and Büyüköztürk (2006b). This paper is organized as follows. First, the effects of continuous and cyclic exposure to moisture on the FRP-concrete bond system are briefly discussed. The development of the predictive model based on the experimental results of the peel and shear fracture specimens is then described. Based on this predictive model and the concept of fracture mechanics, a scheme for predicting the debonding failure in an FRP-retrofitted structural element is presented through an example of its application to a precracked FRP-strengthened RC beam.
Quantification of Bond Strength by Tri-Layer Fracture Toughness Model
Service Life Prediction
Peel and Shear Fracture Specimens and Test Setup
In a civil infrastructure, each of the structural components is initially designed according to the design guidelines to meet its own strength and serviceability criteria. For example, an RC beam girder in a bridge needs to be checked during the design process for flexural and shear capacity, acceptable crack opening, and maximum deflection. Similar criteria will need to be established for the durability and life cycle performance of the structure. Owing to physical changes in the structure during its service life, and possible chemical changes in the surrounding, the performance of the structural components may decrease in various ways, which in turn affects the overall structural integrity of the infrastructure in service. Knowing when the performance of a structural component will fall below an acceptable limit could be helpful in operation and maintenance planning. There are three aspects to be identified when determining the service life: limit state, damaging factors that affect material properties, and deterioration mechanism (Cheung and Kyle 1996; Hong and Hastak 2006). In the case of
The effect of continuous moisture ingress and its reversibility was investigated quantitatively and qualitatively by means of peel and shear fracture tests. Figs. 3(a) and 3(b) show the dimensions of the peel and shear specimens, respectively. The CFRP plate in both specimens is 1.28 mm thick and made of unidirectional carbon fibers. 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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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
over the bond region. In each specimen, an initial crack of 75 mm was introduced at the epoxy-concrete interface next to the CFRP cantilever arm by Teflon tape. For the peel fracture test, the specimens were placed horizontally in a loading frame and constrained from any movement by alignment screws and an end plate [Fig. 4(a)]. Load was applied by vertically pulling the tip of the CFRP plate. Shear specimens were placed vertically in the loading
frame and pulled upward [Fig. 4(b)]. Detailed discussion on instrumentation and test procedure can be found in Au and Büyüköztürk (2006b). Specimens were conditioned in a moisture environment at 23°C using water tanks, and at 50°C using an environmental chamber before testing. The load-displacement behavior and debonding modes were observed and correlated with the moisture level obtained from the finite-element diffusion simulation.
Fig. 4. Test setups: (a) peel fracture; (b) shear fracture JOURNAL OF COMPOSITES FOR CONSTRUCTION © ASCE / SEPTEMBER/OCTOBER 2011 / 745
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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 time period of 2 to 10 weeks (only peel fracture specimen at room temperature shown)
Predicting the Interface Moisture Content Because it is difficult to directly measure the moisture content at the interface in peel and shear fracture specimens during the test, a numerical simulation of moisture diffusion was performed. In this case, the governing equation for mass diffusion is basically an extension of Fick’s equation, which allows nonuniform values of diffusivity and solubility in multiple constituent materials of the fracture specimens (Crank 1975). In finite-element analysis, moisture diffusion is driven by a concentration gradient with concentration normalized by solubility being the nodal variable of an element. Three-dimensional models of the peel and shear fracture specimens (Fig. 5) were created with exactly the same dimensions for the analysis by a general purpose finite-element program (ABAQUS 2006). Eight-node three-dimensional mass diffusion elements were used throughout the models, with temperaturedependent diffusion coefficients for room temperature and 50°C, as shown in Table 1 (Au 2009). Because the models involve three materials, elements were constructed such that nodes were shared at the concrete-epoxy and CFRP-epoxy interfaces. The epoxy layer and the CFRP plate were modeled using one layer of diffusion elements with thicknesses of 1 and 1.28 mm, respectively. For concrete block, the 5 × 5 × 4:7 mm3 diffusion elements were used throughout. The boundary condition was specified as 100% moisture concentration on the outer surface of concrete, epoxy, and CFRP plate to represent the total submersion of the specimens under water. Time integration of the transient diffusion analysis was conducted with backward Euler method (also known as the modified Crank-Nicholson operator) because it is unconditionally stable for this type of linear problem (Butcher 2008). The temperature and mass diffusion are not coupled in solving the differential equation for mass diffusion because moisture diffusion took place at a constant temperature during moisture conditioning. The average moisture content in terms of weight percentage (C) or the transient moisture content corresponding to various conditioning Table 1. Diffusion Coefficients of Concrete, CFRP, and Epoxy Material Concrete CFRP Epoxy
Temperature (°C)
Diffusivity (1011 m2 =s)
Solubility (wt%)
23 50 23 50 23 50
3.24 3.24 0.068 0.081 0.023 0.048
7.71 7.76 0.34 0.9 2.58 5.42
Table 2. Moisture Content (Weight %) at the Interface in Peel and Shear Fracture Specimens from Finite-Element Simulation of Moisture Diffusion Moisture content (%) Duration (weeks)
23°C
50°C
2 4 6 8 10
0.41 0.77 1.01 1.29 1.41
0.87 1.63 2.14 2.71 3.26
durations are shown in Table 2 for the tri-layer fracture specimens. These values were used to obtain the corresponding mechanical properties (from the tensile and compression tests) of the epoxy and concrete in the interface fracture toughness calculation. As predicted, under higher temperature, moisture diffuses more into the bond line of the fracture specimens. This simulation method will be used later in this study to determine moisture content in the bond line of other FRP-concrete structures, such as a precracked FRPstrengthened RC beam.
Effect of Continuous Moisture Ingress The objective of continuous moisture ingress is to investigate the extent of bond strength degradation caused by prolonged exposure to moisture. Peel and shear fracture specimens were subjected to moisture condition for durations ranging between two and eight weeks at room temperature and 50°C. They were then tested while they were still in a wet condition. The relationship between moisture content in the bond line and bond degradation were obtained. Figs. 6(a) and 6(b) show the effect of moisture on the peel and shear fracture toughness, respectively. The values of fracture toughness are the average of three specimens in each condition group. Significant reduction in facture toughness after moisture conditioning in both peel and shear fracture specimens indicated that moisture had a detrimental effect on the strength of the FRP-concrete bond system. More than 50% of the initial bond strength is reduced by the exposure to moisture, even after an initial duration of two weeks. For both peel and shear fracture specimens, there was a shift in the failure mode from concrete delamination in dry specimens to concrete-epoxy interface separation in wet specimens, at both room and high temperatures. This indicates the weakening of the interface owing to the presence of moisture. It was observed that the fracture toughness approximately reaches
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Fig. 6. Effect of continuous moisture condition on: (a) peel fracture toughness; (b) shear fracture toughness
an asymptotic value after eight weeks for both peel and shear fracture specimens. Hence, Table 2 shows that the threshold moisture contents (C th ), beyond which no additional degradation is registered, are 1.29 at room temperature and 2.71 at high temperature. The extent of strength degradation and its correlation with interface moisture content in terms of the ratio of transient and threshold moisture contents (C=C th ) is shown in Figs. 7(a) and 7(b). The fracture toughness values corresponding to these moisture contents were later used in the analysis of the effect of moisture reversal and moisture cyclic conditioning on the bond strength of the FRP-concrete bonded joint.
Effect of Cyclic Moisture Condition The difference between continuous moisture ingress and cyclic moisture condition is that in the former, specimens are tested after continuous exposure to moisture as they are still wet, whereas in the latter, specimens are allowed to dry after a series of wet-dry cycles before being tested. A wet-dry cycle involves submersing a specimen for a period of time, followed by drying the specimen. The drying duration has been determined by observing the weight change during drying of bulk epoxy coupons and separate group of the peel and shear fracture specimens that were conditioned for various periods of time. For this part of the study, dry condition is defined as the duration after which small change in weight is registered in such specimens. It has been found that at least four days are required for the specimens to attain a small weight change (less than 0.05%). Therefore, drying duration is four days in this study. Any irreversible effect will be shown by comparing the residual fracture toughness from the cyclic moisture condition tests with that from the continuous moisture ingress tests.
Peel and Shear Fracture Toughness under Moisture Reversal Peel and shear fracture specimens were conditioned under the moisture environment for one, two, three, four, six, and eight weeks at 23 and 50°C. They were then left to dry for four days before testing. Characterization of plain concrete and the epoxy under moisture reversal were also conducted by means of compressive and tensile tests, respectively (Tuakta and Büyüköztürk 2011). The epoxy was unable to regain its initial mechanical property in spite of drying. This may be attributed to the loss of cross-linking density and permanent swelling damage owing the presence of water. On the other hand, the residual Young’s modulus of concrete after moisture reversal did not show any significant change, implying that concrete can regain its initial properties after drying. Correlation between the residual fracture toughness and the intermediate moisture content is shown in Fig. 8. In this case, the intermediate moisture content is defined as the amount of water in the bond line at the end of each wet interval. Longer intermediate conditioning durations result in higher permanent deterioration of the interface. Irreversible effect of moisture conditioning was evident in both peel and shear specimens conditioned at both room and high temperatures, as shown in Figs. 9 and 10, respectively. It was found that although the specimens were dried before testing, deterioration in bond strength owing to prior continuous exposure to moisture could still be captured during the fracture tests. The specimens could not fully regain their initial bond strength, and the residual strength decreased for increasing intermediate conditioning durations. In general, the specimens could regain some bond strength from drying, when compared to those tested in wet condition. Nonetheless, sharp loss in the ability to regain bond strength is apparent at conditioning durations longer than three weeks. At high temperature, however, bond strength regain
Fig. 7. Empirical relationship between moisture content and the effect of continuous moisture condition on: (a) peel fracture toughness; (b) shear fracture toughness JOURNAL OF COMPOSITES FOR CONSTRUCTION © ASCE / SEPTEMBER/OCTOBER 2011 / 747
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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
was observed only in specimens conditioned for less than six weeks. The peel and shear fracture specimens conditioned for longer periods at this temperature seemed to have even lower strength than the wet specimens. With respect to the failure surface, more concrete debris was found on the debonded epoxy layer in specimens that had higher residual bond strength. Peel and Shear Fracture Toughness under Moisture Cyclic Condition To determine the effect of conditioning duration and the number of wet-dry cycles on the residual strength of the adhesive bond, peel and shear specimens were subjected to a conditioning program shown in Fig. 11, with three weeks being the longest continuous
Fig. 11. Condition groups in moisture cyclic condition test
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Fig. 12. Effect of cyclic moisture condition on Young’s modulus of epoxy at: (a) room temperature; (b) 50°C
conditioning duration. Similar to continuous moisture condition, three specimens were tested for each condition group. After each brief continuous moisture ingress, the specimens were left to dry for four days in the laboratory at room temperature and approximately 60% relative humidity. For example, each fracture specimen in the two-weeks-two-cycles group underwent conditioning sequence as follows: two weeks under water, followed by four days in dry condition, followed by two weeks under water, and finally four days in dry condition. At the end of the conditioning program, the specimens were tested in dry condition using the same configurations as in Fig. 4. Corresponding material characterization was also conducted for plain concrete and the epoxy to obtain mechanical properties as functions of durations and cycles by curve-fitting, which were used in calculating the tri-layer fracture toughness. The properties of the concrete are not affected significantly by the wetdry cycles. On the other hand, Young’s modulus of the epoxy at both temperatures decreased for longer period of intermediate conditioning (and hence higher intermediate moisture content). This effect is shown by the plots in Fig. 12. Figs. 13 and 14 show the effect of wet-dry cycles on the residual interface fracture toughness in the peel and shear fracture specimens. Both the number of wet-dry cycles and the intermediate conditioning duration affect the residual bond strength. Reduction in residual interface fracture toughness with the increase in number of wet-dry cycles is observable in both peel and shear fracture specimens. Longer intermediate conditioning duration results in smaller residual strength. In most cases, higher temperature seems to accelerate the deterioration process, resulting in further reduction in residual bond strength. This is possibly attributable to higher moisture uptake between each wet-dry cycle. Similar to moisture reversal, higher residual strength is associated with more concrete debris left 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 on the epoxy. This suggests that strength degradation can take place in the CFRP-concrete interface as the FRP-strengthened concrete element is exposed to wet-dry cycles during its service-life.
Fig. 13. Effect of number of wet-dry cycles on the residual fracture toughness of peel fracture specimens
Fig. 14. Effect of number of wet-dry cycles on the residual fracture toughness of shear fracture specimens
Application: Prediction of Debonding in a Precracked FRP-Strengthened RC Beam under Moisture Cycles Conceptual Predictive Model for FRP-Concrete Bond Strength under Moisture Cycles Considering the results of the peel and shear fracture tests, the reduction in the FRP-concrete bond strength under continuous moisture exposure can be expressed in the form of an exponential decay with respect to interface moisture content: Γ ¼ AebðC=Cth Þ
ð1Þ
where the coefficients A and b are obtained from the continuous moisture condition tests (Fig. 7). As discussed earlier, reduction in the residual bond strength was found to increase with increased number of wet-dry cycles. For simplicity, it is assumed here that the rate 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 high during the first few wet-dry cycles, but will decrease to an almost constant value as the number of wet-dry cycles increases beyond three cycles. Because civil structures are designed to withstand much more wet-dry cycles during service life, this assumption is deemed reasonable for this analysis. Therefore, owing to the cyclic nature of the problem, a general form of the moisture cyclic degradation model is proposed as follows:
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Fig. 15. Relationship between the rate of deterioration and the ratio of intermediate and threshold moisture contents for specimens under cyclic moisture condition: (a) peel fracture specimens; (b) shear fracture specimens
dΓ ¼ qðC=C th Þn dN
ð2Þ
where Γ = interface fracture toughness obtained from Eq. (1); N = number of wet-dry cycles. The coefficients q and n are determined from fracture tests on peel and shear specimens under several sets of moisture cyclic duration, the results of which were discussed earlier. Their values at room temperature and 50°C were obtained by statistically curve-fitting the relationship between the deterioration rate of the bond strength (dΓ=dN) and the intermediate moisture content in the bond line obtained from the cyclic moisture condition tests (Fig. 15). Eq. (2) implies that as the moisture concentration approaches the threshold value, a fewer number of wet-dry cycles will be required for the fracture toughness to reach an asymptotic value. To determine the number of cycles, N th , that cause the fracture toughness to reach the asymptotic value, Eq. (2) is to be integrated: Z
N th
Z dN ¼ N th ¼
0
Γ0 Γth
1 dΓ qðC=C th Þn
ð3Þ
where Γ0 and Γth = initial fracture toughness of the control specimens (dry) and the asymptotic fracture toughness (wet), respectively. The coefficients in Eq. (1) and (2) are shown in Table 3. These coefficients are specific to the certain type of adhesive used in this study. Nonetheless, the methodology presented here is generally applicable to other commercially available structural adhesives, and further studies are needed to establish the variation of the coefficients based on the variety of epoxy types used in practice. The integration of Eq. (3) results in a function of C, which is the level of intermediate moisture content between each wet-dry cycle: N th ¼
Γ0 Γth qðC=C th Þn
ð4Þ
Table 3. Coefficients Obtained from the Moisture Reversal and Moisture Cyclic Condition Tests Peel
Shear
Coefficients
Room
50°C
Room
50°C
A b C th q n
647.97 1.24 1.29 223.73 0.83
587.09 1.30 2.71 190.85 0.78
1,040.40 0.49 1.29 218.29 0.48
1,013.50 0.73 2.71 406.42 0.63
Fig. 16. Number of wet-dry cycles required to reach the asymptotic value of the bond strength
Substituting various values of C=C th into Eq. (4), the number of cycles at which the residual bond strength reaches an asymptotic value is plotted in Fig. 16 for the peel and shear fracture specimens at room and high temperatures. It is predicted that higher intermediate moisture content and higher temperature will require slightly fewer wet-dry cycles for the fracture toughness to reach the asymptotic value. Predicting Debonding Failure in an FRP-Strengthened RC Beam Exposed to Moisture Cycles In real-life applications, existing RC beams are designed such that the service load should not cause any structural failure during the service life. This design philosophy also applies to the case of an FRP-strengthened RC beam. Given a loading history during the design service life of an RC beam, the driving force that can cause premature debonding may be characterized by the energy release rate (ERR) of an existing interfacial crack at a given time. According to ACI (2008), the stress in steel reinforcement is limited to 0.8 times its yield strength to avoid any inelastic deformation. This limitation implies the maximum load a beam will carry during its service life. However, this design principle is not conservative, in that a premature failure by debonding may occur at a lower level of the load. The ERR corresponding to the maximum load can indicate potential premature debonding failure when compared to available fracture toughness of the interfaces and the bulk materials (i.e., concrete and epoxy). A schematic is given in Fig. 17 for predicting debonding under moisture cycles in a precracked FRP-strengthened RC beam based on the proposed predictive model and the finite-element method. The two input parameters of the proposed predictive model are the ERR and the interface moisture content, both of which are calculated from FEM.
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debonded region, which may occur during or after application of the CFRP plate owing to poor workmanship or environmental exposure. This value of crack length was selected based on its criticality compared to the asymptotic value of the bond strength after a number of crack lengths were investigated using FEM. A set of finite-element models of the beam was built using a commercial finite-element program (ABAQUS 2006). Each model, representing half of an actual beam, had a preexisting diagonal crack in concrete connected to the interface crack (Fig. 19). This diagonal crack represents existing intermediate shear-flexural cracks in a preloaded RC beam before FRP strengthening is applied. A pair of a diagonal crack and an interface crack is positioned at different locations in each model to investigate its criticality on the ERR. Except for the case of plate-end debonding, which has no diagonal crack, the interface crack is located at 5, 35, 65, 95, 125, and 155 cm from the loading point. Constitutive Model of Materials, Finite Elements, and Loading Scheme
Fig. 17. Schematic of service life prediction under moist conditions
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 interface crack was investigated. The beam has a span length of 7.2 m, and its geometry and reinforcement are given in Fig. 18. An interface crack 5 cm in length was initially placed at the interface between concrete and the epoxy layer to simulate a possible initially
In finite-element implementation of the FRP-strengthened RC beam, concrete was modeled by 4-node plane-strain elements. A concrete damage plasticity model was used to describe the compression and tension behavior of concrete, using properties from material characterization. In both regimes, a linear elastic behavior is assumed up to the yield stress of concrete, with Young’s modulus being 35 GPa from material characterization. In the compression zone, the concrete is assumed to deform in a nonlinear manner (Fig. 20) with yield and ultimate stresses of 15 and 36 MPa, respectively. With this model, the stiffness of the concrete elements is reduced to zero when cracking is determined to have occurred at an element integration point. The effect of biaxial loading (i.e., biaxial failure of concrete) is taken into account by specifying
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 JOURNAL OF COMPOSITES FOR CONSTRUCTION © ASCE / SEPTEMBER/OCTOBER 2011 / 751
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Fig. 20. Material constitutive models of concrete, steel reinforcement, CFRP, and epoxy
failure ratios. Interaction between the concrete and the steel reinforcement in the tension zone is governed by a tension stiffening model, in which the stiffness of concrete in the vicinity of the reinforcement decreases linearly as the crack opening increases. Cracking in the concrete is initiated when the tensile stress exceeds 3.72 MPa. The area under this softening curve is controlled by the mode I fracture energy of concrete, which is 124 N=m (Meyer et al. 1994). These values were chosen to ensure convergence of the solution for the purpose of demonstrating the application of the proposed model. Modeled using 2-node truss elements, the steel reinforcement is assigned a bilinear material behavior with specified Young’s modulus of 200 GPa and yield stress of 552 MPa, and the CFRP plate and adhesive were modeled by 4-node plane-strain elements with linear elastic behavior (Fig. 20). The Young’s moduli of CFRP plate and the adhesive are 148 and 1.5 GPa, respectively. By assuming a perfect bond between the steel reinforcement and the concrete, the truss elements are embedded at the edges of concrete elements, meaning that the nodal displacements of the two element types are the same at the contact. Regarding boundary conditions, a displacement was applied at the top of the beam to simulate loading of the beam under displacement control. The model is allowed to move 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 support (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 contour plot of the principal stresses in the model. The load level corresponding to the first occurrence of steel reinforcement yielding was then used as the maximum allowable load for the beam in the next step of the analysis when calculating the maximum ERR. Owing to the nonlinear behavior of concrete in the tension region after cracking, a quasi-Newton technique (ABAQUS 2006) called the Broyden-Fletcher-Goldfarb-Shanno (BFGS) method was used to improve the convergence rate in the analysis. In cases when the BFGS method led to a difficulty to converge to a solution, an energy dissipation scheme was implemented to overcome rapid
change in the kinetic energy of the elements owing to softening behavior of the material. Energy Release Rate Calculation Prenotch in the concrete beam and initial interface crack at the concrete-epoxy interface were modeled by having the regenerated nodes on the opposite surfaces of the cracks sharing initial coordinates. This allows an initially closed surface to separate as a result of the external load. To calculate the stress intensity factors, K I and K II , at the interfacial crack tip, the interaction integral method (Shih and Asaro 1988) was implemented together with 8-node singular elements at the crack tip in a separate submodel (Fig. 19). The nodal displacements of all the elements in the submodel are governed by the displacement field from the half-beam model described previously. Knowing K I and K II , the driving force for crack propagation can be calculated in terms of the corresponding ERRs. Unlike fracture in a homogenous material, K I and K II are complex stress intensity factors in interface fracture (He and Hutchinson 1989; Rice 1988). Assuming plane-strain condition, the energy release rates in mode I and mode II (GI and GII ) are given by GI ¼
1 β2 2 ðK I Þ E
and GII ¼
1 β2 2 ðK II Þ E
ð5Þ
where
1 1 1 1 ¼ þ 1 E 2 ; E 2 E
β¼
μ1 ðκ2 1Þ μ2 ðκ1 1Þ μ1 ðκ2 þ 1Þ þ μ2 ðκ1 þ 1Þ
i ¼ E i =ð1 ν 2i Þ; μi = shear modulus; vi = and κi ¼ 3 4vi ; E Poisson ratio; E i = Young’s modulus, with i denoting the individual constituents. Switching the materials changes the sign of β, but will not affect the value of the ERR. In this case, material 1 is defined as concrete, and material 2 is the epoxy. Interface Moisture Content during Service Life Because the predictive model is derived from the relationship between the rate of bond strength deterioration and the intermediate
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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 beam soffit)
moisture content, a finite-element simulation of moisture diffusion in the FRP-strengthened RC beam has to be performed. The relative humidity (RH) in the United States is generally in the range of 30 and 80 during a year. At some point, RH may become as high as 100%, for example, in Florida and Louisiana during a rainy season. An FRP-strengthened beam would be exposed to high moisture conditions during a rainfall. Using this as the boundary condition in a moisture diffusion simulation and the solution method discussed earlier, the predicted moisture content present in the bond line of the full-scale FRP-strengthened RC beam after various durations is calculated, as shown in Fig. 21. According to precipitation frequency information published by the National Oceanic and Atmospheric Administration National Weather Service (Hershfield 1961), the typical rainfall durations range from 30 min to 24 h. For this rainfall durations, the predicted interface moisture content would be as large as 0.02 weight%; or C=C th is 1.55%. Prediction of Debonding Failure under Moisture Condition For a beam model of the same configuration and reinforcement without any interface crack, the maximum allowable service load under four-point bending is 368 kN to avoid inelastic deformation of the reinforcement. This value is close to the one obtained analytically using elasticity and strain compatibility (ACI 2008). In practice, a beam with the same configuration as the model would have the maximum value of the driving force for interface crack propagation limited by this load level. The criticality of the crack location on the ERR is shown in Fig. 22. When the interface crack is located further from the loading point toward the support,
GI will increase [Fig. 22(a)]. On the other hand, GI will reach its maximum value in the early stage of loading, and will decrease when the interface crack is closer to the loading point (i.e., when the interface crack mouth is closing). For mode II, GII increases as the load increases in most cases, except for the case when the interface crack is located 35 cm from the loading point [Fig. 22(b)]. Both energy release rates are very much negligible when the location of the interface crack is at the plate-end. The maximum energy release rates attainable within the limit of the service load for all cases are listed in Table 4. Table 4 shows that GI for all cases are smaller than the threshold value of the peel fracture toughness obtained from the continuous moisture condition test. This implies that interface debonding owing to the moisture effect is unlikely to occur by mode I fracture. The same conclusion can also be made for GII in most cases, except for the location of interface crack at 35 cm. The value of GII at this location is higher than the threshold value of shear fracture toughness, implying that premature failure by debonding in an FRP-strengthened RC beam is most likely governed by the mode II fracture. Therefore, an existing interface crack at this location may be considered critical and most likely to cause extensive debonding after extended period of exposure to cyclic moisture condition. Solving Eq. (2) with the original fracture toughness and the corresponding ERR from the FE analysis as the upper and lower bounds of the integration on the right side of the equation, the number of wet-dry cycles required for the concrete-epoxy bond strength to reach that particular value of fracture toughness, GII is given as
Fig. 22. ERRs in FRP-strengthened RC beams with an interface crack at various locations: (a) mode I; (b) mode II JOURNAL OF COMPOSITES FOR CONSTRUCTION © ASCE / SEPTEMBER/OCTOBER 2011 / 753
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Table 4. Maximum Mode I and II Energy Release Rates Limited by the Service Load
conservative approximation. Nonetheless, mode-mixity should be taken into account when such data is available.
Maximum ERR (N=m)
Location of interface crack 5 35 65 95 125 155 Plate-end
Nf ¼
Mode I
Mode II
35.87 30.07 32.33 40.04 48.13 76.21 0.000622
297.29 455.70 261.14 263.93 234.17 120.40 0.08
Γ0 GII qðC int =C th Þn
ð6Þ
where C int = intermediate moisture content (from diffusion simulation); and GII = maximum ERR of the FRP-strengthened beam in consideration. The number of wet-dry cycles to cause permanent deterioration in the bond, resulting in residual shear fracture toughness of GII ¼ 455:70 N=m, is shown in Fig. 23 for various interface moisture contents. For typical rainfall durations, 30-min, 1, 6, and 24-h, the ratio of threshold moisture contents are 3 × 104 , 6 × 104 , 3:7 × 104 , and 0.015, respectively. Correspondingly, the number of wet-dry cycles required to reach the residual fracture toughness of 455:7 N=m are 129, 94, 41, and 21 cycles. Nonetheless, the probability of having a rainfall of longer duration, 24-h for example, in a year is quite small. Therefore, the service life is likely to be much more than 21 cycles. To obtain the service life in terms of the expected number of years, an in-depth statistical analysis on rainfall data similar to that of Hershfield (1961) should be performed. The effect of mode-mixity on the interface bond strength is neglected in this analysis because only one mode of fracture is deemed critical when considering the maximum energy release rate in conjunction with the minimum bond strength, resulting in a more
Fig. 23. Number of wet-dry cycles to reach residual shear fracture toughness equal to GII ¼ 455:7 N=m
Potential Effect of Sustained Load on Interface Fracture Toughness In a real service condition, strengthened concrete structures are under both mechanical and environmental stresses at the same time. To simulate this condition and as a preliminary investigation, fracture tests on peel specimens under coupled moisture diffusion and stress were conducted. The shear fracture specimen was not studied here because the load required to fail in this mode is a few orders of magnitude larger than the case of peel fracture, which renders conditioning process impractical under regular laboratory conditions. Stress in the interface was created by applying loads corresponding to 10, 20, and 30% of the initial bond strength on the cantilever tip of peel fracture specimens. The loading frames were left in water containers at 23 and 50°C (Fig. 24). The level of sustained load was a fraction of the threshold value obtained in normal continuous moisture condition testing (i.e., 10, 20, and 30 N). Vertical displacement of the tip of the CFRP cantilever was recorded. In all levels of sustained load, there was a brief jump in deflection during the first few hours, which could be attributed to instantaneous microcracking in the epoxy. The deflection then increased in small magnitudes owing to the creep effect in the bond line. This effect is significantly pronounced in specimen under 30 N sustained load at high temperature. It was found that specimens under sustained load of 30 N at 50°C failed after only five days of conditioning time, with the last CFRP tip deflection measured at approximately 7 mm before a jump in deflection owing to creep crack propagation. Recall that peel specimen under continuous moisture ingress failed at a tip deflection in the range of 5 to 10 mm. This corresponds to maximum load between 45 and 60 N, depending on the duration of moisture conditioning. On the other hand, specimens under sustained loads of 10 and 20 N did not fail by creep fracture. Instead, they were tested in peel fracture after four and six weeks. Comparing the maximum force at crack initiation, it was found that the effect of coupled stress-diffusion on bond strength is not obvious for these specimens under 10 and 20 N. This implies that the interface fracture toughness could be affected by an existing sustained load, if the load level was higher than a certain lower bound value, which is 30 N in this case. Such effect of sustained stress coupled with moisture diffusion can further degrade the strength of FRP-concrete interface leading to premature failure at load levels much lower than predicted by the model. The effect of sustained load on interface fracture toughness in a specimen under moisture effects needs to be further studied for the modification of the proposed model to take into account the effect of stress-diffusion coupling.
Fig. 24. Loading frame for coupled stress-diffusion test (photo by C. Tuakta) 754 / JOURNAL OF COMPOSITES FOR CONSTRUCTION © ASCE / SEPTEMBER/OCTOBER 2011
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Conclusion In this study, the effects of moisture cyclic conditions on the fracture toughness of a CFRP-concrete bond system have been determined 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 adhesive bond cannot regain its original bond strength after successive wet-dry cycles at both room and high temperatures. Significant loss in the ability to regain original bond strength was observed after three weeks of exposure to moisture. The residual bond strength decreases as the number of wet-dry cycles and the intermediate conditioning duration increases. 2. Based on this deterioration behavior, a predictive model has been developed for predicting the service-life of FRP-concrete bond systems. 3. Based on the concept of fracture mechanics, application of the proposed conceptual model to a precracked FRP-strengthened RC beam was demonstrated for the prediction of debonding failure under moisture cycles. 4. Possible effect of sustained stress is noted; this effect should be further investigated. Areas of further research includes conducting a comprehensive experimental program considering both controlled laboratory and field conditions for further validation and refinement of the proposed model. In addition, integration of debonding failure under cyclic moisture condition to other deterioration mechanisms, such as chloride ion attack on steel reinforcement or carbonation of concrete, needs to be developed for a more complete framework as a basis for service life prediction.
Acknowledgments This research was supported by the National Science Foundation (NSF) CMS Grant No. 0510797. The authors are grateful to the former program manger, Dr. Lawrence C. Bank, for his interest and support of this work.
Notation The following symbols are used in this paper: C = transient moisture content (weight percentage); C int = intermediate moisture content; C th = threshold moisture content; E = Young’s modulus of material; GI = mode I energy release rate; GII = mode II energy release rate; K I = mode I stress intensity factor; K II = mode II stress intensity factor; N = number of wet-dry cycles; Γ = fracture toughness; μ = shear modulus of material; and ν = Poisson ratio of material.
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