Fiber-reinforced polymer (FRP) bars are increasingly used as a substitute for steel reinforcements in the construction of concrete structures, mainly due to their excellent durability characteristics. When FRP bar-reinforced concrete (referred to as FRP-RC for simplicity) members are used in indoor applications (e.g., in buildings), the fire performance of FRP-RC members needs to be appropriately designed to satisfy safety requirements. The bond behavior between the FRP bar and the surrounding concrete governs the composite action between the two materials and the related structural performance of the FRP-RC flexural member that will be affected when exposed to fire. However, there is a lack of reliable numerical models in the literature to quantify the effect of bond degradations of the FRP bar-to-concrete interface at high temperatures on the fire performance of FRP-RC flexural members. This paper presents a three-dimensional (3D) finite element (FE) model of FRP-RC flexural members exposed to fire and appropriately considers the temperature-dependent bond degradations of the FRP bar-to-concrete interface at high temperatures. In addition, the thermal properties of concrete and FRP bars are considered in the heat transfer analysis to predict the cross-sectional temperatures of the FRP-RC members under fire exposure. In the FE model, the mechanical properties and constitutive laws of concrete and FRP bars at high temperatures in addition to the bond degradations between them have been properly defined, thereby accurately predicting the global and local structural responses of the FRP-RC members under fire exposure. The proposed FE model has been validated by comparing the FE predictions (both temperature and midspan deflection responses during fire exposure) and the full-scale fire test results reported in the literature. The validated FE model is then used to study the effects of bond degradations on the global and local structural responses of the FRP-RC members under fire exposure. It is proved that the temperature-dependent bond degradations need to be considered to achieve accurate predictions of the failure mode and deflection responses.
flexural members, FRP bar, fire performance, bond degradations, high temperatures
Fiber-reinforced polymer (FRP) bars are increasingly used as a substitute for steel reinforcements in the construction of concrete structures, mainly due to their excellent durability properties. In the literature, a large number of studies have been conducted on the performance of FRP bar-reinforced concrete (referred to as FRP-RC for simplicity) members at ambient temperature [1,2,3,4], and the related design provisions have been specified in the current design guidelines [5,6]. However, the FRP-RC members are likely to be exposed to fire hazards during their service life, especially when these members are used in indoor applications (e.g., in buildings) [7,8,9,10]. Under high-temperature exposure in a fire, the material properties of FRP bars and concrete as well as the bond behavior between them will usually be significantly reduced [11,12], possibly leading to a significant reduction in the load-carrying capacity of the FRP-RC members [13,14]. Therefore, fire performance of the FRP-RC members is an essential issue in the design process and should be properly considered to meet the requirements specified in the current design guidelines [5,6].
Existing studies in the literature mainly focus on the mechanical and bond properties of externally bonded FRP laminates at high temperatures [15,16,17,18,19,20,21,22,23,24,25,26,27,28] and the related fire performance evaluation of FRP-strengthened RC members [29,30,31,32,33,34,35,36,37,38,39,40,41], while relatively limited information is available on the fire performance of FRP-RC members. A number of fire tests have been carried out on full-scale FRP-RC flexural members under standard fire exposure conditions [42,43,44,45,46]. The test results have indicated that if the FRP-RC member is properly designed (such as using a thick concrete cover and/or well-protected anchorage zone), it can achieve a satisfactory fire-resistance rating. Moreover, it is generally believed that the fire resistance period of the FRP-RC flexural member is lower than that of the corresponding conventional steel-RC member. This is because compared with steel bars, the FRP bars exhibit more significant reductions in the mechanical and bond properties at high temperatures. Apart from the fire tests, some numerical or finite element (FE) models are also proposed in the literature to predict the fire performance of FRP-RC flexural members [14,47,48,49,50,51]. The numerical and test results provided in the existing literature have promoted a good understanding of the thermal and structural responses of FRP-RC flexural members under fire exposure [51,52].
It is noteworthy that under fire exposure, high thermal stresses may be generated at the interface between the FRP bar and the surrounding concrete cover, mainly due to the different thermal expansion coefficients between FRP and concrete. When the thermal stress increases to the tensile strength of the concrete cover during fire exposure, it will be partially cracked, resulting in the weakening of the bond between FRP and concrete [53,54]. Moreover, the existing literature has indicated that the bond strength degradations between the FRP bars and the surrounding concrete at high temperatures are more severe than the mechanical property reductions of the FRP bars [11,55,56,57]. Therefore, the bond behavior between the FRP bars and the concrete plays a crucial role in governing the load transfer between FRP and concrete as well as the structural responses and fire performance of FRP-RC flexural members [58,59]. However, almost all existing numerical and FE studies [14,47,48,49,50,51] neglect the influence of bond degradations at high temperatures on the fire performance of FRP-RC flexural members. The proposed FE model is expected to act as a reliable computational tool for the parametric study of FRP-RC flexural members under fire exposure. Based on the parametric study results, a rational design method will be established for the fire resistance design of FRP-RC flexural members in the future.
Given the above research background, this paper has proposed a three-dimensional (3D) FE model to study the effect of bond degradations of the FRP bar-to-concrete interface at high temperatures on the fire performance of FRP-RC flexural members. The FE model has appropriately considered the constitutive laws of FRP and concrete as well as their bond interface at high temperatures, and therefore, it is expected to accurately predict the thermal and structural responses of FRP-RC flexural members under fire exposure. Then, the proposed FE model is verified by comparing the FE results with the test data of the full-scale fire tests in the literature. The validated FE model is further used to study the effect of the interfacial bond degradations at high temperatures on the fire performance of FRP-RC flexural members. The results have indicated that the consideration of the bond degradations of the FRP bar-to-concrete interface can capture the pull-out failure mode of the FRP bars and yields more accurate predictions of the deflection responses of FRP-RC flexural members under fire exposure.
The modeling procedure of the FRP-RC members in fire includes two main steps: heat transfer analysis and mechanical analysis. Heat transfer analysis is used to determine the cross-sectional temperature distributions of the FRP-RC flexural member under fire exposure, while the mechanical analysis takes the cross-sectional temperature distributions as the initial state to determine the structural responses. In other words, the modeling procedure follows a sequential thermo-mechanical analysis in which it is assumed that the results of the mechanical analysis have no effect on the heat transfer analysis of the same FRP-RC member under fire exposure. This sequential thermo-mechanical analysis was also successfully adopted by the corresponding author for predicting the fire performance of RC beams and insulated FRP-strengthened RC beams [39,60,61]. The following subsections give the details of the thermal properties of concrete and FRP bars and the boundary conditions considered in the heat transfer analysis, while the modeling of the temperature-dependent constitutive laws of the material and bond properties of concrete and FRP bars at ambient and high temperatures for the mechanical analysis will be provided in detail in the next sections.
The thermal properties of concrete have been extensively studied in the literature, including thermal conductivity, specific heat capacity, and density at high temperatures. The temperature-dependent changes of these parameters are provided in current design guidelines, such as EN 1992-1-2 . It provides design formulas for the specific heat capacity of concrete made of siliceous and calcareous aggregates at high temperatures ( a). By considering the heat absorption of water evaporation, the increase in the specific heat is considered at 100–115 °C, depending on the moisture content of the concrete. a shows the changes in the peak specific heat capacity of concrete with different moisture contents of 0, 1.5, and 3%. For other moisture contents, linear interpolation can be used to calculate the peak value. b shows the upper and lower bound limits of the thermal conductivity of ordinary concrete at ambient and high temperatures. In this study, each of the lower and upper bound limits has been incorporated into the heat transfer analysis to determine which one is more accurate to achieve a closer agreement with the fire test results. Through a trial-and-error analysis, the lower bound limit usually yields more accurate temperature predictions of FRP-RC flexural members under fire exposure. More details of the temperature predictions are given in Section 6. A similar method was also adopted by Hajiloo and Green  to obtain a reliable definition of the thermal conductivity of concrete at high temperatures. The density of concrete is considered to be 2300 kg/m3, which is usually assumed to be constant at high temperatures [47,61].Open in a separate windowOpen in a separate window
Limit information is available on the thermal properties of FRP composites at high temperatures. In the heat transfer analysis, the temperature-dependent thermal properties (i.e., thermal conductivity, specific heat capacity, and density) of FRP bars are determined based on the experimental results reported by Griffis et al. . Such thermal properties of FRP composites were also used in previous numerical and FE studies to predict the temperature responses of RC members with externally bonded or internally reinforced FRP reinforcements [29,39,41,47].
The heat exchange between the hot fluxes of fire and the surfaces of the FRP-RC member is realized through heat convection and heat radiation, which is controlled by the Robin boundary conditions as follows:
where k is the thermal conductivity, n is the normal direction of the surface, and qc and qr are the heat fluxes produced by heat convection and heat radiation, respectively, which can be described as follows:
where hc is the convective heat transfer coefficient, hc = 25 W/(m2·K) is used for the surfaces of the FRP-RC member exposed to fire, and hc = 9 W/(m2·K) for the unexposed surface [64,65]. εm represents the thermal emissivity of the member surface, and εf represents that of the hot fluxes of fire, which are determined to be 0.8 for concrete and 1.0 for the standard fire conditions as per EN 1991-1-2 . Tf is the hot flux temperature of the fire, T is the surface temperature of the FRP-RC member, and Tz is the absolute zero temperature. σ is the Stefan-Boltzmann constant and is equal to 5.67 × 10−8 W/(m2·K4).
The heat transfer within the FRP-RC member is realized by heat conduction, which is described by the following equation:
where ρ and c are the density and specific heat capacity, respectively, and t is the fire-exposure time. The solution of Equation (4) can be obtained by the above boundary conditions and initial temperature distribution. The latter at t = 0 is described as:
Tx, y, z, tt=0=T0x, y, z
The concrete damaged plasticity (CDP) model provided in ABAQUS 6.14  software (Hibbitt, Karlsson & Sorensen, Inc., Pawtucket, RI, USA) was used as a theoretical framework to model the behavior and failure of concrete at ambient and high temperatures. The CDP model adopts the concepts of isotropic damage elasticity and isotropic tensile and compressive plasticity to represent the inelastic behavior of concrete. The theoretical framework of the CDP model includes the accurate definitions of the damage variable, the yield surface (i.e., criterion), the hardening/softening rule, and the flow potential function. The yield surface used to describe the constitutive law of concrete was originally proposed by Lubliner et al.  and later modified by Lee and Fenves , which is defined as a function of the effective stress tensor (σ¯) and equivalent tensile and compressive plastic strains (ε˜tpl and ε˜cpl) as follows:
Fσ¯, ε˜tpl, ε˜cpl =11−ααI1+3J2+βσ¯max−γ−σ¯max−σ¯cε˜cpl
where I1 is the first stress invariant; J2 is the second deviatoric stress invariant; σ¯max and σ¯c are the algebraic maximum eigenvalue and uniaxial compression of σ¯; and is the Macaulay bracket, x=x+x/2. The dimensionless material constants α and β in Equation (6) can be calculated based on the uniaxial compressive yield stress fc0, T, equibiaxial compressive yield stress fb0, T and uniaxial tensile yield stress ft 0, T. More details of the calculation formulas for α and β at high temperatures can be found in Gao et al. . Interestingly, as the high temperature increases, the yield surface is changed from a nearly oval shape to an “egg-shape” due to the fact that the uniaxial compressive strength decreases faster than the biaxial compressive strength at high temperatures. The parameter γ is not required except for the concrete under a triaxial compression loading, i.e., the stress state of σ¯max < 0. The expression of γ is defined as a function of Kc as follows:
where Kc represents the ratio of the second stress invariant on the tensile meridian to that on the compressive meridian and is determined as 2/3 by default. The non-associated flow rule is used to define the flow potential function G in the CDP model, which is expressed by the following Drucker–Prager hyperbolic function:
In the above equation, ψ is the dilation angle and ϵ is the flow potential eccentricity. In this study, ψ = 36° is determined based on an initial trial-and-error analysis using the proposed FE model to obtain excellent consistency with the fire test results. ϵ = 0.1 is determined as the default value suggested by the ABAQUS user manner . In addition, the CDP model does not include damaged variables because the fire tests of the FRP-RC flexural members simulated in this study were carried out under constant service loadings, and therefore, the loading and failure of concrete do not involve the loading/unloading process. Such a consideration was also adopted in the previous study to predict the structural responses of RC beams under fire exposure .
The hardening/softening rule controls the subsequent evolution of the yield surface and failure mode of concrete at ambient and high temperatures, which is related to the uniaxial compressive and tensile stress–strain curves of concrete. Under uniaxial compression at ambient and high temperatures, concrete behavior is defined according to the stress–strain relationship specified in EN 1992-1-2 . It is worth noting that the initial stress–strain relationship is considered to be linear elastic when the compressive stresses at each temperature are less than 0.33 times the corresponding compressive strength of the concrete. a shows the compressive stress–strain curves of concrete at ambient and high temperatures, where the high-temperature stresses are normalized by the ambient-temperature compressive strength. The tensile behavior of concrete is assumed to be elastic before cracking occurs. Concrete cracks are simulated by using a smeared crack approach in combination with the crack band model in which the tensile stress within the crack band gradually decreases with the cracking opening displacement . In other words, post-peak stress behavior is defined by the softening branch (i.e., tensile softening behavior), which is described as the tensile stress versus the cracking opening displacement curve at each temperature (see b for more details). In addition, the tensile stresses at different temperatures are normalized by the tensile strength at ambient temperature for a clear presentation. It is noteworthy that the area enclosed by the normalized tensile stress versus the cracking opening displacement curve is proportional to the fracture energy of concrete, which is assumed to be constant at ambient and high temperatures . In addition, the curve of the tensile stress versus the crack opening displacement is used in the FE model instead of the tensile stress–strain curve to achieve a mesh-insensitive solution, as explained in detail in the numerical study of RC beams under fire conditions conducted by the corresponding author . When the cracking opening displacement is larger than the calculated displacement corresponding to the zero tensile stress at each temperature, a residual tensile stress of 5% tensile strength is also considered to avoid possible difficulty in achieving numerical stability.Open in a separate window
Some tensile tests were carried out on FRP bars at ambient and high temperatures, and the results showed that the mechanical properties such as the tensile strength and elastic modulus of FRP bars decreased at moderately high temperatures [49,69,70]. The tensile stress–strain curves measured at different temperatures were almost elastic before the tensile rupture of the FRP bars. The reductions of the mechanical properties of the FRP bars were affected by the type of FRP bar and the polymer matrix, the volume ratio of the FRP fibers, and the curing conditions. collects the experimental data of the previous tensile tests of GFRP bars in the literature [49,69,70], and the measured results show large dispersion with the temperature changes. In the present study, the material models of GFRP bars proposed by Bilotta et al.  are used to describe the tensile strength and stiffness degradations at high temperatures since all fire tests of FRP-RC flexural members simulated by the FE model for validation are made of GFRP bars. As shown in , the two rapid reduction processes at around 100 and 400 °C are related to the glass transition and decomposition processes of the polymer matrix, as explained by Reid et al. . It should be noted that more tensile tests are needed to investigate the mechanical property degradations of FRP bars at high temperatures, and more accurate material models are needed to accurately describe the reductions in the tensile strength and elastic modulus at high temperatures.Open in a separate window
The bond interaction between the FRP bar and the surrounding concrete governs the load transfer between the two materials, which is usually described by the local bond stress–slip relationship at the FRP bar-to-concrete interface. Due to the bond action, the FRP bars located between two adjacent concrete cracks have a stiffness contribution to the tensile behavior of the concrete between the two cracks. This phenomenon is termed the “tension-stiffening” effect [72,73], and it significantly influences the deformation behavior of the FRP-RC flexural member, especially in the post-cracking stage. Such a tension-stiffening effect can be appropriately reflected by accurately simulating the bond–slip behavior of the FRP bar-to-concrete interface of the FRP-RC flexural member under bending loads. In the literature, some analytical studies were carried out to derive the local bond stress–slip behavior of the FRP bar-to-concrete interface at ambient temperature [74,75,76]. Among them, the Bertero–Popov–Eligehausen (BPE) model, originally proposed by Eligehausen et al.  for describing the local bond–slip relationship of deformed steel bars, was used by Cosenza et al.  and Rossetti et al.  to describe the bond–slip behavior of FRP reinforcing bars. In addition, a modified BPE model (mBPE) was proposed in previous studies [74,75] in which a two-branch model without a peak bond stress plateau was adopted. The effect of the surface treatment of FRP bars was considered by both the BPE and mBPE models, but the effects of the fiber type and bar diameter were ignored. Cosenza et al.  proposed a new model (i.e., the Cosenza–Manfredi–Realfonzo (CMR) model) to better describe the ascending branch of the bond–slip relationship.
At high temperatures, some pull-out tests on FRP bars have indicated that the decreases in the bond strength are more severe than the corresponding reductions in the tensile strengths of the same FRP bars [11,12,58]. In other words, the bond behavior of the FRP bar-to-concrete interface at high temperatures is the most crucial factor that governs the fire performance of FRP-RC flexural members . Moreover, the loss of the bond action between FRP bars and concrete at high temperatures may lead to pull-out failure (i.e., anchorage failure) of FRP bars, resulting in a possible sudden collapse of the FRP-RC member in a fire. However, there is very limited information about the local bond–slip model that can be used to describe the bond behavior of FRP reinforcing bars at high temperatures . Only Aslani  proposed a local bond–slip relationship to describe the interfacial behavior of GFRP bars in concrete at high temperatures. In the proposed model, the effects of some design parameters including the concrete compressive strength, bar diameter, embedment length, and concrete cover depth were considered. The accuracy of the proposed bond–slip model was only validated by a limited database of bond–slip curves measured by the pull-out tests. However, due to the lack of information available in the literature, the bond–slip model proposed by Aslani  is still used in the FE model to define the local constitutive law of the GFRP bar-to-concrete interface at high temperatures. Once more test data are available, it will be necessary to develop a more accurate bond–slip model that can be incorporated into the proposed FE model to more precisely describe the interfacial bond behavior at high temperatures. The bond–slip model proposed by Aslani  is based on the mBPE model, which consists of two branches, namely, the ascending branch before attaining the peak bond stress and the softening branch. The two branches of the local bond–slip model are expressed by the following equations:
τs, Tτmax, T= ssmax, Tα s≤smax, T
τs, Tτmax, T=1−ps−smax, Tsmax, T s>smax, T
where τs, T is the bond stress at temperature T; s is the local interfacial slip; α is a curve-fitting parameter with the value less than 1; τmax, T is the peak bond stress at temperature T; smax, T is the slip corresponding to the peak bond stress τmax, T; and p is determined based on the curve-fitting of test data. τmax, T and smax, T are computed by the following equations (i.e., Equations (11)–(14)).
τmax,Tτmax,0=1T=20 °C1.26−0.0063×T+7×10−6⋅T220 °C<T≤350 °C
τmax,Tτmax,0=1T=20 °C0.989−0.00025×T−3×10−6⋅T220 °C<T≤350 °C
smax,Tsmax,0=120 °C0.9739−0.0019×T−3×10−5⋅T220 °C<T≤350 °C
smax,Tsmax,0=120 °C0.9219−0.001×T−5×10−6⋅T220 °C<T≤350 °C
In above equations, τmax, T and smax, T have two different expressions depending on the tensile strength of GFRP bars at ambient temperature (fpm,0). That is, Equations (11) and (13) are used for the cases of 500 ≤ fpm,0 ≤ 1000 MPa, while Equations (12) and (14) are adopted for the cases of 1000 < fpm,0 ≤ 1500 MPa. The parameter τmax,0 in Equations (11) and (12) can be calculated as follows:
τmax, 0=0.55cdb0.6+3dbldfcm, 00.52
where fcm, 0 is the concrete compressive strength at ambient temperature (MPa); db is the diameter of the GFRP bar (mm); and ld is the embedment length (mm); c is the concrete cover which is determined as the smaller one of the centroid of the bar to the nearest surface or the half of the center-on-center spacing of the GFRP bars (mm). smax,0 can be computed by Equation (16), which is a modified version of Baena et al.’s  model.
where m0 and m1 are two curve-fitting parameters, which are determined as 0.01 and 0.291, respectively .
In the FE model, four parts, i.e., the concrete section, FRP bars and loading plates, and the supporting plates of the FRP-RC flexural member, need to be simulated. In the heat transfer analysis, the eight-node linear heat transfer solid element with a temperature degree of freedom (DC3D8) and the two-node heat transfer link element (DC1D2) provided by the ABAQUS software were used to model the concrete section and the GFRP bars, respectively. In other words, the loading plates and the supporting plates were not modeled in the heat transfer analysis. For the mechanical analysis, the eight-node solid element with reduced integration and hourglass control (C3D8R) was adopted to model the concrete section, the loading plates and the supporting plates, while the two-node linear 3D beam element (B33) was used in modeling the GFRP rebars. The nonlinear spring element was used to simulate the bond–slip behavior along the two tangential directions of the FRP bar-to-concrete interface in the mechanical analysis. For the normal behavior of the spring elements, the interaction between the GFRP bar and the concrete cover was defined by setting a large stiffness almost equal to the elastic stiffness of the concrete. The mesh size of all the solid elements was determined as 50 × 50 × 25 mm based on the convergence study, and the corresponding element size was adopted for the beam and spring elements. It should be noted that the configurations of all the nodes and elements between the heat transfer analysis and the mechanical analysis are the same. Therefore, the results of the cross-sectional temperature distributions generated by the heat transfer analysis can be used as an initial condition that can be properly applied to the corresponding time step of the mechanical analysis.
The loading plates were tied to the top surface of the flexural member, and the service loads acting on the member during the fire exposure were applied to the reference points on the loading plates. The supporting plates were attached (tied) to the bottom of the flexural member to ensure that there was no slip at the interface between the supporting plates and the concrete surface during the loading and fire process. The pinned boundary conditions were assigned at the reference points at the bottom of the supporting plates during the entire fire test.
This paper has proposed a 3D FE model to predict the fire performance of FRP-RC flexural members with appropriate considerations of the constitutive models of FRP bars, concrete, and their bond interface at high temperatures. The latter issue has not been accurately simulated by the previous numerical studies. The proposed FE model has been validated by comparing the FE results with the test data of the full-scale fire tests of FRP-RC slabs in the literature. The following conclusions can be drawn based on the results presented in the paper:
The proposed FE model has good accuracy in predicting the thermal and structural responses of FRP-RC flexural members under fire exposure. The constitutive models used to define the thermal and mechanical properties of concrete and FRP bars at high temperatures are reliable. The temperature predictions of the proposed FE model are very similar to the measured results, with a maximum deviation of about 10% during the entire fire test.
The perfect bond consideration of the FRP bar-to-concrete interface at high temperatures often yields less accurate predictions of midspan deflection responses. Thus, proper consideration of the local bond–slip behavior of the FRP bar-to-concrete interface at high temperatures is required for accurately predicting the midspan deflection responses of FRP-RC flexural members exposed to fire.
The consideration of the local bond–slip behavior also gives detailed information on the interfacial slip responses at the FRP bar-to-concrete interface at high temperatures during a fire, which can reveal the concrete cracking pattern and failure mode of the tested member under fire exposure. The predicted maximum interfacial slips of the FRP bars near the end of the fire test are almost 20 mm.
The proposed FE model can accurately predict the anchorage failure of FRP bars in the FRP-RC flexural member during fire exposure, which is a typical failure mode in the existing fire tests in the literature. The previous numerical studies based on a perfect bond consideration cannot provide a reliable prediction for this failure mode.
Further research is needed to develop more reliable constitutive models of FRP bars and bond interface at high temperatures, which are necessary for more accurate predictions of the deflection responses of the FRP-RC flexural members under fire exposure.
Conceptualization, D.D., L.O. and W.G.; methodology, W.G. and J.Y.; software, D.D. and W.G.; validation, D.D., L.O. and W.G.; investigation, D.D.; resources, Q.X.; writing—original draft preparation, D.D., L.O. and W.G.; writing—review and editing, W.G. and J.Y.; visualization, D.D.; supervision, W.G.; project administration, Q.X. and W.L.; funding acquisition, W.G. All authors have read and agreed to the published version of the manuscript.
The authors are grateful for the financial support received from the National Natural Science Foundation of China (NSFC) (No. 51978398) and the Natural Science Foundation of Shanghai (No. 19ZR1426200). We would also like to acknowledge the Open Fund of Shanghai Key Laboratory of Engineering Structure Safety (No. 2019-KF06).
All data, models, and code generated or used during the study appear in the published article.
The authors declare no conflict of interest.
Publisher’s Note: MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations.