Finite element investigation of fatigue performance of CFRP-strengthened beams in hygrothermal environments

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Finite element investigation of fatigue performance of CFRP-strengthened beams in hygrothermal environments ⁎

Y.L. Wanga, X.Y. Guoa, , P.Y. Huanga,b, K.N. Huanga, Y. Yanga, Z.B. Chena a b

School of Civil Engineering and Transportation, South China University of Technology, Guangzhou 510640, China State Key Laboratory of Subtropical Building Science, South China University of Technology, Guangzhou 510640, China

A R T I C LE I N FO

A B S T R A C T

Keywords: Hygrothermal environment Fatigue loading Coupling action Carbon fiber reinforced polymer (CFRP) RC beam

The effectiveness of reinforced concrete (RC) external bonded with carbon fiber reinforced polymer (CFRP) laminates is bound by the negative effect of hygrothermal environment and cycle load. In order to prove the durability of CFRP-strengthened RC beams in hygrothermal environment, this paper concentrates on a numerical and experimental research of the failure modes and fatigue life of CFRP-strengthened RC beams under the coupling action of hygrothermal environment and cyclic load. Considering that two main failure modes of CFRPstrengthened RC beams are debonding of CFRP-concrete interface and main reinforcement fracture, the failure criterion of interface debonding and main reinforcement are involved in finite element method (FEM). Based on the fatigue damage accumulation, the failure mode which occur first can be predicted. The results show that the main failure mode of CFRP-strengthened RC beams in indoor environment is main reinforcement fracture. With the increase of temperature and humidity, interface debonding become the main failure mode. The fatigue life corresponding to failure mode under different hygrothermal environments can be calculated, which is in good agreement with experimental results.

1. Introduction The reinforced concrete (RC) structures strengthened with carbon fiber reinforced polymer (CFRP) has gained increasing attention due to the inadequate strength of concrete structures and the need to improve structures' performance with acceptable margin of safety. FRPs are remarkable reinforcement material because of their light weight, high tensile strength, superior corrosion resistance, thermal performance and designable performance. So far, many studies have been used to assess the performance of RC structures strengthened with FRP [1–4]. In recent years, many researchers have been doing research on the fatigue behavior of RC members strengthened with FRP [5–9]. Because the fatigue behavior of such members is a complicated topic, most of the research progress rely on experimental tests. As noted by many fatigue experimental investigations, the use of CFRP increases the fatigue life of RC beams and the increase of the number of CFRP laminates further prolongs the fatigue life of RC beams. For RC structures with externally bonded FRP, the failure modes are usually classified into two categories: main reinforcement fracture and FRP-concrete interface debonding failure. O. Chaallal [10] found fatigue life of RC beams strengthened with two layers of CFRP was far less than 5 million cycles. Nonetheless it was noted that the failure mode was a

⁎

combination of local debonding of CFRP and fracture of main reinforcement. Y.T. Dong [11], through the fatigue test, found that the fatigue failure of CFRP-strengthened RC beams was primarily controlled by fatigue behavior of main reinforcement. Following the fatigue damage of main reinforcement, rapid and brittle failure occurred due to debonding of the CFRP or peeling of the concrete cover along the bottom of main reinforcement. Recently, increasing but limited theories have been done to provide fatigue prediction models corresponding to failure mode of RC beams strengthened with FRP. Based on the fatigue behavior of the tensile steel bars and Miner’s rule [12], some methods [13–15] were proposed to analyze fatigue life under bending loads. In these models, the time dependent behavior of concrete was considered. Besides the failure mode of main reinforcement fracture, there has been a strong concentration about fatigue failure mode of interface, and a considerable progress has been made in understanding the reasons and mechanisms of FRP-concrete interface debonding failure. Some researchers believed that FRP-concrete interface debonding failure initiated when the maximum normal stresses and shears reached critical values [16,17]. Other failure criteria include interfacial fracture criterion, which mean that crack growth and interfacial debonding initiate when the energy release rate exceed interfacial fracture toughness [18]. However, previous

Corresponding author. E-mail address: [email protected] (X.Y. Guo).

https://doi.org/10.1016/j.compstruct.2019.111676 Received 31 July 2019; Received in revised form 29 September 2019; Accepted 4 November 2019 0263-8223/ © 2019 Elsevier Ltd. All rights reserved.

Please cite this article as: Y.L. Wang, et al., Composite Structures, https://doi.org/10.1016/j.compstruct.2019.111676

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interface layer due to effect of the exposure environment. Overall, the predicted failure modes, cracks patterns and strain along the bond line appeared well coherence with test results. Although FEM has been successfully applied to explore the fatigue performance of FRP-strengthened beams, a comprehensive research with regarding to FE modelling of RC beam strengthened with CFRP under the coupling of hygrothermal environment and cyclic load remains a complex challenge. A full understand of the failure mode of CFRP-strengthened RC beams in hygrothermal environment is still not available. In this paper, the fatigue performance of RC beams strengthened with CFRP under the coupling of three different hygrothermal environments and cyclic load were simulated by FEM. In order to simulate the effects of fatigue loading and hygrothermal environment, the degradation of elastic modulus of concrete, CFRP-concrete interfacial stiffness and shear strength induced by fatigue loading, and the variation of interfacial stiffness as well as shear strength induced by hygrothermal environment were considered in the FE calculation. Considering that the two main failure modes of CFRP-strengthened RC beams are debonding of CFRP-concrete interface and main reinforcement fracture, the failure criterion of interface debonding and main reinforcement are involved in FEM. Based on the fatigue damage accumulation, the failure mode which occur first can be predicted. The fatigue life corresponding to failure mode is predicted. The validity of FE model is verified by comparing the predicted life with experimental life in this study.

studies have been based on a specific failure mode of certain assumption. But the failure mode is a combination of local debonding of CFRP and fracture of main reinforcement, it is difficult to predict which is the real failure mode. Although ever-increasing numbers of studies of concrete members strengthening with FRP under fatigue load, to date very limited research involved the effect of environment on the fatigue behavior of RC beams strengthened with CFRP. With regard to the effects of environment on fatigue behavior, tests have been conducted on the FRP-reinforced members [19–23]. It has been concluded that temperature and humidity have a significant impact on the fatigue behavior of FRP-reinforced concrete members. For example, G. Qin et al. [19] took temperature and humidity seasonal fluctuations into account. In the test, different hot-wet environments were set for RC beams strengthened with CFRP. A. S. El-Dieb et al. [20] studied the performance of RC members strengthened by externally bonded FRP, which were exposed to six different conditions: site, cyclic sea water, cyclic drinking water, high temperature and humidity, laboratory as well as being embedded in Sabkha soil. To explore the influence of environment on the durability of CFRP-concrete interface, single or double shear test specimens with CFRP were tested under different environments. Existing studies have shown that FRP-concrete interfaces are more prone to delaminate under extreme environment [24,25]. Moreover, the influence of these unfavorable factors is magnified under the influence of external environment such as temperature and humidity [26–28]. B.L. Wan et al. [29] studied the effect of the presence of water on the CFRP-RC interface during CFRP application and after the CFRP cured by experiment. The test results indicated that the existence of water significantly reduced the bonding quality of the FRP-concrete interface. The longer the impregnation time, the higher the moisture content and the lower the bond strength of the resin adhesive. X.H. Zheng et al. [30] demonstrated the test temperature and relative humidity (R·H) unfavourably affected the bond behavior of CFL–concrete interface by carrying on 17 double shear specimens with carbon fiber laminate (CFL) under constant temperature and R·H (60 °C, 95%). The test results also showed that the fatigue life of specimens under hygrothermal environment (60 °C, 95%) was notably less than control group. Leone et al. [31] experimentally investigated the CFRP–concrete interface behavior at elevated service temperatures. Specimens were tested under doubleface pure shear test and at varying test temperatures: 20, 50, 65 and 80 °C. It was found that the maximum bond stress decreased and the type of failure changed with increasing adopted temperature. In particularly, specimens tested at T = 50°C showed the maximum bond stress on CFRP sheet decreased by 54% with respect to the indoor temperature, and cohesion failure existed within the concrete. The fatigue behavior of RC beams strengthened with FRP is a complicated subject, especially the mechanical behavior of FRP-concrete interface. In some studies, finite element analysis has been used to simulate the debonding failure of FRP-concrete interface. The earlystage study focused on linear elastic analysis and the elastic stress distribution on the FRP-concrete interface [32]. Afterwards, Z.S. Wu et al. [33,34] proposed the use of a layer of interface elements between FRP and concrete to solve the problems of fracture propagation and nonlinear interfacial stress transfer. In the finite element modeling (FEM), the destruction of the interface elements meant that the interface was peeled off. According to the research results of the meso-element finite element [35], X.Z. Lu et al. [36,37] proposed a group of new constitutive models and formulas for calculating the interfacial peel strength, including the bond-slip model I applied to in-plane shear and bond-slip model II applied to the concrete crack area. As for the influence of environment on FRP-concrete interface, FEM can obtain more accurate interface data such as distribution of the stresses and strains. K. Gamage [38] presented a non-linear FE model to predict the CFRPconcrete interface performance under long-term exposure to the cyclic temperature and constant humidity. A parametric was introduced to evaluate the equivalent mechanical properties of CFRP-concrete

2. Experimental program 2.1. Specimen design The experimental work included 27 replicated 1850×100×200 mm RC beams strengthened with carbon fiber laminate (CFL). The design strength of concrete was C25, and the gradation design was: cement (1.0): water (0.5): sand (2.06): gravel (3.66). All concrete specimens were cured in a water bath at a fixed temperature of 20 °C for 28 days. The structure reinforcements and stirrups were ∅8 HRB235 bars, and the main reinforcements were grade II bars of ∅10. The reinforcement ratio of concrete was 0.981%, as shown in the Fig. 1. CFL with a size of 1600 mm long×100 mm wide×0.23 mm thick was weaved of T700-12k carbon fiber silk made in Toray Advance d Materials Korea Inc. CFL were attached to the bottom of RC beams with epoxy resin as shown in Fig. 2. The tensile strength and elasticity modulus of CFL were 4750 MPa and 230 GPa, respectively. The adhesive between concrete and CFL was made of Lica-301 epoxy resin adhesive (A, B adhesive), with thickness of about 0.1mm and shear strength of 12 MPa. Elasticity modulus and tensile strength were 10 GPa and 35 MPa provide by manufacturer. 2.2. Material properties In this study, the test beams were made based on the above gradation design. According to the national standard (GB50010-2010) [39], four concrete cube specimens were tested on YE-5000A hydraulic pressure tester. The mean compressive strength and tensile strength of concrete were 47.6 MPa and 4.45 MPa . Moreover, the elasticity modulus and Poisson’s ratio of concrete were 34 GPa and 0.19, respectively. The tensile test showed that the yield strength and tensile strength of the main reinforcement were 400 MPa and 560 MPa. The test also gave the elasticity modulus and Poisson’s ratio were 206 GPa and 0.3, respectively. The CFL were externally bonded RC beam with epoxy resin. 2.3. Experimental facility In this study, the hygrothermal environment required for the test was simulated by hot-wet environment simulation and control device 2

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Fig. 1. Schematic diagram of RC beam (unit: mm).

(Type SDH4036L), which had ability to support Material Testing System (MTS810) with 100 kN capacity machine load, shown in Fig. 3. A total of 27 simply supported RC beams strengthened with CFL were tested in three-point bending. The stress ratio R and frequency of constant amplitude load in fatigue loading were 0.2 and 10 Hz, respectively. Taking metal plane bending fatigue testing as a reference, the load levels of the specimen range from 0.6 to 0.7. Moreover, based on the constant-amplitude fatigue test by our research group before, the cycle numbers of same specimen (RC beam strengthened by CFL) were be more than 2 million when the load was less than 25 kN. In this paper, four peak loads (25 kN, 27.5 kN, 30.0 kN, and 32.0 kN) were applied to specimens, corresponding load levels SR were 0.56, 0.61, 0.66, and 0.71, respectively. The acquisition frequency of readings was set to 100 Hz in order to obtain more measurement points. In addition, the cycle numbers, fatigue loading and midspan deflections of RC beam were also collected and recorded automatically by load sensor and displacement meter of MTS810 test machine system. In order to explore the influence of environment on the specimens, three different temperature and R·H environmental conditions were simulated in this experiment, namely 23 °C, 78% R·H (indoor environment), 50 °C, 78% R·H, and 50 °C, 95% R·H. There were three specimens for each condition, all were tested by coupling the action of constant hygrothermal environment and fatigue load. The fatigue life and failure modes of the test beams obtained from the experiment are shown in Table 1. According to the experimental data obtained by the research group before, when the environment was set at 23 °C, 78% R·H, and the load level was 0.56, the fatigue life of the specimen exceeded 2×106, which was considered to be an infinite life in engineering. For 50°C condition, the bond behavior and fatigue life of specimen were decreased rapidly when the high load level SR = 0.71. Therefore, these conditions were not considered in this paper.

Fig. 3. Hygrothermal environment simulation and control system.

The degradation of concrete and interface properties under fatigue load was considered in the finite element model. Additionally, this paper only considered the effect of the hygrothermal environment on bond properties of CFRP-concrete interface, and the failure criteria of RC beam was discussed. 3.1. Material constitutive laws and element attributes Referring to the concrete model in ABAQUS, this paper used the concrete damage plasticity (CDP) model to simulate the mechanical properties of concrete. The concrete was modeled as 3-D with reduced integral 8-node (C3D8R) in ABAQUS. The stress-strain relationship of concrete was shown in Fig. 5. According to the national standard (GB50010-2010), the constitutive relation of concrete was as follows: (1)

σ = (1 − dk ) E0 ε (k = c, t ) 3. Finite element modeling (FEM)

k = c , dc =

For the complex structure of RC beams strengthened with CFRP and the influence of hygrothermal environment on the strengthened members, the FE calculation software (ABAQUS) was used for theoretical analysis and modeling. According to the dimension of the test beam described in the previous section, the FE model was built according to the ratio of 1:1, and the meshing of the model was shown in the Fig. 4.

k = t , dt =

⎧ 1− ⎨1 − ⎩

ρc n n − 1 + xn ρc

α c (x − 1)2 + x

,x>1

5 ⎧1 − ρt (1.2 − 0.2x ), x ≤ 1 ρt ⎨1 − α (x − 1)1.7 + x , x > 1 t ⎩

Fig. 2. RC beam strengthened with CFL (mm). 3

,x≤1 (2)

(3)

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Es ε , ε ≤ εy σs = ⎧ ⎨ fy , ε > εy ⎩

Table 1 Experimental results of fatigue life of the test beams under hygrothermal environment. Hygrothermal conditions

Load levels, SR

Fatigue life, N

Failure modes

23 °C, 78% R·H

0.61

1153118 921580 786534 607974 711981 635327 423784 554142 530279 586229 881618 695919 635422 874341 511281 188260 177196 158680 42386 106644 153022 19667 49425 44523 35680 36522 19670

B B B B B B B B B B B B B B B B B A A A A A A A A A A

0.66

0.71

50 °C, 85% R·H

0.56

0.61

0.66

50 °C, 95% R·H

0.56

0.61

0.66

where, σs is the stress of rebar, Es is the elasticity modulus of rebar, εy is the yield strain of rebar, f y is the yield stress of rebar. CFRP laminate was considered as an ideal elastic model under uniaxial tension due to good linear elasticity. In FE model, CFRP laminate were built by shell elements (SR4). Fully bonding between the concrete and the reinforcement was assumed throughout the loading process until failure. The bonding behavior of the interface in ABAQUS was used to model separation and slip in the tangential direction of interface. Since the CFRP-concrete interface adhesive layer was relatively thin (approximately 0.1mm), and the calculated results were very sensitive to the thickness of the adhesive layer. If the adhesive layer elements were established, it was easy to cause non-convergence due to too small meshing. Therefore, in this paper, the bonding behavior in ABAQUS was adopted to define the bonding relationship between concrete and CFRP based on the interface characteristics of the strengthened beam. K. Nakaba [40] had conducted 30 in-plane shear experiments. Based on the measured FPR strain distribution and Popovics’ function [41], a bond-slip model of FRP-concrete interface was proposed. The model is shown in Fig. 6, which can be expressed by the following formula:

⎡ s 3 τ = τmax ⎢ ∙ ⎢ s0 s 2+ s ⎢ 0 ⎣

3.2. Degradation of material under fatigue load

(4)

x=

ε εk

(5)

n=

E0 ε c E0 εc − fc

(6)

(8)

where, τmax is the ultimate shear strength of interface, s0 is the slip corresponding to ultimate shear strength τmax .

fk E0 εk

⎤ ⎥

3⎥

( ) ⎥⎦

Note: A represents debonding of CFL-concrete interface, and B represents main reinforcement fracture.

ρk =

(7)

Under fatigue loading, the fundamental cause of performance degradation and damage of RC members strengthened with CFRP was the degradation of component materials and interface properties. In the process of fatigue loading, the performance of concrete and FRP-concrete interface decreased with the increase of fatigue cycle, which made the ultimate load, stiffness, elasticity modulus and bond-slip performance of the material deteriorate continuously until they were found to exceed the ultimate state of some materials, and ultimately leaded to the failure of the whole reinforced structure. Since the fatigue deformation of rebar and CFRP material was very small, the effect of fatigue degradation was not considered in the numerical simulation process.

where E0 (MPa) is the initial elastic modulus, dk is damage factor, in which k = c, t represent the compression and tension state of concrete, αk is the shape parameter of descending section of the stress-strain curve of concrete, fk is the uniaxial compressive or tensile strength of concrete, εk is the strain when σ reaches fk . Through the experimental research, it was found that the force imposed was not enough to make the rebars yield during the most time of the reinforced beam subjected to cyclic loading until failure. Therefore, in order to simplify the model and improve the calculation efficiency, the rebars were regarded as the ideal elastoplastic model, and the truss elements (T3D2) were used to build rebars in FE model. The constitutive equation of rebars was as follows:

3.2.1. Concrete The elastic modulus and strength of concrete will gradually decrease with the increase of the number of fatigue cycle. Holmen [42] obtained the formula of the relationship between the elastic modulus of concrete and the number of cycles through experimental research.

Fig. 4. The meshing of finite element model. 4

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Fig. 5. Uniaxial stress-strain relationship of concrete.

n Eci = ⎛1 − 0.33 i ⎞ E N ci ⎠ 0 ⎝ ⎜

where, Sci is the ratio of the maximum compressive stress σci to the compressive strength fc of concrete after ni cycles. Some researchers [44] proposed the residual strength envelope of concrete to study the strength degradation law of concrete under fatigue loading. The envelope of fatigue residual strength referred to the relation curve between residual strength and fatigue loading times after any number of fatigue loading. The envelope of fatigue residual strength of concrete (Fig. 8) can be approximately expressed by the softening section curve of concrete uniaxial stress-strain model as shown in Fig. 7. The corresponding degradation formula is as follows:

⎟

(9)

where, ni is the number of loading cycles, Eci is the elastic modulus of concrete after ni cycles, E0 is the initial elastic modulus of concrete, Nci is the fatigue life of concrete, while it is an unknown quantity in the process of finite element simulation. Song [43] gave the life calculation formula:

Nci = 10(15.99 − 16.18Sci)

Sci =

σci fc

(10)

(11)

Fig. 6. Bond-slip curves based on Nakaba’s formula. 5

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Fig. 9. Bond-slip model of CFRP-concrete interface under fatigue loading.

Fig. 7. Cyclic stress-strain curve of concrete.

coordinate of the intersection of unloading loop and envelop curve, Ki is the CFRP-concrete interface stiffness at the ni cycle. As the number of fatigue cycles increased, the stiffness of the curve decreased gradually. Each time a new cycle started, the interface slid with attenuated stiffness, so the maximum shear stress under this cycle decreased (Fig. 10). This model adopted a linear approximation of the unloading–reloading path for simplicity. The maximum shear stress τmax , i can be calculated by the following two formulas:

τmax , i s 3 = i∙ τmax s0 2 + si s

3

() 0

τmax , i = Ki si

(16) (17)

where τmax , i is the maximum shear stress at the ni cycle, si is the slip corresponding to the maximum shear stress at the ni cycle. Fig. 8. Residual strength envelope of concrete.

σc (ni ) = fk ∙

logni [x (Nci ) logNci

− x (1)] m

logn

3.2.3. Simulation of hygrothermal environment Since the influence of the hygrothermal environment on the RC structure was quite limited compared with that on the CFRP-concrete interface, in order to simplify the model and improve the calculation efficiency, only the influence of the hygrothermal environment on the bonding strength of the CFRP-concrete interface was considered in this paper. Epoxy resin adhesive used in the CFRP -concrete interface was very sensitive to the change of temperature and humidity. Therefore, it was critical for the accuracy of the model to select appropriate bondslip relationship of CFRP-concrete interface under the hygrothermal environment. The effect of temperature and humidity on the interface was reflected in the decrease of the maximum shear strength of the interface. Liu [46] obtained the relationship between the maximum shear stress and the corresponding slip at the CFRP-concrete interface under different hygrothermal environment by experimental fitting:

αk ⎡ logN i [x (Nci ) − x (1)] − x (1) ⎤ ⎣ ci ⎦

+

logni [x (Nci ) logNci

− x (1)] (12)

σc (ni ) = σci ; where, relative life rate is defined as [x (n ) − x (1)] x x (1) = 1, r (ni ) = [x (N i ) − x (1)] = logni /logNci . Therefore, ci when α c = 0.74 – 3.99 (Nci ) =(logNci /logni )[x (Nci ) − 1] + 1; fc = 20–80 MPa; αt = 0.31–5 when ft = 1–4 MPa; m = 2 when k = c; m = 1.7 when k=t. 3.2.2. CFRP-concrete interface For the fatigue behavior of CFRP-concrete interface, Zhang [45] carried on double-lap shear fatigue test, and found that the residual slip increased with the number of loading cycle, and the shape of the loading curve had a strong correlation with the loading stiffness Ki as well as the position of the loading slip on the envelope curve. Therefore, a local bond stress-slip model under fatigue loading (Fig. 9) was proposed by assessing the stiffness and envelope curve generated by the Popovics’ model and combining with Eq. (8). The bond-slip model of CFRP-concrete interface under fatigue loading is as follows:

τeu s 3 = eu ∙ τmax s0 2 + seu s

τmax = (68.397 − 0.908T − 0.320H + T∙H /90) s0

where T represents temperature and H represents relative humidity. This formula has a good fitting effect for the ascending segment of the bond-slip relationship adopted in this paper. Zheng [47] studied the influence of different temperatures on the slip corresponding to the maximum shear stress of CFRP-concrete interface under the condition of high humidity, and obtained the corresponding semi-empirical formula:

s0 T = 0.029 + 0.041e−0.092T

3

( ) 0

(13)

seu = 0.046exp(0.26∙logni )

(14)

Ki = 1.25 − 0.2∙logni K1

(15)

(18)

(19)

With reference to Table 2 combined the research of Zheng and Liu, the parameters of FE simulation corresponding to the CFRP-concrete interface under hygrothermal conditions could be obtained. Therefore, based on the bond-slip relation of interface mentioned in Section 3.2.2 and 3.2.3, the bond-slip relation of CFRP-concrete interface under the coupling of hygrothermal environment and fatigue loading was obtained.

where τmax is the maximum bond stress, s0 is the slip corresponding to ultimate shear strength, τeu and seu are the x-coordinate and y6

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Fig. 10. Interface stiffness degradation based on bond slip model. k

Table 2 CFL-concrete interface parameters in hygrothermal environment.

Ds =

n

∑ Nsi i=1

Hygrothermal conditions

Ultimate shear strength, τmax (MPa)

Slip corresponding to τmax ,s0 (mm)

23 °C, 78% R·H 50 °C, 85% R·H 50 °C, 95% R·H

2.13 1.06 0.896

0.0339 0.0294 0.0294

3.3. Failure criterion

si − s0 su − s0

(23)

U

Db =

In general, the fracture of main reinforcement is the main mode of fatigue failure for CFRP-strengthened RC beam. In the hygrothermal environment, the CFRP-concrete interface debonding may also occur because interfacial bond property decreases sharply. To sum up, the failure criterion is defined as:

∑k = 1 Db, k U

=1

(24)

where, Db, k is the damage degree at the kth element , su is the ultimate slip when the interface is completely peeled of, U is the number of elements on the interface meshed in finite element. 3.4. Computing procedure

(20)

For the fatigue simulation of RC beams strengthened by CFRP in hygrothermal environment, the method of step-by-step calculation is adopted. The process of finite element model is as follows (Fig. 11):

where, Ds and Db are the damage value of the main reinforcement in the strengthened beam and the damage value of the CFRP-concrete interface, respectively. At present, there have been a lot of researches on fatigue failure model of main reinforcement. For the model predicting life, Wang [15] summarized a large number of experimental data and models, and proposed a model predicting fatigue life of main reinforcement based on stress amplitude of main reinforcement, which was expressed by the following formula: 4 ⎧ 797.7 − 94.34logNsi , 1 < Nsi ≤ 10 ⎪ 458.8 − 9.566logNsi , 10 4 < Nsi ≤ 105 Si = ⎨ 1208 − 159.4logNsi , 105 < Nsi ≤ 106 ⎪ 6 7 ⎩ 601.3 − 58.45logNsi , 10 < Nsi ≤ 10

(22)

where, nsi is the cycle number of main reinforcement corresponding to the specified stress amplitude. The damage value of the CFRP-concrete interfaceDb can be defined as the average damage value of each element on the interface.

Db, k =

D = max (Ds , Db) = 1

=1

si

1) Input the initial parameters of concrete, main reinforcement, CFRP and other materials. 2) Select a hygrothermal environment. Based on the bond-slip relationship of interface (Eq. (8)) in indoor environment, using Eq. (18 and 19) to calculate and input the constitutive equation of CFRPconcrete interface under the hygrothermal environment. 3) The stress of each component is calculated by applying the load in the FE model. 4) According to the calculation results of the previous cycle (i-1th) of ABAQUS, the degradation of material properties Eci , τmax , i and Ki after ith cycle are calculated according to Eq. (9-17). The material parameters after degradation are substituted and recalculated. 5) The stress amplitude Si of main reinforcement calculated by finite element analysis (FEA) under current cycle is substituted into Eq. (21) to obtain the fatigue life Ni of main reinforcement. 6) The damage of main reinforcement Ds is obtained by substituting Ni into Eq. (22), and the damage value of the CFRP-concrete interfaceDb is calculated by FE method (Eq. (23) and (24)). 7) Comparing Ds with Db by Eq. (20), if D is less than 1, continue the third step of operation for the next cycle; otherwise, the cycle ends.

(21)

where, Si is a stress amplitude of main reinforcement, and Nsi is the final fatigue life of main reinforcement corresponding to the specified stress amplitude. In this model, the curve equation of stress amplitude-fatigue life is given in a piecewise form, in which the stress amplitude can be calculated by finite element method. The damage value of the main reinforcement Ds was calculated by introducing Palmgren-Miner accumulated fatigue damage rule:

7

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Fig. 11. Flow chart of numerical analysis of fatigue damage cumulative process.

4. FEA results and discussion

50 °C, the higher the relative humidity, the greater the deflection of the strengthened beam. It could be seen that hygrothermal environment had a very significant influence on the deflection of the strengthened beam. Under hygrothermal environment, the stiffness of the whole component of the strengthened beam significantly decreased during the fatigue loading, and the deflection and the growth rate of deflection of the strengthened beam further increased with the increase of relative humidity.

4.1. Deflection of the strengthened beam Based on FE calculation, the deflection-relative life curves under different load levels and different hygrothermal environment were plotted as shown in Fig. 12. It could be seen that all of the curves had the same trend, that was, the deflection increased rapidly at first, and then slowly and steadily until the beam was destroyed. For Fig. 12(a)(c), when deflection of the strengthened beam at different load levels were compared, it could be clearly seen that the higher the load level was, the greater the deflection of the strengthened beam was. In addition, when the load levels were the same, it could be noticed that the deflection at 50 °C, 95% R·H environment and 50 °C, 85% R·H environment increased significantly compared with 23 °C, 78% R·H environment. In particular, when the environment temperature was

4.2. Stress and strain of main reinforcement To reflect the change of stress and strain of main reinforcement at the midspan of the reinforced beam, stress (strain) versus load cycle curves of main reinforcement under different load levels and hygrothermal environment were obtained based on FE calculation. The stress (strain) versus load cycle diagram of main reinforcement was very 8

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Fig. 12. Deflection versus relative life curves under different load levels and hygrothermal environments.

Fig. 13. Stress (strain) versus load cycle curves of main reinforcement under different load levels (50 °C, 85% R·H).

the reinforced beam increased with the increase of temperature and humidity. It was worth noting that the life of the reinforced beams under 50 °C, 95% R·H environment was significantly shorter than that of reinforced beams under the other two environments. These results indicated that high temperature and high humidity had a great influence on the reinforced beams, which greatly shortened the service life of the reinforced beams.

similar under 50 °C, 85% R·H environment (Fig. 13). In the evolution of the two stages, the stress of main reinforcement first increased rapidly, and then slowly increased with the increase of the deflection of the reinforced beam. Although the main reinforcement stress increased with the increase of the load, it was not found to exceed its yield load (400 MPa), so presented a good linear constitutive. Fig. 14 showed the numerical simulation curve of the main reinforcement stress at the midspan of the reinforced beam varying with the cyclic number of loads under the same load level (SR=0.56) and different hygrothermal environments. It could be clearly seen that the variation law of the main reinforcement stress at the midspan of the reinforced beam with the number of loading cycles under the different hygrothermal environment was basically consistent with Fig. 12. That was to say, with the same load level and cycle times, the deflection of

4.3. Stress/strain of mid-span CFRP Figs. 15 and 16 show the stress versus load cycles relationship of CFRP at midspan under different load levels and hygrothermal environment. It could be seen from the same hygrothermal environment (50 °C, 85% R·H) or load level (SR=0.56) as Figs. 15 and 16, the stress 9

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Fig. 17. Predicted shear strain distribution along the CFRP laminate at 2×105 cycles and 0.56 load level.

Fig. 14. Stress versus load cycle curves of main reinforcement under different hygrothermal environment (SR=0.56).

growth stage, accounting for about 95% of the whole fatigue life. At the same cycle number, the stress of CFRP increased with the increase of temperature, relative humidity and load level. However, unlike the main reinforcement, the stress of CFRP was less affected by the hygrothermal environment (less than 5%) and more affected by the load level. Additionally, it could be seen from Fig. 16 that the maximum stress of CFRP under 50 °C, 95% R·H environment was less than 50 °C, 85% R·H environment when the strengthened beam was loaded to failure. This was because the fatigue life of the strengthened beam fell sharply under 50 °C, 95% R·H environment due to poor interface bonding, which was far less than that under 50 °C, 85% R·H environment. This also showed that the relative humidity had a great influence on the CFRP-concrete interface. To be able to analyze the influence of hygrothermal environment on interfacial bonding performance, the distribution of the CFRP-concrete interfacial stresses should be quantified. The predicted strain variations along the CFRP laminate by FEM was plotted for two different hygrothermal environment at the same load cycles (N=2×105) and load level (SR=0.56). Fig.17 show the strain variations along the CFRP laminate predicted by FEM. It could be seen that CFRP strain under high temperature and humidity environment were larger than the corresponding strain under indoor environment in each part of the CFRP laminate. Further, the strain value of the middle 1/3 part of CFRP was the largest. The interface damage of some joints would lead to severely decline of bonding performance. Therefore, special attention should be paid to the bond quality of mid-span CFRP when making CFRPstrengthened members or applying them to engineering practice, so as to avoid the adverse effects of air bubbles and hollows on the reinforcement effect.

Fig. 15. Stress versus load cycle curves of CFRP at different load levels (50 °C, 85% R·H).

4.4. Damage evolutions of main reinforcement and CFRP-concrete interface To be able to explore fatigue failure mode, the damage evolutions of main reinforcement and CFRP-concrete interface should be quantified. Fig. 18(a) to (c) show the relationship between the predicted damage evolutions of main reinforcement and the number of loading cycles under different environments while Fig. 19(a) to (c) show the same of relationship on the CFRP-concrete interface. It could be seen from Fig. 18 that the damage of main reinforcements increased linearly with the loading cycles under different environments. In the same environment, the higher the load level, the faster the damage accumulation of main reinforcement. It could be found from the comparison of Fig. 18(a)–(c) that for SR = 0.61, the damage growth rate of the main reinforcement under two different hygrothermal environment increased by 44.8% and 56.4% respectively compared with the indoor

Fig. 16. Stress versus load cycle curves of CFRP under different hygrothermal environment (SR=0.56).

versus load cycles curve of CFRP was similar to the strain (stress) curve of the main reinforcement above. It could be divided into two stages: the first stage was rapid growth stage, and the second stage was stable 10

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Fig. 18. Damage evolutions of main reinforcement. Fig. 19. Damage evolutions of CFRP-concrete interface.

environment. These indicated great effect on the damage growth rate of main reinforcement after exposing to hygrothermal environment. The reason could be due to the fact that the decrease of interfacial bond performance caused by hygrothermal environment induced the main reinforcement to withstand greater stress. The fatigue interface damage could be physically interpreted as the average damage value of each element on the interface as shown schematically in Fig. 20. For the damage evolution of CFRP-concrete interface, it could be seen from Fig. 19(a) and (b) that the damage of interface presented two linear stages under indoor environment or the 50 °C, 85% R·H environment at a relatively small load level (SR = 0.56 or 0.61). The growth rate of interface damage in the early stage of development was greater than that in the second stage. As shown in Fig. 19(c), the damage evolution under high temperature and high humidity environment presents an obvious three-stage development

law, which is similar to deflection-load curve. In the first stage, the interfacial damage increased rapidly with development of the loading cycles. When loading to the first 5% of the final fatigue life, the interfacial damage was more than 0.5, which reflected the degradation of the interface stiffness and shear strength under high temperature and high humidity environment. In the second stage, the rate of damage growth slowed down. At the third stage, the rate of interface damage increased abruptly. This curve trend was due to the fact that the interface stiffness and shear strength had become very low at the later stage of fatigue loading. When the load exceeded the maximum bearing capacity of the interface, brittle fracture initiated at the interface and the strengthened beam was destroyed. It could also be seen from the damage nephogram of CFRP-concrete interface showed in Fig. 20 that 11

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Fig. 20. Finite element nephograms of interface damage (SR = 0.61).

under the same load level (SR=0.61), the hygrothermal environmental conditions significantly increased the damage amount of the interface. As can be seen from the comparison between Fig. 18 (a) and 19 (b), when the damage of main reinforcement reached 1while the interface damage was only about 0.4 in the indoor environment, which meant that the strengthened beam was destroyed due to the CFRP-concrete interface debonding caused by the fracture of main reinforcement. When the environment was set at 50 °C, 85% R·H, the damage of main reinforcement reached 1 earlier than that of CFRP-concrete interface, but it could be seen that the damage of interface was much higher than that of Fig. 19(a). These indicated that the simulated hygrothermal environment had a significantly adverse effect on the bond behavior of CFRP-concrete interface. It was noteworthy that for high load level (SR= 0.66), the interface damage reached 1 before that of the main reinforcement, which meant that the failure mode of the strengthened beams was the debonding failure of CFRP-concrete interface. When the environment was set at 50 °C, 95% R·H, the damage of CFRP-concrete interface reached 1 while the main reinforcement damage was less than 0.2. These indicated that with the increase of relative humidity, the bonding performance of CFRP-concrete interface decreased significantly. As discussed above, under fatigue loading, the failure mode of RC beams strengthened by CFRP in indoor environment was the main reinforcement fracture, while under the environment of high temperature and high humidity, it was easy to occur the failure caused by the debonding of CFRP-concrete interface. Therefore, the hygrothermal environment had a remarkably disadvantageous effect on the CFRPconcrete interface of RC beams strengthened by CFRP.

Fig. 21. Test fatigue life versus predicted life.

beams strengthened with CFRP in high temperature and humidity environments was larger than that of strengthened beams in indoor environment. In fact, this was because the fatigue life of the strengthened beam was determined by the damage of the CFRP-concrete interface under the hygrothermal environment, and the bonding slip constitutive relationship and performance degradation criterion of the interface were relatively complex under the high temperature and high humidity environment. Considering the discreteness of fatigue life of the specimens, it could be concluded that the FE model adopted in this paper could better predict the fatigue life of RC beams strengthened with CFRP under the different hygrothermal environments.

5. Experimental results 5.2. Fatigue failure mode of reinforced beams under environment 5.1. Life prediction and experimental results comparison From the experimental results, the fatigue failure mode under the coupling action of indoor environment and fatigue load is main reinforcement fracture, as shown in Fig. 22 and Table 1. It could be seen from Fig. 22 (b) that a large amount of crushed concrete was adhered to the surface of the CFL after RC beam failure. Since CFL was bonded to the bottom of RC beam with A, B adhesive, it could be considered that the shear strength of A, B adhesive layer was much greater than that of concrete layer at the bottom of RC beam and main reinforcement in

The comparison between the predicted results and the test fatigue life of the strengthened beams under three different hygrothermal environment is shown in Fig. 21. It could be seen the absolute value of the relative error of the life prediction results by numerical calculation were between 7.79% and 37.04%, and the absolute value of the average relative error was 20.5%. For the life prediction results in different environments, the relative error of the life prediction results of RC 12

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Fig. 22. Fatigue failure mode under 23 °C, 78% R·H environment.

6. Conclusion

indoor environment. The fatigue failure mode under the coupling action of 50 °C, 95% R·H environment and fatigue load is only a failure mode: debonding of CFL-concrete. Different from the control group, in the 50 °C, 95% R·H environment, a small amount of A, B adhesive was adhered to the surface of CFL after the CFL-concrete peeling failure. In addition, the bottom of the RC beam was relatively flat, as shown in Fig. 23. The possible reasons might be that the hygrothermal environment reduced the mechanical properties of the adhesive interface layer, and the fatigue load accelerated the failure of the CFL-concrete interface layer. Therefore, the adverse effects of hygrothermal environment on the overall mechanical properties of the strengthened beam was reflected in the reduction of the mechanical properties of the adhesive interface layer and the epoxy resin matrix material, which was accompanied by the reduction of mechanical properties of the entire CFL-concrete interface.

A total of 27 RC beams strengthened with CFRP were tested under 3-point bending to failure in hygrothermal environment. The experimental results showed that the strengthened beams exhibited different fatigue life and failure mode in different hygrothermal environment. In order to further study the fatigue performance of the strengthened beams under the hygrothermal environment, a FE model of RC beams strengthened with CFRP considering material degradation was established in this paper. The influence of different hygrothermal environments and constant amplitude cyclic loading on the fatigue performance of the strengthened beams was analyzed by numerical simulation. The following were the main conclusions: 1) The FE model was used to analyze the influence of different hygrothermal environment on the deflection of the strengthened beams. The results showed that the deflection of the strengthened

Fig. 23. Fatigue failure mode under 50 °C, 95% R·H environment. 13

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2)

3)

4)

5)

beams under cyclic fatigue loading was greatly affected by the hygrothermal environment. At the same load level, the deflection of the strengthened beams under high temperature and high humidity condition increased by about 20% compared with indoor condition. With the increase of temperature and relative humidity, the deflection and the growth rate of deflection increased further. At the same cycle times, the higher the temperature and relative humidity, the greater the stress and strain in the mid-span of main reinforcement and CFRP. In the same hygrothermal environment, the higher the load level was, the greater the mid-span stress and strain of main reinforcement and CFRP were. The hygrothermal environment reduced the stiffness and strength of CFRP-concrete interface, increased the stress and strain of the main reinforcement and CFRP surface, accelerated the damage of CFRPconcrete interface and main reinforcement, and leaded to the reduction of the service life of the strengthened beams. Based on numerical simulation, the failure modes of main reinforcement fracture and CFRP-concrete interface debonding were discussed in this paper. Under fatigue loading, the failure mode of RC beams strengthened with CFRP in indoor environment was the main reinforcement fracture. While under the high temperature and high humidity environment, the damage value of the interface between CFRP and concrete reached 1 before that of main reinforcement, and the interface debonding leaded to the failure of the strengthened beams. As the experimental results shown, the high temperature and high humidity environment greatly reduced the fatigue life of specimens. In addition, for the analysis of the failure modes of specimens, it could be found that the hygrothermal environment degraded the mechanical properties of the adhesive interface layer and the epoxy resin matrix material.

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