Moisture Absorption/Desorption Effects on Flexural Property of Glass-Fiber-Reinforced Polyester Laminates: Three-Point Bending Test and Coupled Hygro-Mechanical Finite Element Analysis

Influence of moisture absorption/desorption on the flexural properties of Glass-fibre-reinforced polymer (GFRP) laminates was experimentally investigated under hot/wet aging environments. To characterize mechanical degradation, three-point bending tests were performed following the ASTM test standard (ASTM D790-10A). The flexural properties of dry (0% Mt/M∞), moisture unsaturated (30% Mt/M∞ and 50% Mt/M∞) and moisture saturated (100% Mt/M∞) specimens at both 20 and 40 °C test temperatures were compared. One cycle of moisture absorption-desorption process was considered in this study to investigate the mechanical degradation scale and the permanent damage of GFRP laminates induced by moisture diffusion. Experimental results confirm that the combination of moisture and temperature effects sincerely deteriorates the flexural properties of GFRP laminates, on both strength and stiffness. Furthermore, the reducing percentage of flexural strength is found much larger than that of E-modulus. Unrecoverable losses of E-modulus (15.0%) and flexural strength (16.4%) for the GFRP laminates experiencing one cycle of moisture absorption/desorption process are evident at the test temperature of 40 °C, but not for the case of 20 °C test temperature. Moreover, a coupled hygro-mechanical Finite Element (FE) model was developed to characterize the mechanical behaviors of GFRP laminates at different moisture absorption/desorption stages, and the modeling method was subsequently validated with flexural test results.


Introduction
During the last two decades, fibre-reinforced polymer (FRP) bridge decks are increasingly being used for the rehabilitation of old concrete-steel composite bridges and new construction of pedestrian and highway bridges [1][2][3][4][5][6][7], due to their various advantages [8]: high strength to weight ratio, corrosion resistance, controllable quality, rapid installation with minimum traffic disruption and low maintenance cost. Although FRP decks are increasingly being employed in civil infrastructure applications, their durability and long-term performance are still not comprehensively understood. In the normal The layup configuration of each piece of the standard 0.94 mm EQX1200 is illustrated in Table 1. The mechanical properties of GFRP laminates supplied by the manufacturer are shown in Table 2. The nominal length and width of the specimens were selected to be 150 and 20 mm respectively. According to the test code ASTM D790-10 [27], the specimen length shall be sufficient to allow for overhanging on each end of at least 10% of the support span. The specimen width shall not exceed one fourth of the support span for specimens greater than 3.2 mm in depth.
Polymers 2016, 8,290 3 of 15 0.94 mm EQX1200. The layup configuration of each piece of the standard 0.94 mm EQX1200 is illustrated in Table 1. The mechanical properties of GFRP laminates supplied by the manufacturer are shown in Table 2. The nominal length and width of the specimens were selected to be 150 and 20 mm respectively. According to the test code ASTM D790-10 [27], the specimen length shall be sufficient to allow for overhanging on each end of at least 10% of the support span. The specimen width shall not exceed one fourth of the support span for specimens greater than 3.2 mm in depth.  The numbering of specimens is given in Table 3, with regard to the moisture uptake content, test temperature, absorption/desorption process and replicated number. Two test temperatures 20 and 40 °C were selected for the three point bending tests, which were controlled by the climate chamber with the tolerance of ± 2 °C, as shown in Figure 2.   The numbering of specimens is given in Table 3, with regard to the moisture uptake content, test temperature, absorption/desorption process and replicated number. Two test temperatures 20 and 40˝C were selected for the three point bending tests, which were controlled by the climate chamber with the tolerance of˘2˝C, as shown in Figure 2. As listed in Table 3, the test in each condition was repeated five times to investigate the spread of test results. The hydrothermal aging condition was 40 °C-water, which is supposed to be a severe hot/wet condition for GFRP laminates, as discussed in previous research [28]. In total, 70 pieces of specimens were prepared. During the hydrothermal aging process, all the specimens were immersed in the water at 40 °C, except the F-0-20 °C and F-0-40 °C specimens, which are the as-received reference specimens (Set-1 in Table 3). The as-received specimens were stored in the laboratory environment. The moisture content of them is very low, and thus can be ignored. As illustrated in Table 3, the Set-2 specimens (F-30%-20 °C and F-30%-40 °C) were tested at 30% relative moisture uptake content. The Set-3 specimens (F-50%-20 °C and F-50%-40 °C) were tested at 50% relative moisture uptake content. The Set-4 specimens (F-100%-20 °C and F-100%-40 °C) were tested at the moisture saturation level (100% relative moisture uptake content). Until this time point, the above test process was considered as the moisture absorption process. Then, the remaining specimens were all taken out of the hydrothermal aging environment, and put into an oven at 42 °C to dry them, which was considered as the moisture desorption process. In this way, the Set-5 specimens (F-50%-20 °C -D and F-50%-40 °C -D) were tested at 50% relative moisture uptake content after a certain time of moisture desorption. Subsequently, the Set-6 specimens (F-30%-20 °C -D and F-30%-40 °C -D) were tested at 30% relative moisture uptake content after the moisture desorption.

Numder of specimens
Set-4 F- 100%-20˝C  flexural  100%  20˝C  no  5  F-100%-40˝C  flexural  100%  40˝C  no  5   Set-5  F-50%-20˝C-D  flexural  50%  20˝C  yes  5  F-50%-40˝C-D  flexural  50%  40˝C  yes  5   Set-6  F-30%-20˝C-D  flexural  30%  20˝C  yes  5  F-30%-40˝C-D  flexural  30%  40˝C  yes  5   Set-7  F-0%-20˝C-D  flexural  0  20˝C  yes  5  F-0%-40˝C-D  flexural  0  40˝C  yes  5 As listed in Table 3, the test in each condition was repeated five times to investigate the spread of test results. The hydrothermal aging condition was 40˝C-water, which is supposed to be a severe hot/wet condition for GFRP laminates, as discussed in previous research [28]. In total, 70 pieces of specimens were prepared. During the hydrothermal aging process, all the specimens were immersed in the water at 40˝C, except the F-0-20˝C and F-0-40˝C specimens, which are the as-received reference specimens (Set-1 in Table 3). The as-received specimens were stored in the laboratory environment. The moisture content of them is very low, and thus can be ignored. As illustrated in Table 3, the Set-2 specimens (F-30%-20˝C and F-30%-40˝C) were tested at 30% relative moisture uptake content. The Set-3 specimens (F-50%-20˝C and F-50%-40˝C) were tested at 50% relative moisture uptake content. The Set-4 specimens (F-100%-20˝C and F-100%-40˝C) were tested at the moisture saturation level (100% relative moisture uptake content). Until this time point, the above test process was considered as the moisture absorption process. Then, the remaining specimens were all taken out of the hydrothermal aging environment, and put into an oven at 42˝C to dry them, which was considered as the moisture desorption process. In this way, the Set-5 specimens (F-50%-20˝C-D and F-50%-40˝C-D) were tested at 50% relative moisture uptake content after a certain time of moisture desorption. Subsequently, the Set-6 specimens (F-30%-20˝C-D and F-30%-40˝C-D) were tested at 30% relative moisture uptake content after the moisture desorption. The final Set-7 specimens (F-0-20˝C-D and F-0-40˝C-D) were the fully dry specimens after one cycle of moisture absorption-desorption process. Herein, the symbol "D" indicates the moisture desorption.
As shown in Figure 3, the whole three-point bending test set-up was put into the chamber. According to ASTM D790-10 [27], the support span-to-depth ratio is 16:1. Thus, the support span was proposed to be 90.24 mm, but it varied between different groups of specimens, since the value of the support span was exactly calculated based on the average real thickness of each group of specimens. The radii of the loading nose and supports were 5.0˘0.1 mm. The specimens were loaded at the strain rate 0.01 mm/mm/min. Correspondingly, the rate of crosshead motion was 2.4 mm/min, which is calculated as follows [27]: R = rate of crosshead motion, mm/min, L = support span, mm, d = depth of FRP beam tested, mm, Z = rate of straining of the outer fiber, mm/mm/min. The final Set-7 specimens (F-0-20 °C -D and F-0-40 °C -D) were the fully dry specimens after one cycle of moisture absorption-desorption process. Herein, the symbol "D" indicates the moisture desorption. As shown in Figure 3, the whole three-point bending test set-up was put into the chamber. According to ASTM D790-10 [27], the support span-to-depth ratio is 16:1. Thus, the support span was proposed to be 90.24 mm, but it varied between different groups of specimens, since the value of the support span was exactly calculated based on the average real thickness of each group of specimens. The radii of the loading n ose and supports were 5.0 ± 0.1 mm. The specimens were loaded at the strain rate 0.01 mm/mm/min. Correspondingly, the rate of crosshead motion was 2.4 mm/min, which is calculated as follows [27]: R = rate of crosshead motion, mm/min, L = support span, mm, d = depth of FRP beam tested, mm, Z = rate of straining of the outer fiber, mm/mm/min. The specimen was deflected until the load dropped to 30% of the maximum load or the maximum displacement of mid-span reached 10 mm, whichever occurred first (as illustrated in Figure 4). The experimental data was recorded per second. To track the moisture absorption process in GFRP laminate specimens, gravimetric tests were also conducted, the detailed test procedure of which can be found in previous research [28].    The final Set-7 specimens (F-0-20 °C -D and F-0-40 °C -D) were the fully dry specimens after one cycle of moisture absorption-desorption process. Herein, the symbol "D" indicates the moisture desorption. As shown in Figure 3, the whole three-point bending test set-up was put into the chamber. According to ASTM D790-10 [27], the support span-to-depth ratio is 16:1. Thus, the support span was proposed to be 90.24 mm, but it varied between different groups of specimens, since the value of the support span was exactly calculated based on the average real thickness of each group of specimens. The radii of the loading n ose and supports were 5.0 ± 0.1 mm. The specimens were loaded at the strain rate 0.01 mm/mm/min. Correspondingly, the rate of crosshead motion was 2.4 mm/min, which is calculated as follows [27]: R = rate of crosshead motion, mm/min, L = support span, mm, d = depth of FRP beam tested, mm, Z = rate of straining of the outer fiber, mm/mm/min. The specimen was deflected until the load dropped to 30% of the maximum load or the maximum displacement of mid-span reached 10 mm, whichever occurred first (as illustrated in Figure 4). The experimental data was recorded per second. To track the moisture absorption process in GFRP laminate specimens, gravimetric tests were also conducted, the detailed test procedure of which can be found in previous research [28].    The specimen was deflected until the load dropped to 30% of the maximum load or the maximum displacement of mid-span reached 10 mm, whichever occurred first (as illustrated in Figure 4). The experimental data was recorded per second. To track the moisture absorption process in GFRP laminate specimens, gravimetric tests were also conducted, the detailed test procedure of which can be found in previous research [28]. Figure 5 shows the moisture absorption process of GFRP laminate flexural test specimens immersed in water of 40˝C, compared with the FE moisture diffusion analysis. The moisture uptake content (M t ) absorbed by each specimen was calculated according to its weight before exposure (w 0 ) and after exposure (w t ) as follows:

Results and Discussion
Moisture content is established as the function of the square root of time. It can be found that the moisture saturation level (M 8 ) is about 0.77%, which is in line with the gravimetric experimental results obtained in the previous research [28]. The specimens developed a similar moisture diffusion curve as that simulated by the FE analysis [28], which verifies the accuracy of the FE moisture diffusion model.  Figure 5 shows the moisture absorption process of GFRP laminate flexural test specimens immersed in water of 40 °C, compared with the FE moisture diffusion analysis. The moisture uptake content (Mt) absorbed by each specimen was calculated according to its weight before exposure (w0) and after exposure (wt) as follows:

Results and Discussion
Moisture content is established as the function of the square root of time. It can be found that the moisture saturation level (M∞) is about 0.77%, which is in line with the gravimetric experimental results obtained in the previous research [28]. The specimens developed a similar moisture diffusion curve as that simulated by the FE analysis [28], which verifies the accuracy of the FE moisture diffusion model. The typical failure mode of specimens under flexural tests is shown in Figure 6, where rupture occurs in the outer surface of the test specimen. In order to obtain the E-modulus of GFRP laminates, the stress and strain at the mid-span of GFRP specimens were calculated as follows.
According to ASTM D790-10 [27], the flexural stress in the outer surface of the specimen at midpoint was calculated by means of the following equation: where:  = stress in the outer fibers at midpoint, MPa, P = load at the mid-span on the load-deflection curve, N, b = width of FRP beam tested, mm. The flexural strain, that nominal fractional change in the length of an element of the outer surface of the test specimen at mid-span, was calculated for any deflection using Equation (4): where:  = strain in the outer fibers at midpoint, MPa, Dmax = maximum deflection of the center of the beam, mm. The typical failure mode of specimens under flexural tests is shown in Figure 6, where rupture occurs in the outer surface of the test specimen. In order to obtain the E-modulus of GFRP laminates, the stress and strain at the mid-span of GFRP specimens were calculated as follows.
According to ASTM D790-10 [27], the flexural stress in the outer surface of the specimen at midpoint was calculated by means of the following equation: where: σ = stress in the outer fibers at midpoint, MPa, P = load at the mid-span on the load-deflection curve, N, b = width of FRP beam tested, mm. The flexural strain, that nominal fractional change in the length of an element of the outer surface of the test specimen at mid-span, was calculated for any deflection using Equation (4): where: ε = strain in the outer fibers at midpoint, MPa, D max = maximum deflection of the center of the beam, mm. The stress-strain curves are presented in Figure 7. To make the comparison more clear, the curve of only one specimen under each test condition is presented, which was selected visually as the average curve of the five specimens. The stress-strain curves are presented in Figure 7. To make the comparison more clear, the curve of only one specimen under each test condition is presented, which was selected visually as the average curve of the five specimens.   The E-modulus is represented by the chord modulus, which was calculated from two discrete points on the load-deflection curve, using Equation (5) [27]:  are the flexural stress and strain selected at two points of stress-strain curves (see Figure 7) in the linear stable range. The flexural strength is the maximum flexural stress sustained by the test specimen during the flexural test. The environment-dependent flexural properties (including E-modulus and strength) are shown in Figure 8 and Table 4. The R-square value for each curve is also present in Figure 8, which indicates how well the curve fits test data points. The stress-strain curves are presented in Figure 7. To make the comparison more clear, the curve of only one specimen under each test condition is presented, which was selected visually as the average curve of the five specimens.   The E-modulus is represented by the chord modulus, which was calculated from two discrete points on the load-deflection curve, using Equation (5) [27]:  are the flexural stress and strain selected at two points of stress-strain curves (see Figure 7) in the linear stable range. The flexural strength is the maximum flexural stress sustained by the test specimen during the flexural test. The environment-dependent flexural properties (including E-modulus and strength) are shown in Figure 8 and Table 4. The R-square value for each curve is also present in Figure 8, The E-modulus is represented by the chord modulus, which was calculated from two discrete points on the load-deflection curve, using Equation (5) [27]: σ 1 , ε 1 and σ 2 , ε 2 are the flexural stress and strain selected at two points of stress-strain curves (see Figure 7) in the linear stable range.
The flexural strength is the maximum flexural stress sustained by the test specimen during the flexural test. The environment-dependent flexural properties (including E-modulus and strength) are shown in Figure 8 and Table 4. The R-square value for each curve is also present in Figure 8, which indicates how well the curve fits test data points.  To be simplified, the predictive equation for the E-modulus degradation as the function of moisture content was curve fitted by the linear interpolant function, while for the flexural strength the exponential function was used. All the curve fitting processes were conducted by MATLAB R2011b, employing the least square method. The obtained predictive equation is as follows: E-modulus, 20 °C, absorption process:  To be simplified, the predictive equation for the E-modulus degradation as the function of moisture content was curve fitted by the linear interpolant function, while for the flexural strength the exponential function was used. All the curve fitting processes were conducted by MATLAB R2011b, employing the least square method. The obtained predictive equation is as follows: E-modulus, 20˝C, absorption process: E-modulus, 20˝C, absorption-desorption process: Flexural strength, 20˝C, absorption process: Flexural strength, 20˝C, absorption-desorption process: E-modulus, 40˝C, absorption process: E-modulus, 40˝C, absorption-desorption process: Flexural strength, 40˝C, absorption process: Flexural strength, 40˝C, absorption-desorption process: All the predictive curves are illustrated in Figure 8 for comparison with the experimental results. For the specimens tested at 20˝C (Figure 8a), the E-modulus of GFRP laminates decreases gradually as the moisture content increases from fully dry to fully saturated. The E-modulus of the moisture saturated specimen is 14,022 MPa (as shown in Table 4), which is 15.6% lower than that of the unconditioned dry specimen. For the specimens with the moisture contents 30% and 50% of the saturation level, the loss of E-modulus is 4.4% and 9.5% respectively. With regard to specimens in the moisture desorption process, the E-modulus does not decrease significantly as compared to the specimens at the same moisture uptake level. Accordingly, the slight loss of E-modulus is 1.7%, 5.1% and 4.2% at the moisture uptake levels 0%, 30% and 50% respectively. In terms of flexural strength (see Figure 8b), there is a general exacerbation of decrease between the fully dry specimens and 30% moisture content specimens, regardless of the moisture absorption/desorption process. More than 20% loss of flexural strength is evident. After this stage, as the moisture uptake content increases, the flexural strength of specimens slightly decreases, until reaching 265 MPa for the moisture fully saturated specimens. At the end, the total drop of flexural strength is 35.4% of the fully dry specimens. Similar to the E-modulus degradation, the difference of flexural strength between absorption process and desorption process is very limited.
With regard to the environment-dependent flexural properties of GFRP laminates at 40˝C, the E-modulus of GFRP laminates regularly decreases from 15,409 MPa (dry) to 12,780 MPa (moisture fully saturated), and then slightly increases to 13,095 MPa after being fully dried in the moisture desorption process. Different from that at 20˝C, there is a significant unrecoverable loss (15.0%) of the E-modulus for the dry specimens tested at 40˝C. Accordingly, the loss of 11.1% and 6.1% of the E-modulus is evident for the specimens with 30% and 50% moisture content respectively in the desorption process. As to the flexural strength of specimens tested at 40˝C, a rapid decrease is observed at a moisture content of about 30% of moisture saturation level, and then the flexural strength slightly decreases to 214 MPa of the moisture fully saturated specimens, which is the lowest value among the whole series of tests. It is 42.9% lower than that of the unconditioned dry specimens (375 MPa, as listed in Table 4) tested at 40˝C, and 47.9% lower than that of the unconditioned dry specimens (410 MPa) tested at 20˝C. The most severe loss of flexural strength indicates that the combination of moisture and temperature effects can significantly influence the mechanical properties of GFRP laminates. Comparing the unconditioned dry specimens with the dry specimens after the moisture desorption, a decrease of 16.4% of the flexural strength is observed for the specimens tested at 40˝C. However, for the specimens with moisture contents 30% and 50%, the loss of flexural strength is not obvious. Even a slight increase is observed for the specimens with 30% moisture content in the moisture desorption process.
It is clear that the hot and wet environment seriously degrades the flexural properties of GFRP laminates, and in turn influences the durability of FRP composite structures. For the moisture effects, as stated in the researches [21,29,30], the absorbed moisture can cause both reversible and irreversible changes to the FRP composites, such as water plasticization and the disruption of hydrogen bonds between the molecular chains in the polymer. It is because the matrix often has hydrophilic groups that attract water molecules, which can form hydrogen bonds with water molecules via the hydroxyl groups [21]. Plasticization is a physical mechanism, which degrade the stiffness and strength of the polymer. It can be reversible at the initial stages of aging when the absorbed water is removed and no chemical reaction occurs. Furthermore, prolonged environmental exposure often leads to irreversible changes that induce permanent property alterations within the matrix, the fibre surfaces and the fibre/matrix interface. For instance, the polymer relaxation process is related to the polymer chain rearranging or redistribution of free-volume elements to provide additional sites of suitable size and accessibility to accommodate more penetrant molecules. It is a long-term and complicated process, which is a combination of chemical and physical reaction. Moreover, the fibre/matrix debonding, matrix cracking due to moisture/thermal cycles and ultimately fiber breaking would also contribute to the mechanical degradation. The fibre/matrix interface and the interphase region around fibres, are susceptible to deterioration due to moisture absorption. With the fibre/matrix debonding [31], there is enhanced interfacial capillary action along the fibres that can offer more space for moisture penetration and further promote their degradation. With regard to the temperature effects, when the test temperature is approaching the T g of FRP composite materials, the mechanical performance such as E-modulus, strength and fatigue resistance significantly decreases [32,33]. Sometimes, the mass loss of FRP composites occurs following high-temperature exposure [28,34]. The recommended working temperature for FRP composite structures should be at least 20˝C lower than the T g of FRP composite materials. Furthermore, the researches [33,35] confirmed that a decrease of T g was evident when the moisture uptake content increased in the FRP composite materials. Meanwhile, as already proven in previous research [28], the high temperature can speed up the moisture diffusion process. Thus, the interaction between moisture and temperature effects accelerates the environmental degradation process on the FRP composite material, which in turn explains why the combination of moisture and temperature seriously deteriorates the mechanical properties of FRP materials.

Coupled Hygro-Mechanical FE Analysis
Generally, the environmental degradation experiments (mainly concerning moisture and temperature effects) for FRP composite materials are limited to a fairly short time, normally no more than 5 years. However, the expected service life of infrastructures such as bridges exceeds 50 years. Thus, the short-term experimental investigations are not sufficient to estimate the long-term performance of FRP structures. To achieve this aim, some accelerated experimental methods were developed by the researches [10,[36][37][38], in which the temperature or atmospheric pressure of the environmental aging conditions were raised beyond the normal service conditions to accelerate the moisture diffusion and degradation process. These accelerating experimental methods were confirmed useful and time-effective to investigate the durability of FRP composites and adhesive materials. But, researches indicated that the high aging temperatures approaching glass transition temperature of specimens would improve the mechanical performance by post-cure or deteriorate the materials by inducing thermal cracks, which do not occur in the real use of FRP composite structures. Another method for studying the environmental degradation of mechanical behaviour of FRP materials and structures is the predictive FE modeling [39]. The first step is modeling moisture transport through FRP structures in order to determine the moisture concentration distribution through the cross-sections as a function of time. The material parameters required for the transient diffusion FE analysis are the diffusion coefficient and the solubility coefficient, which can be obtained from the short term gravimetric experiments, as stated in previous research [28]. And then, based on the obtained moisture concentration distribution, the environment-dependent mechanical behaviour of FRP structures can be investigated using the coupled hygro-mechanical FE analysis. The input moisture-dependent material properties of FRP composites are obtained by the material tests (such as flexural test, tensile test and short-beam shear test).
To develop the coupled hygro-mechanical FE modeling method, the FE model of the GFRP flexural test specimen was calibrated (as shown in Figure 9). The moisture diffusion process in the FRP specimen was modeled by the transient diffusion FE analysis (thoroughly described in previous research [28]) and validated by comparing with the gravimetric experimental results, as shown in Figure 5. From the moisture diffusion analysis, the moisture concentration distribution across the FRP specimen section was obtained as a function of time, which can be read into the stress analysis as a predefined field variable. The predictive equations (Equations (6), (7), (10) and (11)) of environment-dependent material properties served as the input of field-dependent material properties of FRP composites, which was obtained by the flexural tests. Hence, the E-modulus of each element was determined by the local moisture concentration. Thus, the coupled hygro-mechanical FE modeling was realized on the flexural test specimen. Subsequently, it can be employed to simulate other material tests (such as short-beam shear tests) and FRP structures. the materials by inducing thermal cracks, which do not occur in the real use of FRP composite structures. Another method for studying the environmental degradation of mechanical behaviour of FRP materials and structures is the predictive FE modeling [39]. The first step is modeling moisture transport through FRP structures in order to determine the moisture concentration distribution through the cross-sections as a function of time. The material parameters required for the transient diffusion FE analysis are the diffusion coefficient and the solubility coefficient, which can be obtained from the short term gravimetric experiments, as stated in previous research [28]. And then, based on the obtained moisture concentration distribution, the environment-dependent mechanical behaviour of FRP structures can be investigated using the coupled hygro-mechanical FE analysis. The input moisture-dependent material properties of FRP composites are obtained by the material tests (such as flexural test, tensile test and short-beam shear test).
To develop the coupled hygro-mechanical FE modeling method, the FE m odel of the GFRP flexural test specimen was calibrated (as shown in Figure 9). The moisture diffusion process in the FRP specimen was modeled by the transient diffusion FE analysis (thoroughly described in previous research [28]) and validated by comparing with the gravimetric experimental results, as shown in Figure 5. From the moisture diffusion analysis, the moisture concentration distribution across the FRP specimen section was obtained as a function of time, which can be read into the stress analysis as a predefined field variable. The predictive equations (Equations (6), (7), (10) and (11)) of environment-dependent material properties served as the input of field-dependent material properties of FRP composites, which was obtained by the flexural tests. Hence, the E-modulus of each element was determined by the local moisture concentration. Thus, the coupled hygro-mechanical FE m odeling was realized on the flexural test specimen. Subsequently, it can be employed to simulate other material tests (such as short-beam shear tests) and FRP structures. To validate this coupled hygro-mechanical FE modeling method, two groups of FRP specimens were selected: F-50%-20 °C and F-30%-40 °C -D. Firstly, the moisture concentration distributions throughout the mid-section of these two specimens are shown in Figures 10 and 11. Based on these two predefined fields, the coupled hygro-mechanical FE analysis was executed. The FE stress analysis was linear-elastic. The element used was C3D8R, which is an 8-node linear brick element, with the capacity of reduced integration and hourglass control. In total 2000N load was applied at mid-span of the specimen. To validate this coupled hygro-mechanical FE modeling method, two groups of FRP specimens were selected: F-50%-20˝C and F-30%-40˝C-D. Firstly, the moisture concentration distributions throughout the mid-section of these two specimens are shown in Figures 10 and 11. Based on these two predefined fields, the coupled hygro-mechanical FE analysis was executed. The FE stress analysis was linear-elastic. The element used was C3D8R, which is an 8-node linear brick element, with the capacity of reduced integration and hourglass control. In total 2000N load was applied at mid-span of the specimen.
were selected: F-50%-20 °C and F-30%-40 °C -D. Firstly, the moisture concentration distributions throughout the mid-section of these two specimens are shown in Figures 10 and 11. Based on these two predefined fields, the coupled hygro-mechanical FE analysis was executed. The FE stress analysis was linear-elastic. The element used was C3D8R, which is an 8-node linear brick element, with the capacity of reduced integration and hourglass control. In total 2000N load was applied at mid-span of the specimen.  The comparisons of experimental results and FE results on the load-deflection curves of F-50%-20 °C specimens and F-30%-40 °C -D specimens are illustrated in Figures 12 and 13 respectively. Good agreement is obtained in the linear stage, which means the environment-dependent stiffness of GFRP specimens with different moisture uptake contents can be predicted by the coupled hygro-mechanical FE model. Hence, the accuracy of the FE model is validated, and the methodology of the hygro-mechanical numerical analysis is proven.   The comparisons of experimental results and FE results on the load-deflection curves of F-50%-20˝C specimens and F-30%-40˝C-D specimens are illustrated in Figures 12 and 13 respectively. Good agreement is obtained in the linear stage, which means the environment-dependent stiffness of GFRP specimens with different moisture uptake contents can be predicted by the coupled hygro-mechanical FE model. Hence, the accuracy of the FE model is validated, and the methodology of the hygro-mechanical numerical analysis is proven. The comparisons of experimental results and FE results on the load-deflection curves of F-50%-20 °C specimens and F-30%-40 °C -D specimens are illustrated in Figures 12 and 13 respectively. Good agreement is obtained in the linear stage, which means the environment-dependent stiffness of GFRP specimens with different moisture uptake contents can be predicted by the coupled hygro-mechanical FE model. Hence, the accuracy of the FE model is validated, and the methodology of the hygro-mechanical numerical analysis is proven.

Conclusions
This paper describes the investigation on the environment-dependent flexural properties of the FRP laminate material, which is achieved by the three-point bending tests according to the ASTM test code D790-10. The hydrothermal aging condition is a typical hot/wet aging environment (40˝C-water) for the application of FRP bridge decks. The test conditions vary in terms of test temperature, moisture uptake content and absorption/desorption process. The following conclusions can be drawn: (1) For GFRP laminates tested at 20˝C, the E-modulus and flexural strength of moisture saturated GFRP laminates dropped 15.6% and 35.4% respectively, comparing with the fully dry materials. While, the difference of E-modulus and flexural strength between absorption process and desorption process was very limited. (2) For GFRP laminates tested at 40˝C, the E-modulus and flexural strength of moisture saturated GFRP laminates dropped 17.1% and 42.9% respectively, comparing with the fully dry materials. There were significant unrecoverable losses of E-modulus (15.0%) and flexural strength (16.4%) for the GFRP laminates experienced both moisture absorption and desorption process.
Experimental results confirmed that the combination of moisture and temperature seriously deteriorated the flexural properties of GFRP laminates, on both strength and stiffness. (4) Predictive equations for environment-dependent flexural properties of FRP laminates were obtained by using the least square method for the curve fitting. These predictive equations can be employed as the input parameters for a coupled hygro-mechanical FE model, as well as a contribution to the design code as far as the long-term performance of FRP structures is concerned.
A coupled hygro-mechanical FE modeling method was developed to analyze the environment-dependent mechanical behaviours of FRP laminates, and was validated by the experimental results of flexural tests. In the following research works, it could be employed in the parametric FE analysis, and predict the environment-dependent behaviours of other material tests or FRP structures.