Durability Prediction Model for Shear Behavior of GFRP Connectors in Precast Concrete Sandwich Panels

Abstract

To achieve the same service life of glass fiber reinforced polymer (GFRP) connectors and precast concrete sandwich panels, ensuring the structural stability and safety of the walls during long-term service, it is necessary to research the durability of GFRP connectors. In accordance with the ACI 440.3R-12 test method, an accelerated aging study was conducted by immersing 90 GFRP connectors in a simulated concrete pore solution at temperatures of 40 °C, 60 °C, and 80 °C for durations of 3.65, 18, 36.5, 92, and 183 days. This investigation aimed to analyze the effects of temperature and exposure time on the shear strength of the GFRP connectors. Scanning Electron Microscopy (SEM) was employed to analyze the micro-morphology of the specimens before and after exposure. The SEM observations revealed that after 183 days at 40 °C, the fiber-matrix interface remained relatively intact without significant debonding. However, at 60 °C, noticeable degradation occurred, characterized by corrosion of fibers and evident debonding from the surrounding matrix. At 80 °C, the GFRP specimens were severely damaged, precluding the extraction of viable samples for SEM analysis. The results further indicated that the most rapid decline in the shear strength occurred within the initial 3.65 days of exposure, with reductions of 8.62%, 10.12%, and 10.77% at 40 °C, 60 °C, and 80 °C, respectively. The degradation rate subsequently decelerated with prolonged exposure. After 183 days, the residual shear strength retention rates decreased by 21.03% and 26.89% at 40 °C and 60 °C, respectively. This behavior is primarily attributed to a high moisture absorption rate driven by a significant humidity gradient between the surface and the interior, leading to rapid swelling and plasticization of the vinyl ester resin matrix, which consequently reduced the stiffness and strength of the GFRP connectors. Finally, a predictive model for the time-dependent shear strength of GFRP connectors under various temperature conditions was developed based on Fick’s law.

1. Introduction

Precast Concrete Sandwich Panel (PCSP) is a prefabricated wall integrating structural load-bearing, thermal insulation, and decorative functions. It exhibits excellent economic, social, and environmental benefits, and aligns well with the development trends of industrialized construction and building energy efficiency [1]. External wall thermal insulation measures include three types: internal insulation, external insulation, and sandwich insulation. Among them, internal insulation is susceptible to the influence of indoor decoration, while external insulation faces some problems regarding durability and fire resistance. In contrast, PCSP embeds thermal insulation material between the inner and outer concrete wythes, effectively protecting the insulation layer and achieving a service life comparable to that of the main structure. As a result, PCSP has become the most widely used exterior wall enclosure system and has experienced development in China since 2010.

PCSP consists of an inner concrete wythe, an outer concrete wythe, and a central insulation layer, which are integrated into a monolithic component through connectors, as illustrated in Figure 1. The behavior of connectors influences both the structural and thermal behavior of the PCSP. At present, FRP connectors and stainless steel connectors are the most commonly used types in engineering. Compared with stainless steel connectors, FRP connectors (especially glass fiber-reinforced polymer, GFRP) feature extremely low thermal conductivity—approximately 1/150 that of steel and 1/30 that of concrete, excellent durability under extreme environments, high strength-to-weight ratio, and efficient construction. These advantages effectively prevent the formation of thermal bridges in the wall [2]. significantly enhance the wall’s thermal efficiency, and improve the wall’s structural safety throughout its lifecycle, demonstrating great potential for widespread application [3,4]. FRP connectors can be categorized into three main types: plate-shaped, rod-shaped, and truss-shaped connectors, illustrated in Figure 2. These connectors have been extensively used in countries such as the United States, Canada, and Australia [5]. In China, over 10 million GFRP connectors have been installed in more than 2 million square meters of PCSP projects [6].

In addition, the corrosion and degradation of connectors are difficult to detect at an early stage [7,8]. Once the connectors are deteriorated and their load-bearing capacity is reduced, interlayer slip and shear failure between the inner/outer concrete wythes and the insulation board are highly likely to occur. Therefore, the shear behavior of GFRP connectors exposed to alkaline environments deserves attention [9,10,11,12].

Current research on the durability of GFRP materials mainly focuses on the mechanical properties and long-term behavior of GFRP bars. Except for our research group, there is a lack of experimental studies specifically addressing the durability of GFRP connectors. Durability behavior is commonly evaluated via accelerated aging tests that simulate the in-service environment of the target material. In 2005, Abbasi A et al. [13] employed a 1 mol/L NaOH solution to simulate the alkaline environment of concrete. In 2006, Chen et al. [14] simulated concrete solutions with pH values of 12.7 and 13.6 by adding different proportions of NaOH, KOH, and Ca(OH)₂. While numerous durability studies have been carried out, no consensus has been reached on the optimal simulation of the concrete pore solution. Many researchers adopt the simulated alkaline solution specified in ACI 440.3R-12 [15] (comprising 0.9 g/L NaOH, 4.2 g/L KOH, and 118.5 g/L Ca(OH)₂), and numerous experimental studies have been performed based on this solution. Al Rifai M et al. [16] immersed basalt fiber-reinforced polymer (BFRP) bars in this simulated alkaline solution to investigate their durability under different temperatures and exposure durations. The results showed that after 3000 h of exposure at 60 °C, the tensile strength decreased by 30–40% and the elastic modulus reduced by 15–20%. Ceroni F [17] immersed GFRP bars in alkaline solutions with a pH ranging from 12.5 to 13 at 60 °C for 2 to 3 months, and found that the tensile strength of specimens decreased by 55.6% to 72.6%. Zhang et al. [18] investigated the durability of glass fiber reinforced thermoplastic self-anchor plate cables in alkaline solution environments, and the results showed that alkaline erosion would cause the degradation of the interfacial bonding performance of thermoplastic GFRP composites, leading to the reduction in mechanical properties such as tensile and shear strength. Yu et al. [19] carried out comparative research on the durability of carbon-glass hybrid fiber reinforced polymer (HFRP) bars and pure GFRP bars in water and alkaline solutions, and found that the carbon fiber coating could effectively inhibit the reaction between alkali ions and internal glass fibers, significantly improving the interlaminar shear strength retention of HFRP bars in alkaline environments, but it would accelerate the water diffusion process of the material and reduce its durability in water environments.

In 2006, The ICC Evaluation Service (ICC-ES) AC320 [20], which remains the only specification providing durability requirements for GFRP connectors. AC 320-06 stipulates that the residual tensile strength retention rates of GFRP connectors should be 85% and 90% after 1000 h (41.67 days) and 3000 h (125 days) of immersion in a pH 12 solution at 23 °C, respectively. Moreover, the composition and pH value of the simulated alkaline solution differ from those recommended in ACI 440.3R-12. In addition, the aging test is not accelerated by elevated temperature, and the exposure durations is extremely short compared with the design service life of structures (at least 50 years), making it difficult to predict the long-term behavior of GFRP connectors over their design life. Notably, the research results presented in this paper provide technical support for the Chinese industry standard Fiber-Reinforced Polymer Connectors for Precast Sandwich Insulated Wall [21], which specifies that the residual interlaminar shear strength should be at least 50% of the initial value after 183 days of alkaline exposure at (60 ± 3) °C.

Based on accelerated aging tests, diffusion models derived from Fick’s laws have been increasingly applied to predict the strength retention of FRP bars [22,23]. Fick’s law relates ion concentration to the diffusion coefficient and diffusion time through hygroscopic behavior, providing a method to model durability behavior.

Based on the literature review, the following conclusions can be drawn.

(1)

GFRP connectors are key components of PCSP. Durability and mechanical properties directly determine the overall service life of the walls. It is necessary to investigate the behavior of GFRP connectors.

(2)

Most studies have focused on the durability and mechanical properties of GFRP bars, and the relevant research has been well established; however, research on the long-term durability of GFRP connectors in alkaline environments remains almost absent.

(3)

AC320-06 specifies that GFRP connectors are exposed to a solution at 23 °C and pH 12 for 1000 h (41.67 days) and 3000 h (125 days). These exposure durations are too short compared with the minimum 50-year design service life of structures, making it difficult to predict the long-term behavior of GFRP connectors over the design life. In addition, neither ACI 440.3R-12 nor AC320-06 specifies the interlaminar shear strength retention rate of GFRP connectors. Hence, it is necessary to investigate this retention rate, so as to enrich the experimental database and lay a foundation for formulating new standards.

On this basis, accelerated aging tests were performed on GFRP connectors in accordance with ACI 440.3R-12, with a primary focus on their shear strength under varied temperatures (40 °C, 60 °C, 80 °C) and exposure durations (3.65 d, 18 d, 36.5 d, 92 d, 183 d). Morphological changes of the GFRP connectors were observed at both macroscopic and microscopic scales, and the degradation mechanism of GFRP was investigated from a microscopic perspective. In addition, based on the measured hygroscopic properties of GFRP connectors, a durability prediction model for their shear strength was established according to Fick’s law.

2. Experimental Program

2.1. Specimen Parameters

The GFRP connectors used in this study were manufactured by Nanjing Spare Composite Materials Co., Ltd. (Nanjing, China) using the pultrusion process. These connectors consist of E-glass fibers embedded in a vinyl ester resin matrix, with a fiber content of 75.0% by weight. The TM-glass fiber, which was provided by Chongqing Polycomp International Corp. (Chongqing, China), is a kind of free-boron glass fiber. Compared to conventional E-glass fiber, TM-glass fiber has higher tensile strength, tensile modulus alkaline resistance and acid resistance [24]. The accelerated aging tests were conducted in a custom-built constant- temperature solution tank, with the exposure temperatures maintained at 40 °C, 60 °C, and 80 °C. The designated exposure durations were 3.65, 18, 36.5, 92, and 183 days. It is noted that exposure at 60 °C corresponds to approximately 1, 5, 10, 25, and 50 years of service in a natural environment, respectively [25,26]. For each combination of temperature and exposure duration, five replicate specimens were tested, resulting in a total of 90 specimens. The key parameters of the test specimens are summarized in

Table 1. Specimen parameters.

Temperature/°C	Exposure Time/Day	Number of Specimens	Total Number of Specimens
40/60/80	0	5	90
	3.65	5
	18	5
	36.5	5
	92	5
	183	5

.

2.2. Testing Methods

The alkaline exposure solution was prepared in accordance with ACI 440.3R-04 specifications to simulate the concrete pore environment. The solution, with a pH maintained between 12.6 and 13.0, contained 118.5 g/L of Ca(OH)₂, 4.2 g/L of KOH, and 0.9 g/L of NaOH. The pH was monitored and adjusted periodically throughout the testing period to ensure a constant hydroxyl ion concentration.

The interlaminar shear strength of GFRP connectors was determined via the three-point bending short-beam method in compliance with ASTM D2344 [27], with the loading process sustained for 2~4 min, as illustrated in Figure 3. The ILSS tests were conducted on a hydraulic universal testing machine manufactured by Shanghai Testing Machine Works Co., Ltd. (Shanghai, China).

Hygroscopic properties tests of GFRP connectors were carried out following the relevant provisions of ACI 440.3R and ASTM D5229 [28]. The moisture absorption properties of GFRP connectors were investigated by measuring the mass changes of the connectors before and after corrosion, to derive the variation law of moisture absorption properties with time. Before the tests, the connectors were thoroughly dried in an oven until a constant mass was achieved. After the tests, the surface of the GFRP connectors was blotted dry with filter paper, and their mass was immediately measured using an analytical balance with an accuracy of 0.001 g.

The internal morphologies of GFRP connectors before and after corrosion were observed using an XL-30 scanning electron microscope (SEM) manufactured by Philips (Eindhoven, The Netherlands), so as to explore the degradation mechanism of GFRP connectors from a microscopic perspective.

3. Results and Discussion

3.1. Observation and Image Analysis

3.1.1. Surface Condition

Based on the experimental observations, the surface degradation of GFRP connectors was significantly less pronounced at 40 °C and 60 °C compared to that at 80 °C. To better illustrate the surface deterioration, Figure 4 presents the visual appearance of GFRP connectors before exposure and after exposure durations of 3.65, 18, 36.5, 92, and 183 days at 80 °C [6]. The surface characteristics, including cracking, glossiness, blistering, and transparency, were visually inspected for each specimen according to the standard “Fiber-Reinforced Plastics—General Guidance for Testing” (GB/T 1446-2005) [29]. The key observations are as follows.

(1)

Before exposure, the GFRP connectors exhibited a smooth surface. With increasing exposure duration, resin dissolution became apparent, and the initially uniform resin distribution turned increasingly non-uniform. This phenomenon was more severe at higher temperatures.

(2)

After 36.5 days of exposure in the alkaline solution, the specimens showed a noticeable reduction in surface gloss. Their color changed from initially semi-transparent white to an opaque, milky white with a slight yellowish tint. Surface blistering was also observed at this stage.

(3)

After 183 days of exposure at 80 °C, the GFRP connectors suffered complete macroscopic failure, the overall structure of the connectors was loose and brittle, with severe peeling and shedding of the surface resin matrix, and the internal glass fiber bundles were exposed and even broken into loose filamentous structures; the connectors lost their original structural integrity and mechanical bearing capacity, and could not maintain the basic rod/plate shape, showing brittle fracture and interfacial debonding mixed failure mode—the resin matrix was completely hydrolyzed and cracked, the fiber-matrix interface was completely debonded, and the glass fiber bundles were corroded and fractured due to chemical reaction, leading to the overall collapse of the material structure. It was impossible to obtain complete and valid samples from the failed connectors for SEM microscopic observation.

3.1.2. Microstructural Analysis

Scanning Electron Microscopy (SEM) was employed to examine microstructural changes in the internal architecture of GFRP connectors before and after exposure. Figure 5 illustrates the cross-sectional morphology of the connectors prior to exposure and following immersion in alkaline solutions at 40 °C, 60 °C, and 80 °C for durations of 3.65, 18, 36.5, 92, and 183 days. The key observations are summarized as follows.

(1)

The unexposed GFRP connectors exhibited a dense internal structure with well-rounded fibers and a tight fiber-matrix interface. After exposure, the extent of degradation progressively increased with both longer exposure times and higher temperatures.

(2)

Following alkaline exposure, a tendency for interface debonding between the fibers and the resin matrix was observed. The condition of this interface varied significantly with temperature and exposure duration. For instance, after 18 days at 60 °C, the fiber-matrix interface remained relatively tight without significant debonding. In contrast, specimens exposed to the 80 °C solution displayed pronounced debonding. After 183 days at 60 °C, severe interface debonding was evident within the degraded regions of the connectors. For specimens subjected to the 80 °C, the solutions were completely damaging by this stage, precluding the extraction of viable samples for SEM observation.

(3)

With increasing temperature and exposure durations, micro-cracks initiated and propagated within the resin matrix. The number and width of these cracks increased over time. This phenomenon is attributed to the hydrolysis reaction between the resin and water molecules, leading to a progressive loss of adhesion between the resin and the fibers. Concurrently, the glass fibers underwent a chemical reaction with hydroxyl ions (OH⁻) in the alkaline solution, resulting in the breakdown of Si-O bonds. These combined mechanisms ultimately led to the deterioration of the mechanical properties of the GFRP connectors.

3.2. Hygroscopic Properties

The hygroscopic process of GFRP connectors is accompanied by complex physical and chemical changes, including plasticization and hydrolysis of the resin matrix, as well as degradation of the fiber-matrix interface. These changes are the primary causes of behavior degradation in GFRP connectors. Hygroscopic behavior reflects the diffusion regime of ions within GFRP connectors; measuring such behavior enables the revelation of the aging mechanism and the establishment of strength degradation models for GFRP connectors in alkaline environments.

Hygroscopic properties are generally characterized by the mass change of GFRP connectors before and after exposure.

Table 2. GFRP connector weight variation/g.

Temperature /°C	Exposure Time/Day
	0	3.65	18	36.5	92	183
40	27.557	27.579	27.596	27.603	27.608	27.609
60	27.448	27.581	27.670	27.709	27.728	27.730
80	27.398	28.203	28.747	29.022	29.069	29.164

presents the mass variations of GFRP connectors in alkaline solutions, and Figure 6 shows the evolution of the hygroscopic rate as a function of the square root of time at different temperatures.

(1)

At the initial corrosion stage, the hygroscopic curve of GFRP connectors increased approximately linearly. With corrosion time, the curve gradually flattened and approached equilibrium. This suggests that the physical diffusion of corrosive ions within GFRP connectors follows Fick’s law.

(2)

For relatively short exposure durations (≤36.5 d), the hygroscopic rate of GFRP connectors was approximately proportional to the square root of time, and the hygroscopic kinetic curve exhibited an approximately linear behavior. After 36.5 d of corrosion, the rate of increase in hygroscopic rate gradually slowed and stabilized. This was mainly caused by the reaction between OH⁻ ions and fibers during diffusion, which produced new products and blocked the internal diffusion pathways of OH⁻ ions, eventually leading to hygroscopic equilibrium.

(3)

Temperature had a significant effect on the hygroscopic behavior of GFRP connectors. After 183 days of exposure in alkaline solutions at 40 °C, 60 °C, and 80 °C, the hygroscopic rates of GFRP connectors were 0.19%, 1.03%, and 6.45%, respectively. This was primarily because higher solution temperature accelerated the formation of internal pores and debonding at the fiber–matrix interface, creating interfacial voids that enhanced the hygroscopic capacity of GFRP connectors and thus increased the hygroscopic rate.

3.3. Shear Strength

The shear strength of GFRP connectors was evaluated using the three-point bending short-beam shear test. Under increasing load, the deformation of the connectors in the loading direction progressively increased. Upon reaching the ultimate load, failure occurred abruptly, accompanied by a distinct audible sound and visible delamination, resulting in a rapid loss of load-bearing capacity. Figure 7 presents the variations in shear strength before and after exposure.

The following observations are drawn from Figure 7.

(1)

The shear strength of GFRP connectors decreased with prolonged exposure time. After exposure to the alkaline solution at 60 °C for 3.65, 18, 36.5, 92, and 183 days (corresponding to approximately 1, 5, 10, 25, and 50 years in a natural environment, respectively), the shear strength decreased by 10.12%, 16.14%, 17.22%, 20.80% and 26.89%, respectively. Following exposure to the 40 °C alkaline solution, the reductions were 8.62%, 9.26%, 11.84%, 15.05%, and 21.30%, respectively. Under the 80 °C alkaline environment, exposure for 3.65, 18, 36.5, and 92 days led to reductions of 10.77%, 24.02% 29.04%, and 33.55%, respectively. Specimens exposed for 183 days at 80 °C experienced complete failure. These results indicate a continuous decline in shear strength with extended exposure duration, primarily due to progressive degradation within the simulated concrete pore solution. Notably, the degradation rate was more pronounced during the initial exposure period (up to 18 days for 40 °C and 60 °C, and up to 36.5 days for 80 °C) and gradually decelerated thereafter.

(2)

Elevated temperatures significantly accelerated the degradation of the shear strength. Compared to the strength reduction observed at 40 °C, the additional reductions (refer to the increased percentage of the shear strength reduction in GFRP connectors at a certain temperature compared with that at 40 °C for the same exposure durations) at 60 °C after 3.65, 18, 36.5, 92, and 183 days were 1.49%, 6.89%, 5.40%, 5.75%, and 5.59%, respectively. At 80 °C, the additional reductions after 3.65, 18, 36.5, and 92 days were 2.15%, 14.76%, 17.21%, and 23.86%, respectively. The vinyl ester resin in GFRP rapidly absorbs moisture in hygrothermal environments. Initially, a significant moisture gradient between the surface and the interior leads to a high diffusion rate, causing swift resin matrix swelling and plasticization. The aged specimens exhibited continuous micro-crack propagation and minor apparent deformation before reaching the peak load, which originated from surface resin cracking, shrinkage and local interface debonding; After the peak load, the bearing capacity decreased rapidly. Furthermore, higher temperatures accelerate the corrosive action of the medium, enhancing the mobility of OH⁻ ions within the GFRP connectors.

(3)

After exposure at 60 °C for 183 days (equivalent to approximately 50 years in a natural environment), the shear strength decreased by 26.89%, respectively. Accordingly, environmental influence factors of 1.4 are recommended for 50-year service life predictions, respectively, to incorporate an appropriate safety margin.

4. Deterioration Mechanism and Degradation Model

4.1. Deterioration Mechanism

In alkaline environments, the degradation of GFRP connectors involves both resin hydrolysis and fiber corrosion, with the latter being the dominant mechanism [22]. On one hand, the vinyl ester resin matrix undergoes hydrolysis upon contact with water molecules, leading to microcrack formation within the resin. The hydrolysis reaction is represented by Equation (1). Once surface cracks develop, water molecules from the alkaline solution penetrate deeper into the resin, continuously eroding the internal structure. This process induces progressive debonding at the fiber-matrix interface, thereby compromising stress transfer efficiency.

$$\mathrm{R}\mathrm{-COO-}{\mathrm{R}}^{\prime }+\mathrm{HO-}\mathrm{H}\to \mathrm{R}\mathrm{-COOH}+{\mathrm{R}}^{\prime }\text{-}\mathrm{C}\mathrm{-OH}$$

(1)

On the other hand, the primary component of glass fibers, SiO₂, chemically reacts with hydroxyl ions (OH⁻) in the alkaline solution, as shown in Equation (2).

$$2{\mathrm{OH}}^{-}+\mathrm{Si}{\mathrm{O}}_2\to {\mathrm{SiO}}_3^{2-}+{\mathrm{H}}_2\mathrm{O}$$

(2)

During this corrosion process, the aggressive medium diffuses and penetrates the material, while certain components within the fibers migrate outward and eventually dissolve into the medium. This results in continuous dissolution and corrosion of the fibers.

By comparing SEM micrographs of GFRP connectors after various exposure durations, changes in fiber content over time can be assessed. Figure 8 presents SEM images (3000× magnification) of GFRP connectors after 18 days and 92 days of exposure in a 60 °C alkaline solution, serving as an example.

As shown in Figure 8, after 18 days of exposure at 60 °C, initial debonding between the fibers and the surrounding resin is observed. At this stage, sporadic voids appear in the cross-section, and the fiber surfaces show signs of corrosion. After 183 days of exposure, pronounced debonding is evident between the fibers and resin, accompanied by numerous microcracks within the resin matrix. The cross-section exhibits increased void density, reduced compactness, and noticeably reduced fiber cross-sectional areas.

4.2. Degradation Model

In 1855, the renowned scholar Fick proposed Fick’s laws of diffusion, which state that the rate of change of ion concentration with respect to time is equal to the negative gradient of the diffusion flux (the rate of change of ion concentration with time is proportional to the negative second gradient of the concentration distribution). Fick’s laws establish a relationship between ion concentration, diffusion coefficient, and diffusion time, thereby providing a quantitative framework for evaluating material durability. This relationship is expressed by Equation (3) [30]. In this model, it is assumed that the OH⁻ ion concentration on the surface of GFRP connectors remains constant, because the simulated concrete pore solution used in the experiment is a constant volume and constant temperature system, and the pH value is regularly monitored and adjusted to maintain the stability of OH⁻ ion concentration.

$${\displaystyle \frac{𝜕C}{𝜕t}}=D{\displaystyle \frac{{𝜕}^{2}C}{𝜕x^2}}$$

(3)

where C represents the concentration of the alkaline solution (mol/L); D represents the diffusion coefficient (mm²/s); x represents the depth of alkali erosion (mm); t represents the diffusion time (s).

In the durability testing of GFRP connectors in alkaline environments, the primary source of OH⁻ ions is the dissociation of NaOH, KOH, and Ca(OH)₂ present in the alkaline solution. Furthermore, as illustrated by the hygroscopic properties of GFRP connectors under alkaline exposure (Figure 7), the diffusion of OH⁻ ions in FRP materials conforms to Fick’s laws. The diffusion of OH⁻ ions in FRP materials can be described by Equation (4).

$${\displaystyle \frac{𝜕C_{\mathrm{OH}}}{𝜕t}}={\displaystyle \frac{𝜕}{𝜕x}}(D_{\mathrm{OH}}{\displaystyle \frac{𝜕C_{\mathrm{OH}}}{𝜕x}})$$

(4)

where C_OH represents the concentration of the alkaline solution (mol/L); D_OH represents the diffusion coefficient (mm²/s).

Assuming the OH⁻ ion concentration at the surface of the FRP material is Cs, and the initial OH⁻ ion concentration at a depth x from the surface is C₀, the corresponding initial and boundary conditions can be expressed as:

$$\left\{\begin{array}{l}{C}_{OH}(x,t=0)=C_0\\ C_{OH}(x=0,t)=C_s\end{array}\right.$$

(5)

Based on the initial and boundary conditions, the solution to Equation (4) is obtained as:

$$C_{\mathrm{x},\mathrm{t}}=C_{\mathrm{s}}[1-erf({\displaystyle \frac{x}{\sqrt{4D_{\mathrm{OH}}t}}})]$$

(6)

where C_x,t represents the OH⁻ ion concentration at the maximum depth x at time t, and erf(z) represents the Gaussian error function, the values of which can be calculated using Equation (7).

$$erf(z)={\displaystyle \frac{2}{\sqrt{\pi }}}{\displaystyle {\int }_0^x\exp (-z^2)dz}$$

(7)

By rearranging Equation (7), the expression for the corrosion depth x at time t can be derived as shown in Equation (8).

$$x={erf}^{-1}(1-{\displaystyle \frac{C_{\mathrm{x},\mathrm{t}}}{C_{\mathrm{s}}}})\sqrt{4D_{\mathrm{OH}}t}$$

(8)

where C_s represents the concentration of the alkaline solution (mol/L); C_x,t represents the OH⁻ ion concentration at the maximum depth x at time t.

4.2.1. Critical Concentration (C_x,t)

Analysis of the microstructural morphology of GFRP connectors before and after exposure reveals that the degradation of FRP materials in alkaline solutions primarily initiates at the geometric edges and surface corners of the GFRP connectors and progressively propagates inward with prolonged exposure time. This observation indicates that the degradation caused by OH⁻ ions is closely related to their diffusion path within the material. Specifically, when the penetration depth of OH⁻ ions along the radial direction reaches x, a Cartesian coordinate system (X, Y, Z) is established with the thickness center line as the Z-axis, and the radial direction is the Z direction (perpendicular from the thickness center line to the plate surface). And the local OH⁻ ion concentration attains the threshold concentration C_x,t required for the chemical reaction with glass fibers, significant fiber corrosion occurs. This critical concentration can be determined based on the chemical reaction equation [31].

The chemical reaction between OH⁻ ions in the alkaline solution and the glass fibers essentially involves the interaction between hydroxyl ions and SiO₂, the primary component of glass fibers. The reaction is expressed as Equation (2).

The equilibrium constant K_c of a chemical reaction, which depends solely on temperature, is defined as the ratio of the product of the concentrations of the products (each raised to the power of its stoichiometric coefficient) to the product of the concentrations of the reactants (each raised to the power of its stoichiometric coefficient) when the reaction reaches equilibrium [32]. Thus, the equilibrium constant K_c for the reaction between OH⁻ ions and SiO₂ can be expressed as:

$$K_c={\displaystyle \frac{\left[si{o}_3^{2-}\right]}{{\left[{OH}^{-}\right]}^2}}$$

(9)

That is:

$$K_c={\displaystyle \frac{\left[{\mathrm{C}}_{x,t}\right]/2}{{\left[0.1\text{-}{\mathrm{C}}_{x,t}\right]}^2}}$$

(10)

From Equation (10), the following relationship can be obtained.

$$C_{x,t}={\displaystyle \frac{0.4K_c-\sqrt{0.8K_c+1}+1}{4K_c}}$$

(11)

where C_x,t represents the OH⁻ ion concentration at the maximum depth x at time t, for GFRP connectors in alkaline environments, this value is determined to be 2.98 × 10⁻⁴ mol/L; K_c represents the equilibrium constant of a chemical reaction. K_c is a constant value at a given temperature. When T ≤ 80 °C, K_c exhibits negligible variation and may be reasonably approximated as K_c = 0.015.

4.2.2. Diffusion Coefficient (D)

The diffusion coefficient D is defined as the amount of a substance passing through a unit area per unit time along the diffusion direction. A higher diffusion coefficient indicates a shorter time required for the corrosive medium to penetrate to a specific depth within the material. For FRP materials, the diffusion coefficient D can be calculated using the following expression [33,34].

$$D={\displaystyle \frac{\pi h^2}{16M_m^2}}{\left({\displaystyle \frac{M_{t2}-M_{t1}}{\sqrt{t_2}-\sqrt{t_1}}}\right)}^2$$

(12)

where M_m represents the equilibrium hygroscopic moisture content of the specimen (%); M_t1 represents the hygroscopic moisture content at time t₁; M_t2 represents the hygroscopic moisture content at time t₂; h represents the thickness of the GFRP connectors.

Figure 9 illustrates the relationship between the diffusion coefficient of OH⁻ ions in GFRP connectors and both time and environmental temperature, after exposure to alkaline environments at 40 °C, 60 °C, and 80 °C for durations of 3.65, 18, 36.5, 92, and 183 days. The diffusion coefficient of OH⁻ ions in GFRP connectors decreases with time but increases with rising environmental temperature. Therefore, when calculating the long-term diffusion coefficient of OH⁻ ions in GFRP connectors under alkaline environments, it is essential to account for its variations with both time and environmental temperature.

The temporal evolution of the diffusion coefficient was obtained by fitting the data presented in Figure 9, yielding the following relationship.

As summarized in

Table 3. The variation law of the diffusion coefficient with time.

Temperature	Calculation Formula
40 °C	$D_{OH}=D_T{t}^{-m}=5.28\times {10}^{-4}{t}^{-0.72}$
60 °C	$D_{OH}=D_T{t}^{-m}=6.86\times {10}^{-4}{t}^{-0.72}$
80 °C	$D_{OH}=D_T{t}^{-m}=7.51\times {10}^{-4}{t}^{-0.72}$

, the mathematical expressions for the diffusion coefficient of GFRP connectors at different temperatures are as follows.

$$D_t=D_T{t}^{-0.72}$$

(13)

$$D_T=0.0117\exp (-{\displaystyle \frac{971}{T}})$$

(14)

where D_t represents the diffusion coefficient considering time dependence (mm²/s); D_T represents the diffusion coefficient at an absolute temperature environment of T (mm²/s); T represents the absolute temperature environment (K); t represents the diffusion time (s).

Thus, the diffusion coefficients of OH⁻ ions in GFRP connectors under alkaline environments at 40 °C, 60 °C, and 80 °C can be, respectively, determined as:

$$D_{OH}=0.0117\exp (-{\displaystyle \frac{971}{T}})t^{-0.72}$$

(15)

where D_OH represents the diffusion coefficient of OH⁻ ions in GFRP connectors

Substituting Equation (15) into Equation (8) yields the progression of corrosion depth as a function of the diffusion coefficient, expressed as:

$$x={erf}^{-1}(1-{\displaystyle \frac{C_{\mathrm{x},\mathrm{t}}}{C_{\mathrm{s}}}})\sqrt{0.047\exp (-{\displaystyle \frac{971}{T}})t^{0.28}}$$

(16)

4.2.3. Degradation Model

Assuming the fibers in the FRP material are aligned parallel in the longitudinal direction with uniform length. They are homogeneously distributed within the resin matrix; the fiber volume fraction can be equivalently expressed as the fiber area fraction in the cross-section of the FRP material. Denoting the initial fiber volume fraction as V_f and the fiber volume fraction after exposure as V_fx, the relationship between corrosion depth and fiber content can be expressed as Equation (17).

$${\displaystyle \frac{{(h-x)}^2}{h^2}}={\displaystyle \frac{V_{fx}}{V_f}}={\displaystyle \frac{f_x}{f_0}}$$

(17)

where f_x is the residual tensile strength of the GFRP connector after erosion; f₀ is the tensile strength of the GFRP connector before erosion.

Similarly, substituting Equation (16) into Equation (17) yields the strength degradation model for GFRP connectors in alkaline environments.

$$f_x=f_0(1-{\displaystyle \frac{{erf}^{-1}(1-\frac{C_{\mathrm{x},\mathrm{t}}}{C_{\mathrm{s}}})\sqrt{0.047\exp (-\frac{971}{T})t^{0.28}}}{h}}{)}^2$$

(18)

In reference [35], the influence of stress levels on the mechanical behavior of GFRP connectors in alkaline environments was investigated. The study demonstrated that the effect of stress levels (s) can be characterized by introducing a stress acceleration factor.

$${\tau }_s=\exp (0.34s)$$

(19)

where τ_s is stress acceleration factor; s represents the ratio of the actual stress to the ultimate stress.

In summary, the mechanical behavior degradation model for FRP materials in alkaline environments, based on Fick’s law, is formulated as:

$$f_{\mathrm{x}}=f_0(1-{\displaystyle \frac{{erf}^{-1}(1-\frac{C_{x,t}}{C_s})\sqrt{0.047\exp (-\frac{971}{T})\exp (0.34s)t^{0.28}}}{r}}{)}^2$$

(20)

Aside from the experimental work presented in this study, no other accelerated aging tests on the shear strength of GFRP connectors were identified in the literature [36]. Therefore, the experimental results were compared with theoretical values calculated using the proposed degradation model.

Table 4. Comparison of test values and calculated values of residual shear strength of GFRP connectors based on Fick’s law.

Temperature	Time	Test Value (ft)/MPa	Calculated Value (fc)/MPa	ft/fc
40 °C	3.65 d	53.12	54.24	0.98
	18 d	52.75	52.70	1.00
	36.5 d	51.25	51.83	0.99
	92 d	49.38	50.48	0.98
	183 d	45.75	49.29	0.93
60 °C	3.65 d	52.25	53.61	0.97
	18 d	48.75	51.81	0.94
	36.5 d	48.12	50.80	0.95
	92 d	46.04	49.23	0.94
	183 d	42.50	47.85	0.89
80 °C	3.65 d	51.87	52.97	0.98
	18 d	44.17	50.91	0.87
	36.5 d	41.25	49.76	0.83
	92 d	38.63	47.96	0.81
Average value	0.93
Standard deviation	0.06

presents a comparison between the model-predicted values and the experimentally measured residual shear strength of GFRP connectors in alkaline environments, and a comparison chart as shown in Figure 10. The theoretically calculated values are generally slightly higher than the residual shear strength measured in the experiments. The deviation increases gradually with the rise in temperature and the extension of exposure time. This is mainly because, in an alkaline environment at 80 °C, the resin matrix undergoes hydrolysis and degradation, and the interface area develops microcracks due to alkali corrosion. These processes accelerate the attenuation of strength. However, the model fails to fully capture these coupled effects, resulting in calculated values that overestimate the long-term residual strength. The average ratio of experimental to theoretical values is 0.93, with a standard deviation of 0.06. Overall, the theoretically calculated values show good agreement with the experimental results, indicating that Equation (20) effectively predicts the time-dependent shear strength of GFRP connectors under varying temperatures in alkaline environments.

5. Discussion on Durability Behavior in AC 320 and ACI 440.3R-12

AC 320-06 specifies that the tensile strength retention rates of GFRP connectors shall be 85% and 90% after exposure in a solution at 23 °C and pH = 12 for 1000 h (41.67 days) and 3000 h (125 days), respectively.

From the perspective of temperature, the standard specifies a test temperature of 23 °C, without considering the accelerating effect of temperature on the aging rate of GFRP connectors. In engineering, the temperature of PCSP fluctuates considerably, and the surface temperature can exceed 60 °C in summer. A high temperature accelerates the diffusion rate of OH⁻ ions in alkaline solutions, thus intensifying the hydrolysis of the resin matrix and the corrosion of fibers. From the perspective of pH, the standard specifies a test solution pH of 12, whereas the pore inside real concrete represents a strongly alkaline environment with a pH range of 12.6–13.5 (the pH of the test in this study was 12.6–13.0, consistent with the actual concrete environment). Differences in pH directly affect the concentration of OH⁻ ions and further alter the corrosion mechanism and degradation rate of GFRP connectors. From the perspective of exposure durations, the standard specifies exposure periods of 1000 h (41.67 days) and 3000 h (125 days), while the design service life of building structures is generally no less than 50 years, and some century-residence building projects impose even higher durability requirements. Short-term exposure cannot reflect the long-term behavior degradation of GFRP connectors over a service life of 50 years or more. In addition, due to the lack of experimental data at 23 °C for 125 days, the degradation rate of the interlaminar shear strength of GFRP connectors was calculated as 16.33% using the proposed prediction model (Equation (20)). On this basis, this study recommends a conservative environmental impact factor of 1.4 for the interlaminar shear strength of GFRP connectors.

ACI 440.3R-12 specifies the test procedure for accelerated aging of GFRP bars in alkaline solutions. It indicates that their strength exhibits an aging pattern of “rapid initial degradation followed by a gradual slowdown”. It also states that the acceleration factor for alkaline aging of GFRP materials is approximately 3 to 5 times for every 20 °C increase in temperature. The degradation trend of the interlaminar shear strength of GFRP connectors in this study is highly consistent with this pattern, which aligns with the inherent anisotropic properties of GFRP materials. Notably, ACI 440.3R-12 does not specify a concrete limit for the strength retention rate of GFRP connectors, nor does it define the environmental impact factor for long-term service. Based on the test method specified in this code and considering the test results at 60 °C for 183 days (equivalent to approximately 50 years in a natural environment), this study proposes an environmental impact factor of 1.4 for the interlaminar shear strength of GFRP connectors. This not only fills the gap in the ACI code regarding the durability study of GFRP connectors but also verifies the engineering safety of the results obtained in this research.

In summary, as an early durability evaluation standard for GFRP connectors, AC 320-06 presents obvious limitations in the setting of test conditions and the coverage of behavior indicators. ACI 440.3R-12 does not specify specific strength retention rate limits for GFRP connectors. It is recommended that the standard be supplemented and improved by considering the temperature, pH value, and design service life of actual service environments, and by referring to the environmental impact factor proposed in this study (conservatively taken as 1.4) and the relevant test methods, to enhance the engineering applicability and safety of the standard.

Notably, the findings on the shear behavior of GFRP connectors in this study provide support for the Chinese industrial standard Fiber-Reinforced Polymer Connectors for Precast Sandwich Insulated Wall [21], which specifies that the residual interlaminar shear strength after exposure at 60 ± 3 °C for 183 days shall be no less than 50% of the initial value.

6. Conclusions

Based on the test method specified in ACI 440.3R-12, a total of 105 GFRP connectors were exposed in simulated concrete pore solutions at 40 °C, 60 °C, and 80 °C for exposure durations of 3.65 d, 18 d, 36.5 d, 92 d, and 183 d. The evolution of the interlaminar shear strength of GFRP connectors with temperature and exposure time was investigated, and the main conclusions are drawn as follows.

(1)

With increasing exposure time, the surface of the GFRP connectors exhibited blistering, a reduction in glossiness, and the development of cracks. Microscopically, significant debonding between fibers and the surrounding resin was observed in the degraded regions. This phenomenon became more pronounced with longer exposure durations and higher environmental temperatures.

(2)

The interlaminar shear strength of GFRP connectors decreased with increasing exposure time. After exposure to the alkaline solution at 60 °C for 3.65, 18, 36.5, 92, and 183 days (corresponding to approximately 1, 5, 10, 25, and 50 years in a natural environment, respectively), the strength decreased by 10.12%, 16.14%, 17.22%, 20.80%, and 26.89%, respectively. At 40 °C, the strength decreased by 8.62%, 9.26%, 11.84%, 15.05%, and 21.30% for the respective exposure durations. At 80 °C, exposure for 3.65, 18, 36.5, and 92 days resulted in strength reductions of 10.77%, 24.02%, 29.04%, and 33.55%, respectively. Specimens exposed for 183 days at 80 °C experienced complete failure.

(3)

After exposure at 60 °C for 183 (equivalent to approximately 50 years in a natural environment), the shear strength decreased by 26.89%. Based on these results, for a 50-year service life in natural environments, a conservative environmental impact factor of 1.4 is recommended for the interlaminar shear strength of GFRP connectors.

(4)

A predictive model for the time-dependent interlaminar shear strength of GFRP connectors under different temperature conditions was established based on Fick’s law. The model predictions show good agreement with the experimental results.