Influence of Long-Term Moisture Exposure and Temperature on the Mechanical Properties of Hybrid FRP Composite Specimens

Abstract

The present experimental study assesses the mechanical properties of glass/carbon/glass hybrid composite laminates after being exposed to moisture in a deep freezer and elevated temperatures for extended periods. The top and bottom layers of the hybrid laminates are reinforced with glass fibre, and the middle layer is reinforced with carbon fibre using the epoxy matrix as a binder polymer material. The hybrid laminates were manufactured using the resin transfer moulding method, and their compressive and tensile properties were determined using a tensile testing machine. The storage modulus, loss modulus, and damping factors of all groups of laminates were identified using a dynamic mechanical analysis as a function of temperature and vibration frequency. The experimental results on compressive and tensile properties revealed slight variations when the hybrid laminates were kept at low temperatures in a deep freezer for extended periods. This might occur due to the increasing molecular crosslinking of the polymer network. As the testing temperature increased, compressive, tensile, storage modules, loss modulus, and damping factors decreased. This might occur due to the increasing mobility of the binder material. Particularly, the highest stiffness parameters were obtained at −80 °C/GCG (glass/carbon/glass) laminates due to the presence of a beta transition in the glassy region. The relationships between the glass transitions and the targeted frequencies were characterized. The values of the glass transition shift towards higher temperatures as the frequency increases. This might occur due to a reduction in the gaps between the crosslinking of the epoxy network when the frequency increases. The accuracy of the storage modulus results was compared with the empirical models. The model based on the Arrhenius law provided the closest correlation. Meanwhile, another model was observed that was not accurate enough to predict when gamma and beta relaxations occur in a glassy state.

1. Introduction

Recently, carbon fibre, glass fibre, and hybrids of the two composite materials have been used in several engineering fields, including aerospace, automotive, marine, and civil engineering applications. Mainly, a fibre-reinforced polymer (FRP) composite is a candidate material in the structural design of wind turbine blade components owing to their high strength and stiffness-to-weight ratios, as well as their excellent corrosion resistance and lower density compared to traditional materials, as noted in several studies [1,2,3,4,5]. Particularly, carbon fibre has a lower density as well as stronger and stiffer mechanical properties as compared to glass fibre [6]. Applications of carbon fibre-reinforced polymer (CFRP) material in racing cars, aerospace structures, and wind turbine blades can reduce their weight, increase strength, and optimize energy efficiency [7,8]. Despite the advantages of carbon fibres, their lower strain and damping properties, as well as their higher costs, make them challenging to use in these applications [9]. Reducing the cost and obtaining optimum mechanical properties of composite structures are critical considerations in the composite industry. One approach to achieving tailored material properties is a hybridization of carbon and glass fibres, which has the potential to reduce the cost and improve the mechanical performance of the composite structures, as noted in [10,11,12]. The demand for FRP composite material in engineering applications has been increasing. In contrast, the composite structures in their design lifetime might be exposed to lower and higher environmental conditions that affect both the immediate and the long-term performance. There are concerns about the durability of FRP composite structures exposed to lower and higher environmental conductions during their operational lifetime, as discussed in [13,14,15]. Knowing the mechanical performance of fibre-reinforced polymer materials under lower and higher environmental conditions is important [16].

Several studies investigated the mechanical performance of FRP materials subject to lower and higher environmental conditions. For example, the mechanical performance of FRP materials exposed to higher environmental conditions was examined by Bazli and Abolfazli [17], which involved near and above the glass transition temperatures of the epoxy matrix. Lower levels of degradation were observed below the glass transition temperature of the epoxy matrix. Higher values of glass transition temperature have a detrimental effect on the mechanical performance of FRP composites. The polymer matrix softens and weakens the bonding at the fibre/matrix interface when the temperature exceeds the glass transition temperature, resulting in the rapid reduction in strength, as noted in [18,19]. Cao et al. [20] conducted an experimental study on the tensile properties of pure carbon/epoxy and hybrid carbon fibre combined with glass and basalt fibre sheets at elevated temperatures. The tensile performance of the pure and hybrid sheets was significantly reduced as the temperature increased. Additionally, the tensile, compressive, flexural moduli, and energy absorption properties of carbon fibre-reinforced polymer (CFRP) materials under low and high temperatures were investigated in several studies, as noted in [21,22,23,24,25,26,27]. The compressive and tensile strengths of CFRP laminates severely deteriorated at high temperatures. Meanwhile, the flexural and energy absorption properties were improved at the lower temperatures. Similarly, Hawileh et al. [28] studied the tensile and stiffness properties of carbon laminates, glass laminates, and the hybrids of the two fibres exposed to ambient and elevated temperatures. Severe reductions in the mechanical performance of the laminates were observed in the case of pure laminates rather than hybrid laminates.

Long-term effects of moisture absorption on the mechanical performance of CFRP, glass fibre-reinforced polymer (GFRP), and a hybrid of the two fibre materials have been investigated in [29,30,31]. The results confirmed that the performance of the laminates was not significantly affected at the lower temperatures. This might be due to the effect of moisture on making them closely packed epoxy chain segments and the transition of the polymer material into beta and delta relaxation phases in the glassy state, as investigated in [32,33]. Long-term moisture absorption affected the growth of residual stresses in the FRP composite laminates, leading to changes in their mechanical performance and failure properties [34].

Spagnuolo et al. [35] studied the tensile properties of GFRP bars under elevated temperatures to replace them with ordinary steel reinforcement materials. It is an effective and economical solution to corrosion problems and durability. Additionally, Mathiev and Brahim [36] conducted an experimental study on the flexural, shear, and tensile strength properties of GFRP bars exposed to lower and elevated temperatures. The experimental results confirmed that the flexural, shear, and tensile strengths of GFRP bars increased when the temperature decreased. A change in mechanical performance was observed when a high level of moisture absorption caused the volume expansion of GFRP bars, which aggravates microcrack initiation when it freezes [37]. Moreover, the moisture absorption properties of GFRP laminates and their effect on mechanical performance were examined after being immersed in distilled water at ambient and 90 °C temperatures [38]. It was observed that the degree of damage strongly depends on the applied temperature. In particular, the moisture uptake of the laminates impairs the fibre/matrix interface, which contributes to lowering the mechanical performance in the matrix-dominated direction.

FRP composite structures are a combination of a polymer matrix reinforced with glass and carbon fibres. The fibres provide strength and stiffness, while the polymer matrix contributes to binding and load transfer activities. Particularly, stress relaxation in polymer materials can occur due to internal structural changes in response to sustained loads that affect their properties. Researchers obtained the viscoelastic properties of FRP composites, such as the glass transition temperature, damping factors, storage modulus, and loss modulus of laminates exposed to different environmental conditions, as noted in [39,40]. Thermomechanical properties of CFRP, GFRP, and hybrid composite laminates were studied using the dynamic mechanical analysis (DMA) tool after being exposed to moisture for extended periods and to elevated temperatures in the studies [41,42,43,44]. The performance of all groups of laminates showed an increase in stiffness properties, and different relaxation phases were observed in the glassy region. However, as the temperature approaches the glass transition, the storage modulus of the composite laminates decreases as expected.

Researchers have been developing theoretical models to predict the thermomechanical properties of FRP composites as a function of temperature. The cost of production and the time spent on testing can be reduced by utilizing theoretical models [45,46,47,48,49,50]. In particular, Gibson et al. [51] proposed an empirical model to determine the temperature-dependent properties of FRP composites involving compressive, tensile, and storage modulus properties. The values of the parameters were studied at the glass transition regions of the polymer materials. The proposed empirical model shows a close correlation with the experimental results obtained for the storage modulus properties of the glass/polyester laminates. Recently, Bai et al. [52] used the Arrhenius law to model the temperature-dependent storage modulus and the viscosity properties of pultruded glass fibre-reinforced polyester laminates under elevated temperatures. Moreover, Feng and Guo [53] developed a theoretical model for temperature–frequency-dependent dynamic mechanical properties of epoxy resin and glass/epoxy composites, considering the degree of conversion in the glass transition and the decomposition regions. Arrhenius’s law has been one of the methods used to determine the mechanical performance of FRP composite material as a function of temperatures and frequencies.

Structural components made from FRP composite materials can be exposed to lower and higher environmental conditions for extended periods. For instance, Marin-based structural components and composite wind turbine blades installed in colder and hotter wind farms are exposed to varying temperatures [54]. The design lifetime of these composite structures might be affected due to the temperature-dependent properties of the epoxy materials. Therefore, it is essential to conduct further experimental and theoretical studies on FRP composite materials after exposing the laminates to lower and higher environmental conditions, before constructing the components.

This study examines the influence of long-term moisture exposure and temperatures on the thermomechanical properties of hybrid glass/carbon/glass (GCG) composite laminates. The laminates were kept in a deep freezer at temperatures of −80 °C, −20 °C, and 0 °C for 60 days and at higher temperatures. The tensile and compressive properties of all groups of laminates were determined using a tensile testing machine under targeted and higher temperatures. Additionally, the stiffness parameters, such as the storage modulus, loss modulus, damping properties, and glass transition temperatures of all groups of hybrid laminates, were determined using the DMA tool. As the testing temperature increased, compressive, tensile, storage modulus, and loss modulus properties decreased due to increased molecular mobility. Conversely, these mechanical properties improved at lower testing temperatures due to increased molecular crosslinking of the polymer network. The relationship between glass transition temperature, vibration frequency, and the presence of beta transitions in the glassy regions of the laminate was identified. A change in the values of glass transition temperature was observed as the frequency increased. Finally, the accuracy of the storage modulus results with the empirical models was assessed at different test temperatures and frequencies. A more suitable empirical model that was fitted with the experimental results was obtained, and its accuracy was investigated.

2. Experimental Programme

Hybrid composite laminates were prepared using glass and carbon fibres. Before testing, the hybrid composite laminates were kept in a deep freezer at temperatures of −80 °C, −20 °C, and 0 °C for 60 days and at higher temperatures. Tests in tension, compression, and bending under lower and higher environmental conditions were conducted to determine their thermomechanical properties. Specifically, the tensile and compressive properties of all GCG groups of hybrid laminates were determined using a tensile testing machine at the targeted temperatures. Additionally, the storage moduli, loss moduli, damping factors, and glass transition temperatures of the laminates as a function of temperatures and frequencies were determined using a DMA tool.

2.1. Materials

Unidirectional E-glass fibre, unidirectional T-300 carbon fibre, prime 27 LV epoxy resin, and prime 27 LV hardener were purchased from AMT Composites, Durban, South Africa (SA). The top and bottom layers of the hybrid laminates are reinforced with glass fibre, and the middle layer is reinforced with carbon fibre using the epoxy matrix as a binder polymer material. The epoxy matrix for all groups of the hybrid specimens was prepared with a weight mixing ratio of 10:2.6. The mechanical and physical properties of the fibres and epoxy resin are shown in

Table 1. The mechanical properties of carbon fibre, glass fibre, and epoxy resin [55].

Materials	Young’s Modulus [GPa]	Tensile Strength [MPa]	Density [Kg/m3]	Poisson’s Ratio
T-300 carbon	230	3530	1760	0.30
E-glass	72.5	2350	2570	0.25
Epoxy resin	3.3	69.9	1020	0.36

.

Composite Laminate Preparation Procedures

The hybrid GCG composite laminates were produced using resin transfer moulding (RTM) methods. Compressive, tensile, and bending tests were performed based on ASTM standards [56,57,58]. A total of four layers of glass and carbon fibres were used to construct the hybrid laminates for the tensile and compressive testing processes. Two layers of carbon fibres were used in the middle layers using epoxy resin as a binder material. In the case of DMA tests, a total of ten layers of glass and carbon fibres were used. Four layers of carbon fibre were used in the middle of the hybrid laminates with a common epoxy resin as a binder. The procedures for laminate preparation using the RTM method are shown in Figure 1.

All groups of specimens were cured at room temperature for 24 h before being post-cured at 65 °C in the oven for 16 h. The specimens were cut to the desired dimension using a computer numerical control (CNC) machine with a tolerance of 0.02 mm, then cleaned, and the flash was removed using sandpaper. Five samples were considered for each group of hybrid laminates during the testing process.

The volume fractions of all groups of specimens were determined as 55% using burn-off test methods based on ASTM standards [59]. The hybrid composite laminate preparation process, fibre orientation, and the test methods used in this study are shown in Figure 2.

2.2. Test Methods

The compressive and tensile properties of all groups of GCG composite laminates were conducted using a Lloyd LR testing machine by measuring at a rate of 2 mm/min. Before testing, all groups of GCG composite laminates were preserved in a deep freezer at temperatures of −80 °C, −20 °C, and 0 °C for 60 days. Additional specimens were preserved at room temperature, and tests were carried out at lower and higher test temperatures. A heat-con thermocouple was used to measure and control the existing temperatures on each hybrid laminate during the testing process. An Epsilon digital extensometer of a 25 mm gauge length was used to determine the strain of hybrid laminates at different testing temperatures.

The dynamic mechanical properties of all groups of GCG composite laminates were measured using a DMA Q 800 TA tool. The hybrid specimens were preserved in a deep freezer at a temperature of −80 °C, −20 °C, and 0 °C for 60 days. Additionally, the controlled GCG specimen was maintained at 25 °C before testing. Experimental work was conducted on hybrid specimens under the three-point bending modes using the dynamics oscillation frequency of 1 Hz, 10 Hz, and 100 Hz. An amplitude of 15 μm was applied. The heating rate was increased at 2 °C/min. Liquid nitrogen was used as the cooling agent. The test temperatures were set for all groups of hybrid laminates ranging from −80 °C to 140 °C, −20 °C to 140 °C, 0 °C to 140 °C, and 20 °C to 160 °C. The dimensions of the hybrid laminates were set at a height of 4.60 mm, a width of 13 mm, and a length of 64 mm to determine the storage modulus (E′), loss modulus (E″), damping factor, and glass transition temperature $\left(T_g\right)$ of the polymer material.

3. Results and Discussion

3.1. Mechanical Properties of the Hybrid Laminates at Different Temperatures

3.1.1. Compressive Properties

The compressive properties of all groups of GCG composite laminates at different testing temperatures are shown in

Table 2. The compressive properties of the hybrid composite laminates at different test temperatures.

Temperature (°C)	Designation of GCG Composite Laminates	Maximum Force during Failure (N)	Compressive Strength (MPa)	Standard Deviation (SD) and Coefficient of Variation (CV)
−80	−80/GCG	14,382.19	668.19	(63.78, 9.54%)
−20	−20/GCG	12,072.99	589.46	(60.11, 9.83%)
0	0/GCG	12,414.76	591.41	(23.25, 3.93%)
25	25/GCG	9004.27	441.42	(34.34, 7.78%)
50	50/GCG	5572.57	249.47	(21.78, 8.73%)
75	75/GCG	4370.02	216.88	(17.08, 7.87%)
100	100/GCG	1412.86	68.06	(6.39, 9.40%)

. The highest and lowest compressive strength results were obtained in the cases of −80 °C/GCG and 100 °C/GCG groups of laminates. The reduction ratios are about 11.78%, 11.49%, 33.94%, 62.66%, 67.54%, and 89.81% as the testing temperature increased from −80 °C to 100 °C. The highest compressive property might be obtained due to the closely compacted nature of polymer molecules at lower temperatures. Conversely, the lowest compressive property was obtained due to the ease of mobility of polymer molecules under higher environmental conditions. Particularly, as the testing temperatures of the laminates were close to the glass transition temperature of the epoxy matrix, the force needed to break the laminates started to decrease. The reduction in compressive loading and stress distribution as a function of the targeted test temperatures is shown in Figure 3a. The force needed to break the laminates decreased as the testing temperature increased. This might occur due to the weak bonding at the fibre/matrix interface. Based on the compressive strength results obtained from these experiments, an extended lifetime on the −80 °C/GCG laminate was observed. The compressive load needed for the failure of the laminates increased as the preservation temperatures on the samples decreased.

3.1.2. Tensile and Stiffness Properties

The tensile properties of all groups of GCG laminates at various testing temperatures are listed in

Table 3. The tensile properties of the hybrid composite laminates at different test temperatures.

Temperature (°C)	Designation of GCG Composite Laminates	Force during Failure (N)	Tensile Strength (MPa), SD, and CV	Tensile Modulus (GPa), SD, and (CV)
−80	−80 °C/GCG	27,234.64	1321.20 (37.53, 2.84%)	74.63 (1.71, 2.29%)
−20	−20 °C/GCG	23,365.99	1125.01 (35.63, 3.17%)	70.89 (0.53, 0.74%)
0	0 °C/GCG	27,437.70	1358.16 (29.54, 2.18%)	74.35 (5.64, 7.58%)
25	25 °C/GCG	20,715.62	1005.39 (92.28, 9.18%)	59.78 (5.14, 8.60%)
50	50 °C/GCG	12,958.90	637.66 (1.09, 0.17%)	41.55 (3.31, 7.96%)

and Figure 3b. As the testing temperatures increased to 0 °C, 25 °C, and 50 °C, the tensile strength and tensile modulus of the hybrid laminates decreased. A slight change in the tensile properties was observed as the temperature decreased to −20 °C and −80 °C. This may occur due to increased moisture absorption in the laminates, which improves the crosslinking network of polymers and increases the failure limit of the hybrid laminates. Increasing the crosslinking networks improved the bond between fibre and epoxy to delay failure. Compared with the tensile strength of 1358.16 MPa at 0 °C, the tensile strengths of GCG groups of laminates were reduced by 25.97% and 53.05% as the temperatures increased to 25 °C and 50 °C, respectively. Additionally, the tensile modulus of the hybrid laminates changed by 19.60% and 44.16%, respectively. In this case, the mobility of the polymeric molecules increased due to the increase in the testing temperature. Additionally, the bond between the fibre and epoxy was weak, and the load-transferring capacity of the epoxy matrix was reduced, so the forces needed to break the laminates decreased.

3.2. Dynamic Mechanical Properties of Hybrid Laminates

DMA tests were conducted to determine the change in the mechanical properties of four groups of GCG laminates after being preserved at different temperatures for 60 days. The experimental storage modulus results were normalized by the initial values to minimize small discrepancies at the initial testing temperatures as shown in Figure 4. It should be noted that the storage modulus of all groups of the laminates decreased at the glass transition temperature and dropped further at decomposition. These results confirmed the temperature-dependent mechanical properties of FRP composite materials. The mobility of the polymer molecules increased as the temperature increased. Additionally, the glass transition temperature of the epoxy matrix as a function of the targeted preserved temperatures was characterized. A delay in the $T_g$ value was observed when the hybrid laminates were preserved in the deep freezer for extended periods. This might occur due to the higher intact bonding properties of polymer molecules at lower temperatures. Particularly, the first transitions occurred in the case of −20 °C/GCG (−20 °C to 17 °C) and −80 °C/GCG (−80 °C to 17 °C) hybrid laminates, and this is attributed to the β-relaxation of the polymer chain molecules [32]. The second α-transition is observed in −20 °C/GCG (17 °C to 86 °C) and −80 °C/GCG (17 °C to 90 °C) hybrid laminates, which correspond to the glass transitions of the polymer networks.

The relationships between the glass transition temperature and the dynamic oscillation frequency were assessed. The results confirmed that the $T_g$ values of the polymer network increased as the frequency increased. This might occur due to a reduction in the gaps between the crosslinking of the polymer network, which causes the laminates to behave elastically for extended periods at higher frequencies. Mainly, moisture swelling for extended periods at the lowest temperatures contributed to increasing the storage modulus of the hybrid laminates in the glassy regions. This might occur due to the reduction in the crosslinking of the polymer network, which needs a higher temperature to increase the mobility of the polymer molecules.

The kinetic parameters can be estimated from the experimental results and used to develop theoretical models. Mostly, as the temperature is raised, the polymer material changes its state to glassy, leathery, rubbery, and decomposed. The common phase transitions of the polymer material are the glass transition, the leathery to rubbery transition, and the rubbery to decomposition transition. For the case of −20 °C/GCG and −80 °C/GCG composite laminates, one additional state, beta (β) transition, was observed before the glass transition occurred. These transactions were obtained due to extended periods of preserving the laminates at the lowest temperature conditions.

It is important to find the kinetic parameters of the hybrid laminates from a glassy to a leathery state for use in developing a theoretical model and applying it to design different composite structural components. The values of the conversion degree at the glass transition region of the four groups of GCG composite laminates can be estimated by the following relation:

$${\alpha }_g={\displaystyle \frac{E_g^{\prime }-E^{\prime }}{E_g^{\prime }-E_r^{\prime }}}$$

(1)

where $E_g^{\prime }$ is the storage modulus of the hybrid laminates in the glassy state, $E^{\prime }$ is the instantaneous storage modulus in the glass transition region, and $E_r^{\prime }$ is the storage modulus of the hybrid laminates in the rubbery state.

As shown in Figure 5, the values of the conversion degree of the hybrid laminates increased as the testing temperature increased due to the mobility of the polymer molecules. The lowest conversation degree was observed in the case of −80 °C/GCG laminates. Additionally, the influence of frequencies on the values of the conversion degrees of the hybrid laminates was observed. The values of the conversion degree were lower as the frequency increased. It needs additional time to increase the mobility of the polymer molecules.

The loss modulus and tan $\delta$ value of the four GCG composite laminates under different temperatures and frequencies are shown in Figure 6. The values of the loss modulus are used to determine the amount of energy dissipated as heat when the FRP composite material turns viscous. The tan $\delta$ value is the ratio of the loss modulus to the storage modulus properties of the materials, which is used to determine the damping capability of FRP composite materials. As shown in Figure 6, the energy dissipation and damping properties of the hybrid laminates reached a peak at the glass transition temperature of the epoxy matrix. This might occur due to the mobilization of the polymer molecules with increasing temperatures. The peaks of the curves are used to determine the glass transition temperature of the material. The values of $T_g$ at the loss modulus and the tan $\delta$ curves were compared in Figure 6. A delay in $T_g$ was observed in the case of the tan delta curves. Mostly, the values of glass transition obtained from the storage modulus curves have been considered to be used for the structural design of composite structural components.

Additionally, the relationship between glass transition, preserved temperatures, damping properties, and frequencies was assessed from the three peak curves, as shown in Figure 6. The peaks of the curves show a right shift to higher values at the highest frequency and lowest preserved temperature condition. This might occur due to decreased crosslinking of the polymer molecules under the swelling of moisture for extended periods. More heat is needed to increase the mobility of the polymer network to turn viscous. In particular, −80 °C/GCG hybrid laminates provided the highest storage modulus and damping properties and a longer period to attain their glass transition temperatures. Based on these experimental data, the hybrid laminates that are preserved at lower temperatures for longer periods offer advantages in terms of obtaining longer lifespans and better damping properties. This could happen because it takes longer for the polymer molecules to reach the glass transition temperature.

The glass transition temperature of the FRP composite materials follows a typical Arrhenius law with the loading frequency [53]. The values of activation energy for all groups of the hybrid laminates were identified based on the Arrhenius relationship. This is represented by

$$f=A\mathit{exp}\left(-\left({\displaystyle \frac{E_a}{R{T}_g}}\right)\right)\mathrm{o}\mathrm{r}\mathit{ln}\left(f\right)=\mathit{ln}\left(A\right)-\left({\displaystyle \frac{E_a}{R}}\right)\times \left({\displaystyle \frac{1}{T_g}}\right)$$

(2)

where $f$ is the frequency, $A$ is a constant, $E_a$ is the activation energy, $R$ is the universal gas constant, and the $T_g$ value is in Kelvin and obtained from storage modulus, loss modulus, and tan delta curves.

As shown in Figure 7, the targeted logarithmic frequencies and the reciprocal of the $T_g$ values of all groups of hybrid laminates have a linear relationship. The activation energy of each hybrid laminate was obtained using the slope of ($-E_a/R)$ by the linearized curves of $ln\left(f\right)$ versus $\left({\displaystyle \frac{1}{T_g}}\right)$ and their values are summarized in

Table 4. The values of activation energy ${(E}_a)$ of the GCG groups of laminates obtained at the glass transition regions of the storage modulus, loss modulus, and delta curves.

Activation Energy (kJ/mol) Group of Hybrid Laminates	Tgmax (Storage Modulus)	Tgmax (Loss Modulus)	$${\mathit{T}}_{\mathbf{gmax}}\left(\mathbf{tan}\mathit{\delta }\right)$$
Control GCG	781.03	672.05	439.00
0 °C/GCG	981.15	933.28	534.95
−20 °C/GCG	805.02	797.49	453.33
−80 °C/GCG	1130.87	783.79	491.47

. The linearly fitted curves were compared with the curves obtained from storage modulus, loss modulus, and tan delta curves as a function of the targeted frequencies. All groups of the hybrid laminates showed a close correlation, and their values were obtained between 0.9812 and 1, respectively.

4. Models of Temperature-Dependent Storage Modulus

FRP composite materials have gained widespread use in the aerospace, automotive, marine, and wind turbine blade manufacturing industries by providing lightweight, durable, and corrosion-resistant solutions for various structural components. At elevated temperatures, FRP materials have reduced mechanical properties due to the softening of the polymer matrix and degradation of the reinforcing fibres. Conversely, at low temperatures, FRP composites may become stronger, brittle, and prone to fracture. These temperature-dependent mechanical properties of FRP materials can be determined using experimental methods. It is a costly and time-consuming process to obtain the appropriate material to be applicable under different environmental conditions. Different researchers developed analytical methods to estimate the mechanical properties of FRP composites as a function of temperature. For example, an empirical model developed by Gibson et al. [51] was used to determine the storage modulus of FRP materials as a function of temperature. The parameters obtained under the glass transition regions were used to estimate the empirical model and were described by

$$E\left(T\right)={\displaystyle \frac{E_u+E_r}{2}}-{\displaystyle \frac{E_u-E_r}{2}}\tanh \left[k\left(T-T^{\prime }\right)\right]$$

(3)

where $E\left(T\right)$ is the value of the storage modulus at a specified temperature T, $E_u$ is the value of the storage modulus at room temperature, $E_r$ is the value of the storage modulus at the rubbery state, and $kand{T}^{\prime }$ are variables determined by fitting data using a regression analysis. The value of $T^{\prime }$ is recommended to be considered when the storage modulus of the material falls rapidly.

Most polymeric materials have four states, such as glassy (g), leathery (l), rubbery (r), and decomposition (d) states, and three transitions: glass transition, leathery to rubbery transition, and rubbery to decomposition transition. Preserving composite materials at lower temperatures for extended periods has an impact on obtaining the gamma ($\gamma$) and beta ($\beta$) transitions in the glassy state [53]. From the current experimental results, beta ($\beta$) transition is observed in the case of −20 °C/GCG and −80 °C/GCG hybrid laminates due to preserving the laminates in a deep freezer for extended periods. Therefore, it is important to include the beta transitions of the laminates to develop and validate them with the empirical model under consideration.

Let us consider the unit volume of the initial hybrid composite laminates at specific temperatures. The volume of the laminates at different states can be determined as follows:

$$V_{\beta }=\left(1-\beta \right)$$

(4)

$$V_g=\beta ·\left(1-{\alpha }_g\right)$$

(5)

$$V_l=\beta ·{\alpha }_g·\left(1-{\alpha }_r\right)$$

(6)

$$V_r=\beta ·{\alpha }_g·{\alpha }_r·\left(1-{\alpha }_d\right)$$

(7)

$$V_d=\beta ·{\alpha }_g·{\alpha }_r·{\alpha }_d$$

(8)

where V is the volume of the laminates in different states.

Assuming that $E_{\beta }$, $E_g,$ $E_l,$ $E_{r,}\mathrm{and}{E}_d$ are the storage moduli in the specified states, the values of the storage modulus at a different state $E_m$ are determined by

$$\begin{gathered} E_m=E_{\beta }·\left(1-\beta \right)+E_g·\beta ·\left(1-{\alpha }_g\right)+E_l·\beta ·{\alpha }_g·\left(1-{\alpha }_r\right)+E_r·\beta ·{\alpha }_g·{\alpha }_r·\left(1-{\alpha }_d\right) \\ +E_d·\beta ·{\alpha }_g·{\alpha }_r·{\alpha }_d \end{gathered}$$

(9)

Considering that the storage modulus of the laminates at the leathery and rubbery states is nearly the same and neglecting the $\beta$ transitions, Equation (9) can be reduced to

$$E_m=E_g·\left(1-{\alpha }_g\right)+E_r·{\alpha }_g·\left(1-{\alpha }_d\right)$$

(10)

Comparison of the Storage Modulus Results with Analytical Models

The storage modulus results obtained on GCG hybrid composite laminates as a function of temperature and frequency are compared with the specified empirical models. As shown in Figure 8, the storage modulus of the control GCG composite laminate was compared with the empirical models specified in Equations (3) and (10). The minimum errors observed using Equation (3) are 0.50% and 0.43% at frequencies of 1 and 100 Hz, respectively. Meanwhile, the errors are reduced below 0.02% in the case of Equation (10). Moreover, the empirical models are further compared with the storage modulus results of the hybrid laminates preserved in a deep freezer at different temperatures for extended periods.

Figure 9 shows the comparison between the storage modulus result of 0 °C/GCG laminates and the specified empirical models at frequencies of 1 and 100 Hz. The minimum errors obtained using Equation (3) are 0.39% and 0.60% at frequencies of 1 Hz and 100 Hz, respectively. However, the errors are reduced below 0.02% in the case of Equation (10). In all cases, both empirical models have a very close correlation with the storage modulus results.

Furthermore, a comparison was made between the storage modulus result of −20 °C/GCG laminates and the empirical models, as shown in Figure 10. The minimum errors obtained using Equation (3) are 0.39% and 0.37% at 1 and 100 Hz frequencies, respectively. However, close correlations are observed, and the minimum errors are reduced below 0.03% with the empirical model specified in Equation (10). The curves generated using the theoretical modulus exhibit a proper fit with the storage modulus results.

Figure 11 shows the comparison between the storage modulus result of −80 °C/GCG composite laminates and the specified empirical models. The empirical model proposed by Gibson et al. [51] exhibits significant deviations from the storage modulus curves, with the minimum errors approaching 5%. Notably, it lacks close correlations with the experimental data at a lower preservation temperature for extended periods. The theoretical model, developed based on the principles of Arrhenius’s law, exhibits properly fitted curves that closely align with the storage modulus results. Arrhenius’s law is often employed to describe the temperature dependence of various material properties, in particular, in the context of kinetics. In general, the utilization of Arrhenius’s law in developing the theoretical model enhances our understanding of the temperature-dependent properties of the FRP composite materials. It reinforces the predictive power of the model in capturing its mechanical behaviour across different temperatures and frequencies.

5. Conclusions

The effect of the long-term perseverance on the mechanical properties of GCG composite laminates under different environmental conditions is examined using a tensile testing machine and a DMA tool. Tensile, compressive, and stiffness parameters, such as the storage modulus, loss modulus, and damping properties, are assessed. Additionally, the storage modulus results of the hybrid laminates are validated using various empirical models. The following observations and conclusions are drawn:

• The highest and lowest compressive strength properties were obtained when the GCG laminates were tested at temperatures of −80 °C and 100 °C, respectively. This variation is likely due to an increased crosslinking of the polymer network at lower temperatures and an increased mobility of the polymer material at higher environmental conditions.
• The tensile strength and tensile modulus results of all groups of GCG composite laminates exhibited minor differences between them for the laminates preserved in a deep freezer for extended periods. Both properties were reduced as the test temperature approached 50 °C. This indicates the initial onset of the mobility of polymeric matrix material, which reduces the transfer capacity of the loads to the fibres before reaching their glass transition temperature.
• The storage modulus, loss modulus, and damping properties of the GCG laminates decreased as the testing temperature approached the glass transition. The highest stiffness parameter was observed at −80 °C/GCG laminates, likely due to the presence of beta transitions in the glassy regions of the laminates.
• The relationships between the glass transition temperatures of the polymer matrix and vibration frequency were assessed. A delay in glass transition temperature was observed as the testing frequency increased.
• The storage modulus results of GCG composite laminates are compared with empirical models. The model developed using the Arrhenius law accurately predicted the storage model results. However, the model developed by Gibson et al. [51] requires further research to accurately predict the storage modulus results of laminates that were preserved at the lowest temperatures for extended periods.