Mechanical behaviour of carbon fibre reinforced polymer composite material at different temperatures: Experimental and model assessment

In the present study, temperature and frequency effects are studied involving carbon fibre reinforced polymeric materials with unidirectional fibers. Before testing, laminates were preserved in a deep freezer at −80, −20, 0, and 25°C for 60 days. Compressive, tensile, and stiffness behaviors of the laminates were assessed. The results confirmed that the compressive strength, tensile strength, and tensile modulus of laminates severely deteriorate at high temperatures. This might happen because of the weakening of the fibre/matrix interface, resulting in the load-carrying capacity of the carbon fibre being severely reduced. Lower temperatures did not significantly affect the mechanical performance of the laminates. This is due to minor deformation of the frozen laminates and closely compacted epoxy chain segments. The effects of temperature and vibration on the storage modulus, loss modulus, and damping behaviour of laminates are discussed. The results confirm that a reduction in mechanical performance is a strongly temperature-dependent phenomenon. Laminate damping properties are also evaluated. According to the results of the experiments, −80°C has the greatest permanence. Finally, the accuracy of the results on storage modulus was compared with empirical models. The model suggested by Gibson et al. provided the most accurate estimates for the storage modulus of the laminates. Other models were less accurate and gave non-conservative estimates.


Introduction
Fibre-reinforced polymeric (FRP) composites have received considerable attention for components used in aerospace, automobiles, and wind turbine blades. [1][2] Currently, carbon fibre reinforced polymeric (CFRP) composites have been the choice to develop large wind turbine blade structures. [3][4][5] A blade can be exposed to moisture, temperature, and mechanical loads during its life span. Moisture often induces swelling and forms residual stresses, leading to degradation. [6][7][8] Moisture absorption in a polymeric matrix can influence the thermophysical, mechanical, and chemical properties. [9][10][11] Stress can develop under loading conditions on tension, compression, and fatigue leading to interlaminar cracks, and consequently delamination. [12][13] At low temperatures, the relaxation of residual stress is low, and this may lead to larger debonded, causing brittle failure. Zafar et al. 14 assessed the effects of long-term moisture on the mechanical behavior of CFRP laminates. Results indicated that the glass transition temperature (T g ) decreased and the strength was reduced as the moisture content increased. This was due to increased residual stresses and plasticizing of the polymer networks, resulting in an increase in the mobility of polymer chains.
Composite structures that use thermosetting polymer matrix as a binder deteriorate when exposed to elevated temperatures. 15 The polymer matrix will soften and decompose when the temperature exceeds T g and the decomposed temperature (T d ). The softening and decomposition of the resin not only reduce the strength of the resin itself, but also weakens the bonding of fibres, resulting in the rapid reduction of the strength. [16][17][18] Ogi et al. 19 conducted a tensile test on dry and wet CFRP specimens to assess the stress/strain response at different temperatures. They reported a decrease in tensile strength when temperature increased and decreased during higher moisture immersion periods. In another study, Ogi 20 investigated the influence of thermal history on CFRP laminates. Results indicated that a reduction in strength occurs due to higher degradation at the fibre/matrix interface. Hawileh et al. 21 studied the effect of temperature on the mechanical performance of carbon, glass, and carbon-glass fibre with a common epoxy matrix as the binder. They found that the stiffness and tensile strength were reduced as the temperature increased. Other researchers [22][23] investigated the mechanical response of CFRP and hybrid FRP laminates at elevated temperatures. They observed that the mechanical properties decreased significantly when the temperature increased.
Understanding the viscoelastic properties of CFRP composites at different states is essential. Melo and Radford 24 used the DMA tool to assess the viscoelastic properties of CFRP laminates. They observed a decrease in storage modulus and an increase in damping properties as the temperature changed. Many researchers have been developing empirical models to validate the experimental results. 25 Hawileh et al. 26 reported an analytical model to predict the tensile strength and elastic modulus of FRP composites at elevated temperatures. The test data and the proposed analytical model agreed well.
Carbon fibre reinforced polymeric composite has been used to produce the spar cap sections of the blades to increase their stiffness. The spar cap sections are exposed to fluctuating wind loads and different environments. It is important to assess the mechanical response of CFRP materials under different environmental conditions before using them for designing purposes.
This paper presents further research about the mechanical response of CFRP under different environmental conditions. Tensile and compressive responses under low and high-temperature tests were assessed. Additionally, storage modulus, loss modulus, damping ratio and T g of laminates were assessed. Finally, the accuracy of experimental results with empirical models was assessed to estimate the variation as a function of temperature and frequency. A better empirical model from the authors was proposed, and its accuracy was compared with the measured results.

Material properties
Carbon fibre, prime 27 LV epoxy resin, and prime 27 LV slow hardener were purchased from AMT composites in South Africa. Table 1 shows the properties of carbon fibre and epoxy matrix. The matrix material was prepared with a weight mixing ratio of 10:2.6.

Laminate preparation and test methods
Laminates were prepared under ASTM standards. [28][29][30] Three-ply carbon fibre with epoxy matrix was used to prepare laminates. Fourteen-ply carbon fibre was used to prepare the samples for the dynamical mechanical analysis. Laminates were produced using the resin transfer moulding (RTM) method and cured for 24 h at 25°C, then post-cured at 65°C for 16 h. Laminates were cooled at room temperature and tabs were produced by the hand lay-up method using plain weave glass fibres. Laminates were cut using a CNC machine with a tolerance of 0.02 mm, then cleaned, and flash was removed with sandpaper.
Matrix digestion using burn-off method was used to determine the volume fractions according to ASTM 3171 standard. 31 The volume fraction of fibres was found to be 55%. Laminates preparation process, fibre orientation and testing methods are shown in Figure 1.
Compressive and tensile strength tests were carried out using a Lloyd LR testing machine. The testing machine was equipped with a 30 kN load cell, and measurements were taken at a rate of 2 mm/min. Laminates were preserved in a deep freezer at À80, À20, and 0°C for 60 days. Compressive tests were performed at À80, À20, and 0°C, and tensile tests were performed at À20 and 0°C. Additional tests were carried out at 25, 50, 75, and 100°C. A heat-con thermocouple was used to measure the temperatures. An epsilon digital extensometer of 25 mm gauge length was used.
DMA tool was used to assess the change in storage modulus, loss modulus, and damping factors of laminates as a function of temperature and frequency. These tests were carried out under ASTM D5023 standard, using DMA Q 800 TA Instrument. Three-point bending modes were used. The heating rate was increased at 2°C/min, and frequencies were set at 1, 10 and 100 Hz. Liquid nitrogen was used as a cooling agent and test temperatures ranged from À80 to 140°C, À20 to 140°C, 0 to 140°C, and 20 to 160°C. Dimensions were set at a height of 4.57 ± 0.03 mm, a width of 13 ± 0.02 mm, and a length of 64 ± 0.02 mm.

Weibull distribution
Tensile and compressive results were analysed using the Weibull distribution. 32 The basic form of the cumulative probability density function is given by where σ is tensile or compressive strength and σ a is a scalar parameter and m is a shape parameter. The shape parameter was obtained from test data using a linear fit to linearise the form of the two-parameter Weibull probability function.

Compressive tests
A compressive test was performed to assess the response of CFRP laminates as a function of temperature. As shown in Figure 2, at testing temperatures of À20 and 100°C, the highest and lowest compressive strength were obtained. When the temperatures were raised from 0 to 100°C, the compressive strength decreased by 1.22%, 2.97%, 32.28%, 67.84%, and 93.11%, respectively, compared to À20°C laminate. The compressive strength of the laminates was affected less and was almost the same when the temperature dropped from 25 to À80°C. The reason is that the polymer chain segment motion is frozen and more closely compacted due to absorbed moisture. The compressive strength of the laminates was degraded little when the temperature was below À20°C. This could occur due to rapid fibre/matrix interface debonding and delamination caused by more moisture absorption and swelling. 33 The compressive strength response between 50 and 75°C was reduced due to resin softening as approached the T g of the epoxy matrix. At 100°C, the lowest compressive strength was obtained. The load-carrying capacity of the fibres was reduced due to the softening of the resin. Mobilizations of resin molecules were the main reason for a reduction in the compressive strength of laminates. The van der Waals forces weaken leading to lower hydrogen bonds. 34 Compressive strength properties with the cumulative failure probability distribution of laminates are shown in Figure 3. A higher reduction in compressive strength was observed as the testing temperature increased from ambient to higher temperatures. Additionally, the accumulated compressive failure probability of each laminate was observed using the curves. The distribution of test results was characterized by the shape parameter (m) and the scale parameter ðσ a Þ. 35 The scale parameter is related to the failure distribution of laminates at compressive stress levels. The average compressive results and model data were found to be within the range of 1.63%-2.88%, which is acceptable.

Tensile tests
A tensile test was performed to assess the tensile performance of CFRP laminates at various temperatures. As shown in Figure 4(a) and (b), the tensile and stiffness properties of laminates decreased as the temperature increased from 0 to 100°C. The tensile strength decreased by 0.76%, 13.19%, 19.82%, and 67.58% when compared to the tensile strength at 0°C. The reduction in tensile modulus was about 3.24%, 12.66%, 19.28%, and 67.09%. A high level of moisture swelling may increase plasticization to lower elastic deformation. Lower tensile properties were observed on À20°C laminates. This might occur due to the presence of moisture, which degrades the interface strength rapidly and induces debonding and delamination. 33 The tensile strength and stiffness of the laminates were evaluated between 50 and 75°C. Results show that the tensile and stiffness properties were reduced as the temperature increased. In this case, the force transfer capacity of the resin was reduced due to the resin's softening effects. 34 At 100°C, the lowest tensile strength and stiffness properties were obtained. The cumulative failure probability of laminates at different temperatures is shown in Figure 5.

Dynamic mechanical analysis
Storage modulus ðE 0 Þ. Storage modulus is a measure of how stiff or flimsy a sample is. It provides useful information about the degree of cross-linking and fibre/matrix interfacial strength. [36][37][38] Figure 6 shows the E 0 of laminates held at temperatures of À80, À20, 0, and 25°C and frequencies of 1, 10 and 100 Hz. Below T g , E 0 of the laminates decreased as the temperature increased. In the vicinity of T g , a sharp decrease in E 0 was observed. This indicates that the material is going through a glassy/ rubbery transition stage. The highest and lowest E 0 were obtained on À80°C and CE laminates. In the case of glassy/rubbery regions, the molecules become free for mobilization, and E 0 is reduced. It may occur due to the softening and weak load transfer capacity of the epoxy matrix. The lowest E 0 was observed after T g , corresponding to the decomposed state.
E 0 and T g of laminates were characterized under different frequencies. At a frequency of 1 and 10 Hz, E 0 of laminates were nearly similar. This might occur due to the flow behaviour of the polymer matrix at low frequencies, acting similarly to flow at higher and elevated temperatures which increased the mobility of the molecules. In the case of 100 Hz, gaps between the crosslinking of the polymer matrix tend to close. This caused the material to behave with less elastic deformation and thus obtain a better E 0 . In particular, E 0 of the À80°C group of laminates varied from the other laminates. This might happen due to the lower mobility of the molecules which reduces the gaps in the cross-links of molecules. T g of the polymer matrix was estimated using E 0 curves. A substantial drop in T g occurred in the case of À20 and À80°C laminates as the frequency increased. This might have occurred due to rapid degradation in the fibre/matrix interface, resulting in induced debonding and delamination. 32 However, the T g of the remaining groups of laminates increased as the frequency increased.
Loss modulus ðE 00 Þ. Figure 7 plots E 00 of laminates as a function of temperature and frequency. It is noted that E 00 of the laminates significantly decreased as the temperature exceeded T g and had nearly similar dissipation properties at 1 and 10 Hz.   This might have happened due to an increase in the internal friction that enhances the mobility of polymer molecules to dissipate more heat. However, the highest value of E 00 was observed at 100 Hz.
The T g values of the laminates were assessed. It is observed that T g of CE laminate shifted to a higher temperature as the frequency increased. This shows that the epoxy molecules need a higher temperature to increase their mobility. In the case of 0, À20, and À80°C laminates, the lowest T g values were observed at 100 Hz. This might occur due to the plasticization effects. The T g values estimated from the curves of E 00 were higher than those obtained from the E 0 curves. Mostly, T g values obtained from E 0 curves are recommended for composite structural design applications.  Damping factor ðtan δÞ. Figure 8 shows the damping behavior of the laminates. Results show that the damping properties of the laminates increased slightly up to T g and then decreased drastically. These changes in damping behavior may occur due to molecular mobility. As the frequency increased from 1 to 100 Hz, the damping behavior of CE, 0, À20, and À80°C laminates increased by 3.18%, 4.94%, 7.62%, and 3.14%. The damping behaviors of the laminates were compared with each other at the specified frequency. Results from the curves indicate that À80°C laminate has the highest damping property. At 100 Hz, À80°C laminates dissipate their maximum stored energy. It might occur due to the plasticization effect of the CFRP laminates. The highest T g values were obtained from the damping curves. While the lowest and intermediate T g values were obtained from E 0 and E 00 curves.

Comparison of experimental results and prediction models
The storage modulus results of laminates are compared with existing empirical models. Bai and Keller 39 summarized the available models used to assess the mechanical behavior of FRP composites at elevated temperatures. According to Gibson et al., 40 the modulus of FRP composites at a temperature T can be determined by the equation where EðT Þ is the modulus at a temperature T , E u is the modulus at room temperature and E r is the relaxed modulus of a material. In equation (2), k and T 0 are variables obtained by fitting the data using regression analysis. The value of T 0 was recommended when the modulus fell rapidly (assumed T g values).
An empirical model proposed by Gu and Asaro 41 computes the mechanical properties of the laminates as a function of temperature using degradation parameters. The equation is given by where T ref is the temperature at which the modulus tends to zero, T r is the ambient temperature and g is a power index between 0 and 1.    Mahieux and Reifsnider 42 predicted the degradation of stiffness of FRP as a function of temperature which has the effect of breaking, relaxing and increasing intermolecular bonds in the polymeric matrix. Their empirical model is given by where T 0 is the relaxation temperature and n is the Weibull exponent. A close fit of the data could be achieved with several possible n values between 0 and 1. The coefficient k in equation (2), g in equation (3) and n in equation (4) were determined using an Excel solver. Regression analysis was carried out to achieve the minimum error between storage modulus and empirical models. Figure 9 shows the comparison between E 0 of CE laminate and targeted empirical models. The minimum square errors based on equation (3) and equation (4) were between 6.28% and 8.0%. While equation (2) has a close correlation to the experimental result. The errors were between 0.71% and 0.82% as the frequencies changed from 1 to 100 Hz. Figure 10 shows the comparison between E 0 of 0°C laminates with the specified empirical models. The descriptive empirical model provided in equation (4) moved away from E 0 curve as the temperature exceeded 86°C. The minimum square errors were between 8.95% and 9.33%. In the case of equation (3), the minimum errors were between 5.92% and 6.39%. The empirical model provided in equation (2) has close correlations. The errors were between 0.70% and 0.80% as the frequencies changed from 1 to 100 Hz. Figure 11 shows a comparison of measured E 0 of À20°C laminates with the targeted empirical models. The empirical models specified in equation (4) deviate from the curves when the temperature exceeds 72°C. The minimum errors were between 9.19% and 9.41%. While the errors in the case of equation (3) were between 4.98% and 6.65%. The empirical model denoted in equation (2) has close correlations. The errors were between 0.99% and 1.38% as the frequency increased from 1 Hz to 100 Hz. Figure 12 illustrates the comparisons of E 0 of À80°C laminates with the specified empirical models. Empirical models provided in equations (3) and (4) correlate with measured data below 70°C. The minimum errors were between 3.56% and 12.42%. While the empirical model represented in equation (2) has a close correlation. The errors were between 2.44% and 3.09% as the frequencies increase from 1 to 100 Hz.

Proposed empirical model
The storage modulus of laminates was compared with the empirical models. Based on the least square regression analyses, the empirical model represented in equation (2) is chosen to predict the E 0 of laminates with the minimum square errors being less than 5%. The values of coefficients were determined by calibrating the test data. The parameters used to minimize the errors are given in Table 2.

Conclusions
The mechanical properties of CFRP laminates at different testing temperatures and frequencies were assessed using the DMA tool and a tensile testing machine. The following observations and conclusions could be drawn: 1. The compressive strength, tensile strength, and tensile modulus of laminates are not significantly affected below 25°C. This indicates that the epoxy chain segment motion was frozen and tightly compacted, and small elastic deformations occur at low temperatures. 2. At a temperature of 75°C, the compressive strength, tensile strength, and tensile modulus of laminates decrease by 66.85%, 19.20%, and 16.58%, respectively, compared to room temperature. When the test temperature increases to 100°C, the compressive strength, tensile strength, and tensile modulus of laminates decrease by 92.89%, 67.33%, and 65.99%, respectively, compared to room temperature. In this case, the load-carrying capacity of the carbon fibre is severely compromised. 3. The stiffness parameters of laminates decreased as the testing temperature increased. This happens due to the presence of higher mobilization of the epoxy matrix in the rubbery region. The highest damping property was observed on À80°C laminates. Based on this, CFRP material is noted to have good vibration capacity in moist conditions and is recommended for use in the spar cap sections. 4. Finally, the storage modulus results were compared with empirical models to reduce the material, test costs, and design time. The empirical model developed by Gibson et al. 40 was found to be accurate in predicting the storage modulus of laminates in the temperature and frequency ranges implemented in the present study.