Moisture absorption and cyclic absorption–desorption characters of fibre-reinforced epoxy composites

Abstract

In this study, the temperature effects on moisture diffusion of epoxy resin and its glass/carbon fibre-reinforced epoxy composites in distilled water were tested. In 70 °C, their diffusion coefficients were found 20.9 times, 16.5 times and 29.5 times higher than those in room temperature (25 °C); meanwhile, their saturated moisture contents were measured increased by 1.68 times, 2.39 times and 2.55 times, respectively. Furthermore, a cyclic moisture absorption–desorption experiment of composite materials was designed and implemented. The results revealed that moisture weight gain is no longer well described by Fick’s law during the second and the third cycle of moisture absorption processes, e.g., moisture diffusion coefficients in these two periods are obviously higher and lower than the predictions by Fick’s law during the first half and second half of moisture absorption processes. A flux-dependent moisture diffusion model proposed represents this phenomenon. In this model, moisture diffusion coefficient is formulated exponentially depending upon water flux. Flexural strength degenerations of the bulk epoxy and composite materials were tested corresponding to saturated state and re-dried state of per cycle, after three moisture absorption–desorption cycles, the dry state strength retention rates of bulk epoxy, UD-GFRP and UD-CFRP are 93, 79 and 80%, and in wet state these rates decrease to 53, 48 and 78%, respectively.

Introduction

Fiber-reinforced epoxy composites (aka fiber-reinforced plastics, FRPs) have merits of high specific strength, high specific stiffness, good property designability and good fatigue and corrosion resistances; thus, they have found wide applications in many industries. For example, they are potential candidate materials used in marine engineering and naval ships for their inherent good corrosion resistances [1, 2]. For ships, the another benefit of composite application in their structure design is the significant reduction in structural weight and consequently, cargo carrying capacity is increased and fuel is saved [3]. In present, FRPs have increasingly used in superstructure and hull structures of navy ships [3].

However, epoxy matrix composite is vulnerable to hygrothermal aging in high temperature and high humid environments. Moisture absorption degrades mechanical properties of composite reversibly or irreversibly [4,5,6,7,8,9]. Water absorption can plasticize and soften epoxy matrix in composite and results in its stiffness as well load-bearing capacity decreasing. The moisture swollen can also introduce structural dimension change or additional load of dimension mismatch. These adverse impacts to properties partly recover after moisture desorption. On the other hand, the mismatch of thermal and humid expansion rates for fiber and matrix is possible causing micro-scale residual stress which might introduce diffuse micro-cracks in matrix or debonding of fiber/matrix interface. This damage is permanent and notably degrades mechanical properties of composite. Therefore, hygrothermal behavior is critical for durability of composite especially serving in high temperature and high humid circumstance.

For carbon fiber-reinforced plastic (CFRP) and glass fiber-reinforced plastic (GFRP), reinforced fibers are considered non-hygroscopic or moisture absorption ignorable. Moisture is absorbed mainly by epoxy matrix or fiber/matrix interphase. The moisture properties of composites, e.g., moisture diffusion rate and saturated moisture content, are influenced by many factors which have been studied extensively [10,11,12]. Among these factors temperature is found the one of the most ones. Elevated circumstance temperature notably increases the moisture diffusion coefficient and the saturated moisture concentration of polymers and polymer matrix composite.

Many researchers reported that moisture uptake of epoxy matrix composites can be characterized by Fick’s law; in other words, it is named as Fickian moisture diffusion. Shen and Springer gave the analytic solution of Fick equation in 1975 [13]. However, some studies have found that it often no longer follows Fick’s law in case of long-term measurements [14,15,16], especially for conditions of high temperature and high humid. Moisture absorption is often observed to increase continually after it has reached the saturation concentration predicted by Fick’s law. This phenomenon is called two-stage moisture uptake. Moisture absorbed in polymer material consists of two parts: one is moisture freely diffusing into the polymer, and the other is the water polymerized with hydrophilic groups. The former is assumed following Fick law and dominating the early stage of water uptake; the latter contributes the moisture weight gain in late period. Scholars added an additional water uptake term in Fick equation, and his model is named as Langmuir equation. Gurtin [15] gave a solution of one-dimensional Langmuir equation; Suri [16] further simplified the expression of this solution.

The molecular structure of polymer chain as well as micro-defect state in epoxy matrix composite is possibly change with moisture absorption (and also desorption) process, and these changes will lead variations of moisture behaviors in macro-phenomena level. Compared with monotonous moisture uptake, the study on cyclic of absorption–desorption for composite materials is relatively rare. Sun et al. [17] studied the effects of temperature and cyclic moisture aging on shear strength of carbon fiber/bismaleimide; they found that wet–dry cycles led to diffusion coefficient increase and the saturated concentration decrease. Lin and Chen [18] adopted molecular dynamics method and experimental way to study the processes of monotonous moisture absorption and cyclic moisture absorption–desorption. The experiment results revealed that the reabsorption speed is faster than the first one. The process of moisture sorption–desorption–resorption does not exactly fit Fick’s law, e.g., Fick’s law underestimates the diffusion speed during first half of resorption and overestimates it in the second half of resorption. Unfortunately, this phenomenon was not explored by the authors. Yagoubi et al. [19] studied the water sorption–desorption–resorption of a thermosetting epoxy resin and found two-stage phenomenon all in absorption and resorption processes. They suggested a phenomenological reaction–diffusion model to describe this behavior. Cyclic moisture absorption–desorption of epoxy matrix composites exhibits a quit complicity and has not been well understood in mechanism and well predicted by model.

In this paper, monotonous and cyclic moisture diffusion properties of an epoxy resin and its CFRP/GFRP were investigated. The temperature-dependent moisture diffusivities and saturated contents of these three materials were measured; though moisture absorption curve for bulk epoxy resin meets Fick’s law well, two-stage features are observed in curves for its composites in long-term period. Moisture diffusion rates in these three materials were found all increasing with the cycle of resorption, and meantime water uptake curves deviate Fick’s predictions increasingly. An empirical formula was proposed to represent this variation. The retentions of flexural strength for epoxy resin matrix and its CFRP/GFRP decrease in a decelerated way with cycles of moisture absorption–desorption. A form uniform model was employed to predict the strength aging of these three materials under conditions of both dry state and wet state.

Basic theories

Fick’s law

Diffusion is the result of random molecular movement in mass, and its math governing equation is similar to that of heat conduction process. This factor was recognized by Fick in 1855, and he gave a material diffusion equation which is similar to heat conduction. For one-dimensional diffusion problems of isotropic materials, the Fick’s equation can be written as follows:

$$ J = - \,D\frac{\partial C}{\partial x} $$

(1)

where $J$ is the flux rate in section perpendicular to flux direction, $C$ is the concentration of diffusing material, $D$ is the diffusion coefficient, and $x$ is the diffusion direction.

Moisture diffusion in composites is a kind of mass diffusion; therefore, it meets Fick’s law. If the diffusion coefficient keeps constant in the process of water diffusion, take the derivative of both sides of Eq. (1) with $x$ which can obtain another expression of Fick’s law, namely Fick’s second law:

$$ \frac{\partial C}{\partial t} = D\frac{{\partial^{2} C}}{{\partial x^{2} }}. $$

(2)

For an initially dry state plane sheet specimen of thickness $h$, the boundary conditions are assumed to be constant $C_{0}$ at both surfaces as shown in Fig. 1; the diffusion equation and boundary conditions can be expressed as:

$$ \begin{aligned} &\frac{\partial C}{\partial t} = D\frac{{\partial^{2} C}}{{\partial x^{2} }} \\ &C(x,0) = 0 \\ &C(0,t) = {\text{C}}_{0} ,C(h,t) = {\text{C}}_{0} \\ \end{aligned} $$

(3)

Figure 1

Schematics of boundary condition and moisture concentration distribution versus time of one-dimensional moisture diffusion

Solving the differential Eq. (3) with the method of separation of variables, the time-dependent concentration distribution along the thickness direction can be derived as:

$$ C(x,t){\text{ = C}}_{0} \left( {1 - \frac{4}{\pi }\sum\limits_{k = 1}^{\infty } {\frac{1}{2k - 1}\sin \frac{(2k - 1)\pi }{h}x \cdot {\text{e}}^{{ - \frac{{(2k - 1)^{2} \pi^{2} Dt}}{{h^{2} }}}} } } \right) $$

(4)

$C(x,t)$ is the moisture concentration at point its distance from central plane is $x$ at time $t$.

The analytical expression of the weight gain of one-dimensional moisture diffusion process can be obtained by integrating the concentration $C(x,t)$ in the thickness, i.e., $x$, direction.

$$ W(t) = {\text{C}}_{0} h\left( {1 - \frac{8}{{\pi^{2} }}\sum\limits_{k = 1}^{\infty } {\frac{1}{{(2k - 1)^{2} }} \cdot {\text{e}}^{{ - \frac{{(2k - 1)^{2} \pi^{2} Dt}}{{h^{2} }}}} } } \right) $$

(5)

where $W(t)$ is the weight gain at time $t$.

Diffusion coefficient $D$ is determined from the initial slope of moisture uptake $W(t)$ versus $\tau$, the square root of time, as $\tau = \sqrt t$.

$$ D{ = }\frac{{\pi h^{2} }}{16}\left( {W^{\prime } (\tau )} \right)^{2} . $$

(6)

Langmuir equation

Langmuir equation describes a two-stage phenomenon of moisture absorption in which concentration is still increasing after it has reached the saturation state predicted by Fick’s law. The Langmuir equation can be written as follows:

$$ \begin{aligned} &D\frac{{\partial^{2} C}}{{\partial x^{2} }} = \frac{\partial C}{\partial t} + \frac{\partial c}{\partial t} \\ &\frac{\partial c}{\partial t} = \beta C - \alpha c \\ &\beta {\text{C}}_{\infty } = \alpha {\text{c}}_{\infty } \\ \end{aligned} $$

(7)

where $C$ denotes the free water concentration, and its saturated value is $C_{\infty }$, $c$ is the bound water concentration, and $c_{\infty }$ is its saturation concentration. Two positive constants $\alpha$ and $\beta$ denote the probabilities of water releasing and bonding in composites during unit time, respectively. When the rates of free and bound water reach the equilibrium state, moisture absorption is considered as saturated in second uptake stage.

Solving Eq. (7), considering the following hypothesis of $\alpha ,\beta \ll \frac{{D\pi^{2} }}{{h^{2} }}$, concentrations of free water and bound water over time can be expressed as:

$$ C(x,t) = {\text{C}}_{\infty } \left( {1 - \frac{4}{\pi }\sum\limits_{k = 1}^{\infty } {\frac{1}{2k - 1}\sin \frac{(2k - 1)\pi }{h}x \cdot {\text{e}}^{{ - \frac{{(2k - 1)^{2} \pi^{2} Dt}}{{h^{2} }}}} } } \right) $$

(8)

$$ c(x,t) = \frac{\beta }{\alpha }C_{\infty } \left( {1 - \frac{4}{\pi }\sum\limits_{n = 1}^{\infty } {\frac{1}{2n - 1}\sin \frac{(2n - 1)\pi }{h}x \cdot {\text{e}}^{ - \alpha t} } } \right). $$

(9)

It can be seen that Eq. (8) is same with Eq. (4), this concentration is the Fickian part. Integrating the sum of two water concentrations along thickness of $h$, the water gain is obtained:

$$ \begin{aligned} G(t) & = \int_{0}^{h} {(C(x,t) + c(x,t)){\text{d}}x} \\ & = G_{So} \left[ {\frac{\alpha }{\alpha + \beta }\left( {1 - \frac{8}{{\pi^{2} }}\sum\limits_{n = 1}^{\infty } {\frac{1}{{n^{2} }}} {\text{e}}\frac{{ - n^{2} \pi^{2} Dt}}{{h^{2} }}} \right) + \frac{\beta }{\alpha + \beta }\left( {1 - {\text{e}}^{ - \alpha t} } \right)} \right]. \\ \end{aligned} $$

(10)

The detailed steps of the solution could be found in references [15, 16].

Experiments

The materials used in the moisture uptake experiment include bulk epoxy resin of WSR618, unidirectional E-glass fiber-reinforced composite (UD-GFRP) and unidirectional T300 carbon fiber-reinforced composite (UD-CFRP). The matrix of these two UDs was WSR618 epoxy. For these three kinds of specimens, the curing agent is xylylene amine and the plasticizer is dibutyl phthalate. Epoxy, curing agent and plasticizer were mixed with ratio of 10:2:1; they were stirred evenly to remove small bubbles. Two UDs were made by vacuum-assisted resin injection (VARI). All the specimens of bulk epoxy and UDs were cured in 50 °C drying oven for at least 36 h. Thickness of bulk epoxy, UD-GFRP and UD-CFRP specimens was measured of 1.51, 0.71 and 0.90 mm in average, respectively. The fiber volume contents of UD-GFRP and UD-CFRP were 41% and 39%, respectively. All the specimens of these three materials were cut to 50 mm × 50 mm, and their lateral surfaces were coated by waterproof coating to avoid edge effect.

Moisture absorption tests were conducted using water bath method with constant temperature. Before moisture absorption, the specimens were placed in the 60 °C oven for dehydration processing until the weight has no change. Their initial weights were measured by AL-104 electronic balance. The weight gains were calculated by the following formula:

$$ M_{t} = \frac{{W_{t} - W_{0} }}{{W_{0} }} \times 100\% $$

(11)

where $M_{t}$ is percentage of weight gain, $W_{0}$ and $W_{t}$ are weights of specimen at initial and $t$ moments.

To investigate the influence from temperature to moisture absorptions for both bulk epoxy and composites, the specimens were divided into two groups, one group was dipped in 25 °C distilled water, and the other group was dipped in 70 °C distilled water.

In order to reveal the variation of moisture behavior of composite with the moisture experience, cyclic moisture absorption–desorption experiment was designed for both UC-GFRP and UC-CFRP. For shortening experiment duration, the water bath temperature was used of 70 °C. In this experiment, the thickness of bulk epoxy resin specimen was reduced to 1 mm for letting its saturation time identical to the Fickian saturation times of UD-GFRP and UD-CFRP. Periods of water absorption and desorption in one cycle were chosen both as 110 h, or in this time duration moisture diffusion is dominated by free water process and water uptake still described by Fick’s law, as illustrated afterward in “Dependences of moisture absorptions of bulk epoxy and its composites on temperature” section. Within this period, the bulk epoxy resin and the two composites can nearly reach the Fick’s saturated contents from dry state under 70 °C, or desorbed to dry state in dry oven from state of Fick’s saturated moisture content under the same temperature.

Three cycles of absorption–desorption of the three sorts specimens were carried out in distilled water at 70 °C. One complete cycle needs total 220 h and the thoroughly dry condition of specimen was judged as the weight variation rate less than 1/10000 between two weight measures.

Flexure strength of all three materials was tested at initial dry state, saturated state re-dry state of each moisture absorption–desorption cycle. The experiments were conducted by INSTRON2360 material testing machine according to the test standard of ASTM D7264. The flexure strength was calculated by following formula:

$$ \sigma_{f} = \frac{3P \cdot l}{{2b \cdot h^{2} }} $$

(12)

where $\sigma_{f}$ is the tension stress at the outer surface at mid-span, $P$ is the applied force, $l$ is the support span, $b$ is the width of specimen, and $h$ is the thickness of specimen.

The maximum positive strain locates at the bottom surface of middle point of specimen; it is:

$$ \varepsilon = \frac{6\omega h}{{l^{2} }} $$

(13)

$\omega$ is the maximum deflection of the specimen.

The Chord method is used to measure the flexure modulus of materials. Two points on stress–strain were selected corresponding to 25% and 50% of the limit strain, respectively. The modulus can be expressed as:

$$ E{ = }\frac{\Delta \sigma }{\Delta \varepsilon } $$

(14)

where $E$ is the bending modulus; $\Delta \sigma$ and $\Delta \varepsilon$ denote the stress and strain increment between the two selected points.

Result and discussion

Dependences of moisture absorptions of bulk epoxy and its composites on temperature

Moisture uptake curve of bulk epoxy, UD-GFRP and UD-CFRP specimens in 25 °C and 70 °C distilled water is shown in Figs. 2, 3 and 4, respectively. The temperature rising significantly accelerates diffusion speeds and saturated contents for all three materials as shown in Figs. 2–4. From these figures, one can find the moisture uptake process of bulk epoxy keeps complying with Fick’s law under both room and elevated temperatures. For UD-GFRP and UD-CFRP, in early stage water uptakes can meet well with the Fick’s predictions, but in later period they deviate Fick’s model greatly. The moisture weight gains are observed still increasing after the saturation points predicted by Fick’s law. The two-stage water uptake phenomenon for composites is more notable under higher temperature. This phenomenon suggests that the fiber/matrix interface plays a non-ignorable role in moisture diffusion process for composite. Additionally, the microscopic hygrothermal residual stress has possibility of introducing micro-defects in composite which could become moisture concentrated port.

Figure 2

Moisture absorption of bulk epoxy under different temperatures

Figure 3

Moisture absorption of UD-GFRP under different temperatures

Figure 4

Moisture absorption of UD-CFRP under different temperatures

The Langmuir equation is found well to describe both Fickian part water uptake and two-stage water uptake phenomenon of moisture uptake of composite.

The moisture parameters of Fick’s model for bulk epoxy resin and of Langmuir model for UD-GFRP and UD-CFRP are fitted from the experimental curves and are listed in Table 1.

Table 1 Moisture absorption model types and model parameters of three materials

Cyclic moisture absorption–desorption of bulk epoxy and its composites

The absorption periods of the three water absorption–desorption cycles for bulk epoxy, UD-GFRP and UD-CFRP in 70 °C water bath are shown in Figs. 5, 6 and 7, respectively. The fitted Fick curves from these experiment data are also illustrated in these figures. From these figures, we could see that moisture diffusion coefficients of all three materials increase with the cycle index in water absorption period. It is also worth noting that for the two UDs the experimental water gains do not conform the fitted Fick’s curves anymore from the second cycle; for the bulk epoxy resin this inconformity appears in the third cycle. For the water absorption processes which are not well fitted by Fick’s law, their experimental water uptake rates are higher than Fick’s predictions during their first halves, and lower than Fick’s predictions during their second halves.

Figure 5

Cyclic absorption characteristics of bulk epoxy

Figure 6

Cyclic absorption characteristics of UD-GFRP

Figure 7

Cyclic absorption characteristics of UD-CFRP

The moisture contents at 110 h of bulk epoxy resin and UD-GFRP and UD-CFRP increase after the cyclic moisture absorption–desorption process. The absorption–desorption period is not long enough, so the two-stage phenomenon in Figs. 6 and 7 was not notably demonstrated. Merely in Fig. 6, one can find water uptake rate for the third absorption process obviously increases again at around 40 h after a short period of it approaches to flat. This could be considered an evidence that absorption–desorption cycle advances the second period of the two-stage water uptake process of composite.

For these three specimens, the top weight gains in a cycle (110 h) increases and the dry weight in a cycle (220 h) decreases with the number of cycle increasing, as listed in Table 2. The scanning electron microscope (SEM) photographs of bulk epoxy specimen surface at original state and after three absorption–desorption cycles are visually compared in Fig. 8, where water dissolved pits are observed on the surface of the samples which have experienced three absorption–desorption cycle. Besides surficial mass loss, some polymer segments inside also believe dissolving out. This explains the weigh lost in the re-dry state. The tiny channels left by the dissolved mass promotes water penetration process and so elevates the water uptake rates likewise moisture contents in 110 h in a cycle for all the three kinds specimens.

Table 2 Weight change rate (%) after cyclic absorption–desorption process

Figure 8

SEM photographs of bulk epoxy after cyclic absorption- desorption process

Flux-dependent moisture diffusivity on cyclic moisture absorption

From the experiment results of “Cyclic moisture absorption–desorption of bulk epoxy and its composites” section, one can find the moisture absorption process of bulk epoxy, UD-GFRP and UD-CFRP will no longer meet Fick’s law after two cycles of water absorption–desorption process. As shown in Table 2, after cyclic water absorption–desorption process, all these specimens have a small amount of quality reduction at dry state. It is believed that hydrolysis and mass loss of epoxy and epoxy phase in composites take place during the cyclic water absorption–desorption process. The hydrolysis introduced tiny channels inside epoxy material (or epoxy phase in composites) which leads to the promotion of moisture diffusion. The density of the tiny channel in a position is reasonably considered relevant to accumulated water flux which has penetrated there. In 1980, Barrie [20] suggested diffusion coefficient which is a function of water flux, that is:

$$ D_{\text{absorp}} = D_{0} \left\{ {1 + f(F)} \right\} $$

(15)

where $F$ is the water flux, and $D_{0}$ is the original diffusion coefficient. Barrie also pointed out that water flux is proportional to distance to moisture surface in one-dimensional diffusion problem, that is to say, the diffusion coefficient can be converted to a function of distance to surface:

$$ D_{\text{absorp}} = D_{0} \left\{ {1 + f(x)} \right\}. $$

(16)

Barrie gave several expressions of $f(x)$ in polynomial form. Based on this idea, an exponential form flux-dependent moisture diffusion coefficient model on cyclic moisture absorption is proposed in this paper. Flux term in it is formulated as parameters of depth and recycle number in practical form:

$$ D_{\text{absorp}} = D_{0} \left\{ {1 + a{\text{e}}^{{ - \frac{b}{n - 1} - c\left( {\frac{h}{2} - x} \right)}} } \right\},\quad n \ge 2 $$

(17)

where $n$ is the number of the cycle, $h$ is the thickness of the specimen, and $x$ is the distance from symmetry plane, as shown in Fig. 1. $a$, $b$ and $c$ are moisture constants need calibrated by experiment data. We can see that from Eq. (17) the diffusion coefficient reaches largest at moisture surface of a plate-shaped specimen where it experiences maximum water flux. The diffusion coefficient at surface is:

$$ D_{\text{absorp}} = D_{0} \left( {1 + a{\text{e}}^{{ - \frac{b}{n - 1}}} } \right),\quad n \ge 2. $$

(18)

The cycle-dependent surficial diffusion coefficient is calculated through the slope of the weight gain curve at each initial stage of the cycle, and then the value of the coefficient $a$, $b$ is fitted. The whole weight gain points are used to fit a Fickian formula, and the fitted diffusivity is assumed identical to that in a certain depth in specimen. Submitting the fitted diffusivity into Eq. (17) and then parameter $c$ is calibrated. In this study this coordinated depth is chosen as ${h \mathord{\left/ {\vphantom {h 4}} \right. \kern-0pt} 4}$. Original diffusivity $D_{0}$ and parameters $a$, $b$ and $c$ of bulk epoxy, UD-GFRP and UD-CFRP are listed in Table 3.

Table 3 Parameters of flux-dependent model

Submitting depth and cycle number-dependent diffusivity into Eq. (1), it obtains:

$$ \frac{\partial C}{\partial t} = \frac{\partial }{\partial x}\left( {D_{\text{absorp}} \frac{\partial C}{\partial x}} \right). $$

(19)

There is no explicit solution for this variable coefficient differential equation, so a numerical solution is needed. Here it was implemented by using a user-defined field subroutine (USDFLD) on platform of commercial soft package of ABAQUS. The simulation results are shown in Figs. 9, 10 and 11. This model offers improved descriptions of cyclic moisture absorption–desorption processes of the bulk epoxy and its two composites.

Figure 9

Cyclic water absorption simulation of bulk epoxy by flux-dependent diffusion model

Figure 10

Cyclic water absorption simulation of UD-GFRP by flux-dependent diffusion model

Figure 11

Cyclic water absorption simulation of UD-CFRP by flux-dependent diffusion model

Moisture content and cycle-dependent flexural moduli and strengths of bulk epoxy and its composites

Flexural moduli and strengths degradations of bulk epoxy, UD-GFRP and UD-CFRP are shown in Fig. 12a–f, respectively. The original flexural moduli of them are 3.50 GPa, 27.22 GPa and 71.34 GPa, and original strengths of them are 116 MPa, 550 MPa and 851 MPa, respectively. For all these three specimens, both flexural moduli and strengths degrade monotonously with the water absorption–desorption recycle, especially for the latter. This is the evidence that water absorption–desorption cycle introduces damages in epoxy material likewise in epoxy matrix phase (and fibre/matrix interface) in composites. The degradations are more notable in wet state than those in dry state attributing to factor that the moisture plasticizing of epoxy material is not only detrimental to its strength, but also weakens the support effect of matrix to fiber, thus causing fiber failure in advance. After three moisture absorption–desorption cycles, for dry state flexural moduli retention rates of bulk epoxy, UD-GFRP and UD-CFRP are 89, 93 and 87%; flexural strengths retention rates are 53, 48 and 78%, respectively. For wet state, retention rates of flexural moduli are 77, 82 and 85%; strength retention rates are 93, 79 and 80%, respectively.

Figure 12

Cyclic absorption–desorption effects on three-point bending

The environmental aging of composites can be characterized by the following formula [21]:

$$ \Pi =\Pi _{0} + \phi \left( {1 - {\text{e}}^{ - \delta t} } \right) - \varphi ln\left( {1 + \theta t} \right) $$

(20)

where $\Pi$ and $\Pi _{0}$ mean the physical (or mechanical) property of material in original state and environmental degraded state, respectively, $\phi$, $\delta$, $\varphi$ and $\theta$ are parameters of the material relevant to postcure and aging, and $t$ is the aging time.

To represent the influence of moisture state on the retentions of materials property, a normalized moisture content is employed in Eq. (20) in this study. Ignoring the postcure effect on composite, Eq. (20) is rewritten as:

$$ \Pi =\Pi _{0} - \left( {\varphi + k \cdot \frac{{C_{t} }}{{C_{\infty } }}} \right)ln(1 + \theta \cdot n) $$

(21)

$$ \frac{{C_{t} }}{{C_{\infty } }} = \left\{ {\begin{array}{*{20}l} 0 \hfill & {\text{dry state}} \hfill \\ 1 \hfill & {\text{saturated state}} \hfill \\ \end{array} } \right. $$

(22)

where $k$ is a constant, $C_{t}$ and $C_{\infty }$ are moisture concentration and saturated concentration of the composites, respectively, and $n$ is the moisture absorption–desorption cycle number. The retention curves of flexural moduli and strengths of the three materials fitted by Eq. (21) are also shown in Fig. 12; the property retentions according to dry and wet states are denoted by red curves and black curves, respectively. The parameters of fitting curves are listed in Table 4.

Table 4 Curve fitting parameters of the three materials

Figure 13 illustrates the photomicrographs (recorded by KH7700 digital display optical microscope) of the failure regions of UD-GFRP and UD-CFRP after three-point bending test. The specimens are according to original dry state, wet saturated and re-dry states in the third cycle. Delamination becomes more visible after cyclic absorption–desorption. More serious delamination occurs at failure region after three moisture cycles compared to the original state.

Figure 13

Profile photomicrograph of UD-GFRP and UD-CFRP after bending test

Conclusions

Firstly, the temperature effects on moisture absorption processes of bulk epoxy and its UD-GFRP and UD-CFRP are studied experimentally. For bulk epoxy, water uptake curve is found well described by Fick’s law under room and elevated temperatures, for the two composites, though during short-term water uptake curves can fit Fick’s predictions, during long-term obvious two-stage phenomenon is observed. Increments of the saturated moisture concentrations of the two composites are much larger than that of bulk epoxy with the same temperature elevation. This is an evidence of that influence from fiber/matrix interface in composites on moisture behaviors is not ignorable. Then, cyclic moisture absorption–desorption of this epoxy and its composites are investigated. Moisture diffusivities of these three materials are found promoted by the absorption–desorption cycle, and mass losses are also measured especially for the two composites. Furthermore, notable deviations between the test and Fickian water uptake data exist for the third round of water reabsorption. A flux-dependent diffusivity model is proposed to interpret this discrepancy. Finally, flexural moduli and strengths of the epoxy and its two UD composites are tested in a three-cycle water absorption–desorption experiment. All of their moduli and strengths trend monotonously decline with the cycle number, but the decline rates are decreasing. Generally, the strength reductions are more notable than modulus reductions for all these specimens, for bulk epoxy this trend is adverse under dry condition. Additionally, in wet condition these declinations are much larger than in dry condition. This phenomenon indicates that water plastication introduced matrix softening greatly reduces the mechanical properties of composites, and these reductions can recover partly by water desorption.

Some results obtained in this study, e.g., non-Fickian moisture behaviors water absorption–desorption cycle process, have rarely reported in-depth in the literature. This phenomenon should receive attention in design of composite structures, especially which serve in environment with severe hygrothermal fluctuation.