## 1. Introduction

Fiber-reinforced polymer (FRP) composites such as Carbon FRP (CFRP), Glass FRP (GFRP) and Aramid FRP (AFRP) have been widely used in infrastructure construction and other fields [

1,

2,

3,

4,

5,

6,

7,

8,

9,

10,

11]. However, large-scale applications of FRP composites in infrastructure construction are still limited for some reasons, e.g., high cost of CFRP and AFRP composites, poor chemical stability of GFRP composites [

12,

13,

14,

15,

16]. Over the past few years, basalt fiber has gradually received more attention as a new inorganic green fiber for its environment-friendly features. The basalt fiber is made of basalt stone after melting at 1450–1500 °C. There is no pollution during its production process [

17,

18]. The basalt fiber has a greater elongation at break than carbon fiber, higher elastic modulus, and greater chemical stability than glass fiber, and lower cost than carbon fiber and aramid fiber [

18,

19,

20,

21]. Moreover, the basalt fiber is also a good flame retardant [

21,

22]. Therefore, basalt FRP (BFRP) composites are increasingly used in civil engineering, such as externally strengthening sheets of reinforced concrete (RC) structure. The literature [

23,

24] revealed that BFRP laminates would be degraded due to the strong alkaline environment inside concrete (pH = 12–13), and such degradation would be further accelerated when the BFRP laminates were exposed to hygrothermal environments. The reason is that the resin matrix of BFRP laminates is highly sensitive to the change of the temperature and the moisture [

25,

26,

27], which is seriously harmful to BFRP laminates. Therefore, the hygrothermal ageing properties of BFRP laminates in alkaline solution need to be studied.

At present, some researches [

28,

29,

30,

31,

32] have been done on the hygrothermal ageing properties of BFRP laminates subjected to alkaline solution. Lu et al. [

28,

29] investigated the long-term mechanical properties of pultruded BFRP laminates after a long-term immersion. The test results showed that as the increase of immersion time, the water absorption increased, and the tensile strength and interlaminar shear strength decreased dramatically due to the severe interfacial debonding between the basalt fiber and resin matrix after ageing. Ma et al. [

30] tested the tensile strength of BFRP laminates fabricated by the vacuum assistant resin infusion (VARI) method. The tensile strength of BFRP specimens decreased by 37% and 34% at 20 °C and 40 °C for distilled water and decreased by 67% and 90% for alkaline solution after 180 ageing days, respectively. Xiao et al. [

31] studied the tensile properties of wet-layup BFRP laminates. After immersion of 180 ageing days, it was observed that a higher temperature (e.g., 60 or 80 °C) would cause a greater reduction of tensile strength during the same ageing time. Wu et al. [

32] studied the degradation of basalt fiber and BFRP laminates and concluded that the tensile properties of BFRP laminates were superior to that of basalt fiber in alkaline solution. The tensile properties reduction of BFRP laminates might be attributed to the severe degradation of interfacial adhesion between the basalt fiber and epoxy resin, which was observed by scanning electron microscopy (SEM) images, rather than the ageing of basalt fibers. It can be concluded from the existing studies that the long-term mechanical properties of BFRP laminates were greatly affected by the hygrothermal environment. A higher temperature and alkaline solution would aggravate the ageing process, leading to a severe interfacial debonding between the basalt fiber and resin matrix.

Although the above researches showed that the hygrothermal ageing properties of BFRP laminates have been studied by many test methods, the long-term durability of BFRP laminates still cannot be evaluated comprehensively. One reason is that different specimen thicknesses (ranging from 0.45 to 4.5 mm) were adopted for test specimens in the existing researches [

21,

28,

30,

31,

32,

33]. For example, Lu et al. [

28] measured the water absorption of BFRP specimens with a thickness of 1.4 mm, which were immersed in 60 °C distilled water, and found that water absorption was 0.32% after 90 days of ageing. Xiao et al. [

31] also immersed the BFRP specimens with a thickness of 1.0 mm in the 60 °C distilled water for the same ageing time (i.e., 90 days), while the water absorption of the specimens was 2.8%. Lu et al. [

29] studied the tensile properties of the BFRP laminates with a thickness of 1.4 mm in alkaline solution. After ageing for 90 days, the tensile strength retention of the BFRP laminates decreased to 71.9%, 61.1%, and 56.8%, respectively, at 20, 40, and 60 °C. As reported by Xiao et al. [

31], the tensile strength retention of 1.0 mm thickness BFRP laminates decreased to 77.3%, 33.3%, and 40.8% after the immersion in alkaline solution for 90 days. It can be seen from the above studies that although the same hygrothermal ageing tests were conducted for BFRP laminates, the test results cannot be compared directly due to the difference of specimen thickness. It has been reported that the durability test results of FRP composites were probably dependent on the dimensions of the adopted specimen. For example, the influence of diameter on the long-term durability of FRP bars was previously investigated [

34,

35]. According to the existing test results [

34,

35], for the same ageing time, the deterioration degree of BFRP bars was inversely related to the diameter of the specimen, which means that the specimen dimension should not be neglected on exploring the durability of BFRP composites. Therefore, the investigation of the influence of specimen dimension (especially specimen thickness) on long-term durability of BFRP laminates was very necessary.

Additionally, the ageing time adopted in above hygrothermal ageing tests was much shorter than the actual service duration of FRP composites, meaning that these test results were unsuitable to evaluate the long-term performances. Therefore, some efforts have been made to explore test methods to accelerate the ageing process of FRP composites. So far, the temperature-dependent accelerated ageing method was widely adopted in hygrothermal ageing tests [

36,

37]. The efficiency of the accelerated test is highly dependent on the accelerated factor, which is determined by experimental parameters. For example, the accelerated factor of temperature-dependent acceleration is calculated by considering at least three ageing temperatures in the test. In theory, the greater accelerated effect could be achieved by using higher test temperatures. However, the accelerated efficiency of temperature-dependent acceleration for FRP composites was not improved significantly because the adopted ageing temperature must be lower than the glass transition temperature (

T_{g}) of FRP composites [

36]. The excessive ageing temperature would change the resin matrix of FRP composites from glassy to viscous fluid status, deteriorating the properties severely and changing the ageing mechanism. To this end, it is significant to explore alternative accelerated ageing methods for which the aforementioned limitation should be solved.

In this paper, the influence of specimen thickness on the water absorption behavior and tensile properties of BFRP laminates in 60 °C deionized water and alkaline solution were first experimentally investigated. Through analyzing and summarizing the rules between the specimen thickness and the test results, an accelerated ageing method dependent on specimen thickness was proposed for the water absorption and tensile strength of BFRP laminates. Two accelerated ageing factors were theoretically established considering specimen thicknesses for water absorption and tensile strength of BFRP laminates, respectively. The test results were also adopted to verify the accuracy of the proposed method. The proposed accelerated ageing method in this study provides a new way for the prediction of the long-term ageing properties of BFRP laminates, which is simple and easy to apply.

## 5. Theoretical Model of Accelerated Factor

The above experimental results indicated clearly that the water absorption and tensile strength retention of BFRP laminate were dramatically influenced by specimen thickness. As illustrated in

Figure 3 and

Figure 6, it could be observed that the ageing degradation (i.e., the changing trends of water absorption and reduction of tensile strength retention) of BFRP laminates with thinner specimens was more severe than that of thicker specimens when the BFRP laminates were soaked in the solution for a same long time. Therefore, there is a possibility to deduce an accelerated ageing model based on specimen thickness for water absorption and tensile strength retention of BFRP laminates under hygrothermal ageing environment. In this section, a theoretical accelerated ageing model based on specimen thickness was developed and the accelerated factors (

AFs) related to specimen thickness were theoretically deduced.

#### 5.1. Accelerated Factor of Water Absorption

Considerable researches show that the water absorption of FRP composites can be described by two models as shown in

Figure 13, i.e., the Fick’s model and Two-stage model [

39,

42,

51]. The Fick’s model assumes that the initial phase of water absorption increases linearly with

t^{1/2} in the initial phase, and then increases non-linearly until the water absorption reaches a dynamic equilibrium without obvious changes. For the Two-stage model, the water absorption is identical to Fick’s model in the initial phase. But the water absorption cannot reach the equilibrium stage due to the water immersion constantly and the degradation of resin matrix. In the current study, the test results of water absorption conform to the Two-stage model.

According to the ageing mechanism reported in the literature [

49,

50], the following assumptions can be used to establish the water absorption model. First, the specimens with different thicknesses have the same diffusion rate for the same immersion solution because the diffusion rate is controlled by the concentration gradient of the immersion solution. Second, although the water absorption at the regular time varies with specimen thickness, the ageing mechanism of the composite remains unchanged. Third, the specimens with different thicknesses fabricated by the same material will eventually reach the same water absorption rate under the same immersion solution.

The Fick’s and Two-stage models can be used to describe the relationship between specimen thickness and ageing time in stage I (mass gain due to swelling of FRP composites) and stage II (mass loss due to relaxation of FRP composites), respectively. In the two models, the stage I of water absorption is identical. The Fick’s model is shown in Equation (5), but it is difficult to find the relationship among different parameters in this expression, which is needed to be simplified as presented in Equation (6) [

36,

40].

where

M_{∞} is the effective moisture equilibrium content,

D is the diffusion coefficient.

When two specimens with the thicknesses of

h_{1} and

h_{2} soaked in the same solution reach the same water absorption at ageing time

t_{1} and

t_{2}, respectively. The equilibrium equation, i.e.,

M(

t_{1}) =

M(

t_{2}) can be expressed as Equation (7) according to Fick’s model, which can be simplified to Equation (8).

According to the previous assumptions, the diffusion coefficient

D is identical when the specimens are soaked in the same solution, yields

Therefore, the

AF of water absorption in stage I of Two-stage model can be expressed in

After the above derivation of

AF in Stage I, it can be found that there is a certain relationship between ageing time

t and specimen thickness

h indeed. To further explore the relationship between water absorption, ageing time

t and specimen thickness

h in stage II of Two-stage model, the abscissa of water absorption curves can be changed from

t^{1/2} to

t/

h^{2}, as shown in

Figure 14. According to the literature [

48], the changing the abscissa (from

t^{1/2} to

t/

h^{2}) does not change the trends of water absorption in Stage I and Stage II. The water absorption curve of Two-stage model in Stage II was regarded as declining linearly that is determined by the slope of the descending section,

tanα, which is only related to the materials of FRP composite and conditional environment [

42,

51]. It is known clearly that the

tanα of water absorption curves in Stage II is identical for the specimens B

_{1} B

_{2} and B

_{4} due to the same materials of BFRP laminates and conditional environment. Therefore, in the whole Stage II of the Two-stage model, the relationship between water absorption

M(

t) at any given time and the maximum water absorption

M_{m} can be expressed as

When the specimens with two thicknesses

h_{1} and

h_{2} reach the same water absorption at

t_{1} and

t_{2}, respectively, the equilibrium equation can be expressed as Equation (12)

Equation (12) can be simplified as

It has been known by the derivation of Stage I in the two water absorption models that the Equation (10) is applicable when the value of water absorption increases to

M_{m}, i.e.,

Thus, the AF of stage II in Two-stage model can be expressed by Equation (10).

Therefore, the accelerated factor based on specimen thickness for water absorption is deduced theoretically, which can be applied in Fick’s model and Two-stage model.

#### 5.2. Accelerated Factor of Tensile Strength Retention

When the tensile specimens are soaked in the solution, the tensile strength decreases due to the gradual increase of the ageing area. The ageing condition of tensile specimens can be represented by the change of the cross section as shown in

Figure 15, which is assumed that the specimen is uniformly aged along the thickness direction on the upper and lower sides. Thus, the actual tensile strength

σ can be expressed by Equation (15).

where

σ_{u} and

σ_{a} are the initial (unaged) and residual (aged) tensile strength of the specimen, respectively.

A_{u} and

A_{a} are the unaged area and aged area of the specimen, respectively.

b and

h are the width and thickness of the specimen, respectively.

x is the total ageing depth along the thickness of the laminates.

It has been reported by study [

49,

52,

53] that the total ageing depth

x of the laminates is proportional to the square root of the immersion time

t, which is as follows regarded as a function of

where

α is a constant of the FRP composite that is irrelevant to specimen thickness

h.

Then Equation (15) can be transformed as follows

According to the literature [

50,

54], for the given resin matrix, fiber, fabrication and immersion condition, the specimens with different thicknesses will decrease to the same strength when the ageing time is long enough. As a result, the equilibrium equation can be expressed as Equation (18) when the tensile strengths of the specimens when two thicknesses,

h_{1} and

h_{2}, decrease to the same value at ageing time

t_{1} and

t_{2}, respectively.

Thus, the AF of tensile strength retention of BFRP laminates can also be written as Equation (10).

From the previous theoretical derivation, for BFRP laminates with two thicknesses, when the water absorption or tensile strength retention of the BFRP laminates with two different thicknesses reaches the same value, the ratio of the ageing time of the BFRP laminates with the two thicknesses is proportional to the square of the ratio of the corresponding two thicknesses. The square of the ratio of the two thicknesses is considered as accelerated factor (AF). As a result, it is feasible to accelerate ageing by reducing the specimen thickness. For example, if the water absorptions or tensile strength retentions of two BFRP laminates with different thicknesses reach a certain same value, the predicted ageing time of thicker specimen (t_{1}) can be calculated/accelerated by multiplying the real ageing time of thinner specimen (t_{2}) by the corresponding accelerated factor, AF = (h_{1}/h_{2})^{2}, based on the two thicknesses of the thicker specimen (h_{1}) and thinner specimen (h_{2}).

#### 5.3. Model Validation and Discussions

In this study, the ageing accelerated method was taking the BFRP specimen with the thickness

h = 4 mm as the standard specimen. The

AFs of BFRP specimens with

h = 1 mm,

h = 2 mm, and

h = 4 mm are calculated by Equation (10) and the results are shown in

Table 3. The obtaining of accelerated ageing days is transformed by multiplying the actual ageing days of the thicker specimen by the corresponding

AF based on the two thicknesses of the thicker specimen and the standard specimen. According to the existing test results, the accelerated time is up to eight years on the water absorption trend and tensile strength retention of BFRP specimen with

h = 4 mm. It should be noted that the transformed results of the specimens with 1 and 2 mm represent the predicted results of the standard specimen

h = 4 mm.

Figure 16 shows the long-term prediction of water absorption of BFRP specimens with

h = 4 mm according to the transformed results of 1 and 2 mm specimens in deionized water and alkaline solution. The predicted curves were fitted by using Matlab (2018a Version, MathWorks, Inc., Massachusetts, USA, 2018). It can be seen from

Figure 16 that the predicted curves are fitted well with a Two-stage model in whole. It reveals that the predicted law of water absorption in deionized water was better with Two-stage model than that in alkaline solution.

Figure 17 shows the long-term prediction of tensile strength retention of BFRP specimens with

h = 4 mm according to the transformed results of 1 and 2 mm specimens in deionized water and alkaline solution, which is also fitted well with Phani-Bose’s model [

55] in whole.

Compared with the traditional temperature-dependent accelerated ageing method, there are two main advantages of the proposed new specimen thickness-dependent accelerated ageing method in this study. First, the proposed thickness-dependent accelerated ageing method is easy to apply because this method does not need the activation energy, which must be required in the temperature-dependent method. In order to obtain the activation energy in the temperature-dependent method, at least three different temperature environment tests must be conducted [

56], which increases the test difficulty. In contrast, the accelerated factor calculating in the proposed method is only dependent on specimen thickness, which would be easy to be conducted. Second, the

AF of the temperature-dependent accelerated ageing method is limited due to the limitation of

T_{g} of FRP composites, leading to the acceleration times being relatively small. The

AF of the proposed method is only dependent on specimen thickness and thus eliminates the limitation of

T_{g}. Therefore, greater

AF can be obtained in the proposed method.

## 6. Conclusions

In this paper, the BFRP laminates with the thickness of h = 1, h = 2, and h = 4 mm were fabricated by wet-layup method and the influence of thickness on their water absorption and tensile properties were experimentally studied under hygrothermal environment as well as degradation mechanism. A specimen thickness-dependent accelerated ageing method was proposed. The following conclusions can be drawn from the testing results and discussions in this study:

The long-term properties of BFFRP laminates were greatly affected under hygrothermal environment. The water absorption trend of BFRP laminates soaked in both 60 °C deionized water and alkaline solution increased first before reaching their peak water absorption and then decreased with the increase of immersion duration, which was caused by the hydrolysis of the epoxy matrix. The tensile properties of BFRP laminates degraded apparently after ageing, especially in alkaline solution. SEM images show basalt fiber deteriorated due to the solution immersion.

Specimen thickness had a significant influence on the water absorption and tensile strength of BFRP laminates after ageing. When the BFRP laminates with different thicknesses were immersed in the water or alkaline solution for the same ageing time, the water absorption decreased in early stage of immersion and then increased in late stage of immersion as the specimen thickness increased, while the tensile strength retention kept increased during the whole ageing process. The reason is that the ratio of aged area to the total area in the thinner specimens was larger than that of the thicker specimens, leading to the more severe ageing degree of the thinner specimens.

An innovative thickness-dependent accelerated ageing method for water absorption and tensile strength retention of BFRP laminates was proposed, in which the accelerated factors were theoretically deduced based on specimen thickness. The proposed method is in good agreement with test results. Compared with the traditional accelerated ageing method based on temperature, the proposed method is much easier to be conducted and has the potential to obtain a greater accelerated factor.