Effect of moisture in flax fiber on viscoelastic properties of the manufactured flax fiber reinforced polymer by fractional-order viscoelastic model

Flax Fiber Reinforced Polymer (FFRP) composites, known for their eco-friendliness and mechanical strength, find extensive application in construction. This study investigates the influence of moisture content in flax fiber fabrics on FFRP ’ s viscoelastic properties. Isothermal frequency sweep tests were conducted to assess dynamic mechanical properties under varying moisture levels. The Huet-Sayegh viscoelastic model, with fractional order integration, was employed for analysis. Results indicate optimal viscoelastic properties when fabric humidity matches manufacturing conditions. However, the correlation between the loss factor and the humidity is not straightforward. In summary, FFRP ’ s capacity to store and dissipate energy diminishes with the increased moisture content, but the reduction does not follow a specific pattern with humidity levels.


Introduction
Fiber reinforced polymer composites (FRP) made of polymer matrix and fiber fabrics offer widespread application in engineering products.Their advantages include high strength, convenient manufacturing, resistance to fatigue and corrosion, as well as a substantial reduction in structural self-weight.However, the predominant use of carbon and glass fiber poses environmental concerns due to their high energy consumption and non-renewable nature.In response to the growing emphasis on environmentally friendly construction materials, there has been a rapid development in the usage of natural fiber derived from plants.Flax fiber emerges as a promising alternative to traditional fiber in the construction industry.Flax Fiber Reinforced Polymer (FFRP) has successfully served various construction objectives, e.g. the reinforcement for concrete columns [1], concrete beams [2], and working in sandwich panels alongside core foam [3][4][5].Notably, in 2016, Eindhoven, the Netherlands, witnessed the construction of the first pedestrian bridge around the world which was entirely crafted from FFRP [6].This pioneering engineering venture underscores the considerable potential of FFRP in constructing load-bearing structures.However, more thorough research is required because the mechanical performance of flax fiber is sensitive to external variables, especially moisture.
The vulnerability of FFRP to moisture is attributed to the porous microstructure of flax fiber [7], which results in higher moisture absorption capacity than other kinds of fiber (e.g.glass fiber) [8,9] and fiber volume expansion after water absorption [10].Thuault et al. revealed a significant decrease in flax fiber in the tensile test when the fiber was exposed to relative humidity exceeding 68 % [11].In parallel research, Burges et al. observed that though the strength of the flax-epoxy laminate remains unaffected, the tensile modulus experiences a substantial reduction [12] when the samples were placed in a high relative humidity environment.Kollia et al., through hydrothermal aging tests on flax fiber/bio-based resin composites, noted an irreversible decrease in both strength and stiffness [13].Wang et al. explored chemical treatment methods for flax fiber, demonstrating that such treatments can effectively mitigate moisture absorption [14].
Another characteristic of flax fiber that differs from synthetic fiber is its obvious viscoelastic properties.The relationship between moisture in the environment and the viscoelasticity of FFRP has been attempted to be established in previous studies.Li et al. [15] conducted an impact hammer test on FFRP beams manufactured in environments with various humidity levels, the damping ratio of the beams was found to increase with relative humidity.According to Prabhakaran et al. [16], the damping ratio of FFRP is 51.03 % higher than that of the glass fiber composites.The viscoelastic nature of flax fiber and energy dissipation at the fiber-matrix interface are the main causes of this phenomenon [17].Xu et al. [18] investigated the viscoelasticity of the FFRP samples in different humidity levels and found that increasing humidity could lead to a decreasing storage modulus in FFRP.Although it has been acknowledged that humidity has an impact on the viscoelastic property of FFRP, previous research primarily examines moisture content in the manufactured FFRP sample.Separate consideration of how fiber moisture content specifically affects the viscoelastic performance of the final FFRP product has not been fully studied.
The mechanical characteristics of a structure constructed from flax fiber are significantly influenced by its moisture content, as demonstrated by earlier studies.The research by Moudood et al. [19] on the tensile and flexural properties of the FFRP samples made with flax fiber pre-conditioned in environments with various humidity levels indicated that both the strength and stiffness of the material increased with the humidity level.However, the tensile strength of the FFRP sample is highest when flax fiber is pre-conditioned at around 50 % RH.Lu et al. [20] found that composites made of flax fiber with various moisture content showed different moisture sorption behavior and instantaneous mechanical properties.This phenomenon was attributed to the change arising in the interface between the fiber and the matrix due to the volume change of the flax fiber.Changes in the moisture content of flax fiber can cause changes in the microstructure of FFRP, thus affecting its mechanical properties.The viscoelastic properties of FFRP have been studied extensively in earlier studies.However, the specific influence of flax fiber's moisture content on the viscoelastic properties of FFRP remains unclear.
The calculation model is powerful for analyzing and comparing FFRP's dynamic viscoelastic behavior of the FFRP made of fiber with different moisture content as it enables parameterization of the viscoelastic properties of FFRP.Several calculation models have been proposed in previous research to present the viscoelastic change of the FRP material.Cardoso et al. [21] proposed a model for the Glass-FRP by taking glass fiber as an elastic Hook spring and the matrix is represented as the Hook spring and Newton dashpot together.Considering the viscoelastic characteristic of the flax fiber, the analysis of FFRP needs a more accurate constitutive model in the description of its viscoelasticity.The Burgers model and Kelvin-Voigt model are both popular models for the viscoelastic behavior of polymer-based composites [22,23].These models express the viscoelasticity of the material using series and parallel combinations of springs and dashpots.However, the performance of the Burgers model in high frequencies load is not ideal and it can't reflect the change of viscoelastic properties in different temperatures due to the lack of temperature-related parameters in their equations.
The schematic diagram of the Huet-Sayegh model is shown in Fig. 1  (a).It has been proven valid for the analysis of FRP composites in the practical analysis regardless of frequencies [24].There are two additional variable dashpots in the model which could provide a more accurate representation of the viscoelasticity [25].The two variable dashpots defined as Eq. ( 1) are rheological elements that represent the viscoelasticity determined by temperature.Therefore, the value of the parameter a ranges from 0 to 1.
where i is the complex number while i 2 = − 1, ω is the frequency of the load during the test (rad/s), η is the dimension of viscosity (Pa⋅s), and τ is a constant depends on time.
The Huet-Sayegh model can be expressed by integrating rheological elements into the model: where E 0 is the amount of complex modulus when there is an infinitesimal frequency (ω), E ∞ is the amount of complex modulus when there is an infinite loading frequency, and δ 1 and δ 2 are constant parameters.
There is a limited application of the Huet-Sayegh model in previous research due to the challenge of determining its complex parameters.To define the complex models accurately and easily, fractional derivatives are employed in the viscoelastic models to replace the integer-order differential models [26][27][28][29][30].By integrating the Riemann-Liouville fractional derivative as a coefficient term in the Huet-Sayegh model, fractional calculus can be integrated into the Huet-Sayegh model [31]: where D α is the differential operator for the order in Huet-Sayegh mode, and the parameter α is between 0 and 1. Hence the Huet-Sayegh parametric model with Fractional order differential treatment could be presented as: While set E 1 =E 2 =E, τ 1 =τ 2 , by integrating the above equations, the storage and loss modulus can be transferred to: where A=τ α ω α , B=τ β ω β .
The objective of this study is to investigate how the moisture content of flax fiber affects the viscoelastic properties of FFRP by investigating the FFRP samples manufactured with flax fabrics pre-conditioned in different humidities.The dynamic mechanical analysis experiment is employed in the research and the results were arranged with the differential Huet-Sayegh model.The viscoelastic performance of FFRP manufactured with flax fabrics pre-conditioned in different moisture content has been studied.The performance of FFRR under loading frequencies ranging from 10 − 8 Hz to 10 12 Hz is studied and compared to provide design parameters as a reference.The effects of moisture content in fiber fabrics and finished products on FFRP samples are also compared and reported.

Sample preparation
Using the vacuum infusion procedure, 40 % of the fiber volume was used to create the FFRP samples.Unsaturated polyester (Polynt S.p.A.).made up the matrix of the unidirectional flax fiber fabrics (Bcomp Ltd., areal density 300 g/m 2 ).Before infusing the resin, the fiber fabrics were firstly dried in a vacuum drying oven, then divided into six groups and placed in different environments with relative humidity ranging from 11 % RH to 97 % RH until the fabrics got a constant weight.The flax fiber fabric was weighed every 12 hours until the weight remained unchanged for three consecutive times, and it was considered that the fiber was saturated with water under this humidity.As stated in Table 1, the hygroscopicity equilibrium of saturated salt solutions in a small space granted the environment's consistent humidity.During the infusion of resin, the vacuum pressure was kept at − 1 Bar compared with the atmosphere pressure.The initial 6-hour curing period was followed by a 120 • C heating of the vacuum infusion system.Then the manufactured FFRP plate was cut into pieces in size 50×5×0.6(mm), and the fabricated samples were stored at 60 % relative humidity for at least two weeks until the test.The stress-strain relationship of the FFRP studied in this research is presented in supporting information Figure S1.

DMA test
The isothermal dynamic sweep test was carried out on the DMA Q800 analyzer with a tension clamp system (Fig. 1(b)).The isothermal mode was employed with a temperature interval of 20℃ ranging from 20℃ to 180℃.During each isothermal step, changing loading frequency was applied to the sample range from 0.01 Hz to 10 Hz.The dynamic amplitude during the test was 15 μm.During the test, the storage modulus, loss modulus, and loss factor were recorded under each isothermal step at various loading frequencies.

Moisture absorption
The moisture absorbed by the flax fiber fabrics was calculated by the increase in weight as follows: where t is the conditioning time, M r (t) is the ratio of the moisture absorbed (%) in flax fiber fabrics at time t, M(t) is the weight measured at time t, and M 0 is the dried weight measured after the fabrics taken out from drying oven.Table 1 lists the saturated moisture amount of the flax fabrics in various humidity levels following Eq.( 7).

Dynamic mechanical analysis (DMA) results
Direct measurements of the storage and loss moduli are made during the isothermal step tests.The material's capacity to store elastic energy during deformation is shown by the storage modulus, represented by the letter E', while its capacity to release energy during the deformation is indicated by the loss modulus, represented by the letter E''.The ratio of the loss modulus to the storage modulus is often expressed as tan (δ) = E''/E′, and it is known as the loss tangent.This dimensionless quantity provides insight into the relative amounts of elastic and viscous behavior exhibited by a material.As either of the storage modulus and loss modulus can help to provide viscoelastic models in Eq. ( 5) and Eq. ( 6), the storage modulus measured would work as the basic data to calculate the parameters in Eq. ( 5) to build the fractional-order model to describe the viscoelastic behavior of the FFRP and compare the effect of moisture in flax fiber in the manufactured FFRP samples.
Fig. 2 shows the variations in the storage modulus E' with frequency.It was discovered that the storage modulus increases with the loading frequency.The trend was not affected by the humidity conditions.Meanwhile, the storage modulus decreased while the temperature was increasing.This is explained by how the material's dynamics and molecular structure change as temperature rises.However, it was found the proportion of elastic modulus decreased with temperature gradually when the temperature was over 140 • C.This phenomenon suggests that the glass transition of FFRP samples occurred between 120 • C and 140 • C.This is because the material almost completely lost its ability to recover with a low storage modulus and began to convert to a rubber state at this temperature.Because of the material's rubber condition at this point, the impact of frequency on the storage modulus was also decreasing.
The storage modulus was sorted out using the time-temperature superposition principle (TTSP) to further evaluate the link between fiber loading frequency and viscoelasticity.Using Eq. ( 8), a master curve for the storage modulus was created.

Eʹ
( where ω is the testing frequency, ω ref is the reference frequency, T is the temperature during the test, T ref is the reference temperature, and α T is the factor for shifting calculated by the Arrhenius equation. where C 1 and C 2 are determined constant factors, R is the universal gas constant (8.314J/mol), and E a is the calculated activation energy.As a result, the findings in Fig. 2 can be adjusted to construct the storage modulus master curve which spans a larger frequency range, as illustrated in Fig. 3.A polynomial fitting was carried out on the master curves obtained in Fig. 3 following the Huet-Sayegh Model with fractional order equation as shown in Eq. ( 3) to Eq. ( 6) to fulfill the viscoelastic model.The parameters used for constructing master curves are listed in supporting information Table S1.The loss modulus and loss factors could be presented by the Huet-Sayegh Model for the parametric study.
The viscoelastic properties including storage modulus, loss modulus, and loss factor of FFRP manufactured with flax fiber pre-treated in different humidity environments are presented in Fig. 4(a) to (c).These results indicate a consistent viscoelastic behavior across all environments.Specifically, the storage modulus (E') exhibits a monotonic increase with the loading frequency, suggesting a positive correlation between the storage modulus E' and the applied frequency.While the loss modulus E'' demonstrates an initial increase, reaching a peak followed by a decline as the frequency continues to rise.When the relative humidity of the fiber treatment is below 60 % RH, the storage modulus increases monotonically with the relative humidity.However, the FFRP sample with fiber pre-treated in 75 % RH presents a storage modulus of less than 11 % RH fiber and the difference gets bigger and bigger as the

Table 1
The saturated moisture content in flax fiber.frequency increases.Samples with fiber in 97 % RH present a storage modulus similar to 33 % RH in all frequency ranges.Similar rules can also be found in the study of the loss modulus peak interval with loading frequency ranging from 10 − 4 to 10 4 Hz.The loss factors that characterize the damping or energy dissipation properties of a viscoelastic material present a different changing mode from storage modulus and loss modulus.The flax fiber treated at relative humidities between 50 % and 97 % exhibits similar tan [[___]]amp; values, whereas the fiber treated at 11 % relative humidity before manufacture shows a significantly higher loss factor, approximately 1.5 times greater than the average value of other conditions.Previous research on FFRP has demonstrated that the impact of moisture on FFRP's viscoelastic properties primarily manifests in its effect on both the flax fiber and the fiber-matrix interface.Through the analysis of scanning electron microscope (SEM) results, it is found that both the microfibril and the fiber-matrix interface are affected by the initial moisture of flax fiber before the manufacture of FFRP.For the samples made of flax fiber conditioned in a very low humidity level (11 % RH), traces of microfibrils being embedded in each other can be found within the fiber bundles, which indicates there was squeezing between microfibrils and resulted in cracks in the area around the fiber bundle.Such a phenomenon indicates that dry flax fiber absorbed water and expanded when it was exposed to laboratory humidity, which caused serious damage inside the fiber.Such damage resulted in the lowest storage modulus and loss modulus.The corresponding situation is that the FFRP sample made of high moisture content flax (fiber in 97 % RH) presents a relatively high storage modulus and loss modulus but is still lower than the FFRP samples made of fiber pretreated in 60 % RH.As for the FFRP made of fiber pretreated in 50 % RH, since the fiber is manufactured and tested at 60 % RH, both the interior of the fiber bundle and the fiber-matrix interface remain stable and thus exhibit the best deformation and energy dissipation capacity.It's found the FFRP sample with 97 % RH fiber presents obvious porosity in the fiber-matrix interface which is believed to severely decrease the elastic property.However, within the fiber bundle, the bonds between the fiber are much tighter compared with the FFRP made of fiber pretreated in 50 % RH and 11 % RH.Fig. 5 The results of the test further indicate that there might be a partial monotonic relationship between the water content of flax fiber and the viscoelastic properties of FFRP: when the humidity is below 60 % RH, the storage modulus and loss modulus had an upward correlation with the water content of the fiber.Given the testing environment is at 60 % relative humidity, it is speculated that the fiber performs best in terms of storage modulus and loss modulus when the fiber treatment humidity is near the ambient humidity of use.This speculation aligns with the conclusion of previous studies on the instantaneous mechanical properties of FFRP which suggested keeping the manufacturing humidity consistent with the usage environment of FFRP [20].However, more experiments are needed to further confirm the validity of the theory in FFRP viscoelastic analysis.
As a dimensionless quantity, the loss factor provides insight into the ability of a material to dissipate energy using the ratio of the loss modulus to the storage modulus.The results show that when the processing humidity of flax fiber ranges from 30 % to 97 %, the loss factors remain relatively stable, suggesting consistent damping properties under these conditions.However, at very low moisture levels (fiber conditioned in 11 % RH), though both the storage modulus and loss modulus decreased, the loss factor increased significantly, indicating  enhanced damping performance.The elasticity of the FFRP is primarily determined by the high elastic properties of the crystalline cellulose in the flax fiber while the cellulosic polymer and amorphous cellulose in the fiber as well as fiber-matrix interface are responsible for the viscoelastic behavior.The reason for this phenomenon could be that when the moisture content of the fiber is very low during manufacturing, and it works in a high-humidity environment after manufacturing, the expansion of the fiber due to moisture absorption would destroy the crystalline cellulose inside the fiber and reducing the elastic properties of the FFRP.Nevertheless, a tighter interface between the fiber bundle and the matrix can enhance the energy dissipation capabilities of Fiber-Reinforced Polymer (FRP).Additionally, it is hypothesized that hydrogen bonds formed by water molecules contribute to strengthening the interfacial bond between the fiber and the matrix.
The results of this study differ markedly from previous research on the impact of humidity on the viscoelastic properties of fabricated Fiber-Reinforced Polymer (FRP) specimens [18].For the manufactured FFRP, the storage modulus and loss modulus are negatively correlated with the relative humidity of the specimens, while for the specimens made of flax fiber fabrics conditioned at different humidity, there is no monotonic correlation between their viscoelasticity and the relative humidity conditioning flax fiber.This variation highlights the different mechanisms through which humidity during manufacturing and subsequent service affects the viscoelastic properties of Fiber-Reinforced Polymers (FRP).These findings indicate that to optimize viscoelasticity, it is essential to carefully control humidity levels both during the fiber processing stage and within the final FRP product.

Conclusion
This study has investigated the impact of moisture in flax fiber fabrics absorbed before manufacture on the viscoelastic performance of the manufactured FFRP.Through the application of isothermal frequency sweeping tests and analysis using the updated Huet-Sayegh model with fractional differential elements, the study has illustrated the relationship between pre-conditioning humidity and FFRP's viscoelastic properties.
The key conclusions of this study are as follows: • The fractional-order modified Huet-Sayegh model effectively describes the viscoelastic properties of FFRP, confirming its suitability for modeling the viscoelasticity of FFRP manufactured with flax fiber conditioned varying humidity conditions.• When the flax fiber is conditioned in an environment with relative humidity (RH) below 60 % (RH of the conditioning environment for manufactured FFRP sample), both storage modulus and loss modulus of FFRP increase with the RH for conditioning flax fiber before manufacture.The samples made of fiber conditioned in 11 % RH present the highest loss factors while samples made of fiber conditioned in higher RH present similar loss factors.• The effect of humidity change on the viscoelasticity of FFRP is different during the manufacturing process and the use process.It is essential to carefully control humidity levels both during the fiber processing stage and within the final FRP product to optimize the viscoelasticity of FFRP.
Further research is suggested to explore broader environmental conditions, particularly different relative humidities beyond the 60 % used in this study, to better understand the interaction between manufacturing and use environments.Such studies will help in enhancing the predictability and environmental robustness of FFRP.

Declaration of Competing Interest
The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Fig. 2 .
Fig. 2. Relationship between storage modulus and loading frequency under different environments.

Fig. 3 .
Fig. 3. Master curves of the relationship between storage modulus and loading frequency.

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Fig. 4 .Fig. 5 .
Fig. 4. A comparison of viscoelastic properties in different relative humidity under a reference temperature of 120 • C.

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