Effect of geometric dimensions and fibre orientation on 3D moisture diffusion in flax fibre reinforced thermoplastic and thermosetting composites

Accepted Manuscript Effect of geometric dimensions and fibre orientation on 3D moisture diffusion in flax fibre reinforced thermoplastic and thermosetting composites Abderrazak Chilali, Mustapha Assarar, Wajdi Zouari, Hocine Kebir, Rezak Ayad PII: DOI: Reference:

S1359-835X(16)30448-1 http://dx.doi.org/10.1016/j.compositesa.2016.12.020 JCOMA 4525

To appear in:

Composites: Part A

Received Date: Revised Date: Accepted Date:

10 July 2016 15 December 2016 18 December 2016

Please cite this article as: Chilali, A., Assarar, M., Zouari, W., Kebir, H., Ayad, R., Effect of geometric dimensions and fibre orientation on 3D moisture diffusion in flax fibre reinforced thermoplastic and thermosetting composites, Composites: Part A (2016), doi: http://dx.doi.org/10.1016/j.compositesa.2016.12.020

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Effect of geometric dimensions and fibre orientation on 3D moisture diffusion in flax fibre reinforced thermoplastic and thermosetting composites Abderrazak Chilali a*, Mustapha Assarar a, Wajdi Zouari a, Hocine Kebir b, Rezak Ayad a a

b

University of Reims Champagne-Ardenne, LISM EA 4695, IUT de Troyes, 9 rue de Québec 10026 Troyes cedex, France

Sorbonne Universities, University of Technology of Compiègne, Roberval Laboratory (UMR 7337), Research Center of Royallieu, BP20529, 60205 Compiègne, France

Abstract In this work, we investigate the diffusion behaviour of twill flax fabrics reinforced thermoplastic and thermosetting composites elaborated by the vacuum infusion technique. Water absorption tests were conducted by immersing composite specimens into tap and salt water at room temperature. In particular, the effects of aspect ratio, thickness and fibre orientation are considered. The principal three-dimensional (3D) diffusion parameters are identified by 3D Fick’s and Langmuir’s models using an optimization algorithm. It is found that the flax reinforced thermoplastic composite absorbs less water than the flax thermoset composite. In addition, the obtained absorption curves indicate that the equilibrium mass gain linearly increases with fibre orientation, decreases with thickness and strongly related to the diffusion rate. Furthermore, 3D water diffusion kinetics are shown to depend on the samples aspect ratio and governed by a privileged direction. Keywords: Flax fibre; water ageing; 3D diffusion models, thickness effect, fibre orientation effect, edge effect.

1. Introduction The problem of moisture ingress into natural fibre reinforced polymer composites is of great importance in different sectors in particular the automotive and the marine industries [1-4]. Indeed, the presence of moisture in these materials can significantly affect their general properties and may lead to a limitation of their use. Therefore, it is crucial to investigate and understand the diffusion kinetics in this type of materials when exposed to humid conditions to ensure their expansion and development. Several works dealing with the ageing of natural fibre reinforced thermosetting

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composites have been published up to now (see [5-12], among others). A large number of these contributions indicate that the fibre-matrix interface of natural fibre reinforced polymer composites plays a major role in their long term durability. Indeed, water diffusion at the fibre-matrix interface induces differential swelling of the natural fibre principally related to its hydrophilic character [13]. Consequently, fibre swelling could develop stress at the interface level and then causes damage and micro-cracking of the matrix which further aggravates water uptake [3, 14]. These mechanisms are well discussed by Le Duigou et al. [12] who investigated the influence of wet ageing on flaxepoxy micro-composites constituted of single flax fibres embedded in epoxy microdroplets. In particular, Le Duigou et al. [12] found that the apparent interfacial shear strength quickly decreases with the immersion time. Concerning natural fibre reinforced thermoplastic composites, the number of contributions dealing with their ageing remains limited and they principally concern composites reinforced with short fibres [15-17]. For instance, Espert et al. [15] studied water absorption and its influence on the mechanical properties of four short fibres (sisal, coir, cellulose from pulp, Luffa sponge) reinforced polypropylene composites. Water absorption tests were conducted by immersing these composites in water at three different temperatures: 23, 50 and 70 °C. The authors found that the process of water absorption follows the kinetics and mechanisms described by Fick’s theory. In addition, the diffusivity coefficient depends on the temperature as estimated by Arrhenius’s law. In another work, Doan et al. [17] investigated the ageing behaviour of short jute fibre reinforced polypropylene composites subjected to a relative humidity of 95% at 25°C. In particular, it was found that the diffusion process follows a Fickian behaviour and an increase in moisture absorption is obtained with fibre content. The same observations

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were reported by Assarar et al. [18] in the case of short hemp fibre reinforced polypropylene composites. In addition to that, the durability of natural short fibre reinforced biopolymers was also investigated in some works [1, 2, 19-23]. For example, Le Duigou et al. [1] studied the effect of seawater ageing, at different temperatures, on the properties of short flax fibre reinforced PLLA (Poly(l-Lactic acid)) composites. They found that the weakening of the fibre-matrix interface is the main damage mechanism induced by seawater ageing, which leads to the reduction of the mechanical properties of flax-PLLA composites. In another work, Regazzi et al. [21] studied the influence of coupled hydro-mechanical ageing on short flax fibre reinforced PLA biocomposites with varied fibre contents. They reported that the mechanical loading, combined with water immersion, results in a strong loss of stiffness especially for flaxPLA composites with high fibre fractions. To analyse the diffusion kinetics in synthetic fibre reinforced polymer composites, several authors used 3D Fick’s model to identify the diffusion parameters [24-26]. Pierron et al. [25] proposed a novel method to identify 3D moisture diffusion parameters of glass-epoxy composites from gravimetric curves based on an optimization algorithm to fit experimental data. In a more recent work, Post et al. [26] used the method developed by Pierron et al. [25] to analyse water diffusion kinetics in selectively sealed glass-polyester samples. Contrary to synthetic fibre reinforced composites, water diffusion in long natural fibre reinforced thermoset composites has been principally analysed by one-dimensional (1D) approaches [5, 8, 15-17]. To the authors best knowledge, only one contribution has investigated moisture absorption in flax fibre reinforced epoxy composites by considering 3D Fick’s model [9]. Saidane et al. [9] found that the morphology and anisotropy of the flax fibre have a significant influence

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on the diffusion direction. Diffusion kinetics predicted by 3D Fick’s model were found to be in good agreement with the experimental curves. The identification of the diffusion parameters is a necessary step to understand the diffusion kinetics in natural fibre reinforced composites. Their evolution with respect to several parameters such as reinforcement architecture, fibre and resin natures, temperature, fibre treatment and ageing conditions has been thoroughly investigated in several works [5, 8-11, 15, 17]. Despite these valuable contributions, works dealing with the effects of sample geometric dimensions and fibre orientation are limited and the few studies found in the literature principally deal with synthetic fibre reinforced composites. For instance, Boukhoulda et al. [27] studied the effect of fibre orientation on moisture diffusion in unidirectional glass-epoxy and carbon-epoxy composite materials. They reported that fibre orientation influences the humidity concentration in glass and carbon composites. The lowest values of humidity concentration calculated through the thickness of the composite plates correspond to the 90° fibre orientation. In an earlier work, Neumann and Marom [28] studied the moisture absorption of graphiteepoxy composites of different fibre contents and fibre orientations under different mechanical stress levels. They found that there is no significant change in diffusion parameters when varying fibre orientation. In this work, we investigate water diffusion in twill flax fabrics reinforced liquid thermoplastic and thermoset resins aged in tap and salt water at room temperature. Sealed and unsealed composite samples were immersed in water in order to determine their 1D and 3D diffusion parameters based on Fick’s and Langmuir’s models using an optimization algorithm. In particular, the effects of sample aspect ratio, thickness and fibre orientation on the diffusion parameters of both composites are examined.

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2. Materials and methods 2.1 Materials and manufacturing process In this study, two laminate materials constituted of 2/2 twill flax fabrics reinforced thermoplastic and thermoset resins were fabricated using the vacuum infusion process. Flax fabrics were provided by Depestele group with an areal weight of 330 g/m2 and a density of 1450 kg/m3. The thermoplastic resin is based on a high-molecular-weight acrylic polymer and commercialized by Arkema company under name Elium 150. Its polymerization is initiated by 2-3 % peroxide compounds (Luperox A40FP-EZ9) and its density is equal to 1190 kg/m3. The thermoset matrix is the SR 8100 epoxy resin associated with the SD 88225 hardener (mixing ratio of 100:33 by weight) and this mixture density is about 1158 kg/m3. This resin and its associated hardener were provided by Sicomin. The manufactured thermoplastic and thermoset laminates are composed of several layers of twill flax fabrics. The number of layers was chosen so as to obtain plates with thickness of ~ 3, 4, 6, 8 and 10 mm for both composites. In the following, flax fibre reinforced Elium and epoxy composites are designated by Flax-Acrylic and FlaxEpoxy, respectively. In order to determine the fibre volume fraction and porosity content of each composite plate, the same procedure detailed in Chilali et al. [29] was used. The obtained results are summarized in Table 1. We remark that the increase of thickness does not considerably affect the fibre volume fraction and porosity content of the composite plates. Nevertheless, the Flax-Acrylic plates present a higher fibre volume fraction and lower porosity content than Flax-Epoxy plates. It is worthy to note that flax fabrics were not dried before composite manufacturing to avoid a decrease in their

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tensile properties [30] which probably explains the obtained void contents. Furthermore, the expression used to calculate the porosity content [29] is very sensitive to sample dimensions so that a very small fluctuation induces an important variation of the porosity content. On the other hand, the porosity content values of Table 1 remain comparable to those reported in the literature [31-33]. For instance, Monti et al. [31] found a void content between 2.5% and 7.5% for a flax-Elium composite elaborated by the liquid resin infusion technique. In another work, Poilâne et al. [33] reported a porosity content between 2% and 13% for several quasi-unidirectional flax fibre reinforced epoxy composites manufactured by the platen press process. 2.2 Composite samples conditioning The laminate plates were cut in square samples of side ~20 mm and thickness ~3 mm by using a diamond cutting disk. In order to force water diffusion in a given direction (1, 2 or 3 with 1 being the warp direction, 2 the weft direction and 3 the thickness direction), the square samples were polished and sealed with silicone as shown in Figure 1. These specific tests aim at assessing the experimental principal parameters D1, D2, and D3 as well as the saturation mass gains M 1∞ , M 2∞ and M 3∞ from 1D diffusion models. The effect of thickness on the diffusive behaviour in Flax-Epoxy and FlaxAcrylic composites was also investigated by considering sealed samples (Figure 1e) with five thicknesses (3, 4, 6, 8 and 10 mm) and the same square surface (20×20 mm2). In order to determine the 3D diffusion parameters, other 20×20×3 mm3 unsealed samples were considered for both materials (Figure 1a). To analyse the aspect ratio effect on moisture diffusion, other unsealed samples with equal thickness (3 mm) and different surface dimensions: 50×50, 100×100 and 180×180 mm2 were also prepared

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(Figure 1a). In addition, the effect of fibre orientation is also investigated by considering 20×20×3 mm3 unsealed samples with fibre orientation of 15, 30 and 45° (Figure 1b). The effect of sample length on the diffusive behaviour was also investigated by considering sealed samples with three lengths (20, 40 and 80 mm) and fixed width 20 mm so as to force water diffusion only in the warp direction (Figure 1d). Specimens of each composite were totally immersed into tap and salt water (with salinity of 37 g/l) at room temperature. They were removed from water at regular intervals of immersion time, wiped dry to remove surface moisture, and then weighed with a balance of ±1 mg precision. It is important to note that the weighing of specimens was performed in a short time period to minimize the discontinuity effects in water diffusion process. After an immersion time t, the amount of absorbed water Mt in composite specimens was calculated using the following expression: Mt =

Wt − W0 × 100 (%), W0

(1)

where W0 is the dry initial weight of each sample and Wt its weight at time t. It is worth noting that the results of section 5 were taken as the average values of at least five samples and a ± max/min standard deviation was used. 3. Analytical models In the literature, several analytical models are proposed to describe water diffusion kinetics in composite materials. The well-known are Fick’s and Langmuir’s models. Fick’s model is often used to describe water diffusion in natural fibre reinforced composites [9, 10, 15] while Langmuir’s model is sometimes considered to predict especially anomalous diffusion processes.

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3.2 Fick’s model The fundamental differential equation allowing to describe moisture diffusion in a given material according to time and space is given by Fick’s law [34]:




 ∂C = div ( D. grad C ) ∂t

(2)

where C is the moisture concentration and D the diffusion tensor which is supposed symmetric. For an anisotropic material, Fick’s law is described by the following equation: ∂C ∂ 2C ∂ 2C ∂ 2C ∂ 2C ∂ 2C ∂ 2C = Dxx 2 + D yy 2 + Dzz 2 + 2 Dxy + 2 Dxz + 2 D yx ∂t ∂x ∂y ∂z ∂x∂y ∂x∂z ∂y∂z

(3)

where Dxx, Dyy and Dzz are the diffusion coefficients through the x, y and z directions, respectively, while Dxy represents the diffusion rate in the x-direction due to a moisture concentration gradient in the y-direction (the same definition holds for Dxz and Dyz). In particular, when the material principal directions (1, 2, 3) coincide with the reference directions (x, y, z), Fick’s law becomes:

∂C ∂ 2C ∂ 2C ∂ 2C = D1 2 + D2 2 + D3 2 ∂t ∂x ∂y ∂z

(4)

An analytical solution to Equation (4) is possible and is given by [34, 35]: 2 2  2   2i + 1 2  2 j +1   2k + 1    exp  −π t  D1  + D2   + D3    3   L    l   h    Mt  8  ∞ ∞ ∞   = 1 −  2  ∑∑∑ 2 M∞  π  i =0 j =0 k =0 ( ( 2i + 1)( 2 j + 1)( 2k + 1) )

(5)

where M∞ is the saturation mass gain and L, l and h are the sample dimensions. When the principal directions 1 and 2 do not coincide with the reference directions x and y (θ ≠ 0°, Figure 1b), the analytical solution of Equation (3) becomes complex. In

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this case, the global diffusion coefficients Dxx, Dyy, Dzz, and Dxy can be expressed in terms of the principal diffusion coefficients D1, D2, D3 and the orientation angle θ as:  D xx = D1 cos2 (θ ) + D2 sin 2 (θ )   D xy = ( D1 − D2 )sin(θ ) cos(θ )  2 2  D yy = D1 sin (θ ) + D2 cos (θ )   D zz = D3

(6)

3.2 Langmuir’s model Langmuir’s model is based on Fick’s laws and introduces two extra parameters γ and

β . The first parameter γ represents the probability of a free water molecule to become bonded to the polymer network and reciprocally β is the probability of a bonded molecule to become free. In this case, the differential equation allowing to predict the moisture diffusion in a composite material, whose principal directions (1, 2, 3) coincide with the reference directions (x, y, z), is given by the following expressions [36]: ∂n ∂N ∂ 2C ∂ 2C ∂ 2C + = D1 2 + D2 2 + D3 2 ∂t ∂t ∂x ∂y ∂z ∂N =γn −βN ∂t

(7)

where n is the quantity of free molecules (by volume unit) diffusing inside the matrix and N the quantity of bonded molecules (by volume unit). An approximated solution to Equation (7) is given by the following expression [36]: Mt M β β e−γ t t + (e − β t − e − γ t ) + (1 − e − β t ) = M∞ γ + β M∞ γ + β

where

Mt is given by Equation (5). M∞

(8)

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4. Optimization procedure In order to identify Fick’s and Langmuir’s models, an optimization algorithm based on the Nelder and Mead method [37] was developed to minimize the quadratic error q between the analytical solution and the experimental points as: n

q=

∑ (M

a

( t k ) − M exp ( tk ) )

2

(9)

k =1

where M a ( tk ) is the moisture content at time tk evaluated from the analytical solutions (Eq. (5) for Fick’s model and Eq. (8) for Langmuir’s model and M exp ( t k ) is the experimental moisture content at time tk. In particular, the optimization problem of Langmuir’s model is solved with two constraints on the probabilities β and γ as explained in [36]:

β << 5.

D3π 2 D3π 2 and γ << h2 h2

(10)

Results and discussion

5.1 Identification of diffusion parameters from 1D Fick’s and Langmuir’s models The aim of this part is to assess the diffusion parameters of Flax-Epoxy and FlaxAcrylic composites from the experimental absorption curves of sealed samples (Figure 2). We recall that for each privileged direction only one diffusion coefficient can be identified from Fick’s model (D1, D2 or D3) and three parameters for Langmuir’s model (Di, βi, γi with i=1, 2, 3). Figure 2 presents a comparison between the experimental and analytical water uptake of the sealed samples. In addition, Tables 2 and 3 summarize the diffusion parameters of Fick’s and Langmuir’s models obtained with the optimization procedure. The results of Figure 2 show that Fick’s and Langmuir’s models correctly describe the evolution of

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water uptake in the studied materials for both ageing conditions. Furthermore, Langmuir’s and Fick’s analytical curves are superimposed (Figure 2). This is due to the fact that the obtained values of the probability γ are negligible compared with β (Table 3). For example, in the case of Flax-Epoxy composite, the probability γ is 900 to 1200 times greater than β. Although the fibre content of Flax-Acrylic composite is ~ 4 % higher than Flax-Epoxy, the saturation weight of the former is ~ 12% lower than that of the latter for the three diffusion directions. This could be related to the porosity content of Flax-Epoxy which is about 22.44% higher than that of Flax-Acrylic. We also remark that both composites present the same diffusive behaviour in the warp and weft directions showing that flax fabrics are well balanced. However, the diffusion coefficients through the thickness direction are found to be 10 to 21 times lower than D1 and D2. Indeed, when water spreads through the fibre direction (warp and weft directions), it essentially infiltrates by capillarity in the micro-cracks of the fibre-matrix interface. This helps the water absorption by the flax fibre hydrophilic components and inside lumen which increases the kinetics of water diffusion in the composite. These explanations are globally confirmed by Scanning Electron Microscope (SEM) observations on the cross sections of 30 days aged Flax-Epoxy and Flax-Acrylic samples as depicted in Figure 3. These composite samples were prepared as follows. First, square shape samples of 20×20 mm2 were cut from the composite plates. Then, they were polished using a double disc polishing machine with 1200 and 600 grit size abrasive papers. After 30 days of water ageing, all specimens were dried in an oven at 40 C to remove water molecules and facilitate SEM observations. In particular, Figures 3a and 3c show that the hollow part of the lumen that was not filled with resin could further contribute to

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water absorption. The size of this hollow part could be related to an incomplete cellulose filling linked to the environmental conditions during flax growing such as drought, lodging and low temperature. Figures 3a and 3c also show that the fibre-matrix interface is severely affected by water absorption which can be related to intermolecular interactions (hydrogen bonding) between water and the fibre surface (cellulose), reducing adhesion between fibres and the matrix [12]. Besides, Figures 3b and 3d reveal several micro-cracks which increase by capillarity the water diffusion in the studied composites. Tables 2 and 3 also indicate that water salinity decreases the kinetics of sorption by ~ 5% to 10 % and the saturation weight by ~ 20% compared with tap water. This decrease is mainly related to the presence of salt molecules and ionic content of salt water in fibre-matrix interface micro-cracks and porosities which reduce diffusion kinetics. 5.2 Identification of diffusion parameters from 3D Fick’s and Langmuir’s models In this section, we try to describe the 3D water diffusion in unsealed Flax-Epoxy and Flax-Acrylic samples using the principal diffusion parameters of sealed specimens determined in section 5.1. Figure 4 shows a comparison between the experimental and analytical water uptake curves of unsealed Flax-Epoxy composite. We remark an important difference between the experimental and analytical results indicating that water diffusion has a more complex behaviour (note that the same difference is obtained for Flax-Acrylic). Accordingly, the use of sealed samples parameters is not appropriate to predict water diffusion in unsealed composites. In this case, a 3D diffusion analysis is necessary to simultaneously determine the diffusion coefficients of Fick’s and

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Langmuir’s models. Figure 5 depicts a comparison between the experimental and analytical water uptake curves. 3D Fick’s and Langmuir’s models are found to correctly fit the experimental results. In addition, Flax-Acrylic composite absorbs less water than Flax-Epoxy, as previously remarked with sealed samples. Tables 4 and 5 summarize Fick’s and Langmuir’s optimal diffusion coefficients, respectively, obtained from the optimization procedure. Although flax fabrics are balanced as verified in section 5.1, the principal plane diffusion coefficients D1 and D2 are found to be overall different. This could be related to the interaction between the water molecules absorbed from each direction. To better understand the 3D water diffusion kinetics in the studied materials, three effects are considered in the following sections. Besides, as 3D Fick’s and Langmuir’s analytical solutions are found practically superimposed in the water uptake curves, only Fick’s model will be used in the following. In fact, it implies a lower computational cost than Langmuir’s model and it is currently the only diffusion model available in the finite element software Abaqus which will be used to simulate the effect of fibre orientation on water diffusion. 5.3 Effect of aspect ratio In this section, the aspect ratio effect on water diffusion in Flax-Epoxy and FlaxAcrylic composites is evaluated. To this end, unsealed samples with equal thickness (3 mm) and four surface dimensions 20×20, 50×50, 100×100 and 180×180 mm2 were immersed in tap water. Figure 6 depicts the obtained water uptake curves and Table 6 summarizes the optimal Fick’s diffusion parameters. These results are further compared

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with those of samples sealed perpendicularly to warp and weft directions as shown in Figure 1e. The water uptake curves of Figure 6 show that the rate of water absorption drops when increasing the aspect ratio of composite samples to reach approximately the same saturation weight. This indicates that the saturation process is mainly governed by the thickness direction. In addition, the saturation weight and diffusion coefficient across the thickness D3 of the 180×180×3 mm3 samples are approximately equal to those of sealed specimens (Table 6). This result clearly illustrates that water mainly diffuses through the thickness for an aspect ratio greater than 60 as D1 and D2 are negligible compared to D3 ( D3 D1 and D3 D2 are ~ 125 for both materials). This result agrees with the ASTM standard that recommends an aspect ratio l/h greater than 100 to avoid edge effects in polymer matrix composites [38]. For the unsealed 20×20×3 mm3 and 50×50×3 mm3 samples, the diffusion coefficient D3 is 3 to 5 times higher than D1 and

D2. This shows that water diffusion along the warp and weft directions is not negligible in this case compared to the diffusion across the thickness. 5.4 Effect of thickness In this section, we investigate the effect of another geometric parameter, which is the sample thickness, on the diffusion kinetics in Flax-Epoxy and Flax-Acrylic composites. To this end, sealed samples with equal surface dimensions 20×20 mm2 and five thicknesses 3, 4, 6, 8 and 10 mm were aged in tap water. All samples edges were sealed so as to force diffusion through the thickness. Figure 7 shows the obtained water uptake curves and Figure 8 depicts the evolution of the diffusion rate and the saturation weight with respect to thickness. The diffusion rate represents the slope of the linear part of the

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water uptake curves. We remark that the diffusion kinetic drops when increasing sample thickness. For example, 3 mm thick specimens of both composites are found to absorb water ~ 50% faster than 10 mm thick samples (Figure 8a). As depicted in Figure 8b, the maximum water uptake decreases quasi-linearly with the thickness which can be attributed to the decrease of water diffusion rate (Figure 8a). The decrease of saturation weight with thickness was also reported in the case of traditional composites [24, 39-41] and several explanations were given. For example, Bunsell [40] related this behaviour to a molecular rearrangement of the polymeric network when samples are thicker which would slow down the water diffusion in the composite. For natural fibre reinforced polymer composites, the variation of the saturation weight with thickness could also be accentuated by the increase of diffusion kinetic which causes more swelling of natural fibres and matrix leading to more micro-cracks in the composite and more absorbed water. To better illustrate the correlation between the diffusion rate and thickness, the thickness variations of 3 mm and 10 mm thick sealed Flax-Epoxy and Flax-Acrylic specimens were measured at saturation. Concerning the 3 mm thick specimens, the thickness measurements showed a swelling of ~ 6.17±0.15 % and ~ 6.05±0.21 % for Flax-Epoxy and Flax-Acrylic composites, respectively, compared to ~5.47±0.13 % and ~5.23±0.24 % for the 10 mm thick specimens. 5.5 Effect of fibre orientation In this section, the effect of flax fabrics orientation on water diffusion in FlaxAcrylic and Flax-Epoxy composites is investigated. Unsealed 20×20×3 mm3 samples with four fibre orientations 0, 15, 30 and 45° (Figure 1b) were aged in tap water. As

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explained in section 3.2, an analytical solution of 3D Fick’s model is not easy to obtain when the principal directions (1, 2, 3) of the laminate do not coincide with the reference axes (x, y, z). Accordingly, the diffusion coefficients of an orientation θ in the reference directions Dxx, Dyy, Dzz and Dxy were determined in terms of the principal diffusion coefficients of non-oriented samples (D1, D2 and D3) using Equation (6). Table 7 summarizes the global diffusion parameters for each fibre orientation. We remark that the diffusion coefficient Dxy increases with the orientation angle θ

reaching a

maximum value at θ = 45°. However, this coefficient remains largely lower than the other in-plane diffusion coefficients Dxx and Dyy. In order to verify if the calculated global diffusion coefficients allow to correctly predict the 3D diffusion behaviour of Flax-Epoxy and Flax-Acrylic samples, a finite element modelling was considered using the commercial finite element code Abaqus. Owing to symmetry, only one eighth of each composite sample was modelled as depicted in Figure 9. Water immersion was modelled by applying constant moisture concentration boundary conditions on the three external faces as explained in Figure 9. The eight-node linear heat transfer hexahedral element DC3D8 of Abaqus was considered in the finite element simulations and water uptake of each composite sample was calculated as an arithmetic average of all nodal moisture concentrations. A preliminary study of convergence was conducted to choose the appropriate mesh giving sufficiently accurate results. It was found that converged solutions are obtained with 51200 elements and this converged mesh was applied to all simulations of Flax-Acrylic and Flax-Epoxy composite materials. Figure 10 shows a comparison between the obtained experimental and numerical water uptake curves and a good agreement between them is found for all fibre

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orientations. In addition, we remark that the diffusion rate and saturation weight increase with fibre orientation. The increase of diffusion rate is principally related to the edge effects and confirms the difference between the principal coefficients D1 and D2 of unsealed samples even though flax fabrics are balanced (Table 4). In fact, if D1 was equal to D2, water diffusion kinetics would be the same for all fibre orientations i.e. Dxx = D1 , D yy = D2

and D xy = 0 (Equation (6)). However, water uptake curves of

Figure 10 clearly show that diffusion kinetics vary with fibre orientation. 5.6 Discussion The analysis of the aspect ratio, thickness and fibre orientation effects presented in the previous sections show that the saturation weight is strongly related to water diffusion rate as depicted in Figure 11 for Flax-Epoxy. Indeed, an increase of ~ 48% in water diffusion rate of the 45° oriented sample compared to the 0° oriented specimen is accompanied by an increase of about ~ 45% in saturation weight. This tendency is also confirmed by considering sealed non-oriented samples with three lengths (20, 40 and 80 mm) and the same width 20 mm so as to promote water diffusion only in the warp direction (Figure 11b). A decrease of ~ 100% in water diffusion rate of the 80 mm length sample compared to the 20 mm length specimen induces a decrease of ~ 30% in saturation weight. Similarly, a decrease of ~ 64% in water diffusion rate of the thickest sample compared to the thinnest one leads to a drop by ~ 20% in saturation weight (Figure 11c). This dependency between the diffusion rate and saturation weight may be related to the fact that an increase of diffusion rate further influences the swelling of flax fibre which leads to matrix swelling and propagation of micro-cracks at the fibrematrix interface. These mechanisms result in a higher absorbed water by the flax

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composites. To illustrate this correlation between the diffusion rate and saturation weight, thickness variations of unsealed specimens oriented at 0 and 45° were measured during the water absorption experiments. For the Flax-Epoxy composite, the swelling of the 45° oriented specimens was ~ 7.87±0.21 % compared with ~ 6.45±0.32 % for the non-oriented specimens. The same tendency was found for the Flax-Acrylic composite with thickness variations of ~7.61±0.35% and ~ 6.13±0.17% for the 45° and 0° oriented specimens, respectively. On the other hand, the obtained results show that diffusion mechanisms in flax fibre composites are very complex and strongly influenced by the hydrophilic nature of the flax fibre. Nevertheless, the analysis of these results allows us to draw a diagram illustrating the different modes of water diffusion within the studied composites. Diffusion through the thickness direction: first, water molecules diffuse inside microcavities, porosities, defects and by capillarity through micro-cracks present in the resin (Figure 12a). Then, water molecules reach the fibre-matrix interface (Figure 12b) and infiltrates the different hydrophilic components of the flax fibre. This finally leads to completely fill the hollow parts of the flax fibre (lumen) initially not reached by the resin flow during the composite manufacturing process (Figure 12c). It is important to note that this diffusion mode induces a longer diffusion kinetic compared to diffusion along the direction of fibres. Diffusion through the direction of fibres: in this case, water molecules principally diffuse by capillarity through the micro-cracks present at the fibre-matrix interface and through lumen parts that are not covered by the resin (Figure 13a). This significantly increases water diffusion kinetics within the composite and accordingly promotes more swelling of the flax fibre and saturation weight compared to the first diffusion mode.

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3D water diffusion: in this case, the water diffusion process is governed by the thinner dimension. When the thinner dimension is the thickness, water predominately diffuses following the first mode (Figure 12) but also along the warp and weft directions because of edge effects (Figure 13). When the thinner dimension is the length or width, water diffusion principally follows the second mode (Figure 13) and is influenced by edge effects across the thickness (Figure 12).

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6. Conclusion In this paper, we studied water diffusion in twill flax fabrics reinforced liquid thermoplastic (Acrylic) and thermoset (Epoxy SR8100) resins aged in tap and salt water at room temperature. Sealed and unsealed composite samples were immersed in water and diffusion parameters were obtained from 1D and 3D Fick’s and Langmuir’s models using an optimization algorithm. In particular, the effects of aspect ratio, thickness and fibre orientation on 3D water diffusion in both composites were investigated. Overall, several conclusions may be drawn through this work. First, the weight gain at saturation of Flax-Acrylic composite is found to be lower than that of Flax-Epoxy composite. This may be explained by the higher porosity content of Flax-Epoxy compared to Flax-Acrylic. Second, salt molecules induce both a decrease of the mass gain at saturation and water diffusion kinetics for both composites. Third, it was highlighted that sample dimensions and fibre orientation considerably affect the saturation weight, the diffusion direction and the diffusion rate. On the other hand, we showed that the water diffusion process is very complex which necessitates a full 3D analysis of the problem as considered in this work. Thanks to this analysis, an illustrated scheme was proposed to better understand the 3D water diffusion in flax composites.

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[10]

[11]

[12] [13]

[14]

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[17] Doan T.T.L., Brodowsky H., Mader E. Jute fibre/polypropylene composites II. Thermal, hydrothermal and dynamic mechanical behaviour. Composites Science and Technology 2007, 67: 2707–2714. [18] Assarar M., Scida D., Zouari W., Saidane E.H., Ayad R. Acoustic emission characterization of damage in short hemp-fiber reinforced polypropylene composites. Polymer Composites 2016; 37:1101–1112. [19] Zandvliet C., Bandyopadhyay N. R., Ray D. Proposition of an Accelerated Ageing Method for Natural Fibre/Polylactic Acid Composite. Journal of The Institution of Engineers (India): Series D 2015, 96(2): 151–158. [20] Le Duigou A., Bourmaud A., Baley C. In-situ evaluation of flax fibre degradation during water ageing. Industrial Crops and Products 2015, 70: 204–210. [21] Regazzi A, Corn S, Ienny P., Bergeret A. Coupled hydro-mechanical aging of short flax fiber reinforced composites. Polymer Degradation and Stability 2016, 130: 300–306. [22] Regazzi A, Léger R., Corn S, Ienny P. Modeling of hydrothermal aging of short flax fiber reinforced composites. Composites Part A 2016, 90: 559–566. [23] Regazzi A, Corn S, Ienny P, Bénézet J. C, Bergeret A. Reversible and irreversible changes in physical and mechanical properties of biocomposites during hydrothermal aging. Industrial Crops and Products 2016, 84: 358–365. [24] Arnold J.C, Alston S.M, Korkees F. An assessment of methods to determine the directional moisture diffusion coefficients of composite materials. Composites Part A 2013; 55:120–128. [25] Pierron F., Poirette Y., Vautrin A. A Novel Procedure for Identification of 3D Moisture Diffusion Parameters on Thick Composites: Theory, Validation and Experimental Results. Journal of Composite Materials 2002, 36 (19): 2219–2243. [26] Post N.L., Riebel F., Zhou A., Keller T., Case S.W., Lesko J.J. Investigation of 3D Moisture Diffusion Coefficients and Damage in a Pultruded E-glass/Polyester Structural Composite. Journal of Composite Materials 2009, 43 (1): 75–96. [27] Boukhoulda B.F., Adda-Bedia E., Madani K. The effect of fiber orientation angle in composite materials on moisture absorption and material degradation after hygrothermal ageing. Composite Structures 2006, 74: 406–418. [28] Neumann S., Marom G. Prediction of moisture diffusion parameters in composite materials under stress. Journal of Composite Materials 1987, 21, 0068–13. [29] Chilali A., Zouari W., Assarar M., Kebir H. and Ayad R. Analysis of the mechanical behaviour of flax and glass fabrics-reinforced thermoplastic and thermoset resins. Journal of Reinforced Plastics and Composites 2016, 35(16): 1217–1232. [30] Hermann A., Nickel J., Riedel U. Construction materials based upon biologically renewable resources – from components to finished parts. Polymer Degradation and Stability 1998, 59:251–61. [31] Monti A., El Mahi A., Jendli Z., Guillaumat L. Mechanical behaviour and damage mechanisms analysis of a flax-fibre reinforced composite by acoustic emission. Composites Part A 2016, 90: 100–110. [32] Madsen B., Lilholt H. Physical and mechanical properties of unidirectional plant fibre composites—an evaluation of the influence of porosity. Composites Science and Technology 2003, 63: 1265–1272.

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27 Figures z, 3

z, 3

D3 ≠ 0

2 y, 2 l

h = 3mm

y

D2 ≠ 0

θ 1

l

x, 1

x

D1 ≠ 0

θ = 0, 15, 30, 45 °

l = 20, 50, 100, 180mm

(a)

Unsealed Sealed

(b)

h = 3,4,6,8,10mm l = 20mm

h = 3mm

l = 20mm

L = 20,40, 80mm l = 20mm

h = 3mm

l = 20mm l = 20mm

(D1 ≠ 0, D2 = D3 = 0)

(c)

(D1 = D3 = 0, D2 ≠ 0)

(d)

(D1 = D2 = 0, D3 ≠ 0)

(e)

Fig.1 (a) Unsealed sample and its principal water diffusion directions (1: warp direction and 2: weft direction and 3: thickness direction), (b) local and global coordinate systems, (c), (d) and (e) sealed samples.

28 10

10

Flax-Epoxy

9

9 8

Flax-Acrylic

7 6 5

Fick's model Langmuir's model

4 3

Flax-Epoxy

7

Water uptake (%)

Water uptake (%)

8

6

Flax-Acrylic

5 4

Fick's model Langmuir's model

3

2

2

1

1

0

0

0

400

800

1200

1600

2000

2400

2800

0

400

0.5

800

1200

(a)

2000

2400

2800

(b) 10

10

9

9

Flax-Epoxy 8

8

7

7

Flax-Acrylic

6 5 4

Fick's model Langmuir's model

3

Water uptake (%)

Water uptake (%)

1600

Square root of time (s0.5)

Square root of time (s )

Flax-Epoxy

6

Flax-Acrylic

5 4 3

2

2

1

1

Fick's model Langmuir's model

0

0

0

400

800

1200

1600

2000

Square root of time (s0.5)

(c)

2400

2800

0

400

800

1200

1600

2000

2400

2800

0.5

Square root of time (s )

(d)

Fig.2 (a) and (b): Evolution of water uptake in sealed samples along the warp or the weft direction aged in tap water and salt water, respectively. (c) and (d): Evolution of water uptake in sealed samples across the thickness aged in tap water and salt water, respectively.

29 Voids in Lumen

Microcracks

(a)

(b) Void in lumen

(c)

Microcracks

(d)

Fig.3 SEM micrographs of the cross sections of 30 days aged flax composite samples: (a) and (b) Flax-Acrylic, (c) and (d) Flax-Epoxy

30 8 Langmuir's model 7

Water uptake (%)

6 5

Fick's model

4 Unsealed sample 3 2 1 0 0

200

400

600

800

1000

1200

1400

1600

1800

2000

Square root of time (s0.5)

Fig.4 Experimental water uptake curve of unsealed Flax-Epoxy sample aged in tap water compared with Fick’s and Langmuir’s analytical solutions obtained by optimized diffusion parameters of sealed specimens.

31 8 7

Tap water Salt water

Water uptake (%)

6 5 4

3D Fick's model

3

3D Langmuir's model 2 1 0 0

200

400

600

800

1000

1200

1400

1600

1800

0.5

Square root of time (s )

(a)

8 Tap water 7

Salt water

Water uptake (%)

6 5 4 3D Fick's model 3D Langmuir's model

3 2 1 0 0

200

400

600

800

1000

1200

1400

1600

1800

Square root of time (s0.5)

(b) Fig.5 Water uptake curves of unsealed samples aged in tap and salt water: (a) Flax-Acrylic and (b) Flax-Epoxy.

32

8 7

Water uptake (%)

6 5

20 x 20 mm

2

2

50 x 50 mm

4

2

100 x 100 mm 3

180 x 180 mm

2

Thickness direction 2

Fick's model (3D)

1 0 0

200

400

600

800

1000 1200 1400 1600 1800 2000

Square root of time (s0.5)

(a)

(b) Fig.6 Water uptake curves of unsealed samples with equal thickness and four surface dimensions aged in tap water: (a) Flax-Acrylic and (b) Flax-Epoxy.

33 8 3 mm 4 mm 6 mm 8 mm 10 mm

7

Water uptake (%)

6 5 4 3

Experimental results

2

Fick's model

1 0 0

350

700

1050

1400

1750

2100

2450

2800

0.5

Square root of time (s )

(a) 8

3 mm 4 mm 6 mm 8 mm 10 mm

7

Water uptake (%)

6 5 4

Experimental results

3

Fick's model 2 1 0 0

350

700

1050

1400

1750

2100

2450

2800

Square root of time (s0.5)

(b) Fig.7 Water uptake curves of sealed samples with five thicknesses and equal surface dimensions aged in tap water: (a) Flax-Acrylic and (b) Flax-Epoxy.

34

0.5

Diffusion rate (% / s )

0.008

Flax-SR8100 Flax-Epoxy

0.007

0.006

Flax-Acrylic 0.005

0.004

0.003 2

3

4

5

6

7

8

9

10

11

9

10

11

Thickness (mm) (a)

Equilibrium mass gain (%)

8.0 7.5

Flax-SR8100 Flax-Epoxy 7.0 6.5

Flax-Acrylic

6.0 5.5 5.0

2

3

4

5

6

7

8

Thickness (mm) (b) Fig.8 Evolution of (a) diffusion rate and (b) saturation weight gain with regard to sample thickness

35

Fig.9 (a) Finite element modelling of water diffusion in Flax-Epoxy and Flax-Acrylic samples, (b) Moisture concentration distribution in the 0° oriented Flax-Epoxy sample after 1 hour of ageing.

36 12

Water uptake (%)

11 10

θ = 45°

9

θ = 30°

8

θ = 15° θ = 0°

7 6 5 4

Experimental results

3

Finite element analysis

2 1 0 0

200

400

600

800

1000

1200

1400

1600

1800

0.5

Square root of time (s )

(a) 12 11

θ = 45°

10

θ = 30° θ = 15°

Water uptake (%)

9 8

θ = 0°

7 6 5

Experimental results Finite element analysis

4 3 2 1 0 0

200

400

600

800

1000

1200

1400

1600

1800

Square root of time (s0.5)

(b) Fig.10 Comparison between experimental water uptake curves and finite element results of: (a) Flax-Acrylic and (b) Flax-Epoxy with four fibre orientations.

37

(a)

(b)

(c) Fig.11 Variation of normalized equilibrium mass gain and diffusion rate as function of (a) fibre orientation, (b) length and (c) thickness of Flax-Epoxy composite samples.

38

Fig.12 Scheme of water diffusion across the thickness in flax composites.

39

Fig.13 Scheme of water diffusion along the direction of fibres in flax composites.

39

Tables

Table 1: Fibre volume fractions and porosity contents of Flax-Epoxy and Flax-Acrylic composites. Flax-Epoxy

Flax-Acrylic

Thickness (mm)

Fibre volume fraction Porosity content Fibre volume fraction Porosity content 3

32.00±1.13

6.11±0.54

37.10±1.28

4.99±0.32

4

31.42±1.05

6.02±0.31

37.07±1.09

5.04±0.27

6

31.98±1.17

5.92±0.65

36.95±1.17

4.89±0.51

8

31.87±0.95

6.13±0.24

37.12±1.11

4.95±0.42

10

31.67±1.07

5.97±0.77

37.15±1.31

5.11±0.29

40

Table 2: Diffusivity parameters of sealed Flax-Epoxy and Flax-Acrylic composites determined from 1D Fick’s analysis in the three princiapl directions (1, 2, 3).

Ageing condition

Material

D1 D2 D3 (×10 mm2/s) (×10-6mm2/s) (×10-6mm2/s)

Saturated weight M ͚ (%)

-6

M1

M2

M3

Flax-Epoxy

28.38±0.92

28.11±0.87

1.73±0.03

9.01±0.12 9.00±0.11 7.43±0.11

Flax-Acrylic

27.19±0.63

27.14±0.74

1.23±0.02

8.09±0.10 7.98±0.08 6.81±0.09

Flax-Epoxy

26.02±0.88

26.01±0.67

1.41±0.04

6.90±0.09 6.90±0.10 6.88±0.11

Flax-Acrylic

25.82±0.71

25.84±0.56

1.30±0.02

6.25±0.14 6.30±0.12 6.01±0.10

Tap water

Salt water

42

Table 3: Diffusivity parameters of sealed Flax-Epoxy and Flax-Acrylic composites determined from 1D Langmuir’s analysis in the three principal directions (1, 2, 3). Diffusion coefficients (mm /s) Ageing condition

Material

D1 -6

(×10 )

D2 -6

(×10 )

Probability β

Saturated weight M ͚ (%)

2

D3 (×10-6)

M1

M2

M3

Probability γ

-6 -1

(×10-6 s-1)

(×10 s ) β1

β2

β3

γ1

γ2

γ3

Flax-Epoxy 107.11±3.04 106.17±2.97 6.92±0.09 9.01±0.11 8.97±0.10 7.43±0.10 3.68±0.11 5.15±0.12 7.08±0.14 0.00±0.00 0.02±0.00 0.01±0.00 Tap water Flax-Acrylic 101.08±2.21 100.15±2.16 4.97±0.08 8.08±0.09 7.99±0.09 6.81±0.09 3.36±0.08 4.87±0.10 0.02±0.01 0.07±0.01 0.07±0.01 0.00±0.00 Flax-Epoxy

69.52±1.14

69.74±1.35 4.38±0.03 7.09±0.09 7.07±0.11 7.04±0.09 1.02±0.06 1.05±0.05 0.52±0.01 0.02±0.00 0.02±0.00 0.00±0.00

Salt water Flax-Acrylic 116.21±3.04 123.04±2.87 5.73±0.04 6.15±0.12 6.15±0.11 6.01±0.11 6.56±0.13 6.98±0.11 5.83±0.09 0.08±0.02 0.09±0.02 0.02±0.00

1

Table 4: Principal diffusivity parameters of unsealed Flax-Epoxy and Flax-Acrylic composites determined from 3D Fick’s model. Materials

D1 -6

D2 2

-6

M ͚ (%)

D3 2

-6

2

q (×10-5)

(10 ×mm /s)

(10 ×mm /s)

(10 ×mm /s)

Flax-Epoxy

0.93±0.02

0.83±0.03

2.76±0.14

7.45±0.06

2.50

Flax-Acrylic

0.88±0.03

0.72±0.04

2.72±0.17

6.87±0.11

4.60

Flax-Epoxy

0.12±0.01

0.14±0.01

2.37±0.21

6.94±0.11

17.72

Flax-Acrylic

0.19±0.02

0.14±0.03

2.85±0.23

6.18±0.10

19.20

Tap water

Salt water

_______________ * Corresponding author. Tel.: +33 325 467 144; fax: +33 325 427 098 E-mail address: [email protected]

Effect of geometric dimensions and fibre orientation on 3D moisture diffusion in flax fibre reinforced thermoplastic and thermosetting composites 2

Table 5: Principal diffusivity parameters of unsealed Flax-Epoxy and Flax-Acrylic composites determined from 3D Langmuir’s model Materials

D1 D2 D3 (×10-6mm2/s) (×10-6mm2/s) (×10-6 mm2/s)

M ͚ (%)

β (×10-6 s-1)

γ q (×10-6 s-1 ) (×10-5)

Flax-Epoxy

0.88±0.01

0.78±0.02

2.61±0.07

7.47±0.05 0.21±0.03 0.00±0.00

3.55

Flax-Acrylic

0.30±0.04

0.48±0.03

3.48±0.11

6.94±0.10 0.94±0.04 0.09±0.00

2.12

Flax-Epoxy

0.91±0.03

1.11±0.04

2.09±0.07

7.03±0.11 0.07±0.01 0.00±0.00 21.27

Flax-Acrylic

0.52±0.04

0.71±0.05

2.63±0.09

6.21±0.10 0.06±0.00 0.00±0.00 22.75

Tap water

Salt water

Effect of geometric dimensions and fibre orientation on 3D moisture diffusion in flax fibre reinforced thermoplastic and thermosetting composites 3

Table 6: Principal diffusivity parameters of unsealed Flax-Epoxy and Flax-Acrylic samples with constant thickness and four surface dimensions aged in tap water. Materials

Flax-Epoxy

Flax-Acrylic

Sample surface (mm2 )

D1 (10-6×mm2/s)

D2 (10-6×mm2/s)

D3 (10-6×mm2/s)

M ͚ (%)

20×20

0.93±0.02

0.83±0.03

2.76±0.14

7.45±0.06

50×50

0.12±0.01

0.12±0.01

2.47±0.10

7.41±0.07

100×100

0.02±0.01

0.02±0.01

2.18±0.09

7.43±0.07

180×180

0.01±0.01

0.01±0.01

1.76±0.09

7.48±0.09

Sealed sample

-

-

1.73±0.03

7.43±0.11

20×20

0.88±0.03

0.72±0.04

2.72±0.17

6.87±0.11

50×50

0.17±0.01

0.14±0.01

2.21±0.12

6.85±0.08

100×100

0.01±0.01

0.01±0.01

1.74±0.10

6.91±0.06

180×180

0.01±0.01

0.01±0.01

1.37±0.01

6.88±0.08

Sealed sample

-

-

1.23±0.02

6.81±0.09

Effect of geometric dimensions and fibre orientation on 3D moisture diffusion in flax fibre reinforced thermoplastic and thermosetting composites 4

Table 7: Diffusivity coefficients expressed in the global coordinate system. Materials

θ (°)

Dxx (10-6×mm2/s)

Dyy (10-6×mm2/s)

D zz (10-6 ×mm2/s)

Dxy (10-6×mm2/s)

0

0.93±0.02

0.83±0.03

2.76±0.14

0

15

0.92±0.02

0.84±0.03

2.76±0.14

0.02±0.00

30

0.90±0.02

0.85±0.03

2.76±0.14

0.04±0.00

45

0.88±0.02

0.88±0.02

2.76±0.14

0.05±0.00

0

0.88±0.03

0.72±0.04

2.72±0.17

0

15

0.87±0.03

0.73±0.04

2.72±0.17

0.04±0.00

30

0.84±0.03

0.76±0.04

2.72±0.17

0.07±0.00

45

0.80±0.03

0.80±0.03

2.72±0.17

0.08±0.00

Flax-Epoxy

Flax-Acrylic