# Analysis of the tensile behaviour of flax fibre bundles as a function of the loaded volume

Margot Chalard, Frédéric Bedel, Coralie Buffet, Adèle Hue, Alessia Melelli,

Timm Weitkamp, Pierre D'arras, Alain Bourmaud, Christophe Baley

► To cite this version:

Margot Chalard, Frédéric Bedel, Coralie Buffet, Adèle Hue, Alessia Melelli, et al. Analysis of the tensile behaviour of flax fibre bundles as a function of the loaded volume. Composites Part A: Applied Science and Manufacturing, 2025, 190, pp.108704. 10.1016/j.compositesa.2024.108704. hal-05369535

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# Analysis of the tensile behaviour of flax fibre bundles as a function of the loaded volume

Margot Chalard<sup>a, *</sup>, Frédéric Bedel<sup>a</sup>, Coralie Buffet<sup>a</sup>, Adèle Hue<sup>a,b</sup>, Alessia Melelli<sup>c</sup>, Timm Weitkamp<sup>c</sup>, Pierre D'arras<sup>b</sup>, Alain Bourmaud<sup>a</sup>, Christophe Bailey<sup>a</sup>

<figure><img src="image_3.png" /></figure>

## ARTICLE INFO

**Keywords:**

Fibres

Physical properties

Microstructure

Mechanical testing

Natural fibre composites

## ABSTRACT

Addressing the mechanical behaviour of flax bundles is a key point when used as reinforcements in composite materials. To determine their mechanical properties, the bundle cross-sectional area must be correctly assessed and has been estimated here using three types of models: elliptical, circular or polygonal. The circular model shows the higher disparity with twice the polygonal standard deviation. Innovatively, 3D rendering of bundles were carried out using microtomographic acquisitions, highlighting their partially cohesive unidirectional composite structure. Then, to analyse the phenomenon involved in the characterisation of bundles, mechanical properties were determined from a threshold value (first damage detected) and expressed as a function of the loaded volume (depends on the bundle cross-section area and the gauge length). To consider the dispersion of the bundles cross-sections, these properties were also weighted using the cross-section distribution curve. The results show their dependence on the volume and morphology of the tested bundles.

## 1. Introduction

Plant fibres such as flax are biodegradable, have a low density [1] and specific mechanical properties equivalent to glass fibres [2] which make them suitable to be used as reinforcement in composite materials [3–7]. Flax fibres are bast fibres, located at the periphery of the stem, in the phloem area [8,9] and organised in bundles, composed of elementary fibres (10 to 40) linked together by the middle lamellae [9]. This remarkable organisation is generated during intrusive growth [10]. During this growth phase (which takes place during the development of the stem), the rate of elongation of some fibre cells exceeds that of neighbouring cells [8]. Hence, they have pointed ends (elongation of the cells upwards and downwards), allowing them to penetrate into the middle lamellae [11]. This gives the bundles a unidirectional composite structure reinforced with discontinuous fibres and a high fibre volume fraction with limited strain concentration areas [12]. Once extracted from the stem, elementary fibres and bundles can then be used as composite reinforcement materials [13] or may undergo additional steps, for textile or other technical applications [14]. For example, Martin et al. [13] measured a Young’s modulus of 25.4 ± 1.1 GPa for a

unidirectional composite (48 % fibre volume ratio) made from epoxy resin and flax fibre bundles. In comparison, the modulus is 34 ± 1.8 GPa for an equivalent material reinforced with glass fibres [4]. Composites can also be manufactured by thermocompressing nonwovens composed of a mixture of flax bundles with a thermoplastic polymer such as polypropylene. This type of composite is already used in the automotive sector [15].

The mechanical properties of composites reinforced with flax fibre bundles are influenced by the mechanical properties of the bundles [16,17]. It is therefore necessary to mechanically characterise the bundles (quality assessment) before taking them to further processing stages [18]. Their cross-sectional area (CSA) must be assessed as it influences the mechanical properties of the bundles. It has been shown that the mechanical properties of the bundles decrease as the CSA increases [19]. However, the bundles’ CSA varies along their length [20], and bundles with a uniform CSA are more suitable to limit stress concentration areas [21]. An accurate determination of the CSA is therefore important but complex since flax fibres have a polygonal [9] and irregular cross-section [22]. The CSA is usually determined by measuring the average diameters along the bundles assuming they have a circular cross-section

<footnote><sup>a</sup> Université de Bretagne-Sud, UMR CNRS 6027, IRDL, F-56100 Lorient, France</footnote>

<footnote><sup>b</sup> Van Robaey Frères, 83 rue Saint-Michel, 59122 Killem, France</footnote>

<footnote><sup>c</sup> Synchrotron SOLEIL, 91190 Saint-Aubin, France</footnote>

<footnote>* Corresponding author at: Université de Bretagne-Sud, Laboratoire IRDL rue de Saint Maudé 56100 Lorient, France.</footnote>

<footnote>E-mail address: margot.chalard@univ-ubs.fr (M. Chalard).</footnote>
and a constant diameter along their length [23]. This method can lead to an overestimation of the CSA and therefore an underestimation of the mechanical properties of flax fibre bundles [24]. To avoid this problem, several alternatives have been proposed, including the use of a laser to obtain dimensions along the entire length of the bundle, while limiting the user's influence [25]. It is based on an elliptical model and the results show that, for bundles, this method provides a better approximation of the cross-section than the circular method [25]. Another alternative method was developed by Ilczyszyn et al [26], involving the measurement of the diameters of hemp bundles under the microscope by tilting them at five different angles (0°, 36°, 72°, 108° and 144°) using a special fixture. The CSA is therefore considered to be polygonal [26].

Once the CSA is measured, it is possible to realise tensile tests on flax fibres bundles [18]. It allows to qualitatively characterise the quality and resistance of flax batches, usually assessed visually and manually by flax producers. Test results depend on the gauge length, as the mechanical properties of the fibres are better characterised at short gauge lengths than at longer ones [18]. As gauge length increased, mechanical properties of bundles decreased. Increasing the gauge length also increases the probability of having critical defects (kink-bands) [27,28], fibre interfaces are mainly loaded and intrinsic fibre properties are not necessarily evaluated. Hence, the probability of having a fracture in the middle lamellae is higher [29], as its mechanical properties are weaker than those of the elementary fibres [30]. This trend is illustrated in Fig. 1, which shows the modulus and strength at break evolution as a function of the gauge length of flax fibre bundles subjected to tensile tests reported elsewhere [23,27–29,31–33]. To identify fibre or middle lamellae behaviour and decohesion mechanisms, it is also possible to combine tensile tests with acoustic emission tests [29]. However, interpretation remains challenging, due to issues in precisely defining the damage ranges associated with composite materials [34].

Simple tensile tests results can be used to determine the influence of several parameters such as climatic conditions during cultivation. They can influence the elongation and thickening of the fibres and thus their morphology [35]. For example, in drought conditions, flax fibres can undergo a biochemical change (19 % and 47 % increase in the rate of lignin and protein respectively) and a morphological change, becoming thinner (the average diameter is 19 % smaller) [36] and shorter [35]. This has an impact on bundles and composites' mechanical properties. Indeed, fibres with thin cell walls have low mechanical properties which is not suitable for composite reinforcement [17]. The retting process also affects the mechanical properties of the bundles since it acts on the middle lamellae but also on the cell wall ultrastructure and maturity.

Bourmaud et al. [37] have evidenced a progressive removing of the middle lamellae as the retting time increases but also a stiffening of the flax cell wall in the same time [37].

The main scientific objective of the present study is to understand the relationship between the tensile behaviour of a bundle, considered as a unidirectional composite material, and the loaded volume (CSA × gauge length). To achieve this, flax fibre bundles were selected and, in a first approach their main features were characterised through computed X-ray microtomography (micro-CT) scans and scanning electron microscopy (SEM) investigations. Then, a panel of different methods for CSA calculations were compared, to assess their reliability in estimating the CSA of fibre bundles. The last part of this work is dedicated to the evaluation of the bundles' mechanical properties as a function of the loaded volume considering the CSA distribution of the batch.

## 2. Materials and methods

### 2.1. Plant materials: flax fibre, bundles and stems

Industrial textile flax of the Damara variety (2021) was cultivated in Oise (France) and was then mechanically scutched by the Van Robaeys Frères Company (Killem, Département Nord, France). Flax bundles were extracted from long scutched fibres and used for the analysis and the morphological and mechanical characterisation. Single flax fibres were also manually extracted from this batch and mechanically tested.

Green flax stems from the same batch were also used to study the morphology of the stem and the organisation of the bundles in the mid-height of the stem.

### 2.2. Flax stem morphology analysis

The green flax stems (middle part) were preserved in a solution of 70 % ethanol and 30 % distilled water. Cross-sections with thicknesses between 250 and 300 µm were made using a vibratome (Leica VT1000, USA) and observed using a high-precision digital microscope (Keyence VHX-7000, France).

### 2.3. Cross-section measurement

#### 2.3.1. Cross-section measurement of elementary fibres

The cross sections of 50 elementary fibres (Damara 2021) were measured using a laser scanning micrometer (Dia-Stron, FDAS770, UK). The fibres were manually individualised and fixed on standardised

<figure><img src="image_4.png" /><figcaption>Fig. 1. Comparison of modulus (a) and strength at break (b) measured on flax fibre bundles from [23,27–29,31–33].</figcaption></figure>
plastic tabs using a photo-curing adhesive (DYMAX, Wiesbaden, Germany). They were then inserted into the instrument, and a total of 10 sections were taken over 10 mm (distance between the tabs). The sections were obtained from the minimum and maximum diameters measured (elliptical section). The CSA used to determine the mechanical properties was the average CSA.

### 2.3.2. Method for measuring CSA of flax fibre bundles

Before mechanical properties' characterisation of the bundles, it is necessary to determine their CSA. To measure the cross-section of the flax bundles, a measuring device was set up based on Ilczyszyn et al [26] and presented Fig. 2. The diameters of the bundles were measured at 3 points along their length: P1 (top), P2 (middle) and P3 (bottom) and for 5 different inclinations (0°, 36°, 72°, 108° and 144°) using the digital microscope presented in section 2.2. With this method, the cross-section was assimilated to an average polygon as shown in Fig. 2. To determine the CSA, the area of each triangle in the polygon was measured. As this method assumes that the CSA has an axis of symmetry, it is sufficient to measure the area of five triangles from the same side.

### 2.3.3. Comparison of the polygonal method with standard measurement methods on flax fibre bundles

In order to check that the polygonal method used in this study gives values close to reality on flax fibre bundles (complex, more or less cohesive structures), the CSA obtained were compared with the real cross-section as well as with other conventional measurement methods. Two of the conventional methods were obtained using the same micrometer used for elementary fibres (Dia-stron, FDAS770, UK):

- Elliptical method: the ellipse was obtained from the minimum and maximum diameters measured by the laser,

- Circular method (Dia-stron): obtained from the average diameter. The section was assumed to be circular.

The last method used is also based on a circular model. The diameter was measured at three different positions under the digital microscope Keyence. This time, the sample were not tilted and the CSA was calculated by assuming that the section is circular.

For these comparisons, the circular and polygonal CSA of 21 flax bundles were measured using the microscope (gauge length of 30 mm). The bundles were previously marked with a felt-tip pen to ensure that the measurements were always taken at the same points. They were then placed on plastic tabs for the laser measurement (elliptical method).

Measurements were made along the length of the bundles (gauge length of 10 mm). The bundles were then placed in moulds, coated with an agar medium viscosity resin (AGR1078) and placed in an oven at 50 °C for 24 h. An ultramicrotome (Leica EM UC7, Leica Microsystems, Germany) was then used to make cuts with a diamond knife (trimtool 45°, Diatome, USA) at the reference points. These cuts were observed using the optical microscope. Finally, the real CSA was measured using the ImageJ software. Since the bundles have a different grey level than the resin in which they are embedded, they were isolated using the threshold function. This operating mode is graphically detailed in Fig. 3.

### 2.3.4. Study of the reliability of the polygonal method

It was also necessary to determine if the polygonal measurement method (procedure described in section 2.3.2) was reliable and gave representative values for a given batch. It was therefore decided to take measurement errors into account and to study the distribution of the CSA of the bundles. Since the polygonal method measures the diameter at three different locations (P1, P2 and P3), the study of the reliability and representativeness of the polygonal method was divided into three sub-studies. Firstly, the distribution of the polygonal sections resulting from the diameter measurements at P1 (CSA 1) was studied, and then a study of the CSA measured at P2 (CSA 2) and P3 (CSA 3) was performed.

To determine the maximum error at each position (P1, P2 and P3), an analysis of the evolution of the CSA over a 500 µm window was carried out on 5 bundles from the same batch (Damara 2021). Diameters were measured on bundles laid flat under the microscope (Keyence) at each position. The difference between the maximum and minimum diameter measured over 500 µm gave the maximum deviation and was considered to be the maximum error for the measurement of the diameter of the bundle.

The impact of the measurement error on the CSA measurement was then determined by calculating the standard uncertainty using the formula of the CSA given in Eq. (1) (1). D1, D2, D3, D4 and D5 are defined in Fig. 2 and are expressed in µm, α is the inclination angle (36° here). This formula was obtained from trigonometric calculations and corresponds to the sum of the areas of each triangle.

$$CSA(\mu m^2) = \frac{\sin(\alpha)}{2} (D1D2 + D2D3 + D3D4 + D4D5 + D5D1) \quad (1)$$

Using the formula for calculating standard uncertainty described by Veronika R. Meyer [38], it is possible to determine the formula for the standard uncertainty of the CSA:

$$u_c(\text{CSA}) = \frac{3\sqrt{5}}{2} \sin(\alpha) \sqrt{(D2 + D5)^2 + (D1 + D3)^2 + (D2 + D4)^2 + (D3 + D5)^2 + (D4 + D1)^2} \quad (2)$$

<figure><img src="image_5.png" /><figcaption>Fig. 2. Principle of the polygonal measurement method.</figcaption></figure>
<figure><img src="image_6.png" /><figcaption>Fig. 3. Operating mode for the comparison of the different CSA measurement methods.</figcaption></figure>

This formula was then applied to each CSA measured with the polygonal method and considered in the study of the distribution of the CSA of the bundles.

## 2.4. Tensile testing

Tensile tests on 50 elementary fibres from the middle of the stem were carried out in accordance with standard NF T 25-501-2 using a high-resolution tensile tester (Dia-Stron, LEX820, UK). Hence, tests were carried out on specimens with a gauge length of 10 mm at a speed of 1 mm/min. The aim of these tests on elementary fibres was to know the mechanical properties of the single fibres, which is a main indicator of the quality of the batch.

The tensile tests on flax fibre bundles were performed using a tensile testing machine (MTS criterion, model 42) equipped with a 50 N capacity load cell. These tests were carried out with the aim of analysing the behaviour of a flax fibre bundle and finding relevant test parameters. Mechanical characterisation tests were inspired from NF T 25-501-3. For all tests, the elongation gradient was constant (10 % per minute). Tensile tests were performed at 23 °C and 50 % relative humidity in a controlled environment according to the NF EN ISO 291 standard. The gauge lengths chosen for the tests were: 30, 40, 50 and 75 mm. For each gauge length, at least 25 specimens were validated. More precisely, 28 tests were validated with a gauge length of 30 mm, followed by 29, 30 and 27 tests with gauge lengths of 40, 50 and 75 mm, respectively. Finally, the average CSA (based on the values measured at P1, P2 and P3) of the bundles were measured using the “polygonal” method introduced in section 2.3.2. Mechanical properties, e.g. Young’s modulus and strain at break, were calculated considering the compliance of the system (0.044 mm/N).

The results were presented as a function of the gauge length. To consider the CSA of the bundles (and therefore the volume loaded), a statistical distribution curve (modelled by a ln-normal distribution) of

the average CSA was determined (the statistical model requires a sufficiently large amount of data to be applied). More precisely, the average CSA measured by the polygonal method were divided into nine classes (interval between the classes of 2000 µm²) and a frequency was assigned to each class. For each mechanical parameter (modulus, strain and stress), an average result was measured in each class and this result was multiplied by the frequency associated with its class.

## 2.5. SEM observations

To observe the bundles' rupture characteristics (after tensile tests), samples were recovered and metallised using gold sputtering. They were then observed using a Jeol JSM 6460 LV (Tokyo, Japan) scanning electron microscope (SEM).

## 2.6. X-ray micro-tomography under Synchrotron radiation

X-ray computerised microtomography (micro-CT) measurements on flax fibre bundles were carried out at Synchrotron SOLEIL (France), at the Anatomix beamline [39] in order to obtain a segmented three-dimensional rendering. The microtomographic images were used to illustrate the bundles. The sample preparation consisted of cutting and glueing Terumo® Agani™ needles (diameter of 0.5 and 25 mm long) to Huber 1002-18MS specimen carrier with a diameter of the central hole of 0.8 mm. The needles were mounted leaving 15 mm protruding from the specimen carrier. The bundles were successively extracted and glued in the tip of the needles in a perfectly vertical position, leaving a free length for scanning of approximately 5 mm. A total of 8 samples from the Damara batch were prepared and investigated. The samples were mounted at a distance of 15 mm from the detector.

A monochromatic x-ray beam (DCM Si-111) with a photon energy of 11.5 keV was used to perform high resolution phase-contrast images and avoid fibres' damage. The detector used for microtomography measurements consists of a Hamamatsu Orca Flash camera (CMOS) with a
resolution of 2048 × 2048 pixels coupled with a scintillator (Lu₃Al₅O₁₂: Ce) and a 20 × magnifying optics (Mitutoyo, Kawasaki, Japan), which gave an effective pixel size of 325 nm and a field of view of 0.65 × 0.65 mm². For each scan there were 2000 projection angles (range of 180°) and the exposure time per projection was set at 200 ms. PyHST2 software (ESRF, Grenoble) [40] was used for the tomographic reconstruction and a Paganin filter [41] with a kernel length of 15 µm and double flat field, which is used to minimise the ring artefacts, were used. Once the reconstructions were completed, ImageJ was first used to crop each image. Finally, Avizo (version 2021.1) made it possible to obtain a 3D volume rendering (length of 650 µm) for each bundle by segmenting the tomographic slices obtained with ImageJ.

# 3. Results and discussion

## 3.1. Fine description of a bundle

A flax fibre bundle can be considered as a unidirectional composite material, reinforced with discontinuous fibres, partially embedded in a non-cellulosic polysaccharide (NCP) matrix made of middle lamellae residues, the quantity of which is highly dependent on both the retting degree and the extraction conditions. On the stem cross-section (Fig. 4 (a)), the bundles are located at the periphery, in the phloem region, and are quite clearly delimited. This image shows highly cohesive bundles within the stem.

To observe the surface of the bundles, SEM images of bundles were then taken. One of the bundles observed is shown in Fig. 4(b). This image shows a bundle of partially individualised fibres. Where the retting step has removed cortical residues and the middle lamellae, the fibres can be clearly distinguished. However, there are areas where the fibres are completely covered with residues and middle lamellae. These observations highlight the heterogeneity of the retting process. The SEM images give an idea of the degree of retting and fibre individualisation in a batch, based on the presence of cortical residue content.

Synchrotron microtomography was applied to show the structural specificities of a bundle. This gives an overview of the fibre distribution within a bundle, the degree of retting (amount of residues), the level of cohesion and the presence of defects (kink-bands). A 3D-rendering of two bundles from the same batch, bundle 1 and bundle 2, and three tomographic longitudinal slices extracted from the same bundles at different heights are shown in Fig. 5 and Fig. 6, respectively.

Fig. 5 evidences the presence of a bundle with rather cohesive fibres (but not as much as in the stem), as well as areas with more residues

which may be due to poor retting level. However, one should bear in mind that this batch is only scutched and not combed. It also shows the presence of kink-bands (defects present on elementary fibres that are known to be zone of failure). Moreover, some of the elementary fibres from Fig. 5 are less filled than the others.

Another reconstruction was made on a bundle from the same batch on Fig. 6 in order to make a comparison. The heterogeneity of the two bundles can be seen in Fig. 5 and Fig. 6. Indeed, fibres from Fig. 6 are more scattered than those from Fig. 5 (fibre distribution can differ from one bundle to another) and the distribution of the middle lamellae is also different. Moreover, the surface of the bundle is less cleaned and has more residues, which highlights the heterogeneity of the retting process on a same batch. Nevertheless, the observed bundles demonstrate a good quality with a high cellulose filling and relatively low lumen size.

These observations highlight the complexity of precisely defining what constitutes a bundle, given its changing morphology resulting from complex phenomena dependent on climatic conditions. However, this morphology has a major impact on the properties of the bundles, which is why it is important to understand and define it precisely.

## 3.2. Analysis of the cross-section of a bundle

### 3.2.1. Cross-section area (CSA) measurement

The cross-sectional measurements of 21 bundles were compared using four different measurement methods: elliptical (Dias-stron), polygonal (microscope) and two circular methods measured from microscope and Dia-stron respectively. The different models (circular, elliptical and polygonal) are schematically illustrated on two bundle cross-sections in Fig. 7. According to Fig. 7, the reliability of the approximations seems to depend strongly on the cohesion of the fibres within the bundle (the models do not consider the spaces between the fibres), as well as on the shape of the section. In all three cases they appear to overestimate the bundle cross-section. To compare these four different diameter measurement methods more accurately, the ratios between the CSA measured (CSA_m) with the models and the real CSA (CSA_r) are calculated for each tested bundle. Results are presented in Fig. 8. A line representing a ratio of 1 (perfect approximation of the experimental CSA) was drawn to highlight the tendency of the models to over- or under-estimate reality.

These results highlight the difficulties of accurately measuring the CSA of flax fibre bundles. The method that gives the closest values to the actual CSA (CSA_r) is the elliptical model. Indeed, the average ratio with this method is the closest to 1. This trend is statistically demonstrated by

<figure><img src="image_7.png" /><figcaption>Fig. 4. Zoom on a part of the section of a flax stem (a) and SEM observation of a flax fibre bundle (b).</figcaption></figure>
<figure><img src="image_8.png" /><figcaption>Fig. 5. 3D rendering of bundle 1 obtained from volume scanned by X-ray micro-CT on Anatomix beamline.</figcaption></figure>

<figure><img src="image_9.png" /><figcaption>Fig. 6. 3D rendering of bundle 2 obtained from volume scanned by X-ray micro-CT on Anatomix beamline.</figcaption></figure>

the use of the Student t-test (95 % interval) which shows a statistical
difference between the elliptical values and the other measurement
methods. The least dispersed method is the polygonal method. In fact,
the interquartile range (a measure of dispersion between the first and
the third quartiles, to avoid extreme cases) is the smallest one. The

interquartile ranges measured are 0.5, 0.3, 1.28 and 0.48 for the ellip-
tical, polygonal, circular (microscope) and circular (dia-stron) models
respectively. Conversely, the circular method (microscope) gives highly
dispersed values with almost half of them much higher than the actual
CSA (ratio greater than 2). All the models tend to overestimate the actual
<figure><img src="image_10.png" /><figcaption>Fig. 7. Schematic representation of the three measurement models on two bundle cross-sections.</figcaption></figure>

<figure><img src="image_11.png" /><figcaption>Fig. 8. Comparison of the CSA measured with each model. Values with the same letters (a, b and c) can be considered as not statistically different (p > 0.05).</figcaption></figure>

<table><caption>**Table 1**

Comparative table of the measurement method [25]</caption><thead><tr><th>Model</th><th>Measuring device</th><th>Advantages (+) / disadvantages (-) associated with the measuring device</th><th>Advantages (+) / (-) of the measurement method</th><th>Advantages (+) / disadvantages (-) of the approximation</th></tr></thead><tbody><tr><td>Elliptical</td><td>Dia-stron</td><td>+ Not dependent on the operator (automated)<br/>- No control over what is measured</td><td>- Ellipse drawn considering the minimal and maximal diameters as orthogonal<br/>- Distorted measurements in the case of detachment of elementary fibres or concavity of the section<br/>- Limitations in the gauge length of the chosen specimen</td><td>+ Approximation that gives results closer to reality than other models<br/>+ Takes better account of the real CSA<br/>- CSA doesn't necessarily have an axis of symmetry</td></tr><tr><td>Polygonal</td><td>Microscope</td><td>- Dependent on the operator<br/>+ Control over what is measured</td><td>+ Can be used with any gauge length<br/>- Measurement errors > laser method</td><td>- CSA not necessarily convex and doesn't always have an axis of symmetry</td></tr><tr><td>Circular</td><td>Microscope</td><td>- Dependent on the operator<br/>+ Control over what is measured</td><td>+ Can be used with any gauge length<br/>- Dependence of sample placement on the objective (wide dispersion of values)<br/>- Large measurement errors</td><td>- The cross-section of the bundles is not circular<br/>+ Approximation closer to reality than proposed by the dia-stron (circular method)</td></tr><tr><td>Circular</td><td>Dia-stron</td><td>+ Not dependent on the operator (automated)<br/>- No control over what is measured</td><td>- The average diameter calculated makes no real physical sense<br/>- Limitations in the gauge length chosen</td><td>- Bundles do not have a circular cross-section</td></tr></tbody></table>
cross-section since the ratio in all the cases is generally greater than 1. According to these observations, a comparative table of the measurement methods is presented (Table 1).

In all cases, none of the models consider the inter-fibre space (pores), underlining that none of them could be considered as perfect, as demonstrated by the numerical results and the general overestimation of the CSA. In the next sections of the study, the polygonal method will be used, as it provides the least scattered results, fairly close to the actual CSA, with better control of what is measured and that can be automated in the future.

### 3.2.2. Reliability of the polygonal method

In order to check if the polygonal model provides representative values for a batch of flax bundles, relative error measurements were carried out. The aim was to maximise the measurement error associated with the polygonal method. The maximum error in diameter measurement using the polygonal method is 6 µm. This value was kept for the calculation of maximum measurement error and used to investigate how this error affects CSA measurements. The results obtained by measuring the diameter of the bundles at the position P1 allow to calculate a CSA (CSA 1) for each bundle. Results are shown in Fig. 9 for CSA 1 and in Appendix 1 for CSA 2 and CSA 3. Calculation details for class 4 (values between 6000 and 8000 µm²) are explained in Fig. 9(a).

Fig. 9 shows that the distribution of CSA (CSA 1 here) follows a In-normal distribution. Thus, the In-normal distribution was plotted and the squared deviation between the distribution and the experimental values was calculated. The In-normal distribution curve was then fitted thanks to a coefficient ($\lambda$ = 1.96), specific to this batch, that allows to minimise this squared deviation, and the result is shown in Fig. 9(b). The In-normal law follows the experimental points. Thus, the use of the polygonal method provides representative results (same observations with CSA 2 and 3), which justifies its use in the study.

### 3.3. Mechanical characterisation of elementary fibres

Prior to the bundle tests, and to get an idea of the quality of the batch, tensile tests were carried out on elementary fibres (average cross-section $160 \pm 70$ µm²). The mechanical properties obtained are presented in Table 2. They are compared with the average values obtained from tensile tests on 2954 elementary fibres from literature [42].

An analysis of the results shows that these elementary fibres appear to have mechanical properties in line with the average from literature tests [42]. For this reason, the bundles from this batch have been chosen for study.

## 3.4. Mechanical characterisation of the bundles

### 3.4.1. Tensile test results: tensile behaviour of a bundle

#### 3.4.1.1. Interpretation of curves: study of bundles' behaviour in tension.
To determine the mechanical properties of the bundle, the average CSA were measured using the polygonal method (average of CSA 1, CSA 2 and CSA 3). The bundles were then subjected to a tensile test and an example of a stress versus strain curve is shown in Fig. 10. When a bundle is subjected to a tensile test, its initial behaviour is quasi-linear (area 1). The first significant singularity marks the start of area 2 and is considered as the threshold value (identified thanks to the derivative of the tensile curve). Following the first damage event (threshold value), there is an accumulation of damage within the bundle, represented by the numerous peaks in area 2, leading to a sudden rupture of the bundle (marker 3). Damage mechanisms involved during the test may be the result of fibre crack, middle lamellae failure (interface and matrix) or debonding. To illustrate this, SEM images were taken of flax bundles from the same batch, with the aim of observing damage mechanisms. SEM images taken after mechanical tensile loading of the bundles are shown in Fig. 11.

Fig. 11(a) shows the consequence of a sharp fracture in two fibres. It is also possible to observe their polygonal cross-section, as well as the presence of a hollow fibre with a bigger lumen. The bigger lumen found in one of the two fibres agrees with the observation of Fig. 5, in which the fibres of the bundles were more or less filled, and confirms the heterogeneity of the batch. Fig. 11(b) illustrates the fracture surface of a bundle, showing areas with cohesion, decohesion and fibres breakage. Finally, Fig. 11(c) highlights crack propagation at the bond between two fibres provided by middle lamellae.

#### 3.4.1.2. Study of the average CSA of bundles.
A statistical study was carried out on the bundles. As in Section 3.2.2, the distribution of average CSA was analysed over the total of 114 measured values, considering the maximum measurement error associated with the polygonal measurement method. The In-normal distribution obtained is shown in Fig. 12(a). Once again, a coefficient $\lambda$ of 1.96 (depending on this batch) was applied to minimise quadratic deviation.

One can notice that the distribution follows the experimental points with a In-normal distribution, and the values measured are representative of the batch. The same analysis was performed for the different gauge lengths (30, 40, 50 and 75 mm) in order to determine their distribution curves and to compare them (Fig. 12(b)). Fig. 12(b) shows slight differences between the curves, which may be due to sampling

<figure><img src="image_12.png" /><figcaption>Fig. 9. CSA distribution of all bundles measured at P1 (CSA 1) (a) considering measurement errors (b).</figcaption></figure>
<table><caption>**Table 2**
Average mechanical properties of elementary fibres and flax fibre bundles and comparison with the mechanical properties of elementary fibres from literature [42]</caption><thead><tr><th></th><th>Elementary fibres / bundles</th><th>Modulus (GPa)</th><th>Threshold stress (MPa)</th><th>Strength at break (MPa)</th><th>Threshold strain (%)</th><th>Strain at break (%)</th></tr></thead><tbody><tr><td>Damara 2021</td><td>Elementary fibres</td><td>53.7 ± 15.9</td><td></td><td>1163 ± 447</td><td></td><td>2.15 ± 0.52</td></tr><tr><td>Baley et al. [36]</td><td>Elementary fibres</td><td>52.5 ± 8.6</td><td></td><td>945 ± 200</td><td></td><td>2.07 ± 0.45</td></tr><tr><td>Damara 2021</td><td>Bundles</td><td>26.6 ± 2.7</td><td>148 ± 37</td><td>313 ± 62</td><td>0.59 ± 0.07</td><td>1.29 ± 0.11</td></tr></tbody></table>

<figure><img src="image_13.png" /><figcaption>**Fig. 10.** Stress-strain curve and phenomena involved during the tensile test of a flax fibre bundle.</figcaption></figure>

<figure><img src="image_14.png" /><figcaption>**Fig. 11.** SEM observations of flax fibre bundles after tensile tests.</figcaption></figure>
<figure><img src="image_15.png" /><figcaption>Fig. 12. Ln-normal distribution of the average CSA considering the measurement error (a) superimposed with the distribution curves for each gauge length selected for tensile tests (b).</figcaption></figure>

heterogeneity. However, the curves have the same overall shape, with peaks more or less positioned at the same position. In fact, for each sub-batch, the CSA associated with each curve peak was compared with that of the global curves. The deviations are 13.2 %, 13.6 %, 9.5 % and 6.4 % for gauge lengths of 30, 40, 50 and 75 mm respectively. The position of the peaks in relation to the overall distribution curve thus varies between 6 and 14 %. These deviations are small, and it can therefore be assumed that in this case, the curves are not influenced by the gauge length. Hence, the frequencies associated with the global distribution curve can be used to calculate mechanical properties.

### 3.4.1.3. Analysis of results.
In order to evaluate the influence of the gauge length, the mechanical properties of the flax bundles were assessed by tensile tests. The mechanical results are shown in Fig. 13. Fig. 13(a1, a2) shows a slight decrease in modulus and strength at break when the gauge length is increased. This agrees with literature (Fig. 1). For a gauge length of 30 mm, the modulus and strength at break measured are 28.8 ± 7.3 GPa and 325 ± 103 MPa respectively. At a higher gauge length (75 mm), the modulus and strength at break are 23.8 ± 3.9 and 302 ± 107. There is therefore a decrease of 17.5 % and 7 % respectively. Concerning the strain at break Fig. 13(a3), there is no noticeable change when the gauge length is increased. Indeed, at 30 mm, the strain at break in Fig. 13(a3) is 1.24 ± 0.11 % and, at 75 mm, it is 1.21 ± 0.19 %. However, the trend observed with the strain at break is consistent with that of the strength at break. Hence these values appear to reflect the same damage mechanisms that can be related to fibre defects, bundle cohesion or fibre filling rate.

Regarding the elementary fibres, the modulus, breaking stress and strain for this batch were 53.7 ± 15.9 GPa, 1163 ± 447 MPa and 2.07 ± 0.45 respectively (Table 2). These values are higher than those found for the bundles extracted from the same batch. This result is consistent with the fact that the bundles are assemblies of discontinuous fibres, comparable to a unidirectional composite material. This difference is accentuated at higher gauge lengths, and can be explained by the discontinuity of the elementary fibres, by the middle lamellae and interfaces more or less altered by the retting process. Retting is carried out on the ground and is highly dependent on climatic conditions, making it difficult to obtain a homogeneous result on the scale of the bundles.

In all three datasets presented in Fig. 13(a), there is a wide dispersion in the values (high standard deviations) that can be partly due to the elementary fibres properties [12], to the cohesion level of the tested bundles or to the cell wall thickness of elementary fibres that can strongly differ from a bundle to another. An example is the cell filling

rate, which is highly dependent on plant growth conditions [6,43]. Moreover, the trend is not clear and this highlights the complexity of rigorously qualifying a batch and understanding the mechanisms involved in bundle rupture. Hence, it was decided to seek for a more relevant parameter that would highlight the influence of the loaded volume on the mechanical properties of the bundles. The solution consists in considering the moment when the bundle undergoes its first significant damage during tensile stress. From this value, a threshold stress and strain can be calculated (Fig. 10). They are expressed as a function of the CSA, the gauge length and, consequently the loaded volume in Fig. 13(b)(c). Firstly, the threshold strains and stresses represented in Fig. 13(b3,c3) are significantly lower than the strengths and strains at break (Fig. 13(a2,a3)), dropping down at a gauge length of 40 mm and then stabilising. At 30 mm, the threshold strain is 0.84 ± 0.12 % and decreases to 0.55 ± 0.07 % at 40 mm. The threshold stress decreases from 245 ± 91 MPa (30 mm) to 127 ± 35 MPa at 40 mm. At 75 mm, the threshold strain and stress remain almost unchanged at 0.51 ± 0.08 % and 107 ± 27 MPa. Moreover, a representation of the results as a function of the threshold stress clearly demonstrates the decrease in mechanical properties of the bundles when the loaded volume increases. Indeed, Fig. 13(b2) highlights the decrease in threshold stress as the CSA increases, showing a 82 % reduction in threshold stress as the CSA increases from 3000 to 19000 µm². It is therefore preferable to have thin bundles to obtain high stresses. To explain this phenomenon, it can be assumed that when the CSA is small, the probability of having defects (kink-band, cortical residues) decreases, and thus limits the areas of weakness (Fig. 14). For the threshold strain (Fig. 13(c2)), there is no clear trend but it is important to remember that the results come from tests on bundles tested at different gauge lengths. Moreover, these trends are also influenced by the CSA measurement method chosen (polygonal method in this case). The gauge length trend is also marked, with a 54 % decrease in threshold stress and a 38.5 % decrease in threshold strain when the gauge length is increased from 30 mm to 75 mm (Fig. 13(b3, c3)).

In view of the observations made above, it seems consistent that the threshold strain and stress decrease when the loaded volume increases (Fig. 13(b1,c1)). In both cases, the trend is very clear with a decrease toward a limit which seems to be reached at a volume of around 1 mm³. The study of the threshold stress and strain therefore clearly demonstrates the effect of the loaded volume on the mechanical properties of the bundles. Results allow to highlight the load transfer between the fibres and the middle lamellae during tensile tests. Beyond the threshold value, the notion of cumulative damage is involved. Hence, such
<figure><img src="image_16.png" /><figcaption>**Fig. 13.** Modulus (a1), strength at break (a2) and strain at break (a3) as a function of the gauge length; threshold stress (b) and threshold strain (c) as a function of the loaded volume (1), of the CSA (2) and of the gauge length (3).</figcaption></figure>

<figure><img src="image_17.png" /><figcaption>**Fig. 14.** Influence of the gauge length and CSA (loaded volume) on the mechanical properties of the bundles.</figcaption></figure>

parameters could be used to compare the mechanical properties of different batches. In the future, the developed method could be used to set up automated control tools.

Average mechanical properties (gauge lengths not considered) could be calculated for bundles from the Damara 2021 batch and the results

are presented in Table 2. These average mechanical properties could be used to determine the mechanical properties of unidirectional composites (UD) reinforced with fibres of the same flax variety. However, it is important to bear in mind that within the bundles, load transfer is ensured by the middle lamellae. In the case of UD, load transfer is highly
dependent on the quality of the interface between the fibres and the matrix, which depends on adhesion, fibres impregnation and the fibres distribution [4].

## 4. Conclusion

The aim of this work is to understand the relationship between the tensile behaviour of a bundle and the loaded volume, in order to guarantee better-controlled quality. First analyses have shown that the bundles have a composite-like structure with a complex architecture, more or less cohesive and composed of fibres with dispersed properties and morphologies (some of them have a larger or smaller lumen). In order to determine their mechanical properties, it is necessary to precisely define their CSA. For the purposes of this study, the polygonal method was chosen, as it is the method with the least dispersed values and with control over what is measured.

The tensile tests revealed the appearance of a threshold value, characterised by the first major discontinuity in the tensile curve (stress vs. strain). From this value, two mechanical parameters can be calculated: the threshold strain and stress. They highlight the load transfer between the fibres and the middle lamellae and show a clear decrease in mechanical properties as the volume loaded increases. This decrease can be explained in particular by the composite structure of the bundles reinforced with discontinuous fibres, which increases the probability of having singularities when the volume loaded increases.

In line with this work, studies of the influence of middle lamellae degradation methods on the mechanical properties of the bundles (retting, chemical or physical methods) could be done. It would also be interesting to extend micro-tomographic analyses to better describe a bundle.

### CRediT authorship contribution statement

**Margot Chalard:** Writing – original draft, Methodology, Investigation, Formal analysis, Data curation, Conceptualization. **Frédéric Bedel:** Writing – review & editing, Supervision, Methodology, Investigation, Formal analysis. **Coralie Buffet:** Writing – review & editing, Visualization, Data curation. **Adèle Hue:** Data curation. **Alessia Melelli:** Writing – review & editing, Validation, Supervision. **Timm Weitkamp:** Writing – review & editing, Validation, Supervision. **Pierre D'arras:** Writing – review & editing, Funding acquisition. **Alain Bourmaud:** Writing – review & editing, Visualization, Validation, Supervision, Resources, Methodology, Funding acquisition, Conceptualization. **Christophe Baley:** Writing – review & editing, Visualization, Supervision, Resources, Funding acquisition, Conceptualization.

### 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.

### Acknowledgements

The authors want to thank the ANR (Agence Nationale de la Recherche) for funding the labcom NewFlax (21-LCV3-0011-01) that carried out this project. The authors also want to thank Synchrotron SOLEIL for its support and access to the Anatomix beamline (proposal 20231643). ANATOMIX is an Equipment of Excellence (EQUIPEX) funded by the *Investments for the Future* program of the ANR, project *NanoimagesX*, grant no. ANR-11-EQPX-0031.

## Appendix A. Supplementary material

Supplementary data to this article can be found online at https://doi.org/10.1016/j.compositesa.2024.108704.

## Data availability

Data will be made available on request.

## References

[1] Bourmaud A, Morvan C, Baley C. Importance of fiber preparation to optimize the surface and mechanical properties of unitary flax fiber. Ind Crops Prod 2010;32:662-7. https://doi.org/10.1016/j.indcrop.2010.08.002.

[2] Lefeuvre A, Bourmaud A, Morvan C, Baley C. Tensile properties of elementary fibres of flax and glass: analysis of reproducibility and scattering. Mater Lett 2014;130:289-91. https://doi.org/10.1016/j.matlet.2014.05.115.

[3] Arbelaiz A, Fernández B, Valea A, Mondragon I. Mechanical properties of short flax fibre bundle/poly (ε-caprolactone) composites: Influence of matrix modification and fibre content. Carbohydr Polym 2006;64:224-32. https://doi.org/10.1016/j.carbpol.2005.11.030.

[4] Coroller G, Lefeuvre A, Le Duigou A, Bourmaud A, Ausias G, Gaudry T, et al. Effect of flax fibres individualisation on tensile failure of flax/epoxy unidirectional composite. Compos Part Appl Sci Manuf 2013;51:62-70. https://doi.org/10.1016/j.compositesa.2013.03.018.

[5] Zimniewska M, Stevenson A, Sapieja A, Kicińska-Jakubowska A. Linen fibres based reinforcement for laminated composites. Fibres Text East Eur 2014;103-8.

[6] Lefeuvre A, Bourmaud A, Baley C. Optimization of the mechanical performance of UD flax/epoxy composites by selection of fibres along the stem. Compos Part Appl Sci Manuf 2015;77:204-8. https://doi.org/10.1016/j.compositesa.2015.07.009.

[7] Omrani F, Wang P, Soulat D, Ferreira M. Mechanical properties of flax-fibre-reinforced preforms and composites: influence of the type of yarns on multi-scale characterisations. Compos Part Appl Sci Manuf 2017;93:72-81. https://doi.org/10.1016/j.compositesa.2016.11.013.

[8] Gorshkova TA, Sal'nikov OV, Chemikosova SB, Ageeva MV, Pavlencheva NV, van Dam JEG. The snap point: a transition point in Linum usitatissimum bast fiber development. Indust Crops Prod 2003;18. https://doi.org/10.1016/S0926-6690(03)00043-8.

[9] Baley C. Analysis of the flax fibres tensile behaviour and analysis of the tensile stiffness increase. Compos Part Appl Sci Manuf 2002. https://doi.org/10.1016/S1359-835X(02)00040-4.

[10] Goudenhoofc C, Bourmaud A, Baley C. Flax (linum usitatissimum L.) fibers for composite reinforcement: exploring the link between plant growth, cell walls development, and fiber properties. Front Plant Sci 2019;10. https://doi.org/10.3389/fpls.2019.00411.

[11] Snegireva AV, Ageeva MV, Amenitskii SI, Chernova TE, Ebskamp M, Gorshkova TA. Intrusive growth of sclerenchyma fibers. Russ J Plant Physiol 2010;57:342-55. https://doi.org/10.1134/S1021443710030052.

[12] Baley C, Goudenhoofc C, Gibaud M, Bourmaud A. Flax stems: from a specific architecture to an instructive model for bioinspired composite structures. Bioinspir Biomim 2018;13. https://doi.org/10.1088/1748-3190/aaa6b7.

[13] Martin N, Davies P, Baley C. Comparison of the properties of scutched flax and flax tow for composite material reinforcement. Ind Crops Prod 2014;61:284-92. https://doi.org/10.1016/j.indcrop.2014.07.015.

[14] Yan L, Chouw N, Jayaraman K. Flax fibre and its composites – a review. Compos Part B Eng 2014;56:296-317. https://doi.org/10.1016/j.compositesb.2013.08.014.

[15] Maity S, Gon DP, Paul P. A review of flax nonwovens: manufacturing, properties, and applications. J Nat Fibers 2014;11:365-90. https://doi.org/10.1080/15440478.2013.861781.

[16] Marrot L, Lefeuvre A, Pontoire B, Bourmaud A, Baley C. Analysis of the hemp fiber mechanical properties and their scattering (Fedora 17). Ind Crops Prod 2013;51:317-27. https://doi.org/10.1016/j.indcrop.2013.09.026.

[17] Bourmaud A, Mérotte J, Siniscalco D, Le Gall M, Gager V, Le Duigou A, et al. Main criteria of sustainable natural fibre for efficient unidirectional biocomposites. Compos Part Appl Sci Manuf 2019;124:105504. https://doi.org/10.1016/j.compositesa.2019.105504.

[18] A. Bourmaud L. Nuez C. Goudenhoofc C. Baley Multi-scale mechanical characterization of flax fibres for the reinforcement of composite materials. In: Maria, editor. Handb. Nat. Fibres Second Ed., Woodhead Publishing; 2020, p. 205-26.

[19] Thygesen A, Madsen B, Bjerre A, Lilholt H. Cellulosic fibers: effect of processing on fiber bundle strength. J Nat Fibers 2011;8:161-75. https://doi.org/10.1080/15440478.2011.602236.

[20] Charlet K, Jernot JP, Eve S, Gomina M, Bréard J. Multi-scale morphological characterisation of flax: from the stem to the fibrils. Carbohydr Polym 2010;82:54-61. https://doi.org/10.1016/j.carbpol.2010.04.022.

[21] Baley C, Gomina M, Bread J, Bourmaud A, Davies P. Variability of mechanical properties of flax fibres for composite reinforcement a review. Ind Crops Prod 2020;145:111984. https://doi.org/10.1016/j.indcrop.2019.111984.

[22] Charlet K, Jernot J-P, Bread J, Gomina M. Scattering of morphological and mechanical properties of flax fibres. Ind Crops Prod 2010;32:220-4. https://doi.org/10.1016/j.indcrop.2010.04.015.

[23] Depuydt D, Hendrickx K, Biesmans W, Ivens J, Van Vuure AW. Digital image correlation as a strain measurement technique for fibre tensile tests. Compos Part Appl Sci Manuf 2017;99:76-83. https://doi.org/10.1016/j.compositesa.2017.03.035.

[24] Thomason JL, Carruthers J, Kelly J, Johnson G. Fibre cross-section determination and variability in sisal and flax and its effects on fibre performance
characterisation. Compos Sci Technol 2011;71:1008-15. https://doi.org/10.1016/
j.compscitech.2011.03.007.

[25] Garat W, Corn S, Le Moigne N, Beaugrand J, Bergeret A. Analysis of the morphometric variations in natural fibres by automated laser scanning: towards an efficient and reliable assessment of the cross-sectional area. Compos Part Appl Sci Manuf 2018;108. https://doi.org/10.1016/j.compositesesa.2018.02.018.

[26] Ilczyszyn F, Cherouat A, Montay G. Mechanical modeling of hemp fibres behaviour using digital imaging treatment. Adv Mater Res 2012;423. https://doi.org/
10.4028/www.scientific.net/AMR.423.143.

[27] Bos HL, Van Den Oever MJA, Peters OCJJ. Tensile and compressive properties of flax fibres for natural fibre reinforced composites. J Mater Sci 2002;37:1683-92.
https://doi.org/10.1023/A:1014925621252.

[28] Barbulée A, Gomina M. Variability of the mechanical properties among flax fiber bundles and strands. Procedia Eng 2017;200:487-93. https://doi.org/10.1016/j.
proeng.2017.07.068.

[29] Romhány G, Karger-Kocsis J, Czigány T. Tensile fracture and failure behavior of technical flax fibers. J Appl Polym Sci 2003;90:3638-45. https://doi.org/10.1002/
app.13110.

[30] Melelli A, Arnould O, Beaugrand J, Bourmaud A. The middle lamella of plant fibers used as composite reinforcement: investigation by atomic force microscopy. Molecules 2020;25:632. https://doi.org/10.3390/molecules25030632.

[31] Alix S, Lebrun L, Marais S, Philippe E, Bourmaud A, Bailey C, et al. Pectinase treatments on technical fibres of flax: effects on water sorption and mechanical properties. Carbohydr Polym 2012;87:177-85. https://doi.org/10.1016/j.
carbpol.2011.07.035.

[32] Perremans D, Hendrickx K, Verpoest I, Van Vuure AW. Effect of chemical treatments on the mechanical properties of technical flax fibres with emphasis on stiffness improvement. Compos Sci Technol 2018;160:216-23. https://doi.org/
10.1016/j.compscitech.2018.03.030.

[33] Gautreau M, Durand S, Paturel A, Le Gall S, Foucat L, Falourd X, et al. Impact of cell wall non-cellulosic and cellulosic polymers on the mechanical properties of

flax fibre bundles. Carbohydr Polym 2022;291:119599. https://doi.org/10.1016/j.
carbpol.2022.119599.

[34] Barbulée A, Jernot J-P, Bréard J, Gomina M. Damage to flax fibre slivers under monotonic uniaxial tensile loading. Compos Part Appl Sci Manuf 2014;64:107-14.
https://doi.org/10.1016/j.compositesesa.2014.04.024.

[35] Chemikosova SB, Pavlencheva NV, Gur'yanov OP, Gorshkova TA. The effect of soil drought on the phloem fiber development in long-fiber flax. Russ J Plant Physiol 2006;53:656-62. https://doi.org/10.1134/S1021443706050098.

[36] Melelli A, Durand S, Alvarado C, Kervoëlen A, Foucat L, Grégoire M, et al. Anticipating global warming effects: a comprehensive study of drought impact of both flax plants and fibres. Ind Crops Prod 2022;184:115011. https://doi.org/10.1016/j.indcrop.2022.115011.

[37] Bourmaud A, Siniscalco D, Foucat L, Goudenhooft C, Falourd X. Evolution of flax cell wall ultrastructure and mechanical properties during the retting step. Carbohydr Polym 2019;206. https://doi.org/10.1016/j.carbpol.2018.10.065.

[38] Meyer VR. Measurement uncertainty. J Chromatogr A 2007;1158:15-24. https://doi.org/10.1016/j.chroma.2007.02.082.

[39] Weitkamp T, Scheel M, Giorgetta JL, Joyet V, Roux VL, Cauchon G, et al. The tomography beamline ANATOMIX at synchrotron SOLEIL. J Phys Conf Ser 2017; 849:012037. https://doi.org/10.1088/1742-6596/849/1/012037.

[40] Mirone A, Brun E, Coan P. A dictionary learning approach with overlap for the low dose computed tomography reconstruction and its vectorial application to differential phase tomography. PLoS One 2014;9:e114325. https://doi.org/10.1371/journal.pone.0114325.

[41] Paganin D, Mayo SC, Gureyev TE, Miller PR, Wilkins SW. Simultaneous phase and amplitude extraction from a single defocused image of a homogeneous object. J Microsc 2002;206:33-40. https://doi.org/10.1046/j.1365-2818.2002.01010.x.

[42] Bailey C, Bourmaud A. Average tensile properties of French elementary flax fibers. Mater Lett 2014;122:159-61. https://doi.org/10.1016/j.matlet.2014.02.030.

[43] Casa R, Russell G, Lo Cascio B, Rossini F. Environmental effects on linseed (Linum usitatissimum L.) yield and growth of flax at different stand densities. Eur J Agron 1999;11:267-78. https://doi.org/10.1016/S1161-0301(99)00037-4.