# Flax fibre bundle: A remarkable multi-scale unidirectional composite material

Margot Chalard, Camille Goudenhooft, Alessia Melelli, Mario Scheel, Timm

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

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## To cite this version:

Margot Chalard, Camille Goudenhooft, Alessia Melelli, Mario Scheel, Timm Weitkamp, et al. Flax fibre bundle: A remarkable multi-scale unidirectional composite material. Composites Part A: Applied Science and Manufacturing, 2025, 196, pp.108990. 10.1016/j.compositesa.2025.108990. hal-05333756

HAL Id: hal-05333756

https://hal.science/hal-05333756v1

Submitted on 27 Oct 2025

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# Flax fibre bundle: A remarkable multi-scale unidirectional composite material

Margot Chalard<sup>a, *, †</sup>, Camille Goudenhooft<sup>a †</sup>, Alessia Melelli<sup>b</sup>, Mario Scheel<sup>b †</sup>, Timm Weitkamp<sup>b</sup>, Pierre D'arras<sup>c †</sup>, Alain Bourmaud<sup>a</sup>, Christophe Baley<sup>a †</sup>

## ARTICLE INFO

### Keywords:

Flax fibre bundles

Fibre tips

Mechanical properties

Intrusive growth

## ABSTRACT

Flax fibre bundles possess a remarkable structure, mainly generated through intrusive growth, that can be likened to a unidirectional composite reinforced with discontinuous fibres, resulting in complex mechanical behaviour. The main objectives of the present work are to provide a detailed description of the microstructure and local mechanical properties of the bundle components to better explain their specific mechanical behaviour. Their tensile behaviour was examined using tensile testing and scanning electron microscopy, revealing disparities in the fracture phenomena. Micro-tomographic and multi-photon microscopy images revealed the presence of fibre ends (tips) with a high fraction of crystalline and oriented cellulose. Additional tests were conducted using atomic force microscopy to estimate the thickness and indentation modulus of the middle lamellae, the primary cell wall as well as the S1 and S2 layers. These observations elucidate the origin of the remarkable multi-scale structure of the flax bundles.

## 1. Introduction

Flax fibres are a renewable resource [1], with remarkable specific tensile mechanical properties comparable to those of glass fibres [2], making them suitable for use as reinforcing elements in composite materials [3–5]. They are best fibres located at the periphery of the stem, in the phloem region (Fig. 1.a) [6] and are organised in fibre bundles, each consisting of elementary fibres linked by the middle lamellae [1] (Fig. 1.b).

Flax fibres are produced by complex growth mechanisms that are difficult to observe and characterise [8]. Despite these challenges, Gorshkova et al. [6] showed that flax fibres differentiate from other cells at the onset of stem growth, about three weeks after germination, by undergoing two main developmental stages, namely elongation followed by a thickening of the secondary cell wall [6,8]. Elongation occurs first, starting above a specific point called the snap point (SP), located between 45 and 90 mm from stem's apex, with its position varying during the growth period [6]. During the initial elongation phase the fibrous cells undergo symplastic (or coordinated) growth during which neighbouring cells exhibit similar growth rate [8]. The second phase is

intrusive growth, during which the growth rate of certain cells exceeds that of neighbouring cells. Cells with higher growth rates elongate by intruding into the middle lamellae. Following this phase, which extends over a period of between two and four days, the cells reach their maximum size and progressively evolve into long fibres. After elongation, the secondary cell wall of the fibres thickens (below the SP), with the fibres located at the periphery of the stem thickening first. This phase concludes just before flowering, at the end of stem elongation, around 50 days after germination [6,7]. Fig. 2 illustrates the stages of plant growth up to flowering, highlighting the fibre formation period [6,7,9].

These stages of cell growth, particularly intrusive growth, are also observed in other natural structures such as wood [10,11]. Table 1 provides a summary of published values for flax fibre diameter and length.

Flax fibres exhibit a hierarchical organisation analogous to the structure of a composite material [16]. They comprise two polygonal cell walls: the primary and secondary cell walls, with a central cavity called the lumen [1,17]. The primary cell wall (PCW) is the outer layer, approximately 0.2 µm thick [18]. The secondary cell wall (SCW) has a high degree of crystallinity, ranging from 67 to 75 % [19], and consists

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

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

<footnote><sup>c</sup> Van Robaeys Frères, 83 rue Saint-Michel, 59122 Killem, 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>
of three sub-layers: S1, S2, and S3 (with average total thicknesses of between 5 and 15 µm) [20]. S1 is thin and in contact with the primary cell wall. S2 layer (also known as the G-layer) is a unidirectional layer with fibrils oriented at an angle of between 4 and 10° (depending on the measurement method) to the fibre axis [21,22]. This is the thickest layer (ranging from 10 to 15 µm) and significantly influences the fibres' mechanical properties due to its high cellulose content (between 80 and 85 %) [19]. Finally, S3 (also known as Gn) is a thin layer that surrounds the lumen [21] (Fig. 3). The indentation modulus of flax fibres measured using atomic force microscopy (AFM PF-QNM) is around 18 GPa [23,24], while for middle lamellae, the average stiffness is $10.2 \pm 1.2$ GPa [17].

To facilitate the extraction of fibres from the stem following the pulling-out step, flax stems are laid on the ground for the retting stage. During this phase, the alternation of rain and sun facilitates the development of bacteria and fungi that produce enzymes to colonise the stem and partially degrade the pectin [25]. The pectin, present in the middle lamellae, epidermis, and cortical parenchyma, ensures the cohesion of the fibres within the stem [25,26]. Retting quality affects the cell wall's indentation modulus, with longer retting times resulting in elementary fibres with a higher indentation modulus [27]. During scutching, the fibres are extracted from the stem and remain organised in bundles [28]. Studying their arrangement remains a significant challenge for flax scutchers as they aim to ensure consistent levels of quality across batches. With a thickness of around 40 µm, flax bundles are organised in a way that is comparable to unidirectional composites reinforced with discontinuous fibres. Bailey et al. [14], comparing the cross-sections of a flax fibre bundle and of ply reinforced with carbon fibres (Fig. 4), highlighted how flax fibre bundles possess a remarkable polygonal cross-section, while, synthetic fibres are organised in a more circular fashion, leaving more room between fibres which can lead to more structural defects [14].

The mechanical properties of fibre bundles can be measured using tensile tests. Failure during tensile testing can be caused by several phenomena described by Romhány et al. [29]. It can occur at the interface between the fibres and the middle lamellae, causing slippage of elementary fibres. Microcracks may also develop in the elementary fibres, and failure can result from cumulative damage. These phenomena are affected by the gauge length (the distance between the jaws) chosen for tensile testing [30,31]. As the gauge length decreases, the probability of discontinuities within bundles diminishes. Consequently, the mechanical properties approach those of elementary fibres without ever fully reaching them due to inaccuracies in measuring the cross-section and the presence of the middle lamellae, which are damaged by the retting process [17,32]. When the gauge length exceeds the length of elementary fibres, the likelihood of defects such as kink-bands increases. Consequently, there is a higher probability of fracture occurring within the middle lamellae, specifically at the interface with the elementary fibres [29,32–34].

The main objective of this study is to conduct a detailed analysis of the structure of a flax fibre bundle. This is achieved through tensile tests

followed by scanning electron microscopy (SEM) of fracture surfaces of bundles. To establish a link between their mechanical behaviour under tension and their microstructure, their structure was then analysed using X-ray microtomography (micro-CT) scans and second harmonic generation (SHG) microscopy. This highlighted the fibre tips, whose shape and, in particular, the evolution of the cross-sectional area at the end were studied. Subsequently, for the precise analysis of the structure and properties of a bundle, atomic force microscopy (AFM) acquisitions were performed to determine the average thickness of the different layers of a bundle along with the evolution of the indentation modulus.

## 2. Materials and methods

### 2.1. Plant materials: Flax fibre bundles

Scutched flax fibre bundles of the Damara variety grown in Oise (France) in 2021 and provided by Van Robaeys Frères (Killem, France) were used for the experiments. Damara is a mid-range variety, cultivated in France since 2011, known for its high fibre yield (44.7 %) according to the official catalogue of varieties grown in France (https://www.infalis.fr/).

Sowing was carried out on April 10, 2021. The plants exhibited rapid and uniform development until August 4, the date of harvesting. The stems were subsequently retted until September 6, 2021. Meteorological data, including precipitation, as well as minimum and maximum temperatures recorded between April 10 and September 6, 2021, were obtained from the nearest weather station (Beauvais-Tille) via https://www.infoclimat.fr (Fig. 5).

For the present study, bundles were taken from the middle part of the stem.

### 2.2. Tensile tests on flax fibre bundles

To prepare samples for tensile tests, the bundles were glued onto two pieces of paper 11 mm apart (gauge length of the device). They were then fixed in a Deben (UK) microtest 200 N tensile testing machine (Fig. 6) and tested at a rate of 0.1 mm/min. The testing machine was viewed under a scanning electron microscope (SEM), Jeol JSM 6460 LV (Tokyo, Japan), to better understand the phenomena involved in the tensile loading of a bundle.

### 2.3. X-ray micro-tomography

X-ray computerised microtomography (micro-CT) was performed on the ANATOMIX beamline at Synchrotron SOLEIL (France) to study the cross-sectional area and obtain a segmented three-dimensional rendering of flax fibre bundles and fibre tips [35]. Samples were prepared using Terumo® Agani™ 0.5 mm diameter needles, which were cut to a length of 25 mm and glued onto a Huber 1002–18 MS specimen carrier (with a 0.8 mm diameter central hole) leaving 15 mm of the needles protruding. Manually extracted bundles were then glued to the

<figure><img src="image_5.png" /><figcaption>Fig. 1. Location of the fibres within the stem (a) and zoom on a fibre bundle (b) image from [7].</figcaption></figure>
<figure><img src="image_6.png" /><figcaption>Fig. 2. Stages of stem growth up to flowering (a); locations and stages of fibre growth within the stem (b), images adapted from [6,7,9].</figcaption></figure>

ends of the needles in a vertical orientation leaving a free length for scanning of approximately 5 mm (Fig. 7.a). The distance between the samples and the detector was 15 mm. Eight bundles from the Damara 2021 batch were analysed, but only one was measured at five different heights to increase the chances of observing the fibre tips within the bundles. A photon energy of 11.5 keV, provided by a monochromatic X-ray beam (DCM Si-111), was used to acquire high-resolution images, ensuring the fibres remained undamaged. For the micro-CT measurements, detector comprised of a Hamamatsu Orca Flash CMOS camera with 20 × optical magnification (Mitutoyo, Japan) and a scintillator (Lu₃Al₅O₁₂) were used. The principle of image acquisition is as follows: an X-ray beam is emitted and interacts with the rotating sample. The transmitted signal is then detected by the scintillator, which converts the X-rays into visible light, and is subsequently captured by the camera through the attached 20x magnifying optic (Fig. 7.b and 7.c). This setup yielded images with a field of view of 650 × 650 µm² and an effective pixel size of 325 nm. For each acquisition 2000 projection angles were used from within the range of 0 to 180° with an exposure time of 200 ms. The tomographic data were reconstructed using PyHST2 software (ESRF, Grenoble) [36] and, a 25 Paganin filter [37] was incorporated to reduce the ring artefacts.

To obtain three-dimensional rendering, ImageJ was used to analyse the tomographic slices. Two areas in which fibre tips were visible inside the bundles were selected and imported to AVIZO software (2021.1) in 16-bit. This yielded two three-dimensional renderings of the same bundle obtained at different heights. For the reconstruction, only the fibres near the tips were considered and segmented. The outer zone (i.e., the part containing no fibres) was defined using a threshold tool that uses pixel grey levels to trace the outline of an object. Then, each fibre was manually isolated using the brush tool and the keyboard shortcut (Ctrl + i) to extend the selection over a small portion of images. Finally, the surface tool was used to smooth the contour reconstruction.

## 2.4. Evaluation of single fibre length

To determine the lengths of the elementary fibres in the batch, around 100 elementary fibres were manually extracted from the middle of the stem. They were placed on a black paper and observed under a high-precision digital optical microscope (Keyence VHX-7000, France). After an initial check to ensure that they were elementary fibres, their lengths were measured using a microscope, yielding the lengths of 52 elementary fibres, measured from the middle of the stem.

## 2.5. Microscopic observation of single fibre tips

After metallisation by gold sputtering, some of the previously studied elementary fibres were glued onto conductive supports and their tips were observed under a Jeol JSM 6460 LV SEM (Tokyo, Japan).

## 2.6. Multiphoton imaging microscopy

To analyse the morphology of fibre tips and the organisation of microfibrils within them, observations were conducted using a multiphoton Nikon A1 MP + microscope (Nikon Corp., Japan), equipped with a long working distance (LWD) 25× (NA 1.1) water immersion objective (Nikon Corp., Japan), a tuneable Mai Tai XF mode-5 locked Ti:sapphire femtosecond pulsed laser (SPECTRA PHYSICS, France), a half-wave plate (MKS-Newport, USA), and a motorised stage. Microscopic imaging analyses were performed after setting the excitation wavelength to 810 nm. The average laser power was 1525 mW, it was attenuated to 5 % of this value to avoid bleaching and fibre damage. The microscope is equipped with GaAsP non-descanned detectors (NDDs), four each for collecting emissions in the backward (reflection) and forward (transmission) directions, although only three were used per direction, with bandpass filters at 460/60 nm and 550/88 nm for two-photon excitation fluorescence (2PEF) and at 406/15 nm for the second harmonic generation (SHG). The polarisation angle was set at 0° to obtain the highest

<table><caption>**Table 1**
Length and diameter of elementary fibres reported in the literature [12–15].</caption><thead><tr><th rowspan="2">References</th><th colspan="2">Fibre length (mm)</th><th colspan="2">Fibre diameter (µm)</th></tr><tr><th>Average</th><th>Range</th><th>Average</th><th>Range</th></tr></thead><tbody><tr><td>Harris M, 1954 [12]</td><td>33</td><td>9–70</td><td>19</td><td>5–38</td></tr><tr><td>McDougall, G J et al., 1993 [13]</td><td>/</td><td>2–40</td><td>/</td><td>20–23</td></tr><tr><td>Baley et al., 2018 [14]</td><td>35.5 ± 16.3</td><td>11–87</td><td>Between 14.4 ± 4.7 and 17.1 ± 5.4</td><td></td></tr><tr><td>Baley, 2020 [15]</td><td>/</td><td>13–60</td><td>/</td><td>12–30</td></tr></tbody></table>
<figure><img src="image_7.png" /><figcaption>Fig. 3. Structure of an elementary fibre and orientation of the fibrils in each layer (a); cross section of an elementary fibre (b) images adapted from [2,17].</figcaption></figure>

<figure><img src="image_8.png" /><figcaption>Fig. 4. Cross-sections of a (a) flax fibre bundle, and (b) ply composite reinforced with carbon fibres, images from [14].</figcaption></figure>

<figure><img src="image_9.png" /><figcaption>Fig. 5. Minimum and maximum temperatures, as well as rainfall data from the nearest weather station (www.infoclimat.fr) during the growth period of the plant.</figcaption></figure>

<figure><img src="image_10.png" /><figcaption>Fig. 6. Position of the bundle within the device (a); picture of the device used to perform tensile tests under SEM (b).</figcaption></figure>
<figure><img src="image_11.png" /><figcaption>Fig. 7. Sample preparation (a), measuring device used for microtomographic observations (b) and schematic representation of the image acquisition process at the synchrotron (c).</figcaption></figure>

second harmonic emission as described in Melelli et al. [38].

Images were acquired with NIS Elements software (Nikon Corp., Japan) using scan speed of 0.5 frame/sec with a line average of 8. The yielded images had a resolution of 512 × 512 pixels and, using a numerical zoom of 4×, a pixel size of 250 nm. The stack-in-depth was acquired with a step size of 0.5 µm, resulting in a total stack of 47 images. In the plane showing the highest SHG signal, a single image of the tip was also acquired with a zoom of 6× (pixel size: 170 nm) and the line average set at 16. The images were then processed using ImageJ software. A composite image was created using both 2PEF (blue: 460/60 nm, magenta: 550/88 nm) and SHG (yellow) channels.

The SHG channel acquired at 6 × magnification was also analysed using the OrientationJ plugin [39–41] after rotating the image by + 17° to make the fibre axis coincide with the abscissa (using bicubic interpolation). A region of interest (ROI) was created with the rectangle tool to remove the image edges and select only the fibre. The OrientationJ analysis plugin was then used with a Gaussian gradient and a local window of 4 pixels, corresponding to the average thickness of the fibrils to be evaluated. This resulted in a false-colour image where the angle of orientation of the microfibrils corresponded to the colour at the same angle of the colour wheel (hue). The OrientationJ distribution plugin was also used with a minimum coherency of 10 % to generate a histogram of the normalised distribution of angles.

## 2.7. Atomic force microscopy (AFM)

AFM acquisitions of flax fibre bundles provided information on morphology and local mechanical properties. Sample smaller than 5 mm was first encapsulated in Agar Low Viscosity resin (epoxy resin, Agar Scientific, UK) and kept at 60 °C overnight for polymerisation. The sample was then cut and glued onto a stainless-steel AFM mounting disk. To prepare the sample surface, an Ultracut S microtome (Leica Microsystems, Wetzlar, Germany) fitted with Trim and Ultra diamond knives for AFM (Diatome, Nidau, Switzerland) was used. The final thickness of the cut sample was 60 nm. A multimode 8 AFM instrument (Bruker Corporation, Massachusetts, USA) in peak force quantitative nano-mechanical mapping (PF-QNM) imaging mode was used for the mechanical characterisation of the bundles. The instrument was equipped with a RTESPA-525 (Bruker) probe with a spring constant of 152 N/m, calibrated using the Sader method (https://sadermethod.org/). To calibrate the tip and obtain reliable and pertinent indentation modulus, measurements on the cross-section of a K305 aramid fibre were conducted, a tip radius of 40 mm was selected, yielding an indentation

modulus of approximately 20 GPa. This value (range: 18 to 22 GPa) aligns with those found in the literature [24,42,43]. The maximum load applied during all measurements was 200 nN. The images were acquired with a scan rate of 0.1 Hz and a gain of 50. The two images showing several fibres had a resolution of 256 × 256 samples/line (15 µm window), while the zoomed image of the middle lamellae had a resolution of 512 × 512 samples/line (5 µm window). The image showing an elementary fibre near the fibre tip had a resolution of 256 × 256 samples/line (10 µm window). All images were processed using the Gwyddion software (https://gwyddion.net/).

# 3. Results and discussion

## 3.1. SEM observations of flax fibre bundles after tensile testing

The aim of this study is to understand the mechanisms of load transfer between elementary fibres within a bundle. Flax fibre bundles can be considered as unidirectional composite materials [14]. Under tensile loading, the failure of a unidirectional composite occurs after the accumulation of damage (which develops during the test as strain increases) [44,45]. SEM observations of two bundle fracture surfaces after tensile testing illustrate the mechanisms involved pre- (Fig. 8.a and b) and post-rupture (Fig. 8.c and d). Fig. 8.a displays a tensile failure across all the fibres of the bundle, representing a single failure mode. In this case, the full stress potential of the fibres was engaged. Fig. 8.b and 8.c show a panel of bundle failures illustrating the diversity of damage involved, with factures confined to a cohesive region of the bundle, while other areas show signs of decohesion and ruptured fibre bonds. These decohesion zones may correspond to interfacial breaks, which may occur either within the middle lamellae or at the interface between fibres and middle lamellae. Alternatively, they may be linked to intra-fibre degradations, which are not visible at this scale. Finally, Fig. 8.d illustrates a complex fracture mode involving fibre decohesion. In this case, the middle lamellae did not allow stress transfer between the fibres, likely due to dew-retting, which weakens the inter-fibre lamellae facilitating the extraction of bundles from the plant [27].

While these observations revealed that there are several mechanisms at play during tensile testing, they do not serve to identify and quantify the initial damage. This will be achieved though morphological analyses presented in the following sections.
<figure><img src="image_12.png" /><figcaption>**Fig. 8.** Fractured surfaces of two flax fibre bundles (a), (b) and longitudinal view of two bundles under SEM after tensile tests (c) and (d); the areas circled in (b) and boxed in (c) show cohesive zones of the bundle where rupture within the fibres occurred.</figcaption></figure>

<figure><img src="image_13.png" /><figcaption>**Fig. 9.** 3D render of bundle 1 (length 240 µm) (a), and bundle 2 (length: 470 µm) (b), obtained through volume-scanned X-ray micro-CT on the ANATOMIX beamline to show fibre tips; surface residues are not represented; the dashed rectangle delimits a kink-band area.</figcaption></figure>

## 3.2. Organisation of elementary fibres within a flax fibre bundle

### 3.2.1. 3D rendering of a flax fibre bundle

Micro-CT cross-sections were used to create a 3D render of two bundles, segmenting their elementary fibres to highlight their structure (Fig. 9).

Both bundles are fairly cohesive and clearly show a polygonal cross-section of fibres, optimised by nature to have as few defects as possible

(limiting the strain concentration areas) and a high fibre volume fraction [14]. Interestingly, the kink-band areas visible in Fig. 9.a (dashed rectangle) appear at the same location in each fibre, suggesting that they were generated through bundle buckling or bending during the extraction stage. A link can be done with the ruptures observed within fibre bundles (Fig. 8.a), which likely occurred in zones of weakness, i.e., where fibre porosities are present [46]. However, this observation is hypothetical, as the images do not provide clear evidence of this. From a
<figure><img src="image_14.png" /><figcaption>**Fig. 10.** 3D rendering of bundle 1 (a) and bundle 2 (b) obtained through volume-scanned X-ray micro-CT on the ANATOMIX beamline, highlighting the presence of fibre tips; ratio of the fibre volume divided by the length of the bundle for each fibre taken from bundle 1 (c) and from bundle 2 (d).</figcaption></figure>

different angle, it is possible to see the fibre tips (Fig. 10).

Bundle 1 has a highly cohesive part and another part with two slightly debonded fibres with a fibre tip in between (Fibre tip 1, Fig. 10. a). The three remaining fibres were probably detached from the main bundle during the manipulation processes. There are two fibre tips in bundle 2 (Fibre tips 2 and 3, Fig. 10.b). Both reconstructions highlight how the tips are much finer than the rest of the fibre due to intrusive growth. The fibres also exhibit different cross-sectional sizes and filling ratios, particularly in bundle 2 where the pink fibre appears hollow and slightly flat, while the light green fibre has no visible lumen. To confirm

these observations, the fibre volume-to-bundle length ratio (Fig. 10.c and d) was measured. Both bundles show similar distributions, with two fibres visible larger than the others (volume-to-bundle length ratio > 125), five fibres with ratios between 100 and 125, while three fibres in bundle 1 and five in bundle 2 have ratios < 100. The tips have ratios < 25. To analyse these fibre tips in more detail, elementary fibres were examined.

<figure><img src="image_15.png" /><figcaption>**Fig. 11.** Determining the average length of elementary fibres.</figcaption></figure>
<figure><img src="image_16.png" /><figcaption>Fig. 12. Evolution of the cross-section of three fibre tips starting from the ends.</figcaption></figure>

### 3.2.2. Elementary fibres

#### 3.2.2.1. Tip shapes.
The average length of elementary fibres was determined as 26.5 ± 16.0 mm, with a minimum of 3.8 mm and a maximum of 79.6 mm (Fig. 11). These results are in line with those reported for the Marylin 2012 variety by Baley et al. [14]. For this variety, the elementary fibres in the middle part of the stem are between 11 and 87 mm long, with an average length of 35.5 ± 16.3 mm [14].

To analyse the fibre tip morphology, the cross-sectional area (CSA) of each fibre was measured at several distances up to a maximum of 400 µm from the tip. These measurements were used to examine variations in fibre CSA near the tip (Fig. 12).

All fibre tips exhibit smaller CSA at the ends, although the variations are fairly irregular. Tips 1 and 3 show average initial slopes of 0.51 ± 0.16 µm and 0.47 ± 0.14 µm, and slopes between the first and third points of 0.10 ± 0.03 µm and 0.27 ± 0.04, respectively. In contrast, the CSA of tip 2 varies linearly, exhibiting a constant slope of 0.13 ± 0.01 µm over its entire length. Furthermore, the shape of the CSA varies considerably near the end, yielding an average angle of 8.7 ± 3.8° (minimum: 3°, maximum: 13°) at the end of the fibre tips.

SEM analysis showed that the CSA of tip 4 varies fairly regularly over the first 15 µm (tip width varies with an average slope of 0.07 ± 0.01) (Fig. 13.a). This is followed by a steeper increase in width from 1.7 µm to 4.25 µm over a distance of 5 µm (slope: 0.21). Finally, in the last visible part of the fibre, the variation in width becomes more regular (0.10 ± 0.01). Similar patterns are observed for tip 5 (Fig. 13.b), which exhibits a very small width of 0.2 µm at the end, widening to 1.4 µm (+ 600 %) 5 µm from the tip and continuing to widen steadily over the next 15 µm.

These observations, which are only illustrative, support the hypothesis that flax fibre tips can have a variety of shapes, bearing in mind that human intervention may have altered their shape.

Furthermore, these SEM and micro-CT images clearly showed the influence of intrusive growth on fibre morphology (yielding very fine ends). However, characterising and quantifying this phenomenon is challenging due to the unique specificity and morphology of each fibre.

#### 3.2.2.2. Studying fibre ultrastructure through multi-photon microscopy.
Fig. 14 shows different observations obtained through second harmonic generation (SHG) microscopy and the fluorescence channel of the multi-photon microscope. Fig. 15.a depicts changes in micro-fibrillar angle (MFA) for the tip shown in Fig. 14.a, while Fig. 15.b presents a histogram of MFA values.

In Fig. 14.a, the SHG channel clearly shows a fibre tip and its specific organisation. The SHG signal allows the visualisation of non-centrosymmetric molecules; such as crystalline cellulose, the primary component of flax fibres. Previous studies have demonstrated the suitability of multiphoton microscopy in assessing microfibril angles of plant fibres [38,47]. The nearly longitudinal orientation of the cellulose fibrils with respect to the fibre axis is also evident in the terminal region of the tip (Fig. 14.a and Fig. 15.a), suggesting that the crystalline cellulose remains well-ordered even at the tip's end. These observations are corroborated by the histogram in Fig. 15.b which shows two main peaks corresponding to the angles of 2.5° and 5.5°, along with a secondary lower peak at 0°. These results fall within the typical range measured for flax MFA [38]. Some misorientations with angles up to 30° are also apparent in specific tip regions both in the colour image and histogram (Fig. 15.a and b).

Just before the fibre narrows to form the tip, a thicker, rounded area is visible (dotted area in Fig. 15.a) where the crystalline cellulose microfibrils achieve their highest angles, ranging between 20° and 30° (Fig. 15.b). Notably, the reduced SHG emission along the fibre axis in the centre of this region can be attributed to the presence of the lumen, which remains visible just prior to the drastic shape modification of the fibre. Furthermore, one hypothesis for the formation of the thickened area, exhibiting a significant MFA deviation, is that intrusive growth through neighbouring fibres leads to the accumulation of material at the point where the fibre begins to penetrate the middle lamellae of the adjacent cells.

A striction zone is also visible (indicated by the arrow in Fig. 14.a), which likely developed during the cellulose thickening stage that occurred following the intrusive elongation of the fibre.

In this specific region, a local increase in the MFA is observed. In the tip area, the SHG signal is intense, likely due to a high concentration of crystalline cellulose and a decrease in the thickness of the primary cell wall and of the S1 layer, which provides greater accessibility to the S2 crystalline cellulose.

<figure><img src="image_17.png" /><figcaption>Fig. 13. SEM observations of two flax fibre tips; tip 4 (a) and tip 5 (b).</figcaption></figure>
<figure><img src="image_18.png" /><figcaption>**Fig. 14.** Multi-photon microscopy observations of a fibre tip showing the SHG (a) and fluorescence (b) signals; SHG signal in another focal plane, focusing on a flax fibre located below the observed tip (c); composite image of SHG and fluorescence signals (d).</figcaption></figure>

<figure><img src="image_19.png" /><figcaption>**Fig. 15.** Fig. 14a treated with the OrientationJ analysis plugin in ImageJ (a₁), the corresponding colour wheels (a₂) and histogram of the micro-fibrillar angle (MFA) distribution in the tip (b). The dotted zone in (a₁) indicates the area where the crystalline cellulose microfibrils reach their highest angles.</figcaption></figure>
<figure><img src="image_20.png" /><figcaption>**Fig. 16.** Longitudinal (1) and transverse (2) sections of bundles 1 (a) and 2 (b); the coloured fibres are those from the 3D rendering.</figcaption></figure>

In Fig. 14.a, a flax fibre is also visible beneath the tip. Its SHG intensity appears lower; however, this is attributed to the selected focal plane. With the depth stack and the change in the focal plane (Fig. 14.c), the intensity of the fibre behind reaches a similar range.

Multi-photon microscopy also provides a fluorescence signal (Fig. 14.b), primarily attributed to lignin, pectin, and waxes, which are predominantly located in the outer layers of the fibre, as the S2 layer is poorly enriched in lignin. As observed in the region with the greatest MFA deviation in the thickest area of the fibre – just before it narrows to form the tip – the accumulation of fluorescent material at both 460 nm and 550 nm suggests the presence of lignin, pectin, and possibly a small amount of wax [48,49]. This accumulation of fluorescent material may result from remnants of the middle lamellae of neighbouring fibres or from a product of the fibre itself that reinforces the area in contact with neighbouring fibres during the intrusive elongation phase.

### 3.2.2.3. Tip arrangements.
To obtain a clearer view of the arrangement of the fibre tips within the bundles, longitudinal and transverse sections were extracted from the micro-tomography acquisitions shown in Fig. 16. Longitudinal cross-sections of bundles 1 and 2 are shown in Fig. 16.a₁ and Fig. 16.a₂, respectively. Additionally, cross-sections of bundles 1 and 2 are presented in Fig. 16.b₁ and b₂, respectively.

The longitudinal sections of bundles 1 and 2 in Fig. 16 illustrate the interlocking of the fibres within these bundles. In particular, Fig. 16.a₁ depicts the imbrication of tip 1 from two different angles. The tip has influenced the shape of the fibres in contact with it. Specifically, the two longitudinal sections demonstrate that tip 1 is perfectly shaped to fit between the two fibres it contacts. In the longitudinal sections of tip 2

shown in Fig. 16.a₂, the organisation differs because the tip is located at the periphery of the bundle. A portion of the tip does not contact a fibre; however, the other part of the tip aligns perfectly with the shape of the neighbouring fibre. In both cases, a reduction in the diameter of the fibres adjacent to the tip is evident. For instance, in the first longitudinal section (Fig. 16.a₁), the diameter of the pink fibre decreases by 54 %, while that of the blue fibre decreases by 28 % between the tip's extremity and the top of the image. The cross-sections in Fig. 16.a₂ and b₂ further illustrate the imbrication of the fibres within the bundles. As with the longitudinal sections, the ends of the fibres are shaped to match the sides of the adjacent fibres. Consequently, the bundles form cohesive structures composed of fibres with varying shapes, cross-sections, and lengths. In all cases, nature optimises the overlapping of fibres within the bundles, particularly through intrusive growth. This results in bundles with a high fibre volume fraction (95 % within the stem [11]), attributable to the shape of the fibres, which is influenced by the adjacent fibres, while minimising areas of strain concentration (i.e. reducing local strains). Based on these observations, a summary diagram of the structure of flax bundles in two dimensions is presented in Fig. 17.

The micro-tomography analysis enabled the generation of a 3D-rendering of flax fibre bundles; however, it did not allow for the differentiation between the middle lamellae and the elementary fibres. As both the fibres and the middle lamellae possess densities, they are represented with the same colour in the software (i.e. the same grey level) and thus remain indistinguishable. Consequently, additional studies employing AFM indentation were conducted to obtain more detail information regarding the structure of the bundles, specifically to identify the distinct layers of the elementary fibres and any heterogeneities

<figure><img src="image_21.png" /><figcaption>**Fig. 17.** Schematic view of a cross-section (a) and longitudinal section of a flax bundle (b).</figcaption></figure>
<figure><img src="image_22.png" /><figcaption>**Fig. 18.** Indentation modulus of a flax fibre bundle; Residual indents from nanoindentation can be observed. The circled area shows porosities within the fibre, while the dotted square highlights the junction between the three fibres.</figcaption></figure>

within the middle lamellae (ML) [17], by examining variations in rigidity.

### 3.3. Morphological and mechanical analysis of a bundle using AFM

The AFM PF-QNM indentation modulus of a flax fibre bundle is shown in Fig. 18. The colour contrasts indicate differences in indentation modulus.

Fig. 18 reveals three elementary fibres separated by a triangular junction corresponding to the middle lamellae. It clearly demonstrates the difference in stiffness between the fibres and the ML region. A defect in the fibre can be observed at the bottom left, which is attributed to porosity, at the beginning or end of a kink-band region (area circled in Fig. 18) [50]. Fig. 19.a provides a zoomed-in view of the junction between the fibres, focusing on the area outlined by the dotted square in Fig. 18. The S2 layer can be identified by its superior mechanical properties compared to the other layers, which can be attributed to its higher cellulose content [19]. The boundary between the PCW and the S1 layer is more challenging to differentiate; however, an approximation can still be made based on the thin yellow and green regions between the ML and the fibres, which appear to correspond to the S1 layer and the

PCW, respectively. Based on the variations in indentation modulus, the boundaries between each layer can be identified (Fig. 19.a), and Fig. 19. b illustrates the evolution of the average indentation modulus within each zone.

The average indentation modulus for the S2, S3, PCW and ML layers is $21.2 \pm 2.3$, $16.6 \pm 1.9$, $14.4 \pm 2.0$, and $11.21 \pm 1.92$ GPa, respectively. These values align with those reported in the literature and are summarised in Table 2 [14,17,23,24,27]. Notably, a progressive and gradual decrease in indentation modulus is evident from the S2 to the ML layer. Specifically, in the fibres from this batch, a 22 % reduction in mechanical properties was observed between the S2 and S1 layers, and a 13 % reduction was noted between the S1 layer and the PCW. Consequently, mechanical properties vary significantly within a fibre, with the S2 layer exhibiting the highest mechanical properties. Heterogeneous mechanical properties within the ML are also illustrated in Fig. 19.a.

A fibre cross-section measuring 49 µm², possibly located near a fibre end, was examined using AFM. The indentation modulus mapping is presented in Fig. 20. The average indentation modulus in the S2 layer is $20.5 \pm 2.2$ GPa, which is very similar to the value indicated in Fig. 19.b. Moreover, there is no discernible difference in the structural or property gradient, indicating the homogeneous maturity of the S2 layer. However, the indentation modulus mapping reveals a concentric arrangement of cellulose layers surrounding the lumen, highlighting the progressive deposition of cellulose from the exterior of the fibre to the lumen over time.

Analysis of Fig. 19.a enabled the calculation of average thicknesses for the ML, PCW and S1 layers for each fibre (Table 3).

While the average thickness of the ML found in this study aligns well with the average values reported in the literature, the thickness values obtained for the PCW and S1 layers are relatively low. However, the thickness measurements of the PCW and S1 layers in references [18] and [52] were derived from measurements of images with lower resolutions than those obtained using AFM. Consequently, the results of the present study are likely to be more reliable. Nevertheless, as our findings are based on average measurements from only three fibres, further measurements on additional fibres are necessary to validate these results.

Overall, it is evident that both the mechanical properties and layer thicknesses measured in flax fibres exhibit considerable variability, which can be attributed to the inherent natural characteristics of flax [32].

### 3.4. Remarkable organisation of a flax fibre bundle

The flax stem has a highly optimised internal architecture, reinforced by a peripheral ring of unidirectional fibres located in the phloem

<figure><img src="image_23.png" /><figcaption>**Fig. 19.** Differentiation of the different layers within the elementary fibres (a) and average properties (calculated from the AFM mechanical mapping) associated with each zone (b). The standard deviation was calculated from values measured using Gwyddion software.</figcaption></figure>
<caption>**Table 2**</caption>

Average mechanical properties measured by AFM in the S1 and S2 layers and in the middle lamellae (ML) [14,17,23,24,27].

<table><thead><tr><th>Variety</th><th>Layer</th><th>Stiffness (GPa)</th><th>Reference</th></tr></thead><tbody><tr><td rowspan="4">Damara, 2021</td><td>ML</td><td>11.2 ± 1.9</td><td rowspan="4">This study</td></tr><tr><td>PCW</td><td>14.4 ± 2.0</td></tr><tr><td>S1</td><td>16.6 ± 1.9</td></tr><tr><td>S2</td><td>21.2 ± 2.3</td></tr><tr><td rowspan="2">Marylin, 2012</td><td>S2</td><td>18</td><td rowspan="2">Baley et al., 2018 [14]</td></tr><tr><td>ML</td><td>8</td></tr><tr><td>Eden, 2015</td><td>ML</td><td>10.2 ± 1.2</td><td>Melelli et al., 2020 [17]</td></tr><tr><td rowspan="4">Eden, 2016</td><td>60 days after sowing</td><td>S2</td><td>18.0 ± 1.9</td><td rowspan="4">Goudenhooft et al., 2018 [23]</td></tr><tr><td rowspan="2">120 days after sowing</td><td>S3</td><td>14.0 ± 1.8</td></tr><tr><td>S2</td><td>18.4 ± 1.3</td></tr><tr><td>60 days after sowing</td><td>S2</td><td>18.0 ± 2.9</td><td rowspan="2">Arnould et al., 2017 [24]</td></tr><tr><td></td><td>S3</td><td>13.0 ± 3.8</td></tr><tr><td rowspan="4">Alizée, 2011</td><td>Between 1 and 9 days of retting</td><td>S2</td><td>Between 17.2 ± 1.5 and 21.1 ± 1.8</td><td rowspan="4">Bourmaud et al., 2019 [27]</td></tr><tr><td>Between 14 and 19 days of retting</td><td>S2</td><td>Between 20.3 ± 1.2 and 22.3 ± 1.4</td></tr><tr><td>Between 1 and 9 days of retting</td><td>S2</td><td>Between 12.4 ± 1.7 and 13.6 ± 0.8</td></tr><tr><td>Between 14 and 19 days of retting</td><td>ML</td><td>Between 5.4 ± 0.2 and 6.0 ± 0.3</td></tr></tbody></table>

<figure><img src="image_24.png" /><figcaption>**Fig. 20.** Cross-section of an elementary fibre close to the tip.</figcaption></figure>

(support tissues), giving to the plant an exceptionally high slenderness ratio (height-to-diameter) [57]. The fibres are organised into bundles (Fig. 1.b), providing natural structural reinforcement. Under wind loading, the stem undergoes bending, which induces tensile strains in the fibres on one side and compressive strains in those on the opposite side (Fig. 21.a) [57,58].

For bundles in compression, there is a risk of local buckling due to instability [60]. However, the presence of bundles with a high fibre volume fraction increases local rigidity and helps prevent micro-

<caption>**Table 3**</caption>

Average thickness of the PCW and of the S1 layer for the three elementary fibres observed by AFM [18,24,51–56].

<table><thead><tr><th rowspan="2">References</th><th colspan="5">Thicknesses (μm)</th></tr><tr><th>ML</th><th>PCW</th><th>S1</th><th>S2</th><th>S3</th><th>Lumen</th></tr></thead><tbody><tr><td>This study</td><td>0.4 ± 0.38</td><td>0.07 ± 0.05</td><td>0.06 ± 0.04</td><td></td><td></td><td></td></tr><tr><td>Thuault et al., 2015 [51]</td><td></td><td>0.15–0.60</td><td></td><td></td><td></td><td></td></tr><tr><td>Arnould et al., 2017 [24]</td><td></td><td>0.4</td><td></td><td></td><td></td><td></td></tr><tr><td>Bos and Donald, 1999 [18]</td><td></td><td>0.2</td><td></td><td></td><td></td><td></td></tr><tr><td>Bourmaud et al., 2013 [52]</td><td></td><td></td><td>0.5–2</td><td>5–10</td><td>0.5–1</td><td></td></tr><tr><td>Gorskhova and Morvan, 2006 [53]</td><td></td><td></td><td></td><td>7–10</td><td></td><td></td></tr><tr><td>Gorshkova et al., 2018 [54]</td><td></td><td></td><td></td><td></td><td>90 % of the total CSA</td><td></td></tr><tr><td>Baley et al., 2014 [55]</td><td></td><td></td><td></td><td></td><td>At least 80 % of the weight</td><td></td></tr><tr><td>Charlet et al., 2010 [56]</td><td></td><td></td><td></td><td></td><td></td><td>5 ± 2.2</td></tr></tbody></table>

buckling. Similar to wood fibres [61], the growth of the flax plant generates residual tensile strains in the fibres at the periphery known as tensile maturation strains [62]. To maintain mechanical equilibrium, the central part of the stem experiences residual compressive strains. However, the combination of residual tensile and compressive strains caused by the bending of the stem reduces the intensity of local residual compressive strains (Fig. 21.b). Maturation strains play a critical role in reinforcing the stem against bending while the plant is alive. These strains are gradually released during wilting, retting, and mechanical extraction of the fibre bundles. To date, the potential influence of these maturation strains on the mechanical properties of the extracted bundles remains largely unexplored. Nevertheless, they appear to be essential for maintaining the stem structural stability of the stem and reducing the risk of buckling from external forces during plant growth.

For bundles subjected to tensile strains, their remarkable behaviour can be explained by:

- Intrusive fibre growth results in elementary fibre cells being arranged longitudinally. Their lengths (L) can vary from 2 to 87 mm, (average around 35 mm) (Table 1). Assuming an average diameter (D) of 15 µm [1], their average aspect ratio is 2333 (L/D), which is very high. This ratio can be used to characterise composite materials. When it exceeds the critical aspect ratio (approximately 27 for a polypropylene composite reinforced with flax fibres), the likelihood of failure within the reinforcement fibres becomes greater than that of a fibre loosening [63,64] (Fig. 8.a). For example, in the case of flax bundles, which can be likened to unidirectional composite materials [14], rupture is more likely to occur within the flax fibres than at the interface between the fibres and the middle lamellae.

- Limited strain concentration areas due to their tapered geometry (a result of the intrusive development phase) and are characterised by a slow variation in section (the angle at the end ranges from 3 and 13°, see section 3.2.2.1) and a gradual variation in stiffness. A cell comprises a primary cell wall of constant thickness, ranging from 0.02
<figure><img src="image_25.png" /><figcaption>**Fig. 21.** Schematic representation and distribution of residual strains within a flax stem at equilibrium (a) and under the effect of wind (b), image adapted from [59].</figcaption></figure>

<figure><img src="image_26.png" /><figcaption>**Fig. 22.** Schematic representation of a fibre tip.</figcaption></figure>

and 0.2 µm (Table 3), which initially extends and is subsequently filled with a secondary cell wall consisting of three layers (Fig. 3) [6,8]. The S2 layer, which determines the stiffness of the fibre (majority layer) [19], is less prominent at the end of the fibre, resulting in a local variation in stiffness. Fig. 22 is a schematic representation of a flax fibre tip based on the assumption that only the primary cell wall remains at the end of the fibres. Indeed, during intrusive growth, the cells expand and only the PCW may persist at both ends (the skin of the cell).

- There is a gradual increase in local stiffness between the middle lamellae and the S2 layer (G layer) (Fig. 19), which prevents a sudden discontinuity in stiffness and enhances the dissipation of excess strains.

- The fibres' polygonal cross-section results in a very high-volume fraction of reinforcement within the bundles (over 95 %) [14]. In contrast to a circular cross-section, a polygonal fibre cross-section increases the outer surface area of the fibre and thus the interface. This notion of interface warrants further exploration. Given the multilayer and hierarchical structure of fibres, numerous interfaces must be considered within a bundle (Fig. 3) [55].

## 4. Conclusion

The aim of this study was to explain the tensile behaviour of flax bundles by examining their microstructure and local mechanical properties. Initially, tensile tests were conducted under SEM and various bundle fracture surfaces were observed. Since bundles are composite materials akin to unidirectional composites reinforced with discontinuous fibres, the SEM analyses revealed several phenomena that can occur during tensile testing. For instance, ruptures may occur in the middle lamellae (which serve as the matrix for load transfer between fibres), potentially leading to decohesion of the elementary fibres. Additionally, ruptures in the elementary fibres can result in the failure of the entire bundle.

These SEM observations were linked to the analysis of the microstructure of the flax bundles, specifically focusing on the organisation of the elementary fibres. Three-dimensional rendering obtained through micro-tomographic measurements revealed the presence of weak areas

(kink-bands) within the fibres, which may be concentrated in specific regions of a bundle, resulting from the processing methods employed. Such areas can influence the failure mode during tensile tests, acting as preferred breaking points. Additionally, the cross-section of the elementary fibres is not uniform, and both SEM and SHG microscopy have highlighted the presence of fibre tips filled with crystalline and organised cellulose. These observations facilitated the construction of cross-section evolution profiles for three flax fibre tips.

To further explore the specificities of the bundles, a complementary study employing indentation through AFM PF-QNM was conducted on flax bundles. This study highlighted the gradual evolution of mechanical properties via indentation across the different areas: S1, S2, the primary cell wall, and the middle lamellae. An average value was calculated for each area, and the thickness of the middle lamellae, primary cell wall, and S1, layers was measured.

All these observations contributed to a better understanding of the structure of flax bundles and underscored their remarkable multi-scale organisation. They possess a unidirectional composite structure composed of discontinuous fibres with a high aspect ratio. Furthermore, their organisation, generated during intrusive growth, is optimised to maximise the fibre volume ratio, featuring polygonal fibre cross-sections. The geometry of the fibre tips helps to limit areas of strain concentration. This highly optimised structure serves as a source of bioinspiration for future composite materials, offering valuable insights into fibre placement and the exceptional compatibility between elementary fibres and the middle lamellae.

To enhance this work, it would be beneficial to study the behaviour of the bundles in a living plant, as well as the structural evolution of the layered organisation (primary cell wall, S1, S2, and S3) along the length of flax fibres through AFM observations. Additionally, examining the durability of flax fibre-reinforced biocomposites would be particularly important, especially given the sensitivity of flax fibres to moisture [16]. Finally, presenting bundle ruptures caused by fibre tip decohesion could provide valuable complementary insights to the fracture surface observations shown in Fig. 8.

## CRediT authorship contribution statement

**Margot Chalard:** Writing – original draft, Methodology, Investigation, Formal analysis, Data curation, Conceptualization. **Camille Goudenhooft:** Writing – review & editing, Validation, Investigation, Formal analysis, Data curation, Conceptualization. **Alessia Melelli:** Writing – review & editing, Validation, Supervision, Investigation, Data curation.

**Mario Scheel:** Writing – review & editing, Methodology, Supervision, Validation. **Timm Weitkamp:** Writing – review & editing, Methodology, Supervision, Validation. **Pierre D'arras:** Writing – review & editing, Funding acquisition. **Alain Bourmaud:** Writing – review & editing,
Visualization, Validation, Supervision, Resources, Methodology, Fund-
ing acquisition, Formal analysis. **Christophe Baley:** Writing – review &
editing, Visualization, Validation, Supervision, Resources, Methodol-
ogy, Funding acquisition, Formal analysis.

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 gratefully acknowledge the ANR (Agence Nationale de la Recherche) for funding the labcom NewFlax (21-LCV3-0011-01), the project holder. Synchrotron SOLEIL is acknowledged for providing support and facilitating access to their Anatomix beamline (proposal 20231643). The authors are also grateful to the Investments for the Future program, also funded by the ANR, which enabled the construction of the ANATOMIX beamline, Equipment of Excellence (EQUIPEX), project NanoimagesX, grant no. ANR-11-EQPX-0031. Finally, they thank Anthony Magueresse for conducting the SEM observations and Coralie Buffet for her support with the tomographic acquisitions. Editorial assistance, in the form of language editing and correction, was provided by XpertScientific Editing and Consulting Services.

Data availability

Data will be made available on request.

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