# Experimental and numerical approach to understand the role of defects in damage mechanisms of flax fibers at bundle scale

Vasuki Rajakumaran, Alessia Melelli, Anita Quiles, Timm Weitkamp, Jonathan Perrin, Henry Proudhon, Alain Bourmaud, Johnny Beaugrand, Sofiane Guessasma

► To cite this version:

Vasuki Rajakumaran, Alessia Melelli, Anita Quiles, Timm Weitkamp, Jonathan Perrin, et al. Experimental and numerical approach to understand the role of defects in damage mechanisms of flax fibers at bundle scale. Industrial Crops and Products, 2024, 218, pp.119025. 10.1016/j.indcrop.2024.119025. hal-05344497

HAL Id: hal-05344497

https://hal.univ-brest.fr/hal-05344497v1

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1 **Experimental and numerical approach to understand the role of defects in damage mechanisms of flax fibers at bundle scale**

3 Vasuki Rajakumaranª, Alessia Melelliᵇ, Anita Quilesᶜ, Timm Weitkampᵇ, Jonathan Perrinᵇ

4 Henry Proudhonᵈ, Alain Bourmaude, Johnny Beaugrandª, Sofiane Guessasmaª*

5 <sup>a</sup>UR1268 Biopolymères Interactions Assemblages, INRAE, F-44316 Nantes, France

6 <sup>b</sup>Synchrotron SOLEIL, ANATOMIX beamline, L'Orme des Merisiers, Départementale 128,

7 91190 Saint-Aubin, France

8 <sup>c</sup>Institut français d'archéologie orientale, 4262024 Cairo, Egypt

9 <sup>d</sup>MINES Paris, PSL University, MAT - Centre des matériaux, CNRS UMR 7633, BP 87, 91003

10 Evry, France

11 <sup>e</sup>Univ. Bretagne Sud, UMR CNRS 6027, IRDL, F-56100 Lorient, France

12

13 * Corresponding author: vasuki.rajakumaran@inrae.fr

14

15 **Abstract**

16 Flax fibers represent a valuable reinforcement in composite materials. However, the
17 presence of defects known as kink-bands in flax fiber has the capacity to influence their
18 mechanical properties. The primary objective of this research is to gain a comprehensive
19 understanding of the damage mechanism in flax fiber bundles presenting a novel aspect due
20 to the intricate structure of bundle fibers, which is more complex compared to elementary
21 fibers. The study specifically explores flax fiber bundles under tensile loading and
22 investigates the impact of kink-bands on their failure through a combined approach, utilizing
both experimental and numerical methods. In the experimental part, X-ray
microtomography *in situ* tensile testing is carried out, which reveals complex failure
mechanisms. Furthermore, a 3D-Finite Elements (FE) model is implemented utilizing 3D
reconstructed fiber and used for numerical tensile analysis. Our findings highlight that the
kink-band region acts as prominent failure site in fiber bundles with significant stress
concentration at the kink-band region, mainly induced by local porosity.

**Keywords:** X-ray microtomography; *in situ* tensile testing; kink-bands; pores; finite element methods; damage mechanisms

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## 1. Introduction

Flax fibers have gained attention as eco-friendly, possess exceptional tensile strength and
stiffness (Richely et al. (2022), Khalid et al. (2021)), making them an attractive choice or an
alternative to synthetic fibers for reinforcing composite materials in industries such as
automotive, aerospace, and construction (Rahman (2021)). To optimize their practical use, a
thorough understanding of the factors affecting flax fiber's mechanical behavior is essential
(Hosseinzadeh et al. (2020)). Despite sustainability benefits, flax fibers have inherent defects
called kink-bands, (Madsen et al. (2016)) influencing their mechanical characteristics (Baley
(2004)). Kink-bands in bio-based composites are significant as they can weaken the fibers
and, in turn, compromise the overall mechanical strength and integrity of the composite
(Hbib et al. (2011), Wang et al. (2017)). Consequently, understanding and mitigating the
impact of these defects are crucial considerations when developing bio based composite
materials.
The origin of kink-bands in flax fibers remains uncertain, with studies proposing various theories. While some suggest that abiotic stress during development may contribute (Thygesen (2011), Hänninen et al. (2012)), others argue that these factors alone might not induce such defects without significant growth or lodging accidents. Bourmaud et al. (2022) investigated the presence and characteristics of kink-bands within flax fibers. Their study reveals that a significant number of kink-bands, identifiable by their substantial voids, are evident in all extracted fibers, when they undergo processes such as scutching, combing, or stretching. However, tomographic examination does not reveal any kink-bands at the scale of the green or retted stems. These findings suggest that the stresses experienced by plants during growth are insufficient to induce these structural defects, which only become apparent after mechanical fiber extraction or significant growth or occurrence of lodging incidents. Similar findings were observed by Kozlova et al. (2022). Studies also explored how fiber extraction methods impact properties (Placet et al. (2018)). Bos et al. (2002) compared hand-isolated and decorticated flax fibers, noting differences in ultimate tensile stress values, also suggesting that factors beyond dislocation frequency contribute to strength variations.

Flax fibers exhibit a hierarchical structure, featuring the primary cell wall (PCW), that allows elasticity and plasticity in view of cell wall modelling and adaptation to growth and the secondary cell wall with the dominant S2-G layer, constituting over 90% thickness and displaying strong longitudinal mechanical properties due to its high cellulose content (Richely et al. (2022), Goudenhooft et al. (2018)), primarily composed of 80% crystalline cellulose, and a minimal fibrillar angle (Melelli et al. 2020). Understanding this structure is crucial to strengthen the flax fibers in composite materials. However, structural defects like kink-bands, causing alterations in fiber structure within defect zones, can compromise their
69 reinforcing capability. According to Aslan et al. (2011), kink-bands refer to segments of the 70 cell wall characterized by an irregular arrangement of cellulose microfibrils within the 71 amorphous matrix polymers. These kink-bands are believed to function as structural 72 anomalies that impact the mechanical properties of the fibers. Despite dislocations 73 constituting up to 20% of hemp fiber cell walls, Thygesen et al. (2007) found no apparent 74 impact on mechanical properties during tensile testing. Dislocations initiated cracks, but 75 shear failures within microfibrils occurred. A negative correlation between the area of an 76 average kink-band and the Young's modulus of the fiber is demonstrated by Morgillo et al. 77 (2023). Fibers exhibiting a Young's modulus exceeding 75 GPa generally have a kink-band 78 density below 15%, on average. The defects in elementary fibers result in significant shifts in 79 cellulose orientation (30°-40°) (Melelli et al. (2021)), changes in crystallinity, and the 80 presence of pores at elementary fibers, particularly within the S2 layer (Quereilhac et al. 81 (2023)), leading to weakened fibers. It has been observed that kink-bands in elementary 82 fibers lead to deviations in microfibrillar angles and an increase in localized porosity with a 83 concentric pore arrangement, which act as specific rupture points and potentially impacting 84 fiber mechanical properties (Zhang et al. (2015), Quereilhac et al. (2023)).

85 Despite of studies at the cell wall and elementary scale, few studies exist at the bundle 86 scale. Beaugrand et al. (2017) explored damage mechanisms in hemp fibers, emphasizing the 87 significance of kink-bands in crack initiation. Some studies examined kink-bands impact in 88 bio-based composites, introducing significant heterogeneity to the fiber structure (Hughes et 89 al. (2000), Le Duc et al. (2011), Wang et al. (2017)). Despite the fact that these authors have 90 studied hemp fibers and bio-based composites, a better knowledge of the link between kink- 91 bands and tensile characteristics is required at the bundle scale for flax fiber. Turning our 92 attention towards modeling plant fiber bundles, only few studies exist (Charlet and Beakou
93 (2014), especially in creating 3D models using 3D reconstruction of the fibers, for example
94 Richely et al. (2022) studied elementary flax fibers and Guessasma and Beaugrand (2019)
95 studied hemp bundle fibers. X-ray microtomography appears as a method of choice to
96 create realistic numerical models based on experimental 3D microstructures, in particular
97 using finite element meshes obtained from 3D tomographic reconstructions.

98 The innovative aspect of this work is a comprehensive exploration of flax fiber bundles, by
99 integrating experimental testing and advanced numerical simulations with a specific focus
100 on the influence of kink-bands on their tensile characteristics. *In situ* tensile testing with X-
101 ray microtomography is conducted to investigate the damage behavior of fiber bundles,
102 capturing dynamic images during the process of tensile loading. The finite element method
103 was utilized to analyze the accurately defined fiber volume acquired through X-ray
104 microtomography in order to determine global properties such as elastic modulus, along
105 with examining the local stress distributions in kink-band regions of fiber bundles.

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107 **2. Materials and methods**

108 **2.1. Materials**

109 The flax fibers, provided by the IFAO (Institut français d'archéologie orientale) archaeometry
110 department, originated from cultivation in the Nile's Delta near the Zefta area in Egypt. Flax
111 fiber of Malika variety, was sowed on November 7th, 2022 and they reached maturity in
112 March 2023, which underwent grubbing, drying, and mechanical crushing, followed by
113 retting in large water reservoirs in May 2023 for 1 to 2 weeks. Later, they were air-dried over
114 several weeks before undergoing industrial scutching in July 2023 which was then combed
115 for producing textile ribbons. The ribbons were then transformed into yarns in a family farm
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in the region of Zefta (Egypt). The fiber bundle was then extracted manually from the
transformed yarns.

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## 2.2. Synchrotron X-ray microtomography coupled with in-situ tensile testing

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X-ray microtomographic images were acquired at the Synchrotron SOLEIL, ANATOMIX
beamline. Tensile testing was performed with "Bulky," a mechanical testing apparatus
developed for *in situ* Synchrotron microtomography studies (Pelerin et al. 2019). Specific
grips were designed to install the fiber/bundles glued on cardboards where the lateral parts
can be removed using small scissors through slightly off-axis lateral holes and the
fibers/bundles are in place while maintaining a 360° visibility for the tomographic
acquisition. The load was applied by moving the crosshead continuously until failure, at a
rate of 50 µm/s. The apparatus was adjusted to allow for gauge lengths of 10 mm (as shown
in Figure 1) in order to monitor the damage and rupture processes. To scan the samples, the
inline phase contrast was selected to perform microtomography in the second ANATOMIX
hutch at 200 m distance from the X-ray source (Weitkamp et al. 2017). A white beam was
used with a flux of 40 keV, chosen in function of the minimum distance allowed between the
detector and the sample (30 mm), which was limited by the rotation of the "Bulky" tensile
machine. A camera CMOS ORCA Flash 4.0 V2 (Hamamatsu, Hamamatsu city, Japan) was
used in full-frame unbinned mode (2048x2048 pixels, pixel size of 6.5 µm, speed of 100 fps)
(Weitkamp et al. 2022) coupled with a 10x M Plan APO (Mitutoyo, Kawasaki, Japan)
objective to reach a pixel size of 0.65 µm. Regarding the filters used, two brazed CVD
diamond coupled with Gold (Au) coatings of 10 µm thick and a Copper (Cu) filter of 100 µm
were selected. The scan geometry chosen was 180° (standard geometry) with 2000
projections angles per scan. For the reconstructions, PyHST2 software was used and

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140 Paganing correction with a Paganing length of 100 pixels (Paganin unsharp filter length: 3

141 pixels; Paganing unsharp filter coefficient 0.7) was applied (Paganin et al. 2002).

<figure><img src="image_2.png" /><figcaption>Figure 1: Experimental setup a) x-ray microtomography with in situ tensile testing b) Magnified view of tensile machine</figcaption></figure>

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Three-dimensional segmentation was conducted on the reconstructed volumes of fiber bundle, to separate the void from the solid phase within the bundles and elementary fibers.

Typical image analysis processes include grey level image conversion from 32 bits to 8 bits, image filtering and rotation, threshold and Region of Interest (ROI) selection, porosity mask generation and image superposition to isolate inner porosity from the air background.
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Finally, the flooding procedure is carried out in order to distinguish the fiber and porosity
from the background.

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**2.3. Ex situ Tensile Testing**

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The tensile properties of elementary flax fibers to be incorporated into numerical models are
determined through a tensile experiment utilizing the Dia-Stron LEX820 Extensometer (Dia-
Stron Limited, Andover, UK) with a 20N load cell and a displacement rate of 1 mm/s. A total
of 5 elementary flax fibers from the Malika variety were tested. The samples were placed in
plastic tabs and bonded with adhesive, which then undergoes exposure to ultraviolet light
for 15 seconds to facilitate adhesive curing, maintaining a sample length of 10 mm. The
dedicated software UvWin serves as an interface to both control and analyze the
measurements obtained by the LEX820. Photonic fluorescence microscopy (LEICA) was
utilized for optical imaging of the fiber under bright light conditions, enabling diameter
measurements at 3 to 5 locations along each fiber element, considering the presence of
lumen. The mean diameter was then utilized to calculate the cross-sectional area, assuming
a circular cross section. The measured average diameter was 16.74 µm (standard deviation
of 3.64) with a cross-sectional area of 228.31 µm² (standard deviation of 94.58). The average
Young's modulus of 39 GPa (standard deviation of 3.04) was found, which was used in the
numerical model of the fiber bundle.

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**2.4. Finite element computation**

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The static image captured from the X-ray microtomography were converted into a numerical
model using a combination of surface tessellation using triangular elements and propagating

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tetrahedral elements in the core. The total number of mesh elements in the model is around 311,000 elements and the meshed 3D volume of the fiber bundle is shown in Figure 2. The mesh produced has about 1 million degrees of freedom with a mean volume element of 12 µm³ and the meshed volume features a height of 300 µm (approximately 130 elements along the fiber length). The average mesh elements in transverse cross section is around 2170 with the average surface area of 0.012 mm². Both FIJI (https://fiji.sc/) and Simpleware ScanIP software were used for this process (https://www.synopsys.com/simpleware.html). Quadratic tetrahedral elements are used from the meshing, which are defined with 4 nodes and 3 degrees of freedom corresponding to the structural displacement in the 3D space. All computations are performed using structural mechanics module from COMSOL software (Version 5.6).

<figure><img src="image_3.png" /><figcaption>Figure 2: Meshed 3D volume of fiber bundle</figcaption></figure>

The material is assumed to be linear, elastic and isotropic with Young's modulus of 39 GPa and Poisson's ratio of 0.2 (Richely et al. 2022) and the change in microfibril angle was not considered. However, flax fibers are often anisotropic due to their complex structure,
assuming isotropy in numerical modeling can be a practical simplification for computational efficiency. In order to replicate the tensile conditions, the following boundary conditions were used: the lower surface of the fiber was clamped (i.e., displacement was equal to 0 in all directions at all nodes of the surface), and a displacement 'd' was applied in the z-direction to the top surface using the following equations:

$$ Ux = Uy = Uz = 0 \quad \text{For the lower surface} \qquad (1) $$

$$ Ux = Uy = 0; Uz = d \quad \text{For the upper surface} \qquad (2) $$

The applied displacement (d) is 3 µm, which corresponds to 1% strain over the entire simulated length L. The average stress (σ) and strain values (ε%) are determined using the Equation 3 and Equation 4, where Fz is the reaction force in z-direction, S is the surface of the filled fiber, d is the imposed displacement, and L is the length of the fiber. Given that the reaction forces at the nodes of both fiber edges have distinct transverse surface areas, the resultant stress is computed from the mean between these integrals (Equation 3).

$$ \sigma = \frac{1}{2} \iint \frac{FZ_{(x=0)}}{S_{(x=0)}} + \iint \frac{FZ_{(x=d)}}{S_{(x=d)}} \qquad (3) $$

$$ \varepsilon\% = 100 * \left(\frac{d}{L}\right) \qquad (4) $$

# 3. Results and discussion

## 3.1. Analysis of experimental tomographic data

Within the stem, elementary fibers are bound together into bundles connected by a pectin-rich interface known as the middle lamella (Zamil and Geitmann 2017). After extraction, these fibers often contain imperfections referred to as kink-bands, which are areas in plant fibers where microfibrils show less orientation and exhibit a kinked structure. The middle lamella binds the primary cell walls of adjacent plant cells, creating a complex layer known as
the compound middle lamella (CML), which plays a crucial role in influencing the mechanical properties of flax fiber bundles (Melelli et al. (2021)). The primary objective of this analysis is to provide an in-depth examination of the intricate damage mechanisms encountered during the tensile loading of flax fiber bundles. The fiber bundle was observed under an optical microscope which shows the presence of kink-band in the fiber bundle as shown in Figure 3. These kink-bands are of significant importance, as they serve as pivotal indicators of potential damage initiation sites within the fiber bundle (Beaugrand et al. (2017)).

<figure><img src="image_4.png" /><figcaption>Figure 3: Flax fiber bundle observed under optical microscope with some kink-bands highlighted</figcaption></figure>

In Figure 4, the presentation of transverse cross sections of the fiber bundle under varying loading conditions is of a particular interest. Interestingly, the images do not predominantly manifest the typical cracking behavior, but instead, they showcase a phenomenon of shrinkage occurring between fiber bundles which can be observed in Figure 4. Nonetheless, one facet (shown in Figure 5) of the fiber bundle exhibits a rupture behavior (Figure 5e and f), implying that the deformation and damage processes during loading are not consistently uniform across the whole bundle. The wide range of damage mechanisms that affect flax fiber bundles at different loading stages in the XZ plane is shown in Figure 6.
<figure><img src="image_5.png" /><figcaption>Figure 4: Transverse Cross section of the flax fiber bundle at different loading stage (Facet 1)</figcaption></figure>

<figure><img src="image_6.png" /><figcaption>Figure 5: Transverse Cross section of the flax fiber bundle at different loading stage (Facet 2)</figcaption></figure>
<figure><img src="image_7.png" /><figcaption>Figure 6: Collection of damage mechanism of flax fiber bundle at different loading stage in XZ plane (1- crack initiation and crack development and separation of elementary fiber from bundle, 2- breaking of elementary fiber, 3- crack initiation, 4- Shrinkage in in porosity, 5-Rupture of fiber bundle)</figcaption></figure>

To obtain better understanding of the damage mechanisms, the longitudinal view of the fiber bundle at successive loading points was analyzed by employing X-ray tomography imaging, as shown in Figure 7. The magnified view in Figure 7 unveils the existence of kink-bands, recognized as defects in the fibers situated in proximity to the clamping region. Figure 7b shows the rupture initiation and it can be observed that the elementary fibers detaching from the bundle which sheds light on the potential role played by the middle lamella in influencing the mechanical behavior of the bundle. Figure 7c shows rupture occurring in proximity to the kink-band region, elucidating the role of kink-bands in the failure of fiber bundles subjected to tensile loading (Beaugrand et al. (2017)). Stevens (2010) states that during the strength test, flax fibers frequently fracture at these kink-band regions. The rupture initiation near the kink-band region for elementary fiber was also observed by Baley (2004), and such rupture initiation could also be due to the misalignment of the micro-fibril
or meso-fibrils in the secondary cell wall due to its perpendicular orientation to the fiber axis in Kink-band region (Ahmed and Ulven 2018). Additionally, Mott et al. (1996) noted that individual black spruce latewood fibers had early plastic failure in the kink-band region. In order to better quantify this behavior, Figure 8b shows the magnified view of ruptured region of the bundle and Figure 8c shows the cross-sectional view of rupture site exposing the porosities in kink-band region, confirming that the rupture occurred near kink-band region.

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<figure><img src="image_8.png" /><figcaption>Figure 7: Longitudinal view of flax fiber bundle at successive loads with magnified images</figcaption></figure>

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<figure><img src="image_9.png" /><figcaption>Figure 8: a) Longitudinal view of flax fiber bundle b) Magnified view of the ruptured fiber bundle c) Cross-sectional view of bundle at rupture site exposing the porosities in kink-band region</figcaption></figure>

Furthermore, Figure 9 effectively illustrates a spectrum of intricate failure mechanisms with the help of longitudinal cross section images of the fiber bundle at a displacement of 450 µm. These encompass the delamination of elementary fibers, the tearing of fibers in the vicinity of the kink-band region and fiber separation, all of which collectively contribute to the propagation of cracks within the bundle which further leads to failure of the fiber bundle. Similar kind of damage mechanism that includes debonding of elementary fibers and tearing of fibers were observed in flax fiber bundles (Romhany et al. 2003). The following numerical analysis were carried out to have a complementary understanding of this behavior.
<figure><img src="image_10.png" /><figcaption>Figure 9: Collection of damage mechanism at Longitudinal cross section of flax fiber bundle in YZ plane</figcaption></figure>

## 3.2. Predicted stress state and overall properties

The overall elasticity modulus is determined considering the variability in the bundle geometry and the heterogeneity produced by the loading conditions. For the fiber bundle, the calculated average elastic modulus value is 37.5 GPa which is close to the implemented value in the model. Figure 10 shows the displacement plot of the fiber bundle in z, y and x direction. The displacement plot in z-direction verifies the boundary conditions which correspond to the tensile testing where the bottom surface is clamped and the top surface has been given a maximum displacement of 3µm. The displacement plot in the y and x direction shows that there is a lateral shrinkage in the x and y directions due to the elongation in the z-direction. It seems that this shrinkage is not fully symmetrical, which indicates the influence of the geometry in the surface on the effectiveness of the test to produce uniaxial extension. Figure 11 shows stress magnitude component σ33 where the stress heterogeneity can be observed at the surface of the fiber bundle. Note that these
large values are due to the linear elastic constitutive model which does not account for any plastic or viscous behavior, as well as the properties of the middle lamella, which will be included in future analysis in order to better align with the experimental results. The stress heterogeneity is due to the structure composition and morphology of the fiber bundle such as change in MFA in S2 layer in kink-band region (Melelli et al. (2021)) as well as pores in kink-band boundaries, which causes the stress plot to vary all along the fiber. The model captures the stress concentrations caused by surface roughness and in particular the stress concentration is moderately higher in the boundaries of the kink-band region which is highlighted in black box in the Figure 11 and Figure 12. The increased stress concentration in the kink band region may cause crack initiation in the fibers at this location leading to fiber breakage (Sliseris et al. 2016, Guillou et al. 2024). The higher stress concentration in the kink-band region might arise from significant deviations in the microfibril angle within this area, as noted by Melelli et al. (2021). These alterations in the microfibril angle can likewise impact the mechanical characteristics of the fiber bundle, especially in this case where using a low gauge length, i.e. 3 mm, maximizes the impact of single fiber on kink-band property. The 3D view of fiber bundle is shown in Figure 12 to better visualize the kink-band region, with highlighting the kink-band region as well as central lumen present in elementary fiber.
<figure><img src="image_11.png" /><figcaption>Figure 10: a) Displacement in tensile direction (z) in the plane XZ b) Displacement in transverse directions (y) in the plane XZ c) Displacement in transverse directions (x) in the plane XZ</figcaption></figure>

<figure><img src="image_12.png" /><figcaption>Figure 11: Axial Stress (σ33) contour plot in the XZ plane (the black box shows the kink-band region)</figcaption></figure>
<figure><img src="image_13.png" /><figcaption>Figure 12: 3D view of Axial Stress (σ33) contour plot (the black box shows the kink-band region and the white box shows the central lumen present in elementary fiber)</figcaption></figure>

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Figure 13 displays the axial stress distribution (σ33, σ22, σ11) for the fiber bundle, plotted along the longitudinal cross section in the YZ planes. In Figure 13a (σ33), it can be observed that the stress heterogeneity, with prominent stress concentrations, is evident in the surface areas and within the porosity of the kink-band region and this is may be due to pores in the boundaries of kink-band. On the other hand, Figure 13b (σ22) and Figure 13c (σ11) reveal relatively less variability in stress distribution. Notably, axial stress σ22 exhibits higher stress levels in both the clamping region and boundary surface area, while axial stress σ11 showcases increased stress concentrations in both the surface area and the porosity region within the kink-band as well as in clamping region. Figure 14 illustrates the maximum stress values for σ33, σ22, and σ11, revealing that σ33 exhibits a higher value (2101 MPa) than σ22 (401 MPa) and σ11 (375 MPa).

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Moving on to Figure 15 it illustrates the shear stress distribution (σ12, σ13, σ23) for the fiber bundle plotted within the longitudinal cross section in the YZ planes. In shear stress, the
heterogeneity is comparatively less, but elevated stress concentrations are observable in the porosity and surface area. Figure 14 shows the maximum stress values for σ12, σ13, and σ23, highlighting that σ23 (372 MPa) exceeds the magnitudes of both σ12 (251 MPa) and σ13 (294 MPa). Additionally, the axial stress values (σ33, σ22, and σ11) are noticeably higher than the shear stress values (σ12, σ13, σ23), as evident from Figure 14. It's worth noting that the appearance of the fibers in Figure 13 appears distinct when compared to Figure 11 and Figure 12. This distinction arises solely from the visualization plane, with Figure 11 being represented in the XZ plane and Figure 15 and Figure 13 in the YZ plane. The choice of the YZ plane for Figure 13 and Figure 15 was made to obtain a more comprehensive view of the kink-band section for the analysis.

<figure><img src="image_14.png" /><figcaption>Figure 13: Distribution of axial stress on longitudinal cross section of fiber bundle in the plane YZ a) σ33 b) σ22 c) σ11</figcaption></figure>
<figure><img src="image_15.png" /><figcaption>Figure 14: Maximum Axial and shear stress components in longitudinal cross section of fiber bundle</figcaption></figure>

<figure><img src="image_16.png" /><figcaption>Figure 15: Distribution of shear stress on longitudinal cross section of fiber bundle in the plane YZ (a) σ12 (b) σ13 (c) σ23</figcaption></figure>

The optimal longitudinal cross section view of fiber bundle (Figure 16a) is chosen to compare with the numerical analysis (Figure 16b). The porosity that appears in boundaries of kink-bands can be observed from the binary image of the fiber bundle (Figure 16a) and the
orientation of the porosity in kink-band is aligned at an angle of ~45° with respect to the
longitudinal fiber axis as observed by Quereilhac et al. (2023) in elementary fibers. Figure 16b
shows the stress concentration is maximum at this particular region, reaching up to 2101
MPa which is overestimated and is approximately twice the tensile strength. Since the
porosity in the kink-band region indicates where the maximum stress is found, this can lead
the bundle to crack, which further develops and may lead to a rupture behavior. Trivaudey
et al. (2015) observed the stress concentrations in kink-band region can act as the most
prominent site for the failure to occur under linear elastic nature. Contrary to their initial
observations, under the assumption of viscoelastic material, they also observed a constant
stress level along the fiber's length. Nilsson and Gustafsson (2007) developed a finite
element model for hemp and flax with large dislocations, or kink-bands and discovered that
kink-bands in fibers significantly affect the elastic stiffness of a fiber.
<figure><img src="image_17.png" /><figcaption>Figure 16: a) Binary image of longitudinal cross section of fiber bundle b) Axial stress distribution (σ33) in longitudinal cross section of the fiber</figcaption></figure>

The maximum stress values are determined in the fiber bundle's transverse cross section 20 µm apart along the fiber, which is depicted in Figure 17a in order to better understand the stress distribution in the bundle. The stress distribution within the fiber appears to amplify the diversity of stress in both the axial and shear directions. Figure 17b shows the stress concentration σ33 in longitudinal cross section, which illustrates the kink-band region with pores. Line 1 in Figure 17b covers the pores, while line 2 excludes them. In Figure 17c the graph corresponds to line 1 and line 2 which shows the stress variation in fiber bundle along the diameter and line 1 includes the porosity region which reflects highest peak in the stress
374 and the discontinuity of line 1 in the graph is due to porosity present in fiber bundle while

375 line 2 shows lower stress values which may be due to exception of pores in this region. In the

376 axial stress, a peak value of 1625 MPa (for maximum displacement of 3µm) was observed in

377 σ33 and axial stress components exhibits higher stress compared to shear stress

378 components, as evident from Figure 17a. Within the shear stress field, the maximum shear

379 stress ranges between 50 and 550 MPa, indicating the existence of concentrated shear

380 stresses in the fiber bundle. However, a comparison between the maximum axial stress and

381 experimental data suggests an overestimation of the obtained value, highlighting the need

382 to incorporate damage criteria into the bundle model to better align with experimental

383 results.
<figure><img src="image_18.png" /><figcaption>Figure 17: a) Maximum axial and shear stress along transverse cross section of fibers with varying length b) Axial stress distribution (σ33) in longitudinal cross section of the fiber bundle representing kink-band region c) resulting axial stress profile along two lines (1 and 2) and black line represents the experimental average stress value</figcaption></figure>

In summary, the porosity within the kink-band region exhibits a higher degree of stress concentration, suggesting a potential competition in influencing the failure of the fiber bundle through distinct loading paths, such as shear or tensile forces. The outcome depends on which of these factors demands less energy to propagate the crack. The experimental findings emphasize that rupture behavior occurs within the kink-band region. The accompanying numerical analysis corroborates this observation, providing an explanation
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that suggests the presence of pores within the kink-band may facilitate crack propagation,

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ultimately leading to rupture behavior even at bundle scale.

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## 4. Conclusions

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The investigation into the impact of defects in flax fiber at the bundle scale on its tensile

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properties involved a combination of experimental (in situ tensile testing with X-ray

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microtomography) and numerical methods. Experimental results specifically identify the

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occurrence of rupture in the kink-band region, with noticeable shrinkage between bundles

402

observed in the transverse cross section. Additionally, various damage mechanisms,

403

including fiber detachment indicating the influence of the middle lamella, were observed.

404

The numerical study revealed higher stress levels in the axial direction compared to the

405

shear directions. Concentrations of both axial and shear stresses were identified in close

406

proximity to the kink-band region, emphasizing the pores in the kink-band as potential

407

damage sites capable of initiating cracks leading to rupture. Notably, the maximum axial

408

stress tensors were found to be 2101 MPa, 401 MPa, and 375 MPa, while maximum shear

409

stress tensors were 372 MPa, 294 MPa, and 251 MPa along the fiber bundle indicating stress

410

concentrations, even if the stress values are overestimated due to the assumption of a linear

411

elastic model. Overall, the experimental results indicate that bundle failure occurs in the

412

kink-band region in addition to other damage mechanisms like elementary fiber

413

delamination and fiber tearing, while the numerical results clarify that the porosity in the

414

kink-band region acts as a potential crack initiator, ultimately leading to bundle rupture. As a

415

future prospect, incorporating non-linear behavior of the fiber into the model is suggested
416 to enhance the alignment with experimental data and the influence of kink-bands in tensile
417 properties of flax fiber at elementary scale can also be investigated.

418

419 Acknowledgements

420 The authors wish to acknowledge the funding provided by the French National Research
421 Agency (ANR) through the Anubis project ANR-21-CE43-0010. ANATOMIX is an Equipment of
422 Excellence (EQUIPEX) funded by the Investments for the Future programme of the French
423 National Research Agency (ANR), project NanoimagesX, grant no. ANR-11-EQPX-0031.
424 Access to Anatomix was provided through SOLEIL beamtime proposal #20221519.

425

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592 • **Figure captions:**
593 Figure 1: Experimental setup a) x-ray microtomography with in situ tensile testing b) Magnified view of tensile machine

595 Figure 2: Meshed 3D volume of fiber bundle

596 Figure 3: Flax fiber bundle observed under optical microscope with some kink-bands
597 highlighted

598 Figure 4: Transverse Cross section of the flax fiber bundle at different loading stage
599 (Facet 1)

600 Figure 5: Transverse Cross section of the flax fiber bundle at different loading stage
601 (Facet 2)

602 Figure 6: Collection of damage mechanism of flax fiber bundle at different loading
603 stage in XZ plane (1- crack initiation and crack development and separation of
604 elementary fiber from bundle, 2- breaking of elementary fiber, 3- crack initiation,
605 4- Shrinkage in in porosity, 5-Rupture of fiber bundle)

606 Figure 7: Longitudinal view of flax fiber bundle at successive loads with magnified images
608 Figure 8: a) Longitudinal view of flax fiber bundle b) Magnified view of the ruptured
609 fiber bundle c) Cross-sectional view of bundle at rupture site exposing the
610 porosities in kink-band region

611 Figure 9: Collection of damage mechanism at Longitudinal cross section of flax fiber
612 bundle in YZ plane

613 Figure 10: a) Displacement in tensile direction (z) in the plane XZ b) Displacement in
614 transverse directions (y) in the plane XZ c) Displacement in transverse directions
615 (x) in the plane XZ

616 Figure 11: Axial Stress (σ33) contour plot in the XZ plane (the black box shows the
617 kink-band region)

618 Figure 12: 3D view of Axial Stress (σ33) contour plot (the black box shows the kink-
619 band region and the white box shows the central lumen present in elementary
620 fiber)

621 Figure 13: Distribution of axial stress on longitudinal cross section of fiber bundle in
622 the plane YZ a) σ33 b) σ22 c) σ11

623 Figure 14: Maximum Axial and shear stress components in longitudinal cross section
624 of fiber bundle

625 Figure 15: Distribution of shear stress on longitudinal cross section of fiber bundle in
626 the plane YZ a) σ12 b) σ13 c) σ23

627 Figure 16: a) Binary image of longitudinal cross section of fiber bundle b) Axial stress
628 distribution (σ33) in longitudinal cross section of the fiber

629 Figure 17: a) Maximum axial and shear stress along transverse cross section of fibers
630 with varying length b) Axial stress distribution (σ33) in longitudinal cross section of
631 the fiber bundle representing kink-band region c) resulting axial stress profile along

632 two lines (1 and 2) and black line represents the experimental average stress value