# Boosting the reinforcing potential of flax co-products: Biomass fractionation and composite microstructure as keys

Ali Nour El Dein, Nicolas Le Moigne, Monica Francesca Pucci, Antoine Barbulée, Olivier Gamond, Anne-Sophie Caro

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Ali Nour El Dein, Nicolas Le Moigne, Monica Francesca Pucci, Antoine Barbulée, Olivier Gamond, et al.. Boosting the reinforcing potential of flax co-products: Biomass fractionation and composite microstructure as keys. Industrial Crops and Products, 2025, 236, pp.121925. 10.1016/j.indcrop.2025.121925. hal-05282275

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# Boosting the reinforcing potential of flax co-products: Biomass fractionation and composite microstructure as keys

Ali Nour El Dein<sup>a,b,c</sup>, Nicolas Le Moigne<sup>b,*</sup> ID, Monica Francesca Pucci<sup>a</sup>, Antoine Barbulée<sup>c</sup>, Olivier Gamond<sup>d</sup>, Anne-Sophie Caro<sup>a,*</sup>

## ARTICLE INFO

### Keywords:

Flax shives

Biocomposites

Fibre orientation

Tensile properties

Micromechanical modelling

## ABSTRACT

The growing demand for sustainable thermoplastic composites has increased interest in using agricultural co-products as reinforcements due to their low cost, wide availability, and low density. This requires an optimization of fractionation processes, i.e. milling and sieving procedures, to develop mechanically efficient composite microstructures. This study investigates the influence of flax shives (a co-product of the flax industry) fractionation on the microstructure and mechanical performance of injection-moulded polypropylene composites. A multi-scale experimental approach, including 2D particle size and shape analysis, X-ray tomography, tensile testing, and micromechanical modelling, was employed. Our results show that optimizing flax shives size and shape distribution via fractionation improves their aspect ratio and orientation in the composite, thus enhancing the composite stiffness and strength by up to 17.9 % (95 % CI: 9.6–26.2 %) and 25.2 % (95 % CI: 24.0–26.5 %), respectively, when comparing composites with the lowest and highest properties. To understand the origin of the reinforcement mechanisms, the stiffness of flax shives was back-calculated based on different micromechanical models using both analytical (Halpin-Tsai, Mori-Tanaka) and numerical finite element modelling. The findings highlight that model selection and orientation assumptions strongly influence the estimated stiffness. Based on realistic microstructural inputs, the flax shives stiffness was estimated to be in the range of 21.84–36.45 GPa using Mori-Tanaka model and 11.83–23.0 GPa using Finite Element modelling depending on the tested flax shives fractions. This integrated approach demonstrates the importance of tailoring plant-based filler morphology to optimize their reinforcing capacity while offering a transferable methodology for valorising agricultural co-products in composite materials.

## 1. Introduction

Due to growing environmental concerns, there is an urgent need for innovation in the field of sustainable renewable materials derived from agricultural products, in line with circular economy principles (Tofanica et al., 2024). The use of agricultural by- and co-products to reinforce high-performance composites directly addresses this challenge by valorising agricultural waste, decreasing fossil fuel emission through the replacement of synthetic fibres, and providing sustainable materials. In this context, lignocellulosic biomass derived from agriculture, such as flax fibres and its co-products, offers an interesting opportunity (Mujtaba et al., 2023). Indeed, Flax is cultivated in over 50 countries

primarily for its seeds and high-value fibres (Perera et al., 2025), with Europe emerging as the world's leading producer (Alliance for European Flax-linen and Hemp, 2025). Flax fibres are widely used in clothing, home interior items, and technical applications (Bourmaud et al., 2018; Yan et al., 2014). The exceptional mechanical properties and low environmental impact of flax fibres, compared to other natural and synthetic fibres (Muthu et al., 2012), have driven a 128 % increase in flax cultivation between 2014 and 2024, with the cultivated area reaching 185,849 ha by 2024 in Europe (Alliance for European Flax-linen and Hemp, 2025).

During flax fibre production, the valuable bast fibres are extracted from the flax stem via the scutching process, leaving behind the main co-

<footnote><sup>a</sup> LMGC, IMT Mines Ales, Univ Montpellier, CNRS, Ales, France</footnote>

<footnote><sup>b</sup> Polymers Composites and Hybrids (PCH), IMT Mines Ales, Ales, France</footnote>

<footnote><sup>c</sup> DEPESTELE, Teillage Vandecandelaere, 5 rue de l'Eglise, Bourguébus 14540, France</footnote>

<footnote><sup>d</sup> AG PLAST, Route de Matafelon, Nurieux-Volognat 01460, France</footnote>

<footnote>* Corresponding authors.</footnote>

<footnote>E-mail addresses: nicolas.le-moigne@mines-ales.fr (N. Le Moigne), anne-sophie.caro@mines-ales.fr (A.-S. Caro).</footnote>
product, flax shives (FS), which is the woody part of the plant origi-
nating mainly from the xylem. Flax shives constitute approximately
50 % of the dry stem weight (Bert, 2013). For every ton of flax fibres
produced, approximately 2.5 ton of flax shives are generated (Cox et al.,
1999). Despite their abundance, the use of flax shives is currently
limited to applications such as animal bedding (Borhan et al., 2014),
particle board production (Sam-Brew and Smith, 2015), thermal insu-
lation (Kosiński et al., 2024), and construction (Garikapati and Sade-
ghian, 2020; Khazma et al., 2011). In some regions, they are even
treated as agricultural waste and disposed of by incineration (Perera
et al., 2025). Hence, using flax shives in more advanced applications
directly supports the circular economy by transforming an undervalued
agricultural product into a valuable material. This approach aligns with
the 2030 Agenda for sustainable development launched by the United
Nations in 2015 (United Nations, 2015) by developing bio-based ma-
terials (Goal 9) while reducing agricultural waste (Goal 12). One of the
most promising of these advanced applications is the development of
thermoplastic biocomposites, in which the shives are used as a bio-based
reinforcement.

However, although flax shives particles are biodegradable by
themselves, their incorporation into fossil-based thermoplastics like
polypropylene raises new concerns about the composite's end of life,
resulting in a non-biodegradable material (Sudár et al., 2013). For such
composites, the primary route for the material reuse is via mechanical
recycling, where the product can be grinded and re-processed ensuring
the development of new components (Teuber et al., 2016). In addition,
previous investigations (Burgstaller and Renner, 2023) have shown that
multiple processing cycles (up to five cycles) of wood-plastic composites
have only a slight influence on their tensile properties, despite a
reduction of wood particle size and degradation of the composite's
colour, demonstrating the material's potential for recycling.

Therefore, the growing interest in valorising agricultural by-products
has led to renewed attention on using them for high-value applications.
A key strategy for some by-products, like rice husk, is the mixing with
other fibres in composites to enhance its performance (Haruna et al.,
2025). For flax shives, attention has focused on their direct use as
reinforcement in thermoplastic composite applications such as injection
moulded (Nuez et al., 2020a) and 3D printed (Mayer-Laigle et al., 2021)
parts, owing to their low density and wide availability (Hu et al., 2014).
Nuez et al. (2020a) showed that flax shives can substitute wood flour in
wood-plastic composites (WPC), offering cost reductions and a sustain-
able use for this flax co-product. Moreover, it has been revealed that the
initial size distribution of flax shives prior to composite manufacturing
significantly affects the tensile properties of the composite. However,
combining flax shives with flax fibres tends to reduce the mechanical
performance compared to composites reinforced exclusively with flax
fibres. Their results demonstrated that technical flax fibres provide
higher reinforcing efficiency than flax shives, with both composites
reinforced with 30 wt% reinforcement. Compared with flax shive rein-
forced composites, the flax fibre reinforced composite exhibited a
12.2 % increase in stiffness and a 27.4 % increase in ultimate tensile
strength. These findings highlight that the various components derived
from the flax plant, i.e. fines, flax shives, and flax fibres, differ in their
reinforcement efficiency, mainly due to variations in aspect ratio,
biochemical composition, cell wall structure, and stress transfer effec-
tiveness within the composite (Morgillo et al., 2024; Nuez et al., 2020b).
For instance, flax shives typically contain 34–53 wt% cellulose,
13–26 wt% hemicelluloses, and 23–31 wt% lignin (Perera et al., 2025),
while flax fibres have a significantly higher cellulose content (60–81 wt
%), lower lignin (0.9–5 wt%), and 11–21 wt% hemicelluloses. This
compositional difference influences their breakage mechanism during
processing, with shives breaking into smaller fragments, while flax fi-
bres separate into elementary fibres (Castellani et al., 2016; Di Giuseppe
et al., 2017).

Moreover, to analyse and accurately assess the tensile properties of
flax shives reinforced composites, it is imperative to consider the initial

size and shape distribution and biochemical composition of flax shives,
as well as their specific breakage during composite processing, to better
account for the key role of the resulting microstructure. In this respect,
our previous work (Nour El Dein et al., 2025) revealed that the initial
size distribution of flax shives, resulting from the fractionation process
and successive milling and sieving steps, significantly influences the
final composite microstructure, in particular the aspect ratio and
orientation of the fillers. Furthermore, it has been shown that stress
transfer between the matrix and plant reinforcements is critically
affected by fibre aspect ratio and interfacial adhesion (Boey et al., 2022),
while fibre orientation has a pronounced impact on tensile properties
(Verstraete et al., 2023). Thus, a comprehensive analysis correlating the
effects of the flax shive's fractionation process on both the composite's
microstructure and its tensile properties is essential to better understand
and optimize the reinforcing capacity of flax shives for their use in
composite applications. Such approach is also critical for better imple-
mentation of agricultural by- and co-products in composite applications.

Micromechanical modelling is a powerful tool for predicting the effective elastic properties of composites from their constituents (Kundalwal, 2018). Among analytical approaches, the Halpin-Tsai model has shown a good agreement with experimental results for short fibre composites (Facca et al., 2006; Halpin and Kardos, 1976). Additionally, the Mori-Tanaka model (Lee, 2018; Mori and Tanaka, 1973; Verstraete et al., 2023) has been widely used to account for the effects of the inclusion shape, fibre aspect ratio distribution, and orientation for estimating the composite elastic modulus. However, the accuracy of these models is limited when realistic microstructural features such as fibre morphology, aspect ratio distribution, fibre orientation, and fibre dispersion are not fully accounted for (Breuer and Stommel, 2020; Mentges et al., 2023). To address some of these limitations, more sophisticated models have been proposed recently. Königsberger et al. (2024) proposed a micromechanical multiscale analytical model that estimates the homogenised stiffness for composites reinforced with lignocellulosic fibres. The model first estimates the fibre stiffness at microscale starting from nanoscale elastic properties of the cellulose, hemicellulose, and lignin while considering the cellulose microfibril angle. The macro composite stiffness was then estimated considering the fibre stiffness, fibre orientation and aspect ratio distribution, and a weak interface between the fibre and matrix. In addition, finite element (FE) homogenisation method offers an alternative by explicitly modelling the heterogeneous microstructure through a Representative Volume Element (RVE), but it requires higher computational cost (Sliseris et al., 2016).

In the context of flax shives injected composites, Nuez et al. (2021) applied the Halpin-Tsai and Pagano models assuming in-plane random isotropy, using a volume-weighted average aspect ratio representing the fibre aspect ratio distribution. Verstraete et al. (2023) employed the Mori-Tanaka method while assuming a unidirectional composite. While these approaches provide valuable insights, the simplifications inherent to the models can lead to a discrepancy between predicted and experimental results. Thus, incorporating more realistic microstructural details is essential for improving the accuracy of the estimated mechanical properties.

Therefore, while previous studies highlighted the potential of flax
shives as a reinforcement for injected composites, key research gaps
remain. Firstly, a systematic investigation on the influence of the filler
fractionation, across wide range of particles size, on the composite
microstructure (fibre aspect ratio and orientation) and its resulting
tensile properties and the link between both is still needed. Secondly,
although the existing micromechanical models for the flax shive's
composites are valuable, they are limited by simple assumptions (fibre
orientation, fibre morphology, and the used model). More accurate
mechanical modelling based on realistic microstructural features is
therefore needed.

In this study, injected polypropylene (PP)/maleic-anhydride-poly-
propylene (MAPP) composites with various size distributions and
weight fractions (10, 20, 30, and 40 wt%) of flax shives were prepared by twin-screw extrusion and injection moulding. The biochemical composition of flax shives across different size ranges was analysed. Particle dimensions before and after composite processing were measured using a 2D scanner, and their orientation within the composite specimens was characterized by X-ray tomography. The tensile properties of the composites were then evaluated, and the impact of flax shives on tensile performance was interpreted based on microstructural analysis, linking aspect ratio, dimensions, orientation, and dispersion of flax shives to the observed mechanical behaviour. Furthermore, a comparative micromechanical modelling was conducted using both analytical models (Mori-Tanaka and Halpin-Tsai) and numerical Finite element simulations to back-calculate the stiffness of flax shives. This integrated approach aims to identify the optimal size distribution of flax shives to maximize their reinforcing capacity in polymer composites.

## 2. Materials and methods

### 2.1. Materials

#### 2.1.1. Flax shives and their preparation

Around 150 kg of raw flax shives (FS) from the Mélinage variety, harvested in august 2021 and supplied by Depestele company (France), were subjected to a continuous grinding (knife milling) and sieving process to obtain fillers with various size and shape distributions. The sieving process retained fillers between two sieve meshes, classifying them into the following size categories: FS-200-500, FS-500-800, and FS-800-1600 µm, with around 40 kg for each fraction was prepared. Fillers smaller than 200 µm were collected separately to form FS-0-200 group with a weight of 15 kg. Furthermore, the FS-0-200 and FS-200-500 fractions underwent additional refinement through column sieving with a 40 µm and 315 µm mesh, respectively, resulting in additional subgroups: FS-0-40/FS-40-200 µm and FS-200-315/FS-315-500 µm.

#### 2.1.2. Polymer matrix and coupling agent

PP homopolymer (PPH 9020) was supplied by Total Petrochemicals. It has a melting point of 165 °C, a density of 0.905 g/cm³ (ISO 1183), and a melt flow rate of 25 g/10 min at 230 °C and 2.16 kg (ISO 1133). PP matrix was chosen in this work for its easy processability and thermally stability, in order to study and compare the effect of the FS without bias related to matrix degradation. Multiple methods can be used to improve the compatibility between lignocellulosic fibres and the PP polymer (Le Moigne et al., 2018a). These methods can involve a fibre treatment as silane treatments (Saravanan et al., 2025) or using a compatibilizer directly in the matrix. In this study, we used Maleic-Anhydride-Polypropylene (MAPP) compatibilizer by reactive extrusion, a one-step, solvent-free and ecofriendly process that can be easily implemented in industrial extrusion lines. MAPP (OREVAC® CA100) was supplied by Arkema, it has a melting point of 167°C (ISO 11357-3), a density of 0.905 g/cm³, and a melt flow rate of 10 g/10 min at 230 °C and 0.225 kg (ISO 1133). Prior to extrusion, PP and MAPP pellets were dry mixed.

### 2.2. Methods

This section presents the experimental methods used in this study, including biochemical analysis, composite preparation, particle size and shape characterization, X-ray tomography, uniaxial tensile testing, and micromechanical modelling. The microstructural characterization techniques were initially described in previous work (Nour El Dein et al., 2025), and the essential information is provided here for completeness.

#### 2.2.1. Biochemical composition analysis

**Monosaccharides.** Both the identification and the quantification of monosaccharides were performed according to the protocols reported in

Müssig and Beaugrand (2025). In brief, neutral carbohydrates were quantified by gas chromatography (Clarus 580; Perkin Elmer) whereas acidic monosaccharides (uronic acids) were quantified thanks to a colorimetric method. All tests were done in triplicate independent samples and values given are means values and expressed as a % of the dry matter mass.

**Lignin.** The analyses were performed on three independent spectrophotometric measurements, following the acetyl bromide method as reported earlier (Müssig and Beaugrand, 2025). The lignin content is expressed as a percentage of the dry matter.

**Ash.** Approximately 2 g of FS ($m_s$) were heated at 900 °C for 2 h in accordance with ISO 2171 using LBX MF12 (Muffle Furnace). After cooling to room temperature, the mass of the residuals ($m_r$) was measured. The ash content of the dry fillers was calculated from Eq. (1)

$$ Ash = \frac{m_r}{m_s(1 - w)} * 100 \qquad (1) $$

where w is the moisture content of each FS size distributions, determined on 2 g samples with a Sartorius MA160 Infrared Moisture analyzer. All measurements were done in replicate.

A summary of this compositional analysis is presented in Table 1 and Fig. 1. It is worth noting that finer fractions contain higher amounts of inorganic compounds (and hence less monosaccharides and lignin), with the ash content increasing with the decrease in the filler size distribution, reaching 15 wt% for FS-0-40. Additional Energy-dispersive X-ray spectroscopy (EDX) analysis was performed on ash from different FS size distributions to determine the nature of the inorganic compounds. The results are presented in supplementary data (Figure S1). They show that as the particle size of the FS decreases, the relative weight percentage of Calcium in the ash significantly decreases, while the relative weight percentage of Silicon increases. Traces of metals, i.e. iron and aluminum, are also present in greater amounts in the finer fractions, probably originating from the milling process and tool wear.

#### 2.2.2. Composite preparation

Prior extrusion, FS were vacuum dried at 80 °C for 24 h, and were then compounded with PP/MAPP pellets using co-rotating twin screw extruder BC21 (Cleextral, Firminy, France), which has a length of 900 mm, width of 25 mm, and aspect ratio of 36. The compounding process was conducted at temperature of 180 °C, with screw rotation speed and material flow rate of 250 rpm and 3 kg/h, respectively. The extruded composite was then immersed in a water bath for cooling, and then cut into 3-4 mm pellets, which were vacuum dried at 80 °C for 72 h before the injection moulding process. Through the extrusion process, around 3 kg of each composite fraction was produced.

The injection was carried out using KM 50-180 CX (Krauss-117 Maffei, Vaterstetten, Germany) injection moulding machine. The barrel temperature was set to 180 °C with a rotation speed of 120 rpm. The holding pressure in the mould was applied in two stages: 800 bar followed by 700 bar for 10 s each. The composites produced were type 1A tensile “dog bone” specimens according to the ISO 527-2 standard, with a thickness of 4 mm, a width of 10 mm, a length of the narrow parallel section of 80 mm, and an overall length of 170 mm. Composites with varying weight fractions and FS size distributions were prepared. Previous studies have shown that the optimal MAPP content is proportional to the fibre weight fraction (Rana et al., 1998; Snijder and Bos, 2000). Therefore, our experimental results showed that the optimal increase in the composite tensile strength is achieved by the MAPP/FS weight ratio 1/5 for composites reinforced with 10, 20, and 30 wt% FS. While for 40 wt% FS, the MAPP/FS weight ratio 1/6.6 was sufficient to reach an optimal composite tensile strength. The configuration of the prepared composites is summarized in Table 2.

#### 2.2.3. Particle size and shape distribution

Previous studies have demonstrated that high magnification 2D
<table><caption>**Table 1**
Biochemical composition and ash content (in wt%) of FS for the different size distributions.</caption><thead><tr><th></th><th>FS-Raw</th><th>FS-0-40</th><th>FS-0-200</th><th>FS-40-200</th><th>FS-200-315</th><th>FS-200-500</th><th>FS-315-500</th><th>FS-500-800</th><th>FS-800-1600</th></tr></thead><tbody><tr><td>Glucose (glc)</td><td>29.9 ± 1.2</td><td>22.9 ± 0.8</td><td>26.6 ± 0.9</td><td>30.2 ± 0.8</td><td>26.9 ± 1</td><td>24.2 ± 1</td><td>27.8 ± 1</td><td>30.2 ± 0.4</td><td>31.3 ± 1.1</td></tr><tr><td>Xylose (xyl)</td><td>17.8 ± 1.3</td><td>12.3 ± 0.6</td><td>15.8 ± 0.4</td><td>15.4 ± 0.3</td><td>18.8 ± 0.6</td><td>18 ± 1</td><td>21 ± 0.5</td><td>19.7 ± 0.5</td><td>19 ± 1</td></tr><tr><td>Rhamnose (rha)</td><td>0.5 ± 0.0</td><td>0.4 ± 0.0</td><td>0.4 ± 0.1</td><td>0.6 ± 0.0</td><td>0.5 ± 0.0</td><td>0.5 ± 0.1</td><td>0.5 ± 0.0</td><td>0.5 ± 0.1</td><td>0.5 ± 0.1</td></tr><tr><td>Arabinose (ara)</td><td>0.8 ± 0.1</td><td>1 ± 0.1</td><td>1.2 ± 0.2</td><td>0.9 ± 0.1</td><td>0.6 ± 0.1</td><td>0.8 ± 0.1</td><td>0.7 ± 0.0</td><td>0.6 ± 0.1</td><td>0.8 ± 0.1</td></tr><tr><td>Mannose (man)</td><td>1.7 ± 0.5</td><td>2.2 ± 0.2</td><td>2.6 ± 0.4</td><td>1.8 ± 0.5</td><td>2.7 ± 0.2</td><td>2.4 ± 0.2</td><td>2 ± 0.1</td><td>1.8 ± 0.3</td><td>1.6 ± 0.3</td></tr><tr><td>Galactose (gal)</td><td>1.2 ± 0.5</td><td>1.5 ± 0.0</td><td>2.1 ± 0.2</td><td>1.3 ± 0.2</td><td>1.8 ± 0.2</td><td>1.8 ± 0.1</td><td>1.5 ± 0.2</td><td>0.8 ± 0.1</td><td>1 ± 0.0</td></tr><tr><td>Galacturonic acid (GalA)</td><td>1.2 ± 0.4</td><td>2.4 ± 0.8</td><td>1.6 ± 0.5</td><td>2.1 ± 0.1</td><td>4.2 ± 1.4</td><td>1.3 ± 0.2</td><td>0.8 ± 0.3</td><td>1.2 ± 0.4</td><td>1.9 ± 0.7</td></tr><tr><td>Glucuronic acid (GlcA)</td><td>1.2 ± 0.4</td><td>0.7 ± 0.5</td><td>1.5 ± 0.7</td><td>0.9 ± 0.1</td><td>0.7 ± 1.2</td><td>1.1 ± 0.2</td><td>1 ± 0.1</td><td>1.1 ± 0.2</td><td>0.6 ± 0.6</td></tr><tr><td>Total monosaccharides</td><td>54.2 ± 3.3</td><td>43.5 ± 1.2</td><td>51.8 ± 1.6</td><td>53.1 ± 1.6</td><td>54.8 ± 3.3</td><td>50.1 ± 1.5</td><td>55.3 ± 1.2</td><td>56 ± 0.9</td><td>56.7 ± 2.2</td></tr><tr><td>Lignin</td><td>33.5 ± 0.2</td><td>23.2 ± 0.4</td><td>29.5 ± 0.4</td><td>27.4 ± 0.3</td><td>31.7 ± 0.8</td><td>31.2 ± 1.9</td><td>34 ± 1</td><td>32.8 ± 0.4</td><td>34.7 ± 0.3</td></tr><tr><td>Ash</td><td>1.5 ± 0.2</td><td>15.0 ± 2.7</td><td>4.7 ± 0.3</td><td>3.1 ± 0.1</td><td>1.9 ± 0.0</td><td>1.2 ± 0.2</td><td>0.9 ± 0.1</td><td>1.1 ± 0.1</td><td>0.4 ± 0.5</td></tr></tbody></table>

<figure><img src="image_5.png" /><figcaption>Fig. 1. Biochemical composition (in wt%) of FS for the different size distributions.</figcaption></figure>

<table><caption>**Table 2**
Composition of the produced PP/MAPP/FS composites. The ✓ sign shows that the composite was produced for the corresponding FS size.</caption><thead><tr><th>FS size distribution</th><th>10 wt% FS<br>88 wt% PP<br>2 wt% MAPP</th><th>20 wt% FS<br>76 wt% PP<br>4 wt% MAPP</th><th>30 wt% FS<br>64 wt% PP<br>6 wt% MAPP</th><th>40 wt% FS<br>54 wt% PP<br>6 wt% MAPP</th></tr></thead><tbody><tr><td>FS-0-200</td><td>✓</td><td>✓</td><td>✓</td><td>✓</td></tr><tr><td>FS-200-315</td><td></td><td>✓</td><td>✓</td><td></td></tr><tr><td>FS-200-500</td><td>✓</td><td>✓</td><td>✓</td><td>✓</td></tr><tr><td>FS-315-500</td><td></td><td></td><td>✓</td><td></td></tr><tr><td>FS-500-800</td><td>✓</td><td>✓</td><td>✓</td><td>✓</td></tr><tr><td>FS-800-1600</td><td>✓</td><td>✓</td><td>✓</td><td>✓</td></tr></tbody></table>

scanning is a reliable method for measuring fibre size and shape distribution (Di Giuseppe et al., 2016). Accordingly, a 2D scanner was employed to assess the impact of FS fractionation on its size and shape distribution before and after composite processing, i.e. extrusion and injection moulding. For FS extraction, PP/MAPP/FS composites were immersed into a Decalin® solvent (Thermo Scientific, France) at a temperature of approximately 150–155 °C. This process dissolved the PP/MAPP matrix, allowing for the extraction of FS fillers. Additional details regarding the extraction procedure can be found in Nour El Dein et al. (2025).

FS were dispersed onto a 2D scanner (Perfection V850 Pro, Epson, Suwa, Japan) for size and shape evaluation before and after composite processing. The image resolution was set to 3200 dpi to achieve an optimal balance between resolution and the investigation area (quantity of particles). For small fillers (FS-0-200), 6400 dpi was selected for improved accuracy. It is important to note that FS-0-200 fraction (before and after processing) underwent an additional sieving step using a 40 µm mesh to eliminate smaller fillers that could skew the size

distribution due to their influence on number and surface distribution by underestimating the size of the fillers (Nour El Dein et al., 2025). The scanned images were subsequently analysed using ImageJ software (Schindelin et al., 2012), with particle length and width measured based on the maximum and minimum Feret's diameters, respectively. The analysis was conducted on each FS fraction before composite processing and on FS extracted from PP/MAPP composites reinforced with 30 wt% of the different FS fractions and 10 wt% of FS-200-500 and FS-800-1600. The resulting size and shape distributions were determined based on surface-weighted distribution.

### 2.2.4. Fibre volume fraction measurement

The volume fractions of the flax shives for different size distribution were calculated for each composite, which were prepared with flax shives weight fraction of 10, 20, 30, and 40 %. The samples were sectioned from central region of the injected tensile specimens, then they were dried for 24 h at 80 °C to eliminate moisture prior to measurement. The mass of the specimens following drying ranged between 3 and 3.25 g. Their density ($ρ_c$) was then measured using a AccuPyc 1330 helium pycnometer (Micromeritics Instrument Corporation, Norcross, Georgia, USA). The fibre volume fraction ($V_f$), matrix volume fraction ($V_m$), and porosity ($V_p$) was then calculated using Eqs. (2)–(4).

$$V_f = \frac{\rho_c}{\rho_f} W_f \qquad (2)$$

$$V_m = \frac{\rho_c}{\rho_m} W_m \qquad (3)$$

$$V_p = 1 - V_f - V_m \qquad (4)$$

where $ρ_f$, $ρ_m$, $W_f$, and $W_m$ present the FS density, PP density, fibre weight fraction, and matrix weight fraction, respectively. The density of the FS
fillers, specific to each size distribution, was measured using the same helium pycnometer and ranged from 1.398 to 1.444 g/cm³. For each condition, two specimens were analysed, and the average value was used. In addition, the porosity inside the composites was always below 1 %.

### 2.2.5. Orientation by X-ray tomography

Composites reinforced with 10 wt% of FS-200–500 and FS-800–1600 were analysed by X-ray tomography using an EasyTom system (RX Solutions, Chavanod, France) to investigate the influence of the FS size distribution on the 3D composite microstructure. The investigated specimens were sectioned from the central region of the injected tensile specimens and then cut in half (reducing the width) to maximize the resolution of the images. The final captured volume by the machine was: 4 mm thickness, 5 mm (instead of 10 mm) width, and approximately 5.4 mm height. The X-ray source was operated at a voltage 40 kV and a current of 50 µA during acquisition. Projection images were captured using a 1920 × 1536 px PaxScan® 2520DX detector (Varex Imaging, Salt Lake City, Utah, USA) at 0.25° increments per rotation, with a total acquisition time of two hours and a voxel size of 4.08 µm. The acquired 3D images were processed using Dragonfly software (Comet Technologies Canada Inc., Montreal, 2022), leading to the segmentation of FS, as presented in Fig. 2. Fillers touching the boundary were removed from the computation. In addition, particles smaller than a 19 µm-side cube, representing less than 1 % of the total volume of FS fillers in the composite, were excluded from the measurement to improve computational efficiency. Given the flat elliptical morphology of FS fillers (Benmahidine et al., 2020), a minimal oriented boundary box was employed to characterize their geometrical properties, including length (L), width (W), thickness (T), and 3D vectors presenting fibre orientation within the composite, based on volume distribution analysis. Further details on the X-ray tomography image analysis are available in (Nour El Dein et al., 2025).

### 2.2.6. Tensile testing

The tensile properties of the injected composites were evaluated using a Zwick TH 010 (ZwickRoell, Germany) testing machine equipped of 2.5 kN load probe. Prior to testing, the samples were conditioned for at least one week in a controlled environment at 23 °C and 50 % relative humidity. The tensile modulus of the specimens was measured using a Zwick clip-on extensometer. In accordance with the ISO 527–2 standard, the displacement speeds for determining the tensile modulus and tensile strength were set at 1 mm/min and 10 mm/min, respectively. The slope of the linear trend line between 0.05 % and 0.25 % elongation was used to calculate the tensile modulus. The dimensions of each specimen were measured before each test, and at least five samples were tested for each composite formulation.

<figure><img src="image_6.png" /><figcaption>Fig. 2. X-ray tomography image for the cross-section of composite reinforced with 10 wt% FS-200–500. Each colour of particles presents a different filler.</figcaption></figure>

## 2.3. Micromechanical modelling

### 2.3.1. Analytical modelling

#### 2.3.1.1. Mori-Tanaka model.
The Mori-Tanaka approach (Mori and Tanaka, 1973), which is a micromechanical homogenisation model, was employed to estimate the effective elastic properties of PP/MAPP composites reinforced with FS of various sizes. It extends Eshelby’s inclusion theory for a single ellipsoidal inclusion (Walpole, 1977) by averaging the inclusion-matrix interactions across all phases in the composite through a mean-field approach.

Following Fisher and Brinson (2006) and Lee (2018) derivations, the Mori-Tanaka method for multiphase composite assumes that the composite consists of N phases: the continuous matrix (PP) is denoted as phase 0, while the inclusions (FS fillers) correspond to phases 1 through N – 1. The model is built upon several key assumptions (Fisher and Brinson, 2006):

* Both the inclusions (FS) and the matrix (PP) are considered linearly elastic and isotropic materials.

* A perfect interfacial bonding is assumed between the inclusions (FS) and the matrix (PP).

* The inclusions (FS) are modelled as ellipsoidal fillers (major axis $a_1$, minor axes $a_2 = a_3$), with aspect ratio $\alpha_r = a_1/a_3$.

At low inclusion volume fraction, interactions between inclusions are negligible. The average strain in inclusion $r, \bar{\epsilon}_r, \forall r \in [1, N-1]$, relates to the average matrix strain $\bar{\epsilon}_0$, via the dilute strain concentration tensor $A_r^{\text{dil}}$, as shown in Eq. (5):

$$ \bar{\epsilon}_r = A_r^{\text{dil}} \bar{\epsilon}_0 \quad (5) $$

The dilute strain concentration tensor $A_r^{\text{dil}}$ is expressed in Eq. (6):

$$ A_r^{\text{dil}} = [I + S_r C_0^{-1} (C_r - C_0)]^{-1} \quad (6) $$

where I is the fourth-order identity tensor, $S_r$ is the Eshelby tensor, and $C_0, C_r$ are the stiffness tensors of the PP matrix and FS inclusions, respectively. The stiffness tensor $C_0$ and $C_r$ are defined using their respective Young’s modulus ($E_0, E_r$) and Poisson’s ratios ($v_0, v_r$). The explicit form of $S_r(v_0, \alpha_r)$ accounting for the inclusion shape is provided in the Supplementary data (Tandon and Weng, 1984).

At higher inclusion volume fractions, inclusion-inclusion interactions cannot be neglected. In this case, the strain concentration tensor $A_0$ is used to link the average matrix strain $\bar{\epsilon}_0$ in the composite to the uniform applied strain $\epsilon_a$, as shown in Eq. (7):

$$ \bar{\epsilon}_0 = A_0 \epsilon_a \quad (7) $$

where $A_0$ is given by Eq. (8):

$$ A_0 = \left[ V_0 I + \sum_{r=1}^{N-1} V_r A_r^{\text{dil}} \right]^{-1} \quad (8) $$

here, V denotes the volume fraction. Substituting Eq. (7) into Eq. (5) provides the strain concentration factor $A_r$ for the rth inclusion phase in the non-dilute composite, as expressed in Eq. (9):

$$ A_r = A_r^{\text{dil}} A_0 \quad (9) $$

Finally, by considering the average stress $\bar{\sigma}$ as the weighted sum of the average stresses in all phases, the unidirectional stiffness matrix of the composite C can be estimated using Eq. (10):

$$ C = \left[ V_0 C_0 + \sum_{r=1}^{N-1} V_r C_r A_r^{\text{dil}} \right] A_0 \quad (10) $$

Since the composite is anisotropic, a model that accounts for FS
orientation is required. To this end, the method proposed by Advani and Tucker (1987) was employed. This method considers the fibre orientation state using second-order ($a_{ij}$) and fourth-order ($a_{ijkl}$) orientation tensor. These tensors are computed from the 3d length vectors ($P_r$) for each particle, which were measured using X-ray tomography. The second-order orientation tensor ($a_{ij}$) is defined as the volume average of the dyadic product of the individual fibre orientation vectors, as presented in Eq. (11):

$$a_{ij} = \sum_{r=1}^{K} v_r P_{r,i} P_{r,j}, \quad \forall i, j = 1 \dots 3 \qquad (11)$$

where $v_r$ and $K$ are the volume fraction of the $r^{th}$ individual fibre with respect to the total fibre volume and total number of fillers, as measured by X-ray tomography, respectively. Similarly, the fourth-order orientation tensor ($a_{ijkl}$) is defined in Eq. (12):

$$a_{ijkl} = \sum_{r=1}^{K} v_r P_{r,i} P_{r,j} P_{r,k} P_{r,l}, \quad \forall i, j, k, l = 1 \dots 3 \qquad (12)$$

The effective stiffness tensor of the composite material, denoted as ($T_{ijkl}$), that reflects the influence of the fibre orientation is computed by establishing a relationship between the components of the unidirectional composite stiffness ($C$) and the orientation tensors ($a_{ij}$) and ($a_{ijkl}$) as presented in Eq. (13):

$$T_{ijkl} = B_1 a_{ijkl} + B_2 (a_{ij}\delta_{kl} + a_{kl}\delta_{ij}) + B_3 (a_{ik}\delta_{jl} + a_{il}\delta_{jk} + a_{jl}\delta_{ik} + a_{jk}\delta_{il}) \\ + B_4 (\delta_{ij}\delta_{kl}) + B_5 (\delta_{ik}\delta_{jl} + \delta_{il}\delta_{jk}) \qquad (13)$$

where $\delta$ is the Kronecker delta and the coefficients $B$ are defined as: $B_1 = C_{11} + C_{22} - 2C_{12} - 4C_{66}$, $B_2 = C_{12} - C_{23}$, $B_3 = C_{66} + \frac{1}{2}(C_{23} - C_{22})$, $B_4 = C_{23}$, and $B_5 = \frac{1}{2}(C_{22} - C_{23})$.

The determined fourth $T_{ijkl}$ is then transformed into a 6 × 6 matrix representation in Voigt notation, denoted as $C_{eff}$, presenting the effective stiffness of the composite considering the fibre orientation, resulting in the measurement of the homogenized composite longitudinal Young's modulus ($E_{11}$).

### 2.3.1.2. Halpin-Tsai model.
Halpin-Tsai model (Halpin and Kardos, 1976) is a semi-empirical micromechanical approach that has been well used to predict the effective stiffness for a short fibre reinforced composite by combining fibre ($E_f$) and matrix ($E_m$) moduli with the fibre aspect ratio ($\alpha_f$) (assuming a circular cylinder) and its volume fraction ($V_f$). For a composite with aligned short fibres (unidirectional composite), the longitudinal ($E_L$) and transverse ($E_T$) composite stiffnesses are given by Eqs. (14) and (15), respectively.

$$E_L = \frac{1 + 2\alpha_f \eta_L V_f}{1 - \eta_L V_f} E_m, \quad \text{with } \eta_L = \frac{E_f / E_m - 1}{E_f / E_m + 2\alpha_f} \qquad (14)$$

$$E_T = \frac{1 + 2\eta_T V_f E_m}{1 - \eta_T V_f}, \quad \text{with } \eta_T = \frac{E_f / E_m - 1}{E_f / E_m + 2} \qquad (15)$$

For composites with in-plane randomly oriented fibres, the tensile modulus ($E_c$) is estimated using Eq. (16) based on Halpin-Tsai and Pagano approach (Delgado-Aguilar et al., 2017).

$$E_c = \frac{3}{8} E_L + \frac{5}{8} E_T \qquad (16)$$

### 2.3.2. Numerical modelling

The effective homogeneous elastic properties of PP/MAPP composites reinforced with the different FS fractions were estimated also using a finite element method (FEM) based on micromechanical approach. This process involved two main stages: i) generation of a Representative Volume Element (RVE) that incorporates key microstructural features, and ii) numerical homogenisation via finite element analysis of the RVE

using COMSOL Multiphysics® to compute the homogenised elastic properties.

#### 2.3.2.1. RVE generation.
The RVE geometry was constructed using a custom algorithm developed using MATLAB®. Input parameters included the fibre volume fraction, the desired number of fillers within the RVE, and experimental data characterizing fibre morphology and orientation. These experimental data were obtained from X-ray tomography (fibre orientation) and 2D scanner (aspect ratio).

The fillers were modelled as cylinders of uniform diameter, with length varying according to their aspect ratio. The experimental aspect ratio distribution was discretized into bins, and a surface-weighted average aspect ratio was computed for each bin. The number of fillers allocated to each aspect ratio bin within the RVE was adjusted to ensure that the volume fraction represented by each bin was proportional to its contribution in the experimental data, while maintaining the overall fibre volume fraction in the RVE. It has been shown previously that the number of fillers in the RVE can influence the model accuracy (Breuer and Stommel, 2020), increasing its value will provide an accurate result. In this model, a total of 100 fillers was selected for the RVE to balance statistical representativeness with computational efficiency. The orientation of each particle was assigned by sampling from a volume-weighted orientation distribution function (ODF). This ODF was constructed from the experimental data. Finally, the fillers were placed randomly within a cubic RVE ensuring that there is no overlapping between them. This constraint limited the maximum achievable fibre volume fraction in the RVE to be less than 20 % for random oriented fillers. Additionally, fillers were periodically continued, meaning that when fibre touches an RVE boundary it cut off and it continues on the opposite side. To avoid complexity, fibres were constrained from intersecting more than one RVE boundary simultaneously. The RVE dimensions were defined based on the assigned fibre volume fraction. Fig. 3 illustrates a RVE configuration of 100 fillers of 20 wt% of FS-200-500 embedded in a PP matrix for randomly oriented fibres and unidirectional fibres.

#### 2.3.2.2. Finite element analysis.
Finite element simulations were conducted using COMSOL Multiphysics® software (version 6.3). The geometric data for the RVE (fillers and enclosing box) was used to construct the 3D finite element model. The materials properties (density, Young's modulus, and Poisson's ratio) were assigned to the fillers and matrix domain. Both materials are assumed to be isotropic. For the polymer, the density was used from the material data sheet (0.905 g/cm³), the Young's modulus was measured experimentally, and its Poisson's ratio was set to be 0.4 based on previous measurements (Rouway et al., 2020; Signoret et al., 2021). For flax shives, its density was measured using the helium pycnometer and its Poisson's ratio was assumed to be 0.4 which is in the range of lignocellulosic fibres (Rouway et al., 2020). A perfect interfacial bonding is assumed between the matrix and the FS fillers. The Solid Mechanics interface within the Structural Mechanics module was employed. Periodic boundary conditions were applied to the RVE faces using the “Cell periodicity” feature with the boundary conditions assigned to as average strain. To define the correspondence between opposite faces of the periodicity, boundary pairs were defined for each of the three RVE side-pairs. Finally, the “create load groups and study” functionality was used to automatically generate a stationary study with independent six standard load cases (three uniaxial and three shear average strains). The homogenized longitudinal Young's modulus of the composite ($E_{11}$) was then determined based on the load case corresponding to the longitudinal direction. It is important to note that a mesh convergence analysis was performed ensuring that the results are independent of mesh density.
<figure><img src="image_7.png" /><figcaption>Fig. 3. RVE sample for composite reinforced with 20 wt% of FS-200-500. (left) random orientation; (right) unidirectional orientation.</figcaption></figure>

# 3. Results and discussions

## 3.1. Microstructural analysis

### 3.1.1. Size and shape distribution of flax shives before and after processing

The resulting size and shape distribution of FS after fractionation (and before composite processing), obtained by 2D scanner analysis (see Section 2.2.3) are presented in Fig. 4. It is shown that the FS size and shape is highly affected by the fractionation process, leading to a variation in its aspect ratio across the different groups. Additional information about initial FS size after fractionation and before processing can be found in (Nour El Dein et al., 2025).

Indeed, the elliptical shape of FS fillers (Benmahiddine et al., 2020; Nour El Dein et al., 2025; Nuez et al., 2021) involves that their aspect ratio, i.e. the ratio of the particle's length (L) to its diameter (D), can be determined using several particle dimensions, in particular its thickness (T), width (W), and an equivalent diameter ($D_{eq}$) (Nour El Dein et al., 2025). The latter has been defined as the diameter of a theoretical circular cross-section with the same perimeter as the elliptical cross section of FS particle, where W stands for the major axis and T the minor axis.

Fig. 5 presents the aspect ratio of FS fillers extracted from composites reinforced with 10 wt% FS-200-500 and FS-800-1600. Measurements were conducted using two techniques: X-ray tomography based separately on equivalent diameter ($D_{eq}$) and width (W), and a 2D scanner, which uses the width (W) of the fillers. The results reveal two key observations: first, aspect ratio measurements based on width from both X-ray tomography and 2D scanning yielded nearly identical results, demonstrating consistency between these techniques when considering

<figure><img src="image_8.png" /><figcaption>Fig. 5. Fibre aspect ratio measured using three different approaches for composites reinforced with 10 wt% FS-200-500 and FS-800-1600, (i) X-ray tomography based on equivalent diameter $D_{eq}$ and (ii) particle width (volume-weighted distribution), and (iii) 2D scanning based on particle width (surface-weighted distribution).</figcaption></figure>

the width as the particle diameter. Second, accounting for the elliptical shape of the fillers and using $D_{eq}$ via X-ray tomography increased the measured aspect ratio by 35.6 % and 41.2 % for the median values of FS-

<figure><img src="image_9.png" /><figcaption>Fig. 4. Surface-weighted distributions of size and shape for flax shives after fractionation and before processing, measured using 2D scanner.</figcaption></figure>
200–500 and FS-800–1600, respectively, compared to aspect ratios based solely on width (W).

Since the 2D scanner technique can only measure the particle length and width, it cannot capture equivalent diameter-based aspect ratios. To address this limitation and correctly take into account the elliptical shape of FS, a correction factor of approximately 38 % was applied to 2D scanner-based measurements, according to the average increase in the median aspect ratio observed from X-ray tomography measurements for FS-200–500 and FS-800–1600 composite (Nour El Dein et al., 2025). As will be shown further, these corrected aspect ratios can be used in the analytical and numerical modelling to better estimate the elastic properties of the FS and the composites.

The aspect ratio of FS extracted from composites reinforced with 30 wt% measured using the 2D scanner is presented in Fig. 6. The results indicate that the initial size distribution of the FS resulting from the fractionation process significantly influences the final aspect ratio of the fillers in the composite. In this regard, Di Giuseppe et al. (2017) also showed for miscanthus, sisal, and bast flax and retted hemp fibres that the length breakage constants during compounding were mainly determined by the initial length of the fibres. In the present work, the median aspect ratio after processing for FS-0–200 is 1.91, which sharply increases to 2.61 for FS-200–315, representing the highest measured value. Further increases in initial fibre size distribution led to a decrease in the particle’s aspect ratio to 2.17 and 2.11 for FS-200–500 and FS-315–500 fractions, respectively. Beyond that, aspect ratios plateau at 1.89 for FS-500–800 and FS-800–1600 fractions.

These findings highlight the crucial importance of optimizing the fractionation process of plant-based fillers in order to improve their aspect ratio in the composite, and hence their reinforcement efficiency in terms of both stiffness and strength. Specifically, FS fillers (re)sieved with the 315 µm mesh exhibit a superior aspect ratio, with the FS-200–315 fraction achieving the highest value, thereby indicating an optimal granulometry of FS for composite reinforcement.

### 3.1.2. Orientation of flax shives in injection-moulded composites

Previous studies have shown that the fibre orientation has a significant impact on composite tensile properties. Verstraete et al. (2023) showed that for composites reinforced with flax fibres, the composite Young’s modulus parallel to the injection flow is higher by 27 % compared to its Young’s modulus at the transverse direction. Hence, it is crucial to understand how the fibre size and shape distribution influences the fibre orientation within the composite. Therefore, using

X-ray tomography and volume-based analysis, Fig. 7 presents the distribution of the FS orientation with respect to the tensile direction for composites reinforced with 10 wt% FS-200–500 and FS-800–1600. The results show that FS-200–500 exhibit a lower orientation angle compared to FS-800–1600 across all percentiles, with a median value of 16.3 ° for FS-200–500 compared to 23.4 ° for FS-800–1600. Hence, medium-sized fillers (FS-200–500) tend to be more aligned towards the tensile direction than coarse fillers (FS-800–1600), which is advantageous for the composite’s tensile properties. More details about the FS orientation within the injected composites are given in Nour El Dein et al. (2025).

## 3.2. Composite tensile properties

Typical tensile curves for composite reinforced with FS are presented in Fig. 8(a) for composites reinforced with 30 wt% FS with different size distributions and Fig. 8(b) for composites reinforced with 10, 20, 30, and 40 wt% FS-200–500. Table 3 and Fig. 9 presents the tensile properties for PP/MAPP composites reinforced with FS fillers of various size distribution and volume fraction. Panel (a) shows the Young’s modulus, while panel (b) displays the ultimate tensile strength (UTS). Overall, the results indicate that both the initial FS size distribution and FS volume fraction significantly influence the tensile behaviour of the composites.

Regarding Young’s modulus, the addition of FS consistently increases composite stiffness relative to raw PP regardless of the FS size distribution, and a linear relationship is observed between stiffness and FS volume fraction across the tested FS size ranges. However, the magnitude of the stiffness enhancement varies significantly with the FS fractions. For composites reinforced with 30 wt% of FS (corresponding to a fibre volume fraction between 21.1 % and 21.6 %), those incorporating FS-0–200 exhibit an average stiffness of 3022 MPa. When the particle size increases to FS-200–315, stiffness rises markedly to 3486 MPa. Further increases in filler size led to a slight reduction in stiffness, with FS-200–500 and FS-315–500 achieving 3274 MPa and 3348 MPa, respectively. Finally, composites reinforced with the coarser FS-500–800 and FS-800–1600 fractions show a pronounced reduction in stiffness, with average values of 3050 MPa and 2957 MPa, respectively.

In contrast, UTS exhibits a more complex behaviour. Although a linear relationship with fibre volume fraction can be observed across the different FS size distributions, adding FS at low concentration leads to a decrease in UTS compared to raw PP (33.8 MPa). By extrapolating the UTS of PP along the linear trend established for FS reinforced composites, it becomes apparent that improvements in UTS occur when the fibre volume fraction exceeds approximately 12.3 %, 14.9 %, 23.8 %, and 27.3 % for composites reinforced with FS-0–200, FS-200–500, FS-

<figure><img src="image_10.png" /><figcaption>**Fig. 6.** Non-corrected and corrected (38 %) aspect ratios of FS fillers measured using 2D scanner after extraction from composites reinforced with 30 wt% of FS. The margins indicate the 10th and 90th percentiles of the aspect ratio distribution.</figcaption></figure>

<figure><img src="image_11.png" /><figcaption>**Fig. 7.** Distribution of flax shives (FS) orientation with respect to the tensile direction for composites reinforced with 10 wt% FS-200–500 and FS-800–1600.</figcaption></figure>
<figure><img src="image_12.png" /></figure>

<figure><img src="image_13.png" /><figcaption>**Fig. 8.** Tensile curves for composites reinforced with flax shives: (a) 30 wt% FS with different size distributions, (b) 10, 20, 30, and 40 wt% FS-200-500.</figcaption></figure>

500–800, and FS-800–1600, respectively. Thus, the fibre size and shape distribution are critical in determining the threshold fibre volume fraction necessary for enhancing UTS. For composites reinforced with 30 wt% of FS, the UTS is 38.1 MPa for FS-0–200, increasing the fibre size to FS-200–315 improves the UTS to 40.2 MPa. However, further increases in the FS size results in a decrease in the UTS to reach 37.3 MPa for FS-200–500 and 36.53 MPa for FS-315–500, and a more pronounced drop to 33.3 MPa and 32.1 MPa for FS-500–800 and FS-800–1600, respectively.

Overall, FS fillers sieved below 500 µm yield the best tensile properties. Specifically, composites reinforced with FS-200–315, FS-200–500 and FS-315–500 fractions exhibit high stiffness and optimal tensile strength, whereas those reinforced with FS-0–200, despite their low stiffness, achieve relatively high tensile strength. Notably, the FS-200–315 demonstrate superior overall performance. This observation aligns with previous studies by Nuez et al. (2021, 2020a), which also reported that FS fillers sieved below 500 µm presents optimal tensile properties. Similar behaviour has been also noticed for hemp shives composites demonstrating that particle sieved below 500 µm provide higher tensile properties compared to those sieved between 500 µm and 800 µm (Borowczak et al., 2025).

To elucidate the significant differences in composite tensile

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

Tensile properties (Young's modulus and ultimate tensile strength) for composites reinforced with various size distribution of flax shives across multiple fibre weight fractions. The values present the mean and the standard deviation of at least 5 tests.

<table><thead><tr><th>Composite</th><th>Fibre weight fraction (%)</th><th>Fibre volume fraction (%)</th><th>Young's Modulus (MPa)</th><th>Ultimate tensile strength (MPa)</th></tr></thead><tbody><tr><td>PP</td><td>0</td><td>0</td><td>1823 ± 95</td><td>33.8 ± 0.53</td></tr><tr><td rowspan="4">FS-0-200</td><td>10</td><td>6.5</td><td>2084 ± 100</td><td>30.7 ± 0.62</td></tr><tr><td>20</td><td>13.5</td><td>2459 ± 45</td><td>34.9 ± 0.33</td></tr><tr><td>30</td><td>21.1</td><td>3022 ± 82</td><td>38.1 ± 0.28</td></tr><tr><td>40</td><td>29.3</td><td>3841 ± 84</td><td>41.5 ± 0.33</td></tr><tr><td>FS-200-315</td><td>30</td><td>21.4</td><td>3487 ± 194</td><td>40.2 ± 0.24</td></tr><tr><td rowspan="4">FS-200-500</td><td>10</td><td>6.6</td><td>2277 ± 89</td><td>29.9 ± 0.33</td></tr><tr><td>20</td><td>13.8</td><td>2761 ± 69</td><td>33.3 ± 0.34</td></tr><tr><td>30</td><td>21.5</td><td>3275 ± 161</td><td>37.3 ± 0.19</td></tr><tr><td>40</td><td>29.8</td><td>4109 ± 78</td><td>39.9 ± 0.18</td></tr><tr><td>FS-315-500</td><td>30</td><td>21.4</td><td>3348 ± 91</td><td>36.5 ± 0.16</td></tr><tr><td rowspan="4">FS-500-800</td><td>10</td><td>6.7</td><td>2102 ± 32</td><td>28.2 ± 0.30</td></tr><tr><td>20</td><td>13.8</td><td>2466 ± 112</td><td>30.7 ± 0.27</td></tr><tr><td>30</td><td>21.4</td><td>3050 ± 45</td><td>33.3 ± 0.07</td></tr><tr><td>40</td><td>29.9</td><td>3641 ± 91</td><td>35.5 ± 0.25</td></tr><tr><td rowspan="4">FS-800-1600</td><td>10</td><td>6.7</td><td>2084 ± 67</td><td>27.7 ± 0.36</td></tr><tr><td>20</td><td>13.9</td><td>2455 ± 20</td><td>29.7 ± 0.45</td></tr><tr><td>30</td><td>21.6</td><td>2958 ± 36</td><td>32.1 ± 0.22</td></tr><tr><td>40</td><td>30.0</td><td>3678 ± 91</td><td>34.7 ± 0.35</td></tr></tbody></table>

<figure><img src="image_14.png" /></figure>

<figure><img src="image_15.png" /><figcaption>**Fig. 9.** Tensile properties of PP/MAPP composites reinforced with FS of various size distributions and volume fractions. (a) Young's modulus and (b) Ultimate tensile strength. Symbols represent the mean values, while the error bars indicate the standard deviations.</figcaption></figure>
properties with respect to FS size and shape distribution, Fig. 10 establish a link between the FS fractionation, the composite microstructure, and the composite tensile properties. It presents the tensile properties of composites reinforced with 30 wt% of FS alongside the final FS aspect ratio in injection-moulded composites for the different FS fractions. A clear correlation emerges between fibre aspect ratio and composite stiffness. Composites reinforced with FS exhibiting lower aspect ratio as FS-0-200, FS-500-800, and FS-800-1600 exhibit lower stiffness compared to those reinforced with higher aspect ratio fibres as in FS-200-315, FS-200-500, and FS-315-500. This confirms that controlling the fibre aspect ratio via the fractionation process significantly impacts composite stiffness. Moreover, our earlier findings in Section 3.1.2, indicate that medium sized fillers (FS-200-500) tend to align more with the tensile direction compared to coarse fillers (FS-800-1600), thereby enhancing tensile properties. These observations agree with the literature which shows that the composite stiffness is strongly influenced by fibre volume fraction, aspect ratio, and orientation (Ku et al., 2011; Lau et al., 2018; Verstraete et al., 2023).

The relationship between the fibre aspect ratio and the ultimate tensile strength (UTS) is less straight forward. Typically, fillers with higher aspect ratio as in FS-200-315, FS-200-500, and FS-315-500 present significantly higher UTS compared to coarse fillers with lower aspect ratio as in FS-500-800 and FS-800-1600. Yet, fine fillers (FS-0-200) achieve a relatively high UTS despite their low aspect ratio. This is primarily due to the enhanced stress transfer between the matrix and the reinforcement. Unlike the Young's modulus, which reflects stiffness at low deformation causing no separation in the matrix-fillers interface (Fu et al., 2008), UTS is highly sensitive to the efficiency of stress transfer at the interface between the matrix and the reinforcement under higher loads (Rana et al., 1998; Snijder and Bos, 2000). Additional factors resulting from the fibre-matrix stress transfer can also contribute to the UTS behaviour with respect to the fibre size. Previous studies on nano and micro scale particles have demonstrated that the fibre dispersion critically affect the UTS (Manjunatha et al., 2021; Shibulal and Naskar, 2012). In our earlier work (Nour El Dein et al., 2025), it was shown that FS-0-200 fine fillers are better dispersed within the composite than coarser fillers. Moreover, fine fillers provide higher surface-to-volume ratio than larger fillers, enhancing interfacial area and hence stress transfer, resulting in an additional contribution to the composite tensile strength (Fu et al., 2008). Together, these factors can explain why composites reinforced with fine fillers exhibit relatively high UTS despite their lower stiffness.

<figure><img src="image_16.png" /><figcaption>**Fig. 10.** Ashby diagram for the Young's modulus versus ultimate tensile strength for composites reinforced with 30 wt% of FS for various size distributions. The circle presents the aspect ratio of each FS size distribution after processing.</figcaption></figure>

### 3.3. Micromechanical modelling

The elastic properties of PP/MAPP composites reinforced with FS fillers of varying size distributions and fibre volume fractions were predicted using micromechanical modelling. As no prior study has experimentally determined the stiffness of FS fillers, their Young's modulus $E_{FS}$ was estimated through a back-calculation approach. This involved fitting the model predictions to the experimental composite stiffness. Three models were employed for this purpose: the numerical FEM, and two analytical micromechanical models (Halpin-Tsai and Mori-Tanaka models). For these models $E_m = 1.822$ GPa (average measured PP Young's Modulus) and the Poisson's ratios $v_m = 0.4$ (Rouway et al., 2020; Signoret et al., 2021) and $v_f = 0.4$ (Rouway et al., 2020) (in the range of lignocellulosic fibres) were used.

For analytical modelling: The $E_{FS}$ value was estimated using two strategies: first, a granulometry-specific modulus ($E_{FS-0-200}$, $E_{FS-200-315}$, $E_{FS-200-500}$, $E_{FS-315-500}$, $E_{FS-500-800}$, and $E_{FS-800-1600}$) was determined for each filler size distribution by minimizing the sum of squared differences between the model predictions and the experimental composite modulus across the tested FS volume fractions; second, a single equivalent FS modulus $E_{FS-equivalent}$ was also determined - only for Mori-Tanaka model - by minimizing the total squared error over the entire dataset. For numerical modelling: the $E_{FS}$ value was determined only for composites reinforced with 10 and 20 wt% FS due to the limitation of generating high fibre volume fractions in the RVE. Consequently, a granulometry-specific modulus ($E_{FS-0-200}$, $E_{FS-200-500}$, $E_{FS-500-800}$, and $E_{FS-800-1600}$) was determined from FEM by averaging the back-calculated $E_{FS}$ from the 10 and 20 wt% for each of the granulometry. No FEM measurements were done for FS-200-315 and FS-315-500 composites because they were only reinforced with 30 wt% FS.

During modelling, the FS aspect ratio ($\alpha_f$) obtained from 2D scanner measurements was corrected by a factor of 38 % (as detailed in Section 3.1.1) to account for discrepancy between direct 2D scanner measurements and the actual aspect ratio due to the elliptical cross-sectional shape of FS as detected using X-ray tomography for 10 wt% FS-200-500 and FS-800-1600 composites. Since filler size distribution after processing was only characterized for composites reinforced with 30 wt % as presented in Fig. 6, the same aspect ratio values were applied across all weight fractions for each FS size category, except for composites reinforced with 10 wt% FS-200-500 and FS-800-1600 where the aspect ratio of the fillers were directly measured as shown in Fig. 5. For Mori-Tanaka and FEM, the full distribution of the aspect ratio was incorporated into the models, while for Halpin-Tsai, only the surface-weighted average aspect ratio was used to represent the whole distribution.

The fibre orientation distribution obtained via X-ray tomography for composites reinforced with 10 wt% FS-200-500 and FS-800-1600 were used in Mori-Tanaka and in the numerical FE models. Specifically, the measured orientation angle distribution from the FS-200-500 composite was used for composites reinforced with FS-0-200, FS-200-315, FS-200-500, and FS-315-500, while the orientation from the FS-800-1600 composite was applied to composites reinforced with FS-500-800 and FS-800-1600. A summary of the aspect ratio and fibre orientation data used for mechanical modelling of each composite is given in the supplementary data (Table S1).

Table 4 presents the estimated values of granulometry-specific modulus $E_{FS}$ obtained using the different models and orientation assumptions. For the Halpin-Tsai model, both unidirectional and in-plane random fibre orientations were considered. For the Mori-Tanaka and numerical FE models, predictions were made assuming either a unidirectional fibre orientation or the real orientation distribution obtained from X-ray tomography. The results reveal several key findings.

First, when assuming a unidirectional fibre orientation, the $E_{FS}$ values varied significantly between models: in general, $E_{FS(FEM)} < E_{FS(Halpin-Tsai)} < E_{FS(Mori-Tanaka)}$. This discrepancy can be attributed in how each model predicts the composite modulus $E_{11}$ for a
<table><caption>**Table 4**
Estimated granulometry-specific moduli $E_{FS}$ (in GPa) using the Halpin-Tsai, Mori-Tanaka, and Finite element models under different fibre orientation assumptions.</caption><thead><tr><th>Model</th><th>Orientation</th><th><i>E</i><sub>FS-0-200</sub></th><th><i>E</i><sub>FS-200-315</sub></th><th><i>E</i><sub>FS-200-500</sub></th><th><i>E</i><sub>FS-315-500</sub></th><th><i>E</i><sub>FS-500-800</sub></th><th><i>E</i><sub>FS-800-1600</sub></th></tr></thead><tbody><tr><td rowspan="2">Halpin-Tsai</td><td>Unidirectional</td><td>11.48</td><td>14.59</td><td>14.06</td><td>14.24</td><td>10.85</td><td>10.65</td></tr><tr><td>In-plane random</td><td>17.7</td><td>29.11</td><td>25.03</td><td>26.47</td><td>15.66</td><td>15.22</td></tr><tr><td rowspan="2">Mori-Tanaka</td><td>Unidirectional</td><td>15.18</td><td>19.20</td><td>19.36</td><td>20.44</td><td>14.16</td><td>13.85</td></tr><tr><td>Real orientation</td><td>21.84</td><td>33.0</td><td>32.13</td><td>36.45</td><td>22.89</td><td>22.05</td></tr><tr><td rowspan="2">FEM</td><td>Unidirectional</td><td>9.06</td><td>-</td><td>15.95</td><td>-</td><td>9.29</td><td>8.85</td></tr><tr><td>Real orientation</td><td>11.83</td><td>-</td><td>23.0</td><td>-</td><td>12.9</td><td>12.05</td></tr></tbody></table>

given set of constituent properties. For short fibres with low aspect ratio ($\alpha_f \le 8$), and a given FS modulus, the Halpin-Tsai model tends to predict a slightly lower $E_{11}$ than FEM, while the Mori-Tanaka model predicts significantly lower $E_{11}$ than FEM (see supplementary data Figure S2, consistent with (Tucker III and Liang, 1998)). Consequently, to match the same experimental $E_{11}$ value, models that predict a lower $E_{11}$ (like Mori-Tanaka for low aspect ratio) requires a higher $E_{FS}$. This highlights the importance of considering model-dependent variability in such estimations.

Second, notable differences were observed between $E_{FS}$ obtained under different orientation assumptions (unidirectional vs in-plane random for Halpin-Tsai, and unidirectional vs real orientation for Mori-Tanaka and FEM). Across the tested models, the results showed that composites with unidirectional orientation provided higher $E_{11}$ compared to that for real fibre orientation or in-plane random orientation, which can be noticed by requiring lower $E_{FS}$ to reach the same $E_{11}$. These differences underscore the critical role of the actual fibre orientation in determining the tensile properties of these composites, corroborating previous findings (Verstraete et al., 2023). Furthermore, when considering the real fibre orientation, the Mori-Tanaka model consistently yielded higher $E_{FS}$ values compared to the FEM across the different FS fractions. This again is due to the Mori-Tanaka model's tendency to predict a lower composite stiffness for a given $E_{FS}$ relative to FEM, thus requiring a higher $E_{FS}$ to match experimental data obtained on the composites.

Third, both FEM and Mori-Tanaka models using the real fibre orientation revealed that the $E_{FS}$ varies with FS filler size. Two distinct groups emerged: medium-sized fillers (FS-200-315, FS-200-500, and FS-315-500) exhibit a higher $E_{FS}$ (Mori-Tanaka: 32.13–36.45 GPa; FEM: $E_{FS-200-500}$ at 23.0 GPa), while fine (FS-0-200) and coarse fillers (FS-500-800, FS-800-1600) yield a lower $E_{FS}$ values (Mori-Tanaka: 21.84–22.89 GPa; FEM: 11.83–12.9 GPa). While the structural stiffness of plant fibres, as their stiffness and strength, are generally linked to their biochemical composition and cell wall structure (Le Moigne et al., 2018b; Nuez et al., 2020b), the latter does not significantly differ across the different FS fractions, as shown in Table 1. Thus, the observed variations in the estimated $E_{FS}$ are more likely attributable to microstructural differences between the different FS granulometry and their interactions with the matrix. In particular, FS fillers exhibit a hollow porous structure with capillary-like channels aligned along the growth axis of plant cells and connected by small cavities (Benmahidine et al., 2020). These pores are typically partially or fully filled up by the polymer during composite processing (Nour El Dein et al., 2025) (see supplementary data Figure S3), which can significantly influence the composite's tensile properties. Indeed, although the fibre volume fraction, which implicitly accounts for the polymer within these pores, was applied in the tested models, these models simplify the FS as homogeneous solids. Consequently, they do not explicitly consider the internal interactions and specific load transfer between the FS skeleton and the impregnated polymer within the pores. This simplification may have a significant impact given the distinct size distributions and potentially varying microstructures among the tested FS fractions. In addition, although the impact of the elliptical shape structure may be considered in the models by correcting the aspect ratio, this has been done for all FS size distribution, which may overestimate the true aspect ratios of the

finer FS-0-200 fillers (which consist mainly of cell wall fragments) leading to the underestimation of $E_{FS-0-200}$.

Therefore, the estimated $E_{FS}$ values should be interpreted as effective homogeneous property that implicitly accounts for the porous nature of FS and the polymer penetration, rather than the stiffness of the solid FS material itself. Further research, possibly involving direct characterization of FS porosity and advanced modelling incorporating such features, is needed to fully elucidate these effects.

The equivalent Young's modulus obtained from the Mori-Tanaka model, $E_{FS-equivalent}$, considering the real fibre orientation and fibre size and shape distribution and its volume fraction is estimated to be 26.09 GPa. This value is intermediate between the $E_{FS}$ values of the two groups identified above. Fig. 11 illustrates the correlation between the experimental data and the Mori-Tanaka predictions for both granulometry-specific and equivalent $E_{FS}$. This suggests that a single $E_{FS}$ value of approximately 26.09 GPa can provide reasonable predictions across all tested FS fractions when using Mori-Tanaka model with real orientation data. This value aligns well with literature values: Nuez et al. (2021) estimated the longitudinal Young's modulus of FS to be 27.9 GPa using empirical density-stiffness correlation for wood fillers (Trouy-Triboulot and Triboulot, 2001), while Verstraete et al. (2023) reported a lower value of 22.2 GPa using the Mori-Tanaka approach assuming a unidirectional composite for FS fillers with an aspect ratio of 2.3. Finally, it is important to note that while the Mori-Tanaka equivalent modulus (26.09 GPa) offers a highly efficient parameter for rapid prediction, FE homogenization remains the more accurate approach yielding $E_{FS}$ value ranging from 11.8 to 23.0 GPa.

## 4. Conclusions

This study demonstrates that the fractionation of FS plant-based filler is critical for optimizing the tensile performance of FS reinforced PP/MAPP composites. The reinforcing capacity of FS varied significantly upon all FS granulometry, optimal tensile properties were reached for composites reinforced with medium sized FS. Specifically, composites reinforced with FS-200-315 yielded the highest tensile properties. This superior performance is directly attributed to a more favourable composite microstructure, as these medium-sized fillers retain a higher aspect ratio after processing and exhibit a greater degree of orientation toward the tensile direction.

To better interpret the reinforcement mechanisms, the stiffness of the FS was back-calculated using both analytical (Halpin-Tsai, Mori-Tanaka) and numerical (FE) mechanical modelling approaches. These analyses revealed that the choice of model and its underlying assumptions are critical. Simplified assumptions of idealized fibre orientation can lead to a significant misestimation of the filler's stiffness. Furthermore, both the Mori-Tanaka and numerical FE models identified two groups of $E_{FS}$ depending on the size of the fillers, likely to be due to the differences in the FS microstructure and their interaction with the matrix. The calculated stiffness ranges between 21.84–36.45 GPa for Mori-Tanaka model and 11.83–23.0 GPa for the FE model. As a baseline, the Mori-Tanaka method yielded a single equivalent stiffness of 26.09 GPa when applied to the entire FS size distributions. The models used are limited by assuming an isotropic filler and a perfect interface between the fillers and matrix, which could also lead to a misestimation of the
<figure><img src="image_17.png" /><figcaption>**Fig. 11.** Comparison between the experimental longitudinal modulus of the composites and the Mori-Tanaka model predictions, using either granulometry-specific FS moduli (E<sub>FS</sub>) or an equivalent FS modulus (E<sub>FS-equivalent</sub>). The percentage difference between the model predictions and experimental values is indicated for each composite formulation.</figcaption></figure>

filler's longitudinal stiffness. In addition, the lumen inside the flax shives, which is filled up with polymer, was not considered in the finite element modelling. Hence, further investigations must be done to enhance the micromechanical modelling.

Our results can be generalized to other fillers derived from agricultural by- and co-products, and to maximize their reinforcing capacity in composite materials by optimizing the filler size and shape distribution using well-controlled fractionation processes. Mechanical modelling and back-calculation of elastic properties of such fillers are of particular interest for comparing their reinforcement capacity when classical direct measurement approaches such as single fibre tensile testing cannot be used. Finally, the same approach can be extended to other types of polymer matrices, i.e. bio-based, biodegradable or compostable, such as biopolyesters (e.g. PHAs, PLA), resulting in the development of fully bio-based and biodegradable composites.

### CRediT authorship contribution statement

**Monica Francesca Pucci:** Writing – review & editing, Validation, Supervision, Project administration, Methodology, Funding acquisition, Conceptualization. **Antoine Barbulée:** Writing – review & editing, Validation, Supervision, Resources, Project administration, Methodology, Investigation, Funding acquisition, Conceptualization. **Ali Nour El Dein:** Writing – original draft, Visualization, Validation, Software, Methodology, Investigation, Formal analysis, Data curation, Conceptualization. **Nicolas Le Moigne:** Writing – review & editing, Visualization, Validation, Supervision, Project administration, Methodology, Funding acquisition, Conceptualization, Formal analysis. **Olivier Gamond:** Writing – review & editing, Supervision, Resources, Project administration, Funding acquisition, Conceptualization. **Anne-Sophie Caro:**

Writing – review & editing, Visualization, Validation, Supervision, Software, Project administration, Methodology, Funding acquisition, Formal analysis, Conceptualization.

### Declaration of Competing Interest

The authors declare the following financial interests/personal relationships which may be considered as potential competing interests: the authors report financial support was provided by The French Agency for Ecological Transition. If there are other authors, they declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

### Acknowledgments

Ali Nour El Dein thanks DEPESTELE and ANRT (National Association for Research and Technology) for funding his thesis (2021/0769). The authors would like to thank the French Agency for Ecological Transition (ADEME) for funding the ProACTIF project (GRAINE 2019 - no2103D0029). They also thank Johnny Beaugrand, Lèna Brionne and Lucie Le Bot for their help and skills in biochemical analysis and the MRI platform member of the national infrastructure France-BioImaging supported by the French National Research Agency (ANR-10-INBS-04, «Investments for the future»), the LabEx CEMEB (ANR-10-LABX-0004) and NUMEV (ANR-10-LABX-0020) for their support on the X-ray tomography experiments.
# Appendix A. Supporting information

Supplementary data associated with this article can be found in the online version at doi:10.1016/j.indcrop.2025.121925.

## Data availability

Data will be made available on request.

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