# Fiber-matrix interface characterization in CF/PEEK composites by analysis of single fiber fragmentation

Milena T. Umemura, Florent Dalmas, Pascal Reynaud, Didier Long, Gilbert Fantozzi, Nathalie Godin, Lise Trouillet-Fonti, Jerome Bikard

## ► To cite this version:

Milena T. Umemura, Florent Dalmas, Pascal Reynaud, Didier Long, Gilbert Fantozzi, et al., Fiber-matrix interface characterization in CF/PEEK composites by analysis of single fiber fragmentation. Composites Science and Technology, 2025, 270, pp.111301. 10.1016/j.compscitech.2025.111301. hal-05247811

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# Fiber-matrix interface characterization in CF/PEEK composites by analysis of single fiber fragmentation

Milena T. Umemura<sup>a,b, ID</sup>, Florent Dalmas<sup>a ID</sup>, Pascal Reynaud<sup>a</sup>, Didier Long<sup>a</sup>, Gilbert Fantozzi<sup>a</sup>, Nathalie Godin<sup>a</sup>, Lise Trouillet-Fonti<sup>b ID</sup>, Jérôme Bikard<sup>b ID</sup>

## ARTICLE INFO

**Keywords:**

Thermoplastic matrix composite

Interfacial shear strength

Carbon fiber fragmentation

Acoustic emission

Microtomography

## ABSTRACT

The influence of carbon fiber's surface roughness and chemistry on interfacial properties in a carbon fiber reinforced polyetheretherketone model composite was studied using single fiber fragmentation test. In this study, Weibull parameters determined from acoustic emission data resulting from single fiber fragmentation itself were compared to Weibull parameters determined by carbon fiber dry tow tension. It was shown that interfacial shear strength (IFSS) is deeply influenced by Weibull parameters method used for fiber local strength, $\sigma_f(l_c)$, estimation. Further insight on fragmentation mechanism was obtained from synchrotron X-ray microtomography. Microtomography observations showed a fiber fragment's length shrinkage, even after fragmentation saturation. An innovative micromechanical analysis to estimate IFSS from this shrinkage has been proposed. This approach allows to follow the IFSS evolution during the fiber fragmentation. Resulting IFSS evaluations were consistent with IFSS obtained by $\sigma_f(l_c)$ estimation, and presented an interfacial quality dependent decrease during the fragmentation. These results demonstrate that carbon fiber's surface chemistry has a major influence on IFSS value, comparing to surface roughness. However, surface roughness significantly impacts the interfacial properties evolution after fiber fragmentation.

## 1. Introduction

Carbon fiber reinforced polyetheretherketone (PEEK) is one of the most used thermoplastic matrix composites, due to its high mechanical properties allied to its low density, as well as high thermal and chemical stability, with applications comprising the structural, medical, wear and electronic fields [1,2]. However, the interface between PEEK and carbon fibers is difficult to master due to the low fiber surface wettability and the high matrix chemical stability. Important work has been made for optimizing it [3-7].

Interface quality is key for the final mechanical properties of composite materials, as the interface controls the stress transfer from matrix to fiber, interfering in the final mechanism of fracture of the composite. Interfacial properties are a result of physical and chemical parameters acting simultaneously, creating a complex, commonly micrometric, volume of material with unique properties, different from those of the bulk matrix or of the fiber [8]. Various studies were conducted to evaluate the effect of carbon fiber surface properties on the interface quality. It was shown by bending tests that the effect of mechanical

interlocking tends to be minor compared to chemical bonding [9]. However, mechanical interlocking importance increases for composites with high chemical stability matrix [10]. Nevertheless, it is still not clear which carbon fiber's surface parameters have the largest influence on interfacial properties and how carbon fiber PEEK interfaces can be optimized.

Polymer matrix-fiber interface characterization is itself a challenge [11,12]. The micrometric character of the interface hinders a direct and independent characterization. Bending or transverse tensile tests on composites can serve as an indirect measurement of interfacial quality. However, micromechanical tests, with model single fiber composites, are commonly used for interfacial characterization, allowing a quantification of the interface quality by the calculation of the IFSS (interfacial shear strength, $\tau$) [11]. Micromechanical tests results tend to be accompanied by large dispersions and complex data treatments.

Single fiber fragmentation test is a micromechanical test in which a single fiber is positioned in the axis of a dog bone sample submitted to a tensile load. This sample geometry makes it a good representation of the fundamental damage modes present in a unidirectional composite

<footnote><sup>a</sup> INSA Lyon, Université Claude Bernard Lyon 1, CNRS UMR5510, MATEIS, F-69621, France</footnote>

<footnote><sup>b</sup> Syensqo, Axel'One, 87 Avenue des Frères Perret, CS 70061, 69192, Saint Fons, France</footnote>
<figure><img src="image_2.png" /><figcaption>**Fig. 1.** Schematic representation of Kelly & Tyson model for stress transfer between two consecutive fiber (red) and embedding matrix (gray). f refers to fiber and i to interface.</figcaption></figure>

compared to other micromechanical tests [8]. However, data exploitation is not straightforward as it depends on statistical assumptions and estimations that will be discussed in this manuscript. Under tensile load, fiber breakage eventually occurs, up to a saturation point in which fiber breakings no longer take place. The average length of all fragments at the saturation state, $\bar{l}$, can be related to a critical length, $l_c$, in which the fiber length is not long enough for the fiber's ultimate strength to be reached. As fiber breaking can take place anywhere further than a distance $l_c/2$ from a fiber break, $l_c$ is usually estimated by eq. (1).

$$ \bar{l} = \frac{1}{2} \left( \frac{l_c}{2} + l_c \right) = \frac{3}{4} l_c \quad (1) $$

The theory first proposed by Kelly and Tyson [13] is schematized in Fig. 1, where $\varepsilon_f$, $\sigma_f$ and $E_f$ are the local fiber strain, fiber strength, and fiber elastic modulus, respectively, $\varepsilon_c$ is the composite strain and $\tau_i$ is the interfacial shear stress. The model states that fiber fragments are submitted to a tension due to shear stresses at the interface and once saturation is attained, fiber and matrix are completely debonded. The matrix is a rigid and perfectly plastic material, implying a constant IFSS ($\tau$). Hence, Kelly and Tyson model, used here, considers a linear variation of the tensile stress in zones close to the breakage points according to eq. (2).

$$ \frac{d\varepsilon_f}{dx} = \frac{2\tau}{rE_f} \quad (2) $$

From eq (2), interfacial shear strength $\tau$ can be determined by:

$$ \tau = \frac{\sigma_f(l_c) r}{l_c} = \frac{E_f \varepsilon_{fmax} r}{l_c} \quad (3) $$

where $\sigma_f(l_c)$ is the fiber strength for a gauge length equivalent to the critical fragment length $l_c$, r is the fiber radius, $E_f$ is the fiber elastic modulus and $\varepsilon_{fmax}$ is the maximum local fiber strain, which equals the composite strain if the fiber is not debonded to the matrix at this point [14]. A major obstacle for the proper estimation of IFSS values is the assessment of the $\sigma_f(l_c)$ value, occasionally overlooked. It is difficult to experimentally determine $\sigma_f(l_c)$, as $l_c$ is commonly smaller than a millimeter, and therefore this parameter is commonly estimated using statistical models, such as Weibull distribution [15], with data originating from single carbon fiber tensile testing [16,17]. This assumption considers that the fiber's mechanical properties are not dependent on the fiber's environment, neglecting variations caused by residual stresses, differences in Poisson's ratio, or the surface contact between the fiber and the matrix where a local healing of critical defects by the embedding matrix may be expected.

Weibull distribution has been widely used to statistically describe the individual tensile strength of carbon fibers [18]. The probability of failure P for a fiber to break at a stress $\sigma$ is described by a Weibull distribution modified to account for fiber length L, in relation to a reference fiber length $L_0$ [19] yielding to eq. (4), where $\sigma_0$ is the Weibull scale (stress for which the failure probability is 63 %), and m the shape parameter or Weibull modulus.

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

Characteristics of the 4 types of Carbon Fibers studied.</caption><thead><tr><th></th><th>Smooth Fiber (SF)</th><th>Crenulated Fiber (CF)</th><th>B1</th><th>B2</th></tr></thead><tbody><tr><td>Surface chemical treatment</td><td>No</td><td>No</td><td>Yes</td><td>No</td></tr><tr><td>Surface roughness</td><td>Smooth</td><td>Crenulated</td><td>Smooth</td><td>Smooth</td></tr><tr><td>Diameter (µm)</td><td>6.7</td><td>5</td><td>5.3</td><td>5.3</td></tr><tr><td>Young Modulus (GPa)</td><td>241</td><td>290</td><td>290</td><td>290</td></tr></tbody></table>

$$ P(\sigma) = 1 - \exp \left[ - \left( \frac{L}{L_0} \right) \left( \frac{\sigma}{\sigma_0} \right)^m \right] \quad (4) $$

The knowledge of Weibull parameters is important to consider the volume effect to estimate more accurately the value of the fiber strength at the critical fragment length from fragmentation tests, fundamental for a better estimation of IFSS. Indeed, once the Weibull modulus, m, and scale parameter, $\sigma_0$, determined, $\sigma_f(l_c)$ can be estimated using eq. (5), where $\Gamma$ is the gamma function.

$$ \sigma_f(l_c) = \sigma_0 \left(\frac{l_c}{L_0}\right)^{-1/m} \Gamma\left(1 + \frac{1}{m}\right) \quad (5) $$

Even though, only a few studies carried out single-fiber fragmentation tests for PEEK/Carbon fiber interfacial characterization in literature. Gao et al. [20] performed such tests on PEEK/Carbon fiber composites obtained through different processing conditions. Results were analyzed in terms of critical lengths, without considering $\sigma_f(l_c)$ effect. Nardin et al. [21] used single fiber tensile tests with different gauges lengths to determine Weibull parameters for $\sigma_f(l_c)$ estimation. These authors pointed out that the fragmentation tests is sensitive to interfacial properties, obtaining IFSS values between 34 MPa and 72 MPa.

In this study, fragmentation tests were performed to characterize the interfaces between carbon fibers of different surface roughness and chemical treatments and a PEEK matrix, with the objective to better understand the parameters influencing interfacial properties. Various approaches to properly estimate IFSS values have been developed in this paper and analyzed. First, $\sigma_f(l_c)$ has been estimated by Weibull distributions obtained from carbon fiber dry tow tensile tests on the one hand, and from acoustic emission (AE) recorded during the fragmentation test itself on the other hand. Then synchrotron X-ray microtomography in situ fragmentation tests allowed the development of an innovative method for IFSS evaluation, independent of $\sigma_f(l_c)$, enabling the characterization of IFSS evolutions with the composite macroscopical strain. The aim of this paper is to point out the impact of the statistical estimations compared to micromechanical analyses of the fiber/matrix interactions at a low scale to better investigate the effects of the fiber surface characteristics on damage in carbon fiber/thermoplastic composites.

## 2. Materials and methods

### 2.1. Carbon fibers and carbon fiber's characterization

In this work 4 types of carbon fibers (named SF, CF, B1 and B2) with different surface properties, in terms of roughness and surface treatments, and different mechanical properties (summarized in Table 1), have been studied. Fiber surfaces were characterized by atomic force microscopy (AFM) using a dimension Icon AFM with Nanoscope 6 electronic from Bruker using the PeakForce (PF) tapping mode. AFM tip is OPUS-240 tip from Bruker with a rectangular geometry and stiffness close to 2 N m⁻¹. The PeakForce setpoint and amplitude were set to 2 nN and 50 nm; respectively. The scan rate was 0.6 Hz. Data treatment and roughness measurements were made using Gwyddion software [22].
This tool allowed a background correction using the function “Remove polynomial background” which has been applied to all AFM height images to avoid roughness data bias originated from the fiber’s geometry (see supplementary information section 1).

The tensile strength and tensile strain to failure distributions of dry carbon fiber tow were determined in accordance with the ISO 22459:2024 standard. The aim was to account for the variability in the mechanical properties of individual monofilaments within the tow and to determine the parameters of the Weibull distribution. Samples were prepared as proposed by R'Mili et al. [18]. Details of sample preparation and data treatment can be found in Supplementary information. Tow specimens, of about 100 mm in gauge length were tested with a MTS 810 hydraulic testing machine, resulting in a load-displacement curve from which the parameters of a monomodal Weibull distributions were determined as described in Ref. [18]. The number of fibers initially loaded was calculated from the initial slope of the mechanical curve, considering fiber elastic modulus and cross section. Weibull modulus (m) was assessed graphically as the slope of the plot of the fiber survivability versus fiber strain in a Weibull plan. Weibull scale factor has been estimated by adjusting the Weibull model obtained using eq. (4) onto the experimental data.

## 2.2. Matrix material and single fiber specimen processing

Commercial grade KetaSpire® KT-880 PEEK in the form of extruded semicrystalline films of 400 µm thickness and width of 10 cm was provided by Syensqo. CF/PEEK model single fiber composites were obtained by compression molding using specially conceived molds that allowed fiber positioning and fixation using a ceramic glue. Compression molding cycle details are as follows: a step of heating, with a heating rate of 20 °C/min from 60 °C to 385 °C, an isotherm of 15 min at 385 °C and a last step of controlled cooling at 10 °C/min rate, constant pressure of 0.7 MPa was applied during the cycle. The same cycle was applied for all specimens to ensure a similar crystallinity rate and morphology. The translucid character of the plates allowed to estimate the carbon fiber filaments location without enabling a detailed visualization of the fibers, necessary for fiber fragment length measurement. Single fiber samples with dog-bone shape were obtained using a punch.

## 2.3. Fragmentation tests

Single fiber fragmentation tests instrumented with AE were conducted using a MTS 810 N hydraulic testing machine, with a controlled displacement of 0.1 mm/min. Hydraulic grips were used with controlled very low pressure to provide good fixture without damaging the specimen. The tensile test has been done following the procedure described by ISO15733, in which precautions to assure the good alignment of the specimen are also described. Specimens were obtained from compression molding plates, with a dogbone geometry and 50 mm distance between shoulders. Digital Image Correlation (DIC) was used to measure the specimen elongation and strain field and two PICO sensors were used for the AE monitoring, positioned 40 mm apart. Each sensor is connected to a preamplifier (gain 40 dB, type 20H) and AE signals are recorded by a PCI-2 acquisition system (Mistras Group). Vacuum grease was applied to ensure good contact between the sensor and the sample and ensure good transmission of elastic waves from the material to the piezoelectric sensors. The acquisition threshold is set to 30 dB, and the values of peak definition time (PDT), hit definition time (HDT) and hit lockout time (HLT) were respectively 50 µs, 100 µs and 1000 µs. Wave velocity was determined by lead break tests, resulting in 1600 m/s, for all tested samples.

Preliminary tests with neat PEEK samples using AE monitoring as described above resulted in any signal detected, thus all events detected with single fiber samples were assumed to be correlated to fiber breaks, hypothesis posteriorly confirmed with microscopy and tomography observations. After fragmentation tests, the thermoplastic opaque

matrix samples were heated above the melting temperature and quenched in water, transforming the previously semicrystalline matrix into amorphous and increasing drastically the transparency of the matrix. This method allowed the direct observation of fiber fragments by optical microscopy.

In order to analyze more deeply the mechanisms of interactions between the single filament and the PEEK matrix, in situ microtomography tests have been performed at the ANATOMIX beamline at Synchrotron SOLEIL, in France [23]. A Hamamatsu Orca Flash 4.0 V2 digital camera, with resolution 2048 x 2048 pixels was coupled with a 10x magnification, resulting in a spatial resolution of 0.65 µm. PyHST2 software and Paganin algorithm has been used for reconstruction [24,25].

A tensile rig developed by MateIS Lab, at INSA Lyon, was used for these in situ fragmentation tests. Tests were performed with a displacement rate of 0.3 mm/min and the tensile rig crosshead position was maintained during microtomography scan acquisition, which caused a low stress relaxation. Dogbone samples with 15 mm length between shoulders and 4 mm width were used for these experiments. Strain values were obtained directly from the displacement of the crosshead values, with a correction to account for machine compliance. Specimen strain was caused only by the displacement of the superior grip while no alteration in the stage position was made during testing, causing a small change in the observed zones with strain increase. Once fragmentation saturation was attained, other areas of the sample were observed with the objective of measuring supplementary fiber fragments. ImageJ software [26] was used for image treatment. For measuring fiber fragments and voids length, the “minimum z projection” function was used in a volume dimension of 300 x 300 x 2048 pixels, creating an output image each of 300 x 2048 pixels, whose pixels contain the minimum value over all images in the stack at the particular pixel location, allowing the visualization of a 3D volume in a 2D image highlighting damaged zones of the sample. Following, gray intensities along a rectangular selection containing the fiber were used for precise length measurements.

# 3. Results and discussion

In this paper, the effects of fiber surfaces on fiber/matrix interface and more specifically on IFSS are investigated. Four types of fibers have been studied to distinguish effects linked to interfacial mechanical interactions due to the roughness (studying a smooth-surfaced fiber (SF) and a rougher one (CF)), and due to chemical bonding (studying B1 and B2 fibers). Indeed, in this study, fiber/matrix interactions are assumed to be mainly influenced by fiber surface, as SEM and AFM observations showed no modification of the polymer semi-crystalline microstructure around a single fiber. Moreover, AFM adhesion measurements confirm that adhesion of SF and CF fibers is similar, while the adhesion observed for the B1 fiber is higher than the adhesion observed for B2 fiber (see

<figure><img src="image_3.png" /><figcaption>**Fig. 2.** Schema of single fiber fragmentation test coupled with acoustic emission system acquisition.</figcaption></figure>
<figure><img src="image_4.png" /><figcaption>Fig. 3. SEM and AFM height images of carbon fibers surface.</figcaption></figure>

<table><caption>**Table 2**
Carbon fiber Surface characteristics obtained by AFM.</caption><thead><tr><th></th><th>SF</th><th>CF</th><th>B1</th><th>B2</th></tr></thead><tbody><tr><td>Roughness average (Ra) (nm)</td><td>3.3 ± 0.3</td><td>17.7 ± 1.4</td><td>5.7 ± 0.3</td><td>4.7 ± 0.3</td></tr><tr><td>Root mean square roughness (Rq)(nm)</td><td>4.2 ± 0.4</td><td>20.5 ± 1.2</td><td>6.9 ± 0.2</td><td>5.9 ± 0.3</td></tr><tr><td>Developed Profile length/ line length</td><td>1.018 ± 0.002</td><td>1.090 ± 0.001</td><td>1.016 ± 0.001</td><td>1.012 ± 0.002</td></tr><tr><td>Effective perimeter of fibers(µm)</td><td>20.5</td><td>17.1</td><td>16.9</td><td>16.8</td></tr></tbody></table>

supplementary information). In a first moment, IFSS values were investigated from macroscopic single-fiber fragmentation test based on different approaches for the estimation of Weibull Parameters, in order to properly calculate $\sigma_f(l_c)$. Then, an original approach to estimate IFSS was developed from X-ray microtomography tests based on the estimation of the local strain of the fiber fragments. This will point out the differences in fiber-matrix interactions for each fiber and allow to discuss them in relationships with the fiber surface characteristics.

### 3.1. Carbon fibers surface and mechanical characterization

AFM observations of carbon fiber surfaces are shown in Fig. 3, and in supplementary information. Roughness quantification is given in Table 2. CF presented indeed a higher roughness average and root mean square roughness, in the form of grooves parallel to the fiber's axes, when compared to the 3 other fibers. An estimation of the effective

<table><caption>**Table 3**
Experimental Carbon fibers properties from tow tests results.</caption><thead><tr><th>Carbon Fiber</th><th>Number of fibers</th><th>Scale factor, σ<sub>0</sub> (MPa)</th><th>Weibull modulus, m</th></tr></thead><tbody><tr><td>SF</td><td>7328 ± 863</td><td>4375 ± 206</td><td>4.6 ± 0.6</td></tr><tr><td>CF</td><td>9495 ± 1191</td><td>6067 ± 153</td><td>9.3 ± 0.2</td></tr><tr><td>B1</td><td>1376 ± 679</td><td>4313 ± 259</td><td>8.5 ± 2.3</td></tr><tr><td>B2</td><td>1618 ± 334</td><td>5050 ± 853</td><td>14.3 ± 1.2</td></tr></tbody></table>

perimeter of the fibers, representing the area in which the matrix and the fiber can effectively be in contact, was obtained by multiplying the fiber's mean perimeter by the ratio between the developed profile length by the measured line length, acquired by AFM. A higher effective perimeter results in an augmentation of the number of possible sites for chemical or physical interactions between fiber and matrix. Note that the effective perimeter for CF, B1 and B2 fibers are similar, while SF presented a larger real surface. In other words, the surface of contact between fiber and matrix is mostly determined by the fiber's diameter, even though important variations in roughness were observed.

In order to evaluate more accurately the value of the maximum stress in the fiber after fragmentation $\sigma_f(l_c)$ (see eq. (3)) to calculate IFSS of each fiber, it is necessary to know the Weibull parameters to consider the volume effect on the local fracture stress of the monofilaments as described by eq. (4). These parameters can be determined by carbon fiber tow tensile tests which provide information regarding the mechanical properties of the carbon fibers and an estimation of the Weibull distribution parameters of the individual fiber breaks. Such typical load-strain curves are shown in Fig. 4, from which different distribution

<figure><img src="image_5.png" /><figcaption>Fig. 4. Dry tow tensile test results for studied carbon fibers.</figcaption></figure>
<figure><img src="image_6.png" /><figcaption>**Fig. 5.** Fragmentation tests coupled with acoustic emission results for a) Smooth Fiber (SF); b) Crenulated Fiber (CF); c) B1 fiber; d) B2 fiber. Dashed lines represent location of sensors, each red dot represents a located AE event, according to position axis as represented in Fig. 2.</figcaption></figure>

<caption>**Table 4**</caption>

Arithmetic mean length values obtained by AE, considering all tested specimens for a same carbon fiber/PEEK composite with standard deviation between results of different specimens. For a single specimen, comparison between average length values obtained by optical microscopy after quenching and AE.

<table><thead><tr><th rowspan="2">System</th><th colspan="1">For all tested specimens</th><th colspan="2">For a single specimen</th></tr><tr><th>l̃<sub>Acoustic Emission</sub> (μm)</th><th>l̃<sub>Microscopy</sub> (μm)</th><th>l̃<sub>Acoustic Emission</sub> (μm)</th></tr></thead><tbody><tr><td>PEEK/SF</td><td>420 ± 80</td><td>376 ± 90</td><td>420 ± 270</td></tr><tr><td>PEEK/CF</td><td>394 ± 122</td><td>617 ± 223</td><td>606 ± 307</td></tr><tr><td>PEEK/B1</td><td>286 ± 29</td><td>287 ± 112</td><td>320 ± 203</td></tr><tr><td>PEEK/B2</td><td>419 ± 67</td><td>403 ± 148</td><td>440 ± 310</td></tr></tbody></table>

behaviors arise from the decreasing part of the curves (Table 3). Additional information concerning data treatment can be found in Supplementary information. A sharp decrease, as observed for the B2 fibers, translates into high Weibull modulus (m) values. This characterization indicates that strengths experimentally obtained from tow tests for SF and B1 are slightly lower when compared to CF and B2 fibers. Except for SF, the obtained m and σ₀ values are high compared to values classically obtained for carbon fibers by tow tensile tests [18,27]. High Weibull modulus indicates low strength dispersion in fibers inside a tow, and high scale factor is representative of the high mean strength of the fibers [16].

### 3.2. IFSS evaluation from macroscopic single-fiber fragmentation followed by acoustic emission

In order to evaluate IFSS for the 4 carbon fiber/PEEK matrix systems, single fiber fragmentation has been studied in relation to fiber fragment lengths. An example of fragmentation test result obtained for each type of studied fiber can be found in Fig. 5, where red markers represent located AE events, which happened randomly and were detected all along the samples, between the two AE sensors. AE signals presented similar amplitude distribution and average value (70 dB), energy and duration distribution, indicating the presence of a single group of AE

<caption>**Table 5**</caption>

σf(lc) and IFSS values obtained with Weibull parameters estimated by carbon fiber tow tensile tests and fragmentation tests. lc values estimated with eq. (1).

<table><thead><tr><th rowspan="2">Carbon fiber</th><th rowspan="2">l<sub>c</sub> (μm)</th><th colspan="2">Tow tests</th><th colspan="2">Fragmentation tests</th></tr><tr><th>σ<sub>f</sub>(l<sub>c</sub>)<br>(GPa)</th><th>IFSS<br>(MPa)</th><th>σ<sub>f</sub>(l<sub>c</sub>)<br>(GPa)</th><th>IFSS<br>(MPa)</th></tr></thead><tbody><tr><td>Crenulated<br>fiber</td><td>575 ± 107</td><td>10.1 ± 0.3</td><td>52 ± 14</td><td>11.1 ± 1.1</td><td>55 ± 11</td></tr><tr><td>Smooth Fiber</td><td>526 ± 164</td><td>12.2 ± 0.6</td><td>71 ± 30</td><td>8.0 ± 0.5</td><td>52 ± 21</td></tr><tr><td>B1 Fiber</td><td>381 ± 34</td><td>7.4 ± 0.1</td><td>57 ± 14</td><td>10.1 ± 4.5</td><td>92 ± 36</td></tr><tr><td>B2 Fiber</td><td>559 ± 89</td><td>7.0 ± 0.4</td><td>34 ± 7</td><td>11.5 ± 1.2</td><td>54 ± 16</td></tr></tbody></table>

signals (see supplementary information).

A direct correlation was established between located AE events and fiber breaks. From the location data, arithmetic mean fragment lengths were extracted and are presented in Table 4 considering all tested specimens (5 specimens for each condition). Table 4 also shows that the arithmetic mean fiber lengths measured by microscopy after quenching in one of the five fragmentation specimens were consistent with the values determined by AE for the same specimen, within the range of standard deviation. This consistency supports the validity of the AE approach, ensuring that located events relate directly to fiber breaks, whereas AE events related exclusively to other damage mechanisms are not detected. Values of mean fragment length were then transformed in critical lengths using eq. (1) for the following steps of data treatment and can be found in Table 5.

For all tested samples, fiber breaks took place in a macroscopical strain window between 3.5 and 6.5 %. Fig. 6 shows the evolution of the number of localized signals as a function of the strain to which the sample was submitted. It is possible to observe a plot with S-shaped behavior, in which there is a quick increase in fiber breaks right after the first fracture with a progressive decrease in the fiber break frequency for larger strains. Fig. 6 also allowed the tracking of fiber breaks as a function of the specimen's strain. While data was quite reproducible for SF and CF, a dispersion in strain levels and slope was observed for B1
<figure><img src="image_7.png" /><figcaption>Fig. 6. Cumulative number of localized signals as a function of strain.</figcaption></figure>

<figure><img src="image_8.png" /><figcaption>Fig. 7. Weibull fit for AE data results from fragmentation test for a smooth fiber.</figcaption></figure>

and B2 samples. This dispersion can be originated from sample partic-
ularities, such as small fiber misalignment and the presence of poros-
ities, affecting the stress levels of each specimen. The cumulative
number of AE localized signals, followed a Weibull distribution,
described by eq. (4). Values of Weibull modulus and scale factor were
obtained by graphically matching the theoretical curve of Weibull dis-
tribution to the experimental one obtained by AE, as shown in Fig. 7.
While a very good fit was obtained for the beginning of fiber fragmen-
tation, a significative deviation was observed for the cumulative number
of AE localized signals above 0.6. The main explanation for this phe-
nomenon is that the fiber fragmentation implies the formation of voids
in the vicinity of each fiber break, creating matrix areas with preferential
deformation and increasing the macroscopic strain measured by DIC to

which a fiber break is detected, as observed in microtomography results
presented in section 3.3.

These various experimental results indicate that Weibull scale
parameter (σ₀) values for fibers obtained through single-fiber frag-
mentation followed by AE are higher than values determined by non-
impregnated tow tensile tests, as shown in Fig. 8. The contact between
the thermoplastic matrix and carbon fiber in fragmentation tests may
explain these higher values, as observed for composites [28]. In fact, if
the matrix correctly surrounds the fiber, it can fill previously preexisting
defects on the fiber surface, acting as a healing agent. Accordingly,
higher values obtained for CF and B1 fibers may suggest a better inter-
action between these fibers and the matrix, as expected due to the
increased roughness at CF surface and chemical treatment at B1 surface.
Another phenomenon that may bias single fiber results is the exclusion
of the weakest fibers results, as weak fibers are more likely to fail during
sample preparation. However, this phenomenon is limited, and higher
fiber strengths obtained by single-fiber fragmentation than strengths
obtained through other techniques, such as single-fiber tension tests,
have been previously reported [29,30]. Weibull modulus (m) estimated
from single fiber fragmentation are also higher than for dry tow tension.
It is noteworthy to mention that while fragmentation tests m values refer
to various fiber breaks originated successively in the same single fiber
embedded in the matrix, m values obtained from non-impregnated tow
tensile tests refer to a distribution of tensile strength of different fibers,
in a statistic analysis. Hence non-impregnated tow tensile tests provide
reliable information concerning the distribution of strength of a statis-
tical population of fibers [27]; however, employing Weibull parameters
determined by this technique to treat fragmentation tests supposes that
there is no modification of the fiber mechanical behavior caused by the
contact with the matrix. Weibull parameters calculated from AE frag-
mentation results have the positive point of being determined specif-
ically for each specimen, considering eventually the presence or not of

<figure><img src="image_9.png" /><figcaption>Fig. 8. Weibull scale parameter (σ₀) and Weibull Modulus values determined by different approaches.</figcaption></figure>
<figure><img src="image_10.png" /><figcaption>**Fig. 9.** Minimum Z projection images obtained for different stress/strain conditions for a fragmentation test with in situ microtomography follow up for crenulated fiber (CF). Macroscopic applied stress and strain are indicated for each image.</figcaption></figure>

<figure><img src="image_11.png" /><figcaption>**Fig. 10.** Minimum Z projection images obtained for different stress/strain conditions for a fragmentation test with in situ microtomography follow up for SF fiber.</figcaption></figure>

defects in the tested sample. Moreover, it also considers the effect of matrix contact in the mechanical properties of carbon fibers, providing a more reliable estimation of interfacial properties.

Finally, IFSS values determined from eq. (3), with $\sigma_f(l_c)$ resulting from these two approaches are presented in Table 5. IFSS values are highly dependent on Weibull parameters since they are highly influenced by the estimation of the local fiber strength $\sigma_f(l_c)$. Higher IFSS was observed for CF and SF fibers, considering Weibull parameters obtained by non-impregnated tow tensile tests and for B1 fiber, considering Weibull parameters obtained by single fiber fragmentation followed by AE. As previously discussed, the results obtained using AE instrumentation for Weibull parameter estimation are considered more reliable. This is because AE data enables the direct determination of the mechanical properties of the tested fiber, considering the effects of fiber-matrix interaction and any residual stresses that may be present. IFSS values were obtained from single-fiber fragmentation highlight the relevance of chemical bonding over mechanical interlocking through roughness. However, single fiber fragmentation by itself is not sufficient to demonstrate the roughness effect on interfacial properties, as similar IFSS values for SF and CF were obtained (see Table 5). That is the reason

<figure><img src="image_12.png" /><figcaption>**Fig. 11.** Minimum Z projection images obtained for different stress/strain conditions for a fragmentation test with in situ microtomography follow up for B2.</figcaption></figure>

<figure><img src="image_13.png" /><figcaption>**Fig. 12.** Minimum Z projection images obtained for different stress/strain conditions for a fragmentation test with in situ tomography follow up for B1.</figcaption></figure>

why investigations at a lower scale have been done from direct observation of fiber fragmentation by X-ray microtomography.

### 3.3. Analysis of single-fiber fragmentation mechanisms by X-ray microtomography

Observations by X-ray microtomography allowed complementary analyses with a fine accuracy (0.65 µm per pixel) of single-fiber fragmentation mechanisms under in situ loading. Indeed, the mechanical response of specimens of X-ray microtomography in situ fragmentation tests presented a good reproducibility and accordance with the macroscopic mechanical tests, indicating that small specimens tested under tomograph are representative of the macroscopic specimens tested on universal machines and samples mechanical behavior was not affected by X-ray radiation. Nevertheless, a relaxation phenomenon originating from the stop of the tensile rig crosshead displacement during scans acquisition has been noted. Necking formation for large strains was regularly observed. Minimum Z projections of the fiber region of scans obtained by microtomography are shown in Figs. 9–12. Dark pixels in minimum Z projection images correspond to zones of less X-ray absorption, indicating the presence of voids or interfaces between
<figure><img src="image_14.png" /><figcaption>**Fig. 13.** Minimum projection of scans of voids between fragments for the maximum strain observed for each test.</figcaption></figure>

materials of different X-ray absorptions. For all samples, fiber misalignment with respect to the loading axe was measured and misalignment angles were never found larger than 2°. Fiber fragmentation is marked by the apparition of the void zones between fragments, visible as black regions in Figs. 9–12. For SF and CF fibers, fiber breaks were first observed at 3.1 % macroscopic strain, while fiber breaks were already observed for 2.4 % strain for specimens with B1 or B2 fibers, indicating higher strain-to-failure for SF and CF fibers than for B1 and B2 fibers. Moreover, for fibers SF, CF and B2, it was possible to observe the formation of new fragments between different scans as the load applied increases.

It is important to note that microtomography observation was restricted to a small region of the sample, and other zones were observed only in the final testing conditions. Average fragment lengths measured by microtomography were consistent with those estimated previously on longer specimens when employing the AE technique (Table 4).

No debonding or significant matrix damage around the interface was observed, being the creation of voids between fiber fragments the major damage mechanism seen with the experimental spatial resolution attained, estimated to be equivalent to the pixel size of 0.65 µm. A variation in void length was observed at the end of the test, evidencing heterogeneity in the strain field acting along the fiber. That confirms the

origin of the discrepancy between the experimental cumulative number of AE events and the theoretical Weibull laws obtained on macroscopic fragmentation tests (see Fig. 7 in the previous section). Nevertheless, microtomography images do not provide clear evidence of interface debonding caused by the fragmentation test and further analyses are focused on the variation in lengths of voids and fragments measured for each type of fiber.

**Fig. 13** highlights matrix behavior around voids for the last scan of each of the previously presented tests. CF sample presented small cracks initiated at the voids, observed since the void’s onset, which were not detected for other fibers, suggesting a stronger interfacial bond for the CF/PEEK model composite. Depending on the tested fiber the length of voids also showed different dependencies on the macroscopic strain of the specimen. For example, the void observed in sample B1 at a macroscopic strain of 5.2 % was significantly longer than those observed in other fibers, even at higher strain levels.

Microtomography in situ fragmentation tests provided strong detailed information concerning the mechanical behavior of a model single fiber composite during fiber fragmentation, as well as the measurement of fibers and voids length throughout the test. While fiber fragments tended to decrease its length, voids growth was observed with the increase of the macroscopic strain.

Void length evolution (Fig. 14) depends on the macroscopic strain. However, the formation of necking and the apparition of new fiber breaks influence void development. If the region observed by microtomography is far enough from the necking zone of the specimen, a stabilization in the local strain levels, thus the voids length, was observed (as in the case of SF – Void 2 and B2 – Void 1, in Fig. 14a). Crack formation in CF sample voids did not cause a different void length behavior when compared to other fibers. Therefore, voids length variation is believed to depend on the moment of the fiber break apparition and the proximity to the necking region. The growth rate of voids of sample B1 was higher than other samples.

Fragment length follow-up was possible for CF, SF and B2 fibers, as shown in Figs. 9–12 and has been quantified (see Table 6). For CF and B2 specimens, it was also possible to detect a longer fiber fragment further

<figure><img src="image_15.png" /><figcaption>**Fig. 14.** a) Void evolution as a function of macroscopic strain and b) Relative shrinkage evolution with macroscopic strain for fragments length.</figcaption></figure>

<table><caption>**Table 6**

Fragment length evolution with composite macroscopic strain. Measurement uncertainty equivalent to microtomography spatial resolution, 0.65 µm.</caption><thead><tr><th rowspan="2">Macroscopic strain (%)</th><th colspan="2">CF - Fragment 1</th><th colspan="2">CF - Fragment 2</th><th rowspan="2">SF Frag. 1</th><th rowspan="2">SF Frag. 2</th><th colspan="2">B2 - Fragment 1</th><th rowspan="2">B2 Frag. 2</th></tr><tr><th>Frag. 1A</th><th>Frag. 1B</th><th>Frag. 2A</th><th>Frag. 2B</th><th>Frag. 1A</th><th>Frag. 1B</th></tr></thead><tbody><tr><td>2.4</td><td>No fiber breaks</td><td></td><td>No fiber breaks</td><td></td><td>No breaks</td><td>No breaks</td><td>635.7</td><td></td><td>195.7</td></tr><tr><td>3.1</td><td>397.2</td><td></td><td>501.8</td><td></td><td>-</td><td>-</td><td>360.1</td><td>269.1</td><td>196.3</td></tr><tr><td>3.8</td><td>271.7</td><td>121.6</td><td>226.9</td><td>270.4</td><td>684.5</td><td>-</td><td>360.1</td><td>268.45</td><td>196.3</td></tr><tr><td>4.5</td><td>271.0</td><td>120.9</td><td>226.2</td><td>269.1</td><td>-</td><td>338.7</td><td>359.5</td><td>268.5</td><td>195.7</td></tr><tr><td>5.2</td><td>-</td><td>-</td><td>-</td><td>-</td><td>683.8</td><td>336.7</td><td>-</td><td>-</td><td>-</td></tr><tr><td>6.2</td><td>-</td><td>-</td><td>-</td><td>-</td><td>681.2</td><td>336.0</td><td>-</td><td>-</td><td>-</td></tr><tr><td>7.2</td><td>-</td><td>-</td><td>-</td><td>-</td><td>680.6</td><td>335.4</td><td>-</td><td>-</td><td>-</td></tr><tr><td>7.9</td><td>268.5</td><td>120.9</td><td>-</td><td>-</td><td>-</td><td>334.8</td><td>-</td><td>-</td><td>-</td></tr></tbody></table>
<figure><img src="image_16.png" /><figcaption>Fig. 15. Schematic representation of strain profile in a fiber fragment evolution during fragmentation test.</figcaption></figure>

fracturing itself, and thus, transforming in 2 new fragments (denoted fragment A and B in Table 6). It was observed that the formation of a new fiber break implied a total fragment length shrinkage comparing the sum of the two new fiber fragments' length with the original length. Moreover, once the final fragment was attained, a decrease in its length of a few microns was still measured with the increase of specimen strain.

The experimental relative shrinkages, $\Delta l/l_0$, estimated by eq. (6), where $l_0$ is the fragment length first observed, $l$ is the fragment length for a given strain and $\Delta l$ the fragment shrinkage, is not neglectable as shown for 3 fibers in Fig. 14b.

$$ \frac{\Delta l}{l_0} = \frac{l - l_0}{l_0} \qquad (6) $$

In order to link this shrinkage $\Delta l$ to fiber/matrix interactions and associated IFSS, an original micromechanical analysis has been developed in this study and is detailed below. Indeed, once fragmentation starts, a strain relaxation is expected at the fiber ends due to the debonded zones around each fiber break where a gradient of strain, characterized by the IFSS, occurs. If the fiber fragment is completely debonded with no interactions anymore at the interface with the matrix, the strain relaxation should be sudden and should stop once the fragmentation saturation, when no more fiber breaks take place, is attained. Instead, Fig. 14b indicates a progressive strain relaxation for CF and SF fibers, even after saturation, while fragments of B2 fiber presented a stabilization tendency. This fact led to a more detailed analysis of the strain profiles to which the fiber fragment is subjected at different moments of the test, schematized in Fig. 15.

Considering a portion of fiber with an initial length $l_0$, before fragmentation, fiber and matrix are elastically deformed and submitted to the same strain, the macroscopic strain of the composite $\epsilon_c$, as represented in step 1 in Fig. 15. Following, in step 2, fiber fragmentation originates a debonding length $l_{debonded}$ and a linear strain profile is developed in the fiber extremity (considering Kelly and Tyson's model), implying a first strain relaxation. If $l_0 > 2l_{debonded}$, a part of the fragment remains bonded to the matrix, and submitted to the macroscopic strain of the composite $\epsilon_c$. The fiber fragment is thus submitted to a trapezoid strain profile and another fiber break may appear posteriorly in the bonded part of the fragment. At this step, a first shrinkage ($\Delta l_{1-2}$) due to the strain relaxation at the debonded lengths in the transition from steps 1 to 2 can be described by eq. (7):

$$ \Delta l_{1-2} = \epsilon_c l_{debonded} \qquad (7) $$

For data analysis, the absolute value of experimental shrinkage (in µm) was considered to be equal to the simple average of the two adjacent voids length, allowing thus an estimation of a $l_{debonded}$ according to eq. (7) and then, of IFSS value for CF and B2 samples by eq. (2). Following, represented as step 3 in Fig. 15, a new fragmentation may be observed between the two already existing fiber breaks, and if no other fragmentation appears in the observed region during the test, saturation can

<figure><img src="image_17.png" /><figcaption>Fig. 16. Comparison between IFSS values obtained through different techniques and data treatments.</figcaption></figure>

be considered to be reached. Thus, the previously trapezoid strain profile for the longer fragment $l_0$ evolves to a triangular strain profile for each one of the new fragments formed, here named $l_a$ and $l_b$. This change of profile also implies a new shrinkage ($\Delta l_{2-3}$) for each one of the fragments, described by eq. (8) for a fragment of measured length $l_a$ and obtained from eqs. S2 - S4 (see Supplementary information), under the hypothesis that IFSS variation is similar for both new fragments.

$$ \Delta l_{a,2-3} = \frac{l_{debonded}\epsilon_c}{2} + (l_{a0} - l_{debonded})\epsilon_c - \frac{l_{a0}\epsilon_a}{2} \qquad (8) $$

However, the sum of the theoretical shrinkage for each one of the new fragments $\Delta l_{a,2-3}$ and $\Delta l_{b,2-3}$ remained inferior to the experimental shrinkage measurement. Therefore, this difference due to strain profile variation from trapezoid to triangular was attributed to a decrease in the maximum strain $\epsilon$ to a lower maximum strain $\epsilon'$ for each fragment, thus a decrease in the IFSS value represented by step 4. The maximum strain value $\epsilon'$, for step 4 and a fragment of initial length $l_0$, can be obtained by eq. (9), where $\Delta l$ is the shrinkage observed in relation to the fragment length under strain $\epsilon$. Following, IFSS value can be obtained considering $\epsilon'$ and eq. (2). The same reasoning was applied to evaluate the decrease of $\epsilon$ and IFSS from the shrinkage $\Delta l$ directly measured for the new fragments in the subsequent scans for larger macroscopic strains.

$$ \epsilon' = \frac{l_0 \epsilon - 2 \Delta l}{l_0} = \epsilon - 2 \frac{\Delta l}{l_0} \qquad (9) $$

In the case of fragments that did not further fragment during the test, it was considered that fiber transitioned from a perfectly bonded elastic behavior (step 1) to a completely debonded state (step 3), and the first shrinkage was considered to be half of the adjacent voids. Moreover, as previously stated, fiber length shrinkage was attributed to a decrease in the maximum strain, and therefore, a decrease in the IFSS value.

Fig. 16 gathers IFSS values previously determined by macroscopic single-fiber fragmentation with AE monitoring, where $\sigma_f(l_c)$ is determined by tow tests and fragmentation tests on one hand, and IFSS values obtained by fragment length analysis (length when first observed) obtained by microtomography in situ fragmentation tests on other hand. These values are of the same order of magnitude when compared to previously obtained values and reveal, by comparing CF and SF fibers, a roughness effect on interfacial properties. Fig. 16 also illustrates the effects on IFSS of assumptions and approaches for estimation of $\sigma_f(l_c)$, and even $l_c$ itself, which are the origin of the possible explanations for the differences observed, as the microtomography approach for IFSS is independent of these values. Moreover, for each fragment length measurement (presented in Table 6) a value of IFSS can be estimated by this micromechanical analysis. By this original approach, it has been also possible to determine the evolutions of IFSS for 3 fibers as a function of the macroscopic strain, presented in Fig. 17a, and allowed to go further in the analysis of the fiber/matrix interactions. Maximum IFSS values for
<figure><img src="image_18.png" /><figcaption>**Fig. 17.** a) IFSS evolution for CF, SF and B2 fiber fragment lengths, as presented in Table 6, with the composite macroscopic strain. b) Average absolute values of IFSS variation divided by corresponding strain dependency on carbon fiber roughness (Rq), considering all studied fragments.</figcaption></figure>

samples with CF fibers are superior to values obtained for B2 and SF fibers pointing out and higher fiber/matrix interactions due to the higher roughness of the CF fiber. For fiber B2, fragment 2 presented a length too small to be treated with the above approach, but no variation in the fragment length indicated null values of IFSS for this fragment. The follow-up of the IFSS variation with the macroscopic strain of the composite evidenced also a distinct behavior for each one of the fibers. Fig. 17b shows the link between surface roughness with averaged values of the difference between the first and last calculated IFSS for each fragment, divided by the corresponding difference in strain between the first and last IFSS observation. When comparing SF and CF results, CF showed a faster variation in IFSS with macroscopic strain evolution than SF. Thus, it can be observed that there is a dependency on carbon fiber roughness on the IFSS variation, being higher IFSS variation obtained for fibers of higher roughness. This may be connected to a stronger degradation of the polymer surface for fragment gliding due to the higher roughness of the CF, and for SF fiber a lower wear of the polymer at the fiber/matrix interface. B2 fiber presented an intermediate behavior. These last considerations confirm the higher interfacial interactions linked to the higher roughness of the CF fiber.

Hence, X-ray microtomography during in situ fragmentation allowed the determination of IFSS values following a different method, that does not rely on the previous estimation of $\sigma_f(l_c)$, nor the indirect determination of $l_c$, but depends on a micrometric characterization of fragment length. This detailed analysis allowed also to point out the differences between CF and SF fibers not visible from statistical and macroscopic analysis of fragmentation.

## 4. Conclusions

Interfacial properties of different carbon fibers with a thermoplastic PEEK matrix were investigated by single fiber fragmentation. First, fragmentation tests were studied by macroscopic tests monitored with AE in order to estimate the fiber's critical length. For the estimation of $\sigma_f(l_c)$, considering the volume effect, two different methods were employed based on Weibull distribution: carbon fiber tow tensile tests and the fragmentation test itself. The approach based on AE data analysis of the fragmentation test itself for Weibull parameter estimation is believed to be more relevant as it considers the influence of the direct contact between the carbon fiber and the matrix on the carbon fiber's mechanical properties, already reflecting the interfacial interactions to be characterized. In this case, the presence of a surface chemical treatment on fiber's surface reflected in higher IFSS values, while no obvious effect on IFSS caused by roughness variation was observed. This macroscopic approach considers a high volume of material, increasing representativeness of the results, but depending on estimations of $\sigma_f(l_c)$ and $l_c$.

Secondly, a refined analysis of single fiber fragmentation under

synchrotron X-ray microtomography allowed the visualization of the fragmentation mechanisms in situ. The original analysis of fiber fragment shrinkage with the increase of macroscopic strain developed in this paper allowed the estimation of a local maximum fiber strain and, therefore, of IFSS values at the onset of each fragmentation event. It also allowed to follow IFSS evolutions during the elongation of the model composites. At this scale, model composites with CF fiber presented a higher value of IFSS compared to those containing SF and B2 fiber. Moreover, surface roughness interfered into the IFSS evolution once the fiber fragment was completely debonded. Higher roughness implied a faster IFSS decrease, probably due to a higher wear of the polymer surrounding the fiber. Hence, microtomography tests allowed a deeper analysis of fiber/matrix interaction than macroscopic and statistic approaches, even with reduced material volume observation, and led to a clearer observation of the effects of roughness and chemical properties of carbon fibers surface on interfacial properties. A perspective to this work consists in varying the loading modes of the interfaces for a higher comprehension of damage mechanisms and the effects of fiber surface in final properties, or increasing the quantity of fibers in the samples to make the link between micromechanical properties of a model monofilament system and of a unidirectional ply or a more complex laminate with thermoplastic matrix.

## CRediT authorship contribution statement

**Milena T. Umemura:** Writing – original draft, Methodology, Conceptualization. **Florent Dalmas:** Writing – review & editing, Supervision, Methodology, Conceptualization. **Pascal Reynaud:** Writing – review & editing, Supervision, Methodology, Conceptualization. **Didier Long:** Writing – review & editing, Supervision, Conceptualization. **Gilbert Fantozzi:** Writing – review & editing, Supervision, Conceptualization. **Nathalie Godin:** Writing – review & editing, Supervision. **Lise Trouillet-Fonti:** Writing – review & editing, Supervision, Resources. **Jérôme Bikard:** Writing – review & editing, Supervision, Resources, Conceptualization.

## Declaration of competing interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

## 5. Acknowledgements

Authors acknowledge SOLEIL for providing access to the synchrotron radiation facilities, in particular the ANATOMIX beamline (project number 20231569). ANATOMIX is an Equipment of Excellence (EQUIPEX) funded by the Investments for the Future program of the French
National Research Agency (ANR), project NanoimagesX, grant no. ANR-11-EQPX-0031. The authors thank David Albertini for his help in AFM experiments, and the Consortium Lyon Saint-Etienne de Microscopie (CLYM, FED 4092) for the access to the microscopes. The authors also thank Hugo Girard, Renaud Rinaldi and Jérôme Adrien for their help with microtomography experiments.

## Appendix A. Supplementary data

Supplementary data to this article can be found online at https://doi.org/10.1016/j.compscitech.2025.111301.

### Data availability

Data will be made available on request.

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