# Assessing the validity of micro-pillar compression for determining strength and stiffness of carbon fibres

V. Keryvin, M. Ueda, G. Kermouche, Y. Marthouret, S. Sao-Joao

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V. Keryvin, M. Ueda, G. Kermouche, Y. Marthouret, S. Sao-Joao. Assessing the validity of micro-pillar compression for determining strength and stiffness of carbon fibres. Composites Science and Technology, 2025, 272, pp.111362. 10.1016/j.compscitech.2025.111362. hal-05319095

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# Assessing the validity of micro-pillar compression for determining strength and stiffness of carbon fibres

V. Keryvin<sup>a,†</sup>,*, M. Ueda<sup>b,†</sup>, G. Kermouche<sup>c</sup>, Y. Marthouret<sup>c</sup>, S. Sao-Joao<sup>c</sup>

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

## ARTICLE INFO

**Keywords:**

Carbon fibres

Compression

Micro-pillar

Core/skin structure

Non-linear elasticity

## ABSTRACT

The longitudinal compressive mechanical behaviour of polyacrylonitrile (PAN)-precursor T300 carbon fibres was assessed using micro-pillar compression testing, with direct comparison to published data on entire fibre compression. Micro-pillars, fabricated via focused ion beam (FIB) milling, exhibited compressive modulus, strength, and failure strain values closely matching those of whole fibres, thereby validating this microscale technique for accurate stiffness and strength measurements. A progressive reduction in stiffness with increasing compressive strain — indicative of non-linear elasticity — was directly observed and quantified under compression for the first time. Although the failure modes of micro-pillars differed from those of intact fibres, the results support the hypothesis of a mechanically homogeneous fibre microstructure and suggest the presence of a stabilising outer sheath that delays failure initiation. These findings reinforce the methodological basis for small-scale mechanical testing of carbon fibres and carry implications for multiscale modelling and the prediction of compressive strength in unidirectional composite plies.

## 1. Introduction

Carbon fibres derived from polyacrylonitrile (PAN) precursors constitute the majority of continuous carbon fibres used as reinforcement in polymer matrix composites. Today's high-performance applications — from aerospace structures to wind turbines — demand carbon-fibre composites capable of withstanding severe compressive loads without premature fibre crushing [1]. Despite their dominance in advanced polymer–matrix composites, owing to their low density and exceptional tensile properties, the compressive behaviour of PAN-precursor carbon fibres remains poorly understood. This is primarily due to their sub-10 µm diameter and high aspect ratio, which severely constrain direct mechanical testing.

The manufacture of PAN-based fibres involves four key stages — wet spinning, oxidative stabilisation, carbonisation, and graphitisation — each profoundly influencing the resulting microstructure and mechanical properties [2]. Over the years, a variety of micromechanical techniques have been developed to probe individual fibres under compression, including elastic-loop tests, fibre recoil, direct axial compression, two- and four-point bending, and micro-pillar compression [3–7]. Compressive strength is particularly critical in unidirectional plies, where fibre failure in compression during kinking often governs failure [8,9]. This property is frequently incorporated into predictive

mechanical models [10], although measured values vary significantly depending on the testing method [11].

Beyond strength, two additional parameters are of particular relevance: the initial compressive modulus and the onset of elastic non-linearity [12]. The former is essential for validating microstructure-based predictions [13] and assessing the effects of manufacturing processes [14]. The latter, less frequently characterised, reflects the progressive reduction of modulus with increasing compressive strain (in absolute terms) [15]. This phenomenon, associated with bending or buckling of highly oriented crystallites, can significantly affect stress distribution and deformation predictions in composite structures [16].

Several studies suggest that the microstructure of PAN-based fibres may be heterogeneous, exhibiting a distinct core–skin architecture, notably due to carbonisation gradients initiated at the fibre surface [17–19]. Such a microstructure often results in radial variations in the orientation of graphitic layers, especially between the fibre core and periphery, complicating the fabrication of thicker fibres. This has been demonstrated by Morita et al. [20] through the design of kidney-shaped fibres promoting more homogeneous carbonisation.

Mechanical measurements at different scales confirm this heterogeneity. Chen et al. [21], using plasma thinning and correlating electrical resistivity with tensile modulus, reported a dramatic decrease in

<footnote><sup>a</sup> Univ. Bretagne Sud, UMR CNRS 6027, IRDL, F-56321 Lorient, France</footnote>

<footnote><sup>b</sup> Department of Mechanical Engineering, Nihon University, Tokyo 101-8308, Japan</footnote>

<footnote><sup>c</sup> Mines Saint-Etienne, UMR CNRS 5307, LGF, Centre SMS, F-42023 Saint-Etienne, France</footnote>

<footnote>* Corresponding author.</footnote>

<footnote>E-mail address: vincent.keryvin@univ-ubs.fr (V. Keryvin).</footnote>
modulus at the fibre core. Their work, conducted on several PAN-based fibres, showed tensile modulus contrasts between the fibre core and entire fibre reaching up to a factor of 10. More recently, Guruprasad et al. [11] performed compression tests on micro-pillars extracted from the cores of PAN-based fibres, demonstrating that the compressive modulus in these regions was significantly lower than that of entire fibres, with contrasts of about 2 to 4 between the core compressive modulus and the fibre tensile modulus.

However, results from different studies on the standard modulus T300 carbon fibre appear contradictory. For instance, Chen et al. [21], using the plasma-thinning method described above, reported values ranging from 30 GPa (at the fibre core) to 230 GPa (for the entire fibre) for the tensile modulus. This appears consistent with Scanning Electron Microscopy (SEM) images obtained by Newcomb et al. [22, Supplemental Material], clearly showing a 2.7 µm core in T300 fibres (ø 7 µm). In contrast, modulus maps obtained by atomic force microscopy (AFM, Peak Force Quantitative Nanomechanics, PF-QNM) on T300 fibres by Niu et al. [23] revealed much more homogeneous indentation moduli of 20–30 GPa across the fibre cross-section. Although the relationships between indentation modulus and tensile or compression moduli are not straightforward due to the pronounced anisotropy of the fibres [24], the comparison between a contrast of 7 [21] and 1.5 [23] raises questions.

In this context, several questions remain open:

* Does the PAN-precursor T300 fibre exhibit a pronounced core-skin structure?

* To what extent do the mechanical properties (strength, stiffness) of the core differ from those of the entire fibre?

* How can the contradictory results on T300 fibres be interpreted?

* Can micro-pillar compression testing be used for assessing the longitudinal compressive properties of carbon fibres?

To address these questions, we directly compare the compressive response of entire T300 fibres with that of their cores via targeted micro-pillar compression. Section 2 describes our materials and methods; Section 3 presents the results; and Section 4 discusses their implications for micro-mechanical modelling and composite design.

## 2. Materials and methods

The PAN-based carbon fibre T300 (Toray, Japan) was investigated in this study (T300-B-300-4-0-B). Such fibres exhibit a quasi-circular cross-section, with an equivalent diameter of approximately 7 µm [25]. Micro-pillars were machined from a continuous carbon fibre/epoxy composite material (1 cm in thickness). Any possible surface defects on pristine carbon fibres are therefore irrelevant to this study. The fabrication procedure follows the methodology described in [11]. Micro-pillars were machined by focused ion beam (FIB) milling using a Thermo Scientific Helios NanoLab DualBeam system. Initial coarse shaping was performed with a high ion current (30 kV, 2.5 nA), followed by fine polishing with a lower current (30 kV, 80 pA) to reach the target geometry. Subsequent to the machining process, the geometrical dimensions of the pillars were measured by means of SEM imaging. Pillars exhibited diameters of approximately 2.8 µm and heights of 6.5 µm, maintaining a height-to-diameter ratio (~ 2.3) sufficient to avoid buckling under compression. This reduction in diameter compared to the initial fibre (~ 7 µm) enables focusing on the fibre core properties. One additional pillar with a larger diameter (4.6 µm) and height (8.3 µm) was also prepared. To minimise material redeposition, all pillars were milled using an annular milling strategy from the outside towards the center, ensuring coaxiality with the fibre axis. Pillar geometries, including top and bottom diameters and heights, were measured by scanning electron microscopy (SEM, Gemini Supra 55VP, Zeiss, Germany). The taper angles were estimated to be lower than 2°. They correspond to the difference between the radii at the top of the micro-pillar and its bottom, which is slightly higher due to machining constraints.

Fig. 1 shows representative pillars fabricated by FIB, highlighting also the slightly non-circular shape of T300 fibres. Micropillar compression tests were carried out using an in-situ nano-indenter (Alemnis, Switzerland) installed inside the SEM. The load cell is the Alemnis SLC-05 with a load range up to 0.5 N, and a 4 µN RMS Noise (at 200 Hz). Compression was performed with a flat diamond punch of 10 µm diameter under displacement control at a rate of 100 nm/s, corresponding to an imposed strain rate of ~ 10⁻²s⁻¹. Force (F) versus measured displacement (uₘₐₙ) curves were recorded during the tests. Measured displacements were corrected for thermal drift and for the compliance of the testing system and substrate, giving the pillar displacement (uₚᵢₗ), according to:

$$u_{\text{pil}} = u_{\text{mes}} - \frac{F}{K_{\text{eff}}}, \quad K_{\text{eff}} = \left( \frac{1}{K_f} + \frac{1}{K_s} \right)^{-1} \qquad (1)$$

where Kₐₗ is the effective system stiffness with a frame stiffness, Kᵣ, of 0.25 mN/nm. Substrate stiffness, Kₛ, associated with base penetration under load, was estimated using Sneddon's equation [26]:

$$K_s = 2 M_s r_{\text{bot}} \qquad (2)$$

where Mₛ is the substrate indentation modulus and rₐₗ is the micropillar base radius. The substrate modulus Mₛ was determined by nano-indentation following [24], yielding Mₛ = 55 GPa. Finally, nominal stress-strain curves were derived from the corrected load-displacement data using the initial pillar length and cross-sectional area measured at mid-height.

## 3. Results

Fig. 2 shows a pillar after machining by FIB. The compression test results for a selection of micro-pillars with diameters of 2.8 µm and 4.6 µm are presented in Fig. 3. All samples exhibited similar stiffness values, below an applied stress of 2 GPa, regardless of diameter. The initial phase, the specimen settling, corresponding to the establishment of contact, prevents a reliable determination of the modulus at very small strains. This is a limitation, as the modulus is expected to decrease later with strain due to elastic nonlinearity [15]. Nevertheless, the modulus was evaluated in the stress range 0.75–1.25 GPa, which is more appropriate. (The detailed procedure is discussed hereinafter.) The five micro-pillars with 2.8 µm diameter showed consistent failure strains around 9.4%, and failure stresses around 3.73 GPa. The failure strain corresponds to the strain value at maximum stress. The larger diameter pillar was not tested to failure. All results are summarised in Table 1. Overall, the tests exhibited good reproducibility in terms of stiffness and failure properties, and no significant influence of pillar size was observed on the results.

Fig. 4 presents cyclic tests performed on a micro-pillar. Each loading-unloading cycle exhibits a hysteretic behaviour. This behaviour is related to the formation and propagation of longitudinal cracks as seen in Fig. 2, a quasi-splitting damage mechanism. At each loading stage, the crack reopens and then propagates if the stress level exceeds the maximum stress from the previous loading cycle. These details were reported by Guruprasad et al. [11] for PAN precursor fibres and will not be discussed further here. Nevertheless, Fig. 5 shows the different stages. The Supplemental contains a synchronised video presentation illustrating the force versus time plot alongside the SEM images. This enables the observation of the failure mechanisms. Only the behaviour below 2.5 GPa appears to be reversible, non-linear but reversible (within the drift correction). This stress limit for the reversible behaviour will be used for all tests. The same behaviour is observed on the micro-pillar with a diameter of 4.6 µm, with a distinct hysteresis loop following significant damage on the loading curve and no permanent deformation after unloading.

Fig. 6 presents the different steps involved in measuring non-linear elasticity as a function of compressive strain. These include: (a) plotting the raw stress-strain data; (b) determining the stiffness in a range
<figure><img src="image_4.png" /><figcaption>Fig. 1. Overview of the micro-pillars machined by Focused Ion Beam. Labels are used throughout the paper.</figcaption></figure>

<figure><img src="image_5.png" /><figcaption>Fig. 2. Image of a micro-pillar after FIB machining (left) and after crack initiation (right).</figcaption></figure>

Table 1

<table><caption>Mechanical properties measured from micro-pillar compression tests.</caption><thead><tr><th>Pillar #</th><th>Stiffness [GPa]</th><th>Compressive strength [GPa]</th><th>Failure strain [%]</th></tr></thead><tbody><tr><td>3</td><td>179</td><td>3.25</td><td>8.92</td></tr><tr><td>4</td><td>183</td><td>3.93</td><td>9.10</td></tr><tr><td>6</td><td>207</td><td>3.62</td><td>9.10</td></tr><tr><td>7</td><td>185</td><td>3.91</td><td>10.5</td></tr><tr><td>8</td><td>170</td><td>3.96</td><td>9.41</td></tr><tr><td>Mean value</td><td>185</td><td>3.73</td><td>9.40</td></tr><tr><td>Standard deviation</td><td>12</td><td>0.27</td><td>0.57</td></tr><tr><td>10<sup>a</sup></td><td>161</td><td>&gt; 3.61</td><td>&gt; 6.16</td></tr></tbody></table>

bounded by the specimen settling and the obvious onset of softening; here between 0.75 and 1.25 GPa of applied stress; (c) shifting the curve

to simulate the absence of a specimen settling; (d) determining the apparent secant modulus as a function of strain (the ratio between

<footnote>a indicates the pillar with a diameter of 4.6 µm.</footnote>
<figure><img src="image_6.png" /><figcaption>Fig. 3. Mechanical response of selected micro-pillars with 2.3 µm in diameter (the fibre diameter is ~ 7 µm) except sample #10 with 4.6 µm in diameter.</figcaption></figure>

<figure><img src="image_7.png" /><figcaption>Fig. 4. Cyclic loading of micro-pillar T300-6 (ø 2.3 µm).</figcaption></figure>
<figure><img src="image_8.png" /><figcaption>Fig. 5. Deformation and damage stages of micro-pillar T300-4 (ø 2.3 µm): reversible behaviour (A to B), onset of longitudinal cracking or quasi-splitting (B), sudden crack propagation and associated load-drop (C), permanent strain (D).</figcaption></figure>

applied stress and adjusted strain); (e) quantifying, where possible, the non-linear elasticity in the range (0.5%–1%) of strains following Eq. (3): (f) quantifying the non-linear elasticity in the range (1–1.5%) following Eq. (3)<fnref n="1" /> [15,27].

$$E_p(\epsilon) = E_p^0(1 + \alpha_p' \epsilon) \qquad (3)$$

where $E_p(\epsilon)$ is the secant modulus of the pillar, and ($E_p^0, \alpha_p'$) a couple of fitting parameters. The degree of elastic non linearity $\alpha_p'$ of the pillar is the parameter of interest.

<footnote n="1">¹ The non-linear elasticity is not measured below 0.5% for issues with the specimen settling.</footnote>
<figure><img src="image_9.png" /><figcaption>**Fig. 6.** Steps involved for measuring the degree of elastic nonlinearity in compression for specimen T300-6. (a) The reversible behaviour is determined by cyclic tests as in Fig. 4; (b) an apparent tangent modulus is determined before obvious softening and after the end of the specimen settling; (c) the curve is shifted to remove the latter specimen settling stage; (e) an apparent secant modulus is calculated revealing three phases; (e) a non-linear elasticity slope for strains between 0.5 and 1% (phase 2) is determined; (f) a non-linear elasticity slope for strains between 1 and 1.5% is determined (phase 3). (Phase 1 below 0.5% is not quantified for issues with the specimen settling.).</figcaption></figure>

<table><caption>**Table 2**
Non-linear elasticity parameter $\alpha'_p$ from Eq. (3) for different strain ranges.</caption><thead><tr><th>Pillar #</th><th>(0.25–0.5%)</th><th>(0.5%–1%)</th><th>(1–1.5%)</th></tr></thead><tbody><tr><td>3</td><td>n.d.</td><td>n.d.</td><td>22</td></tr><tr><td>4</td><td>n.d.</td><td>16</td><td>20</td></tr><tr><td>6</td><td>11</td><td>17</td><td>24</td></tr><tr><td>7</td><td>n.d.</td><td>n.d.</td><td>n.d.</td></tr><tr><td>8</td><td>n.d.</td><td>n.d.</td><td>n.d.</td></tr><tr><td>10<sup>a</sup></td><td>n.d.</td><td>n.d.</td><td>18</td></tr></tbody></table>

The apparent secant modulus clearly decreases with strain. Table 2 presents the results of these analyses. The values of $\alpha'_p$ in the range (1-1.5%) are consistent with each other, averaging around 22 for three pillars with a diameter of 2.3 µm and 18 for the one with a diameter of 4.6 µm. The difference is minimal, making it difficult to assert any diameter influence. Two values of $\alpha'_p$ in the range (0.5%–1%) were determined, averaging around 16. A single value in the deformation range before 0.5% was determined to be 11. Thus, a clear increase in elastic non-linearity is observed with the level of strain.

# 4. Discussion

## 4.1. Behaviour of the fibre core with respect to the entire fibre

We make a comparison between two methods of longitudinal compression. The method employed in this study involves an aspect ratio of 2.3, a displacement rate of 100 nm/s, and an indenter diameter

of 10 µm. The study of Ueda and Akiyama [28] involves an aspect ratio of 1.5, a displacement rate of 50 nm/s (with holding times of several minutes to allow for SEM images to be taken), and an indenter diameter significantly larger than the fibre diameter (polished thread). The comparison is therefore made on a quasi-static loading with a flat punch larger than the fibre/pillar diameter and an aspect ratio where buckling is prevented. Fig. 7 presents a comparison of our results on pillars with compression tests on full fibres, conducted by Ueda and Akiyama [28]. The rigidity of the entire fibre and that of the pillars is clearly very similar. This is the only comparison possible for the longitudinal compression modulus from literature results on direct compression tests on T300 carbon fibre. In their study, Ueda and Akiyama [28] report compressive strength values of 3.7 GPa and associated failure strains of 10%. These values were found to be comparable to those of tensile testing for the strength. This is in very good agreement with the results of the present study shown in Table 1. However, Ueda and Akiyama [28] did not observe damage prior to rupture in the form of longitudinal cracks, as we see on our pillars. The ultimate compressive failure was always scattered (like a burst). No debris could be found after the test. This might mean that even if a fracture (splitting) occurs in the core for the whole fibre test, the skin suppresses crack propagation to some extent. The expanding behaviour due to splitting in the core finally could cause burst-like ultimate failure. It is also interesting to note that the failure mode of the entire fibre is different between tension and compression. Tensile failure is transverse cracking, and compression failure is splitting. It can be assumed that there is still a “sheath” type boundary that contains the tendency for cracks to appear due to the orthoradial (hoop) stresses generated by the compression loading.

<footnote><sup>a</sup> indicates the pillar with a diameter of 4.6 µm.</footnote>
<figure><img src="image_10.png" /><figcaption>Fig. 7. Comparison of the compressive behaviour of micro-pillars (this work) vs entire fibre from [28].</figcaption></figure>

Christensen [29] showed that both classic fibre microstructures (radial and onion skin) yield the same mechanical properties. Carbon fibre manufacturing tries to decrease surface defects to improve tensile strength. Thus, the skin should contain smaller defects preventing the formation of cracks. The core could have smaller structures as reported by Guigon et al. [30]. The skin may have more concentric structure than core to prevent defects. Fig. 8 presents a schematics of the T300 fibre structure that could represent both our observations and those of Ueda and Akiyama [28]. It combines a homogeneous radial structure (Newcomb et al. [22] observed by Transmission Electron Microscopy a random crystallite orientation with small crystallites in the radial direction) throughout most of the diameter with an onion skin structure on the periphery. Since we did not test pillars with diameters larger than 4.6 µm (2/3 of the diameter), one could assume a scenario where the onion skin structure starts at 2/3 of the diameter (top) or only concerns the superficial layers (bottom).

## 4.2. Non-linear elasticity in compression

The parameters expressing the non-linear elasticity in compression can be compared with those obtained from other methods. Traditionally, this is done in tension through uniaxial fibre tests. This is much more difficult in compression. Methods based on bending tests on fibre composites allow for this comparison [27]. These methods find that the initial compression modulus in compression is the same as in tension [31–33]. To our knowledge, this is the first time that these parameters are measured at the fibre scale (a part of the fibre). They do not appear to differ between 1/3 and 2/3 of the diameter on the T300 fibre. This elastic non-linearity is not linear and increases with the level of deformation experienced by the pillar, from $\alpha'_p = 11$ (see Eq. (3)) for strains below 0.5% (absolute values) to around $\alpha'_p = 22$ for strains greater than 1% (absolute values). The levels are consistent with those measured by Keryvin and Marchandise [15] over a strain range below 0.5% from measurements on continuous carbon fibre composites.

The present study offers a valuable insight into the physical origin of the non-linear elasticity in continuous carbon fibre composites. The prevailing hypothesis attributes this phenomenon to the buckling of crystallites in the carbon fibres, rather than to initial fibre misalignment in fibre composites, as suggested by Keryvin et al. [32].

## 4.3. Existence of a mechanical difference between the core and the skin of the fibre

There may be a core/sheath structure on the T300 carbon fibre, but it does not generate any significant difference in mechanical properties (stiffness and strength) related to compression. SEM pictures on well prepared surfaces can exhibit a clear visualisation of core/skin microstructure, for example on T700S carbon fibre [18]. In this case, the contrast between the two zones is linked to the orientation angle of the crystallites from 55° in the core to 30° in the skin. With such differences, one should expect a very large contrast in the mechanical properties between the core and the rest of the fibre. Yet, the orientation angles for standard modulus carbon fibres are relatively low and changes do not affect considerably elastic stiffness values [2,15]. Newcomb et al. [22, Supplemental information] also reported the presence of an electronic contrast in SEM pictures of T300 carbon fibres between the core and the rest of the fibre, suggesting different orientation angles. Yet, Liu et al. [34] did not observe a large difference in indentation moduli using nano-DMA (Dynamic Mechanical Analysis) modulus mapping between the core and the periphery on T300 carbon fibre. Niu et al. [23] did not observe any difference at all with AFM PF-QNM. Yet, the indentation moduli that are measured by these two techniques are not the compressive moduli: they are linked to the five elastic constants of transverse isotropy or the nine elastic constants of orthotropy. Guruprasad et al. [24] showed that the indentation moduli for standard to high modulus different carbon fibres were all not very different from 60-80 GPa while their longitudinal tensile moduli were significantly different (from 240 to 370 GPa). This might have to do
<figure><img src="image_11.png" /></figure>

<figure><img src="image_12.png" /><figcaption>**Fig. 8.** Schematics of a core/skin microstructure with a radial core (random distribution of wavy graphene sheets) and onion-like skin of 67% of the fibre radius (top) or 90% of the fibre radius (bottom).</figcaption></figure>

with the buckling of crystallites during sharp indentation testing, and the resulting extracted longitudinal compressive moduli were very low around 100 GPa. At the contrary, performing simple compression tests, even at these very low scales, allow for imposing small strains and measuring compressive moduli without the buckling of crystallites. In this situation, while clearly much lower longitudinal compressive moduli were found on some carbon fibres or at least on their cores [11], the same method used on T300 carbon fibre reports (see Table 1) longitudinal compressive moduli very comparable on the core of the fibres to the entire fibre [28] and very comparable to longitudinal tensile moduli values [25]. Therefore, the results from Chen et al. [21], which reported a contrast of 7 in the tensile modulus between 30% of the diameter and the entire fibre, strongly contrast with our findings and those of the rest of the literature.

### 4.4. Limitations and perspectives

Compression tests on micro-pillars are usually not designed for investigating stiffness but rather strength. Difficulties with the specimen settling makes it difficult to measure an initial compressive modulus. Thus, the values reported in this work underestimate somehow these

values. Taking a value of $\alpha'_p$ of 10 in the range (0-0.5%) and a value for the compression modulus of 185 GPa for 0.5% of strain (see Table 1) would result in initial modulus values of ~ 200 GPa. Only a limited number of sound tests on dedicated strain ranges of pillars made it possible to measure the non-linear elasticity (taken as piecewise linear). It is noteworthy that a single sample, exhibiting a diameter that was 66% of that of the fibre diameter, was subjected to testing. Future studies should include a broader range of pillar diameters to precisely assess radial gradients. The investigation of potential changes in shear modulus through the utilisation of instrumented nanoindentation testing would be a valuable addition to the present research.

The objective of this study was to compare two different methods of characterising the compressive behaviour of carbon fibres. A classical standard modulus one was selected for this purpose. It would be interesting to extend this research to the study of other carbon fibres.

### 5. Conclusion

This study provides direct micro-mechanical evidence of the compressive behaviour of the core region in PAN-precursor T300 carbon fibres, using micro-pillar compression as a targeted testing approach. The results reveal that the compression modulus of the core closely matches the compression and tensile moduli measured for entire fibres, supporting the hypothesis of a mechanically homogeneous fibre microstructure. Although failure strains and strengths of micro-pillars are comparable to those of entire fibres, the observed damage and failure mechanisms differ: longitudinal surface cracks initiate and propagate within the core in micro-pillars, whereas the surrounding skin layer in whole fibres likely suppresses such mechanisms under compressive loading. A key originality of this work lies in the direct quantification of elastic nonlinearity under compression, a feature previously inferred only indirectly.

By clarifying earlier contradictory findings on the mechanical homogeneity of T300 fibres, this study also highlights potential inconsistencies with prior research focusing on the tensile behaviour of the fibre core. It further demonstrates that micro-pillar compression tests provide accurate and useful results for strength and stiffness of carbon fibres when the core-skin contrast in carbon fibres is absent or limited. Conversely, when such contrasts exist, the properties may differ dramatically. These insights pave the way for more accurate micro-mechanical models of carbon fibre behaviour and contribute to the design of next-generation fibres with improved compressive performance. In particular, linking manufacturing conditions, microstructure, and local mechanical behaviour remains a promising avenue to optimise fibre design and enhance composite performance.

### CRediT authorship contribution statement

**V. Keryvin:** Writing – original draft, Visualization, Validation, Project administration, Methodology, Investigation, Data curation, Conceptualization. **M. Ueda:** Writing – review & editing, Validation. **G. Kermouche:** Writing – review & editing, Validation, Supervision, Resources. **Y. Marthouret:** Writing – review & editing, Visualization, Investigation. **S. Sao-Joao:** Writing – review & editing, Visualization, Methodology, Investigation, Data curation.

### Declaration of competing interest

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

### Acknowledgements

We would to thank T.S. Guruprasad for some data analyses. V.K. thanks Univ. Bretagne Sud for funding partially his sabbatical stay (CRCT) at the Univ. of Auckland during which this paper was written. The University of Auckland's Centre for Advanced Materials Manufacturing is gratefully acknowledged for this research stay.
# Appendix A. Supplementary data

Supplementary material related to this article can be found online at https://doi.org/10.1016/j.compscitech.2025.111362.

## Data availability

Data will be made available on request.

## References

[1] E.J. Barbero, Introduction to composite materials design, third ed., in: Composite Materials: Analysis and Design, CRC Press, Taylor & Francis Group, CRC Press is an imprint of the Taylor & Francis Group, an informa business, Boca Raton, ISBN: 978-1-138-19680-3, 2018.

[2] O. Paris (Ed.), Structure and multiscale mechanics of carbon nanomaterials, in: CISM International Centre for Mechanical Sciences, vol. 563, Springer Vienna, Vienna, ISBN: 978-3-7091-1885-6, 2016, ISBN: 978-3-7091-1887-0.

[3] M.G. Dobb, D.J. Johnson, C.R. Park, Compressional behaviour of carbon fibres, J. Mater. Sci. 25 (2) (1990) 829-834.

[4] M. Nakatani, M. Shioya, J. Yamashita, Axial compressive fracture of carbon fibers, Carbon 37 (4) (1999) 601-608.

[5] D. Loidl, H. Peterlik, M. Müller, C. Riekel, O. Paris, Elastic moduli of nanocrystallites in carbon fibers measured by in-situ X-ray microbeam diffraction, Carbon 41 (3) (2003) 563-570.

[6] F. Tanaka, T. Okabe, H. Okuda, I.A. Kinloch, R.J. Young, The effect of nanostructure upon the compressive strength of carbon fibres, J. Mater. Sci. 48 (5) (2013) 2104-2110.

[7] J. Wang, N. Salim, B. Fox, N. Stanford, Anisotropic compressive behaviour of turbostratic graphite in carbon fibre, Appl. Mater. Today 9 (2017) 196-203.

[8] N. Fleck, Compressive failure of fiber composites, in: Advances in Applied Mechanics, vol. 33, Elsevier, ISBN: 978-0-12-002033-1, 1997, pp. 43-117.

[9] S. Pimenta, R. Gutkin, S. Pinho, P. Robinson, A micromechanical model for kink-band formation: part II—analytical modelling, Compos. Sci. Technol. 69 (7-8) (2009) 956-964.

[10] S. Pimenta, R. Gutkin, S. Pinho, P. Robinson, A micromechanical model for kink-band formation: part I — experimental study and numerical modelling, Compos. Sci. Technol. 69 (7-8) (2009) 948-955.

[11] T. Guruprasad, V. Keryvin, G. Kermouche, Y. Marthouret, S. Sao-Joao, Compresive behaviour of carbon fibres micropillars by in situ SEM nanocompression, Compos. Part A: Appl. Sci. Manuf. 173 (2023) 107699.

[12] J. Zhong, C. Zhao, J. Ren, X. Liu, Z. Zhang, A constitutive model for carbon fiber reinforced epoxy resin laminate under compression load: considering the initial non-linearity, Appl. Compos. Mater. 29 (2) (2022) 629-649.

[13] M. Tane, H. Okuda, F. Tanaka, Nanocomposite microstructures dominating anisotropic elastic modulus in carbon fibers, Acta Mater. 166 (2019) 75-84.

[14] S. Nunna, A.R. Ravindran, J. Mroszczok, C. Creighton, R.J. Varley, A review of the structural factors which control compression in carbon fibres and their composites, Compos. Struct. 303 (2023) 116293.

[15] V. Keryvin, A. Marchandise, The non-linear elasticity of unidirectional continuous carbon fibre-reinforced composites and of carbon fibres, Materials 17 (1) (2024) 34.

[16] V. Keryvin, P.-Y. Méchin, Mast design performance - influence of the non-linear elastic behaviour of carbon fibres on the accuracy of fluid/structure interaction models for estimating mast bending, J. Sail. Technol. 9 (01) (2024) 42-56.

[17] D.J. Johnson, Structure-property relationships in carbon fibres, J. Phys. D: Appl. Phys. 20 (3) (1987) 286-291.

[18] X. Guo, Y. Cheng, Z. Fan, Z. Feng, L. He, R. Liu, J. Xu, New insights into orientation distribution of high strength polyacrylonitrile-based carbon fibers with skin-core structure, Carbon 109 (2016) 444-452.

[19] S. Nunna, M. Naebe, N. Hameed, B.L. Fox, C. Creighton, Evolution of radial heterogeneity in polyacrylonitrile fibres during thermal stabilization: an overview, Polym. Degrad. Stab. 136 (2017) 20-30.

[20] S. Morita, M. Ueda, T. Takahashi, K. Kajiwara, A. Yoshimura, N. Sugiura, Performance assessment for fiber tracking of unidirectional carbon fiber reinforced plastic by digital image correlation of X-ray computed-tomography, Adv. Compos. Mater. 32 (1) (2023) 35-47.

[21] L. Chen, L. Hao, S. Liu, G. Ding, X. Sun, W. Zhang, F. Li, W. Jiao, F. Yang, Z. Xu, R. Wang, X. He, Modulus distribution in polyacrylonitrile-based carbon fiber monofilaments, Carbon 157 (2020) 47-54.

[22] B.A. Newcomb, L.A. Giannuzzi, K.M. Lyons, P.V. Gulgunje, K. Gupta, Y. Liu, M. Kamath, K. McDonald, J. Moon, B. Feng, G. Peterson, H.G. Chae, S. Kumar, High resolution transmission electron microscopy study on polyacrylonitrile/carbon nanotube based carbon fibers and the effect of structure development on the thermal and electrical conductivities, Carbon 93 (2015) 502-514.

[23] Y.-F. Niu, Y. Yang, X.-R. Wang, Investigation of the interphase structures and properties of carbon fiber reinforced polymer composites exposed to hydrothermal treatments using peak force quantitative nanomechanics technique, Polym. Compos. 39 (S2) (2018).

[24] T. Guruprasad, V. Keryvin, L. Charleux, J.-P. Guin, O. Arnould, On the determination of the elastic constants of carbon fibres by nanoindentation tests, Carbon 173 (2021) 572-586.

[25] Carbon Fibre T300 Data Sheet, Tech. Rep., Toray Composite Materials, 2025.

[26] I.N. Sneddon, Boussinesq's problem for a flat-ended cylinder, Math. Proc. Cambridge Philos. Soc. 42 (1) (1946) 29-39.

[27] T.W. Murphey, M.E. Peterson, M.M. Grigoriev, Large strain four-point bending of thin unidirectional composites, J. Spacecr. Rockets 52 (3) (2015) 882-895.

[28] M. Ueda, M. Akiyama, Compression test of a single carbon fiber in a scanning electron microscope and its evaluation via finite element analysis, Adv. Compos. Mater. 28 (1) (2019) 57-71.

[29] R.M. Christensen, Properties of carbon fibers, J. Mech. Phys. Solids 42 (4) (1994) 681-695.

[30] M. Guigon, A. Oberlin, G. Desarmot, Microtexture and structure of some high-modulus, PAN-base carbon fibres, Fibre Sci. Technol. 20 (3) (1984) 177-198.

[31] V. Keryvin, A. Marchandise, P.-Y. Mechin, J.-C. Grandidier, Determination of the longitudinal non linear elastic behaviour and compressive strength of a CFRP ply by bending tests on laminates, Compos. Part B: Eng. 187 (2020) 107863.

[32] V. Keryvin, A. Marchandise, J.-C. Grandidier, Non-linear elastic longitudinal behaviour of continuous carbon fibres/epoxy matrix composite laminae: material or geometrical feature? Compos. Part B: Eng. 247 (2022) 110329.

[33] A. Marchandise, V. Keryvin, Y. Grohens, R. Le Borgne, Influence of the lay-up and curing steps in the manufacturing process of thick laminate composites on their compressive strength, Compos. Part A: Appl. Sci. Manuf. 164 (2023) 107302.

[34] X. Liu, C. Zhu, J. Guo, Q. Liu, H. Dong, Y. Gu, R. Liu, N. Zhao, Z. Zhang, J. Xu, Nanoscale dynamic mechanical imaging of the skin-core difference: from PAN precursors to carbon fibers, Mater. Lett. 128 (2014) 417-420.