# Fracture toughness of Khaya ivorensis and Magnolia obovata for mobility applications

Riccardo Houngbegnon, Rostand Moutou Pitti, Valery Doko, Thomas Jailin, Benoît Blaysat, José Xavier, Nicolas Sauvat, Joseph Gril, Naman Recho

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Riccardo Houngbegnon, Rostand Moutou Pitti, Valery Doko, Thomas Jailin, Benoît Blaysat, et al. Fracture toughness of Khaya ivorensis and Magnolia obovata for mobility applications. Theoretical and Applied Fracture Mechanics, 2025, 141, pp.105209. 10.1016/j.tafmec.2025.105209. hal-05332954

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# Fracture toughness of *Khaya ivorensis* and *Magnolia obovata* for mobility applications

Riccardo Houngbegnon<sup>a, b</sup>, Rostand Moutou Pitti<sup>a, e, *</sup>, Valery Doko<sup>b</sup>, Thomas Jailin<sup>a</sup>, Benoît Blaysat<sup>a</sup>, José Xavier<sup>c, d</sup>, Nicolas Sauvat<sup>a</sup>, Joseph Gril<sup>a</sup>, Naman Recho<sup>a</sup>

## ARTICLE INFO

### Keywords:

* Magnolia obovata

* Khaya ivorensis

* Cracking

* Mode decoupling

* Wooden satellite

## ABSTRACT

This work focuses on the study of the fracture toughness of two wood species. It investigates the opportunity of using alternative wood species to *Magnolia obovata*, a Japanese species, to design satellites based on wooden structures. The use of wooden structures would enable us to move towards carbon neutrality in the long term. *Khaya ivorensis*, a tropical species of African origin, is explored in this context. More specifically, a comparison of the fracture processes between *Khaya ivorensis* and *Magnolia obovata* is carried out to assess their durability against the loads they may encounter in extreme applications. Tests are conducted in crack opening and mixed modes configurations, using Localized Spectrum Analysis (LSA), an innovative approach for measuring displacement and strain fields. The energy release rates are evaluated using the compliance method under imposed displacement. The decoupling of the fracture modes allowed for determining the contributions of Mode I and Mode II in mixed mode. Additionally, Scanning Electron Microscope (SEM) observations were performed to examine the impact of wood anatomy on fracture surfaces and fracture parameters. *Khaya ivorensis* demonstrated better fracture performance, revealing results consistent with its density and ribbon-like structure.

## 1. Introduction

In a context marked by the urgency of climate change and the need to develop sustainable materials for mobility infrastructures, wood is attracting renewed interest for its specific mechanical properties, its lightness, its capacity to store carbon and its renewable nature [1,2]. Historically used in shipbuilding, aeronautics [3] and railways, wood is now once again being considered for demanding technical applications, including in extreme environments such as Earth orbit [4]. Witness recent projects such as Japan's LignoSat, which saw the integration of *Magnolia obovata* species in the design of a wooden-structured satellite to be launched in 2024 [5,6]. This pioneering project highlighted the remarkable dimensional stability, thermal resistance and durability of this species in vacuum and orbital environments. However, the use of wood in stressed structures, whether in space, rail, sea or air, requires a detailed characterization of its mechanical properties, particularly in

terms of fracture toughness. Indeed, crack propagation or brittle fracture phenomena can compromise the structural integrity of components in service, hence the importance of studying fracture toughness as a determining parameter. This property describes a material's ability to resist crack initiation and growth, and is crucial in situations where cyclic loads, impacts or thermal gradients are present.

Over the last few decades, fracture mechanics has established itself as a robust theoretical framework for the study of these phenomena. Approaches based on the thermodynamics of irreversible processes and energy criteria [7,8] have made it possible to finely model crack initiation in continuous media. Variational formulations [9,10] have identified cracking trajectories via energy minimization principles, while non-local models have been developed to capture dissipation in diffuse zones [11]. On the numerical front, meshless methods [12] and J-integral approaches [13] and [14] have improved the prediction of crack propagation in heterogeneous materials. Applied to anisotropic materials such as wood, these approaches take on added complexity.

<footnote><sup>a</sup> Université Clermont Auvergne, CNRS, Clermont Auvergne INP, Institut Pascal F-63000 Clermont-Ferrand, France</footnote>

<footnote><sup>b</sup> Université d'Abomey-Calavi, Ecole Polytechnique d'Abomey-Calavi, Abomey-Calavi, Benin</footnote>

<footnote><sup>c</sup> UNIDEMI, Department of Mechanical and Industrial Engineering, NOVA School of Science and Technology, Universidade NOVA de Lisboa, Campus da Caparica, Caparica 2829-516, Portugal</footnote>

<footnote><sup>d</sup> Intelligent Systems Associate Laboratory, Campus Azurém, Guimarães 4800-058, Portugal</footnote>

<footnote><sup>e</sup> CENAREST, IRT, BP 14070, Libreville, Gabon</footnote>

<footnote>* Corresponding author.
E-mail address: rostand.moutou_pitti@uca.fr (R. Moutou Pitti).</footnote>
Nomenclature

<table><thead><tr><th>Symbol</th><th>Description</th><th>Unit</th></tr></thead><tbody><tr><td>a</td><td>Total crack length</td><td>mm</td></tr><tr><td>b</td><td>Wood specimen thickness</td><td>mm</td></tr><tr><td>BING</td><td>Beam Identification by Non-destructive Grading</td><td>–</td></tr><tr><td>CAM 1</td><td>Camera 1</td><td>–</td></tr><tr><td>CAM 2</td><td>Camera 2</td><td>–</td></tr><tr><td>CTS</td><td>Compact Tension Shear</td><td>–</td></tr><tr><td>d</td><td>Imposed displacement</td><td>mm</td></tr><tr><td>DCB</td><td>Double Cantilever Beam</td><td>–</td></tr><tr><td>E</td><td>Energy released</td><td>J/m<sup>2</sup></td></tr><tr><td>f</td><td>Nominal frequency of the periodic pattern</td><td>Hz</td></tr><tr><td>F</td><td>Energy dissipated</td><td>J/m<sup>2</sup></td></tr><tr><td>F<sub>ci</sub></td><td>Critical force inducing crack propagation</td><td>kN</td></tr><tr><td>f<sub>c,0</sub></td><td>Compressive strength parallel to the grain</td><td>MPa</td></tr><tr><td>F<sub>cx</sub> and F<sub>cy</sub></td><td>x and y components of the critical force</td><td>kN</td></tr><tr><td>F<sub>i</sub></td><td>Force inducing crack propagation</td><td>N</td></tr><tr><td>F<sub>i+1</sub></td><td>Force inducing crack propagation</td><td>N</td></tr><tr><td>f<sub>m</sub></td><td>Bending strength</td><td>MPa</td></tr><tr><td>g(x, y)</td><td>Window centered on the pixel with coordinates (x, y)</td><td>–</td></tr><tr><td>g(x - η, y - ξ)</td><td>Kernel function</td><td>Pixels</td></tr><tr><td>G<sub>c</sub></td><td>Critical energy release rate</td><td>J/m<sup>2</sup></td></tr><tr><td>G<sub>I</sub></td><td>Mode I share of energy release rate after decoupling</td><td>J/m<sup>2</sup></td></tr><tr><td>G<sub>II</sub></td><td>Mode II share of energy release rate after decoupling</td><td>J/m<sup>2</sup></td></tr><tr><td>KiPjk</td><td>Khaya ivorensis sample k from planchet j from board i</td><td>–</td></tr><tr><td>LSA</td><td>Localized Spectrum Analysis</td><td>–</td></tr></tbody></table>

<table><tr><td>MiPjk</td><td>Magnolia obovata sample k from planchet j from plate i</td></tr><tr><td>MMCG</td><td>Mixed Mode Crack Growth</td></tr><tr><td>MOE</td><td>Young's modulus measured in bending</td></tr><tr><td>p</td><td>Pitch of the pattern</td></tr><tr><td>ŝ<sub>g</sub>(x, y, θ)</td><td>WFT written for a periodic pattern aligned with the x and y axes</td></tr><tr><td>t</td><td>Time</td></tr><tr><td>U</td><td>Energy absorbed</td></tr><tr><td>U<sub>i</sub></td><td>Crack opening</td></tr><tr><td>U<sub>i+1</sub></td><td>Crack opening</td></tr><tr><td>u<sub>x</sub></td><td>Displacements along the x direction</td></tr><tr><td>u<sub>y</sub></td><td>Displacements along the y direction</td></tr><tr><td>WTF</td><td>Windowed Fourier Transform</td></tr><tr><td>x, y</td><td>Axis</td></tr><tr><td>Φ<sup>cur</sup></td><td>Current phase vector</td></tr><tr><td>Φ<sup>ref</sup></td><td>Reference phase vector</td></tr><tr><td>Φ<sup>ref</sup><sub>x</sub> and Φ<sup>ref</sup><sub>y</sub></td><td>Components of the reference phase vector in the (x, y) base rad</td></tr><tr><td>Φ<sup>cur</sup><sub>x</sub> and Φ<sup>cur</sup><sub>y</sub></td><td>Components of the current phase vector in the (x, y) base rad</td></tr><tr><td>a</td><td>Mixed Mode angle</td></tr><tr><td>Δa</td><td>Crack length</td></tr><tr><td>ΔC</td><td>Compliance</td></tr><tr><td>ε<sub>yy</sub></td><td>Strain along the y direction</td></tr><tr><td>η, ξ</td><td>Integration variables</td></tr><tr><td>σ</td><td>Standard deviation of the Gaussian</td></tr><tr><td>θ</td><td>Orientation angle</td></tr></table>

Cracking in wood is highly directional, due to its orthotropic structure and the presence of planes of weakness such as growth layers or fibrous interfaces. Experimental work [15,16] and [17] has demonstrated highly variable cracking behavior depending on tree-ring orientation and loading (modes I, II or mixed). Other studies on tropical woods [18] have demonstrated the value of experimental tools such as digital image correlation (DIC) or the grid method for locally quantifying deformation fields and damage thresholds. In this regard, approaches based on Localized Spectrum Analysis (LSA), which leads to higher metrological performance than DIC, offer promising prospects for identifying cracking zones and monitoring their evolution in heterogeneous materials. The use of LSA makes it possible, thanks to the use of optimal patterns on the specimen surface, to extract displacement or deformation fields with high local resolution, while limiting the effects of noise [19,20].

In the specific case of wood, these methods have been successfully applied to detect progressive damage mechanisms in specimens subjected to complex loads [21], but also to characterize fundamental physical properties such as density [22]. These works illustrate the potential of full-field measurement methods, combined or not with laser marking techniques [23], to provide a fine reading of the mechanical response of wood. Beyond crack detection, these approaches also contribute to the identification of mechanical parameters via robust inverse methods [24], which enable experimental measurements to be compared more directly with numerical models. The combined contribution of these non-destructive techniques and fracture mechanics models makes it possible to characterize wood performance more comprehensively under stress.

This is the background to the present study, which proposes a comparative analysis of the fracture toughness of two wood species. Magnolia obovata, an emblematic Japanese species recently highlighted for space applications, and Khaya ivorensis, a widely available and mechanically competitive West African tropical species. Khaya ivorensis has interesting characteristics, including medium density, good dimensional

stability, compressive and flexural strength close to those of Magnolia obovata, and sufficient hardness to withstand moderate to severe stresses [25]. Identifying local or regional alternatives to rare and geographically limited species is a lever for the sustainable development of timber industries and for reducing pressure on forest resources with high ecological value [26,27]. The main objective of this work is therefore to characterize and compare the crack resistance properties of these two species under conditions representative of use in a stressed environment. Through experimental toughness tests, the aim is to assess their ability to resist Mode I crack propagation, analyze failure mechanisms, and provide useful data for the design of wood components subjected to mechanical stress. The results of this study are intended to enrich the knowledge base on the fracture behavior of wood, and to contribute to the development of more environmentally-friendly material solutions for the mobility sector. The paper is organized into two parts: the first addresses species selection criteria, their characterization, cracking tests and Charpy impact test; the second presents the results obtained, the main conclusions and the prospects arising from this study.

## 2. Materials and methods

### 2.1. Choice of species and description

The selection of Magnolia obovata as the structural material for the design of the first wooden satellite was motivated by (i) its high lightness and low density/strength ratio, (ii) its high mechanical and thermal strength, and (iii) its ease of processing and durability. Similar characteristics were found in Khaya ivorensis, based on CIRAD data [28], in a multi-criteria analysis. We therefore carried out a comparative study of the two species to determine whether Khaya ivorensis was also eligible for use in space mobility.

Magnolia obovata, belongs to the Magnoliaceae family. It is a deciduous tree that can reach 30 m in height at maturity, with a trunk diameter of up to 1 m [29 30]. Its habit is generally upright, with a
widely-spreading crown formed of sturdy branches. *Magnolia obovata* is native to the eastern region of Asia, where it is mainly found in Japan, eastern China, and parts of Korea. *Magnolia obovata* wood is composed mainly of tracheids, woody fibers and woody rays, which contribute to its lightness and fine texture. The vessels are medium-sized and few in number, giving the wood a low porosity, ideal for a smooth finish. The *Magnolia obovata* used in this study was sourced from a supplier specializing in Japanese wood. Acquired in 600x300x20 mm³ planks cut on slabs, the *Magnolia obovata* wood was artificially dried to an internal moisture content of 12 %, with a density of around 460 kg/m³.

*Khaya ivorensis*, also known as African Mahogany, is a precious wood species, highly prized for its aesthetic and mechanical qualities. This tree belongs to the *Meliaceae* family and is widespread in West and Central Africa. *Khaya ivorensis* is valued not only for the beauty of its wood, but also for its various applications in the timber industry and traditional medicine. *Khaya ivorensis* is native to the tropical regions of West Africa, mainly Ivory Coast, from which it takes its name, as well as other countries such as Ghana, Nigeria, Cameroon, Gabon and Benin [31]. The anatomical structure of *Khaya ivorensis* wood is characterized by distinctive features that contribute to its mechanical and aesthetic properties. The wood features medium to large vessels, often arranged in radial patterns, visible to the naked eye on the transverse surfaces [32,33]. The *Khaya ivorensis* wood used in this study comes from the *Ouémé-Supérieur forest*, one of the largest open forests in southern Benin. The *Khaya ivorensis* was cut from the trunk of a 30 m-high tree, with a diameter of around 1 m. Saw-cut and cut on a slab, the *Khaya ivorensis* wood was dried naturally over a period of 1 month. Freshly cut (green), *Khaya ivorensis* wood had an internal moisture content of 70 % and a density of around 850 kg/m³.

Figs. 1 and 2 show, respectively, for *Magnolia obovata* and *Khaya Ivorensis*, the standing tree (a), the sampling locations in the tree (a), the boards removed from the tree (b), the planks cut from the boards (c), and finally the samples machined for fracture tests (d).

## 2.2. Characterization tests

After acquiring the species *Khaya ivorensis* and *Magnolia obovata*, these were characterized from a mechanical, physical and morphological point of view. The same characterization process has been applied to both species and the tests were carried out at 12 % moisture content. To this end, we measured density, moisture content and Young's modulus, followed by compression and bending tests. The various tests mentioned above were carried out according to the protocol detailed in standard NF EN 408, using a Zwick Roel-type machine with a capacity of 200 kN (Fig. 3). BING© (Beam Identification by Non-destructive Grading) was also used to obtain Young's moduli [34–36] and [37].

Following the tests carried out, we calculated the bending strength, Young's moduli and compressive strength parallel to the grain for the specimens tested. The average of these values measured at 12 % moisture content are presented in Table 1. A comparison of our experimental values with those in the literature (CIRAD) shows slight differences. We measure a higher density for *Khaya ivorensis* (765–789 kg/m³ vs.

500–680 kg/m³ from CIRAD). This may be linked to the different provenance of our samples compared with those studied by CIRAD. The same applies to the Young's modulus and bending stress of *Magnolia obovata*, with values higher than those reported in the literature. As far as Young's moduli are concerned, those obtained with destructive and non-destructive methods are very similar. This again demonstrates the reliability of BING© in determining wood elastic properties [38]. The other properties of *Khaya ivorensis* (bending stress at break and compressive stress at break) are very close to those reported in the literature. This analysis enabled us to note a certain variability in mechanical properties between the literature and the tests carried out, especially for *Magnolia obovata*, with improvements on several criteria.

## 2.3. Fracture mechanics tests

### 2.3.1. Modified MMCG specimens

To perform the tests, modified Mixed Mode Crack Growth (MMCG) specimens were used. The MMCG specimen (Fig. 4) was developed by Moutou Pitti [41], a compromise between DCB (Double Cantilever Beam) variable inertia and CTS (Compact Tension Shear) specimens [42]. The advantage of the MMCG specimen is that, unlike the CTS specimen, the crack propagates under a constant level of energy release rate leading to stable crack growth [43].

*Magnolia obovata* and *Khaya ivorensis* planks were sawn-cut and stored in a controlled environment, with temperatures ranging from 19 to 21 °C and average relative humidity from 57 to 70 %. The boards obtained by the process presented in Figs. 1 and 2, were then laser-cut. The samples were cut using laser technology, selected for its high dimensional precision and reproducibility. Laser cutting is a fast and convenient way to cut wood, as it is performed without mechanical contact with the material itself, ensuring no waste or consumables. Furthermore, this process confines the heat-affected zone (HAZ) to a very narrow region, thereby minimizing potential microstructural modifications. Unlike mechanical cutting techniques, it does not induce plastic deformation from tool contact. In addition, laser cutting ensures rapid and efficient sample preparation with clean and consistent edges. As reported by [44], any local material alterations remain limited to a very small area and do not significantly affect the overall properties or the reliability of the experimental results. It should be noted that before the tests began, the crack was initiated with a cutter to a depth of approximately 1 mm within the 20 mm indicated in Fig. 4. The specimens shown in Fig. 1 (d) and Fig. 2 (d) therefore met this condition before all tests presented in section 3.

### 2.3.2. The LSA method

Localized Spectrum Analysis (LSA) is a technique used to extract displacement and deformation fields from images, based on a spectrum analysis. LSA consists first in calculating the windowed Fourier transform (WFT) of the image of the periodic pattern for a given frequency, which is the nominal frequency of the periodic pattern [45,46]. This frequency is denoted by $f = \frac{1}{p}$, where p is the pitch of the pattern. For a periodic pattern aligned with the x and y axes, the WFT can be written as

<figure><img src="image_3.png" /><figcaption>Fig. 1. *Magnolia obovata* (a) Tree; (b) Board; (c) Planchet; (d) Sample.</figcaption></figure>
<figure><img src="image_4.png" /><figcaption>Fig. 2. Khaya ivorensis (a) Tree; (b) Board; (c) Planchet; (d) Sample.</figcaption></figure>

<figure><img src="image_5.png" /><figcaption>Fig. 3. Test setup for (a) 4-point bending; (b) compression.</figcaption></figure>

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

Properties of studied species.</caption><thead><tr><th rowspan="2">Species</th><th colspan="2">Literature values [32,39]</th><th colspan="2">Test values</th></tr><tr><th><b>Magnolia</b><br><b>Obovata</b></th><th><b>Khaya</b><br><b>Ivorensis</b></th><th><b>Magnolia</b><br><b>Obovata</b></th><th><b>Khaya</b><br><b>Ivorensis</b></th></tr></thead><tbody><tr><td>Density (kg/m<sup>3</sup>)</td><td>450—550</td><td>500—680</td><td>448—480</td><td>765—789</td></tr><tr><td>Hardness</td><td>1.1</td><td>2.4</td><td>—</td><td>—</td></tr><tr><td>Static MOE<br>(GPa)</td><td>7.5—10.3</td><td>9.5</td><td>11.1—12.2</td><td>8.9—10.3</td></tr><tr><td>BING© MOE<br>(GPa)</td><td>—</td><td>—</td><td>9.1—10.2</td><td>8.1—11.3</td></tr><tr><td>f<sub>m</sub>(MPa)</td><td>59—82</td><td>85</td><td>87—101</td><td>77—99</td></tr><tr><td>f<sub>c.0</sub>(MPa)</td><td>31—43</td><td>46</td><td>36—42</td><td>42—50</td></tr><tr><td>Withdrawal</td><td>10—13</td><td>12—13</td><td>—</td><td>—</td></tr></tbody></table>

MOE: Young's modulus measured in bending; $f_m$: bending strength; $f_{c.0}$ compressive strength parallel to grain [40].

follows:

$$ \hat{s}_g(x, y, \theta) = \int_{-\infty}^{+\infty} \int_{-\infty}^{+\infty} s(\eta, \xi)g(x - \eta, y - \xi)e^{-2\pi\xi(x\cos\theta + y\sin\theta)} d\eta d\xi \# \quad (1) $$

where $s$ is the grayscale distribution of the image and $g$ a window centered on the pixel with coordinates $(x, y)$ where $\hat{s}_g(x, y, \theta)$ is calculated. It was shown in [45] and [47] that the Gaussian window is the best compromise between different constraints. It is given by the following function:

$$ g(x, y) = \frac{1}{2\pi\sigma^2} e^{-\left(\frac{x^2 + y^2}{2\sigma^2}\right)} \# \quad (2) $$

where $\sigma$ is the standard deviation of the Gaussian. Displacements along the x and y directions, designated by $u_x$ and $u_y$, respectively, are proportional to the phase change between the current (or deformed) image

<figure><img src="image_6.png" /><figcaption>Fig. 4. Shape and dimensions of modified MMCG specimen [43].</figcaption></figure>

and the reference image [48].

$$ \underline{u}(\underline{x}) = -\frac{p}{2\pi} \left( \underline{\Phi}^{\text{cur}}(\underline{x} + \underline{u}(\underline{x})) - \underline{\Phi}^{\text{ref}}(\underline{x}) \right) \# \quad (3) $$

where $u$ represents the displacement vector of the components $u_x$ and $u_y$ in the base $(x, y)$. $\underline{\Phi}^{\text{cur}}$ and $\underline{\Phi}^{\text{ref}}$ denote the current and reference phase vectors of the components $\underline{\Phi}_x^{\text{ref}}$, $\underline{\Phi}_y^{\text{ref}}$ and $\underline{\Phi}_x^{\text{cur}}$, $\underline{\Phi}_y^{\text{cur}}$ in the $(x, y)$ base, respectively.

### 2.3.3. Specimen preparation

The use of LSA requires the deposition of a checkerboard pattern on the surface of the test specimen. Here, a laser engraver has been used for this purpose. This checkerboard pattern is etched after two coats of white paint have been applied to the specimen surface. To prepare our test specimens (Fig. 5), we used white paint (Spartex RAL 9010).

On each test specimen, two checkerboards were engraved: a 30 µm – square width checkerboard on the first side and a large 70 µm – square width checkerboard on the second. The parameters used to etch the two patterns are given in Table 2.

### 2.3.4. Experimental setup

A Zwick/Roel type tension-compression machine, with a loading capacity of 200 kN and mounted with a 50 kN load cell, was used to carry out the tests.

Two cameras (one on each side of the test specimen) were used to capture images of the checkerboard during the tests. Lights were used to obtain a good illumination of the test specimen surfaces and maximize image contrasts. Fig. 6 shows the complete experimental set-up.

A steel Arcan system was used for the tests. The shape of the Arcan system leaves a gap in the middle, so that the checkerboard pattern
<figure><img src="image_7.png" /><figcaption>Fig. 5. (a) Paint; (b) Specimen surface after painting; (c) Checkerboard.</figcaption></figure>

<table><caption>**Table 2**
Small and large checkerboard features.</caption><thead><tr><td>Features</td><td>Small checkerboard</td><td>Large checkerboard</td></tr></thead><tbody><tr><td>Pattern size (μm)</td><td>30</td><td>70</td></tr><tr><td>Laser power</td><td>70</td><td>40</td></tr><tr><td>Sweep speed</td><td>3600</td><td>5600</td></tr><tr><td>Pulse frequency</td><td>60</td><td>40</td></tr><tr><td>Number of repetitions</td><td>20</td><td>10</td></tr></tbody></table>

<figure><img src="image_8.png" /><figcaption>Fig. 6. Experimental setup.</figcaption></figure>

engraved on the specimens is visible; it is suitable for all stress modes, including mixed mode with its different stress angles [43]. The test machine's movable jaw (upper jaw) is controlled by a 0.05 mm/s imposed displacement. *Magnolia Obovata* and *Khaya Ivorensis* specimens were tested in mode I and mixed mode at 15°, 30° and 45°. The 12 mm-thick specimens were tested at 13 % moisture content.

## 2.4. Charpy impact tests

The Charpy impact test consists in striking a specimen at its center by a pendulum hammer to measure the energy absorbed during fracture. This reflects the material's ability to withstand an impact [49]. The experimental protocol for the Charpy test is described in standard NF

ISO 13061-1. *Magnolia obovata* and *Khaya ivorensis* boards were first machined to obtain specimens 10x10x80 (mm³), the dimensions recommended by the standard (Fig. 7). After machining, the specimens were stored in a controlled environment at 20 to 22 °C. Charpy pendulum impact tests were then carried out on the specimens using a CEAST 9050 type machine capable of delivering energy ranging from 0.5 to 50 J. Specimen moisture content was 12 %.

# 3. Results and discussion

## 3.1. Crack evolution

The cracking tests carried out enabled us to obtain images of the specimens as the crack lengthened. Cameras 1 and 2 (named CAM 1 and CAM 2 respectively) each captured one image per second. By pooling the information provided by each camera, we were able to faithfully retrace the course and direction of the crack at all times (Figs. 8 and 9). Visually, we can see that the crack follows the orientation of the fibers [50].

## 3.2. Force-crack opening curve

The values obtained after fracture tests enabled us to plot force-crack opening curves for the specimens tested (Fig. 10).

The curves for *Magnolia obovata* show a rapid initial progression of force versus displacement for all three specimens (M1P11, M1P13, M1P14) and a sudden drop in force after the maximum, probably indicating frank cracking or cleavage in the material. The curves for *Khaya ivorensis* also show a gradual rise in force with opening, but the elastic zone is wider than for *Magnolia obovata*. After the force peak, *Khaya ivorensis* curves show a gentler descent than those of *Magnolia obovata*, indicating a more gradual cracking process.

Table 3 shows the maximum breaking forces and the corresponding crack opening displacements for three specimens of *Khaya ivorensis* and three specimens of *Magnolia obovata*. For *Magnolia obovata*, the average peak force is 199 ± 31 N, with an average crack opening of 1.42 ± 0.14 mm. For *Khaya ivorensis*, the corresponding values are 454 ± 86 N and 4.52 ± 0.76 mm. These results, in relation to the force-displacement curves, clearly reveals that the forces at failure for *Khaya ivorensis* are significantly higher than for *Magnolia obovata*, as well as crack opening values. This indicates that *Khaya ivorensis* can

<figure><img src="image_9.png" /><figcaption>Fig. 7. (a) CHARPY testing machine; Specimens after testing (b) *Magnolia obovata*; (c) *Khaya ivorensis*.</figcaption></figure>
<figure><img src="image_10.png" /><figcaption>Fig. 8. Images at $t = 0$s, $t = 250$s and $t = 350$s for specimen M1P11 (CAM 1).</figcaption></figure>

<figure><img src="image_11.png" /><figcaption>Fig. 9. Images at $t = 0$s, $t = 750$s and $t = 1000$s for specimen K1P55 (CAM 2).</figcaption></figure>

<figure><img src="image_12.png" /><figcaption>Fig. 10. Force-crack opening curves for (a) *Magnolia obovata* and (b) *Khaya ivorensis* specimens (Mode I).</figcaption></figure>

<table><caption>**Table 3**
Maximum breaking forces values and corresponding crack opening for *Magnolia obovata* and *Khaya ivorensis*.</caption><thead><tr><th rowspan="2">Species</th><th rowspan="2">Specimen</th><th colspan="2">Max Breaking strength (N)</th><th colspan="2">Corresponding crack opening (mm)</th></tr><tr><th>Breaking strength</th><th>Average ± standard deviation</th><th>Crack opening</th><th>Average ± standard deviation</th></tr></thead><tbody><tr><td rowspan="3">Magnolia obovata</td><td>M1P11</td><td>228</td><td rowspan="3">199 ± 31</td><td>1.56</td><td rowspan="3">1.42 ± 0.14</td></tr><tr><td>M1P13</td><td>203</td><td>1.29</td></tr><tr><td>M1P14</td><td>167</td><td>1.42</td></tr><tr><td rowspan="3">Khaya ivorensis</td><td>K1P21</td><td>429</td><td rowspan="3">454 ± 86</td><td>4.20</td><td rowspan="3">4.52 ± 0.76</td></tr><tr><td>K1P23</td><td>550</td><td>5.39</td></tr><tr><td>K1P55</td><td>383</td><td>3.98</td></tr></tbody></table>

withstand higher stresses before breaking. It is therefore stronger and more resistant than *Magnolia obovata*. For illustrative purposes, the highest individual values were 550 N for *Khaya ivorensis* (specimen K1P23) and 228 N for *Magnolia obovata* (specimen M1P11).

With $\alpha = 15^{-\circ}$, *Magnolia obovata* samples show similar maximum forces between 1175 N and 1375 N, with progressive and more or less

abrupt breaks. *Khaya ivorensis* samples, meanwhile, show slightly higher maximum forces for some samples, except for K1P53_15, which hovers around 625 N. Crack openings before fracture are more varied, with fracture generally between 1.2 and 2.3 mm (see Fig. 11).
<figure><img src="image_13.png" /><figcaption>Fig. 11. Force-opening curves for (a) Magnolia obovata and (b) Khaya ivorensis specimens (Mixed Mode with α = 15°).</figcaption></figure>

### 3.3. Displacement and deformation maps

In order to determine the cracking parameters of Magnolia obovata and Khaya ivorensis, it is necessary to obtain crack advancement and crack opening values for all the samples tested. Displacement maps are used to determine crack openings, while strain maps are used to pinpoint the crack tip. Localized Spectrum Analysis (LSA) was used to obtain strain and displacement maps according to the methodology presented in section 2.3.2 [45]. Fig. 12 shows the strain (εyy) and displacement (Uy) maps for some Magnolia obovata and Khaya ivorensis specimens.

The displacement map for specimen M1P11 shows areas of sharp transition, which appear to mark the location of the crack, indicating significant displacement around this region. The displacement map for specimen K1P55, on the other hand, shows a bright region that seems to indicate less localized deformation, suggesting a more uniform displacement distribution. As for the deformation maps, the Magnolia obovata and Khaya ivorensis specimens show a distinct line of high deformation (indicated by dark yellow color), corresponding to the location of the crack. The surrounding areas show lower strains, indicating that the deformation is concentrated along the crack. Strain values are generally zero or close to zero, except in the vicinity of the crack, where high absolute values are observed.

At 15°, crack propagation for both woods is similar, but Khaya ivorensis shows less overall displacement compared to Magnolia obovata (Fig. 13).

### 3.4. Energy release rate

#### 3.4.1. Compliance method

The energy release rate represents the decrease in energy per unit area cracked, associated with crack propagation in a linear elastic material. For our work, the value of the critical energy release rate for the two species was calculated using the imposed displacement compliance method. Its formula is dependent on the loading mode considered. In crack-opening mode, it is given by the relationship [51]:

$$G_C = \frac{(F_{CI})^2}{2b} \times \left(\frac{\Delta C}{\Delta a}\right)_d \quad (4)$$

with FCI the critical forces corresponding to the peaks recorded on the force-crack opening curves (Fig. 14a), ΔC the compliance, Ui the crack opening, Δa the crack length and b the specimen thickness (b = 12mm for our study). Compliance is the ratio between the crack opening and the force that caused it. It is calculated using the following formula:

$$\Delta C = \frac{U_i - U_{i+1}}{F_i - F_{i+1}} \quad (5)$$

In mixed mode, the breaking modes are decoupled. The mixed mode fracture separation consists in determining the share of mode I and mode II in the cracking characteristics of the essences for different mixing angles. Formula (2) thus becomes [51,52]:

$$G_{CI} = \frac{(F_{Cy})^2}{2b} \times \left(\frac{\Delta C}{\Delta a}\right)_d \quad \text{and} \quad G_{CII} = \frac{(F_{Cx})^2}{2b} \times \left(\frac{\Delta C}{\Delta a}\right)_d \quad (6)$$

<figure><img src="image_14.png" /><figcaption>Fig. 12. Typical displacement Uy (a) and strain εyy (b) maps for Magnolia obovata and Khaya ivorensis specimens in mode I just before failure.</figcaption></figure>
<figure><img src="image_15.png" /><figcaption>Fig. 13. Typical displacement $U_y$ (a) and strain $\epsilon_{yy}$ (b) maps for Magnolia obovata and Khaya ivorensis specimens in mixed mode at 15° just before failure.</figcaption></figure>

<figure><img src="image_16.png" /><figcaption>Fig. 14. (a) Force-crack opening curve model; (b) Force projection along axes in mixed mode.</figcaption></figure>

with $F_{Cx}$ and $F_{Cy}$, the projections of the critical force, respectively on the axes (ox) and (oy) shown in Fig. 14b.

### 3.4.2. Critical energy release rate evaluation

In this section, values for the critical energy release rate $G_c$ are calculated for Magnolia obovata and Khaya ivorensis specimens. As wood is a highly heterogeneous material, it is subject to considerable natural variability from one species to another, and even within the same species. To investigate if the crack propagation occurs in the same way on both faces of a specimen, two cameras were used per test, one on each side of the specimen.

Applying the LSA to the data provided by each camera enabled us to obtain and compare crack advancement values ($\Delta a$), the quantities most likely to vary from one side of the specimen to the other. Table 4 shows the crack advancement values given by CAM 1 and CAM 2 for Magnolia obovata and Khaya ivorensis specimens. As a reminder, these are the $\Delta a$ corresponding to peaks (and therefore critical forces) used in the calculation of $G$.

This table shows that crack advance values vary slightly from CAM 1 to CAM 2 and that, for almost all *Khaya ivorensis* and *Magnolia obovata* specimens, crack advance $\Delta a$ is always higher for CAM 1 than for CAM 2. The difference between the $\Delta a$ obtained with CAM 1 and that obtained with CAM 2 varies between 2 and 6 % for *Khaya ivorensis* specimens and 5 to 6 % for *Magnolia obovata* specimens. There are several possible reasons for this difference in $\Delta a$ values. The first is the distance between the camera and the specimen. CAM 1 was positioned 70 cm away, enabling the entire specimen to be seen, while CAM 2 was positioned 20 cm from the specimen, enabling only the cracked part to be

seen (see Fig. 15). This leads to a lower spatial resolution on the displacements measured by CAM 1. This may explain why crack tip detection is less accurate with CAM 1 than with CAM 2.

On the other hand, the difference in checkerboard size (70 µm for CAM 1 and 30 µm for CAM 2) also affects the spatial resolution of the measurements, as a finer checkerboard (CAM 2) can detect smaller deformations more accurately, which results in smaller crack advance measurements compared to CAM 1. Figs. 16 and 17 show the energy release rate as a function of crack length $a$ for Magnolia obovata and Khaya ivorensis respectively, using data obtained from CAMs 1 and 2. Energy release rate values were calculated on the basis of the peaks observed on the force-crack opening curves of the specimens tested, each peak corresponding to a critical force $F_c$. Overall, the force-crack-opening curves of Magnolia obovata specimens show a very large number of peaks, while those of Khaya ivorensis specimens show fewer. This explains why there are more $G_c$ data for Magnolia obovata than for Khaya ivorensis. Comparing the graphs in Figs. 16 and 17, it is clear that CAM 1 and CAM 2 provide broadly similar results, but CAM 2 seems to capture more variation in some curves, which could be linked to the different positioning of the cameras or the different resolution of the checkerboards used.

Table 5 shows the minimum and maximum energy release rate values for Magnolia obovata and Khaya ivorensis specimens. According to this table, the energy release rate values of *Khaya ivorensis* are higher than those of Magnolia obovata, both in terms of minimum and maximum values. In fact, the average $G_{min}$ values for Magnolia obovata and *Khaya ivorensis* are 146 J/m² and 422 J/m² respectively, while the average $G_{max}$ values are 227 J/m² and 1070 J/m² respectively using
<table><caption>**Table 4**
Comparison of Δ a values given by CAM 1 and CAM 2 for some *Magnolia obovata* and *Khaya ivorensis* samples.</caption><thead><tr><th rowspan="2">Species</th><th rowspan="2">Specimens</th><th rowspan="2">Time</th><th rowspan="2">Fc(N)</th><th colspan="2">Δa(mm)</th><th rowspan="2">Difference (%)</th><th rowspan="2">Average (%)</th></tr><tr><th>CAM 1</th><th>CAM 2</th></tr></thead><tbody><tr><td rowspan="16">Magnolia obovata</td><td rowspan="8">M1P12</td><td>250</td><td>192</td><td>20.68</td><td>20.56</td><td>1</td><td rowspan="8">5</td></tr><tr><td>262</td><td>198</td><td>21.64</td><td>21.71</td><td>0</td></tr><tr><td>294</td><td>198</td><td>28.75</td><td>27.04</td><td>6</td></tr><tr><td>306</td><td>202</td><td>29.79</td><td>28.50</td><td>5</td></tr><tr><td>324</td><td>209</td><td>33.11</td><td>29.98</td><td>10</td></tr><tr><td>333</td><td>210</td><td>34.27</td><td>31.09</td><td>10</td></tr><tr><td>362</td><td>210</td><td>39.75</td><td>36.46</td><td>9</td></tr><tr><td>379</td><td>213</td><td>39.10</td><td>38.68</td><td>1</td></tr><tr><td>381</td><td>212</td><td>42.21</td><td>40.05</td><td>5</td></tr><tr><td>180</td><td>150</td><td>23.09</td><td>22.39</td><td>3</td><td rowspan="8">6</td></tr><tr><td rowspan="7">M1P14</td><td>183</td><td>148</td><td>23.23</td><td>22.56</td><td>3</td></tr><tr><td>199</td><td>152</td><td>26.01</td><td>25.23</td><td>3</td></tr><tr><td>214</td><td>155</td><td>27.38</td><td>25.99</td><td>5</td></tr><tr><td>227</td><td>156</td><td>29.14</td><td>26.61</td><td>10</td></tr><tr><td>241</td><td>157</td><td>29.64</td><td>27.92</td><td>6</td></tr><tr><td>345</td><td>177</td><td>43.89</td><td>39.91</td><td>10</td></tr><tr><td>358</td><td>174</td><td>43.43</td><td>41.57</td><td>4</td></tr><tr><td rowspan="15">Khaya ivorensis</td><td rowspan="5">K1P23</td><td>371</td><td>170</td><td>48.78</td><td>43.04</td><td>13</td><td rowspan="15">5</td></tr><tr><td>386</td><td>162</td><td>53.56</td><td>50.59</td><td>6</td></tr><tr><td>522</td><td>291</td><td>28.39</td><td>27.75</td><td>2</td></tr><tr><td>557</td><td>320</td><td>31.41</td><td>28.41</td><td>11</td></tr><tr><td>625</td><td>366</td><td>32.82</td><td>31.67</td><td>4</td></tr><tr><td rowspan="5">K1P55</td><td>968</td><td>535</td><td>51.06</td><td>49.29</td><td>4</td></tr><tr><td>1107</td><td>550</td><td>63.18</td><td>60.90</td><td>4</td></tr><tr><td>439</td><td>248</td><td>28.49</td><td>27.35</td><td>4</td><td rowspan="15">2</td></tr><tr><td>483</td><td>275</td><td>32.42</td><td>30.81</td><td>5</td></tr><tr><td>542</td><td>307</td><td>35.98</td><td>34.07</td><td>6</td></tr><tr><td>561</td><td>316</td><td>36.97</td><td>35.34</td><td>5</td></tr><tr><td>566</td><td>319</td><td>37.46</td><td>35.97</td><td>4</td></tr><tr><td>601</td><td>332</td><td>40.20</td><td>39.88</td><td>1</td></tr><tr><td>665</td><td>359</td><td>43.96</td><td>43.77</td><td>0</td></tr><tr><td>729</td><td>374</td><td>47.99</td><td>49.44</td><td>-3</td></tr><tr><td>739</td><td>373</td><td>50.60</td><td>50.52</td><td>0</td></tr><tr><td>754</td><td>371</td><td>51.73</td><td>52.83</td><td>-2</td></tr><tr><td>826</td><td>378</td><td>59.47</td><td>57.34</td><td>4</td></tr></tbody></table>

<figure><img src="image_17.png" /><figcaption>**Fig. 15.** Areas viewed by each camera: example of specimen M1P12 at t = 300 s (a) CAM 1; (b) CAM 2.</figcaption></figure>

CAM 1 data. Using CAM 2 data, $G_{min}$ values are 148 J/m² for *Magnolia obovata* and 436 J/m² for *Khaya ivorensis*, while $G_{max}$ values are 247 J/m² and 1101 J/m² respectively.

In mixed mode, after decoupling the modes, we have plotted G curves as a function of crack advance. The curves obtained in mixed mode at 15° and 30° are shown below (Figs. 18 and 19). Analysis of the curves for the 15° and 30° angles shows significant differences in energy release rate between *Khaya ivorensis* and *Magnolia obovata* species. Overall, mode I dominates energy dissipation at both angles, with much higher values than for mode II, reflecting the importance of this mode in crack propagation at these mixed angles. Mode I curves for *Khaya ivorensis* show significantly higher energy release, indicating greater resistance to mode I cracking than *Magnolia obovata*, for both angles studied (15° and 30°). This suggests that *Khaya ivorensis* has superior mechanical properties in this context of mixed crack propagation. Mode II, on the other hand, presents lower overall values, showing that this mode contributes less to energy dissipation at these angles. However, *Khaya ivorensis* continues to outperform *Magnolia obovata*, even for the mode II share, although the differences are less pronounced. This indicates that *Khaya ivorensis* has better mixed shear mode resistance, although the influence of mode II remains relatively modest. These results confirm those obtained by [43] and [41] in the sense that the greater the angle of mixing, the greater the share of mode II. *Khaya ivorensis* specimens show greater resistance to crack propagation than those of *Magnolia obovata*, whatever the angle of view (CAM 1 or CAM 2), which is consistent with the difference in density between the two species. It should be pointed out, however, that *Khaya ivorensis*'s high cracking and fracture performance is due to its highly ribboned cell structure, which enhances its performance, as shown by the results from [53].

### 3.5. CHARPY resilience tests

This section presents the results of the Charpy resilience test on *Khaya ivorensis* and *Magnolia obovata*. The first principle of thermodynamics states that energy is conserved: it can neither be created nor destroyed, but can only be transformed. Applied to wood, this principle establishes a relationship between the energy absorbed, the energy dissipated and the energy released. This relationship is given by:

$$U = E + F_{\#}, \qquad (7)$$

with U the energy absorbed, E the energy released and F the energy dissipated. Charpy resilience values are reported in Table 6, which shows that the average resilience of *Magnolia obovata* is 33.57 kJ/m², while that of *Khaya ivorensis* is 20.71 kJ/m².

This reflects the fact that *Magnolia obovata* has greater resilience than *Khaya ivorensis*, enabling it to absorb greater energy. Compared with *Magnolia obovata*, *Khaya ivorensis* absorbs less energy, but releases more.
<figure><img src="image_18.png" /><figcaption>Fig. 16. Mode I energy release rate versus crack length for Magnolia obovata and Khaya ivorensis specimens (CAM 1).</figcaption></figure>

<figure><img src="image_19.png" /><figcaption>Fig. 17. Mode I energy restitution rate versus crack length curves for Magnolia obovata and Khaya ivorensis specimens (CAM 2).</figcaption></figure>

<table><caption>**Table 5**
Minimum, maximum and average $G_c$ values for Magnolia obovata and Khaya ivorensis.</caption><thead><tr><th>Species</th><th>Specimens</th><th>Max value (J/m²)</th><th>Average (J/m²)</th><th>Min value (J/m²)</th><th>Average (J/m²)</th></tr></thead><tbody><tr><td rowspan="3">CAM 1<br>Magnolia obovata</td><td>M1P11</td><td>252</td><td rowspan="3">227 ± 22</td><td>196</td><td rowspan="3">146 ± 44</td></tr><tr><td>M1P12</td><td>219</td><td>128</td></tr><tr><td>M1P14</td><td>211</td><td>115</td></tr><tr><td rowspan="3">Khaya ivorensis</td><td>K1P21</td><td>1132</td><td rowspan="3">1070 ± 403</td><td>223</td><td rowspan="3">422 ± 266</td></tr><tr><td>K1P23</td><td>1438</td><td>724</td></tr><tr><td>K1P55</td><td>640</td><td>318</td></tr><tr><td rowspan="3">CAM 2<br>Magnolia obovata</td><td>M1P11</td><td>286</td><td rowspan="3">247 ± 34</td><td>198</td><td rowspan="3">148 ± 44</td></tr><tr><td>M1P12</td><td>222</td><td>128</td></tr><tr><td>M1P14</td><td>232</td><td>118</td></tr><tr><td rowspan="3">Khaya ivorensis</td><td>K1P21</td><td>1208</td><td rowspan="3">1101 ± 419</td><td>235</td><td rowspan="3">436 ± 268</td></tr><tr><td>K1P23</td><td>1489</td><td>740</td></tr><tr><td>K1P55</td><td>664</td><td>332</td></tr></tbody></table>

This means that it dissipates less energy than Magnolia obovata and is therefore less resistant to violent shocks. However, the high energy release rate of Khaya ivorensis gives it the ability to better resist cracking under load, which is an asset in mobile structures subjected to vibration or cyclic loading.

This ability improves the dynamic performance of structures, notably energy losses due to deformation, and promotes greater efficiency. For example, in systems such as vehicles or mobile structures exposed to load variations, this type of wood can contribute to stability while limiting mechanical wear. These advantages, coupled with the average resilience of Khaya ivorensis, make it a good candidate for use in mobility applications.

With $M_i$ designating Magnolia obovata samples and $K_i$ designating Khaya ivorensis samples.

### 3.6. Microscopic analysis

The scanning electron microscope (SEM) is an imaging instrument that uses a beam of electrons to scan the surface of a sample. Numerous SEM models have been marketed since the very first, designed in 1935 by Knoll [54]. Unlike optical microscopes, which use visible light, the SEM uses electrons, enabling much higher resolution, often in the
<figure><img src="image_20.png" /><figcaption>Fig. 18. Energy release rate as a function of crack length in mixed mode at 15°: mode I (a) and mode II (b) shares.</figcaption></figure>

<figure><img src="image_21.png" /><figcaption>Fig. 19. Energy release rate as a function of crack length in mixed mode at 30°: mode I (a) and mode II shares (b).</figcaption></figure>

<table><caption>**Table 6**
Magnolia obovata and Khaya ivorensis resilience values.</caption><thead><tr><th>Specimens</th><th>Width (mm)</th><th>Thickness (mm)</th><th>Absorbed energy (%)</th><th>Angle (°)</th><th>Resilience (kJ/m²)</th><th>Average resilience (kJ/m²)</th></tr></thead><tbody><tr><td>M1</td><td>10.51</td><td>10.78</td><td>8.32</td><td>-135.00</td><td>36.69</td><td>33.57 ± 2.71</td></tr><tr><td>M2</td><td>10.42</td><td>10.56</td><td>6.73</td><td>-137.45</td><td>30.57</td><td></td></tr><tr><td>M3</td><td>10.90</td><td>10.61</td><td>7.99</td><td>-135.50</td><td>34.52</td><td></td></tr><tr><td>M4</td><td>10.44</td><td>10.80</td><td>7.02</td><td>-137.00</td><td>31.1</td><td></td></tr><tr><td>M5</td><td>10.24</td><td>10.50</td><td>6.67</td><td>-137.55</td><td>30.99</td><td></td></tr><tr><td>K1</td><td>10.47</td><td>10.51</td><td>4.25</td><td>-141.60</td><td>19.32</td><td>20.71 ± 7.30</td></tr><tr><td>K2</td><td>10.67</td><td>10.62</td><td>3.82</td><td>-142.35</td><td>16.85</td><td></td></tr><tr><td>K3</td><td>10.50</td><td>11.04</td><td>7.37</td><td>-136.45</td><td>31.77</td><td></td></tr><tr><td>K4</td><td>10.36</td><td>10.58</td><td>2.73</td><td>-144.30</td><td>12.45</td><td></td></tr><tr><td>K5</td><td>10.34</td><td>10.80</td><td>5.17</td><td>-140.05</td><td>23.14</td><td></td></tr></tbody></table>

nanometer range. When interacting with the sample, electrons generate various signals: secondary electrons, backscattered electrons, X-rays, etc. [55], which are then converted into detailed images of the sample surface. SEM is particularly useful for studying the topography, morphology and composition of materials, providing a precise view of their microscopic structure.

Prior to the observations, the samples were prepared by a process known as “metallization”. Carbon metallization of wood samples for SEM observation improves their electrical conductivity, as wood is an insulating material. First, the sample is carefully dried to remove any moisture, then fixed to a support with a conductive glue. Next, it is placed in a vacuum chamber where sputtering takes place. An inert gas, such as argon, is ionized to bombard a carbon target, dislodging atoms

that are deposited in a thin, uniform layer on the sample, typically between 5 and 20 nm. This layer dissipates the electrical charges accumulated during interaction with the SEM electron beam, without disturbing the image. Carbon metallization offers good conductivity without interfering with observation quality, unlike other metals which can cause undesirable contrasts.

Fig. 20a and Fig. 20b show an overview of the cracked surface of Magnolia obovata and Khaya ivorensis samples. The anisotropic structure of the wood, marked by longitudinally oriented woody rays and vessels, creates zones of weakness along these orientations.

In cracking tests on Magnolia obovata, cracks tend to follow the longitudinal direction of the fibers, exploiting the lower strength in this direction compared to the radial and tangential directions. This
<figure><img src="image_22.png" /><figcaption>Fig. 20. Overview of the cracked surface of the (a) *Magnolia obovata*; (b) *Khaya ivorensis*.</figcaption></figure>

behavior is typical of woods where longitudinally oriented fibers guide crack propagation, which can lead to more localized and less diffuse fractures. Unlike *Magnolia obovata*, *Khaya ivorensis* shows a more complex cell structure with regular perpendicular crossings between tracheids and woody rays. This organization creates a barrier to crack propagation, enabling cleaner, more controlled breakage. This resistance is attributable to the ability of the crossed structures to redistribute stress and deflect cracks, preventing fibrous rupture and limiting spalling. A new criterion of fracture is needed in such a material submitted to mixed mode loading notably when the Mode II shear fracture is dominating [56].

*Magnolia obovata* and *Khaya ivorensis* show distinct fracture behaviors influenced by their unique microscopic structures. *Magnolia obovata*, with its predominantly longitudinal fibers and tracheids vulnerable to breakage along the fiber direction, exhibits a more localized and anisotropic breakage facies. *Khaya ivorensis*, on the other hand, thanks to its cross-banded cell structure, CaCO₃ mineral inclusions, and concentration of woody rays, shows increased resistance to crack propagation, leading to sharper, more predictable fractures.

## 4. Conclusion

This paper presents the research conducted to assess the feasibility of *Khaya ivorensis* as a viable alternative to *Magnolia obovata* for space mobility applications by analyzing and comparing their cracking behavior. The findings of this study provide substantial insights in response to the initial research objectives.

Bending, tensile, compression, and BING tests performed on *Khaya ivorensis* and *Magnolia obovata* enabled a comprehensive characterization of these species, thereby enriching the existing literature while highlighting key differences. The integration of modified MMCG specimens, which allow for the observation of a stable crack propagation range, in conjunction with an innovative image analysis technique (LSA), represents a significant methodological advancement. Typical displacement and strain maps were processed using LSA, while the compliance method was employed to determine the energy release rates for each specimen, offering a refined understanding of the fracture mechanisms governing these materials.

The results showed a slight, albeit small, difference between the crack evolution on the two faces of the specimens tested. The mode I and mixed-mode fracture and cracking strengths given by *Magnolia obovata* specimens remain lower than those given by *Khaya ivorensis* specimens, which is consistent with their density orders, but mainly due to the ribbon-like structure of *Khaya ivorensis*, which makes it a highly fracture-resistant material. However, *Khaya ivorensis* has a lower energy absorption capacity than *Magnolia obovata*, making it less resistant to

impact, even if its resilience is average. Scanning electron microscope observations revealed the influence of the anatomy of the species studied on their cracking behavior. Thus, in a context of mobility where structures are subject to significant stress, we consider on the basis of the data obtained that *Khaya ivorensis* may be an alternative to *Magnolia obovata*.

However, further studies are needed to confirm this. These include carrying out numerical calculations using CAST3M software to confirm the results obtained experimentally, assessing the cracking characteristics of *Khaya ivorensis* under variations in temperature and humidity, running simulations on *Khaya ivorensis* under spatial conditions and evaluating the impact of ageing and repeated stress on the durability of *Khaya ivorensis*. It would also be a good idea to extend this study to other species such as Alder, the second species selected for this work, but not yet tested. In addition, the MMCG specimen can be optimized to prevent fillet fracture during testing. This could be achieved either by modifying the shape or dimensions of the current MMCG specimen, or by starting with a new specimen geometry, while maintaining specimen stiffness and stable crack propagation for all loading modes. Finally, the fracture behavior under a dominating Mode II shear loading could be a significant parameter allowing to compare the fracture toughness of the two species.

## CRediT authorship contribution statement

**Riccardo Houngbegnon:** Writing – review & editing, Writing – original draft, Visualization, Software, Methodology, Investigation, Formal analysis, Data curation. **Rostand Moutou Pitti:** Writing – review & editing, Visualization, Validation, Supervision, Project administration, Methodology, Investigation, Funding acquisition, Conceptualization. **Valery Doko:** Supervision, Project administration. **Thomas Jailin:** Writing – review & editing, Supervision, Software. **Benoît Blaysat:** Writing – review & editing, Supervision, Software, Project administration, Methodology, Conceptualization. **José Xavier:** Writing – review & editing, Supervision, Project administration, Investigation. **Nicolas Sauvat:** Supervision, Methodology. **Joseph Gril:** Supervision, Project administration. **Naman Recho:** Writing – review & editing, Validation, Supervision.

## Declaration of competing interest

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

The authors would like to thank the CIT ITPS CAP 2025 program (UCA) and the Auvergne Rhône Alpes Region through the WoodMob project for supporting this work. This research was also supported by the Foundation for Science and Technology (FCT, IP) under the project UID/00667.

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