## 2 Experimental Procedure  
Figure 1 shows the specimen preparation process. We prepared Bisphenol F epoxy resin (di-epoxide terminated molecule), Amine curing agent (Diethylenetriamine, ST 12), and CNF 2 wt.% slurry (BiNFi-s, IMa-10002, Sugino machine Limited). These three solutions were mixed by a mechanical mixer and stirred twice, both before and after adding the curing agent, for 10 and 14 min, respectively. The rotation speed was 400 r/min or 2000 r/min. The volume fraction of CNF was controlled between 0 and 0.44 vol.% in the final epoxy-CNF composite. Afterwards, the solution was cured at 80 \({}^{\circ}\)C for 3 h. The cured specimens were cut to \(40\times 10\times 2\) mm\({}^{3}\) and polished for a three-point bending test. The flexural tests were performed according to the standard test method JIS K 7017 [10] under a three-point bend configuration, as shown in Figure 2. A load \(P\) was applied directly at the center of the specimen. In this study, loading nose and support roller diameters were \(R\) = 10 and 5 mm, respectively. The support span length was chosen to be \(s\) = 30 mm. We conducted flexural tests using an Autograph (SHIMAZU AG-50 kNNXD) with a 5 kN load cell at a displacement rate of 1 mm/min. We carried out five replications for each test. Figure 1: Schematic illustration of the specimen preparation process. The flexural stress (\(\sigma_{\mathrm{f}}\)), flexural strain (\(\varepsilon_{\mathrm{f}}\)), and flexural modulus (\(E_{\mathrm{f}}^{\mathrm{c}}\)) of the composite were estimated by the following equations:  
\[\sigma_{\mathrm{f}}\;=\;\frac{3 Ps}{2 bh^{2}} \tag{1}\]  
\[\varepsilon_{\mathrm{f}}\;=\;\frac{6\delta h}{s^{2}} \tag{2}\]  
\[E_{\mathrm{f}}^{\mathrm{c}}\;=\;\frac{s^{3}}{4 bh^{3}}\frac{P^{\prime\prime}\;- \;P^{\prime}}{\delta^{\prime\prime}\;-\;\delta^{\prime}} \tag{3}\]  
where \(l\) = 40 mm, \(b\) = 10 mm, \(h\) = 2 mm are the length, width, and thickness of the specimen, \(\delta\) is the deflection of the load point and the superscript c denotes the composite, respectively. To determine the flexural modulus, the deflections \(\delta^{\prime}\) and \(\delta^{\prime\prime}\), corresponding to the given values of the flexural strain, \(\varepsilon_{f}\)\({}^{\prime}\) = 0.0005 and \(\varepsilon_{f}\)\({}^{\prime\prime}\) = 0.0025, were obtained, respectively, using the following equations:  
\[\delta^{\prime}\;=\;\frac  
where \(\varepsilon_{xx}\), \(\varepsilon_{yy}\), \(\varepsilon_{zz}\), \(\varepsilon_{yz}\), \(\varepsilon_{zx}\), \(\varepsilon_{xy}\) are the strain components, \(\sigma_{xx}\), \(\sigma_{yy}\), \(\sigma_{zz}\), \(\sigma_{yz}\), \(\sigma_{zx}\), \(\sigma_{xy}\) are the stress components, \(E^{\rm c}\) is the [PERSON]'s modulus, \(\
u^{\rm c}\) is the [PERSON]'s ratio and \(G^{\rm c}\) is the shear modulus, respectively. The shear modulus \(G^{\rm c}\) is related to [PERSON]'s modulus and [PERSON]'s ratio by the following equation:  
\[G^{\rm c}\ =\ \frac{E^{\rm c}}{2(1\ +\ \
u^{\rm c})} \tag{7}\]  
The elastic properties of the epoxy-CNF composites were determined by the theoretical Halpin-Tsai model for short-fiber-reinforced composite materials [11; 12]. The model includes parameters, such as volume fraction (\(V^{\rm f}\)), length (\(l^{\rm f}\)), and diameter (\(d^{\rm f}\)) of the CNF. The superscript f refers to the CNF.