## 3 Results and Discussion
In order to prevent the agglomeration of the epoxy resin and the HNT nanoparticles, it was dispersed using an ultrasonic dispersion device. An ultrasonic dispersion device was used to incorporate the cavitation effect into the composite material. Figure 4 shows the graph of mode II shear modulus with varying HNT content to evaluate mode II interlaminar fracture toughness of carbon fiber reinforced composite with HNT. The interfacial bond energy increased up to 3 wt % of HNT, but decreased at \(\geq\)5 wt % HNT content. The binding energy of HNT increased for 3 wt % at the interface, but at \(\geq\)5 wt %, the binding energy of HNT was concentrated due to the concentration of HNT. To evaluate the interfacial bond energy of HNT--reinforced carbon fiber reinforced composites and the strengthening effect of HNT addition, HNT was added to the epoxy resin to evaluate the strengthening effect of epoxy resin by HNT. Figure 5 shows the result of the tensile strength by adding HNT to the epoxy resin. The strength of the epoxy resin without HNT was 22 MPa, and the addition of HNT strengthened the effect by two to three times, confirming remarkable epoxy resin strengthening effect by the addition of HNT, and the increase in the tensile strength by addition increased the content of HNT to 5 wt %. In \(\geq\)5 wt % of test specimens, the strengthening effect gradually decreased with addition. Figure 4: Mode II shear modulus of CFRP according to HNT addition. Figure 5: Comparison of tensile strength of HNT added epoxy with HNT content. In order to investigate the correlation between the strengthening effect of HNT in epoxy resin and the mechanical properties of carbon fiber reinforced composite material by the addition of HNT by the improvement of interfacial bonding energy based on the results obtained above, the strength characteristic value of the epoxy resin reinforced with HNT, and the strength characteristics of carbon fiber were obtained by the theoretical strength of the composite material. The displacement and the strain of the composite laminate under load are different from those of the single layer composites, because of the interaction between the layers. In the composite laminate, the lamination angles are different for each layer, so the stiffness and strength are different for the same external force. The force and moment applied to the laminate can be obtained by integrating different forces and moments for each layer depending on the laminate thickness. Assuming the planar stress state of the laminates, the forces and moments applied to the laminates are as follows. \[\left( \begin{array}{c}N_{x}\\ N_{y}\\ N_{xy}\end{array} \right)=\sum_{k=1}^{N}\int_{Z_{k-1}}^{Z_{k}}\left( \begin{array} []{c}\sigma_{x}\\ \sigma_{y}\\ \tau_{xy}\end{array} \right)dz \tag{1}\]  
\[\left( \begin{array}{c}M_{x}\\ M_{y}\\ M_{xy}\end{array} \right)=\sum_{k=1}^{N}\int_{Z_{k-1}}^{Z_{k}}\left( \begin{array} []{c}\sigma_{x}\\ \sigma_{y}\\ \tau_{xy}\end{array} \right)zdz \tag{2}\]  
where \(N_{y}\) is the applied force per unit length of the laminate and \(M_{ij}\) is the applied force per unit length of the laminate. Figure 6 is the moment applied per unit length of the laminates. Here, the average stress of the composite material is given by the following equation, and \(t\) is the total thickness of the composite laminate. \[\overline{\sigma_{ij}}=\frac{N_{ij}}{t} \tag{3}\]  
To compare the strength of the theoretically strengthened composite with the actual strength, the fiber volume fraction was calculated to investigate the strength of the theoretical composite material. The fiber contents of composite specimens were tested in accordance with ASTM D 3171, and determined using the following formula. \[M_{fiber}=100\times\frac{m_{3}-m_{1}}{m_{2}-m_{1}} \tag{4}\]  
where \(m_{1}\), \(m_{2}\), \(m_{3}\) are the initial mass (g) of the dried container only, the mass of the container (g) containing the dried test specimen, and the mass of fiber (g), respectively.