## 2 Mechanical Properties of Aluminum, CFRP Layers, and CFRP-Aluminum Lamination
### Mechanical Properties of CFRP Layers  
Two kinds of commercially available, high-strength cloth carbon fiber sheets were used to investigate the strengthening effects of TSTs under dynamic loads, namely UT70-20 and BT70-20, as shown in Figure 3. UT70-20 is a one-directional carbon fiber sheet (0\({}^{\circ}\) fiber orientation angle) and is used to strengthen the circumferential direction of TSTs; whereas, BT70-20 is a two-directional carbon fiber sheet (0\({}^{\circ}\)/90\({}^{\circ}\) fiber orientation angle) and is used to strengthen the circumferential and vertical directions of TSTs. The carbon fiber was produced in Tokyo, Japan, by Toray Industries, Inc. [33]. Shaped like a sheet, this material is easy to handle and impregnate with resin. The properties of this material were obtained from the manufacturer and are shown in Table 3. The epoxy resin, namely E810 LS (product of Konishi, Osaka, Japan), was adopted to form the CFRP laminates that covered the TSTs. The carbon fiber sheets were bonded with the shells of TSTs using E810 LS epoxy via the vacuum-assisted resin transfer molding (VaRTM) method [34]. The elastic modulus and Poisson's ratio of E810 LS epoxy are 3 (GPa) and 0.37, respectively, according to the manufacturer's measurements.  
The carbon fiber sheets were combined by impregnating epoxy to create CFRP layers that covered the outside of the TSTs. The material properties of the CFRP layers were calculated according to the rules of laminae and laminates for composite materials [35], as shown in Equations (1)-(5):  
\[E_{x}=v_{f}E_{f}+v_{m}E_{m}, \tag{1}\]  
\[E_{y}=\frac{1}{\frac{v_{f}}{E_{f}}+\frac{v_{m}}{E_{m}}}, \tag{2}\]  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Specimen** & **Y1** & **Y2** & **Y3** & **Y4** & **Y5** & **Average value** \\ \hline Elastic modulus (MPa) & 69,620.6 & 70,307.2 & 70,684.1 & 68,923.6 & 66,252.4 & 69,157.6 \\ \hline \hline \end{tabular}
\end{table}
Table 2: The calculated elastic modulus of the aluminum plates in the vertical direction.  
Figure 3: Carbon fiber sheets.  
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multirow{2}{*}{**Type**} & **Direction of Fiber** & **Sheet Thickness** & **Fiber Weight (gm/m\({}^{2}\))** & **Density (gr/cm\({}^{3}\))** & **Elastic Modulus (GPa)** & **Tensile Strength (GPa)** \\ \hline BT70-20 & 0 & 0.056 & 100 & 1.8 & 245 & 2.9 \\  & 90 & 0.056 & 100 & 1.8 & 245 & 2.9 \\ \hline UT70-20 & 0 & 0.111 & 200 & 1.8 & 245 & 3.4 \\ \hline \hline \end{tabular}
\end{table}
Table 3: Characteristics of the carbon fiber sheets.  
\[G_{xy}=\frac{1}{\frac{v_{f}}{G_{f}}+\frac{v_{m}}{G_{m}}}, \tag{3}\]  
\[G_{f}=\frac{E_{f}}{2(1+v_{f})},G_{m}=\frac{E_{m}}{2(1+v_{m})}, \tag{4}\]  
\[v_{xy}=v_{f}v_{f}+v_{m}v_{m}, \tag{5}\]  
where \(E_{f}\) and \(E_{m}\) are the elastic moduli of the carbon fiber and epoxy, respectively; \(v_{xy}\) is the major Poisson ratio; \(v_{f}\) and \(v_{m}\) are the volume fractions of the fiber and epoxy, respectively; and \(v_{f}\) and \(v_{m}\) are the Poisson ratios of the carbon fiber and epoxy, respectively. In addition, \(E_{x}\) and \(E_{y}\) denote the elastic modulus of the CFRP laminae in the circumferential and vertical directions, respectively, after covering the TSTs, and \(G_{xy}\) represents the shear modulus of the CFRP laminate. Table 4 shows the properties of 0\({}^{\circ}\)/90\({}^{\circ}\) and 0\({}^{\circ}\) CFRP layers, which are denoted by 0\({}^{\circ}\)/90\({}^{\circ}\) and 0\({}^{\circ}\), respectively. In the table, \(t_{f}\) and \(t_{m}\) are the thicknesses of the fiber and epoxy, respectively, and \(t_{c}\) is the total thickness of the CFRP layers.