## 2 Mechanical Properties of Aluminum, CFRP Layers, and CFRP-Aluminum Lamination
### Mechanical Properties of the CFRP-Aluminum Composite Plates  
The mechanical properties of the CFRP-reinforced aluminum lamination were calculated based on the macro-mechanical components of laminates assuming that the CFRP layers and aluminum were perfectly bonded through the use of adhesives [35]. Furthermore, if a plate is thin and there are no out-of-plane loads, it can be considered to be under plane stress. Therefore, the properties of CFRP-reinforced aluminum lamination could be calculated according to plane stress conditions. The plane stress condition for CFRP-reinforced aluminum lamination is shown in Figure 4. Consider a laminate made of \(n\) piles, as shown in Figure 4. Each ply has a thickness of \(t_{k}\) and the thickness of the laminate is \(h\). The in-plane properties of the CFRP-reinforced steel lamination can be determined using Equations (6)-(12). Table 5 shows the resulting calculated mechanical properties of the CFRP-aluminum lamination. In the table, UT0 denotes the aluminum section strengthened using a 0\({}^{\circ}\) CFRP layer, whereas BT0/90 represents the aluminum section strengthened using a 0\({}^{\circ}\)/90\({}^{\circ}\) CFRP layer.  
\[\left[\begin{array}{c}c_{x}^{0}\\ c_{y}^{0}\\ c_{xy}^{0}\end{array}\right]=\left[\begin{array}{ccc}A_{11}^{\prime}&A_{12}^ {\prime}&0\\ A_{12}^{\prime}&A_{22}^{\prime}&0\\ 0&0&A_{66}^{\prime}\end{array}\right]\left[\begin{array}{c}N_{x}\\ N_{y}\\ N_{xy}\end{array}\right] \tag{6}\]  
\[E_{x}^{\prime}=\frac{\sigma_{x}}{\epsilon_{x}^{0}}=\frac{N_{x}/h}{A_{11}^{ \prime}\times N_{x}}=\frac{1}{A_{11}^{\prime}\times(t_{a}+t_{c})} \tag{7}\]  
\[E_{y}^{\prime}=\frac{\sigma_{y}}{\epsilon_{y}^{0}}=\frac{N_{y}/h}{A_{22}^{ \prime}\times N_{y}}=\frac{1}{A_{22}^{\prime}\times(t_{a}+t_{c})} \tag{8}\]  
\[G_{xy}^{\prime}=\frac{\sigma_{xy}}{\epsilon_{xy}^{0}}=\frac{N_{xy}/h}{A_{66}^ {\prime}\times N_{xy}}=\frac{1}{A_{66}^{\prime}\times(t_{a}+t_{c})} \tag{9}\]  
\[v_{xy}^{\prime}=-\frac{\epsilon_{y}^{0}}{\epsilon_{x}^{0}}=-\frac{A_{12}^{ \prime}\times N_{x}}{A_{11}^{\prime}\times N_{x}}=-\frac{A_{12}^{\prime}}{A_{1 1}^{\prime}} \tag{10}\]  
\begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline
**CFRP** & \(t_{f}\)**(mm) & \(t_{m}\)** & \(t_{c}\)**(mm) & \(v_{f}\)**(\%) & \(v_{m}\)**(\%) & \(E_{x}\) & \(E_{y}\) & \(G_{xy}\) & **Poisson’s** \\
**Layer** & **(mm)** & **(mm)** & \(t_{c}\)**(mm) & \(v_{f}\)**(\%) & \(v_{m}\)**(\%) & **(MPa)** & **(MPa)** & **(MPa)** & **Ratio** \\ \hline
0\({}^{\circ}\) & 0.111 & 0.139 & 0.25 & 44.4 & 55.6 & 110448 & 5343 & 1951 & 0.34 \\
0\({}^{\circ}\)/90\({}^{\circ}\) & 0.112 & 0.118 & 0.23 & 48.7 & 51.3 & 63601 & 63601 & 2111 & 0.031 \\ \hline \hline \end{tabular}
\end{table}
Table 4: The properties of 0\({}^{\circ}\)/90\({}^{\circ}\) and 0\({}^{\circ}\) orientations of the carbon fiber reinforced polymer (CFRP) layers.  
\[A_{ij}=\sum_{k=1}^{2}\left[\left(Q_{ij}\right)\right]_{k}\left(h_{k}-h_{k-1} \right),\;\;i=1,2,6;\;j=1,2,6 \tag{11}\]  
\[h=\sum_{k=1}^{n}t_{k} \tag{12}\]  
In Equations (6)-(12), (\(\sigma_{x}\), \(\sigma_{y}\), \(\sigma_{xy}\)) and (\(\varepsilon_{x}^{0}\), \(\varepsilon_{y}^{0}\), \(\varepsilon_{xy}^{0}\)) are the principal stress and mid-plane strain components associated with the \(x\)-\(y\) plane, respectively; \(t_{c}\) is the thickness of the CFRP layer; \(t_{a}\) is the thickness of the aluminum; and \(A_{ij}^{\prime}\) denotes the components of the inverse matrix \(A_{ij}\).