# Delamination Localization in Multilayered CFRP Panel Based on Reconstruction of Guided Wave Modes
## 2 Materials and Methods  
### Modeling Setup  
For inspection, a multilayered CFRP plate measuring 450 mm in length and 3.5 mm in thickness was selected. The investigated sample was manufactured from 18 plies of carbon fiber, and the orientation of the plies are (\(-45^{\circ}\), \(0^{\circ}\), \(+45^{\circ}\), \(0^{\circ}\), \(90^{\circ}\), \(0^{\circ}\), \(-45^{\circ}\), \(0^{\circ}\), and \(+45^{\circ}\))\({}^{2}\). The mechanical properties of the CFRP used in the numerical simulation are presented in Table 1. Here, \(E\) is [PERSON]'s modulus, \(G\) is the shear modulus, \(\
u\) is the [PERSON]'s ratio, \(\rho_{c}\) is the density of CFRP, and \(t_{ply}\) is the ply thickness. In this 2D model, the \(x\)-axis is along the fibers, the \(y\)-axis is along the thickness of the CFRP plate, and the \(z\)-axis is assumed to be infinitely long.  
The location of delamination was analyzed in two cases by placing the receivers before and after the delamination. In case 1, two receivers were placed at distances of 10 mm and 20 mm from the leading edge of the delamination. In case 2, three receivers were placed at distances of 10 mm, 20 mm, and 30 mm from the trailing edge of the delamination. The through-thickness location of the delamination (\(X_{h}\)) was 1.7 mm. The cases studied, the delamination and receiver position, and distances are presented in Table 2.  
The 2D simulation was performed to analyze a GW interaction with a delamination-type defect with a length of 20 mm. The delamination was located at 250 mm along the longitudinal direction and 1.7 mm in the thickness direction, as shown in Figure 1. The transmitter-receiver configuration was used to perform the inspection. A normal force was  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Property** & **Units** & **Value** \\ \hline Density & \(\rho_{c}\) & kg/m\({}^{3}\) & 1544 \\ Thickness & \(t_{ply}\) & mm & 0.194 \\ Young’s modulus & \(E_{1}\) & GPa & 131 \\ & \(E_{2}=E_{3}\) & GPa & 8 \\ Shear modulus & \(G_{12}=G_{13}\) & GPa & 4.5 \\ & \(G_{23}\) & GPa & 3.5 \\ Poisson’s ratio & \(\
u_{12}=\
u_{13}\) & - & 0.29 \\  & \(\
u_{23}\) & - & 0.47 \\ \hline \hline \end{tabular}
\end{table}
Table 1: The material properties of the CFRP [53; 54; 55].  
\begin{table}
\begin{tabular}{c c c c} \hline \hline \multirow{2}{*}{**Case**} & \multirow{2}{*}{\
\begin{tabular}{c} **Delamination Position** \\ **(X\({}_{d}\)) (mm)** \\ \end{tabular} } & \multicolumn{2}{c}{**Distance between**} & \multirow{2}{*}{
\begin{tabular}{c} **Distance between** \\ **and Receiver** \\ **(X\({}_{r}\)) (mm)** \\ \end{tabular} } \\  & & **(X\({}_{r}\)) (mm)** \\ \hline
1-1 & 250 & 230 & 20 \\
1-2 & 250 & 240 & 10 \\
2-1 & 250 & 280 & 10 \\
2-2 & 250 & 290 & 20 \\
2-3 & 250 & 300 & 30 \\ \hline \hline \end{tabular}
\end{table}
Table 2: Delamination position in the longitudinal direction.  
applied at the point-type excitation source to propagate the A\({}_{0}\) mode. To minimize the distortion of guided waves, a point-type excitation was selected. The excitation source was placed at 70 mm from the leading edge of the CFRP plate.