## 2 Electro-Thermal Modeling and Analysis of Composite Materials Under Lightning Strike
### Finite Element Model
#### 2.2.2 Material Properties and Damage Assessment Criteria  
As a high-performance composite material, CFRP exhibits significant anisotropic behavior. Its electrical and thermal conductivities vary with fiber orientation (longitudinal and transverse) and through-the-thickness direction. In this study, a homogenization approach was employed, where the properties of fibers and epoxy resin were integrated into equivalent layer properties, rather than modeling each constituent separately. The temperature-dependent properties of the laminate, such as specific heat, density, and electrical conductivity, are crucial for accurately grasping the material's thermal response characteristics under electro-thermal coupling conditions. Tables 1-3 present the temperature-dependent material properties [13; 20; 21; 22].  
\begin{table}
\begin{tabular}{c c c c c c} \hline \multirow{2}{*}{**Temperature/\({}^{\circ}\)C**} & \multirow{2}{*}{**Specific Heat/** \(\mathbf{J\cdot kg^{-1.}}^{\circ}\mathbf{C^{-1}}\)**} & \multicolumn{3}{c}{**Thermal Conductivity/W\(\cdot\)m\({}^{-1.}\)\({}^{\circ}\)C\({}^{-1}\)**} \\ \cline{3-6}  & & **Longitudinal** & **Transverse** & **Thickness** & **Density/kg\(\cdot\)m\({}^{-3}\)** \\ \hline
25 & 1065 & 11.8 & 0.609 & 0.609 & 1520 \\
330 & 2050 & 6.02 & 0.31 & 0.31 & 1520 \\
360 & 4250 & 5.46 & 0.28 & 0.28 & 1520 \\
500 & 4200 & 2.8 & 0.14 & 0.14 & 1170 \\
525 & 1800 & 2.33 & 0.12 & 0.12 & 1170 \\
815 & 1850 & 1.4 & 0.072 & 0.072 & 1170 \\
3316 & 2300 & 1.4 & 0.072 & 0.072 & 1170 \\ \(>\)3316 & 100,000 & 0.02 & 0.02 & 0.02 & 1170 \\ \hline \end{tabular}
\end{table}
Table 1: Density, specific heat, and thermal conductivity of laminate with temperature changes [13; 20].  
Figure 1: Meshing, lightning current loading, and boundary conditions.  
When assessing the lightning-induced damage in CFRP composites, the material's phase transition behavior at specific temperatures significantly alters its physical properties, thereby influencing the distribution of heat within the material. Non-uniform thermal distribution can result in localized overheating and subsequent damage. [PERSON] et al. [11] extensively investigated the behavior of carbon fibers and epoxy resin matrix in CFRP at various temperatures using thermogravimetric analysis (TGA), providing specific temperature thresholds for damage determination. When lightning strikes induce high temperatures, the thermal behavior of CFRP can be delineated into several critical stages: When the temperature rises to approximately 250-300 \({}^{\circ}\)C, resin begins to degrade thermally, causing localized ablation damage on the laminate. As the temperature continues to increase to about 600 \({}^{\circ}\)C, the resin undergoes complete thermal decomposition, leading to delamination within the laminate. Further temperature rise causes the resin to vaporize, while carbon fibers, exhibiting higher temperature resistance compared to the resin, decompose at approximately 3000 \({}^{\circ}\)C. Beyond this temperature, dielectric breakdown occurs at interlayer gaps, causing a sharp increase in through-thickness electrical conductivity. As carbon fibers fracture due to decomposition, Joule heating is prevented. Therefore, areas with temperatures exceeding 250 \({}^{\circ}\)C are considered to have experienced ablation damage due to the thermal degradation of epoxy resin.