# Modelling of High-Velocity Impact on Woven Carbon Fibre-Reinforced Plastic Laminate
## 4 Simulation Results
\begin{table}
\begin{tabular}{c c} \hline \hline Velocity curve intercept, \(c\) & 3230 m/s \\ First slope coefficient, \(S_{1}\) & 0.92 \\ Grüneisen coefficient, \(\gamma_{0}\) & 0.84 \\ First-order volume correction coefficient, \(a\) & 0.50 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Mie–Grüneisen EOS measured in the through thickness direction for CFRP composite [41]. \begin{table}
\begin{tabular}{c c} \hline \hline Density & 7.923 g/cm\({}^{3}\) \\ Shear modulus, G & 77 GPa \\ A & 340 MPa \\ B & 500 MPa \\ m & 1.0 \\ N & 0.35 \\ Specific heat & 423 J/kg K \\ Melting temperature & 2380 K \\ Ambient temperature & 293 K \\ D\({}_{\text{i}}\) & 0.0 \\ \hline \hline \multicolumn{3}{c}{**Mie–Grüneisen EOS–Type 4**} \\ \hline Velocity curve intercept, \(c\) & 4.57 km/s \\ First slope coefficient, \(S_{1}\) & 1.29 \\ Grüneisen coefficient, \(\gamma_{0}\) & 1.93 \\ First-order volume correction coefficient, \(a\) & 0.5 \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Material properties for SS304 steel sphere [42]. The simulation results agree well with the experimental observation, particularly in the top half (impact side) of the composite target. The constitutive model underestimated the size of the damaged area at the back of the target plate, which can be attributed to quasi orthotropic material properties. Consequently, the model was stiffer in the fibre directions, so that initiation of the dominant failure mechanism (fibre failure in tension) was delayed. Another explanation could be that the structural response of the plate is not as localised as for the higher impact velocities, so that boundary conditions contributed to the plate response and damage extent. A similar comparison was conducted for the impact at 354 m/s (the shear-dominated failure mode); see Figure 9. The simulations predicted an increasing size of the damaged area through the thickness of the target plate, which suggests a conical shape of the damaged zone in the through thickness cross-section. And the shape agrees well with the experimental data. However, the constitutive model overestimated the magnitude of the damaged area in the top half of the target plate but shows a good agreement in the rear part of the target. Simulation results for the impact at 1199 m/s are shown in Figures 10 and 11 and reported in Table 6. The latter consists of the hole diameters measured in two principal  
Figure 8: Damage area calculated from simulation results and XCT data for the normal impact at 194 m/s. Figure 9: Damage area calculated from simulation results and XCT data for the normal impact at 354 m/s. material directions, denoted \(x_{1}\) and \(x_{2}\), and the size of the maximum visible delamination in two principal material directions on the impact side and the rear side, which are denoted with \(y_{1}\) and \(y_{2}\). Figure 11: Simulation results for damage distribution for impact at 1200 m/s in the 6 mm thick CFRP: at t = 20 \(\upmu\)s.  
Figure 10: Simulation results for damage distribution in 6 mm thick CFRP after impact at 1199 m/s; t = 20 \(\upmu\)s.  
Wide damage zone and delamination were obtained in the top and bottom plies of a target plate, resulting in an hourglass shape of the damaged zone in the cross-section of the target plate. This numerical result was compared to the post-impact C scans of the A3 specimen, as shown in Figure 12.  
The results compared well with the experimental observation in terms of the following:  
* The calculated average diameter of the hole was within 4%. * The hourglass shape of the delaminated zone was captured within the simulation. * There was a bigger delamination zone at the back of the target plate in comparison to the front and the middle plies. * The numerically obtained size of the delamination zone at the back of the target was within 8% of the experimental measures in the principal material direction. * The model overestimated the size of the delamination zone in the minor material direction, particularly on the rear side of the plate.