# Impact Response of Composite Sandwich Cylindrical Shells
## 3 Results
Nevertheless, because the deflection is lower due to the greater thickness of the shell, and consequent higher stiffness, it is expected that there will be a greater density of delaminations to absorb the same impact energy. On the other hand, smaller thicknesses promote greater deflections and, consequently, lower delamination density ([PERSON] et al., 2019). In fact, according to [PERSON] et al. (2019), thickness is one of the main parameters that determine the impact properties, in particular the perforation velocity or the perforation-threshold energy. However, as an alternative parameter, the literature suggests the areal density (mass per unit area), which has been studied by several authors ([PERSON] et al., 2019; [PERSON] et al., 2020; [PERSON] et al., 2020). A non-linear relationship between perforation-threshold energy and thickness was even proposed by [PERSON] et al. (2020). [PERSON] et al. (2020), for example, found that the perforation velocity varies linearly with the laminate thickness within the range of 3 to 14 mm, while [PERSON] et al. (2020) noticed a non-linear relationship for a wide range of thicknesses below 16 mm. Taking in account these studies, and considering the values shown in Table 4, the maximum load (P\({}_{\text{max}}\)) is plotted against the areal density in Figure 9. It is possible to observe a non-linear relationship between maximum load and areal density (thickness), which is in good agreement with the studies developed by [PERSON] et al. (2020), although the considered impact parameter by these authors is different (perforation-threshold energy). Considering only the six (6C) and eight (8C) layers of carbon, the absorbed energy per areal density is around 1.42 J/kg.m\({}^{-2}\) and 1.08 J/kg.m\({}^{-2}\), respectively. These results evidence that the effect of the thickness on the impact properties is determinant, because, while the absorbed energy increased by around 17%, the areal density increased about 53%. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multirow{2}{*}{**Laminates**} & \multicolumn{2}{c}{**Peak Load (N)**} & \multicolumn{2}{c}{**Max Displacement (mm)**} & \multicolumn{2}{c}{**Elastic Recuperation (J)**} \\ \cline{2-7}  & **Average** & **Std.** & **Average** & **Std.** & **Average** & **Std.** \\ \hline
8C & 1959 & 50 & 4.2 & 0.02 & 1.16 & 0.38 \\
6C & 924 & 12 & 7.8 & 0.19 & 1.71 & 0.19 \\
4C & 589 & 4 & - & - & - & - \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Average values of the peak load, maximum displacement and elastic recuperation for composite cylindrical shells. When composite sandwich cylindrical shells are compared, in terms of impact response, to conventional composite cylindrical shells (Figure 7b), the load-time curves are very similar, showing only a longer contact time for the sandwich shells. In terms of elastic recuperation, the benefits of introducing the cork layer are evident due to the intrinsic properties of this material. Cork has a high damage tolerance to impact loads [24; 25; 26] because under compressive loading (during the impact) the cell walls bend and buckle, promoting, in this case, a large deformation. This explains the larger displacements and lower maximum loads observed in shells that incorporate a cork layer. Simultaneously, when the cell walls bend and buckle, they absorb significant amounts of energy with a high viscoelastic return. Therefore, after each impact, cork continues to have the ability to absorb energy, which does not change due to its elastic deformation [51; 67]. This evidence is quantified in Table 5 in terms of mean values and respective standard deviations, for peak load, maximum displacement and bounced energy (elastic recovery). For example, compared to the conventional shells (8C), the maximum impact load decreased by around 10.4% when the cork layer was inserted into the middle of the shell, while the maximum displacement increased about 11.9%. In terms of elastic recuperation an increase of around 44.8% is observed.