# Optimizing Viscoelastic Properties of Rubber Compounds for Ballistic Applications
## 3 Results
### Energy of Absorption of Armor Plates  
To provide another proof of the proposed rubber compounds, the same rubber formulations were examined as part of steel-rubber-aluminum sandwich plates. Using flash X-ray images, the residual velocity \(v_{r}\) of the projectile was determined. The kinetic energy \(E_{kin}\) before and after the impact can be calculated using  
\[E_{kin}=1/2\cdot m\cdot v2, \tag{9}\]  
with \(m\) being the mass of the projectile (4.6 g) and \(v\) being either the impact velocity \(v_{0}\) or the residual velocity \(v_{r}\). The absorption parameter \(A\) describes the percentual amount of absorbed kinetic energy and can be calculated as follows:  
\[A=\frac{E_{kin,r}}{E_{kin,0}}. \tag{10}\]  
The results show that the kinetic energy absorption is highly dependent on the impact velocity \(v_{0}\). To compare the obtained results, it is necessary to either limit the results used to shots where the impact velocity \(v_{0}\) is in a narrow range around a specific velocity (e.g., 600 m/s) or to take into account the standardization of the absorption values. The dependency between the absorption parameter \(A\) and the impact velocity \(v_{0}\) for the different armor configurations can be seen in Figure 9. As a reference, the same configuration without the rubber interlayer (6 mm steel + 4 mm aluminum) is used. Figure 9: Dependency between absorption parameter \(A\) and impact velocity \(v_{0}\) for different armor configurations. At every impact velocity \(v_{0}\), butyl rubber shows better energy absorption than the other configurations. To better compare the actual energy absorption, the values of the absorption parameter \(A\) are standardized to an impact velocity \(v_{0}\) of 600 m/s according to  
\[A_{600}=A\cdot\frac{600\ m/s}{v_{0}}. \tag{11}\]  
The standardized mean values for each configuration are given in Table 5 and plotted in Figure 10. \(A_{600}/A_{600,ref}\) is used as a measurement for the improvement over the reference configuration without rubber. While all rubbers show at least a small improvement over the reference configuration, butyl rubber shows a significant increase of the energy absorption of 8.3%. Another set of ballistic experiments was carried out to investigate the influence of both hardness and damping of the rubber layer on ballistic protection, in addition to the previously analyzed influence of the glass transition temperature \(T_{g}\). Experiments were carried out with the rubber compound showing the most promising results in the previous experiment (IIR). In principle, the same formulation for IIR like in the previous experiments was used, but hardness and damping were varied by changing the carbon black content of the formulation. It has to be noted that it is not possible to vary both properties individually, as the carbon black content (or any other formulation parameter for that matter) will always have an influence on them simultaneously. With an increase in carbon black content the hardness will increase, and the damping (_tan_\(\delta\)) will decrease. The standardized mean values for each  
Figure 10: Energy absorption during ballistic impact experiments for the configurations with different rubbers. All three rubber compounds possess the same hardness to decrease potential influences besides glass transition and maximized damping. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Specimen** & \(T_{g}\) [\({}^{\circ}\)C] & \(A_{600}\) [-] & \(A_{600}/A_{600,ref}\) [-] \\ \hline Reference (without rubber) & – & \(68.0\pm 1.5\%\) & \(0.0\%\) \\ SBR & \(-19\) & \(73.6\pm 1.8\%\) & \(2.4\%\) \\ IIR & \(-42\) & \(69.6\pm 1.3\%\) & \(8.3\%\) \\ BR/NR & \(-100\) & \(69.8\pm 1.3\%\) & \(2.6\%\) \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Mean values of energy absorption \(A\) with a standardized impact velocity \(v_{0}\) of 600 m/s for the investigated configurations with different rubbers.