# Optimizing Viscoelastic Properties of Rubber Compounds for Ballistic Applications
## 5 Conclusions  
In an attempt to increase the effectiveness of rubber interlayers in sandwich-armors, the research focus was put on optimizing viscoelastic properties. By making use of the principle of time-temperature superposition, the ideal glass transition temperature for the given impact frequency range was calculated. With this knowledge, a butyl rubber compound with its glass transition temperature \(T_{S}\) in the ideal range was manufactured. By using ballistic experiments, it was compared to other rubber compounds (BR/NR, SBR) that feature glass transition temperatures outside of the ideal range. The experimental results support the stated claim that ballistic protection is positively influenced by having the rubber layer undergo its glass transition during impact and thus maximize its damping.  
The influence of hardness and damping of the rubber compound was further analyzed by varying the carbon black content of the rubber formulation, resulting in different values for hardness and damping. The medium carbon black content, and thus medium hardness and damping, showed the best results for the application with an increase of energy absorption by 8% over a reference without the rubber interlayer.  
**Author Contributions:** Conceptualization: J.K., L.P. and T.F.; methodology, J.K. and F.K., software, F.K. and N.F.; validation, J.K.; formal analysis, J.K., F.K. and N.F.; investigation, J.K., F.K. and N.F.; resources, L.P. and T.F.; data curation, J.K., F.K. and N.F.; writing--original draft preparation, J.K.; writing--review and editing, J.K.; visualization, J.K.; supervision, L.P. and T.F.; project administration, T.F.; funding acquisition, T.F. All authors have read and agreed to the published version of the manuscript.  
**Funding:** This research received no external funding.  
**Acknowledgments:** The authors would like to thank Safe Alcan, Hansen and Rosenthal, and Arlanxeo for providing free samples of the materials used.  
**Conflicts of Interest:** The authors declare no conflict of interest.  
**Abbreviation/Symbol**  
\begin{tabular}{l l} \(A\) & Absorption parameter \\ \(\alpha_{V}\) & Thermal expansion coefficient \\ AP & Armor piercing \\ \(\beta_{T}\) & Frequency shift factor \\ BR & Butadiene Rubber \\ \(C_{1}\), \(C_{2}\) & Empirical material and reference temperature \\ dependent parameters \\ CB & Carbon black \\ \(d\) & Armor thickness \\ DMA & Dynamic mechanical analysis \\ \(E^{\prime}\) & Storage modulus \\ \(E^{\prime\prime}\) & Loss modulus \\ \(E_{kin}\) & Kinetic energy \\ \(f_{g}\) & Glass transition frequency \\ _fimpact_ & Impact frequency \\ FSP & Fragment simulating projectile \\ IIR & Butyl rubber \\ \(m\) & Mass of projectile \\ MBTS & Mercaptobenzothiazole disulfide \\ NR & Natural rubber \\ _phr_ & Parts per hundred rubber \\ RHA & Rolled homogenous armor \\ SBR & Styrene-butadiene rubber \\ _ShA_ & Shore A hardness \\ \(T\) & Temperature \\ \(t\) & Time \\ \(T_{0}\) & Reference temperature \\ _tan_\(\delta\) & Loss factor \\ \(T_{g}\) & Glass transition temperature \\ TMTD & Tetramethylenethiuram disulfide \\ \(v\) & Velocity \\ \(v_{0}\) & Projectile velocity \\ \(v_{50}\) & Ballistic limit \\ VPEMI & Vereinigung der Prufstellen fur angrifshemmede \\ Materialien und Konstruktionen \\ \(v_{r}\) & Residual velocity \\ WLF & Williams-Landel-Ferry \\ \end{tabular}