# Optimizing Viscoelastic Properties of Rubber Compounds for Ballistic Applications
## 1 Introduction  
Due to a steadily increasing threat of sniper attacks, it becomes more important to provide more efficient armor systems not only for the military but also for the protection of civilian infrastructure and vehicles. Modern protection systems tend to use lighter and cost-efficient multilayered armors. An example for this are disruptor-absorber systems interlayered with different materials, instead of classic steel-only armors, which would have to be thick and thus heavy to stop a high-energy kinetic threat. These use interlayer materials ranging from ceramics and metal foams to polymers like polyaramide (Kevlar) or ultra-high-molecular-weight polyethylene (Dyneema) [1; 2; 3; 4]. Each part of the multilayered armor plays a specific role. The front-plate is a high-strength and usually brittle layer that shatters incoming projectiles. The back-plate has to be a ductile material that is able to absorb the remaining energy by transforming it into other forms of energy, mostly deformation energy. When a projectile hits a high-strength and usually brittle layer, a compressive stress wave is generated and propagates through the plate. When it reaches the back face of the plate, it is partially reflected back as a tensile wave, which may cause damage and cracks of more brittle materials. The underlying layer should then act as a shock absorber, damp the transmitted impact energy and spread its kinetic energy over a broader area to prevent damage to the first layer [2; 3; 5]. A promising material for such an interlayer could be rubber due to its viscoelasticity and high damping properties. Rubber is a composite material consisting of crosslinked polymer and active filler. This enables it to be stretched under mechanical stress while returning to its original shape when the stress is removed. It was reported in 1993 [6] that natural rubber improves the ballistic properties of a steel-rubber-steel armor in comparison to an armor comprising an air gap. Later more effort was put into researching the effect of rubber in laminated armors [6; 7; 8; 9]. The phenomenon mainly responsible for the positive effect of rubber applied as an interlayer is thought to be its viscoelasticity, resulting in the ability to damp mechanical stress by transforming it into heat. The viscoelasticity of rubber is defined by its dynamic mechanical properties, such as storage modulus \(E^{\prime}\), loss modulus \(E^{\prime\prime}\) and loss factor \(tan\ \delta\). Storage modulus \(E^{\prime}\) and loss modulus \(E^{\prime\prime}\) are used to describe the elastic and the viscous part of the dynamic modulus of a viscoelastic material and measure the stored and dissipated energy. Loss factor \(tan\ \delta\) is used to describe the damping ability of the material and is defined as the ratio of \(E^{\prime}\) and \(E^{\prime\prime}\). These properties are dependent on both the ambient temperature and the frequency of the applied mechanical load. In the range of the glass transition, both loss modulus \(E^{\prime\prime}\) and loss factor \(tan\ \delta\) reach a maximum [7; 10; 11; 12]. The equivalency of temperature and frequency regarding glass transition can be described by the time-temperature superposition principle. It states that the glass transition can occur in two ways. If the temperature is very low, the thermal energy is not sufficient to overcome the energy barriers of certain polymer chain rearrangements. If the frequency of an applied mechanical stress is very high, the chain segments are not able to react to the applied mechanical load, which is the case for strains close to the resonance frequency of the chain rearrangements. In both cases, the material behaves brittle and glasslike. Hence, temperature and frequency can be used equivalently to describe the glass transition [11]. [PERSON] et al. [13] reported that by choosing a rubber with a glass transition in the correct frequency range, the ballistic impact induces the glass transition and thus damping is maximized during a ballistic impact.