Modeling system effects in ballistic impact into multi-layered fibrous materials for soft body armor

An analytical model is developed to study various 'system effects' during impact of a flat-faced, cylindrical projectile into a flexible, multi-layered target with no bonding between layers. Each thin layer is assumed to have in-plane, isotropic, elastic mechanical properties. The model allows variation of the mechanical properties from layer to layer as well as the spacings between the layers in order to study their combined effects on the ballistic performance of the system. In particular, we consider such performance measures as the V-50 limit velocity, the number of layers penetrated when impacting below this limit, and the residual projectile velocity after complete penetration above this limit. The V-50 performance of the target is found to degrade progressively as the spacings between layers are increased relative to the sum of layer thicknesses without spacing. A second finding is that for a given set of layers with differing mechanical properties, both the V-50 and the residual velocity depend on the order of layer placement. A third finding is that among systems with identical layers of a given in-plane tensile strength, the V-50 velocity increases with increasing strain-to-failure of the layers. However the relative magnitude of this increase diminishes with increasing target-to-projectile areal density ratio. The model builds on the authors' previous analysis for impact into a single elastic membrane and the results have important design implications for armor design especially for hybrid material configurations.