An analytical model for ballistic impacts against plain-woven fabrics with a polymeric matrix

The widespread use of composite materials in load-carrying components leads to the need of studying their behaviour also in extreme situations, like ballistic impacts. At present the design of these structures against ballistic impacts is strongly dependent upon expensive experimental tests. To reduce the costs, numerical and analytical models have been developed in recent years, which allow a preliminary setting of the main parameters in the experiments, without substituting for them completely. With this aim, an investigation on the analytical modelling technique for ballistic impacts of blunt projectiles on composite plain-woven fabrics with a polymeric matrix has been carried out and is presented in this paper. An analytical model has been developed with original contributions and has then been compared with experimental results and data from the literature. The analytical model is based on the wave theory and on the energy balance between the kinetic energy of the projectile and the dissipation modes of the target: the kinetic energy is absorbed by the "V-tent" deformation moving ahead the projectile tip, the deformation energy of primary and secondary yarns, the delamination and matrix cracking energies, the energy associated to the bending of the layers (which has a considerable contribution in thick targets), the dissipation by the compression of the layer, and finally the energy dissipated by the shear plugging of the layers (if it takes place). The energy dissipated by friction between the projectile and the target and between the woven yarns is neglected. In addition, the model reproduces the sequential failure of the layers under the impact of the projectile, allowing the prediction of the impact velocities at which the projectile remains stuck inside without complete perforation. The aim is to provide a reliable tool able to work on a broad range of conditions and target configurations (thick and thin). From the energy balance, the deceleration of the projectile and the velocity at every time step, together with other parameters like contact duration, radius and depth of the conoid can be determined. The quasi-static properties of the materials are employed in the model. Performances and the pros/cons are evaluated.