Impact behaviour of composite plates subject to high-velocity impact by rigid projectiles: Analytical modelling of the elastic response

Analytical models are developed to predict the elastic dynamic response of circular clamped composite plates subject to high-velocity impact by a rigid projectile. The models are based on first-order shear deformation theory of plates and take into account the effects of large deformations, anisotropic behavior of the composite material, propagation of flexural waves and higher-order vibrational modes emerging in the boundary-controlled phase of response. The dynamic response was found to be governed by only four non-dimensional parameters: aspect ratio, mass ratio, non-dimensional impact velocity and transverse shear stiffness, respectively. The analytical models were validated by comparing their predictions to those obtained from detailed dynamic FE simulations and a good correlation was found for a wide range of parameters. Both analytical and FE predictions showed very small differences in the responses of cross-ply and a quasi-isotropic composites of equal areal mass, and their elastic deflection response was found to be only mildly sensitive to the projectile radius. In addition, the sensitivity of peak tensile strain to variations of impact velocity was examined for two types of composites, carbon-fiber/epoxy (CFRP) and glass-fiber/epoxy (GFRP) composites. It was shown that the critical velocities associated with the inception of failure were found below the measured limit velocities for full penetration, and the GFRP plates sustained higher impact velocities at the inception of failure compared to plates made from stiffer and more brittle CFRP of equal mass. Finally, the validated analytical models were used to construct design maps in order to aid selection of damage-resistant plate geometries.