Ballistic Impact Behavior of Thick Composites: Analytical Formulation

Abstract

Structures undergo different loading conditions during their service life. Impact is one of the typical cases of loading. In this study, an analytical method is presented for the prediction of ballistic impact behavior of thick composites based on wave theory and energy balance between the projectile and the target. For thick composites the wave propagation along the thickness direction is also considered. During the ballistic impact event, energy transfer takes place from the projectile to the target. As the energy is absorbed by different mechanisms, kinetic energy and velocity of the projectile decrease. Different damage and energy-absorbing mechanisms for a typical woven fabric composite are compression of the target directly below the projectile, possible reverse bulge formation on the front face, compression in the surrounding region of the impacted zone, tension in the yarns, shear plugging, bulge formation on the back face, delamination and matrix cracking, friction between the target and the projectile, and heat generation caused by impact. Based on the analytical method presented, typical results are generated and compared with the experimental values. Nomenclature A = cross-sectional area of the projectile Aql = quasi-lemniscate area reduction factor Ay = cross-sectional area of the yarn d = diameter of the projectile dci = deceleration of the projectile during a given time interval E = energy Ebb = energy absorbed due to bulge formation on the back face of the target Ecf = energy absorbed due to compression of the target directly below the projectile Ecsy = energy absorbed due to compression of yarns in the surrounding region of the impacted zone: region 2 Edl = energy absorbed due to delamination Efr = energy absorbed due to friction Ehg = energy absorbed due to heat generated Emc = energy absorbed due to matrix cracking Emt = energy absorbed by matrix cracking per unit volume Erb = energy absorbed due to reverse bulge formation on the front face of the target Esp = energy absorbed due to shear plugging of the yarns Etf = energy absorbed due to tension in the yarns in a layer ETOTAL = total kinetic energy lost by the projectile F = total force/contact force Fc = compressive force Fi = inertial force GIIcd = critical strain energy release rate in mode II h = thickness of the target hl = thickness of each layer hlc = thickness of a layer after compression h p = length of the plug K = numerical constant (depends on the shape of the projectile)