An analytical model to predict the impact of a bullet on ultra-high molecular weight polyethylene composite laminates

High-performance fiber reinforced polymers are widely used in military and aerospace applications and easily subjected to high-velocity bullet impacts. Despite the abundantly available experimental and numerical studies related to energy absorption mechanisms of laminates under impact loading, measuring levels of the absorbed energy from different failure modes of laminates is a challenging task. Acquiring this important information using simplified analytical models is vital to evaluate the bulletproof ability of laminates and effectively optimize its structures. The present work develops an analytical model to predict the ballistic limit of a laminate and the energy absorption mechanism is considered from matrix crush, laminate shear, laminate compressive, fiber stretch, fiber break and delamination. The penetration process of a bullet striking laminates is divided into four sequential stages, including crush stage, compression-shear stage, stretch-shear stage, and fiber fracture and delamination stage. The analytical model predicts the ballistic limit, energy absorbed by each failure mode, and time histories of velocity and acceleration. The results are validated with experimental data and computational results, and good correlations are found for ballistic limits and thickness of the laminate, diameters of the deformation cone and thickness, ballistic limits, and non-dimension masses as well as energy absorptions and thicknesses.