A three-stage model for the perforation of finite metallic plates by long rods at high velocities

A three-stage theoretical model is presented herein to predict the perforation of a thick metallic plate struck normally by a long rod at high velocities. The model is suggested on the basis of the assumption that the perforation of a thick metallic plate by a long rod can be divided into three stages: (1) initial penetration; (2) plug formation and (3) plug slipping and separation. Various analytical equations are derived which can be employed to predict the ballistic limit, residual velocity and residual length of the long rod. It is demonstrated that the present model predictions are in good agreement with available experimental results for the perforation of finite steel targets struck normally by steel as well as tungsten alloy long rods at high velocities. It is also demonstrated that the dynamic maximum shear stress of a plate material has strong effect on plug formation and plug thickness which, in turn, exerts considerable influence on the residual velocities and lengths of a long rod at impact velocities just above the ballistic limit.     

Statistical variability and fragility assessment of ballistic perforation of steel plates for 7.62 mm AP ammunition

The paper describes field test results of 7.62 × 51 mm M61 AP (armour piercing) ammunition fired into mild steel targets at an outdoor range. The targets varied from 10 mm to 32 mm in thickness. The tests recorded penetration depth, probability of perforation (i.e., complete penetration), muzzle and impact velocities, bullet mass, and plate yield strength and hardness. The measured penetration depth exhibited a variability of approximately ±12%. The paper then compared ballistic test results with predictive models of steel penetration depth and thickness to prevent perforation. Statistical parameters were derived for muzzle and impact velocity, bullet mass, plate thickness, plate hardness, and model error. A Monte-Carlo probabilistic analysis was then developed to estimate the probability of plate perforation of 7.62 mm M61 AP ammunition for a range of impact velocities, and for mild steels, and High Hardness Armour (HHA) plates. This perforation fragility analysis considered the random variability of impact velocity, bullet mass, plate thickness, plate hardness, and model error. Such a probabilistic analysis allows for reliability-based design, where, for example, the plate thickness with 95% reliability (i.e. only 1 in 20 shots will penetrate the wall) can be estimated knowing the probabilistic distribution of perforation. Hence, it was found that the plate thickness to ensure a low 5% probability of perforation needs to be 11–15% thicker than required to have a 50/50 chance of perforation for mild steel plates. Plates would need to be 20–30% thicker if probability of perforation is reduced to zero.