A Study On The Penetration Of Projectiles Into Targets Made Of Various Materials

A combined theoretical and numerical study is given in this paper to examine the penetration and perforation of targets made of various materials struck by projectiles both at normal incidence and obliquely. In the present finite element model, the response of target is approximated by an analytical forcing function which eliminates the need for discretizing the target as well as the need for a complex contact algorithm. Thus, this methodology substantially reduces the computing time and memory requirements. This paper mainly consists of following parts:The approaches used to determine the analytical forcing function of target response are systematically studied in detail, which include empirical, analytical and computational methods. In empirical methods, Forrestal's semi-empirical equation are presented and Wen's semi-empirical equation is modified to obtain the empirical transient forcing functions; in analytical methods, cavity expansion approximations is presented and dilatation-kinematic relation is then introduced to cater for both dilationcy and compressibility of the material in comminuted region; in computational methods, finite element method is used to simulate the cavity expansion and the radial stress on the cavity surface is given. In addition, the advantages and disadvantages of all these methods are discussed in some detail.Analytical equations for the penetration and perforation of targets by normal impact of rigid projectiles are given based on the forcing functions derived. Modified Wen's semi-empirical equation is applied to the penetration and perforation of FRP laminates. Cavity expansion models with dilatation-kinetmatic relation is discussed and used to predict the penetration depth of concrete targets and residual velocity of the projectile after perforation of finite targets. Finally, a simple finite difference code is developed to predict the abrasion effect of projectile nose during penetration. It is demonstrated that the model predictions are in good agreement with the available experimental data in the literatures.Numerical simulations are conducted on the penetration of aluminum alloy and rock targets by spherical and ogival nosed projectiles using dynamic finite element code ABAQUS/Explicit. In the simulations, the target response is represented by a forcing function which applies to the projectile surface as boundary conditions. It is found that the pitch and yaw (inclination angle, or angle of attack) has significant effects on the penetration depth as well as projectile response. It is also found that the most dangerous position usually locates at the quarter of the projectile near its tail. This finding has serious implications for the design of penetrating weapons. Oblique penetration and perforation of thick targets are also investigated numerically with free surface effects being taken into account. For ogival-nosed projectiles, a modified forcing function derived by Warren et al. is employed to simulate the penetration and perforation process from finite spherical cavity expansion theory whilst for conical-nosed projectiles, a new forcing function is proposed based upon finite cylindrical cavity expansion theory. Computational results show that the presence of a free surface has significant influence on projectile's motion and trajectories when it is launched into targets at a big obliquity. The results also show that the dangerous regions are located not only near the tail but also at the part of one third of the projectile near the tip and that free surface has more pronounced effects on the conical-nosed projectile than ogival-nosed missile.For multilayer targets, a cavity expansion model together with a modified forcing function is developed to simulate penetration and perforation of multilayer targets subjected to impact by projectiles. It is shown that the peak of deceleration decreases when the influence of interfaces of multilayer targets is taken into consideration and that thin layer targets are more difficult to be identified from the deceleration curve only.The results obtained in the present study are promising and maybe useful both for design of a new generation of penetrating weapons and for safety calculation and assessment of protective structures.