Normal impact and perforation of thin plates by hemispherically-tipped projectiles—I. Analytical considerations

Abstract

The present development constitutes a very elementary analysis of the penetration and perforation processes involved in normal impact of thin plates by hemispherically-tipped cylindrical hard-steel projectiles. It is principally directwed towards the determination of the force and central plate deflection histories both below and above the ballistic limit. These parameters are considered to be two of the most important facets of the event, and they can be evaluated rapidly and with negligible computational cost. The theory is based on a lumped-parameter system that includes the radial variation in axial target displacement and is completeley predictive below the ballistic limit, but requires either measured information from the plug separation process or corresponding reasonable geometric and kinematic assumptions for a solution in the perforation domain. Surprisingly, considering the simplicity of the theoretical approach, the calculated values were found to be in excellent agreement below and in reasonable correspondence above the ballistic limit with data for soft aluminium targets. Somewhat greater deviations between predictions and measurements for mild steel plates are attributed to the neglect of rate effects in the constitutive description of this material. In spite of the existence of a variety of more complicated phenomenological representations, the current model appears to be the only one that forecasts the drop in peak force upon initiation of perforation and the subsequent simultaneous motion of plug and target plate; both of these features were verified by experiment. These attributes and the case of evaluating the model constitute the predominant justification for its employment. A much more comprehensive continuum-mechanical model, which still awaits development, or else the widely known, but far more expensive, numerical procedures that are crucially dependent on a precise knowledge of all material behavior features, must be utilized for the evaluation of other system variables, such as target strain. A complete description of the test procedures and results are presented in a companion paper.