An Analytical One-Dimensional Penetration Model

In an earlier paper, the authors extended the small parameter analysis of the classic Tate Equations presented by Walters, et al and to the modified penetration equations introduced previously by Jones, et al. The purpose of this extension was to provide an explicit solution to a complex system of nonlinear penetration equations in which penetrator mushrooming was considered, as well as erosion. This has a dramatic effect on the prediction of penetration depth for reasonable values of the strength parameters in the problem. The results were very encouraging and led to our increased understanding of the penetration process. In this paper, we further modify the equations for penetration depth by replacing the fundamental kinematical length relation, considered earlier, by one which was introduced by Wilson, et al. This change does not complicate the system because the mushroom strain is constant, but it does produce some significant changes. In this paper, the results of Cinnamon, et al are used to estimate the mushroom strain. However, instead of applying this result directly, we employ an averaging process to accommodate deviations from cylindrical crater geometry. The changes result in improved penetration depth estimates in high speed metal on metal impacts. A large data set is analyzed using the new results. Application to heavy metal impacts against armor targets is considered as an example.