An Empirical Approach For Penetration Of Tandem Warheads Into Concrete Targets

We develop a semi-empirical or semi-analytical model based on the spherical cavity expansion theory in order to simulate the normal penetration of tandem warheads into concrete targets, which consist of two stages: penetration into a cavity region (or damaged region), and subsequent penetration into an undamaged region. To formulate the semi-empirical model, we consider the first impact of rigid projectiles on the damaged region with a pre-drilled cavity and the second on the undamaged region. For the penetration into the undamaged region corresponding to the second stage, an empirical constant used in the semi-empirical model is determined based on the penetration depth obtained by experiments in the literature. The semi-empirical model is then verified by comparing its results to experimental data and numerical results of the explicit finite element method (FEM) in terms of kinematic quantities of projectiles. For the penetration into damaged concrete targets in which a cavity is considered as a pre-drilled hole, which provides a basis of the formulation for the first stage, the results of the semi-empirical model are compared to experimental data, and an empirical constant is also estimated based on the numerical results of the explicit FEM. Finally, the concrete targets with a finite-length cavity, into which a tandem warhead penetrates, can be regarded as a combination of the damaged region with a finite-length cavity and the undamaged region. In the semi-empirical model for the penetration of tandem warheads, the empirical constants for the first and second stages are employed as those estimated for the damaged region with a cavity of finite length and for the undamaged region, respectively. The results from the semi-empirical model are compared with those from the explicit FEM due to the lack of experimental data. The good agreement of the results of the semi-empirical model and the explicit FEM demonstrates that the proposed semi-empirical model can predict the dynamic behavior of the tandem warheads in a simple and accurate manner.