Abstract
Modern ballistic problems involve the impact of multi-material projectiles. In order to model the impact phenomenon, different levels of analysis can be developed: empirical, engineering and simulation models. Engineering models are important because they allow the understanding of the physical phenomenon of the impact materials. However, some simplifications can be assumed to reduce the number of variables. For example, some engineering models have been developed to approximate the behavior of single cylinders when impacts a rigid surface. However, the cylinder deformation depends of its instantaneous velocity. At this work, an analytical model is proposed for modeling the behavior of a unique cylinder composed of two different metals cylinders over a rigid surface. Material models are assumed as rigid-perfectly plastic. Differential equation systems are solved using a numerical Runge-Kutta method. Results are compared with computational simulations using AUTODYN 2D hydrocode. It was found a good agreement between engineering model and simulation results. Model is limited by the impact velocity which is transition at the interface point given by the hydro dynamical pressure proposed by Tate.
Highlights
The evolution of armor systems has led the development of different types of mult-material projectiles [1]
Some projectiles are composed by a hard nose and a heavy body in order to increase the damage over the armor [2], where the most common materials used are: lead and aluminum and steel and tungsten [1]
It can be seen good agreement between simulation and analytical model, it is lower at high impact velocities
Summary
The evolution of armor systems has led the development of different types of mult-material projectiles [1]. According to Taylor; when a solid cylinder impacts a rigid wall, it suffers elastic and plastic stress inside the projectile moving as waves. Equations govern the state of the cylinder can be obtain from the Taylor model [3]; where the continuity equation in the system (Eq (2)), the mass and momentum equations of non-deformable part. When “a” shrinkage stops, cylinder “b” behaviour can be modeled as a single cylinder according with its velocity (Equations (2), (3), (4) or Equations (5))
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