On analytic modeling of casing and liner thickness variations in a shaped charge

Abstract

The jet from a shaped charge is formed by the collapse of its typically conical liner under the high pressures resulting from a detonation front. Nominally the charge is axisymmetric and the jet travels along the axis of symmetry of the charge. However, when asymmetries are present in the shaped charge the velocities imparted to liner elements at a given axial distance from the cone tip will be different. Thus the jet formation process becomes asymmetrical and a nonzero off-axis component of the jet velocity is generally produced. Such an off-axis component can cause considerable degradation in the penetration achieved by the jet. In this article a recent novel approach to the modeling of shaped charge liner collapse with constant liner projection velocities in the presence of asymmetries is generalized to include Randers–Pehrson acceleration of the liner elements. The Gurney formula for an asymmetric closed sandwich is used for the limiting liner element speed in the Randers–Pehrson model and it is shown how the required mass elements may be calculated in a shaped charge application. Simple illustrative models are used to describe thickness variations in the shaped charge casing and liner.