An analytic model for the prediction of incoherent shaped charge jets

It is now a well recognized fact that the jet from a shaped charge can be overdriven in the sense that the fastest moving particles are not produced as a cohesive mass of material. Rather, the tip material may be produced as a number of discrete particles which possess different nonzero radial components of velocity and hence spread out from the axis of symmetry of the charge. Such a jet is classed as incoherent and when this incoherency occurs the jet's target penetration capability is invariably degraded. This physical phenomenon is the subject matter of this article. Several experimental results using common shaped charge materials are presented first. An analytic model which predicts the jet speed at the transition point between a coherent and incoherent state is then described. This model is based on the assumption that a stagnant core with circular boundaries exists in the flow region. Further, the flow field is assumed to be compressible with circular streamlines. The Murnaghan equation of state is used to relate the pressure and density in the flow region where the jet is produced. It is postulated that the transition between a coherent and incoherent state occurs when the circular flow becomes wholly supersonic. The critical Mach number for coherency is shown to be approximated to high accuracy by a simple formula depending on the collapse angle of the flow and the incoming flow speed. Excellent agreement between the model predictions and the experimental data is demonstrated. [S0021-8979(99)07215-1].