The Formation and Stretching of Bi-material Shaped Charge Jets

The equations for the formation of a bi-material jet from a laminated shaped charge liner are presented. A coupled pair of boundary-value problems is then established for an idealised stretching jet in cases where the outer material occupies a hollow uniform cylinder surrounding the inner material in the uniform hollow. This is done first where the materials are inviscid fluids. Making the assumption that the axial velocity in each part of the jet is the same and linearly decreasing from the front to the rear of the composite jet, solutions for the pressure field in each part are obtained. The problem is then reformulated where the two materials are both perfectly plastic solids but with differing densities and yield strengths. The equations of plastic flow (Levy-Mises with von-Mises yield criterion) are solved for each material to derive the stress field in both parts of the jet. These analytical solutions offer a basis for future stability and target penetration studies.