On instability of rapidly stretching metal jets produced by shaped charges

Dynamics of shaped-charge jets is analysed by using an elastic-viscoplastic rheological model of metal. It is shown that the resulting problem for small perturbations is well-posed and its solution predicts only a bounded growth of small perturbations. A disturbance growth may be delayed drastically in the case of large modulus of elasticity of metal (or short waves) yielding oscillations in perturbation amplitude in the beginning of stretching process. Stress-dependent decrease in plasticity leads to a paradoxical result: small disturbances grow faster. This result is explained. The fastest growing mode is predicted. The existing quasi-one-dimensional analysis of shaped-charge jet dynamics based on the rheological model of perfectly plastic body is revised. It is shown that it yields an ill-posed problem for small perturbations because it predicts perturbation-independent stresses in shaped-charge jet, thus neglecting the regularizing elastic factor. Superiority of the rheological model used in the present work is in the fact that it does not suffer from this defect.