The stability of rapidly deforming rods and jets

Abstract
When a uniform rod is deformed in tension under conditions of pure axial stress it will undergo indefinite uniform deformation. In practice these conditions are not achievable because neither perfect uniformity nor perfect uniaxial stress can be attained. In slow to moderately fast tension, instability (necking) starts at relatively small strains and is governed by the boundary conditions (uniformity and end effects) and the deformation model. If the strain rate is very high, however, then strains of several thousand per cent can be achieved before instability develops as is observed in shaped charge jets. It is shown in the present paper that, at very high strain rates, very large stable strains can be achieved either through certain deformation models (this is uncommon) or, more generally, through the effects of inertia on stability. A quantitative theory is developed which shows the important role of both radial and axial inertia. These inertia1 effects are intimately linked to the deformation model in such a way that, for any perturbation or other effect to initiate instability, a complex set of conditions involving the axial and radial inertia and the deformation model must be satisfied. These define the geometrical, inertial and material characteristics required for large stable extensions.