The stability of rapidly deforming rods and jets

When a uniform rod is deformed in tension under conditions of pure axial st ress it will undergo indefinite uniform deformation. In practice these cond itions are not achievable because neither perfect uniformity nor perfect un iaxial stress can be attained. In slow to moderately fast tension, instabil ity (necking) starts at relatively small strains and is governed by the bou ndary conditions (uniformity and end effects) and the deformation model. If the strain rate is very high, however, then strains of several thousand pe r 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 ra tes, very large stable strains can be achieved either through certain defor mation models (this is uncommon) or, more generally, through the effects of inertia on stability. A quantitative theory is developed which shows the i mportant role of both radial and axial inertia. These inertial effects are intimately linked to the deformation model in such a way that, for any pert urbation or other effect to initiate instability, a complex set of conditio ns involving the axial and radial inertia and the deformation model must be satisfied. These define the geometrical, inertial and material characteris tics required for large stable extensions.