The effect of radial inertia on flow localization in ductile rods subjected to dynamic extension

• A rigid-plastic Cosserat rod with cross-sectional extension and radial inertia.
• Influence of the multi-axial stress state in the necked region.
• Linear stability analysis of an exact nonlinear dynamic solution.
• Effect of radial inertia on the stabilization of the localization process.
• Effect of radial inertia on the expected length of fragments.

The objective of this work is to investigate the influence of radial inertia on the flow localization in ductile rods subjected to dynamic extension. Using the theory of a straight Cosserat rod which includes normal cross-sectional extension it is possible to obtain an exact solution for nonlinear uniform extension of a rigid-plastic material using a functional form of the yield stress that models the effect of the more general stress field in the necking region of the rod. Linear stability analysis of this exact nonlinear solution yields equations that generalize the formulation reported in Ref. [1] to include radial stretching and inertia. Examples show the quantitative effect of radial inertia on the stabilization of the localization process and on the determination of the expected length of fragments.