Necking bifurcations during high strain rate extension

Abstract

Dynamic necking bifurcations which occur during rapid plane strain extension of a block of strain hardening plastic material are investigated. The block is presumed to be a portion of a plate or thin-walled shell deforming at high strain rate. It is found that the rates of growth of both very long and very short wavelength modes of nonuniform deformation are suppressed by inertia, thus promoting a necking pattern at an intermediate wavelength. The analysis indicates that, for blocks of small aspect ratio, the number of necks formed per unit length is proportional to the square root of the mean extensional strain rate of the block. The results of the analysis agree with necking patterns observed in high velocity ring expansion experiments and in detailed numerical simulations.