Random distributions of initial porosity trigger regular necking patterns at high strain rates

Abstract

© 2018 The Author(s) Published by the Royal Society. All rights reserved. At high strain rates, the fragmentation of expanding structures of ductile materials, in general, starts by the localization of plastic deformation in multiple necks. Two distinct mechanisms have been proposed to explain multiple necking and fragmentation process in ductile materials. One view is that the necking pattern is related to the distribution of material properties and defects. The second view is that it is due to the activation of specific instability modes of the structure. Following this, we investigate the emergence of necking patterns in porous ductile bars subjected to dynamic stretching at strain rates varying from 10 3 s -1 to 0.5×10 5 s -1 using finite-element calculations and linear stability analysis. In the calculations, the initial porosity (representative of the material defects) varies randomly along the bar. The computations revealed that, while the random distribution of initial porosity triggers the necking pattern, it barely affects the average neck spacing, especially, at higher strain rates. The average neck spacings obtained from the calculations are in close agreement with the predictions of the linear stability analysis. Our results also reveal that the necking pattern does not begin when the Considère condition is reached but is significantly delayed due to the stabilizing effect of inertia.