Multiple necking patterns in elasto-plastic rings subjected to rapid radial expansion: The effect of random distributions of geometric imperfections

In this paper we have investigated, using finite element calculations performed in ABAQUS/Explicit [1], the effect of ab initio geometric imperfections in the development of multiple necking patterns in ductile rings subjected to dynamic expansion. Specifically, we have extended the work of Rodriguez-Martinez et al. [2], who studied the formation of necks in rings with sinusoidal spatial perturbations of predefined amplitude and constant wavelength, by considering specimens with random distributions of perturbations of varying amplitude and wavelength. The idea, which is based on the work of El Mai et al. [3], is to provide an idealized modeling of the surface defects and initial roughness of the rings and explore their effect on the collective behavior and spacing of the necks. The material behavior has been modeled with von Mises plasticity and constant yield stress, and the finite element simulations have been performed for expanding velocities ranging from 10 m/s to 1000 m/s, as in ref. [2]. For each speed, we have performed calculations varying the number of imperfections in the ring from 5 to 150. In order to obtain statistically significant results, for each number of imperfections, the computations have been run with five random distributions of imperfection wavelengths. For a small number of imperfections, the variability in the wavelengths distribution is large, which makes the imperfections play a major role in the necking pattern, largely controlling the spacing and growth rate of the necks. As the number of imperfections increases, the variability in the wavelengths distribution decreases, giving rise to an array of more regularly spaced necks which grow at more similar speed. A key outcome is to show that, for a large number of imperfections, the number of necks formed in the ring comes closer to the number of necks obtained in the absence of ab initio geometric imperfections.