Analysis of multiple necking in rings under rapid radial expansion

Rapid radial expansion of rings is analyzed in plane strain conditions. The material behavior is viscoplastic and strain hardening is taken into account. Using a linear perturbation technique, the growth rate of a perturbation is evaluated and dynamic necking is captured. Indeed, it is shown that for a given configuration, a finite wavelength associated to the largest growth rate is selected, which will define the size of fragments. A comparison with experimental data of Altynova et al. (Metall. Trans. 27 (1996) 1837) is performed to show the relevance of our approach.