Fragmentation model of a rapidly expanding ring with arbitrary cross-section

A model has been proposed to estimate the average number of fragments produced by ductile fracture of a rapidly expanding ring with arbitrary cross-section. The model uses a minimum number of constants characterizing the material properties of the ring. We assume that material of the ring is incompressible with the density ρ and its mechanical behavior obeys the ideal rigid-plastic model with yield stress Y. It is shown that the average number of fragments weakly depends on the cross-sectional shape, if characteristic size of the cross-section does not change. The results obtained by the model are compared with the experiments of Grady and Benson (Exp Mech 23:393–400, 1983) where the aluminum and copper rings were tested. The comparison shows good agreement with the experiments with the copper rings over the entire range of strain rates realized in these experiments. For the aluminum rings, such agreement is observed only for high strain rates.