Axial Distribution of Fragment Initial Velocities from Cylindrical Casing with Different Length-to-diameter Ratios

Cylindrical casing filled with charge under central point detonation at one end is the frequently-used structure for fragment weapons, whose fragment initial velocity produced by its fracture serves as an important parameter for evaluating the lethal power and the protective structures. To accurately predict the initial velocity distribution of cylindrical casing with different length-diameter ratios (L/D), it studied the impact of L/D ratios on the initial velocity of fragments and the applicability of existing empirical models for the initial velocity of fragments founded on the numerical model of experimental verification. On this basis, a correction term related to L/D ratio, which was often influenced by the axial rarefaction waves, was added to the fragment initial velocity index model. By fitting the data obtained from numerical simulations, the function expression of the correction term was derived and the calculation model for the initial velocity distribution of cylindrical casing with L/D ratio≥1 was obtained. Finally, the applicability of the established fragment initial velocity calculation model was validated through experimental data and numerical simulations. The research results indicate that the initial velocity distribution of fragments under different L/D ratios exhibits a trend where the initial velocities are lower at both ends and higher in the middle. Additionally, as the L/D ratio raises, the initial velocity of the fragment also increases. When the L/D ratio reaches 5, the relative error between the maximum initial velocity of the fragments and the calculated result using the Gurney formula is only 1.99%. However, the existing models for calculating initial velocities of fragment display significant errors when predicting smaller L/D ratios in cylindrical casing. The average error between the formula calculation results and the experimental and numerical simulation results does not exceed 6%, indicating that the proposed model is reliable for predicting the initial velocity distribution of fragments under different L/D ratios. The research work provides valuable insights for assessing the lethal power of fragment weapons and the structural design of protective devices in anti-terrorism projects.