Impact of aspect ratio on fragment velocity distribution for hollow charges

Hollow charges play essential roles in the warhead design, detonation wave control, and lethality tuning. The superficial structure difference with solid charges prevents the direct application of Gurney's formula to determine fragment velocity. Tools are demanded in the design of hollow charges. Apart from checking the actual detonation driving behavior, a variety of different methods were used to solve this problem. And when developing these methods, 2 times the aspect ratio is often believed to be sufficient to treat detonation driving as a plane strain model (removing the influence of rarefaction waves). This study, however, reaches different conclusions about these aspects. Based on the discovered linear velocity distribution of the detonation products, a new formula was developed for the theoretical maximum fragment velocity of hollow charges. The formula applies to the non-plane strain state caused by end-face initiations. Furthermore, new fragment velocity distribution formulae based on results of a broad range of aspect ratios have been developed, the first time for the central line or hollow surface initiation. Based on numerical modeling and experiments, the entire formula system was verified to be precise and more applicable. This study can provide important references for the design of new structure warheads and lethality tuning warheads, as well as for damage effectiveness evaluation.