Fragment velocity distribution formula of the thin-walled structure subjected to two-line asymmetrically initiated explosion

The thin-walled structure enveloping an explosive charge makes an ammunition warhead. Numerous studies have been conducted on the structural dynamics of the center-initiated charge explosion, including the casing fragmentation behavior and the fragment velocity distribution. Although adopting asymmetrical initiation could enhance the casing fragment velocity and energy utilization, the fragment velocity distribution of a two-line asymmetrically initiated warhead has rarely been studied and few formulae exist. However, the velocity distribution formula is valuable and necessary in the rapid design and lethality evaluation of warheads. Based on the concepts of the stationary point and local charge ratio of the Gurney equation, this work establishes a new velocity distribution formula for the two-line asymmetrically initiated warhead. An asymmetrical ratio function of the stationary point is first proposed for the two-line initiation and validated against the verified numerical modeling. Thereafter, to solve the undetermined parameters of the asymmetrical ratio function, it is discovered that there exists an overlapping effect for fragments at angles of 45° and 135° of the asymmetrical two-line initiation of a 90° central angle. Finally, to validate the entire mathematical model, experiments are conducted using X-ray photography. The mathematical model agrees strongly with the experimental results. This work could offer a solid reference for the rapid design and lethality evaluation of warheads.