Construction of a deterministic mathematical model for the spatial-mass distribution of random fragments produced by cased charge explosion

To evaluate the destructive effects of fragment impacts on structures or personnel, it is crucial to assess the velocity, mass, size, and impact location of the fragments, as well as establish the correlation between these factors. This paper presents the experimental measurement of fragment velocities produced by the explosion of a cased charge, the fragments resulting from the explosion are collected and steel plates are used to record the impact locations and sizes of the fragments. Based on the experimental results, the calculation models of fragment velocity, fragment mass distribution and fragment scattering angle are corrected, the spatial distribution models of fragment size and number are established, and the functional relationship between fragment mass and size is constructed. Given the aforementioned research findings, the fragment spatial-mass distribution models based on the size distribution function and based on the mass distribution function are constructed, and the fragment space-mass distributions corresponding to the number of impact regions of 1, 5 and 10 are analyzed, and the effect of the number of impact location divisions on the fragment space-mass distribution is explored. The research results show that, for the current test charge, the fragment spatial-mass distribution model based on the size distribution function aligns most accurately with experimental results when the impact regions is divided into 10. The number of impact locations designated within each region is directly proportional to the number of fragments in that specific region. Notably, the impact location of the largest fragment occurs at 0.8 times the length of the impact region, whereas the peak fragment impact density occurs at 0.743 times the length of the impact region. The spatial-mass distribution model proposed in this paper successfully correlates the velocity, mass, size and impact location of the fragments, providing a realistic theoretical representation of the spatial geometric distribution of the fragments.