Study on the Spatial Distribution of Natural Fragments Based on Fractal Model of Fragment Mass Distribution

In order to solve the problem of using fragment quantity spatial distribution to describe fragment spatial distribution, this paper proposes a fragment mass probability density model to describe fragment spatial distribution. Applying the idea of stress gradient and velocity gradient grade in the process of explosion, the calculation equation of fragment direction angle at different axial positions of warhead is established. Based on the fractal model of natural fragment mass distribution in the form of Weibull function, a two-dimensional joint probability density model of fragment scattering space angle and fragment mass is established, and the model is verified by tests. The research results show that when the space angle is between 90° and 100°, the theoretical calculation error of fragment mass distribution is 4.3%, and the theoretical calculation error of fragment quantity distribution is 19.4%, compared with the test results. This shows that the fragment mass spatial distribution is more suitable for characterizing the fragment spatial distribution law than the fragment quantity spatial distribution. When considering the characteristics of non-uniform fragment mass formed in different regions of warhead, the prediction accuracy of the fragment mass spatial distribution model established in this paper is 18.2% higher than that of previous models, which can more accurately reflect the fragment spatial distribution law.