Fragment size distribution in dynamic fragmentation: geometric probability approach

Belgrade: University of Belgrade. FME Transactions, 2008, 36, 59-65 pp.Dynamic fragmentation is a complex phenomenon inherent in numerous natural and engineering systems. Determination of the fragment size (or mass) distribution law is one of the most important objectives in dynamic fragmentation modeling. In the present paper, a general approach based on the simple assumption of random geometric partition of a body has been considered. Starting from the binomial distribution of fracture sites (points, lines or planes), size distribution laws are derived for 1D, 2D and 3D geometries. Geometric fragmentation models based on Mott's and Grady-Kipp's approaches are analyzed. The models originating from the Voronoi diagrams are also considered. The results of presented models are compared with numerical simulations and experimental data, showing significant compatibility as well as certain limitations. It has been concluded that preferred theoretical model depends on dimensionality of fragmentation process.