Linear Exponential Fragmentation Statistics and Scaling for Cylinders with Thermobaric Explosives

Although historically the Mott equation has been used for describing the fragmentation statistics of naturally fragmenting warheads, there are arguments for using different statistical distributions. This work compares two and three term linear combinations of exponential distributions to describe the experimental fragment distributions from mild steel cylinders exploded with C4 or two thermobaric explosives. While scaling relations for the Mott distribution have been developed, none could be found for multi-term exponential distributions. Relationships are proposed, tested, and findings presented for scaling experimental fragmentation distributions. The initial analysis suggests that there is a characteristic limiting fragment size common across all distributions and that the Chapman Jouget pressure influences the dependence of fragment mass on strain rate and influences the proportion of fine fragments. The question still remains if this approach yields significantly better results over the Mott distribution.