Energy based distribution for multi-layer fragmentation

Abstract A closed form, energy based statistical model of dynamic fragmentation is presented with application to traditional and multi-layer processes. Modern fragmentation predictive tools generally rely on the Mott & Linfoot distribution 1 alongside the Mott physics-based 2 average fragment size. Multi-layer fragmentation sleeves have been observed to produce larger fragments than those predicted by the Mott physics-based model 3 . The experiments that indicate this effect were performed as a part of Insensitive Munitions (IM) efforts to protect munitions from unintentional initiation by adding a barrier layer to the fragmenting sleeve. The present model is developed with the intent of application to this class of multi-layer devices. The energy-based 4–9 extensions to Mott’s theory, meant to reconcile the effect of energy absorption during crack formation, were investigated as a starting point for the present model. The present model is formulated by building the energy-based theory of Kipp & Grady 9 . Modification to the Kipp & Grady theory is made by closing the calculation of average fragment size through the introduction of crack velocity. The crack velocity is used to determine the time required for a fracture to proceed to completion, leading to the average distance a tensile release wave propagates on the formation interval. Multi-layer effects are treated through a method of statistical mixtures. This paper will discuss the model formulation, to include the physical basis and supporting calculations for crack velocity. The model has been integrated with the ALE3D 10 hydrocode through the VisIt Python 11–13 interface, and the implementation will be briefly summarized. Application to fragmentation of a uniformly expanding cylinder and impact fragmentation of flat plates will be presented with supporting experimental results.