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This project will develop an analytical tool to calculate performance of HMX based PBXs in the skid test. The skid-test is used as a means to measure sensitivity for large charges in handling situations. Each series of skid tests requires dozens of drops of large billets. It is proposed that the reaction (or lack of one) of PBXs in the skid test is governed by the mechanical properties of the binder. If true, one might be able to develop an analytical tool to estimate skid test behavior for new PBX formulations. Others over the past 50 years have tried to develop similar models. This project will research and summarize the works of others and couple the work of 3 into an analytical tool that can be run on a PC to calculate drop height of HMX based PBXs. Detonation due to dropping a billet is argued to be a dynamic thermal event. To avoid detonation, the heat created due to friction at impact, must be conducted into the charge or the target faster than the chemical kinetics can create additional energy. The methodology will involve numerically solving the Frank-Kamenetskii equation in one dimension. The analytical problem needs to be bounded in terms of how much heat is introduced to the billet and for how long. Assuming an inelastic collision with no rebound, the billet will be in contact with the target for a short duration determined by the equations of motion. For the purposes of the calculations, it will be assumed that if a detonation is to occur, it will transpire within that time. The surface temperature will be raised according to the friction created using the equations of motion of dropping the billet on a rigid surface. The study will connect the works of Charles Anderson, Alan Randolph, Larry Hatler, Alfonse Popolato, and Charles Mader into a single PC based analytic tool. Anderson's equations of motion will be used to calculate the temperature rise upon impact, the time this temperature is maintained (contact time) will be obtained from the work of Hatler et. al., and the reactive temperature rise will be obtained from Mader's work. Finally, the assessment of when a detonation occurs will be derived from Bowden and Yoffe's thermal explosion theory (hot spot).

An Analytic Tool to Investigate the Effect of Binder on the Sensitivity of HMX-Based Plastic Bonded Explosives in the Skid Test