Plane Shock Initiation of Homogeneous and Heterogeneous Condensed Phase Explosives with a Sensitive Rate

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Abstract
This paper treats the initial value problem of the shock initiation of a condensed phase explosive, which consists of an explosive, initially at rest, that is suddenly struck by a piston (flyer plate). The forward reaction rate is assumed to be sensitive; small changes in the thermodynamic state lead to moderate to large changes in the rate. A large parameter, such as a dimensionless activation energy, characterizes the rate. For these explosives, the first phase of the initiation transient involves the passage of a shock through the explosive, causing little reaction that releases heat. After an induction time, the shocked explosive develops a hot spot (or ignition point) where the reaction rapidly accelerates. Thermal explosion theory calculates an induction time that previously has been the basis of interpretation of experimental results. However, this theory neglects the wave propagation that occurs between the piston and the shock. The present account gives the correct formulation of the induction phase that retains wave propagation. It is shown that initiation behaviour is a strong function of the initiating shock pressure and the chosen form of the sensitive rate. Also, the induction time varies as the equation of state of the material is changed. Finally, we illustrate how it is possible to model the initiation of heterogeneous explosives by adopting a Lagrangian approach, where the individual explosive particles are assumed to have varying dependence on the local thermodynamic state.

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