A thermochemical model for shock-induced reactions (heat detonations) in solids

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Abstract
Recent advances in studies of shock‐induced chemistry in reactive solids have led to the recognition of a new class of energetic materials which are unique in their response to shock waves. Experimental work has shown that chemical energy can be released on a time scale shorter than shock‐transit times in laboratory samples. However, for many compositions, the reaction products remain in the condensed state upon release from high pressure, and no sudden expansion takes place. Nevertheless, if such a reaction is sufficiently rapid, it can be modeled as a type of detonation, termed ‘‘heat detonation’’ in the present paper. It is shown that unlike an explosive detonation, an unsupported heat detonation will decay to zero unless certain conditions are met. An example of such a reaction is Fe2 O3 +2Al+shock→Al2 O3 +2Fe (the standard thermite reaction). A shock‐wave equation of state is determined from a mixture theory for reacted and unreacted porous thermite. The calculated shock temperatures are compared to experimentally measured shock temperatures, demonstrating that a shock‐induced reaction takes place. Interpretation of the measured temperature history in the context of the thermochemical model implies that the principal rate‐controlling kinetic mechanism is dynamic mixing at the shock front. Despite the similarity in thermochemical modeling of heat detonations to explosive detonations, the two processes are qualitatively very different in reaction mechanism as well as in the form the energy takes upon release, with explosives producing mostly work and heat detonations producing mostly heat.