Shock-wave initiation of solid explosives depends on localized regions of high temperature (hot spots) created by heterogeneous deformation in the vicinity of various defects. Current mathematical models of shock initiation tend to fall into two broad categories: (1) thermodynamic-state-dependent reaction-rate models, and (2) the continuum theory of multiphase mixtures. The level of generality possessed by (1) appears to be insufficient for representation of observed initiation phenomena, while that of (2) may exceed necessary requirements based on present measurement capabilities. As a means of bridging the gap between these two models, we present an internal-state-variable theory based on elementary physical principles, relying on specific limiting cases for the determination of functional forms. The appropriate minimum set of internal-state variables are the mass fraction of hot spots p, their degree of reaction J, and their average creation temperature e. The overall reaction rate A, then depends on /1-, f, and e in addition to the usual macroscopic thermodynamic variables (current state as well as their history). Two specific forms of this set of equations are applied to timeresolved shock-initiation data on PBX-9404. Numerical solution is achieved by the method of characteristics for rate-dependent chemical reaction. Additional questions such as the effect of thermal equilibrium between phases (solid reactants and gaseous products) on the theoretical results are discussed quantitatively.

A multistage reaction model developed for general use from initiation through detonation of heterogeneous high explosives is used to specifically simulate the interface vclocimetry and plate push experiments of a triamino‐trinitrobenzene‐based explosive in detonation. A simplification of the unified model leads to a rate relation that ineludes only two dominant stages: a fast one that represents the major portion of reaction dictated by propagation and decomposition, and a slow one that reflects probably the formation of large carbon molecules. The apparent more energetic behavior of the equation of state near the detonation front is actually due to the slow reaction process.

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A model of multiple processes is used to simulate the behavior of reaction in detonation of heterogeneous high explosives. The features of the model are (1) the partition of the explosive medium into hot spots and the region exclusive of hot spots and (2) the separation ofthe mechanical-thermal process and chemical process. For each process, a characteristic time is assigned and is defined by a phenomenological relation. With assumptions, some fast processes are ignored in the governing equations. This investigation indicates the necessity of including a slow process near the end of the reaction. Comparisons with experiments using a Fabry-Perot velocimeter are presented for triaminotrinitrobenzene.[This article is copyrighted as indicated in the article. Reuse of AIP content is subject to the terms at: http://scitation.aip.org/termsconditions. Downloaded to ] IP: 130.216.