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.

The plane shock response of PBX 9502 was measured from 0.5 to 25 GPa. The explosive is 95-wL % triamino-trinitrobenzene powder coated with Kel-F 800 plastic; porosity was 2.6%. Shock initiation sensitivity, the Hugoniot, and dynamic yield behavior were studied. Experiments done were explosively driven wedge tests and particle velocity history measurements using electromagnetic gauges at a light-gas gun. A new analysis of the wedge test was implemented. Based on wedge test results, an approximation for the particle velocity at the shock front is constructed, which is used in functional composition with the Hugoniot to calculate the shock path of each experiment. Optimization on the parameters of the approximation and the Hugoniot simultaneously ensures agreement of the Hugoniot with the overall kinematics of the shock growth as wen as the particle velocity/shock velocity data. The individual shock paths are used to examine the single-curve buildup assumption; the assumption is not valid for PBX 9502. A ramping elastic precursor of 0.073 GPa strength was observed. The yield and weak shock behavior are interpreted in terms of porosity, crystaUine anisotropy, and residual strain in the pressed, plastic-bonded explosive.

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The hydrodynamic operation of the "Forest Flyer" type of explosive launching system for shock physics projectiles was investigated in detail using one and two dimensional continuum dynamics simulations. The simulations were numerically converged and insensitive to uncertainties in the material properties; they reproduced the speed of the projectile and the shape of its rear surface. The most commonly used variant, with an Al alloy case, was predicted to produce a slightly curved projectile, subjected to some shock heating and likely exhibiting some porosity from tensile damage. The curvature is caused by a shock reflected from the case; tensile damage is caused by the interaction of the Taylor wave pressure profile from the detonation wave with the free surface of the projectile. The simulations gave only an indication of tensile damage in the projectile, as damage is not understood well enough for predictions in this loading regime. The flatness can be improved by using a case of lower shock impedance, such as polymethyl methacrylate. High-impedance cases, including Al alloys but with denser materials improving the launching efficiency, can be used if designed according to the physics of oblique shock reflection, which indicates an appropriate case taper for any combination of explosive and case material. The tensile stress induced in the projectile depends on the relative thickness of the explosive, expansion gap, and projectile. The thinner the projectile with respect to the explosive, the smaller the tensile stress. Thus if the explosive is initiated with a plane wave lens, the tensile stress is lower than that for initiation with multiple detonators over a plane. The previous plane wave lens designs did, however, induce a tensile stress close to the spall strength of the projectile. The tensile stress can be reduced by changes in the component thicknesses. Experiments verifying the operation of explosively launched projectiles should attempt to measure porosity induced in the projectile: arrival time measurements are likely to be insensitive to porous regions caused by damaged or recollected material.