Theory of initiation of detonation in solid and liquid explosives

Abstract

The experimentally observed differences in the growth of shock initiated detonation in liquid and in solid explosives are discussed with the object of deciding upon a reaction rate model for numerical calculations on the growth of reactive shock waves in granular solid explosives. It is suggested that while a strongly temperature dependent bulk reaction rate model is indicated for liquids and homogeneous solids, the behavior of granular solids indicates a reaction rate which is a function of the pressure behind the shock front and not of the average temperature. A pressure dependent energy release rate is shown to result in the reaction building up at the shock front rather that at the explosive/barrier interface. Under this condition it is possible to attempt approximate analytical solutions of the reactive shock equations which illustrate the relation between the initial growth or failure behavior of the wave and the initial shock pressure, shock curvature, and the rate of energy release and its pressure dependence. A pressure dependent energy release rate is shown to be a consequence of a grain burning model for the reaction process where the rate of propagation from ignition surfaces is assumed to be a function of the pressure and flame temperature of the products of reaction. The problems in verifying this hypothesis are briefly discussed. In low bulk density explosive where the shock pressure is low enough for it to be possible to make independent measurements of burning rate and its over-all pressure dependence, it is difficult to make sufficiently precise measurements of shock pressure. In high density explosives where the shock pressure/distance to steady detonation relationship can be determined with some precision, the magnitude of the pressure is greatly in excess of those at which burning rate measurements can be made.