The initiation of detonation in solid explosives

We consider the problem of transition from deflagration to detonation in a solid crystalline explosive. A mathematical model is set up for a semi-infinite block of explosive, and the partial differential equations resulting from a one-dimensional flow are integrated numerically, using an electronic computer. The explosive is regarded as a homogeneous fluid so far as the hydrodynamic equations are concerned, but as a two-phase solid/gas system for the equation of state and equation of burning. This leads to the concept of two different temperatures coexisting in the system, solid explosive at one temperature burning to give gaseous detonation products at another temperature some three thousand degrees above the first. We assume that the explosive exists locally in the form of spheres and that the law of burning involves a pressure term. Initiation is by a shock wave incident on the explosive, and in all the cases investigated, we find that the transmitted shock wave accelerates or decelerates steadily, and in the results quoted in the paper, the von Neumann spike can be seen building up out of the front of the initiating shock. This is in accord with experimental evidence on solid explosives, but is in sharp contrast with numerical results obtained by other workers and with experimental evidence on liquid explosives. It is believed that the differences are the result of the introduction of the pressure term into the law of burning.