A model for hot spot formation in shocked energetic materials

Shock initiation and detonation are often attributed to wave interactions in the micro-structure of condensed materials, which involve complex thermo-chemical, fluid and structural processes. Due to their broad range of scales, the simulation of hot spot formation, reaction growth, and transition to detonation is therefore rendered challenging. The extension of these complex couplings to simulate full-scale tests is prohibitively costly. This paper introduces a hot spot formation model to account for heterogeneous effects based on physical and chemical properties. The formulation is first evaluated in a HMX (cyclotetramethylene-tetranitramine) sample where hot spots are known to form due to void collapses. Transition to detonation is achieved with impact pressures that match those found in experiments. Parametric studies are performed to determine the effects of the void size and population on the sensitivity of the material. Then, the same hot spot model is used to study detonation in nanocrystalline PETN (pentaerythritol-tetranitrate) where heating is primarily the result of grain boundary effects such as friction, plasticity, and deformation. The inclusion of the hot spot model increases the sensitivity of the material and predicts shock pressures, again similar to experimental values. Finally, a sensitivity analysis of the results is performed to assess the uncertainty in the input variables of the model and to identify the critical parameters with implications on the accuracy of the results.