Multi-scale modeling of shock initiation of a pressed energetic material III: Effect of Arrhenius chemical kinetic rates on macro-scale shock sensitivity

Abstract

Multi-scale predictive models for the shock sensitivity of energetic materials connect energy localization (“hotspots”) in the microstructure to macro-scale detonation phenomena. Calculations of hotspot ignition and growth rely on models for chemical reaction rates expressed in Arrhenius forms; these chemical kinetic models, therefore, are foundational to the construction of physics-based, simulation-derived meso-informed closure (reactive burn) models. However, even for commonly used energetic materials (e.g., HMX in this paper) there are a wide variety of reaction rate models available. These available reaction rate models produce reaction time scales that vary by several orders of magnitude. From a multi-scale modeling standpoint, it is important to determine which model best represents the reactive response of the material. In this paper, we examine three global Arrhenius-form rate models that span the range of reaction time scales, namely, the Tarver 3-equation, the Henson 1-equation, and the Menikoff 1-equation models. They are employed in a meso-informed ignition and growth model which allows for connecting meso-scale hotspot dynamics to macro-scale shock-to-detonation transition. The ability of the three reaction models to reproduce experimentally observed sensitivity is assessed by comparing the predicted criticality envelope (Walker–Wasley curve) with experimental data for pressed HMX Class V microstructures. The results provide a guideline for model developers on the plausible range of time-to-ignition that are produced by physically correct Arrhenius rate models for HMX.