Microstructural Model of Ignition for Time Varying Loading Conditions

Abstract

A micro‐mechanical based model of ignition was developed about five years ago based on a simple inter‐granular friction model of mechanical dissipation coupled with a fit to extensive direct numerical simulations of the resulting thermally induced decomposition. The chemical model used was the McGuire‐Tarver ODTX based model for HMX decomposition. The resulting power law type model has been reasonably successful in predicting threshold conditions for Steven type experiments. The final power law form was obtained by assuming a constant time history for both the pressure and shear strain rate, resulting in time independent loading conditions for the chemical model. Here we propose to extend the model to handle time varying loading conditions. This is done using a linear operator that models reactive heat transfer simulations done for a wide variety of loading conditions. The linear operator is represented by a convolution integral with Prony series kernel form for efficient numerical implementation. To complete the model the same inter‐granular friction model used previously is employed. Comparisons are made with results of numerical simulations and experiments. The technique used here is based on the notion of linearizing the reactive heat transfer problem. Although the chemical model involves four reactions and is highly nonlinear, we effectively linearize the problem around ignition conditions with a linear operator fit. We use a simple power law approximation that gives useful accuracy over at least 4 orders of magnitude in time and fluence. A non‐dimensional scaling method is used to determine the final form. We believe the techniques used here could also be used with more detailed chemical models and with other types of mechanical dissipation models.