Probabilistic Relations Between Thermo-Mecha Nical Response and Microstructure of Heterogeneous Energetic Materials for Shock/Nonshock Loading
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An approach is developed to predict the ignition sensitivity of heterogeneous energetic materials under shock and nonshock loading as a function of microstructure. The underlying issue of impact-induced initiation of chemical reactions is driven by the deposition of mechanical work into energetic materials in the form of localized heating or the development of hotspots. These hotspots govern the ignition of energetic materials. The aim of this study is to understand the mechanisms of hotspot evolution, computationally predict the ignition sensitivity, and analyze the effects of loading and microstructural attributes on hotspot development and material ignition sensitivity. A computational framework based on a Lagrangian cohesive finite element method (CFEM) is developed. This framework is used to statistically analyze the material sensitivity, accounting for microstructural attributes in terms of morphology, constituent properties, inclusions, and defects. Multiple samples with statistically similar microstructural attributes are generated in a controlled manner and used to obtain a quantitative measure for the statistical variation in ignition behavior due to material heterogeneity. To relate loading and microstructure to the onset of chemical reaction, a hotspot-based criticality criterion is established. The analysis involves the quantification of hotspots via the CFEM simulations. The approach yields criticality conditions in terms of the critical impact velocity, critical time required for ignition, and total energy required for ignition under a given loading rate. The stochasticity of the material behavior is analyzed using a probability distribution as a function of microstructural attributes including grain volume fraction, grain size, amount of metallic inclusions, and specific binder-grain interface area. A probability superposition model is proposed to delineate the effects of different sources of stochasticity. The ignition threshold for granular explosives (GXs) and polymer-bonded explosives (PBXs) under shock and nonshock loading are predicted. The particular thresholds predicted are the James-type ignition threshold and the Walker-Wasley ignition threshold. The dependence of the ignition probability on material and microstructure is analyzed for a wide range of loading conditions. The microstructure – ignition threshold relations with the probability envelopes developed in this study provide a guide for the design of new energetic materials.