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The ignition threshold of an energetic material (EM) quantifies the macroscopic conditions for the onset of self-sustaining chemical reactions. The threshold is an important theoretical and practical measure of material attributes that relate to safety and reliability. Historically, the thresholds are measured experimentally. Here, we present a new Lagrangian computational framework for establishing the probabilistic ignition thresholds of heterogeneous EM out of the evolutions of coupled mechanical-thermal-chemical processes using mesoscale simulations. The simulations explicitly account for microstructural heterogeneities, constituent properties, and interfacial processes and capture processes responsible for the development of material damage and the formation of hotspots in which chemical reactions initiate. The specific mechanisms tracked include viscoelasticity, viscoplasticity, fracture, post-fracture contact, frictional heating, heat conduction, reactive chemical heating, gaseous product generation, and convective heat transfer. To determine the ignition threshold, the minimum macroscopic loading required to achieve self-sustaining chemical reactions with a rate of reactive heat generation exceeding the rate of heat loss due to conduction and other dissipative mechanisms is determined. Probabilistic quantification of the processes and the thresholds are obtained via the use of statistically equivalent microstructure sample sets (SEMSS). The predictions are in agreement with available experimental data. [ABSTRACT FROM AUTHOR]

Graphical abstract Highlights • Contributions of plasticity and friction to hotspots in PBX9501 are analyzed. • Overall, dissipation due to plasticity outweighs frictional dissipation. • Frictional dissipation is localized and very important in development of hotspots. • Constituent plasticity is much less localized and very important. • Increased constituent plasticity results in lower ignition sensitivity. Abstract The ignition of energetic materials (EM) under dynamic loading is mainly controlled by localized temperature spikes known as hotspots. Hotspots occur due to several dissipation mechanisms, including viscoplasticity, viscoelasticity, and internal friction along crack surfaces. To analyze the contributions of these mechanisms, we quantify the ignition probability, energy dissipation, damage evolution, and hotspot characteristics of polymer-bonded explosives (PBXs) with various levels of constituent plasticity of the energetic phase and internal crack face friction. Using PBX9501 consisting of HMX (Octahydro-1,3,5,7-Tetranitro-1,2,3,5-Tetrazocine) and Estane as a reference material, we analyze variants of this material with several values of the yield stress of the energetic phase and coefficients of internal crack face friction, while other parameters are kept unchanged. The impact loading involves piston velocities between 200 and 1200 m/s. The analysis uses a Lagrangian cohesive finite element framework that explicitly accounts for finite-strain elastic-viscoplastic deformation of the grains, viscoelastic deformation of the binder, arbitrary crack initiation and propagation in the grains and the binder, debonding between the grains and the binder, contact between internal surfaces, friction and frictional heating along internal surfaces, heat generation resulting from inelastic bulk deformation, and heat conduction. To determine the ignition status of the material or "go" or "no-go" state, we use a criterion based on a criticality threshold obtained from chemical kinetics calculations. For PBX with various levels of HMX plasticity and friction, the probability of ignition, the evolution of dissipation caused by plasticity and friction, the density of cracks, and the locations of cracks are quantified. Results show that samples with higher levels of constituent plasticity (lower yield strengths) or lower levels of internal friction are less likely to ignite. The relative importance of plasticity and friction depends on load intensity, with frictional heating decreasing as load intensity increases. Although the overall viscoplastic heating outweighs the overall frictional heating, friction plays a very important role in hotspot development at all load intensities analyzed, owing to the fact that frictional heating is more localized than viscoplastic heating. The predicted thresholds and ignition probabilities are expressed in a load intensity-load duration relation for PBX with different constituent properties. [ABSTRACT FROM AUTHOR]