A criterion for the ignition of granular explosives (GXs) and polymer-bonded explosives (PBXs) under shock and non-shock loading is developed. The formulation is based on integration of a quantification of the distributions of the sizes and locations of hotspots in loading events using a cohesive finite element method (CFEM) developed recently and the characterization by Tarver et al. [C. M. Tarver et al., "Critical conditions for impact-and shock-induced hot spots in solid explosives," J. Phys. Chem. 100, 5794-5799 (1996)] of the critical size-temperature threshold of hotspots required for chemical ignition of solid explosives. The criterion, along with the CFEM capability to quantify the thermal-mechanical behavior of GXs and PBXs, allows the critical impact velocity for ignition, time to ignition, and critical input energy at ignition to be determined as functions of material composition, microstructure, and loading conditions. The applicability of the relation between the critical input energy (E) and impact velocity of James [H. R. James, "An extension to the critical energy criterion used to predict shock initiation thresholds," Propellants, Explos., Pyrotech. 21, 8-13 (1996)] for shock loading is examined, leading to a modified interpretation, which is sensitive to microstructure and loading condition. As an application, numerical studies are undertaken to evaluate the ignition threshold of granular high melting point eXplosive, octahydro-1,3,5,7-tetranitro-1,2,3,5-tetrazocine (HMX) and HMX/Estane PBX under loading with impact velocities up to 350 ms À1 and strain rates up to 10 5 s À1. Results show that, for the GX, the time to criticality (t c) is strongly influenced by initial porosity, but is insensitive to grain size. Analyses also lead to a quantification of the differences between the responses of the GXs and PBXs in terms of critical impact velocity for ignition, time to ignition, and critical input energy at ignition. Since the framework permits explicit tracking of the influences of microstructure, loading, and mechanical constraints, the calculations also show the effects of stress wave reflection and confinement condition on the ignition behaviors of GXs and PBXs.

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Random variations in constituent properties, constituent distribution, microstructural morphology, and loading cause the ignition of explosives to be inherently stochastic. An approach is developed to computationally predict and quantify the stochasticity of the ignition process in polymer-bonded explosives (PBXs) under impact loading. The method, the computational equivalent of carrying out multiple experiments under the same conditions, involves subjecting sets of statistically similar microstructure samples to identical overall loading and characterizing the statistical distribution of the ignition response of the samples. Specific quantities predicted based on basic material properties and microstructure attributes include the critical time to ignition at given load intensity and the critical impact velocity below which no ignition occurs. The analyses carried out focus on the influence of random microstructure geometry variations on the critical time to ignition at given load intensity and the critical impact velocity below which no ignition occurs. Results show that the probability distribution of the time to criticality (t c) follows the Weibull distribution. This probability distribution is quantified as a function of microstructural attributes including grain volume fraction, grain size, specific binder-grain interface area, and the stochastic variations of these attributes. The relations reveal that the specific binder-grain interface area and its stochastic variation have the most influence on the critical time to ignition and the critical impact velocity below which no ignition is observed. For a PBX with 95% octahydro-1,3,5,7-tetranitro-1,3,5,7-tetrazocine content, the computationally predicted minimum impact velocity for ignition is in the range of 54-63 ms À1 depending on microstructure. This range is comparable to values measured experimentally for PBX9501 (53 ms À1 by Chidester et al., "Low amplitude impact testing and analysis of pristine and aged solid high explosives," in Eleventh (International) Symposium on Detonation, ONR (1998), 33300. 60-84 ms À1 by Gruau et al., "Ignition of a confined high explosive under low velocity impact," Int. J. Impact Eng. 36, 537-550 (2009)). V