A cohesive finite element method (CFEM) framework for quantifying the thermomechanical response of polymer-bonded explosives (PBXs) at the microstructural level is developed. The analysis carried out concerns the impact loading of HMX/Estane at strain rates on the order of 104–105 s−1. Issues studied include large deformation, thermomechanical coupling, failure in the forms of microcracks in both bulk constituents and along grain/matrix interfaces, and frictional heating. The polymer matrix is described by a thermo-elasto-viscoelastic constitutive formulation, accounting for temperature dependence, strain rate sensitivity and strain hardening. The HMX crystals are assumed to be elastic. The CFEM framework allows the contributions of individual constituents, fracture and frictional contact along failed crack surfaces to heating to be tracked and analyzed. Digitized micrographs of actual PBX materials and idealized microstructures with Gaussian distributions of grain sizes are used in the analysis. The formation of local hot spots as potential ignition sites is primarily due to the viscoelastic dissipation in the matrix in early stages of deformation and frictional heating along crack surfaces in later stages of deformation. The framework is a useful tool for the design of energetic composites and the results can be used to establish microstructure–response relations that can be used to assess the performance of energetic composites.

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.

We report the results of a mechanistic study of energy localization in a HMX (High Melting point eXplosive octahydro-1,3,5,7-tetranitro-1,2,3,5-tetrazocine)=Estane PBX system during dynamic loading. The focus is on the thermal-mechanical response over the strain rate range of 10 4-10 5 s À1 under different confinement conditions. A recently developed cohesive finite element method is used to track and analyze the contributions to heating from different constituents, interfaces, deformation and fracture mechanisms, and internal friction. In particular, energy dissipations due to viscoelastic deformation, grain fracture, interfacial debonding, and friction along crack faces are quantified as functions of time and overall deformation. The materials analyzed have HMX volume fractions between 0.69 and 0.82. Calculations show that variation in strain rate can significantly affect the spatial distribution but not the overall number of hot spots. Higher confining stresses lead to more intense heating in the binder and more uniform distribution of hot spots. The evolution of hot spots is quantified as a function of loading condition, deformation and microstructural attributes. The microstructure-response relations obtained can be used to assess the initiation sensitivity of energetic composites.

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

The effect of transient stress waves on the microstructure of HMX-Estane, a polymerbonded explosive (PBX), is studied. Calculations carried out concern microstructures with HMX grain sizes on the order of 200 mm and grain volume fractions in the range of 0.50-0.82. The microstructural samples analysed have an aspect ratio of 5 : 1 (15 × 3 mm), allowing the transient wave propagation process resulting from normal impact to be resolved. Boundary loading is effected by the imposition of impact face velocities of 50-200 m s −1 . Different levels of grain-binder interface strength are considered. The analysis uses a recently developed cohesive finite element framework that accounts for coupled thermal-mechanical processes involving deformation, heat generation and conduction, failure in the forms of microcracks in both bulk constituents and along grain/matrix interfaces, and frictional heating along crack faces. Results show that the overall wave speed through the microstructures depends on both the grain volume fraction and interface bonding strength between the constituents and that the distance traversed by the stress wave before the initiation of frictional dissipation is independent of the grain volume fraction but increases with impact velocity. Energy dissipated per unit volume owing to fracture is highest near the impact surface and deceases to zero at the stress wavefront. On the other hand, the peak temperature rises are noted to occur approximately 2-3 mm from the impact surface. Scaling laws are developed for the maximum dissipation rate and the highest temperature rise as functions of impact velocity, grain volume fraction and grain-binder interfacial bonding strength.