Complete equation of state for [beta]-HMX and implications for initiation

A thermodynamically consistent equation of state for {beta}-HMX, the stable ambient polymorph of HMX, is developed that fits isothermal compression data and the temperature dependence of the specific heat computed from molecular dynamics. The equation of state is used to assess hot-spot conditions that would result from hydrodynamic pore collapse in a shock-to-detonation transition. The hot-spot temperature is determined as a function of shock strength by solving two Riemann problems in sequence: first for the velocity and density of the jet formed when the shock overtakes the pore, and second for the stagnation state when the jet impacts the far side of the pore. For a shock pressure below 5 GPa, the stagnation temperature from the jet is below the melt temperature at ambient pressure and hence insufficient for rapid reaction. Consequently for weak shocks a dissipation mechanism in addition to shock heating is needed to generate hot spots. When the stagnation temperature is sufficiently high for rapid reaction, the shock emanating from the hot spot is computed, assuming aconstant volume burn. For initial shocks below 20 GPa, the temperature behind the second shock is below 1000K and would not propagate a detonation wave. This analysis, based solely on the equation of state of the explosive, can serve as a check on mesoscale simulations of initiation in a plastic-bonded explosive

Pore collapse and hot spots in HMX

The computing power now available has led researchers to reconsider mesoscale simulations as a means to develop a detailed understanding of detonation waves in a heterogeneous explosive. Since chemical reaction rates are sensitive to temperature, hot spots are of critical importance for initiation. In a plastic-bonded explosive, shock desensitization experiments imply that hot spots generated by pore collapse dominate shock initiation. Here, for the collapse of a single pore driven by a shock, the dependence of the temperature distribution on numerical resolution and dissipative mechanism i s investigated. An inert material (with the constibtive properties of HMX) is used to better focus on the mechanics of pore collapse. ' h o important findings resulted from this study. Eust, too low a resolution can significantly enhance the hot-spot mass. Second, at even moderate piston velocities (< 1W s),s hock dissipation alone does not generate sufficient hot-spot mass. ' b oo ther dissipative mechanism investigated are plastic work and viscous heating. In the cases studied, the integrated lempera!xre distribution has a power-law tail with exponent related to a parameter with dimensions of viscosity. For a particular case, the parameter of either dissipative mechanism can be fit to obtain quantitatively the hot-spot mass needed for initiation. But the dissipative mechanisms scale differently with shock strength and pore size. Consequently, to predict initiation behavior over a range of stimuli and as the micro-stmcture properties of a PBX am varied, sufficient numerical resolution and the correct physical dissipative mechanism are essential

Triple Shock Entropy Theorem and Its Consequences

this article we only consider the problem of multiple intersections of the shock polars and the question it raises for nonuniqueness of shock interactions. For time dependent problems, the incoming wave types are assumed to be known at the initial time. When the solution changes slowly in time the wave pattern is determined by continuity of the polar solution. Some solutions have wave patterns in which the flow behind an outgoing wave is subsonic. In these cases, downstream boundary conditions are needed to determine the rest frame of the node. Time dependent boundary conditions can cause a wave pattern to bifurcate or change form. Bifurcations can be triggered by acoustic waves impacting a node (the limiting case in which a weak node collides and scatters off another node) or forced by a sudden change in geometry, e.g., a shock impacting a wedge. Thus, for time dependent problems the nonuniqueness of shock interactions is a consequence of the ambiguity of when a wave pattern bifurcates and the nonuniqueness of the possible wave patterns into which another can bifurcate. Both shock tube experiments and numerical experiments have shown that when a shock impacts a wedge leading to a Mach reflection, the path of the triple point can be greatly affected by a boundary layer due to either viscosity or heat conduction Henderson et al. (1997). Thus, dissipative mechanisms at small scales can lead to local downstream boundary conditions which affects the bifurcation process. Additional complications arise when determining the wave patterns that occur in steady state flows. In steady state, the wave pattern must be compatible with the global flow. Moreover, the identification of incoming and outgoing waves may depend on the downstream flow; e.g, figure 6b indicates how a downstre..

Elastic properties of HMX.

Atomistic molecular dynamics simulations have been used to calculate isothermal elastic properties for {beta}-, {alpha}-, and {delta}-HMX. The complete elastic tensor for each polymorph was determined at room temperature and pressure via analysis of microscopic strain fluctuations using formalism due to Rahman and Parrinello [J. Chem. Phys. 76,2662 (1982)]. Additionally, the isothermal compression curve was computed for {beta}-HMX for 0 {le} p {le} 10.6 GPa; the bulk modulus K and its pressure derivative K{prime} were obtained from two fitting forms employed previously in experimental studies of the {beta}-HMX equation of state. Overall, the results indicate good agreement between the bulk modulus predicted from the measured and calculated compression curves. The bulk modulus determined directly from the elastic tensor of {beta}-HMX is in significant disagreement with the compression curve-based results. The explanation for this discrepancy is an area of current research