Reactive Co/Al multilayers are uniformly structured materials that may be ignited to produce rapid and localized heating. Prior studies varying the bilayer thickness (i.e., sum of two individual layers of Co and Al) have revealed different types of flame morphologies, including: (a) steady/planar, (b) wavy/periodic, and (c) transverse bands, originating in the flame front. These instabilities resemble the “spin waves” first observed in the early studies of solid combustion (i.e., Ti cylinder in a N2 atmosphere), and are likewise thought to be due to the balance of heat released by reaction and heat conduction forward into the unreacted multilayer. However, the multilayer geometry and three-dimensional (3D) edge effects are relatively unexplored. In this work, a new diffusion-limited reaction model for Co/Al multilayers was implemented in large, novel 3D finite element analysis (FEA) simulations, in order to study the origins of these spinlike flames. This reaction model builds upon previous work by introducing three new phase-dependent property models for: (1) the diffusion coefficient, (2) anisotropic thermal conductivity tensor, and (3) bulk heat capacity, as well as one additional model for the bilayer-dependent heat of reaction. These novel 3D simulations are the first to predict both steady and unsteady flames in Co/Al multilayers. Moreover, two unsteady modes of flame propagation are identified, which depend on the enhanced conduction losses with slower flames, as well as flame propagation around notched edges. Future work will consider the generality of the current modeling approach and also seek to define a more generalized set of stability criteria for additional multilayer systems.
We present an approach and relevant models for predicting the probabilistic shock-to-detonation transition (SDT) behavior and Pop plot (PP) of heterogeneous energetic materials (HEM) via mesoscopic microstructure-explicit (ME) and void explicit (VE) simulations at the millimeter (mm) sample size scale. Although the framework here is general, the particular material considered in this paper is pressed Octahydro-1,3,5,7-tetranitro-1,2,3,5-tetrazocine (HMX). To systematically delineate the effects of material heterogeneities, four material cases are considered. These cases are homogeneous material, material with granular microstructure but no voids, homogeneous material with voids, and material with both granular microstructure and voids. Statistically equivalent microstructure sample sets (SEMSS) are generated and used. Eulerian hydrocode simulations explicitly resolve the material heterogeneities, voids, and the coupled mechanical-thermal-chemical processes. In particular, it is found that both microstructure and voids strongly influence the SDT behavior and PP. The effects of different combinations of microstructure heterogeneity and voids on the SDT process and PP are quantified and rank-ordered. The overall framework uses the Mie–Grüneisen equation of state and a history variable reactive burn model (HVRB). A novel probabilistic representation for quantifying the PP is developed, allowing the calculation of (1) the probability of observing SDT at a given combination of shock pressure and run distance, (2) the run-distance to detonation under a given combination of shock pressure and prescribed probability, and (3) the shock pressure required for achieving SDT at a given run distance with a prescribed probability. The results are in agreement with general trends in experimental data in the literature.
Using random walk analyses we explore diffusive transport on networks obtained from contacts between isotropically compressed, monodisperse, frictionless sphere packings generated over a range of pressures in the vicinity of the jamming transition p→0. For conductive particles in an insulating medium, conduction is determined by the particle contact network with nodes representing particle centers and edges contacts between particles. The transition rate is not homogeneous, but is distributed inhomogeneously due to the randomness of packing and concomitant disorder of the contact network, e.g., the distribution of the coordination number. A narrow escape time scale is used to write a Markov process for random walks on the particle contact network. This stochastic process is analyzed in terms of spectral density of the random, sparse, Euclidean and real, symmetric, positive, semidefinite transition rate matrix. Results show network structures derived from jammed particles have properties similar to ordered, euclidean lattices but also some unique properties that distinguish them from other structures that are in some sense more homogeneous. In particular, the distribution of eigenvalues of the transition rate matrix follow a power law with spectral dimension 3. However, quantitative details of the statistics of the eigenvectors show subtle differences with homogeneous lattices and allow us to distinguish between topological and geometric sources of disorder in the network.
We have used several configurations of the Sandia Instrumented Thermal Ignition (SITI) experiment to develop a pressure-dependent, four-step ignition model for a plastic bonded explosive (PBX 9407) consisting of 94 wt.% RDX (hexahydro-1,3,5-trinitro-1,3,5-triazine), and a 6 wt.% VCTFE binder (vinyl chloride/chlorotrifluoroethylene copolymer). The four steps include desorption of water, decomposition of RDX to form equilibrium products, pressure-dependent decomposition of RDX forming equilibrium products, and decomposition of the binder to form hydrogen chloride and a nonvolatile residue (NVR). We address drying, binder decomposition, and decomposition of the RDX component from the pristine state through the melt and into ignition. We used Latin Hypercube Sampling (LHS) of the parameters to determine the sensitivity of the model to variation in the parameters. We also successfully validated the model using one-dimensional time-to-explosion (ODTX and P-ODTX) data from a different laboratory. Our SITI test matrix included 1) different densities ranging from 0.7 to 1.63 g/cm3, 2) free gas volumes ranging from 1.2 to 38 cm3, and 3) boundary temperatures ranging from 170 to 190 °C. We measured internal temperatures using embedded thermocouples at various radial locations as well as pressure using tubing that was connected from the free gas volume (ullage) to a pressure gauge. We also measured gas flow from our vented experiments. A borescope was included to obtain in situ video during some SITI experiments. We observed significant changes in the explosive volume prior to ignition. Our model, in conjunction with data observations, imply that internal accumulation of decomposition gases in high density PBX 9407 (90% of the theoretical maximum density) can contribute to significant strain whether or not the experiment is vented or sealed.
Detonation corner turning describes the ability of a detonation wave to propagate into unreacted explosive that is not immediately in the path normal to the wave. The classic example of a corner turning test has a cylindrical geometry and involves a small diameter explosive propagating into a larger diameter explosive as described by Los Alamos' Mushroom test, where corner turning is inferred from optical breakout of the detonation wave. We present a complimentary method to study corner turning in millimeter-scale explosives through the use of vapor deposition to prepare the slab (quasi-2D) analog of the axisymmetric mushroom test. Because the samples are in a slab configuration, optical access to the explosive is excellent and direct imaging of the detonation wave and "dead zone" that results during corner turning is possible. Micromushroom test results are compared for two explosives that demonstrate different behaviors: pentaerythritol tetranitrate (PETN), which has corner turning properties that are nearly ideal; and hexanitroazobenzene (HNAB), which has corner turning properties that reveal a substantial dead zone.
Vapor-deposited hexanitroazobenzene (HNAB) is an explosive with unique physical characteristics resulting from the deposition process that make it desirable for the study of microstructure effects. A relatively understudied high explosive, few data are available on the equation of state (EOS) of HNAB reactants or products. HNAB samples exhibiting high density and sub-micron porosity and grain size were prepared using physical vapor deposition onto polymethyl methacrylate (PMMA) and lithium fluoride (LiF) substrates. The samples were ramp compressed quasi-isentropically using VELOCE, a compact pulsed power generator. Evidence of a low pressure phase transition was observed in HNAB. Interferometric measurements of reference and sample interface velocities enabled inference of the unreacted EOS for HNAB using DAKOTA, an optimization toolkit. Initial simulations of the HNAB critical thickness experiment have been carried out using the parameterized EOS, and a products EOS from thermal equilibrium calculations.
Direct laser irradiation of sputter deposited Al/Pt nanolaminate multilayers results in rapid local heating and exothermic mixing of reactant layers. Milli- and microsecond pulsed laser irradiation under certain test conditions leads to single-point ignition of rapid, self-propagating, formation reactions. Multilayers having bilayer thicknesses of 328 nm, 164 nm, and 65 nm are characterized by their ignition onset times and temperatures. Smaller bilayer thickness multilayers require less laser intensity for ignition compared with larger bilayer designs (when utilizing a particular pulse duration). The relationship between laser intensity and ignition onset time is used to calibrate an activation energy for ignition within a finite element reactive heat transport model. The local heating rate is varied from 104 K/s to 106 K/s by selecting a laser intensity. Kissinger analysis was performed on the heating rate-dependent ignition temperatures measured with high speed pyrometry to experimentally determine an activation energy in the foils of (6.2 ± 1.6 × 104 J/mole atoms). This value is then compared to an activation energy produced from model fits to an ignition onset time of 7.2 × 104 J/mole atoms.
A new paradigm is introduced for modeling reactive shock waves in heterogeneous solids at the continuum level. Inspired by the probability density function methods from turbulent reactive flows, it is hypothesized that the unreacted material microstructures lead to a distribution of heat release rates from chemical reaction. Fluctuations in heat release, rather than velocity, are coupled to the reactive Euler equations which are then solved via the Riemann problem. A numerically efficient, one-dimensional hydrocode is used to demonstrate this new approach, and simulation results of a representative impact calculation (inert flyer into explosive target) are discussed.
A diffusion-limited reaction model was calibrated for Al/Pt multilayers ignited on oxidized silicon, sapphire, and tungsten substrates, as well as for some Al/Pt multilayers ignited as free-standing foils. The model was implemented in a finite element analysis code and used to match experimental burn front velocity data collected from several years of testing at Sandia National Laboratories. Moreover, both the simulations and experiments reveal well-defined quench limits in the total Al + Pt layer (i.e., bilayer) thickness. At these limits, the heat generated from atomic diffusion is insufficient to support a self-propagating wave front on top of the substrates. Quench limits for reactive multilayers are seldom reported and are found to depend on the thermal properties of the individual layers. Here, the diffusion-limited reaction model is generalized to allow for temperature- and composition-dependent material properties, phase change, and anisotropic thermal conductivity. Utilizing this increase in model fidelity, excellent overall agreement is shown between the simulations and experimental results with a single calibrated parameter set. However, the burn front velocities of Al/Pt multilayers ignited on tungsten substrates are over-predicted. Possible sources of error are discussed and a higher activation energy (from 41.9 kJ/mol.at. to 47.5 kJ/mol.at.) is shown to bring the simulations into agreement with the velocity data observed on tungsten substrates. This higher activation energy suggests an inhibited diffusion mechanism present at lower heating rates.
The complex physical phenomenon of shock wave interaction with material heterogeneities has significant importance and nevertheless remains little understood. In many materials, the observed macroscale response to shock loading is governed by characteristics of the microstructure. Yet, the majority of computational studies aimed at predicting phenomena affected by these processes, such as the initiation and propagation of detonation waves in explosives or shock propagation in geological materials, employ continuum material and reactive burn model treatment. In an effort to highlight the grain-scale processes that underlie the observable effects in an energetic system, a grain-scale model for hexanitrostilbene (HNS) has been developed. The measured microstructures were used to produce synthetic computational representations of the pore structure, and a density functional theory molecular dynamics derived equation of state (EOS) was used for the fully dense HNS matrix. The explicit inclusion of the microstructure along with a fully dense EOS resulted in close agreement with historical shock compression experiments. More recent experiments on the dynamic reaction threshold were also reproduced by inclusion of a global kinetics model. The complete model was shown to reproduce accurately the expected response of this heterogeneous material to shock loading. Mesoscale simulations were shown to provide a clear insight into the nature of threshold behavior and are a way to understand complex physical phenomena.
Shock wave interactions with defects, such as pores, are known to play a key role in the chemical initiation of energetic materials. The shock response of hexanitrostilbene is studied through a combination of large-scale reactive molecular dynamics and mesoscale hydrodynamic simulations. In order to extend our simulation capability at the mesoscale to include weak shock conditions (<6 GPa), atomistic simulations of pore collapse are used to define a strain-rate-dependent strength model. Comparing these simulation methods allows us to impose physically reasonable constraints on the mesoscale model parameters. In doing so, we have been able to study shock waves interacting with pores as a function of this viscoplastic material response. We find that the pore collapse behavior of weak shocks is characteristically different than that of strong shocks.
Al/Pt nanolaminates with a bilayer thickness (tb, width of an Al/Pt pair-layer) of 164 nm were irradiated with single laser pulses with durations of 10 ms and 0.5 ms at 189 W/cm2 and 1189 W/cm2, respectively. The time to ignition was measured for each pulse, and shorter ignition times were observed for the higher power/shorter pulse width. Videographic images of the irradiated area shortly after ignition show a non-uniform radial brightness for the longer pulse, while the shorter pulse shows uniform brightness. A diffusion-limited single step reaction mechanism was implemented in a finite element package to model the progress from reactants to products at both pulse widths. The model captures well both the observed ignition delay and qualitative observations regarding the non-uniform radial temperature.
A physically-based form of the Mie–Grüneisen equation of state (EOS) is derived for calculating 1d planar shock temperatures, as well as hot spot temperature distributions from heterogeneous impact simulations. This form utilises a multi-term Einstein oscillator model for specific heat, and is completely algebraic in terms of temperature, volume, an integrating factor, and the cold curve energy. Moreover, any empirical relation for the reference pressure and energy may be substituted into the equations via the use of a generalised reference function. The complete EOS is then applied to calculations of the Hugoniot temperature and simulation of hydrodynamic pore collapse using data for the secondary explosive, hexanitrostilbene (HNS). From these results, it is shown that the choice of EOS is even more significant for determining hot spot temperature distributions than planar shock states. The complete EOS is also compared to an alternative derivation assuming that specific heat is a function of temperature alone, i.e. cv(T). Temperature discrepancies on the order of 100–600 K were observed corresponding to the shock pressures required to initiate HNS (near 10 GPa). Overall, the results of this work will improve confidence in temperature predictions. By adopting this EOS, future work may be able to assign physical meaning to other thermally sensitive constitutive model parameters necessary to predict the shock initiation and detonation of heterogeneous explosives.
Reactive multilayers consisting of alternating layers of Al and Pt were irradiated by single laser pulses ranging from 100 μs to 100 ms in duration, resulting in the initiation of rapid, self-propagating reactions. The threshold intensities for ignition vary with the focused laser beam diameter, bilayer thickness, and pulse length and are affected by solid state reactions and conduction of heat away from the irradiated regions. High-speed photography was used to observe ignition dynamics during irradiation and elucidate the effects of heat transfer into a multilayer foil. For an increasing laser pulse length, the ignition process transitioned from a more uniform to a less uniform temperature profile within the laser-heated zone. A more uniform temperature profile is attributed to rapid heating rates and heat localization for shorter laser pulses, and a less uniform temperature profile is due to slower heating of reactants and conduction during irradiation by longer laser pulses. Finite element simulations of laser heating using measured threshold intensities indicate that micron-scale ignition of Al/Pt occurs at low temperatures, below the melting point of both reactants.
This report summarizes a project in which the authors sought to develop and deploy: (i) experimental techniques to elucidate the complex, multiscale nature of thermal transport in particle-based materials; and (ii) modeling approaches to address current challenges in predicting performance variability of materials (e.g., identifying and characterizing physical- chemical processes and their couplings across multiple length and time scales, modeling information transfer between scales, and statically and dynamically resolving material structure and its evolution during manufacturing and device performance). Experimentally, several capabilities were successfully advanced. As discussed in Chapter 2 a flash diffusivity capability for measuring homogeneous thermal conductivity of pyrotechnic powders (and beyond) was advanced; leading to enhanced characterization of pyrotechnic materials and properties impacting component development. Chapter 4 describes success for the first time, although preliminary, in resolving thermal fields at speeds and spatial scales relevant to energetic components. Chapter 7 summarizes the first ever (as far as the authors know) application of TDTR to actual pyrotechnic materials. This is the first attempt to actually characterize these materials at the interfacial scale. On the modeling side, new capabilities in image processing of experimental microstructures and direct numerical simulation on complicated structures were advanced (see Chapters 3 and 5). In addition, modeling work described in Chapter 8 led to improved prediction of interface thermal conductance from first principles calculations. Toward the second point, for a model system of packed particles, significant headway was made in implementing numerical algorithms and collecting data to justify the approach in terms of highlighting the phenomena at play and pointing the way forward in developing and informing the kind of modeling approach originally envisioned (see Chapter 6). In both cases much more remains to be accomplished.
The subject of this work is the development of models for the numerical simulation of matter, momentum, and energy balance in heterogeneous materials. These are materials that consist of multiple phases or species or that are structured on some (perhaps many) scale(s). By computational mechanics we mean to refer generally to the standard type of modeling that is done at the level of macroscopic balance laws (mass, momentum, energy). We will refer to the flow or flux of these quantities in a generalized sense as transport. At issue here are the forms of the governing equations in these complex materials which are potentially strongly inhomogeneous below some correlation length scale and are yet homogeneous on larger length scales. The question then becomes one of how to model this behavior and what are the proper multi-scale equations to capture the transport mechanisms across scales. To address this we look to the area of generalized stochastic process that underlie the transport processes in homogeneous materials. The archetypal example being the relationship between a random walk or Brownian motion stochastic processes and the associated Fokker-Planck or diffusion equation. Here we are interested in how this classical setting changes when inhomogeneities or correlations in structure are introduced into the problem. Aspects of non-classical behavior need to be addressed, such as non-Fickian behavior of the mean-squared-displacement (MSD) and non-Gaussian behavior of the underlying probability distribution of jumps. We present an experimental technique and apparatus built to investigate some of these issues. We also discuss diffusive processes in inhomogeneous systems, and the role of the chemical potential in diffusion of hard spheres is considered. Also, the relevance to liquid metal solutions is considered. Finally we present an example of how inhomogeneities in material microstructure introduce fluctuations at the meso-scale for a thermal conduction problem. These fluctuations due to random microstructures also provide a means of characterizing the aleatory uncertainty in material properties at the mesoscale.