Al Composites. Part 1: Mechanics of

Article pubs.acs.org/JPCC

Shock Loading of Granular Ni/Al Composites. Part 1: Mechanics of Loading Mathew J. Cherukara,†,‡ Timothy C. Germann,‡ Edward M. Kober,‡ and Alejandro Strachan*,† †

School of Materials Engineering and Birck Nanotechnology Center, Purdue University, West Lafayette, Indiana 47907, United States Theoretical Division, Los Alamos National Laboratory, Los Alamos, New Mexico 87545, United States

‡

ABSTRACT: We present molecular dynamics simulations of the thermomechanical response under shock loading of a granular material consisting of laminated Ni/Al grains. We observe two regimes: At low piston velocities (up ≲ 1km/s), the shock wave is diffuse, and the width of the shock front decreases with increasing piston velocity. Beyond a critical shock strength, however, the width remains relatively constant at approximately the mean grain radius. This change in behavior follows from an evolution of the mechanism of compaction with increasing insult strength. The mechanism evolves from plastic deformation-mediated pore collapse for relatively weak shocks, to solid extrusion and fluid ejecta filling pores ahead of the shock front at intermediate strengths, and finally to atomic jetting into the pore for very strong shocks (up ≳ 2 km/s). High-energy fluid ejecta into pores leads to the formation of flow vorticity and can result in a large fraction of the input energy localizing into translational kinetic energy components in addition to the formation of hot spots. This has implications for the mechanical mixing of Ni and Al in these reactive composites.

1. INTRODUCTION

Two classes of reaction types have been proposed based on the relative time scales of reaction and shock propagation:13 shock-assisted reactions, in which the reaction initiates several microseconds or more after the passage of the shock wave (under the residual pressures, temperatures, and defective conditions left in the wake of the shock), and shock-induced reactions, in which reaction initiation occurs within a few nanoseconds, right behind the shock front. Whereas shockassisted reactions have been studied extensively through experiments,14−16 shock-induced reactions have proved much harder to characterize as a consequence of the extremely short time scales involved. At these time scales (up to a few nanoseconds), it is extremely difficult to probe the processes leading up to and during the initiation of chemistry in real time. In addition, probes average over an area, making it impossible to pick up strongly localized effects such as the generation of hot spots (often a few tens of nanometers in diameter) through void collapse or severe plastic deformation. Fortunately, these length and time scales are becoming accessible to molecular dynamics (MD) simulations, which can explicitly capture the complex interplay of mechanical and chemical processes,17−22 under extreme conditions of temperature and pressure.23−26 In this, the first of two related articles, we describe the mechanical processes during the dynamic compression of a granular composite of Ni/Al; the second part will focus on the subsequent chemical reactions.27 Whereas granular compaction has been studied extensively using continuum models,28,29 comparatively little effort has

The compaction of granular materials is an important manufacturing process in a variety of industries. Examples include the compaction of pills in the pharmaceutical industry,1 reactive sintering of ceramics, 2 food processing, 3 the manufacture of bulk nanomaterials from nanopowders,4 and the synthesis of intermetallic reactive composites with improved performance.5 Our work is motivated by intermetallic reactive composites (IRCs), a class of energetic material that can undergo exothermic reactions under shock or thermal initiation. IRCs have found applications where strong, localized sources of heat are required, such as in environmentally friendly primers,6 in reactive welding or joining7 and as nanoscale energy sources for bioagent neutralization.8 Recent experimental work has shown that the sensitivity of Ni/Al IRCs to shock and thermal initiation and other reaction characteristics can be engineered by altering the micro and nanostructure through the process of high-energy mechanical milling.9 The process of milling powders of nickel and aluminum leads to the formation of a loose granular compact of grains with a finely mixed, lamellar structure of Ni/Al, and is an attractive alternative to other fabrication techniques like sputtering10 due to cost. The internal microstructure of the Ni/Al grains can be controlled through processing,5 and while it is understood that a more intimate mixing leads to increased sensitivity and faster propagation velocity,11,12 we lack quantitative correlations between nano- and microstructure and thermomechanochemical response. This is particularly true for shock initiation, where nonequilibrium loading leads to fast heating rates and the granular nature of the materials leads to energy localization and accelerated intermixing due to the influence of porosity. © 2014 American Chemical Society

Received: August 1, 2014 Revised: October 10, 2014 Published: October 16, 2014 26377

dx.doi.org/10.1021/jp507795w | J. Phys. Chem. C 2014, 118, 26377−26386

The Journal of Physical Chemistry C

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Figure 1. (a) Initial sample configuration after thermalization for 500 ps at 10 K, where colors within each grain represent the layered Ni/Al structure. Two shock waves are generated by the shrinking boundary along the direction shown. (b) Example of a grain with facets cut randomly but weighted to prefer low-energy orientations (Ni is in pink, Al is in blue, and the passivated layer is in yellow). (c) Wulff surface used in the construction of each grain. Values in panel c were taken from Zhang et al.34

dimensional structure with faceted, columnar grains, as shown in Figure 1. The simulation cells are relatively short (∼9 nm) in the longitudinal direction of the columnar grains (normal to the page in Figure 1), which enables us to pack 40 grains each with an average cross-sectional diameter of 40 nm and simulation cell lengths of 320 nm, resulting in a total of ∼41 million atoms. Creating the granular microstructures involves two main steps: (i) creating Ni/Al faceted grains and (ii) packing them into a granular material. 2.1.1. Creating Faceted Ni/Al Grains. Each grain is built independently, with an average of 6 sides and a standard deviation of 1. The distances of the grain faces from the grain center are Gaussian-distributed with a mean of 20 nm and a standard deviation of 2 nm (giving each grain an average diameter of 40 nm). Within each grain, the nanostructure consists of a periodic laminate (∼7-nm period) of Ni:Al ≈ 1:1 with the interface normal oriented along the [111] crystallographic direction of both the Ni and Al fcc layers32,33 and the out-of-plane direction (Y axis) oriented along [101̅]. The orientations of the grain faces are chosen at random, but weighted to prefer low-surface-energy orientations using the mean of the surface energies of the Ni and Al crystals.34 The inverses of these surface energies (mean of Ni and Al) for different crystallographic orientations on the Wulff surface normal to the [101̅] direction (the out-of-plane direction) are used to weight facet orientations that are selected randomly. Multiple facets with the same orientation within one grain are not allowed; if the same orientation if chosen twice, a new direction is selected. The same procedure is repeated for the chosen number of sides, and the polygon vertices are formed from the intersecting facet line segments. At this stage, we have a set of irregular polygons of varying sides, sizes, and facet orientations. These polygons are filled with a periodic laminate of Ni/Al atoms with a random starting position within each grain (random position along the [111] laminate period direction). Finally, the surface of each grain is passivated up to a depth of 1 nm by randomly switching Ni and Al atoms. This is

been made to model the dynamic response of a granular material with subgrain resolution. One such study30 observed stress localization within grains and stress bridging across grains, which leads to the macroscopically observed force chains.1,31 An MD study of the shock compression of nanoporous Cu4 (using idealized cylindrical grains) found local variations in the shock front, with multiple mechanisms of void collapse. In this article, we present fully atomistic simulations of the dynamic shock response of a granular Ni/Al composite with realistic grain shapes, providing hitherto unavailable insight into the shock wave propagation and the mechanisms that govern compaction and void collapse in such composite materials. We find that the shock front profile and the nature of void collapse are closely related, with the front being extremely diffuse when the void compaction is driven by plastic deformation of surrounding grains and becoming sharper for stronger loading when void filling is through fluid ejecta or jetting. In addition, we find that the presence of voids redirects shock energy from thermal modes to translational ones, leading to the formation of mass flux vortices in voids that are favorably oriented with respect to the shock front. The rest of this article is organized as follows: Section 2 describes the process of building and packing of the granular composite, as well as other details of our MD simulation approach. Section 3 describes the effects of particle velocity on shock width and the formation of force chains. Section 4 presents void collapse mechanisms and their relationship to the resulting shock width. Section 5 discusses the influences of porosity and jetting on energy transfer, and section 6 summarizes our results and discusses their potential implications for subsequent chemical reactivity and hot spot formation, the subject of a subsequent article.

2. SIMULATION DETAILS 2.1. Model Nanostructure. To obtain a model granular material that combines loosely packed grains with a Ni/Al laminated internal microstructure, we created a quasi-two26378



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Figure 2. Snapshots of shock propagation and the corresponding velocity profiles at (a) 5, (b) 15, (c) 25, (d) 35, (e) 40, and f) 45 ps for the up = 2 km/s case. Arrows show the direction of shock propagation. Green curves show the shock velocity as a function of position, whereas red lines show an ideal shock at the same position.

Although the problem of packing irregular N-sided polygons is an unsolved one, several algorithms such as the “greedy algorithm” and the “largest area first algorithm” have been proposed.35 The packing densities obtained using the algorithm that we have used (up to ∼70%) are comparable to the best from competing algorithms. The sample used for the shock simulations in this article has a packing fraction of ∼63%, which is comparable to those of the granular compacts used experimentally, which have packing fractions between 60% and 72%.36 The resulting structure is thermalized at 10 K under isobaric−isothermal conditions (NPT ensemble, with constant number of particles, pressure, and temperature) for 500 ps at 1 atm. This allows some relative grain rotation and sliding, as well as surface bonding to develop across grains, leading to a betterrelaxed initial structure for the shock simulations. Figure 1a shows the packed ensemble used for all of the simulations in this article, consisting of 40 grains, each with ∼1 million atoms, giving a structure with dimensions of 320 nm × 8.6 nm x 320 nm (the Y direction being the out-of-plane, periodic direction). 2.2. Shock Simulations and Atomic Interactions. To model the shock compression, the boundaries in the horizontal direction (along X) are compressed at constant particle (or piston) velocity up, giving rise to two shock waves that originate at the periodic boundary along X and meet at the center of the

done to ensure that the free surfaces, which have increased reactivity,12 do not unduly influence the reaction kinetics. Figure 1b shows the section of the Wulff surface used in the construction of each grain, whereas Figure 1c shows a close up of one such grain. Ni atoms are shown in red, Al atoms are shown in blue, and the passivated layer is shown in yellow. 2.2.2. Packing Ni/Al Grains into a Granular Solid. We now have a set of columnar polygonal grains that extend indefinitely through the periodic boundary along Y. To pack the grains into a granular ensemble with a high packing fraction, we employ an algorithm that proceeds as follows: Grains are first sorted by increasing size. The largest grain is first placed in the center of the simulation cell. Then, the next largest grain is brought in and slid and rotated around the grain(s) already in the simulation cell, finding the position and orientation that minimizes the radius of the ensemble. At every point of the analysis, we check for overlap between the grain being introduced to the ensemble and the grains that have already been placed. The process is repeated until all of the grains are grouped into a single ensemble. Finally, the boundaries along X and Z are shrunk to make the simulation cell periodic in all dimensions (recall that the grains are columnar and are hence already periodic along the Y dimension), again taking care to ensure that no grains overlap. 26379



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Figure 3. Shock profiles for different piston velocities during the first shock. A sharper shock is observed for higher piston velocities. The last time on each plot corresponds to a time during the process of reshock.

simulation cell. All simulations were performed using the LAMMPS package37 and the embedded-atom potential published by Purja Pun and Mishin38 to describe the atomic interactions. The potential was parametrized using the lattice parameters and elastic constants of B2 NiAl, as well as the formation energies of several intermetallics including Ni3Al and NiAl, and captures well the melting temperatures of Ni, Al, and the intermetallic phases. To extract local averages of variables of interest, the sample is binned in a two-dimensional (X−Z) grid with cell dimensions of 5 Å × 5 Å. Local temperatures and velocities are calculated by partitioning the atomic velocities as follows: First, the center-of-mass velocity of each bin is calculated as vIcm = MI −1 ∑ mivi i∈I

TI =

∑ I

1 MI |vIcm|2 2

∑ i∈I

1 mi |vi − vIcm|2 2

(3)

where kB is the Boltzmann constant and NI is the total number of atoms in bin I.

3. SHOCK PROPAGATION: EFFECT OF GRANULARITY Figure 2 shows atomistic snapshots of shock propagation through the granular material for up = 2 km/s; the plot below each snapshot shows the corresponding velocity profile (green line), together with a schematic representation of the velocity profile expected for a shock propagating over a homogeneous material (red line). As discussed above, the compressing boundaries generate two shock waves originating from the periodic boundary along X (Figure 2a,b); these propagate toward the interior of the sample. The opposing shocks meet roughly at the center of the simulation cell (Figure 2e); the interaction of the two compressive waves results in two reshock waves that travel outward from the center of the cell (Figure 2f). The reshocked material has nearly zero particle velocity, and the two reshock waves meet again at the boundary. At this point, the translational energy in the twice-shocked material is minimal, and the compressive boundary conditions are stopped to allow for the study of the subsequent chemical reactions, in the same spirit as in the method proposed by Zhao et al.23 The red profiles in Figure 2 show what would occur in the ideal case of a homogeneous material; in the granular case of interest here, the translational velocity of the reshocked material is not zero, because of the broad and irregular shock fronts as well as internal shock reflections.

(1)

where I denotes the bin and the sum runs over all atoms i in bin I, vi denotes the velocity of atom i, and MI = ∑i∈Imi denotes the total mass of bin I. These center-of-mass velocities are used in maps of local velocities, as well as in the calculation of the total translational kinetic energy of the system K trans =

2 3NI kB

(2)

where the sum runs over all bins in the material. Average local temperatures are then calculated from the atomic velocities measured with respect to the center-of-mass velocities of each bin 26380



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Figure 4. Position of the wavefront, wave end, and wave width as functions of time for piston velocities of (a) 0.5, (b) 1.5, and (c) 2 km/s. Arrows denote the range over which the width was averaged. (d) Steady-state wave width as a function of piston velocity. The shock width stabilized at ∼20 nm for piston velocities of up ≳ 1.5 km/s.

Figure 5. Map of the local longitudinal stress σxx for a sample shocked at up = 0.25 km/s, showing real-time development of force chains in the granular sample.

Figure 3 shows the shock profiles at different times and for different piston velocities. Despite the diffuse nature of the

shocks, the general features of the shock and reshock waves discussed above can clearly be seen. It is also clear from Figure 26381



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Figure 6. Transition from (a) plastic deformation at up = 0.5 km/s and (b) plastic and fluid flow at up = 0.75 km/s to (c) fluid flow with Rayleigh instability in the front at up = 0.5 km/s and (d) jetting into the pore at up = 2.5 km/s. Only defective atoms shown in panel a in red are hcp; white are unclassified. In panels b−d, Al atoms are colored red, and Ni atoms are green.

grain. Where the grain orientation is unfavorable, for example, in grains with interfaces oriented normal to the shock direction, the internal stress distribution is more uniform.

3 that the shock front becomes sharper with increasing shock strength. To characterize the shape of the shock front as a function of insult strength, we define the shock beginning and the shock end as the points where the particle velocities reach 20% and 80%, respectively, of up. The steady-state shock width is extracted as shown in Figure 4a−c, by averaging the width over the time during which the wavefront travels between X = 70 and X = 110 nm (the midpoint of the sample is at 160 nm). Figure 4d shows the resulting shock-wave width as a function of piston velocity. Two regimes can be observed: Relatively high-strength shocks (up ≳ 1.5 km/s) exhibit a front width of approximately 20 nm, or roughly equal to the average grain radius. For weaker shocks (up ≲ 1 km/s), the width of the shock front increases with decreasing up and spreads over time. Analysis of the local stresses in the sample reveals that the development of stress localization chains during compression causes the spreading of the shock front. These force chains or fingers have been studied extensively in the static and dynamic compression of granular powders;1,30,31 Figure 5 shows their development during the dynamic compression of a sample at up = 0.25 km/s. A further insight provided by our simulations is the development of heterogeneous stresses within each particle. The preferential loading path adopted by the sample is influenced by three factors: the connectivity of each grain, the relative crystallographic orientations of the grains, and the Ni/Al interfaces within each grain. Figure 5b shows the contrasting stresses experienced by grains that are directly connected to the shock by grain−grain contacts versus those of grains that are more isolated in nature. In addition, the force chains propagate along the path of least resistance, that is, in directions parallel to the Ni/Al interfaces, and in grains where this is possible, the stress localizes in a narrow zone within the

4. VOID COLLAPSE DURING DYNAMICAL LOADING 4.1. Void Collapse Mechanisms. The mechanism of void collapse depends on the magnitude of the shock loading relative to the intrinsic strength of the intragranular material. In the case of the low-velocity shocks (up ≤ 0.5 km/s), void collapse is mediated by the plastic deformation of grains surrounding the pore. Figure 6a shows only the defective (nonfcc) atoms during the process of compression for up = 0.5 km/s. Local atomic structure is determined using the adaptive common neighbor analysis (a-CNA).39 Atoms in red represent local hcp coordination associated with partial dislocations and twin planes, whereas those in white are unclassified. Deformation occurs primarily in the softer Al and is mediated by the motion of partial dislocations through the sample. With increasing shock strength, the void collapse mechanism changes; at 0.75 km/s (Figure 6b), a mixture of plastic extrusion and fluid flow of the softer, lower-melting-temperature Al layers fills the pore. Blue arrows at 50 ps indicate examples of both effects occurring in Al. The layer highlighted on the left is extruded and is initially solid, whereas the other ejecta that is highlighted is due to the fluid flow of Al from four layers across two grains. At 1 and 1.5 km/s (Figure 6c), pores are filled primarily through the fluid flow of Al into the pores. Interestingly, the fluid ejecta at 1.5 km/s exhibits Rayleigh instabilities40,41 and breaks into droplets within the nanometer scales of the pores (Figure 6c). In this intermediate-strength regime, the softer Al preferentially fills voids in either solid or fluid form. In the strongest shock regime (>2 km/s), atomistic jetting of both Ni and Al is observed, with a spray of intermixed 26382



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Figure 7. Velocity magnitude maps in the vicinity of the pore for up = (a) 0.5, (b) 0.75, (c) 1.5, and (d) 2.5 km/s. Higher particle velocity of ejecta contributes to a sharper shock front. Black arrows show the position of the diffuse front ahead of the ejecta or ejecta-driven waves (red arrows); smaller separation is indicative of a more homogeneous shock.

Ni and Al rushing into the pore (Figure 6d).42 The initial burst of atoms into the void (in clusters of a few atoms) is followed by a greater volume of Ni and Al that is squeezed out of grains closest to the shock front. 4.2. Influence of Void Collapse Mechanism on Shock Behavior. The decreasing width of the shock wave with increasing piston velocity (Figure 4d) is directly related to the increasing presence of ejecta at higher piston velocities. For low piston velocities, where the process of void collapse is through plastic deformation, the time it takes for the pore to collapse is much longer than the time required for the shock wave to be transmitted through the grains surrounding the pore. This leads to a broadening shock front as part of the wave is pinned back at the pores. Figure 7 shows local velocity magnitudes in the vicinity of a pore undergoing collapse. Black arrows denote the farthest position of the shock front, whereas red arrows denote the position of the leading jet (or resulting shock due to jetting, as in the bottom panel of Figure 7c) that is transmitted into a void. At higher impact velocities, ejecta and jetting across the pores allows the tail of the shock to catch up with the front, so that, for up ≳ 1.5 km/s (Figure 7c,d), the velocity of ejecta that rushes into the pore is comparable to the shock speed in the sample. This can be explained through momentum conservation when the shock reaches the free surfaces of grains, where the ejecta have twice the particle velocity in the bulk. The net result is a sharper, better-defined shock front that is less influenced by the porosity in the sample. This result is manifested by the stabilization in shock width at higher piston velocities (Figure 4d).

5. INFLUENCE OF POROSITY ON ENERGY TRANSFER As described in the previous section, the process of void collapse is replaced at higher impact velocities by fluid ejecta filling the voids at high temperatures and velocities, occurring over time scales comparable to those of shock propagation across the grains. When the geometry and orientation of the voids are such that fluid ejecta entering the voids can gain a rotational component of velocity, vortices are formed, leading to chemical reactions due to mechanical mixing. Figure 8 shows atomistic snapshots (top), temperature maps overlaid with velocity vectors (middle row), and maps of the curl of the local velocity field (bottom) for different piston velocities. Vortices are seen to develop in regions where the fluid ejecta is forced at an angle to the shock direction, giving the fluid the angular component of velocity it needs. An important consequence of the formation of fluid vortices is the redirection of input shock energy from thermal to translational modes, which could result in mechanical mixing of Ni and Al. To quantify this effect, we compute the fractions of kinetic energy that go into translation and thermal modes. When dense materials (single or polycrystals) are shocked, the input mechanical energy deposited into the shocked material increases the potential energy (elastic deformation plus defect generation), as well as the kinetic energy (temperature plus an acceleration of the shocked material to its particle velocity). To analyze this decomposition of energy during shock loading, we divide the total kinetic energy into translational and thermal components by spatially binning the system with a square grid in the X−Z plane and computing the total translational and thermal kinetic energy of each bin (see eqs 1−3 in section 2.2). 26383



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To have a benchmark against which to compare the behavior of the granular samples, we performed a series of shock simulations on single-crystal Ni using the exact same setup and analysis as used for the granular composites. Figure 9a−c shows the fractions of total kinetic energy in translational (eq 2) and thermal (eq 3) modes as functions of time for shocks in Ni of different strengths. At time zero, essentially all of the kinetic energy is thermal, but this situation changes immediately after the shock starts. During the shock stage (as the two shock waves move toward the center of the cell), a significant fraction of the kinetic energy is translational (this is related to the motion of the shocked material at the piston velocity); this fraction remains relatively constant over time and is only weakly dependent on piston velocity. However, this is not the case for shocks traversing a granular sample; see Figure 9d−f. At low piston velocities, the inhomogeneity in the sample delays the stabilization of the shock wave, leading to large temporal variations in the fractions of kinetic energy in translational and thermal modes. At higher piston velocities, where the shock front is sharper and more clearly defined, the partitioning of kinetic energy during shock resembles that in a single crystal. Contrary to the case of the homogeneous samples, we observe that increasing the piston velocity in the granular material leads to an increase in the fraction of kinetic energy that goes into translational modes during shock. This is counterintuitive, as a stronger shock would decrease the translational kinetic energy fraction, as seen in the singlecrystal results. We now turn our attention to the state of the system at the end of reshock. In the ideal case of a perfectly sharp single shock in a homogeneous material, the sample would be

Figure 8. Atomistic snapshots, temperature maps with velocity vectors overlaid, and curls of the velocity field for up = (a) 0.5, (b) 1.0, (c) 1.5, and (d) 2.0 km/s. Images are from the end of a shock. The number and sizes of vortices increase with increasing shock strength.

Figure 9. (a−f) Ratios of translational and thermal components of kinetic energy (KE) during a shock for (a−c) a single crystal of Ni and (d−f) granular material with piston velocities of 0.5, 1, and 2 km/s. Arrows in blue denote the points at the end of the shock where translational KE is minimum. (g,h) Ratios of thermal and translational KE corresponding to the minima plotted as a function of piston velocity for (g) Ni and (h) granular material. 26384



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experimental particles is the pristine nature of the simulated granular particles. This is in contrast to compacted ball-milled particles that have aged interfaces and large numbers of defects that are generated during the severe deformations encountered during the milling process. The simulations presented here provide a picture of the compaction process in granular materials with an unprecedented resolution of subgrain effects on a subnanosecond time scale. The real-time visualization of force chain development during the compaction of the granular material will be of wider interest to the granular community, highlighting as it does the inhomogeneity in force distributions within each particle and the importance of particle orientation. Although it has been argued for several years that the initiation of energetic materials is likely to occur at sites such as voids, through the temperature increase associated with a pore collapse, we present evidence for the localization of mechanical energy in addition to thermal energy. This insight is of particular importance in the case of reactive intermetallics such as the system studied here, where reaction is limited by the rate of mixing.

completely at rest, with all of the input mechanical energy going into potential energy (compression and defect generation) and thermal modes for kinetic energy, regardless of piston velocity. In our samples, during reshock, the translational fraction of kinetic energy decreases as expected, but a significant fraction of the translational energy remains at the end of the reshock. For the single-crystal case, this is a consequence of the plastic wave lagging behind the elastic precursor43 leading to imperfect cancelation of the shocks at the boundaries. With increasing piston velocities, the fraction of input energy that remains in translational modes at the end of shock decreases as we approach the overdriven shock regime with a single-shock-wave structure.43 For the granular sample, this remnant translation energy has two contributions: the remaining translations due to the fact that diffuse shock fronts cause imperfect cancellation of waves (see Figure 2) and the fluid vorticity. Interestingly, in contrast to the single-crystal case, the remnant translational energy fraction increases with increasing up (see Figure 9g,h) This might appear surprising, as stronger shocks lead to sharper shock fronts, which would cancel each other better at the interface. We find that this remnant translational energy originates from the internal fluid vorticity developed during compression. Several studies have highlighted the role played by porosity in reactive systems as sites where the reaction is most likely to initiate, as a consequence of the high temperatures and pressures in the vicinity of a collapsed void.26,44−47 With the more complex void geometries studied here, a further distinction is made, namely, that porosity leads to a localization of both thermal and translational kinetic energy.

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS We thank John Barber for discussions and suggestions regarding the polygon packing problem. This work was supported by the U.S. Defense Threat Reduction Agency, HDTRA1-10-1-0119 (Program Manager Suhithi Peiris) and used resources provided by the Los Alamos National Laboratory Institutional Computing Program, which is supported by the U.S. Department of Energy National Nuclear Security Administration under Contract DE-AC5206NA25396. E.M.K. acknowledges support from the Institute for Materials Science (LANL), and T.C.G. acknowledges support from the ExMatEx project.

6. DISCUSSION AND CONCLUSIONS In summary, we have studied the behavior and phenomena associated with the dynamical loading of a granular material by MD simulations. We observed two regimes of compaction: At low impact velocities, void collapse is through plastic deformation or plastic flow, and the shock wave fronts are very diffuse, because solid-phase pore collapse occurs at time scales that are slow compared with shock propagation. In this regime, stress chains develop through contacting grains to propagate the shock forward. The second regime, at higher impact velocities, is dominated by voids being filled by fluid ejecta with characteristic time scales comparable to that of shock propagation, leading to sharper shock fronts. A further effect of the fluid filling of the pores is the generation of fluid vorticity, where a significant fraction of the input shock energy is localized into translational modes of kinetic energy. This localization of energy plays an important role in the initiation of the exothermic reactions in these materials, the process of which will be described in our next article.27 Although an effort has been made to build particles that are energetically favorable, these structures necessarily represent idealized grains, and comparison with experiments should be performed carefully. For instance, the jet-driven vorticity produced in the quasi-two-dimensional structure would be different in fully three-dimensional geometries, where mass can be redirected into both transverse directions. A further simplification in our simulations is the use of an alloy layer on the surface, as opposed to an oxide layer, which is computationally extremely expensive. However, we do not believe that these limitations in the design of the particles are likely to affect the qualitative nature of the results presented here. A further divergence of our simulation model from

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REFERENCES

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