2.1 Numerical Simulation of DWIT Experiment

Drop impact loads are of significant duration (hundreds of microseconds) when compared to shock impacts occurring over a period of just several microseconds. This requires that the drop impact simulation uses numerically efficient models. Modeling powder and granular materials using a continuum model is the most efficient but it only captures the bulk thermal behavior of the powder 23, 24 and would not be able to predict the localized heating that occurs due to plastic strain localization and sliding friction. Others studying the compaction and shearing of powdered material have employed discontinuous numerical methods such as the discrete element method (DEM). Commercially-based DEM techniques 25–28 are powerful for their computational practicality in modeling macroscale particulate flow behaviors governed by the elastic or rigid body collisions of thousands of highly mobile particles. However, powdered EM materials have been shown to behave as highly plastic particles under drop hammer dynamic loads 14–29. Modeling those types of impacts require that the plasticity of the particles be considered in the numerical treatment. The use of multi-particle FEM (MPFEM) techniques was adopted over a decade ago to simulate small numbers (tens-to-hundreds) of deformable particles 30–33. The MPFEM approaches are readily adapted to commercial FEA software in both 2D and 3D because they model each particle as a deformable object that requires a FEM mesh for each particle in the simulation. It has been a popular alternative to DEM for modeling the dynamic compaction of metallic powders and pharmaceuticals since contact forces in these applications induce significant particle deformation 23, 33, 34. The main drawback of MPFEM is the computational cost of simulating the plastic deformation of individual particles, which makes it prohibitively expensive to model EM samples with thousands of particles.

In this article, a hybrid approach is introduced, where the EM powder is partitioned into regions of continuum material and regions of discrete particles. The discrete particles in the model capture the localized heating due to friction between particles and the plastic strain that occurs within the particles. Researchers studying bulk storage of particulates have used similar hybrid techniques in conjunction with discrete element methods (DEM) 35–37. The hybrid approach provides the modeler with the flexibility to select regions of the EM powder layer (possibly informed by continuum-based solutions) where mesoscale resolution is desired in order to capture strain localization and frictional heating that causes temperature spikes.

Figure 3 illustrates the FEM simulation framework devised for this study. The nonlinear finite element explicit dynamics code, LS-DYNA 38 was used for all the analysis steps discussed below. There are four tiers (a–d) in the approach depicted in Figure 3 designed to minimize computational time without compromising on the resolution needed to predict localized heating. Towards this end, only a portion of the striker and anvil is modeled for the Thermo-Mechanical simulation and the thin layer of energetic material between the anvil and striker is modeled using a hybrid approach. In the hybrid approach, the powdered energetic material is partly modeled as a continuum and partly as particles. It is important to ensure that the material behaviors of the powder are consistent at the continuum and particle scales. To achieve this material modeling consistency, the parameters of the constitutive model of the RDX powder were derived by numerically simulating the experiments needed to determine these parameters as shown in Figure 3(a). When modeling only a portion of the striker and anvil for Thermo-Mechanical simulation, the model must impart the correct energy input into the powder by applying an accurate striker velocity history as a boundary condition. This was achieved by simulating the motion of the DWIT apparatus using a simplified continuum-based FEA model (Figure 3(b)) to determine the striker velocity history. The powder constitutive model (RDX_PCM) and the striker velocity history, V_s(t) are the numerically derived inputs that are needed in the next tier of more finely resolved DWIT Thermo-Mechanical simulations shown in Figure 3(c) and 3(d) where only a part of the striker and anvil are modeled. Figure 3(c) shows the full continuum case, which was intended to be a benchmark computation for characterizing the macro-behavior and bulk thermal profile of the sample. The hybrid simulation, depicted in Figure 3(d), shows the RDX sample partitioned into continuum and multi-particle regions. The limited region modeled as particles provides the needed heterogeneity to assess energy localization from particle plasticity and frictional contact mechanisms. To minimize computational time, only the region where the most intense energy localization behavior was expected to occur was modeled using particles. In our application of the FEM framework, the center region of the RDX powder layer was choosen as the region to be modeled as particles (MPFEM) based on: (a) the experimental evidence of reaction already discussed in Section 2 and depicted in Figure 2, and (b) thermal results from the full continuum simulation (Figure 3(c)) results, to be discussed in Section 3.3.

Significant computational efficiencies were realized by using a 2D model paradigm to approximate the DWIT cylindrical geometry. The 2D model paradigm for the hybrid model is shown in Figure 4. Here the powder layer is meshed as discrete sections of particles and powder continua. As pictured, symmetry condition was enforced along the left edge to simulate the axis of the striker and anvil. In LS-DYNA, the 3D contact models are fully integrated with the implicit thermal solver for performing coupled Thermo-Mechanical simulations 39 and 3D frictional contact algorithms are highly robust. Therefore, 3D solid elements (8-node hexahedrons) were used with just one element in the out-of-plane direction to approximate a 2D model. Boundary conditions were appropriately set to enforce planar motion in the X−Y plane. As the aspect ratio (length/diameter) of the impacted sample can have a significant influence on its shearing behavior, the aspect ratio of the numerical models was matched with the sample aspect ratio tested in the original DWIT experiments. Consistent mean particle size was also used with the MPFEM approach. To model the contact-impact of relatively soft non-planar RDX particles on the striker and anvil surfaces, a segment-based contact approach was used in conjunction with a penalty-based contact methodology 38. The segment-based contact approach computes a penalty stiffness based on the contacted material properties. Referred to as “SOFT” contact in LS-DYNA, this implementation reduces contact instability and limits the growth of negative contact energy when materials of highly dissimilar stiffness properties are in contact and sliding.

2.2 RDX Powder Constitutive Model (RDX-PCM)

To model regions of the powder as a continuum in the hybrid approach, a constitutive model was sought that adequately reproduces the shear and volumetric behavior of the RDX powder. Powder modeled as a continuum using this constitutive relation is referred to in Figure 3 as the RDX powder constitutive model or RDX-PCM. From the suite of material models available in LS-DYNA, the two-surface Soil-Foam Model developed by Krieg 40 had the requisite features. The Soil-Foam model has been used successfully to model cohesive and granular geomaterials such as sand and soils 41. Krieg intended to provide the analyst a simple constitutive characterization for a class of porous plastic materials that exhibit both deviatoric and volumetric change. Although hydrostatic compression data exists for RDX powders 42, 43, numerical experimentation using MPFEM was preferred to achieve material modeling consistency with the multi-particle regions in the hybrid approach.

The Krieg two-surface model 40 implementation directly couples the pressure-dependent volumetric plastic response and the pressure-dependent deviatoric plastic response in the failure surface. The failure envelope is described by the function below.

(1)

In the preceding equation, P is the hydrostatic pressure, ƒ is a function of the mean volumetric strain and is referred to here as the Compaction Curve and J‘₂ is the second invariant of the deviatoric stress. The deviatoric yield surface is represented as a quadratic function of pressure because the deviatoric stress required to cause shear failure in compacted powder increases with an increase in the confining hydrostatic pressure. The typical method for computing the three parameters from a load cell apparatus for a granular geomaterial characterization is detailed by Schwer 44. In applications involving geomaterials, the grain/particle strength exceeds the loads imparted on them and the material exhibits an elastic response with a shear resistance that increases monotonically with hydrostatic pressure 41. On the other hand, the RDX powder, dispersed in a thin layer in the DWIT apparatus, is more aptly described as a soft inelastic powder with properties more akin to salt or sugar crystals 45. Under the rapid and extreme pressure loads experienced in drop impact 10, 46, the RDX particles exhibit significant volumetric compression as the particles begin to rearrange and plastically deform to close the voids between particles. This highly plastic nature of the RDX particles mitigates much of the particle mobility required for shear collapse. Therefore, for a thin layer of RDX powder, compacted at such high pressure, the deviatoric yield is due to RDX plasticity alone and not due to the shear collapse of the powder. This allows us to simplify the 3-parameter constitutive model to a single-parameter Von Mises continuum. Simplification of Equation (1) to a Von Mises material is made by removing pressure dependence by setting a₁=a₂=0 and setting a₀= /3, where  is the yield strength of RDX. The mechanical properties of the solid state RDX are listed in Table 1.

In the volumetric sense, the yield surface of the Soil-Foam model is the Compaction Curve, ƒ, which is a non-linear pressure-volume curve. In LS-DYNA the Compaction Curve data is provided as a set of pressure-volume pairs (up to 10). The model also accommodates volumetric unloading – with a bulk unloading modulus, computed directly from the tabulated Compaction Curve data. The Compaction Curve can be derived experimentally from hydrostatic compression tests (HCT) conducted on a hydrostatic load cell 44. Therefore, the curve is also sometimes referred to as the HCT Response curve. Two different types of Compaction Curves for granular material are illustrated in Figure 5. The solid curve reflects the Compaction Curve typically obtained for geomaterial/powder that consists of elastic particles. In this case, the initial linear response is followed by a plateau region as elastic grains (particles) experience mobility and rearrangement during hydrostatic compression in a typical load cell device. As the particles start to pack tightly, the HCT curve follows a stiffer elastic and then plastic response until it consolidates to a near solid state material at very high pressures typically in excess of a gigapascal. The yield stress of RDX particles is an order of magnitude less than common geomaterials and for DWIT experiments, the layer of powder is very thin. With the rapid onset of grain plasticity, the mobility phases of the Compaction Curve are significantly arrested in thin layers, resulting in a compaction response that resembles the dashed curve shown in Figure 5.

In this study, the HCT loading was simulated with an MPFEM representative volume. The Compaction Curve was then derived from the force-displacement data from the MPFEM load-cell simulations. A representative volume of 35 particles was modeled in a constant rate hydrostatic compression test (HCT) load cell to determine the volumetric response of the particles as they displaced, deformed, and fully consolidated. The hydrostatic pressures, imposed as pressure boundary conditions, were distributed equally in the vertical and lateral directions on the volume walls as depicted in Figure 6.

The Compaction Curve is influenced by particle mechanical properties, particle shape, size distribution, and packing arrangement 33, 47. For consistency with subsequent DWIT hybrid simulations, a hexagonal packing arrangement of 100 μm diameter particles was used for all MPFEM models. The monomodal particles were packed in a thin layer configuration as a stack of three layers. The friction and mechanical properties of each of the particles were identical and given in Table 1. The particle size is statistically consistent with the nominal size from particle distributions measured in our previous DWIT experiments 13.

2.3 Striker Velocity Determination

In the Drop Weight Impact Test (DWIT) experiments, a 2.5 kg drop weight (hammer) is released from a magnet and under the force of gravity impacts upon a stationary 0.5 kg striker rod that rests on the 20–30 milligram RDX powder sample. The striker velocity is an important history variable used to gain insights on energy transmission and efforts are usually taken to analytically or experimentally extract this data 9. The velocity of the striker as a function of time, V_s(t), was used as a boundary condition in the hybrid models (Figure 3(d)) to ensure that the kinetic energy transmitted into the powder sample is accurate. Coffey and Baker 7, 51 utilized instrumented drop weight testers that provided dynamic data on the striker velocity. Our apparatus had no accelerometer nor motion sensing capabilities to provide data on the striker velocity. Furthermore, the inelastic properties of a copper anvil compound the problem of analytically computing energy transmission into the sample. Therefore, an efficient numerical simulation was necessary to determine the velocity of the striker. Figure 3(b) shows the model of the DWIT setup for computing the striker velocity history. This model, which includes the hammer, striker, anvil, and EM for explicit dynamic simulation, is computationally expensive when the EM powder is modeled either entirely or partly as particles. Therefore, for efficiency, the RDX-PCM model discussed in the previous section was used to model the powder layer.

All simulations were conducted with a hammer drop height of 125 cm. At this drop height, 100 % reaction occurred with steel anvils but no reactions occurred with copper anvils in the experiments. For consistency, the mass proportions among the four dynamic components of the DWIT (striker, hammer, anvil, and powder layer) were matched to our experiments. The 2D approximation of the cylindrical geometry required us to scale densities to achieve consistent mass ratios among striker, hammer, anvil, and sample. Simulations were conducted with both anvil types to compute the velocity of the striker until it came to its initial rest state and before its first rebound event.

3.1 RDX-PCM Constitutive Model Results

The objective for using MPFEM simulation of HCT was to determine the Compaction Curve, ƒ, for the constitutive model to ensure that the compaction behavior of the continuum model will match the particle based simulation accurately. Numerical experimentation was not performed to characterize the deviatoric response of the powder because the simplifications of the yield surface discussed in Section 2.2 allowed us to use the properties of the fully consolidated solid listed in Table 1.

The Compaction Curve derived from such MPFEM simulations is shown in Figure 7. This curve is unique to the particle mechanical strength, particle geometry, and packing density. The RDX powder particles responded only briefly in the elastic range and consolidated rapidly in a highly plastic fashion. The compaction response was computed up to 1 GPa. Figure 8 depicts the particle deformation field at the point nearing full consolidation at 1 GPa; with a volume strain of approximately 22 %. The Compaction Curve extending above 1 GPa in Figure 7 was extended (appearing in red) with an incremental increase in volume strain of less than 0.5 % up to 3 GPa. This extrapolation of the Compaction Curve beyond 1 GPa agrees well with previously reported compaction data for RDX and HMX powders 42, 43.

3.2 Striker Velocity Results

The striker velocity history, V_s(t), computed as described in section 2.3 is provided in Figure 9 for the case of the copper anvil. The computed results for both copper and steel anvils show the characteristic sinusoidal response of the striker, which is similar to elastic analyses provided by Coffey and DeVost 7 for the striker impact energy imparted to thin samples from a drop-weight impact. The computed frequency and magnitude of the sinusoidal behavior were found to be very sensitive to the mass ratios between the hammer, striker, and powder. The full period of striker loading, before the rebound, was approximately 200 microseconds for the copper anvil, with a peak striker velocity of approximately 4.4 m/s occurring at about 90 microseconds. The steel anvil had a similar response during the striker acceleration phase but with a slightly lower peak velocity of 4.2 m/s and a shortened loading period of 150 microseconds. Previous drop weight experimental results 9–11 have shown that RDX ignition occurs during the striker acceleration phase of loading. The anticipated reaction window associated with the striker velocity is highlighted in Figure 9. In this phase, the striker achieves the highest energy input rates into the sample. In the simulation results presented in the next sections, attention is focused on this phase of the hammer-to-striker impact event.

3.3 Continuum and Hybrid Simulation Results

A hammer drop height of 125 cm was selected as the discriminating energy input to judge if the simulations were able to produce thermal indicators of sample ignition. The temperature for ignition of EM materials was experimentally inferred first by Bowden & Gurton 52. Anvil properties used in the comparative simulations are provided in Table 2.

Figure 10 provides a detailed view of the mesh used for the Thermo-Mechanical simulations. The powder layer was meshed as a hybrid composition of continua regions near the axis and periphery of the sample and with the particles packed in the midsection between the axis and periphery where heating is expected to localize. The aspect ratio of the powder layer was modeled to be representative of the DWIT experiments. In the experiments 13, the pre-impacted powder was sieved to a nominal particle size of 100 μm and had a layer thickness that was nominally 100–150 μm in thickness. The hexagonal packing of particles, depicted in the lower right section of Figure 10, has an aspect ratio which represents the loose packing height of the experimental powder before striker placement on the sample.

The striker and anvil contact area mesh was modeled with sufficient refinement such that at least two anvil or striker element segments were in contact with a particle. This resolution was selected to assure accurate transmission of nodal forces during the contact impact period between the striker or anvil and the particles. For the coupled Thermo-Mechanical solution, the implicit thermal solver ran concurrently with the explicit FEM solver but at a larger time step. The key input parameters for the thermal solver are provided in Table 3. The thermal conduction across the anvil and striker contact interfaces was not modeled in these simulations because in the experimental studies the EM powder was physically and thermally insulated from the anvil and striker surface by means of a thin sheet of weighing (wax) paper. The experimental results with steel anvils showed that the paper tends to increase ignition likelihood compared to tests where the paper was not used – supporting the premise that heat is not transferred across the boundary and remains within the powder.

During the DWIT impact process, strain energy and friction heating was anticipated to localize in selected regions to offer discernable indications of heating and potential ignition in the sample. The likelihood of ignition can be qualitatively assessed between anvil types by spatially resolving the temperature distribution across the radial extent and depth of the powder layer. The evaluation is only useful up to the melt temperature of RDX. The melt temperature increases with pressure starting from approximately 200 °C at atmospheric pressure to greater than 500 °C at 1 GPa 8, 54. A model result of interest is therefore the volume of the powder layer reaching this temperature threshold.

3.3.1 Continuum Model – Thermo-Mechanical Results

The first simulations of the drop weight impact were conducted using a continuum model for the entire powder layer as shown in Figure 3(c) for spatially resolving the temperature distribution in the powder layer. The results are later compared to the hybrid model simulations. The computational boundaries of the continuum model are shown in Figure 11a. The model consisted of less than 20,000 elements. The simulations were run in a coupled Thermo-Mechanical manner wherein plastic strain energy and sliding friction energy were converted to heat. The copper and steel anvils were modeled as an elastic-plastic material with Von Mises yield criteria. The striker velocity inputs were unique to each anvil type as they were computed as explained in 3.2. To reduce computational time, the steel striker was approximated as an elastic material. The powder was modeled as a continuum using the RDX_PCM constitutive relation. The Thermo-Mechanical response of the powder layer at 110 microseconds after striker impact are provided in Figure 11(b) and 11(c) for the copper and steel anvil respectively. This plot time, which is 20 microseconds after maximum striker velocity, corresponds to the maximum energy input rate into the powder layer. The thermal solutions in Figure 11 show the tendency for heat to localize in the mid-section of the sample. This result is in agreement with the experimental observations made with the paper impact impressions shown in Figure 2. The bulk temperature behavior from the continuum solutions provided numerical evidence to select the midsection of the sample as the multi-particle region for the hybrid simulation.

Afanasev 8 theorized that mechanisms for energy localization in thin layers are inhibited near the axis of the sample due to limited shear flow and at the periphery due to lower pressures. In other words, pressure attenuates as you move laterally away from the center of the sample and shear flow velocity attenuates as you move towards the axis of the sample. Figure 12 and Figure 13 provides comparative data from our simulations. In Figure 12, the peak pressure averaged over a number of elements located at the center, mid-section, and peripheral (edge) of the sample are plotted at 100 microseconds. The pressures are higher at the symmetry axis (center) and reduce as you move away from the axis. The steel anvil indicates the much higher pressure and a larger gradient in pressure moving away from the axis. The radial velocities were insignificant near the axis and mid-section, revealing that the thin layer stays almost stationary in this region of the powder. Figure 13 compares the average velocity of the sample at the edge. The velocity at the edges of the sample shows a striking similarity for the two anvil types. The edges accelerate and begin moving radially and then are quickly arrested after 100 microseconds. This may be due to the beginning of the rebound of the striker, although both simulations show that pressure on the sample begins to increase monotonically after 100 microseconds. Friction forces may also have a significant role in arresting the radial flow of the thinning layer of powder as the pressure increases and a stagnation effect is experienced on the powder flow.

Figure 12 and Figure 13 show that the continuum solutions are useful in discerning the influential role that the anvil material plays to modify the pressure and material velocity in the thin powder layer. The 2D continuum thermal solutions also showed agreement with Afanasev’s assertion that the mid-section of the sample is a region where compression loads and shear flow optimally co-exist to dissipate the most amount of energy. The 2D solutions also reveal that the radial flow appears to be arrested in thin layers at a time that corresponds to the maximum velocity of the striker.

One significant result of the continuum solutions at the 125 cm drop height was that the bulk temperatures of the layer at the mid-section were predicted to be well below the ignition temperatures of RDX, regardless of anvil type. Figure 14 displays the continuum-based element temperature time-history within the powder for steel anvil confinement up to 110 microseconds. Temperatures were sampled from interior elements within the layer mid-section that are not in direct contact with anvil or striker surfaces. For the continuum model, only a modest temperature increase exists anywhere within the interior of the powder layer, with no elements reaching a temperature higher than 125 °C. This suggests that through thickness melting of the layer is not occurring. These results would indicate a very low likelihood of ignition. This, however, is not consistent with our experimental results, where we obtained a 100 % likelihood of ignition when using the steel anvil. In our experiments, we observed clear visual evidence of melted powder with both anvil types – suggesting that some of the powder is reaching 200 degrees even when using the copper anvil. This points to the limitations of using a continuum model for the powder to study the likelihood of ignition because the localization of strain and frictional energy dissipation is neglected by continuum models.

3.3.2 Hybrid Model – Thermo-Mechanical Results

The hybrid model simulations are intended to offer better insight into how anvil variations can influence localized heating, and the rate and spatial extent to which the powder layer is heated to melt or ignition temperatures. Plastic strain and friction heating was anticipated to localize in the mid-section region to produce discernable thermal indications of potential ignition in the sample. The hybrid solution, which uses MPFEM in the mid-section of the powder layer, is intended to better capture the energy dissipated as heat in this region of the sample layer. As stated earlier, the simulations were considered valid up to the point where melt temperatures are reached, which occurs at slightly beyond 100 microseconds for steel anvil. Figure 15(a) and (b) provides the anvil and powder deformation pattern for the copper and steel anvil respectively. The figures depict the state of deformation at 110 microseconds after striker motion. They display a similar macroscale behavior seen previously with the continuum solutions. The limited extent of radial flow in the powder layer with the copper anvil (Figure 15a) is consistent with our previous experimental observations. Similarly, as was seen experimentally, the steel anvil (Figure 15b) creates more radial (shear) flow. Figure 15(c) and (d) show more enlarged images of the particle motion of the layer also at 110 microseconds. These more detailed MPFEM plots depict the distinct mesoscale deformation pattern of the particles when confined by the copper and steel anvil. It is notable with the steel anvil that the particles collectively exhibit significant shear flow once frictional resistance is overcome. This was also seen in the continuum results. Whereas its equally notable that the MPFEM mid-section does not exhibit this shear flow behavior with the copper anvil. The particle flow is fully arrested from its interaction with the cooper anvil.

Melting was observed experimentally within the sample with both the steel and copper anvils. In the simulations, the likelihood of ignition can be qualitatively assessed between anvil types by resolving the temperature distribution through the extent and depth of the sampled region. Such a volumetric interpretation of the temperature field can help infer the full extent of the melt region and, hence, a correlation to ignition likelihood.

Figure 16 compares the mid-section region Particle Temperatures at 90 microseconds after hammer impact for the steel and copper anvil. This corresponds to a time when maximum striker velocity is achieved. At the striker peak velocity, the average pressure in the midsection starts to exceed 1 GPa. At this stage, particles have fully compacted and radial flow has stagnated. Indications of likely ignition, that is, temperature rise above melt temperatures within the particle layer, begin to materialize at this stage of the simulation. At 90 microseconds, temperatures exceeding 200 °C are far more evident with the steel anvil confinement of the powder. At this stage, the peak temperatures only occur near the contact interfaces.

The temperature profile comparison of the copper and steel anvil cases at 110 microseconds is provided in Figure 17. In the case of the steel anvil, the thermal profile indicates complete melting through the midsection of the powder layer. When the copper anvil is used, only the interface temperatures reach or exceed the melt temperature. This seems consistent with our experimental results where all impacted samples displayed a pasty consistency, suggesting some degree of melting, even in samples that did not react. Both Figure 16 and Figure 17 reveal that the particles experience significant shearing with the steel anvil whereas there is much less energy absorbed for shearing with the copper anvil. This is a direct mesoscale influence of the anvil properties and how the particles mechanically respond.

Recall that the mesoscale localized heating mechanisms are largely not accounted for when the powder was modeled as a continuum. For the multi-particle region shown in Figure 15, the internal energy within the particles due to plastic work is compared with and friction energy to understand their relative contribution at the mesoscale. Figure 18 compares the amount of internal (strain) energy and friction energy transferred into the particles when confined by the steel and copper anvil. During the reaction window between 70–100 microseconds, the magnitude of strain energy absorbed by the particles on the steel anvil is 4–5 times greater than what is absorbed on the copper anvil. The inter-particle friction energy (curve-B in green) observed at this mesoscale is also significant, being an order of magnitude higher than surface friction energy created along the striker and anvil boundaries (curve-C, and D in blue). When comparing curve-A and curve-B, we find from these mesoscale computations, that the relative contribution of stored heat energy in the particles attributed to the energy dissipated to inter-particle friction is higher for the copper anvil. For the steel anvil, far more energy is dissipated from plastic work on the particles.

Figure 19 displays a particle temperature histogram from steel anvil confinement at 110 microseconds, computed by the hybrid model. Within the multi-particle region in the hybrid model, the average Particle Temperatures (averaged over the 64 elements comprising of a particle) in the mid-section region reached well over 300 degrees. Recall that the peak temperatures in the benchmark continuum case were highest at the midsection but never achieved temperatures beyond 125 degrees. This highlights how the multi-particle region is a computational necessity to determine the role of local plasticity and friction. With MPFEM, significant dissipative mechanisms are captured that localize heat generation within the powder and create temperature spikes that cause through thickness melting and the indications for ignition to occur.

The histogram shown in Figure 20 compares Particle Temperatures and the role of frictional heating. Previously, in Figure 18, we compared the relative energy contribution from inter-particle friction. Here we compare actual temperature increases of the 59 particles in the midsection from the contribution of all friction heating sources. The data is displayed at 90 microseconds after striker motion begins when the maximum velocity is attained by the striker. With the copper anvil, the RDX Particle Temperatures remained well below melt temperatures. However, there was a clear shift of more particles to the higher 50–100 °C temperature band. In the case of the steel anvil, a similar shift occurred with about 20 % of the particles now at temperatures exceeding 150 °C. A more detailed study of the histogram data revealed about a 30-degree increase in the average temperature of the particles with the inclusion of dissipative heating due to sliding friction. These magnitudes corresponded well with the internal energy data presented in Figure 18.

The non-recoverable work dissipated by the anvil offers a fundamental explanation on why ignition was inhibited when using a copper anvil. Figure 21 shows the sharp contrast in the level of plasticity reached between the steel anvil and the far softer and ductile copper anvil. The copper anvil undergoes significant plastic strain near the edge of the powder layer. This provides computational evidence that a crater is being formed early in the compaction process. In the experimental results 13, a circular crater with steep edges was observed that had approximately the diameter of the original powder sample and a depth comparable to the layer thickness of the powder.