E ff ect of geometry

The multi-region HMX and binder simulations described above are in one-dimensional plane geometry. They are not easily generalised to cylindrical or spherical geometry because the alternating regions would become concentric rings or shells of HMX and binder, which are not representative of the three-dimensional microstructure of PBX9501 and EDC37. There are two physical effects that are not correctly represented in the 1D planar calculations: shock focusing and heat conduction. A shock front that is travelling through a plastic-bonded explosive microstructure is not flat, but shows perturbations as- sociated with the binder regions (see section7.3). This means that 3D shock focusing can occur, leading to localised high-temperature regions. The effect of heat conduction also depends on the HMX and binder geometry because a spherical HMX crystal surrounded by hot binder will heat up more quickly than a planar sheet of HMX next to a binder sheet. It is necessary to confirm that the simplification to 1D plane geometry in this chap- ter, which neglects the 3D effects of shock focusing and heat conduction, is not affecting the results of the simulations.

One approach is to examine the temperature distributions produced by large mi- crostructure simulations of EDC37 and PBX9501 (see chapter 7). These are relatively insensitive to the choice of one or two-dimensional geometry as will be demonstrated in section7.1.4, indicating that shock focusing effects are not significant. Another approach is to run Peruse simulations of a single HMX crystal surrounded by a layer of binder in plane, cylindrical and spherical geometry, a similar configuration to critical hotspot sim- ulations. As will be described in section6.1.6, such calculations show small differences between plane, cylindrical and spherical geometry but the overall behaviour is unchanged. Both these approaches demonstrate that the results in this chapter are not significantly af- fected by the simplification to 1D plane geometry.

Figure 5.14: Temperature histories for alternating HMX/binder calculations for EDC37 with 5µm meshing (above) and 2.5µm meshing (below), for comparison with figure5.13.

5.2.4

Representative microstructure calculations

The simplified calculations used idealised geometries where the crystal and binder layers have equal thickness. Since PBX9501 and EDC37 contain more than 90 % HMX, this is not representative of the physical microstructures of these explosives. Realistic one- dimensional computational geometries were constructed from micrographs of PBX9501 and EDC37 using the method described in section2.4. A mesh density of 1 zone/pixel, which corresponds to∼0.3µm and is consistent with the calculations in chapter7, was used in “representative” Peruse simulations. Temperature histories were recorded from cells positioned at∼30µm intervals through the calculation, so some of the cells contain HMX while others contain binder. Temperature histories from a representative simulation of EDC37 are shown in figure5.15. The impact velocity was 1.7 km/s which is equivalent to a pressure of∼20 GPa.

The results in figure5.15are broadly similar to the alternating crystal/binder calcula- tion of EDC37 in figure5.13. Temperature histories from the representative simulation show higher-frequency oscillations due to wave reverberations in the fine structure of the

Figure 5.15: Temperature histories for representative calculation of EDC37 shocked to

∼20 GPa, showing that only the binder regions react over the 0.10µs duration of the sim- ulation.

microstructure geometry. Some of the binder regions do react (i.e. their temperature rises significantly), but the HMX regions show very little reaction over the duration of the simulation. Similar calculations for PBX9501 show that even less reaction occurs in the binder regions than for EDC37. The results suggest that hydrodynamics is dominating the behaviour by controlling the initial temperature achieved in each computational cell. Although there is some heat conduction from binder regions into HMX, it is not suffi- cient to cause much chemical reaction in the HMX. This demonstrates the importance of including hydrodynamics in studies of hotspot mechanisms.

At this pressure of∼20 GPa, the experimental Pop-plots of PBX9501 and EDC37 ex- trapolate to a run distance of 1 mm. Although the simulated geometry is only 0.69 mm long in this case (owing to the size of the micrograph), there should certainly be signifi- cant reaction occurring if the EDC37 is to detonate shortly after the end of the computa- tional domain. The disagreement between the simulations, where little reaction occurs in HMX regions as a result of the shock heating of crystals and binder, and the experiments, which detonate, suggests that shock heating of crystals and binder is not a feasible hotspot mechanism in PBX9501 and EDC37.

5.3

Effect of uncertainties in material properties

The results in section 5.2 indicate that, for the HMX-based explosives PBX9501 and EDC37, shock heating of crystals and binder is not a feasible hotspot mechanism, known hereafter as “the conclusion”. It has already been checked that the conclusion is not sensitive to the geometry or mesh resolution. However, there is considerable uncertainty in some of the material properties data (see chapter3), so it is important to check that reasonable changes to these data do not affect the conclusion. Although it is recognised that some parameters are thermodynamically inter-dependent (e.g., Gr¨uneisenΓis related to the thermal expansion coefficient, the sound speed and the heat capacity), the material model coefficients will be varied independently in this section. This has the advantages of allowing the effect of each parameter to be isolated and giving a worst-case estimate of the effect of the uncertainties. It is acknowledged that varying model coefficients that are independent of temperature or pressure does not necessarily lead to the same results as incorporating temperature or pressure dependence. However, it is a simple approach that can be used to identify which features of the material models need further development.