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TECHNICAL PAPERS

# Multiscale Shock Heating Analysis of a Granular Explosive

[+] Author and Article Information
Keith A. Gonthier

Mechanical Engineering Department, Louisiana State University, Baton Rouge, LA 70803gonthier@me.lsu.edu

Venugopal Jogi

Mechanical Engineering Department, Louisiana State University, Baton Rouge, LA 70803

J. Appl. Mech 72(4), 538-552 (Feb 08, 2005) (15 pages) doi:10.1115/1.1934666 History: Received November 26, 2003; Revised February 08, 2005

## Abstract

A multiscale model is formulated and used to characterize the duration and amplitude of temperature peaks (i.e., hot spots) at intergranular contact surfaces generated by shock compaction of the granular high explosive HMX (octahydro-1,3,5,7-tetranitro-1,3,5,7-tetrazocine). The model tracks the evolution of both bulk variables and localized temperature subject to a consistent thermal energy localization strategy that accounts for inelastic and compressive heating, phase change, and thermal conduction at the grain scale (grain size $∼50μm$). Steady subsonic compaction waves having a dispersed two-wave structure are predicted for mild impact of dense HMX (porosity $∼19%$), and steady supersonic compaction waves having a discontinuous solid shock followed by a thin compaction zone are predicted for stronger impact. Short duration hot spots having peak temperatures in excess of $900K$ are predicted near intergranular contact surfaces for impact speeds as low as $100m∕s$; these hot spots are sufficient to induce sustained combustion as determined by a two-phase thermal explosion theory. Thermal conduction and phase change significantly affect hot-spot formation for low impact speeds $(∼100m∕s)$, whereas bulk inelastic heating dominates the thermal response at higher speeds resulting in longer duration hot spots. Compressive grain heating is shown to be largely inconsequential for the range of impact speeds considered in this work $(100⩽up⩽1000m∕s)$. Predictions for the variation in inelastic strain, pressure, and porosity through the compaction zone are also shown to qualitatively agree with the results of detailed mesoscale simulations.

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## Figures

Figure 1

An illustration of multiscale features for the shock compaction of a granular solid

Figure 2

An illustration of the intergranular contact geometry used for the thermal energy localization strategy

Figure 3

Predicted and measured Hugoniot curves for granular and solid HMX in (a) P-ν and (b) D-up planes. The PBX 9404 data is for a pressed mixture of 94% granular HMX and 6% plastic binder.

Figure 4

Predicted variation in bulk quantities through the compaction zone for ϕ0=0.81, up=106m∕s, and D=748.2m∕s: (a) Solid volume fraction, (b) solid density, (c) velocity, (d) solid pressure, (e) solid temperature, and (f) grain number density.

Figure 5

Predicted variation in the compressive (Ŝρ) and inelastic (Ŝϕ) heating rates through the compaction zone for ϕ0=0.81, up=106m∕s, and D=748.2m∕s

Figure 6

Predicted variation in (a) grain radius, localization radii, and (b) grain temperature through the compaction zone for ϕ0=0.81, up=106m∕s, and D=748.2m∕s

Figure 7

Convergence of the numerical algorithm for the subsonic compaction wave structure: (a) predicted variation in grain temperature at the center of the localization volume through the compaction wave, T̂grain=T̂(ξ,r=0μm); (b) radial distribution of grain temperature at the location ξ=−12.07mm, T̂grain=T̂(ξ=−12.07mm,r). Here, Nr is the number of radial grid points within the localization sphere.

Figure 8

Predicted variation in bulk quantities through the compaction zone for ϕ0=0.81, up=1053m∕s, and D=3500m∕s: (a) Solid volume fraction, (b) solid density, (c) velocity, (d) solid pressure, (e) solid temperature, and (f) grain number density.

Figure 9

Predicted variation in the compressive (Ŝρ) and inelastic (Ŝϕ) heating rates through the compaction zone for ϕ0=0.81, up=1053m∕s, and D=3500m∕s

Figure 10

Predicted variation in (a) grain radius, localization radii, and (b) grain temperature through the compaction zone for ϕ0=0.81, up=1053m∕s, and D=3500m∕s

Figure 11

Predicted variation in (a) compaction wave speed, (b) solid volume fraction, (c) compaction zone length, (d) volumetric plastic strain, (e) liquid volume fraction, and (f) ratio of maximum grain temperature to bulk solid temperature with piston impact speed for ϕ0=0.81. Plots (c) and (e) are curve fits to the predicted data.

Figure 12

Predicted variation in (a) compaction wave speed, (b) solid volume fraction, (c) solid pressure, (d) compaction zone length, (e) volumetric plastic strain, and (f) inelastic heating rate with initial solid volume fraction ϕ0 for up=150m∕s

Figure 13

Predicted variation in (a) solid volume fraction and (b)–(d) grain scale temperature through the compaction zone for Ω=1.0×104, 1.0, and 0.1, respectively

Figure 14

Comparison of the predicted variation in plastic strain, pressure, and porosity through the compaction zone with the 2D mesoscale predictions reported in Ref. 11

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