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 100ms; 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 (100ms), 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 (100up1000ms). 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.

1.
Baer
,
M. R.
, and
Nunziato
,
J. W.
, 1986, “
A Two-Phase Mixture Theory for the Deflagration to Detonation Transition (DDT) in Granular Reactive Materials
,”
Int. J. Multiphase Flow
0301-9322,
12
, pp.
861
889
.
2.
Powers
,
J. M.
,
Stewart
,
D. S.
, and
Krier
,
H.
, 1990, “
Theory of Two-Phase Detonation-Part I: Modeling
,”
Combust. Flame
0010-2180,
80
, pp.
264
279
.
3.
Bdzil
,
J. B.
,
Menikoff
,
R.
,
Son
,
S. F.
,
Kapila
,
A. K.
, and
Stewart
,
D. S.
, 1999, “
Two-Phase Modeling of Deflagration-to-Detonation Transition in Granular Materials: A Critical Examination of Modeling Issues
,”
Phys. Fluids
1070-6631,
11
(
2
), pp.
378
402
.
4.
Kang
,
J.
,
Butler
,
P. B.
, and
Baer
,
M. R.
, 1992, “
A Thermomechanical Analysis of Hot Spot Formation in Condensed-Phase Energetic Materials
,”
Combust. Flame
0010-2180,
89
, pp.
117
139
.
5.
Bonnett
,
D. L.
, and
Butler
,
P. B.
, 1996, “
Hot-Spot Ignition of Condensed Phase Energetic Materials
,”
J. Propul. Power
0748-4658,
12
(
4
), pp.
680
690
.
6.
Massoni
,
J.
,
Saurel
,
R.
,
Baudin
,
G.
, and
Demol
,
G.
, 1999, “
A Mechanistic Model for Shock Initiation of Solid Explosives
,”
Phys. Fluids
1070-6631,
11
, pp.
710
736
.
7.
Gonthier
,
K. A.
, 2003, “
Modeling and Analysis of Reactive Compaction for Granular Energetic Solids
,”
Combust. Sci. Technol.
0010-2202,
175
, pp.
1679
1709
.
8.
Powers
,
J. M.
,
Stewart
,
D. S.
, and
Krier
,
H.
, 1989, “
Analysis of Steady Compaction Waves in Porous Materials
,”
J. Appl. Mech.
0021-8936,
56
, pp.
15
24
.
9.
Johnson
,
J. N.
,
Tang
,
P. K.
, and
Forest
,
C. A.
, 1985, “
Shock-Wave Initiation of Heterogeneous Reactive Solids
,”
J. Appl. Phys.
0021-8979,
57
, pp.
4323
4334
.
10.
Tarver
,
C. M.
,
Chidester
,
S. K.
, and
Nichols
,
A. L.
, III
, 1996, “
Critical Conditions for Impact and Shock-Induced Hot Spots in Solid Explosives
,”
J. Phys. Chem.
0022-3654,
100
, pp.
5794
5799
.
11.
Menikoff
,
R.
, and
Kober
,
E.
, 1999, “
Compaction Waves in Granular HMX
,” LA-13546-MS, Los Alamos National Laboratory, Los Alamos, NM.
12.
Park
,
S. J.
,
Han
,
H. N.
,
Oh
,
K. H.
, and
Lee
,
D. N.
, 1999, “
Model for Compaction of Metal Powders
,”
Int. J. Mech. Sci.
0020-7403,
41
, pp.
121
141
.
13.
Swegle
,
J. W.
, 1980, “
Constitutive Equation for Porous Materials with Strength
,”
J. Appl. Phys.
0021-8979,
51
(
5
), pp.
2574
2580
.
14.
Issen
,
K. A.
, 2002, “
The Influence of Constitutive Models on Localization Conditions for Porous Rock
,”
Eng. Fract. Mech.
0013-7944,
69
, pp.
1891
1906
.
15.
Issen
,
K. A.
, and
Rudnicki
,
J. W.
, 2001, “
Theory of Compaction Bands in Porous Rock
,”
Phys. Chem. Earth
1464-1895,
26
(
1–2
), pp.
95
100
.
16.
Cart
,
E. J.
,
Lee
,
R. J.
,
Gustavson
,
P. K.
,
Coffey
,
C. S.
, and
Sutherland
,
G. T.
, 2003, “
The Role of Shear in Shock Initiation of Explosives
,”
Proceedings of the Conference of the American Physical Society Topical Group on Shock Compression of Condensed Matter
, Seattle, WA, in press.
17.
Tamura
,
S.
, and
Horie
,
Y.
, 1998, “
Discrete Meso-Dynamic Simulation of Thermal Explosion in Shear Bands
,”
J. Appl. Phys.
0021-8979,
84
(
7
), pp.
3574
3580
.
18.
Wilson
,
W. H.
,
Tasker
,
D. G.
,
Dick
,
R. D.
, and
Lee
,
R. J.
, 1998, “
Initiation of Explosives Under High Deformation Loading Conditions
,”
Proceedings of the Eleventh (International) Detonation Symposium
, Snowmass, CO, pp.
565
572
.
19.
Gonthier
,
K. A.
, 2005, “
Modeling Shear Enhanced Compaction for Granular Explosive
,”
Khim. Fiz.
0207-401X, to appear.
20.
Cline
,
C. F.
, 1996, “
Dynamic Compaction of Ceramic Powders
,”
Ind. Ceram.
1121-7588,
16
(
3
), pp.
189
194
.
21.
Joshi
,
V. S.
, 1995, “
Materials Processing by Shock Compaction: Status and Application to Nanocrystalline Ceramics
,”
Proceedings of the ASME Materials Division
, ASME, New York, MD-Vol.
69-1
, pp.
633
651
.
22.
Baer
,
M. R.
, 1988, “
Numerical Studies of Dynamic Compaction of Inert and Energetic Granular Materials
,”
J. Appl. Mech.
0021-8936,
55
, pp.
36
43
.
23.
Lubliner
,
J.
, 1990,
Plasticity Theory
,
Macmillan Publishing Company
, New York.
24.
Coyne
,
P. J.
,
Elban
,
W. L.
, and
Chiarito
,
M. A.
, 1985, “
The Strain Rate Behavior of Coarse HMX Porous Bed Compaction
,”
8th International Symposium on Detonation
,
Albuquerque
, NM, July 15–19, pp.
645
657
.
25.
Elban
,
W. L.
, and
Chiarito
,
M. A.
, 1986, “
Quasi-Static Compaction Study of Coarse HMX Explosive
,”
Powder Technol.
0032-5910,
46
, pp.
181
193
.
26.
Gonthier
,
K. A.
,
Menikoff
,
R.
,
Son
,
S. F.
, and
Asay
,
B. W.
, 1998, “
Modeling Compaction Induced Energy Dissipation of Granular HMX
,”
11th International Symposium on Detonation
,
Snowmass
, CO, August 31–September 4, pp.
153
161
.
27.
McAfee
,
J. M.
,
Asay
,
B.
,
Campbell
,
W.
, and
Ramsay
,
J. B.
, 1989, “
Deflagration to Detonation Transition in Granular HMX
,”
9th International Symposium on Detonation
, Portland, OR, August 28–September 1, pp.
265
279
.
28.
Johnson
,
K. L.
, 1985,
Contact Mechanics
,
Cambridge University Press
, New York.
29.
Menikoff
,
R.
, and
Sewell
,
T. D.
, 2001, “
Constituent Properties of HMX Needed for Mesoscale Simulations
,” LA-UR-00-3804-rev,
Los Alamos National Laboratory
, Los Alamos, NM.
30.
Sheffield
,
S. A.
,
Gustavsen
,
R. L.
, and
Anderson
,
M. U.
, 1997, “
Shock Loading of Porous High Explosives
,”
High-Pressure Shock Compression of Solids IV
,
Springer-Verlag New York
, pp.
24
61
.
31.
Sandusky
,
H. W.
, and
Liddiard
,
T. P.
, 1985, “
Dynamic Compaction of Porous Beds
,” Technical Report No. 83-246, Naval Surface Warfare Center.
32.
Marsh
,
S. P.
, 1980,
LASL Shock Hugoniot Data
,
University of California Press
, Berkeley, CA.
33.
Gonthier
,
K. A.
, 2004, “
Predictions for Weak Mechanical Ignition of Strain Hardened Granular Explosive
,”
J. Appl. Phys.
0021-8979,
95
(
7
), pp.
3482
3494
.
34.
Bardenhagen
,
S. G.
, and
Brackbill
,
J. U.
, 1998, “
Dynamic Stress Bridging in Granular Material
,”
J. Appl. Phys.
0021-8979,
83
(
11
), pp.
5732
5740
.
35.
Gibbs
,
T. R.
, and
Popalato
,
A.
, 1980, LASL Explosives Property Data.
36.
Jogi
,
V.
, 2003, Predictions for Multi-Scale Shock Heating of a Granular Energetic Material, M.S. thesis, Louisiana State University.
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