ralph menikoff- pore collapse and hot spots in hmx

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Pore Collapse and Hot Spots in HMX

RALPHMENIKOFF

APS Topical ConferenceShock Compression of Condensed MatterPortland, OregonJuly 20-25, 2003

Los Alamos National Laboratory, an affirmative action/equal opportunit employer, is operated b the University of California for the U.S. DepartmentofEnergy under contrac t W-7405-ENG-36. By acceptance of this article, tKe published recognizes &a t the U.S Government retains a nonexclusive, ro altyfree license to publish or reproduce the published form of this contribution, or to allow others to do so, for U.S. Government purposes. Los Alamos hatiinalLaboratory requests tha t the publisher ident ify this artic le as work performed under the auspices pf the U.S. Department of Energy. Los Alamos National Laboratorstrongly sup orts academic freedom and a researcher's right to publish; as an Institut ion, however, the Laboratory does not endorse theviewpoint or a publication or guarantee its technical correctnas

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PORE COLLAPSE AND HOT SPOTS IN H M XRalphMenikoff

Theoretical Division, MS-R214, ID S Alamos National Laboratory, Los Alamos, NM 87545Abstract. The computing power now available has led researchers to reconsider mesoscale simulations as ameans to develop a detailed understanding of detonation waves in a heterogeneous explosive. Since chemicalreaction rates are sensitive to temperature, hot spots ar e of critical importance for initiation. In a plastic-bondedexplosive, shock desensitization experiments imply that hot spots generated by pore co llapse dominate shockinitiation. Here, for the collapse of a single pore driven by a shock, the dependenceof the tem perature distribu-tion o n num erical resolution and dissipative mechanism i s investigated. An ine a material (with the constibtiveproperties of HMX) is used to better focus on the mechanics of pore collapse. ' h o mportant findings resultedfrom this study. Eust, too low a resolution can significantly enhance the hot-spot mass. Second, at even mod-erate piston velocities (< 1Ws),hock dissipation alone does not generate sufficienthot-spot mass. ' b o therdissipative mechanism investigated are plastic work and viscous heating. In the cases studied, the integratedlempera!xre distribution has a power-law tail w ith exponent related to a param eter with dimensions of viscosity.Fora particular case, the parameter of either dissipative mechanism can be fit to o btain quantitatively he hot-spotmass needed for initiation. But the dissipative mechanisms scale differently with shock strength and pore size.Consequently, o predict initiation behavior over a range of stimuli and as the micro-stmcture propertiesof a PBXam varied, sufficient numerical resolution and the correct physical dissipative mechanism are essential.

INTRODUCTIONIt has been known since the 1950s that initiationin a plastic-bonded explosive (PBX) is due to thermal

reactions but require hot spots (1). Hot spots recon-cile the large discrepancy between the time to deto-nation from Pop plot data and the adiabatic inductiontime based on the bulk shock temperature and anAr-rhenius reaction rate, see figure1.For a strong shock(P = lOGPa) at the high end of the measured Popplot in HMX based PBX-9501, we note that the timeto detonation is N 0 . 2 ~ .ast reaction on this timescale (20ns) require temperatures in range of 800Kfor the liquid phase (9) to 1500K for the solid phase(6),see figure2.

Shock desensitization experiments(2)and the in-creased sensitivity of a PBX with increasing poros-ity, as displayed in Pop plot data, imply that hotspots generated by pore collapse dominate a shock-to-detonation transition. Early hydrodynamic sim-ulations of heterogeneous initiation by Mader (8,

sec. 3.3) utilized artificial viscosity for shock wavesas the only dissipative mechanism. They showed thata micro-jet is formed when a strong shock impingeson a pore, and then a hot spot is produced when thejet impacts the downstream side of the pore. Fur-thermore, Mader's simulations with arrays of poresin an explosive showed a shock-to-detonationtran-sition. When the simulations were performed(2-Dflow in the 1960s and 3-R in the 1980's), the avail-able computer power limited the resolution. In ad-dition, data on the thermal properties of explosiveswere limited. The variationof specific heat with tem-perature is important because of the sensitivityof re-action rates.

With only shock dissipation, the peak pore col-lapse temperature can be estimated based solely onthe equation of state@OS)of the explosive and sim-ple Riemann problems. For beta-=, which isthe stable polymorph at ambient conditions, a com-plete EOS s derived from data currently availableand estimates of the hot-spot temperature have been


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103

102

~ 1013ac

lo-

10-2

FIGURE 1.Time o detonationas function of shock pres-sure forHMX. Redline s Pop plot for PBX-9501(4).Blueand green ines are adiabatic inductiontime or Arrheniusreaction rate based on liquid HMX (9) and global reac-tion mte (6), espectively. Symbols are from wedge ex-periments of single crystalHMX y Craig (2).

presented (10). Since the EOS neglects solid-liquidphase transition, which has a latent heat equivalent toATN200K, we take T=1000K as critical hot-spottemperature for fast reaction. The estimates indicatethat shock dissipation alone does not generate suffi-ciently high hot-spot temperatures, even for a strongshock at the high end of the measured Pop plot

Other dissipative mechanism applicable to porecollapse are viscous heating and plastic work. In thepast, hot-spot temperatures were estimated based onsimplified models due to the limited computer poweravailable at the time, see for example (7, 3) . Here,for the collapse of a single pore driven by a shock,the dependence of the temperature distribution on nu-merical resolution and dissipative mechanism is in-vestigated.

We consider both shear viscosity and rate-dependent plasticity. These mechanisms introducea parameter q with dimensions of dynamic viscos-ity. Forplasticity the parameter determines the relax-ation rate to the yield surface. The viscous parametergive rise to two dimensionless parameters: Reynoldsnumber, Ry = @ and (shock width)/@ore radius).Consequently, scaling of hot-spot temperature withpore radius and particle velocity will depend on thedissipative mechanism. To study this dependence wechoose to hold the pore radius fixed and vary the vis-cosity parameter.

rl

T (K)FIGURE 2. Adiabatic induction time or HMX. Blue andgreen lines are based on Anhenius reaction rate for liquidHMX (9) and global reaction rate (6), espectively.

SIMULATIONSInitial conditions for two-dimensional simula-

tions are a gas filled pore of radius 0 .1mm centeredat (0.4,O)mm surrounded by an inert material withthe mechanical properties ofHMX. he left bound-ary is a piston. A piston velocity of 1. 3kmk is usedto drive a shock wave with a pressure of 13GPa andtemperature of 630K.

For hydrodynamic pore collapse, in which theonly dissipation is at shock fronts,figure 3A showsthe temperature field after the shock front has passedover the pore. We note that the gray region corre-sponds to the piston and the blue region to the gas.Pore collapse gives rise to an outgoing rarefactionwave in the material compressed by the lead shock,followed by an outgoing shock wave. These sec-ondary waves give rise to the main features seen inthe temperature field. We note that the secondaryshock has caught up to the lead shock resulting ina Mach wave pattern. The temperature discontinu-ity corresponds to the contact emanating from theMach triple point at (0.82,0.14). The gas pore hasbeen highly compressed and distorted by the vortexset up from the impact of the micro-jet formed whenthe lead shock overtakes he pore, on thedownstreamside of the pore. Since the vortex and the gas inter-face are expected to be unstable, the shapeof the poreare undoubtedly inaccurate.The temperature distribution is shown in fig-ure 3B . The h t eak at 300K corresponds to theambient state ahead of the lead shock front. The sec-ond peak centered at 575K (greenish region) corre-


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EEvh

0-5

0.40.3

0.2

0.10.0 0.2 0.4 0.6 0.0 0I.uA) x (mm) B) T (K)

FIGURE 3. Temperature&er porecollapse. Simulation with piston velocityof 1.3kmls, shock dissipationonlyand esolutionof 100cells in the initial pore radius (0.1mm). A) 2-D temperature field, gmy region is piston and blue region is gas pore.Bottomboundary s symmetry plane. B) Tempemtare distribution.

sponds to the material heated by the lead shock andthen cooled by the rarefaction from the pore impb-sion. The third peak centered about 675K (yellow-red region) corresponds o the material heated by thelead shock and backward expanding portion of thesecondary shock from the explosion of the pore. Thelow broad peak between 700 and 850K (red region)corresponds to the region between the Mach stemand the material directly impacted by the micro-jet.The highestHMX temperatures, above850K, ccuronly near the pore and are numerical artifacts of thematerial interface treatment

We note that the third peak is similar to whatHayes (5, Fig. 5) used to model initiation in HNS.The temperature of this peak depends on the explo-sive through its equation of state and speciiic heat.For HMX, since lo00K is needed for fast reactions,we conclude that shock dissipation is not sufficientfor initiation.

With additional dissipative mechanisms, plasticwork or viscous heating, the tail of the temperaturedisbhtion can be greatly enhanced. Consequently,the reaction from hot spots are associated with theextreme tail of the temperature distribution. The tailof the temperature distribution is best described bythe integrated temperature distribution, mass(T1) atT >TI. The mass is normalize relative to the equiv-alent mass in the pore volume at the initial explosivedensity.

Before reporting the results of simulations withother dissipative mechanisms we examine the effectof mesh resolution on the temperatare distribution.

Figure 4 hows the integrated temperature distribu-tion for resolution varying from 5 to 100 cells inthe initial pore radius. We note that the distributionsare nearly the same up to SoOK, but differ substan-tially in the high temperaturetail. The differencesare largely due to truncation errors in the region ofhighvorticity mu nd the pore. In fact the low resolu-tion case has sufficient hot-spot mass above lOOOKthat if the simulation included chemical reaction asubstantial amount of burn would occur, roughly abum mass equivalent to 25% of the volume of thepore. Thus, errors from too low a resolutioncan sub-stantially affect simulations of initiation. This is animportant concernformeso-scale simulationsof hot-spot initiation and is a determining factor in the sizeor number of grains in a PBX that can be included inthe computationaldomain.

Simulations with additional dissipative mecha-nisms are 'zed by the integrated temperaturedistribution shown in figure 5. A striking feature ofthe integrated distributions are that they are approx-imately linear on a log-log scale. This implies thatthe tail of the distribution has a power-law behav-ior. Moreover, the slope of the temperature distri-bution or the exponent of the power-law increaseswith the viscous parameter. The viscous parameterhas not been directly measured. Instead it is usualfit to reproduce integral data in a limited class of ex-periments. The fact that both the viscous heating andplastic work have similar distributions implies thateither dissipative mechanism can be used in a fit. Todistinguish these mechanism requires a range of ex-


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A

10.000

---._v-eE 0.100

0.010 . O O o ~

I300 500 700 10000.001 IT (K)

FIGURE 4. Variationof tempemture distdmtion with res-olution for shock dissipation only. Cells in pore radius:red, 100,blue, 50; green, 20; black, solid and dashed 10and 5, respectively.

periments which are sensitive to differences in thescaling behavior of each mechanism.

CONCLUSIONSTwo important findings resulted from this study.

First, too low a resolution can significantly enhancethe hot-spot mass. Second, at even modest piston ve-locities (< 1km/s), shock dissipation alone does notgenerate sufficient hot-spot mass. l k o other dissi-pative mechanism investigated are plastic work andviscous heating. In the cases studied, the integratedtemperatare distribution has a power-lawtailwith ex-ponent related to a parameter with dimensions of vis-cosity. The dissipative mechanisms scale differentlywith shock strength and pore size. Consequently, topredict initiation behavior over a range of stimuliandas the micro-structure properties of a PBX are varied,sufficient numerical resolution and the correct physi-cal dissipative mechanism are essential.

ACKNOWLEDGMENTSThis work was carried out under the auspices ofthe U. S. Dept. of Energy at LANL under contract

W-7405-ENG-36. The author thanks Prof. DavidBenson, Univ. of Calif. at San Diego, for providingthe code used for the simulations.

0.001-00 1000 2000T (K)

FIGURE 5. Variation of temperature distributionwith dis-sipative mechanism. Dissipative mechanisms: red, shockheating; blue, shear viscosity, solid and dashedq = 10 and100Poise, respectively; green, mte dependent plasticity,solid, dashed and dotted q = 800, So00 and SOPoise, re-spectively.

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REFERENCESBowden, F. P., and Yoffe,Y. D., Initiation and Growthof Explosion in Liquids and Solids, Cambridge Univ.Press, Cambridge,UK, 1952.Campbell, A, W., and Travis, J. R, in Proceedingsof Eighth Symposium (International)on Detonation,Albuquerque, NM, July 15-19, 19SS,Naval SurfaceWeapons Center, White Oak, SilverSpring, Maryland

Frey, R. B., in Eighth Symposium (International)onDetonation,1985 pp. 68-80.Gibbs, T. R., and Popalato, A., eds., LASL ExplosiveProperty Data, University of California Press, 1980.Hayes, D. B., in Progress in Astronautics and Aero-nautics,vol. 87, 1983pp. 445-467.

20903-5000,1986 pp. 1057-1068.

Henson, B. F., Asay, B. W., Smilowitz, L. B., andDickson, F M., Ignition chemistryin HMX fromther-mal explosion to detonation, Tech. Rep. LA-UR-01-3499, LosAlamos National Lab., 2001.Khasainov, B. A., Attetkov, A. V., Borisov, A. A., Er-molaev, B. S., and Soloviev, V. S., in Progmss in As-tronautics and Aeronautics,vol. 114, 1988 pp. 303-321.Mader, C. L., Numerical Modeling o Explosives andPropellants, second edn., CRC Press, Baca Raton,FL,1998.Rogen, R N., Thermochimica Acta 11, (1975) 131-139.Sewell,T.D., and Menikoff,R, nshock Compressionofcondensed Matter, 2003 p. this volume.

ralph menikoff- pore collapse and hot spots in hmx

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