On the low pressure shock initiation of octahydro-1,3,5,7–tetranitro-1,3,5,7-tetrazocinebased plastic bonded explosivesKevin S. Vandersall, Craig M. Tarver, Frank Garcia, and Steven K. Chidester Citation: Journal of Applied Physics 107, 094906 (2010); doi: 10.1063/1.3407570 View online: http://dx.doi.org/10.1063/1.3407570 View Table of Contents: http://scitation.aip.org/content/aip/journal/jap/107/9?ver=pdfcov Published by the AIP Publishing Articles you may be interested in A molecular dynamics study of the early-time mechanical heating in shock-loaded octahydro-1,3,5,7-tetranitro-1,3,5,7-tetrazocine-based explosives J. Appl. Phys. 116, 033516 (2014); 10.1063/1.4890715 Anisotropic shock sensitivity for β-octahydro-1,3,5,7-tetranitro-1,3,5,7-tetrazocine energetic material undercompressive-shear loading from ReaxFF- lg reactive dynamics simulations J. Appl. Phys. 111, 124904 (2012); 10.1063/1.4729114 Initial chemical events in shocked octahydro-1,3,5,7-tetranitro-1,3,5,7- tetrazocine: A new initiationdecomposition mechanism J. Chem. Phys. 136, 044516 (2012); 10.1063/1.3679384 Quantitative analysis of damage in an octahydro-1,3,5,7-tetranitro-1,3,5,7-tetrazonic-based composite explosivesubjected to a linear thermal gradient J. Appl. Phys. 97, 093507 (2005); 10.1063/1.1879072 An estimate of the linear strain rate dependence of octahydro-1,3,5,7-tetranitro-1,3,5,7-tetrazocine J. Appl. Phys. 86, 6717 (1999); 10.1063/1.371722

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On the low pressure shock initiation of octahydro-1,3,5,7–tetranitro-1,3,5,7-tetrazocine based plastic bonded explosives

Kevin S. Vandersall, Craig M. Tarver,a� Frank Garcia, and Steven K. ChidesterEnergetic Materials Center, Lawrence Livermore National Laboratory, Livermore, California 94551, USA

�Received 21 October 2009; accepted 24 March 2010; published online 7 May 2010�

In large explosive and propellant charges, relatively low shock pressures on the order of 1–2 GPaimpacting large volumes and lasting tens of microseconds can cause shock initiation of detonation.The pressure buildup process requires several centimeters of shock propagation before shock todetonation transition occurs. In this paper, experimentally measured run distances to detonation forlower input shock pressures are shown to be much longer than predicted by extrapolation of highshock pressure data. Run distance to detonation and embedded manganin gauge pressure historiesare measured using large diameter charges of six octahydro-1,3,5,7–tetranitro-1,3,5,7-tetrazocine�HMX� based plastic bonded explosives �PBX’s�: PBX 9404; LX-04; LX-07; LX-10; PBX 9501;and EDC37. The embedded gauge records show that the lower shock pressures create fewer and lessenergetic “hot spot” reaction sites, which consume the surrounding explosive particles at reducedreaction rates and cause longer distances to detonation. The experimental data is analyzed using theignition and growth reactive flow model of shock initiation in solid explosives. Using minimumvalues of the degrees of compression required to ignite hot spot reactions, the previously determinedhigh shock pressure ignition and growth model parameters for the six explosives accurately simulatethe much longer run distances to detonation and much slower growths of pressure behind the shockfronts measured during the shock initiation of HMX PBX’s at several low shock pressures. © 2010American Institute of Physics. �doi:10.1063/1.3407570�

I. INTRODUCTION

The most frequent method of representing shock initia-tion data for solid explosives and propellants is to measurethe run distances to detonation for several input shock pres-sures and then plot the data on log-log axes. This graphicalrepresentation is called the “Pop Plot,” named after AlphonsePopolato of Los Alamos National Laboratory. Pop Plots firstappeared in the shock initiation study of several explosivesby Ramsay and Popolato.1 These plots give clear indicationsof the relative shock sensitivities of different materials andthe lengths of explosive charges needed for shock to detona-tion transition �SDT� to occur for one-dimensional �1D� sus-tained shock pressures. Over the middle of the shock initia-tion pressure range �2.5 to 20 GPa for octahydro-1,3,5,7–tetranitro-1,3,5,7-tetrazocine �HMX� based plastic bondedexplosives �PBX’s��, linear fits accurately describe Pop Plotdata. Figure 1 contains linear fits for the six HMX basedPBX’s discussed in this paper.2 However, at very high pres-sures produced by detonators and booster charges, the timesand run distances to detonation are much shorter than thosepredicted by the linear fits. At lower shock pressures, thetimes and run distances are much longer than predicted byextrapolation of these linear fits.3 For each explosive chargelength, at some shock pressure SDT cannot occur. Lowshock pressures are representative of many safety and vul-nerability scenarios in which large, relatively slow fragmentsimpact large areas of bare or covered explosive charges. Thislow shock pressure regime of SDT has not frequently been

studied quantitatively, because of difficulties in handlinglarge HMX charges and in producing sustained 1D shockwaves over large volumes. Several two-dimensional �2D�tests, such as confined and unconfined gap tests, are usuallyused instead.2

To understand shock initiation and develop predictivereactive flow models, the most important experimental SDT

a�Electronic mail: tarver1@llnl.gov.

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JOURNAL OF APPLIED PHYSICS 107, 094906 �2010�

0021-8979/2010/107�9�/094906/11/$30.00 © 2010 American Institute of Physics107, 094906-1

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data sets are the pressure and/or particle velocity historiesmeasured by gauges embedded within the explosive charge.Manganin piezoelectric gauges are used to measure the pres-sure buildup caused by exothermic reaction behind the lead-ing shock front at several positions within the explosivecharge.4 Metal particle velocity gauges5 embedded in an ex-plosive charge placed within a strong magnetic field yield theparticle velocity build up rates at several positions within thereacting explosives. The two gauge techniques have beenshown to yield equivalent results.6 Since embedded gaugeexperiments are expensive and measure only 1D flow, mul-tidimensional reactive flow models based on gauge and 2DSDT experiments are needed to assess hazard and vulnerabil-ity scenarios that cannot be tested. Multidimensional ignitionand growth reactive flow model parameters have been devel-oped for SDT in many solid explosives.7 In the experimentalportion of this study, manganin pressure gauges are embed-ded in 90 mm diameter by 45 mm long or 145 mm diameterby 80 mm long cylinders of HMX PBX’s. These cylindersare impacted by flyer plates accelerated by either a 101 mmpowder gun or a 155 mm Howitzer gun, respectively, at vari-ous impact velocities to produce several different run dis-tances to detonation. New and recently reported data arecomplied to show the relative shock sensitivity of 6 HMXPBX’s at low shock pressures. The six PBX’s are: PBX 9404�94% HMX, 3% nitrocellulose, and 3% chloro-ethyl-phosphate �CEF��; LX-04 �85% HMX and 15% Viton�;LX-07 �90% HMX and 10% Viton�; LX-10 �95% HMX and5% Viton�; PBX 9501 �95% HMX, 2.5% bis�2,2–dinitropropyl�acetal/formal �BDNPA/F�, and 2.5% Estane�;and EDC37 �91% HMX, 1% nitrocellulose, and 8%trinitroethylbenzene/dinitroethylbenzene�. Table I containsthe measured densities, the theoretical maximum densities�TMD�, and void percentages for these PBX’s. In the reac-tive flow modeling portion of this study, the measured pres-sure histories and run distances to detonation are used toextend existing high shock pressure ignition and growthmodel parameters for these six PBX’s to accurately simulatethis lower shock pressure data.

II. EXPERIMENTAL PROCEDURE

In this experimental study, embedded manganin pressuregauges are placed along the axes of HMX PBX charges,which are impacted by flyer plates accelerated by two gunswith different barrel diameters. Figure 2 is a photograph of atypical explosive target consisting of alternating disks of

PBX, Teflon encapsulated manganin gauges8, and aluminumcover plates. To measure higher pressures and shorter rundistances to detonation, the 101 mm powder gun accelerates25 mm long by 101 mm diameter aluminum flyer plates intoexplosive targets that are 90 mm diameter by 45 mm long.Various thicknesses of the 90 mm diameter PBX disks areused to measure pressure histories at various distances intothe PBX. To study lower shock pressures and longer rundistances, a 155 mm Howitzer gun accelerates 50 mm longby 155 mm diameter aluminum flyer plates into 145 mmdiameter by 80 mm long explosive targets. In these targets,the manganin gauges are placed between 10 mm thick PBXdisks on the charge axis of the target. Two manganin gaugesare placed in each gauge layer to provide redundancy in caseof gauge failure. The active manganin elements are 0.025mm thick and are encapsulated in 0.25 mm of Teflon, whichis an excellent impedance match for these PBX’s. The totalgauge package thickness is nominally 0.3 mm. The PBX’sare machined to within a few microns of the nominal thick-nesses. The manganin gauge records are only reliable whenthe flow is 1D, because their electrical signals are not cali-brated when they are stretched by lateral rarefaction waves.2D ignition and growth hydrodynamic code calculations areused to help determine when and where this stretching be-gins.

This paper summarizes all of the work done on the sixHMX PBX’s at lower shock pressures. Previously reportedrun distances to detonation are included for completeness,

TABLE I. HMX PBX’s compositions, densities, TMD’s, and void volumes.

Name and compositionDensity�g /cm3�

TMD�g /cm3� Void percentage

PBX 9404 �94% HMX, 3% nitrocellulose, and 3% CEF� 1.84 1.865 1.34LX-04 �85% HMX and 15% Viton� 1.866 1.889 1.22LX-10 �95% HMX and 5% Viton� 1.86 1.896 1.90PBX 9501 �95% HMX, 3% BDNPA/F, and 3% estane� 1.832 1.855 1.24LX-07 �90% HMX and 10% Viton� 1.85 1.892 2.22EDC37 �91% HMX, 1% nitrocellulose, and 8%trinitro-ethylbenzene/dinitroethyl-benzene� 1.841 1.844 0.16

FIG. 2. �Color online� Explosive target showing disks of PBX �yellow� andTeflon encapsulated manganin gauges �black�, aluminum cover and backplates �gray�, and electrical leads.

094906-2 Vandersall et al. J. Appl. Phys. 107, 094906 �2010�

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but only new manganin gauge records and ignition andgrowth calculations are shown in detail. For PBX 9404, theoldest and most sensitive HMX PBX due to the sensitivenitrocellulose component in its binder, three Howitzer gunexperiments were reported by Green et al.3 The manganingauges and reactive flow modeling were still in developmentat that time so they must be considered qualitative, but therun distances at three shock pressures are correct. A verycomprehensive ignition and growth model for PBX 9404was later developed that calculated these run distances todetonation accurately.7 All of the LX-04 experimental andmodeling results were recently published by Vandersall etal.9 Some of the PBX 9501 �Ref. 10� and LX-10 �Ref. 11�experimental and modeling results were previously pub-lished. All of the LX-07 and EDC37 results are new. Table IIlists the details of the new experiments for LX-10, PBX9501, LX-07, and EDC37. The shot numbers for the 101 mmgun experiments in Table II begin with 47, while the 155 mmHowitzer gun shot numbers begin with HG. The impact ve-locities, flyer and impact plate materials, approximate inputpressures, and approximate run distances to detonation arealso listed in Table II. The individual manganin gaugerecords and run distances to detonation for all of these ex-periments are shown in Sec. IV. The flyer velocities weremeasured by two sets of time of arrival pins placed in frontof the target and are accurate within + /−10 m /s. The inputpressures were calculated by an impedance matching tech-nique and verified by hydrodynamic modeling. The run dis-tances to detonation were estimated by two methods: byfinding the intersection of shock velocity measured by thegauges preceding SDT and the detonation velocity measuredby the gauges following SDT and by using the difference inarrival times at the last gauge before SDT and the first gaugefollowing SDT. The two methods agree closely for low

shock pressure SDT in HMX based PBX’s, because the in-crease in shock velocity before SDT is small and SDT occursrapidly.

III. IGNITION AND GROWTH MODEL

The ignition and growth reactive flow model of shockinitiation and detonation has been used to model many shockinitiation and detonation studies of solid explosives in sev-eral 1D, 2D, and 3D codes.12–16 The model uses two Jones–Wilkins–Lee �JWL� equations of state, one for the unreactedexplosive and one for its reaction products, in the tempera-ture dependent form

p = Ae−R1V + Be−R2V + wCvT/V, �1�

where p is pressure in megabars, V is relative volume, T istemperature, w is the usual Gruneisen coefficient, Cv is theaverage heat capacity, and A, B, R1, and R2 are constants.The reaction rate law for the conversion of explosive to prod-ucts is

dF/dt = I�1 − F�b��/�o − 1 − a�x + G1�1 − F�cFdpy + G2�1 − F�eFgpz

0 � F � Figmax 0 � F � FG1max FG2min � F � 1

Ignition Growth Completion,

�2�

where F is the fraction reacted, t is time, � is the currentdensity, �o is the initial density, and I, G1, G2, a, b, c, d, e, g,x, y, and z are constants. The mixture equations assume pres-sure and temperature equilibration between the unreacted ex-plosive and its reaction products.

The unreacted JWL equation of state for each explosiveis fit to all available experimental shock compression data2

and any nanosecond time resolved von Neumann spike data

TABLE II. New experiments fired using LX-10, PBX 9501, LX-07, and EDC37.

Shot numberImpactvelocity

�m/s� Flyerplate ImpactplatePressure

�GPa�Run toDET

�mm�

A. LX-104717 625 Teflon Teflon 1.7 504725 950 Aluminum Aluminum 4.5 5.54726 943 Teflon Teflon 2.7 184727 733 Teflon Teflon 2.1 30.8

B. PBX 95014729 711 Teflon Teflon 2.05 274730 654 Teflon Teflon 1.85 33.5HG08–01 378 Aluminum Aluminum 1.6 52.8

C. LX-074735 973 Aluminum Aluminum 5.5 5.04736 1006 Teflon Teflon 3.1 124737 784 Teflon Teflon 2.25 254738 664 Teflon Teflon 1.8 36HG07–01 349 Aluminum Aluminum 1.55 �80HG08–03 385 Aluminum Aluminum 1.65 61

D. EDC37HG07–03 391 Aluminum Aluminum 1.5 �80HG07–04 429 Aluminum Aluminum 1.8 �80HG07–05 483 Aluminum Aluminum 2.1 �80HG08–02 519 Aluminum Aluminum 2.3 69

094906-3 Vandersall et al. J. Appl. Phys. 107, 094906 �2010�

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for the detonating explosive.17 The reaction product JWLequation of state is fit to the wall velocity expansion datafrom cylinder tests2 and laser interferometric interface veloc-ity data for steady18,19 and overdriven detonations.20 Thethree-term rate law describes the three stages of reaction gen-erally observed in shock initiation and detonation of hetero-geneous solid explosives. For solid explosive shock initiationmodeling, the first term of Eq. �2� represents the ignition ofthe explosive as it is compressed by the leading shock wavecreating “hot spots” that can react and grow or fail to grow.21

The fraction of explosive ignited is assumed to be approxi-mately equal to the void volume of the pressed explosive andto react in nanoseconds. As listed in Table I, for most ofthese PBX’s, the initial void volume is between 1.2% and2.2%. The second reaction rate in Eq. �2� models the rela-tively slow growth of the reacting hot spots as they consumethe neighboring shock heated material. The third term in Eq.�2� describes the relatively fast process of coalescence of thegrowing hot spots and the rapid transition to detonation thatconsumes any remaining unreacted explosive.

TABLE III. Ignition and growth parameters for LX-10, LX-07, PBX 9501, and EDC37.

Unreacted JWL Product JWL Reaction rates

A. LX-10; �o=1.862 g /cm3

A=952 200 GPa A=880.7 GPa I=20 000 �s−1

B=−5.944 GPa B=18.36 GPa a=0.0955R1=14.1 R1=4.62 b=0.667R2=1.41 R2=1.32 x=4.0 Figmax=0.02�=0.8867 �=0.38 G1=0.035 GPa−2 �s−1

Cv=2.7806�10−3 GPa /K Cv=1.0�10−3 GPa /K c=0.667To=298• K Eo=10.4 GPa d=0.667Shear modulus=5.0 GPa D=8.82 km /s y=2.0 FG1max=0.5Yield strength=0.2 GPa PCJ=0.375 Mbar G2=0.000 32 GPa−3 �s−1

e=0.333 z=3.0g=1.0 FG2min=0.5

B. PBX 9501; �o=1.832 g /cm3

A=732 000 GPa A=1668.9 GPa I=20 000 �s−1

B=−5.2654 GPa B=59.69 GPa a=0.0819R1=14.1 R1=5.9 b=0.667R2=1.41 R2=2.1 x=4.0 Figmax=0.02�=0.8867 �=0.45 G1=0.0285 GPa−2 �s−1

Cv=2.7806�10−3 GPa /K Cv=1.0�10−5 GPa /K c=0.667To=298• K Eo=10.2 GPa d=0.667Shear modulus=3.54 GPa D=8.80 Km /s y=2.0 FG1max=0.5Yield strength=0.2 GPa PCJ=0.340 Mbar G2=0.00032 GPa−3 �s−1

e=0.333 z=3.0g=1.0 FG2min=0.5

C. LX-07; �o=1.850 g /cm3

A=952 200 GPa A=871.0 GPa I=20 000 �s−1

B=−5.944 GPa B=13.9 GPa a=0.07117R1=14.1 R1=4.6 b=0.667R2=1.41 R2=1.15 x=4.0 Figmax=0.02�=0.8867 �=0.3 G1=0.0285 GPa−2 �s−1

Cv=2.7806�10−3 GPa /K Cv=1.0�10−3 GPa /K c=0.667To=298• K Eo=10.4 GPa d=0.667Shear modulus=5.0 GPa D=8.64 km /s y=2.0 FG1max=0.5Yield strength=0.2 GPa PCJ=0.355 Mbar G2=0.00032 GPa−3 �s−1

e=0.333 z=3.0g=1.0 FG2min=0.5

D. EDC37; �o=1.841 g /cm3

A=732 000 GPa A=1668.9 GPa I=20 000 �s−1

B=−5.2654 GPa B=59.69 GPa a=0.09114R1=14.1 R1=5.9 b=0.667R2=1.41 R2=2.1 x=4.0 Figmax=0.002�=0.8867 �=0.45 G1=0.012 GPa−2 �s−1

Cv=2.7806�10−3 GPa /K Cv=1.0�10−3 GPa /K c=0.667To=298• K Eo=10.2 GPa d=0.667Shear modulus=3.54 GPa D=8.80 km /s y=2.0 FG1max=0.5Yield strength=0.2 GPa PCJ=0.340 Mbar G2=0.00 032 GPa−3 �s−1

e=0.333 z=3.0g=1.0 FG2min=0.5

094906-4 Vandersall et al. J. Appl. Phys. 107, 094906 �2010�

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In most previous HMX PBX modeling studies, the criti-cal compression required for ignition �parameter a in the firstterm of Eq. �2�� was set equal to zero, because HMX explo-sives react violently at input pressures as low as 0.1 GPa inlong pulse duration, nonshock impact experiments involvingfriction and shear.22 However, for pure shock compression atlow pressure, the strength of the PBX limits the work doneduring void collapse, and a critical pressure or degree ofcompression for shock initiation is observed.3,23 Experimen-tal values2,23 of the unreacted PBX’s shear modulus and “ef-fective” yield strength at the high strain rate obtained duringshock compression were used to simulate the two waveelastic-plastic behavior observed in LX-10 shock compres-sion experiments below 1 GPa input pressure.23 At pressuresexceeding 1 GPa, single sharp shock waves have been mea-sured in LX-04,9 LX-10,23 and PBX 9501.24 All of the inputshock pressures in this study are greater than 1.5 GPa so the

shock compressions are very fast. In this modeling study, avalue for the critical compression parameter “a” in Eq. �2� isfound for each of the HMX PBX’s to account for a criticalshock pressure for SDT. Since a critical compression for ig-nition mainly affects the ignition term of Eq. �2�, which re-acts at most 2% of the explosive, the use of a finite value forthe critical compression has little or no effect on the growthand coalescence reaction rates. Thus the previous highershock pressure modeling results are not affected, and theignition and growth parameters published for PBX 9404,7

LX-04,9 PBX 9501,10 and LX-10 �Ref. 11� are used in thecurrent simulations. These parameters can be used for thecomplete range of shock initiation pressures and for qualita-tive detonation propagation calculations. However, for quan-titative nanosecond time resolved detonation reaction zone

TABLE IV. Gruneisen equation of state parameters for aluminum and Teflon. P=�oc2��1+ �1−�o /2��-a /2�2� / �1− �S1−1��−S2�2 / ��+1�−S3�3 / ��+1�2�2+ ��o+a��E, where �= �� /�o−1� and E is ther-mal energy.

INERT�o

�g /cm3�c

�mm /�s� S1 S2 S3 �o a

Al 6061 2.703 5.24 1.4 0.0 0.0 1.97 0.48Teflon 2.15 1.68 1.123 3.983 �5.797 0.59 0.0

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FIG. 3. �Color online� Pressure histories in LX-10 shocked to 1.7 GPa �topgauges and bottom simulations�.

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FIG. 4. �Color online� Pressure histories in PBX 9501 shocked to 2.05 GPa�top gauges and bottom simulations�.

094906-5 Vandersall et al. J. Appl. Phys. 107, 094906 �2010�

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modeling, a different set of ignition and growth parameters isnecessary to describe the rapid stable, gaseous product for-mation �CO2, N2, H2O, CO, etc.� followed by the slowersolid carbon particle formation �diamond, graphite,etc.�.17,20,25

50 zones per millimeter of PBX and the correspondingimpedance matched zoning of the inert materials are used inthe 1D calculations reported here. The entire experimentalgeometry is modeled, including each 0.3 mm thick manganingauge package. The eighth zone of the 15 zones in each 0.3mm thick Teflon layer is compared to the correspondingmanganin record. The gauge positions are given by the totalPBX thickness preceding that gauge. Table III lists the equa-tion of state and reaction rate parameters used in the ignitionand growth models for LX-10, LX-07, PBX 9501, andEDC37. PBX 9404 and LX-04 ignition and growth param-eters are given in Refs. 7 and 9, respectively. Listed in TableIV are the Gruneisen equation of state parameters for theinert materials Teflon and aluminum.26

IV. COMPARISONS OF EXPERIMENTAL ANDCALCULATED RESULTS

The experimental and calculated results are compared inthis section for each PBX in the following order: PBX 9404;LX-04; LX-10; PBX 9501; LX-07; and EDC37.

As mentioned in the Sec. II, three Howitzer gun experi-ments were fired using PBX 9404 by Green et al.3 The man-ganin gauges and reactive flow modeling were still underdevelopment at that time, but the input shock pressures andrun distances to detonation are correct. The three input shockpressures were approximately 1.2, 1.3, and 1.4 GPa. The 1.2GPa shock did not transition to detonation in a 100 mm longtarget. The run distances to detonation for the 1.3 and 1.4GPa shocks were approximately 90 mm and 70 mm, respec-tively. Extrapolation of the linear higher shock pressure PopPlot for PBX 9404 shown in Fig. 1 yields about 30 mm forthese shock pressures. These PBX 9404 run distances areincluded in the low pressure run distance versus shock pres-sure plot for the six PBX’s, because they represent the upperlimits of HMX PBX shock sensitivity.

All five of the LX-04 experiments and correspondingmodeling results were recently published by Vandersall etal.9 The lower limit of shock pressure that can transition todetonation within 80 mm of LX-04 was between 1.6 and 1.8GPa, because an aluminum flyer with a velocity of 368 m/sdid not cause detonation within 80 mm of propagation andan aluminum flyer with a velocity of 389 m/s caused deto-nation at about 65 mm. The ignition and growth LX-04model parameters, including a critical compression of 0.0794

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FIG. 5. �Color online� Pressure histories in PBX 9501 shocked to 1.85 GPa�top gauges and bottom simulations�.

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FIG. 6. �Color online� Pressure histories in PBX 9501 shocked to 1.6 GPa�top gauges and bottom simulations�.

094906-6 Vandersall et al. J. Appl. Phys. 107, 094906 �2010�

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representing a 1.2 GPa input shock pressure, produced goodagreement with all five experiments. The LX-04 run dis-tances represent the lower limits of shock sensitivity of thethree HMX/Viton PBX’s.

Seven 101 mm gunshots were fired using LX-10. Threeexperimental and calculated pressure history comparisonswere published by Vandersall and co-workers.10 The otherfour are listed in Table II. One of these shots was a highshock pressure experiment, and two other experimentsyielded only run distance to detonation data. Only the gaugerecord comparisons from shot 4717 are included here forcomparison. This was the lowest shock pressure �1.7 GPa�shot and did not transition to detonation at the deepest gaugeposition of 40 mm, but the reaction rate was growing rapidly.Figure 3�top� contains the pressure histories measured at 0,30, 36, and 40 mm. Figure 3�bottom� contains the corre-sponding calculated pressure histories using the LX-10 igni-tion and growth determined by Vandersall et al.11 and listedin Table III. The times used on Figs. 3–14 are the timesmeasured from the time of arrival pins for the experimentalrecords, and the calculated times from flyer plate impacts forthe calculated records. These 1D calculations correctly pre-dict a run distance to detonation greater than 40 mm, but thecalculated pressures are growing faster than the experimental

records at late times. All of the recent LX-10 run distance todetonation data is included in the comparisons for the sixPBX’s. With 95% HMX pressed to 98% TMD and formu-lated with an inert Viton binder, LX-10 is less shock sensi-tive than PBX 9404 and more sensitive than LX-04 �85%HMX and 15% Viton�.

Five experiments were conducted using PBX 9501. Twowere reported by Chidester et al.10 and the other three arelisted in Table II. Figure 4�top� shows the manganin gaugerecords for shot 4729, in which an input shock pressure of2.05 GPa caused detonation at 28 mm. Figure 4�bottom� con-tains the calculated pressure histories using the PBX 9501parameters from Chidester et al.10 listed in Table III. Figures5�top� and 5�bottom� show the experimental and calculatedpressure histories, respectively, for shot 4730, in which a1.85 GPa shock caused detonation at 33.5 mm. Figures6�top� and 6�bottom� contain the experimental and calculatedpressure histories, respectively, for shot HG08–01, in whicha 1.6 GPa pressure caused a transition to detonation at 53mm. The slight decreases in shock front pressure at the 10and 20 mm gauge positions may be due to endothermic pro-cesses dominating before rapid exothermic reaction begins.A previously reported shot HG07–02 with a shock pressureof 1.45 GPa transitioned to detonation at 72 mm.10 Good

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FIG. 7. �Color online� Pressure histories in LX-07 shocked to 2.25 GPa �topgauges and bottom simulations�.

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FIG. 8. �Color online� Pressure histories in LX-07 shocked to 1.8 GPa �topgauges and bottom simulations�.

094906-7 Vandersall et al. J. Appl. Phys. 107, 094906 �2010�

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agreement was obtained between the experimental and cal-culated pressure histories in all five PBX 9501 experiments.PBX 9501 exhibits lower shock sensitivity than PBX 9404.This is due to its plasticizer/binder, which is more pliable andless reactive than PBX 9404’s nitrocellulose-containingbinder. A softer, more pliable binder with lower shear modu-lus flows more easily than a high shear modulus, stiff binderunder shock compression. Less work and localized heatingare done, creating fewer hot spots.27

At the same porosity, LX-07 with 90% HMX and 10%Viton is intermediate in high pressure shock sensitivity be-tween LX-04 �85% HMX/15% Viton� and LX-10 �95%HMX/5% Viton� when pressed to the same TMD. However,as shown in Table I, LX-07 pressed to 1.85 g /cm3 is moreporous than the LX-10 and LX-04 pressings. This increasesthe LX-07 shock sensitivity relative to LX-10 and LX-04.The six LX-07 experiments are listed in Table II. Shots 4735and 4736 are higher shock pressure experiments whose rundistances to detonation agree with previous Pop Plot data onLX-07. The other four experiments extend the LX-07 rundistance data to lower shock pressures. Figures 7�top� and7�bottom� show the experimental and calculated pressurehistories �using the LX-07 Ignition and Growth parameters

listed in Table III�, respectively, for shot 4737, in which a2.25 GPa shock pressure results in a 23.5 mm run distance todetonation. The small pressure peaks in Fig. 7�bottom� some-times occur when the third reaction rate term in Eq. �2�abruptly takes over from the second reaction rate term. Fig-ures 8�top� and 8�bottom� compare the experimental and cal-culated pressure histories, respectively, for shot 4738, inwhich a 1.8 GPa shock transitions to detonation at 34 mm.Figures 9�top� and 9�bottom� contain the experimental andcalculated pressure histories, respectively, for shot HG08–03, in which a 1.65 GPa shock transitions to detonation at 61mm. Figures 10�top� and 10�bottom� show the experimentaland calculated pressure histories, respectively, for shotHG07–01, in which a 1.55 GPa shock does not detonate inthe 80 mm long LX-07 target. Good agreement between ex-periment and modeling was obtained for all four experi-ments. Thus LX-07 shock sensitivity is close to that ofLX-10 at low shock pressures.

EDC37 containing 91% HMX might be expected to besimilar to LX-07 in low pressure shock sensitivity, but itsoily, pliable binder allows it to be pressed to near TMD. Thusonly a small void volume �0.2%� is available to form reactivehot spots.28 Another difference is that the HMX particles in

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FIG. 9. �Color online� Pressure histories in LX-07 shocked to 1.65 GPa �topgauges and bottom simulations�.

FIG. 10. �Color online� Pressure histories in LX-07 shocked to 1.55 GPa�top gauges and bottom simulations�.

094906-8 Vandersall et al. J. Appl. Phys. 107, 094906 �2010�

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EDC37 are manufactured by a different process than theHMX in the other PBX’s. EDC37 is also pressed under dif-ferent conditions. The order of magnitude less porosity inEDC37 causes a larger difference in shock sensitivity thanHMX particle and pressing differences. Four gun shots firedusing EDC37 are listed in Table II, and three of them atpressures of 1.5, 1.8, and 2.1 GPa did not detonate within the80 mm thick targets. The fourth shot with a shock pressure ofapproximately 2.3 GPa resulted in a transition to detonationat 69 mm. The ignition and growth model parameters forEDC37 in Table III are based on the other HMX basedPBX’s and higher pressure embedded particle velocity gaugeexperiments.28 Figures 11�top� and 11�bottom� contain theexperimental and calculated pressure histories, respectively,for shot HG07–03, which had a shock pressure of 1.5 GPa.The manganin gauges show some pressure increases, al-though, at late times, there is most likely due to 2D gaugestretching. The gauges also show more pressure oscillationsthan those seen in other HMX PBX’s, which may be due tothe softness of EDC37. The calculations in Fig. 11�bottom�show no pressure growth. Figures 12�top� and 12�bottom�show the experimental and calculated pressure histories, re-spectively, for shot HG07–04, which has an initial pressureof 1.8 GPa. The gauge records and calculations both showreaction growth to pressures of about 10 GPa. Figures

13�top� and 13�bottom� contain the experimental and calcu-lated pressure histories, respectively, for shot HG07–05,which had a shock pressure of 2.1 GPa. In both the experi-ment and calculations, the pressures are rapidly growing, butthe transition to detonation does not occur within the 80 mmlong charge. Figures 14�top� and 14�bottom� show the ex-perimental and calculated pressure histories, respectively, forshot HG08–02, which has an initial pressure of 2.3 GPa. Theexperimental records show a transition to detonation at 69mm, while the calculations show a transition at 71 mm. Thisagreement between the calculated and experimental pressurehistories for EDC37 was obtained by using: a larger criticalcompression required for hot spot ignition of EDC37 relativeto the other HMX PBX’s; a smaller value of Figmax=0.002corresponding to the lower void fraction in EDC37;28 and aslower growth coefficient G1 in Eq. �2� than the other PBX’s,representing fewer growing hot spots and larger distancesbetween them.

The lower shock pressure experiments on the six HMXbased PBX’s clearly show much longer run distances to deto-nation as the critical pressure for detonation transition is ap-proached than predicted by extrapolation of high pressurePop Plots. Figure 15 shows all of the run distances to deto-nation caused by shock pressures below 2.3 GPa measured

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FIG. 11. �Color online� Pressure histories in EDC37 shocked to 1.5 GPa�top gauges and bottom simulations�.

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FIG. 12. �Color online� Pressure histories in EDC37 shocked to 1.8: GPa�top gauges and bottom simulations�.

094906-9 Vandersall et al. J. Appl. Phys. 107, 094906 �2010�

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for the six HMX PBX’s in this and previous studies,3,9–11

along with the higher pressure Pop Plot linear fits from Fig.1. The effects of varying the initial void volume, HMX per-centage, and binder type are definitely more pronounced thanthey are at higher shock pressures.

V. CONCLUSIONS

Measured run distances to detonation at relatively lowinput shock pressures for six HMX based PBX’s are consid-erably longer than those predicted by extrapolations of linearPop Plot fits to higher shock pressure data. These lowershock pressures SDT’s are primarily due to smaller amountsof HMX ignited in hot spots created during weaker shockcompression and slower growth rates of reaction from ex-panding reactive hot spots into surrounding explosive par-ticles that are shock heated to lower temperatures by weakershocks. Embedded manganin pressure gauges quantitativelymeasured the growth of hot spot reactions in several lowpressure experiments. The resulting pressure histories areused to extend existing ignition and growth models to lowshock pressure results. The main change in the model param-eters is the use of nonzero values of the critical compressioncompressions required for ignition. These critical compres-

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FIG. 13. �Color online� Pressure histories in EDC37 shocked to 2.1 GPa�top gauges and bottom simulations�.

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FIG. 14. �Color online� Pressure histories in EDC37 shocked to 2.3 GPa�top gauges and bottom simulations�.

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094906-10 Vandersall et al. J. Appl. Phys. 107, 094906 �2010�

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sions range from approximately 0.07 to 0.09, correspondingto shock pressures of about 0.9 to 1.4 GPa. These minimumshock pressures for SDT are close to those estimated by pre-vious qualitative low pressure shock initiation studies onHMX based PBX’s using larger diameter charges and weakdecaying underwater shocks.3,9–11,23,29 Even lower initialshock pressure experiments would be very useful but diffi-cult and expensive to do.

The effects of HMX percentage, porosity, and bindercompressibility on low shock pressure initiation are morepronounced than in higher shock pressure initiation of HMXPBX’s. For EDC37, which has an order of magnitude lessporosity than the other five HMX based PBX’s, the lowshock pressure sensitivity is greatly reduced. At the sameinitial porosity, the higher the HMX percentage, the greateris the shock sensitivity. At the same porosity and HMX per-centage, the HMX based PBX’s PBX 9501 and EDC37 withmore compressible binder/plastizer components are lessshock sensitive than LX-10 and LX-07, respectively, with thestiffer Viton binder. Exothermic components, such as nitro-cellulose and BDNPA/F, in the binder increase shock sensi-tivity. These trade-offs in PBX formulation, void volume,binder strength, and binder sensitivity plus the desired deto-nation performance must be taken into account when formu-lating large explosive charges.

The low shock pressure ignition and growth reactiveflow model parameters for these six HMX based PBX’s canbe used to predict shock initiation or failure in large explo-sive charges that cannot be tested experimentally due to cost,explosive weight limits, or other limitations. There are manyscenarios in which large, relatively slow moving fragmentscan impact bare or covered, confined or unconfined HMX-based PBX charges producing low pressure shock waves thatcan cause SDT after many centimeters of propagation. Igni-tion and growth parameters normalized to 1D experimentscan be used in 2D scenarios, because 2D rarefaction waveeffects that decrease the shock pressure, duration time, andreaction rates are calculable. Ignition and growth parametershave been used to determine 2D SDT thresholds for lowvelocity fragment impact.14 If possible, hazard and vulner-ability scenarios that are predicted to be close to predictedshock initiation thresholds should be experimentally verified.However, the application of well-normalized reactive flowmodels can greatly reduce the number of experiments re-quired to evaluate low shock pressure threats to large explo-sive charges.

ACKNOWLEDGMENTS

The 101and 155 mm gun crews are thanked for theirexcellent work building and firing these experiments. Thiswork was performed under the auspices of the United StatesDepartment of Energy by the Lawrence Livermore NationalLaboratory under Contract No. DE-AC52-07NA27344.

1J. B. Ramsey and A. Popolato, Fourth Symposium �International� on Deto-nation, Office of Naval Research ACR-126, White Oak, MD, 1965, p. 233.

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3L. Green, E. Nidick, E. Lee, and C. Tarver, Symposium on High Dynamic

Pressures, French Atomic Energy Commission, Paris, France, 1978, p.115.

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7C. M. Tarver, J. O. Hallquist, and L. M. Erickson, Eighth Symposium�International� on Detonation, Naval Surface Weapons Center NSWCMP86–194, Albuquerque, NM, 1985 �unpublished�, p. 951.

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11K. S. Vandersall, C. M. Tarver, F. Garcia, P. A. Urtiew, and S. K.Chidester, Shock Compression of Condensed Matter, Waikoloa, Hawaii,2007 � AIP Conf. Proc. 955, 1010 �2007��.

12G. de Oliveira and A. K. Kapila, W. Schwendeman, J. B. Bdzil, W. D.Henshaw, and C. M. Tarver, Thirteenth International Detonation Sympo-sium, Office of Naval Research ONR 351–07–2, Norfolk, VA, 2006�, p.13.

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posium, Office of Naval Research ONR-333–05–2, San Diego, CA, 2002,p. 641.

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094906-11 Vandersall et al. J. Appl. Phys. 107, 094906 �2010�

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