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TODISTRIBUTION STATEMENT : A

Approved for public release; Distribution is unlimited.

LIMITATION CODE : 1

FROM NO Prior DoD Distr Scty Cntrl St'mt Assgn'd

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U.S. Naval Ordnance Lab Ltr; Aug 29, 1974

THIS PAGE IS UNCLASSIFIED

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RNAYOR REPORT 6750

THE DETONATION PROPERTIES OF DATB

(2l, 3-DIAMINO#, 2, 4, 6-TRINITROBENZENE (U)

QUALUMIfI ~QUESTERS MILT OB TAIN FROM DD.C

12 OCTOBER 1960

'Us. S. NAVAL ORDNANCE LABORATORY,k <. -WHITE OAK, MARYLAND

p~wN~lA~W T 3 ym-1 NEVI4ZLS1~>A~ 12 YuAD

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Setins73 nd7, hetanmisonorrveato

"ofThishiatanyiancnertoins unfuthotiond persong the

prohibited by law."

NAV RORD Ra ."

THE DETONATION PROPERTIES OF DATB(1, 3-DIAMINO, 2, 4, 6-TRINITROBENZENE) (U)

By:

N. L. Coleburn, B. E. Drimmer, T. P. Liddiard, Jr.

Approved by: Y. .' A. D. SOLEMChief, Explosion Dynamics Division

ABSTRACT: The detonation parameters of the relatively newheat-resistant, shock-insensitive explosive DATB have beenmeasured. At the normal, pressed-loaded density (1.80 g/cm3 ),the detonation velocity is 7,600 m/sec, and the Chapman-Jouguetpressure is 251 kb The detonation velocity (m/sec) varieswith density (g/cam) according to D 2 2480 + 2,52& . Theenergy of detonation is 800 cal/g and 3.1 is the value of theisentropic exponent for product gas expansion. The failurediameter was found to be 0.53 cm. When mechanical shocks areslowly applied, as in the impact-hammer machine, DATB is lesssensitive than TNT, but when the shock is more rapidly applied,.as in the NOL wedge test, the explosive behaves more likeComposition B. Addition of 5% plastic binder desensitizes DATBto rapidly-applied shocks, causing it to fail to build up todetonation in the wedge test even though the pressure withinthe explosive may be as high as 82 kb.

"II

EXPLOSIONS RESEARCH DEPARTMENT •U. 3. NAVAL ORDNANCE LABORATORY

WHITE OAK, SILVER SPRING, MARYLAND

17 7

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-V1

NAvOP.D Report 6T50 12 October 1960

This study of the detonation properties of DATEB is a phase in •

a broad program directed by the Explosions Research Department i ii

toward evaluation of new explosives of superior thermal at&-bilitt The work was authorized by Task No. RUUO 3E012/2121/PW1-0o_-, Exposive Propertie,. formerl Task No. 301-Ji•664/43006/08, Explosives Applied Research, and is directly •related to Explosives Research and Development Key Problem 7.3a"Initiation and Detonation", as given in NAVORD Report 3906.

The data herein reported are considered to be the best avail-able at this date# but may not necessarily reflect the finalopinion of this Laboratory.

W. D. COLEMANCaptain, USN •Commander

By d-&rec~ton ;

Lf

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'7 7 7-7'7777,771777ý7 7 -7'"7 177 7 7ý- 1-777

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NAVODRport 750

CONTENTS?ago

Introduction . . . . I

Detonation Velocity of DAT andDATi-Plastic-Bon4dedCompositions . . . *.....

The Chapman-Jouguet Pressure of DATE . . . . . . .... 2The Energy ofDetonation . . . . . .. . .. . . ..Sensitivity to Rapidly-Applied Shocks * * * * * * * 9P late-Push Teats . . . . . . & a a . . . . * 0 * * 9 0 20C onclus ions . . . . . . . # . * . . . a a a . . . . * 20Appendix . . . . . . . . . . . . . . . a . a 0 . . * . 23References ................ ...... 28

TABLES

Table 1, Detonation Velocity of DATE . . . 3Table II. Detonation Velocity of DATE/EZPON 1001 (95/5) .. 3Table IlljFroperties of DATB Compared to TNT . . . . . . . 10Table IV. Widge-Test Parameters for Pure DATE IT ** 1Table V. Weodge-Test Parameters for Plastic-Bonded

Compositions of D D...q.... 18

ILLUSTRATIONS

Figure 1. Detonation Velocity of DATE as a Function ofCharge Densityy.......... * 1

Figure 2. Arrangement for Measuring the Velocity of theShock Wa ve Trane'uitted into Water at theEnd of an Explosive Charge ... . . . 5

Figure 3. Shaciowgraph of Shock Wave Produced by the Deto-nation of DATE in Water. . . . ........ 6

Figure 4. Side View of NOL Wedge-Test Arrangement . 11Figure 5. Smear Camera Record of the Detonation of DATE

in the NOL Wedge Test Using 1.27-c0 thick

Figure 6. Instantaneous Shock Velocities In DATE for1.27-cm thick Brass Compared with Comp B .. 13

Figure 7. Instantaneous Shock Velocities In DATE for2.514-cm, thick Brass Compared with Comp B . . . 141

Figure 8. Instantaneous Shock Velocities in DATE for3.81-cm thick Brass Compared to Comp B . . 15

Figure 9. Instantaneous Shock Velocities in DATE/BRL27411(95/5), for 1.27-cm thick Brass . 19

_1 1W.1-177

CONFIDENTIALNAVORD Report 6750

THE DETONATION PROPERTIES OF DATS(1, 3-DIAINi, 2, 4, 6TeIN ITEa) has s(U)pi

Introduction

The speeds of modern aircraft, and especially those ofunsanned missiles, have produced many difficult problems

Cn ordnance designe The ability of the explosive componenthto tolerate severe thermal cycles experienced during themission of such ordnance tm an important paraceter in thesedesegns. A promisinuc new, shoak-pi nsensitcal s plostve,1. 3-diamino# 2s 4, 6-trinitrobenzene (DATB)'" has superior

theNal stability under these conditions. DATB tE a yellowsolid having a crstal density of 1.83T a•nm A-lt melts at286OC. and decomposes at a negligible rate at 2040C. while at

260dC its decomposition rate in only about 1% (by weight) perhour, It does not initiate at the maximum height (320 d m) ofthe NOL impact hafrper machine, showing that DATB ts much lesssensitive to such slowly applied mechanical shocks than even

TNT (200 i m). The detonation parameters of DATB and itssensitivity to rapidly applied shocks are reported herein.

Detonation Velocity of DATB and DATB-Plastio-S.... ... . bonded Comaposititons

Detonation velocities as a function of charge densitywere measured for pure DATB and DATB/I;'ON 1001* (95/5) with arotating-mirror smear camera. The velocities obtained from

the photographic measurements (when the charge density was amaximum) checked to within 10 r/sec when camera and electronicpin probes were employed simultaneously. Simple pelletingtechniques produced 5.0-cm diameter pellets for these tests,with densities ranging from 1.4 to 1.9 g/cm3 . To obtaincharges with densities below 1.4 g/cm , the powder (averageparticle size 4 to 5 microns) was loaded in 15-gram incrementsinto 5.1-cm internal diameter, 0.15-cm thick aluminum or glasstubes and pressed (in the aluminum tubes only) at pressures upto 8,000-10,000 psi. When the charges were confined by alumi-num, the detonation wave was observed through a series of small,evenly-spaced holes drilled through the metal casing. Eachtest charge was initiated by an explosive train consisting ofa U. S. Engineer's Special Detonator, a 5.1-cm diameter plane-wave generator (Baratol-Composition B), and a 5.1-cm diameter,5.1-cm long tatryl pellet.

* Epoxy Resin; Shell Epon 1001i Sa Chemical Company,Emeryville, Calitforni .

CONFIDENTIAL


The detonation velocities are listed in Table I andplotted ii Figure 1. At dlensities normally obtainable,1.80 g/cm (98.0% of crystal density), the detonation veloc-ity of pure DATB is 7,600 m/sec. The detonation velocityvaries linearly with the charge density accordinj to theequation

D . 2J,480 + 2,852 p (± 25) m/sec. (1)

The diameter effect of pure DATB (density of 1.81 g/dc3 )was studied by detonating P pyramidal charge of three cylin-drical pellets, 2.54-, 1.27- and O.0,4-cm diameter, stacked inorder of decreasing diameter. On top of the 0.64-cm diameterpellet was placed a 1.25-cm long truncated conical sectiontapering from 0.64-cm diameter at its base to 0.32-cm diameterat the top. Detonation of the pyramidal charge resulted in anormal velocity with detonation failure occurring at a chargediameter of 0.53 cm, L.e. within the tapered region.

Results obtained with DATB/2PON 1001 (95/5), Table IIand Figure 1, show that at a given charge density this plastic-bonded explosive detonates about 150 m/sec slower than doespure DATB. A tapered section was not used in the DATB/iPON1001 (95/5) pyramidal charge. Therefore the failure diameterof this composition was not ascertained. However, its abilityto propagate stable detonation up to the end of a 2.54-cm longcylindrical pellet, 0.64-cm in diameter, demonstrated that itsfailure diameter is near to that of pure DATB.

The Chayman-Jouguet Pressure of DATE

Using a method reported by W. C. Holton3, we have measuredthe Chapman-Jouguet pressure of DATB. This method involvesthe measurement of the velocity of the shock wave transmittedinto water from the end of a plane-wave-initiated charge; then,employing an equation of state of water to obtain the pressure atthe water-explosive interface, the Chapman-Jouguet pressure isinferred. In the experimental arrangement, Figure 2, a charge15.2-cm long by 5.1-cm diameter, initiated by a Baratol-Composition B plane-wave generator, was immersed in distilledwater to a depth of 6.4 cm. The bottom end of the charge waspositioned parallel to, and 1.3 cm above, the optical axis ofthe smear camera. The shock wave within the water, "back-lighted" by collimated light from an exploding wire, produceda time-resolved shadowgraph, Figure 3. From measurements ofthis photographic trace the detonation pressure of the explosiveis calculated using the water-shock wave data of Rice andWalsh", Their data are represented by the following equation:

2CONFIDENTIAL

I ý 02

" 1 I

CONFIDENTIAL *1NAVORD Report 6750

TABLE I

DETONATION VELOCITY OF DATB

Charge Diameter Length Confinement Density DetonationNo. (am) (cm) (g/cm3 ) Ve1ocit.(M/see)

1* Conical** 1.250 None 1.816 *** Io.64 2.540 1.816 7.6201.27 2.644 1.815 7,6202.54 7.861 1.809 7,620

2 5.7 13.4o Glass 0.901 505015.53 1. 3Z5 I470

5 4.44 15.26 Aluminum 1.3 6)4706 4,.4 15.27 " " 1.285 6,130

S4.414 15.27 1 "120 58805.08 15.80 None 1.72 7.570

9 5.08 20.47 1.793 7,580

* Charge 1 was the pyramid charge in four sections.4* Diameter uniformly decreased from 0.64 to 0.32 over 1.25-cm length.* Failure diameter - 0.53 cm.

TABLE II

DETONATION VELOCITY OF DATB/EPON 1001 (95/5)

Charge Diameter Length Density DetonationNo. (cm) (cm) (/cM Velocity(m/sec)

0* 0.638 2.545 1.776 7.3500.953 2.4 1.765 f5501.267 2% 1.756 -51.267 2.629 1.761 7.2802.537 2.573 1.752 7,4002.537 2.614 1.708 T.180

2 5.053 15.00 1.733 7603 2.527 15.67 1.448 L80

* Charge 1 was a pyramid charge in six sections,gi

3CONFIDENTIAL

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CONFIDENTIALNAVORD REPORT 6750

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CONFIDENTIALNAVORD Report 6T50

where U is the shock velocity and ua is the particle velocityof the water in m/meo. Thus a measurement or U at the

4explosive-water interface produces a corresponding value of u'.The pressure, P, In the water at this interface to then ob-tained from the familiar hydrodynamic equation

Pm Uu/%r (3)

where V0 is the specifito volume of mt.terial io the unshockedstate,

A first estimate of P1, the Chapiuan-Jouguet pressure ofthe explosive, is then obtained from the approximate relation5

+l.% ((OD)E h

2(POU)H2O+(4

where 'PH20 is the pressure of the waioar at the explosive-waterinterface and 4'tD)F is the product of the initial densityand detonation velocity of the explosive.

An improved measure of the Chapman-Jouguet pressure ismade using the following analysis which is fully described inAppendix A, From the definition of the isentropic exponent,

IL (5

the Chapuan-Jouguet condition,,J

) (6)

.(tie term Po has been neglected here since Pj1 >>? PO and thejhydrodynamic relation

aone obtain. a

'Vt (k 1). (8)

7,7


The quantities Vo and D are known; however, k is not known Vexactly and therefore Pl cannot be computed with precision.A second relationship for P1 that also involves k and otherknown quantities, derived from application of the Riemannpostulate for an isentropic expansion of the detonationproducts from F, to the initial pressure transmitted into thewater, is

.ut u k (ILwoAW1)/DP,1 N o ""D

Equations (8) and (9) are solved for Pl and k by iterationusing first, the approximate value of P1 given by (4).

The DATS charges were fired each at an initial density of1.790 t 0.001 g/cmr, yielding the following mean values:

D -7585 r/seaU 80 (t 28) m/sec

U g 624 rn/sec

SPH20 - 157 kb.

From these data the isentropic exponent, k, is computed to be3.10 and the Chapman-Jouguet pressure is 251 kb. This pressureis 33% greater than that of TNT(189 kb) 6 and only 13% less thanthat of 65/35 RDX/TNT(290 kb).

The Energy of Detonation

The energy of detonation can be estimated from the assump-tion that on detonation the oxygen in the explosive forms H20(g),CO(g), and C02(g) in that order. For DATh this reaction is

C6HsNsO6 (10)

2.5 H2o(g) + 3.5 CO(g) + 2.5 "2(g) + 2.5 C(0 )

8The measured heat of formation of DATB is. 29.23 kcal/mole.using available heat-of-formation data for the decompositionproducts, the heat of detonation is calculated to be 875 cal/g.

"A -8

CONFIDENTIAL

'--77v'."" -77- 7 •"-7• •


The heat of detonation also can be calculated from theexperimentally determined values of the detonation velocity,the detonation pressure, 18d isentropic exponent. Thus, asshown by Jacobs and Price ', the energy of detonation is

Q. D2

2(k 2 i

From this relation it is calculated that Q is 800 cal/g, dif-fering by 8.7% from the energy calculated from thermal data.For convenience the detonation parameters are assembled inTable III where they are compared to corresponding values forTNT.

Sensitivity to Rapidly-Applied Shocks

Evaluation studies were performed on pure DATB, DATh/%PON1001,495/5)p and DAT/WRL 2741* (95/5) using the NOL wedgetest 1 . In this test, Figure 4, the explosive, formed intoa 25-degree wedge with a maximum thickness of 1.27 cm,is sub-jected to a plane shook wave delivered by an explosively-drivenbrass plate. Plates of 1.27-, 2.34-, and 3.81-cm thicknessesare used in order to vary the shock pressure transmitted intothe explosive. The shock wave within the metal is formed bythe detonation of a 1.27-cm thick Composition B slab, 12.7 cmsquare, initiated by a 10.8-cm diameter plane-wave generator.The shook velocity within the unreacted explosive, as a functionof explosive thickness, and the build-up to the steady deto-nation velocity, are inferred from an analysis of the smear-camera photograph of the shock arrival at the free surface ofthe wedge (Figure 5, central region). Reflected-light techniqueis used to record the shock arrival and to measure the shock-wave parameters of the brass plate.

The results obtained for the build-up-to-detonation testson DATS using the three brass thicknesses are shown in Fig-ures 6-8, where they are compared to those obtained forComposition B. The outstanding feature of these curves is thefact that the instantaneous shock velocity within the explosiverises 10-20% above the normal detonation velocity beforesettling down to that value. An example of this velocity"overshoot" can be seen in the smear-camera photograph forShot 1 (Figur*e 5). In this respect DATB behaves like otherIressed exjlosives. No oast explosive has exhibited such a2

overshoot , while pressed explosives characteristically do 2 .

* Phenolie resin (Bakelite Corporation, New York City, New York).

9CONFIDENTIAL


TABLE III

PROPERTIES OF DATB COMPARED TO TNT

Property DATB TNT

Experimental Density (g/om) 1.800 1.637

Detonation Velocity (rn/see) 7,600 6.9140

d D (/e)2P52 -V25d O* (s/cm )

Failure Diameter (cm) 0.53 1.3(14)

Detonation Pressure (NO) 251 189(6)

Detonation Energy (cal/g) 800 636

50% Impact Initiation Height (cm) >320 200

Isentropic Exponent, k 3.1 3.17

Plate-Push Value, (rt/sec) 1130 9930

10

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INDENT BRASS WEDGE

LUCITE

~ ALUMINIZED

EXTERNAL BRASS WEDGE

FIG. 4 SIDE VIEW OF NOL WEDGE-TEST ARRANGEMENTI

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CONFIDENTI ALNAVORD REPORT 6750

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CONFIDENTIAL

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Another feature shown in Figures 4-6 Is that the build-up-to- ,•detonation of DATB under this rapid shook-loading is not

thsgnificantly son dfferent (oer than the iv"ershot")ofrom

that of cast Composition Thus the sensitivity of DATBto mechanical shocks is strongly dependent on the rate ofshock-loading; when applied slowly as in the impact-hammermachine, DATB is very insensitive tthe 50% initiation pointexceeds 320 cm, whileoror TNT it is 200 cm and for Compo-sition B it is 60 cm)41. When the shock is applied rapidly,as in the wedge test, the sensitivity of DATB is comparable tothat of cast Composition B (TNT fails completely to build-upto normal detonation velocity in the wedge testl).

The NOL wedge test was designed to permit for each shota determination of one point on the Hugoniot curve for theunreacted explosive. Analysis of the upper region of Figure 3yields the free-surface velocity and the shock velocity ofthe brass at its free surface, and thus, by equation (3),the pressure in the brass at the brass, explosive-wedge inter-face (assuming that the particle velocity of the brass is one jhalf its free-surface velocity). An equation analogous toequation (4) then produces the pressure within the unreactedexplosive at the same interface. If its compression, V/V(where Vo and V are respectively, the specific volume of ?heexplosive before and after being shocked), is calculated forthe same state, then the point on the Hugoniot curve will havebeen determined. The compression is calculated from the con-tinuity equation for the explosive

V U - u (12)V0 U

using equation (3) to obtain tie particle velocity, u, of theunreacted explosive. In this manner three points on the jHugoniot curve for the unreacted explosive have been determinedfor pressures of approximately 75, 85, and 100 kb. The exactvalues, as well as the other parameters derived from the wedgetest are tabulated In Table IV and Table V.

A few explanatory remarks on the data in Table IV areappropriate. The final, or steady value of the instantaneousvelocity, D, should be identical with the normal detonationvelocity. The observed deviations from this value are merelythe result of the difficulties of making a precision velocitymeasurement by this method. The smallest tilt, or non-planarityof the wave as It emerges from the explosive wedge would alterthe value of D. Thus the measurement of D, while mot goodenough for a determination of a precise detonation velocity,serves as a useful measure of the normal, plane-wave propagationassumption of the wedge test.

16 "CONFIDENTIAL

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The fact that the shock within the explosive wedge doesnot move always at its normal detonation velocity means thatthe shock (or detonation) wave Is "delayed"' In "reaching aI ~given depth in the explosive. The "delay time" is defined asthe difference in time of arrival of the wave within the explo-sive between its actual time of arrival and the time It wouldhave arrived had It moved always at iLts steady detonationvelocity:

Delay time a (time-of-arrival) - (time-of-arrival). (3"observed" "steady shook" (3

(of course, these times of arrival are calculated for somepoint beyond that where the steady "velocity has been attained).The fact that velocity "overshoots" occur, produces the pos-sibility that negative "delays" could be obtained# i.e., theshock could arrive even before it would have,, had it travelled atits steady velocity at all times. Thus Shot 1 (with a 1.27-cmthick brass p~late) exhibits a delay time of only 0.07 mlcrosecas contrasted with 0.20-0.30 microsec for the other five shots,

Wedge tests also were run for plastic-bonded DAYO/RL 2741(95/5) and DATBhIPOt4 1001 (95/5) With DATB/BRL 27T41 (95/5)9build-up to detonation (Figure 9$ was obtained with a 'wedgeshocked by 1.27-cm thick brass. But when 2.54-cm thick brasswas used, the plastic-bonded explosive failed to build-up todetonation, even though the pressure developed within theexplosive was 82 kb. Build-up to detonation was obtained withDA'1B PON 1001 (95/5) In the 2.54-cm thick brass plate wedgetest,

Plate-Push Tests

The NOL plate-push test measures the ability of a 5.iI-cmdiameter by 6.3-cm long cylinder of explosive to project a5.4-cm diameter steel disc (200 g) from a small expendable1.25-cm thick steel mortar. The velocity imparted to the disc,in ft/eec, is the "plate-push" value of the explosive. PureDAM gives a value of 3130 ft/sec and is thus intermediate toTNT (2,930) and Composition B (3V20).

Conclusions

1, At normal densities (1.78-1.80 g/cm3) the detonationvelocity of DAMN is about 7,600 in/3ec, or more exactly, itsvelocity is represented by

D 2J480. +9 852f (rn/eec).

20CONFIDENTIAL

NAVORD Report 6750

* ~At a density equal to the crystal density of TNT (1.651. g/cm3),charge: of DATB have a detonation velocity of T200 rn/c, or200 rn/sec greater than that of TNT of the same'density.

2. The sensitivity of DATE to rap Idly applied, large-amplitude shocks (as in the wedge test) to comparable to thatof cast Composition B. This contrasts strongly to Its behavior

4 under slowly -applied, low-amplitude shocks (as in the drop-hamer impact test), where it iosmuch loes sensitive than evenTNT.

3. The shock sensitivity of DATE is markedly reduced evenfor rapidly applied, large-amplitude shocks by the addition ofonly 5% of certain plastic binders.

4.* In the wedge test (and presuably for mechanical impactsof a similar nature) the velocity of the shock wave passingthrough DATB starts at Jý5O0-5000 rn/sec and accelerates to avalue exceeding the normal detonation velocity before finallysettling back to normal detonation velocity. In this regard,DAIS behaves similarly to other Vressed explosives, which alsoexhibit this velocity "overshoot

5. The small failure diameter of DATE, 0.53 cm, appearssurpriatm.,.a4tv-ftaglance. Its very large impact-bammer 50%

* height would lead one to expect a much larger failure diametemay something comparable to the 1.3-c. diameter found for 9ThTHowever,, our wedge tests indicate that for high pressure,rapidly applied shocks (such as it might also receive from Itsown detonation) the sensitivity of DATE is comparable to that ofComposition B. 2The small *failure diameter lends further support

to onluio 2aboe no. the failure diameter of Composition B

6. using water as a calibrated manometer# the measuredChapsan-Jouguet pressure of DATE was found to be 251 kcb, thusexceeding that of TNT by about 33% (considering each explosiveat Its normally obtainabVl- aharge density).

7. The isentropic exponent, k, of the product gases atthe detonation front is calculated to be 3.10.

8. With this value of kj, the energ of'detonation of DATE

less than the Yalue of 875 cal/g obtained from its measuredheat of formation.

9. The plate-push value for DATE is 3130 ft/sec, about

6% higher than that of TNT. 2

21p4

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Acknowledgment

The authors are indebted to William A. Brown, James 3.Counthan and David E. Crump for their careful assistance Incarrying out the experiments.

bil

22

UNCLASSIFI EDNAVORD Report 6750

APPENDIX A (U)

Determination of the Chapman-Jouguet Pressureand the Isentropio Exponent of DetonationProducts from Transmitted Shocks A

The Chapman-Jouguet pressure of an explosive can be deter-mined from measurements made on the shook wave its detonationtransmits Into material placed at the end of the charge. Thismethod requires an accurate calibration of the equation ofstate of this inert .ateriai: water is one of the most conven-ient of such materials, its equation of state having been thesubject of intensive study In recent years. We have chosenthe data of Walsh and Rice for this purpose.

In this method a cylindrical explosive charge is immersedin water, its upper end protruding above the surface. Initiated Aby a plane-wave generator, the detonation wave strikes the waterat normal incidence, and the resulting shook in the water isrecorded (by back-lighting) using a rotating-mirror smear camera.A careful analysis of the resulting photograph yields the shockvelocity within the water, at the original water-explosiveinterface, at the instant the shock crosses this Interface.The published equation of state then produces from this number,

- the pressure and particle velocity of the water at the samepoint. From these values the Chapman-Jouguet pressure of theexplosive and the isentropic exponent of its detonation productscan be calculated by means of the equations about to be derived,

It is assumed that the usual conservation equations applyacross the interface, and that all processes are performedadiabatically. After the detonation wave arrives at the explosive-inert interface a shock is transmitted into the inert materialand a shock or a rarefaction (depending on shock impedance con-ditions) Is reflected back into the explosive products. Betweenthese two shock fronts (one of which might ae a rarefaction, asjust stated) it is assumed that the pressures and the particlevelocities tn both media are equal. In the following analysisa square-step shock across the interface is assumed. .y consid-ering the conditions at the Interface at the time when the shockhas barely penetrated into the inert material, i.e. at theextrapolated point where the thickness of the inert materialvanishes, the errors introduced by this assumption are consideredto be negligible.

23

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UNCLASSIFIE)I

NAVORD Report 6750

JIsentropic expansion ofexplosionl products fromjitoP2

Ii

0 U;

Pressure-velocity diagram.

If ui it the particle velocity of the product gases at theC-J plane of a one-dimensional detonation wave, then the par-ticle velocity u2 of the product gases can be obtained fromthe Riemann relation Je1

i:!,% - - - .(14)

Thus a solution of this integral will give a value for u2, whichby the continuity assumption is also the particle velocity inthe shocked water. Conversely, then, if u2 can be determined byindependent means, ul can be calculated, permitting a determin-ation of the C-J pressure. An expression will now be derivedfor the right hand side of equation (14) which by further manip-ulatton will provide an equatic for the C-J pressure of theexplosive to terms of the particle velocity and pressure of thewater at the interface. This equation contains another unknown,k, the isentropic exponent for the product gases. Solution ofchis equation is then obtained by the simultaneous use of anotherequation containing k, the C-J pressure, and the (known, orindependently measured) detonation velocity.

. A24

7 7a77

"777I

S' I UNCLASSIFIED

NAVORD Report 6750

Sa The velocity of sound, a, to the product gpses in definedby the relation

= c" \ av (s(S

and thus at the detonation front

Apan for the product pgses,

so that

,61 (17)

and sinoo

Ti - W

one obtains

-, •(18)D : ,C, C,.

From the isentropic equation of state for the. product gases

pvK : (19)

one obtains from its definition,

C',: " 4 (20)

orC : A (21)

where A and areI constants.

25

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UNCLASSIFIEDNAVORD Report 6750

Since r

Piz D u . , (22) A

substitution of equation (18) for D, and combining the resultwith equation (20) one gets

(23)

From the Chapman-Jouguet assumption,1)=u., (24) •we therefore have

and u /•'(25)and '

,kt/(L4,). (26)

Equation (21) permits a substitution of Cl into the right-hand member of equation (14), making possible its integration,with the result

%17I - (27)

where, it is recalled, subscript 2 refers to the state withinthe product gases behind the C-J plane. Simple substitutionsfor u1 and the sound velocities now produce the desired relationfor tie C-J pressure. From equation (21)

2.. a- (28)

and the isentropic law

y i (29)

tt follows that

P 3. A .~ i ~p )(30)

and thus

16 I

~> >1 :26

UNCLASSIFIED fNAVORD Report 6T50

Substituting for ul and C1 their values in equations (25) and(26), one gets finally for the Chapuan-Jouguet pressure,

and uH2 0 have been substituted for P2 and u2 by workingour assumption of continuity of pressure and particle velocityacross the interface).

A second equation in P, and k is needed to solve equation(32). This is obtained by substituting the value of u1 fromequation (25) into equation (22), yielding the relation

P1 (33)

No simple, explicit solution is obtained for Pl and k, and thesolution i.n therefore obtained by iteration. This process isspeeded by use of equation (4),

''P +fL)~ 4ft)

to produce a close, first estimate for P1 which then is appliedto equation (33), etc.

I I I I III I

2T

777 W"7I: 7w-7-77"T 777=ý,7 -7 '7I

UNCLA.SSIFIXNAvORD Report 6750

References

1. Shipp, K. 0. and Hill, M. E., "Heat Resistant Explosives II;1, 3-Diamino -2, 14 6-Trinitrobenzene, DATB", NAVORD Report6016 (31 March 19581 '(Confidential).

2. Holden, J. R., Rosen, A. H,, Rosen, J, M., "Heat ResistantExplosives VI- Properties of 1 3-Diamino-2, 4, 6-Trinitro-benzene, DATB , NAVORD Report t299 (17 March 1959).(Conf ident ial1)

3. Holton, W. C., "The Detonation Pressures in Explosives asMeasured by Transmitted Shocks In Water", NAVORD Report 3968(1 December 1954) (Confidential).

4. Rice, M. H. and Walsh, J. M., "Equation of State of Waterto 250 Kilobars", J. Chem. Phys. 26, 8214 (1957).

5. Mallory, H. D., "The Measurement of Detonation Pressures in

Explosives", NAVORD Report 1883 (5 March 1953) (Confidential).6. Deal, W. E., "The Measurement of C-J Pressure for Explo-sives", J. Chem. Phys. 9Z, 796 (1957).

7. Deal, W. E,, "Measurement of the Reflected Shock Hugoniotand Isentrope for Explosion Reaction Products". Phys, Fluids,Is 523 (1958).

8. McEwien, William S., NOTS; Informal communication.

9.Jacobs, S. Jo; "The Energy of Detonation", NAVORD Report?366 (1 September 1956).

10. Price, D., "Inter-Relationship of Explosive Characteris-tics III", HAVORD Report 4510 (26 April 1957). (Confidential)

11. Majowicz* J. M. and Jacobs, S. J.p ?Initiation to Detonationof High Explosives by Shocks", NAVORD Report 5710 (1 March 1958)(Confidential).

12. Jacobs, S. J., "Recent Advances in Condensed Media Detonstionn",ARS Journal 30b, 151 (1960).

13. Helier, H., NOL; Informal communication.

14. Cybuiski, W. B., Payman, W., and Woodhead, D. W., "Explosive

Waves and Shock Waves VII. The Velocity of Detonation In Cast

15. Malin, N. E., Campbell, A, W. and Mautz, C. W., "ParticleSize Effects on Explosives at Finite and Infinite Diameters"J. Appi. Phys. 28, 63 (1957).

28UNCLASSMEID

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