vincent m. boyle, robert b. frey and alfred l. bines- parallel/oblique impact on thin explosive...

8/3/2019 Vincent M. Boyle, Robert B. Frey and Alfred L. Bines- Parallel/Oblique Impact on Thin Explosive Samples

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Parallel/Oblique Impact_ on Thin Explosive Samples

Vincent M. Boyle

Robert B3 . Freyc12 Alfred L.Bines

ARL-TR-584 October 1994

I, C,

94-33233

APPROVED FOR PUBLUC RELEASE. WIMUTRIDON ISUNU WnlD.

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T!AMIPI ()I' CON1WIN

L~l• IST l !TALM ............................................... vi

I, INTKODsU('rK)N ......... .................. .............. . I

2. EXPURIMUNTAL APIROACH ,...*.. .................. *...........

I. RESU .TS .............. .... ......................... ... ...... . 10

4. DISC USSIO N ................................ .................. I I

5. CONCLUSIONS .......... ................... . .... .... 17

6. REFEREN(ES, ............... ... ...... ...................... 19

APPENDIX A: DETAILS OF GA S GUN AN D PROJECTILE ............... 21

APPENDIX B; EVALUATION OF TH E STRAIN RATE ................... 25

APPENDIX C: PRESSURE CALCULATION ............................ 31

DISTRIBUTION LIST ............................................ 35

CiI x ~ (

D',. i

A -• •, ""'-• ", • : ,

iii • 1 '



INM~moNALLY LEFr BLANK.

iv



I 181 01I I I

OlURlu

! IPlraileihbllque Imacl (if S flyer piale on a Mini ex.R)osive wuaplc '1lie nonnal

and I010ig1iitll e.omiWinhW of tOW flyer plate be~oro tmpoc, %m Illstruuaed ....... 2

2. '1f1e tcop~npv&bcIlo Wguns Altiwt mounted on ita moblic cart, i'is affanngcmentwh s usedwo wlel SIhun Int•uhe blImt chamber ........................ 4

I. An overall view of the experimental arragilement .......................... . 5

4. '" temperature Incree In an explosivc target plotted as a function of viscosity an dyield strenth of the explosive. 7he sample thickness is 0.06 cm, and ftI transverse

component of the flyer plate velocity Is7,650 cm/s ....................... 13

5. The temperature increase in an explosive target plotted as a function of the transverse

component of the flyer plate velocity an d the explosive viscosity, The samplethickness is 0.06 cm, and Its yield strength, is assumed to be 0.35 kbar ......... 15..1

6. The temperature incwase in an explosive target plotted as a function of the explosive

thickness and viscosity. The transverse component of the flyer plate velocity is7,650 cm/s, and the explosive yield strength is assumed to be 0.35 kbar ........ 16

A-1. Detail of the wraparounid breech showing the gas seal provided by the O-rings on the

projectile body ................................................ 24

B-1. The transverse velocity (the. component parallel to the interfaces) in the flyer plate,explosive target, and the anvil after impact ............................ 29

C-I. The elastic impact of the flyer plate on the anvil is shown in the pressure-particlevelocity plane ................................................. 34

'L.



INTYiEfloNALLY LiFPr BLANK.



LIST OF TABLES

I. Material Propertis of Fyer Plates wW Anvils ...... ....... ......... ...... .7

2. Experimental Data for Tests ....................................... 7

3. Pressurt, Strain Rate of Explosive, and Impact Simultaneity .................. 9

vii



IKNTnTONALLY LEFT BLANK.

viii



1, 1INKODU(IION

'I-e *hcarng of explosive materials mnder pressure Is an effective way to producc !w•nlictd hiallot

0y vI.coplastic work concentratcd in a sm.ll region of the dforming explosive, 11his Iuocalld heatnlki

can cause the explosive to react releasing additional heat to accelerate the maction, In an cnrlicr paper,

we d.scribed tie results obtained when a s"all cylinder of explosive was prtexuhzcd within heavy tccl

confinement and then allowed to slide against the steel confinement (Boyle, Frey, aund BWake 19.89); in a

similar arrangement, we investigated explosive on explosive shear by punching aplug from ihc pressuritzed

explosive cylinder, In those experimens, we demonstrated that the ignition threshold depcndi on both

pressure and shear velocity. Those uxperimcnts had a relatively long duration of about I ms, a maximum

pressure of about 1.0 GPa, and a maximum shearing velocity of about 80 m/s; the pressure and shear

velocity varied during the course of the experiment. The risc time to peak pressu.- was several hundred

ps. Also the shear localization was not well defined so the local strain rate could not be determined. In

the experiments reported here, we have attempted to study ,ie ignition of several explosives as they were

impacted under conditionr that would cause the explosive sample to shear in a known manner under the

high pressure of the impact. A maximum pressure of 1.3 GPa was reached with a strain rate of about

50,000 per second over an explosive layer 0.6 mm thick.

2. EXPERIMENTAL APPROACH

In order to obtain well-defined conditions for pressure-shear impact on explosive, we adapted atechnique described by Abou-Sayed, Clifton, and Hernann (1976), Kim and Clifton (1980), and Li and

Clifton (1981). In this technique, one-dimensional combined pressure shear waves were generated in a

flat target plate by the impact of a flat, high acoustic impedance flyer plate; both the flyer plate and the

target plate were inclined at an angle to the velocity vector of the flyer plate in order to produce a shear

component of particle velocity in the impacted targeL The impact occurred simultaneously at all points

of the flyer-target interface. In addition, a high acoustic impedance anvil supported the target plate. The

flyer plate and anvil have higher acoustic impedance than the target plate in order to prevent unloading

of the target by reflection of waves at the target interfaces. This arrangement is illustrated in Figure 1 for

the flyer plate impacting a target at 30° obliquity. A gas gun was used to accelerate the flyer plate.

Details of the gas gun and projectile are shown in Appendix A. From Figure 1, it can be seen that the

flyer plate velocity has a component normal to the target plate, Vn, and a component parallel to the target

plate, Vt. These components can be calculated as follows:

1



III

1--*1LU



Vn =V(cos a), 1

Vt= V (sin a), (2)

witerv v it the flycr plate velocity and a is he angle of obliquity of the flyer plate with respect to thel111##1111111 (111weigtt W.WCcn the flyer plate velocity and the normal to the target plate). Upon impact,

INw ernnial romixincnt of Oic flyer plate velocity generates astress wave in the target; this stres wave is

cv i lltelt hoiwnr tho hI;h impercd.nc boundaries several times until the target re&.zhes a state of uniform

titet, doWrneilnd by INw flyer plate velocity and the material properties of the flyer plate, target plate, and

divtyl IIkqwiaq, the pardalll component or flyer plate velocity, by its traction with the target surface,

gwdt-olwil wave lit the tarcle which, after several reverberations, induces a state of uniform shear.

'I t Hil.i9, #so# a~s t-iNed with i10A shear Isdetermined by the parallel component of flyer plate velocity;

Okw mehateul pijoeniprils of the flyor plate, target plate, and anvil; and the thickness of the target plate.

A higI sjjwil hoentleeg v~amee i Cordin Model 192. was operated at half speed, 2,500 rps, in its

fti~~f~m ino itNIt ordler to mccorti the Impact of the flyer plate on the explosive target; this impact

~ ~nwli a5(1nu~,lilk Irnsprent Knvil. . - camera records 80 frames, and the interframe

It*i 014t tj&ýW 14 Wpeinohowatly 1.7 jin. However, we were usually l-i.':ed to about 15 jis of

A4*etiotl', Oh efta lw~micume thw Irye surface of the anvil became opaque shortly after the elastic wave

siom~lvhi 'Jwuto#ploulyo HIMsiouuvAs (argon bombs) were used to illuminate the explosive surface

twi.,,f vievtwt! t.y 91 tatinteg '11w argon bombil consisted of a volume of argon gas inside a conical

,utallhifd WunU619*1 %ftill lot lRnIU'111114, reflectifix Inner surface; the container was sealed at the larger en d

It9 iti~so voliejiiw of Worol Wraj), A 340Sg Comp Bi exploxive charge was taped Inside the smaller

#WaW1011 110wilbl4loIve (110100 Is01we,.wd, ia trono shock wave Isproduced In he argon causing it

tn Iuyitte &Al Ofli etigl of be1s'Y I11111 as th, Phock wave progresses through the argon. Fo r the

ha, lov alp'." W11W~b VWd its iliww trAts, wo had Bifficieelt light to record for approximately 60 ps.

I*s -etwhtl uut it:l 'I'ito ctrnipreued pas gun was mounted on amobile cart

Wat%"vitl a. "tasitnet eom OWk lwilkjh i~ewcii eecroviry, H'Iurc 2, Ii practice, we ended up welding

4'.1.kl lt 1t1i t~l II& beieelaifii a 1el1itr ilifid iteucturr wid improve the simultaneity of Impact. An

ov't Wool 110#6; 01111 lowfiI u~jqeyA III tvqijw' wan used to hold tOw anvil rund explosive target and align

uset.haW110 ** V I Owi 11#11)04 ills A og f-lONO ratcicr Itank wit uxcd ito catch the projectile and some

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In the experiments reported here, UOsrujn raw In the cpItuImc tiar•' con tv caliulsicd a•

(VtO - V FA) A (0)

where V anM Vi ate the components of the pr !kwicelocity vid tld anvil vclm.iy pairidicl t1)de

inmerface after Impict iad x is the orilinal tikiisnis of the exploslyc sample T7i1cal'ulaolw Is0 shown

In Appendlx B.

In order to calculate the sirms in the explosive sample, wc assumed thm thr flyer plate and ite anvil

remained clhuic during the impact and. after several revertiratiou. the exp',sivc attained a At'UAS lcvCl

equal to what would be achieved by the impact of Ue flyr plate directly on hie anvil, WIth ithse

asumptions and the requirement dial the paricle velocity and pnesure rmmhln equal at the flyc plate.anvil

interface, we were able to calculate the stress in the exploslve. For a stee flyer plute and a glnss anvil,

the pressure lit the explosive can be calculated (see Appendix C):

PR M prUr) (pu.)Vn / (plUr + paUl) (4)

where

P5 is the pressure In Use explosive sample, dynes'crm2

(101l dynes/cm2a I Maa 10 kbars)

pf is density of the flyer plate, S/cm3

pS is density of the anvil, &/cm3

Vn is the normal component of flyer plate velocity, cm/s

Ur Ix he elastic wave velocity in dte flyer plate., cm/s

U&s the elastic wave velocity In the anvil, cm/u,

Table I lists the relevant material properties for the flyer plates and anvils described in this report.

Trable 2 lists the experimental data for the tests which are being reported here.

Using the data from Table 2, we were able to calculate the strain rate (Appendix B) an d pressure

(Appendix C) in the explosive sample, These values, as well as t1e impact simuancity Wlong the

projcctile/targct interlace, are listed in T'able 3. We should comment that the calculated strain iate dcpcids

on the value assumed for viscosity, The effect of changing the viscosity is shownt in Appendix B.

!



Table I. MMrtal Pwpern of Flyer PMates and Anvils

MiuluiW Denud• I cluaticave Velocity

(S/cm ) (cm/u)

Wwal, 1020 7.19 5.96 X 10

aluminum, 2024.T4 2,711 6.30 x 1C0$

ilJM 2.23 5,64 x 10 s

Plexlgla 1.1 2.70 x I0

IU ;lass. awuti whil. 5ouooiii"is, wu ad aAn invil; 11was Kutully a silnma. m nsisng of tour glas wid thrse pludo

plie, The ovwai ahkjl *a 2 i2uod t indiwdui gaiss pile warr 03 In t• ThiM plasi plies were pulyvinyl butyMyI,

0.01! IAick

Table 2, Expertmcntial Data for Te•tl

Flycr Plate

Shot No. Flyer Plait Velocity Explosive Simple Anvil

(n/,)I flat aluminum 147 1.rmm TNT Plexiglia

2 flat, alumiLnm 148 1.mm TN T PlexglSaS

3 flat, aluminum 174 1.rmm TN T PlcxigtIu

4 angled, aluminum -- I-mm TN T Pixiglas

5 angled, aluminum 148 1 mm DS Plexiglas

6 flat, steel 132 1-mm DS glass

7 flat, steel 125 1-mm DS glassangled, steel 125 g-mmS g ass

9 angled, steel 145 1-mm DS glass

10 flat, steel - I-mm DS glass

II angled, steel 153 1-mm DS glass

12 flat, steel 143 1-mm CS glass

NOTE: DS *Ddulasat is an explosive mude by the DuPont Company; it contains 6396 by weight PMT, 8% dumiroci.

ulose, and 29% aoetyltributykitrate. Its density wu about 1,48 g/cm.,

TNT - out TNT or density 1,60 &0/cm.

7



Table 2. Experimental Dama for Tests (continued)

Flyer Plate

Shot No. Flyer Kimt Velocity Explosive Sample Anvil

13 Mkat, Steel 144 1-mm DS glass

14 angled, steel 148 I-mm DS glass

is angled, gtel 14 3 l-mm DS glass

16 angled, stel -_ - I-mm DS glass

17 angled, steel - 1-minDS glass

1s angled stel 12 0 I-mm DS glass

19 fliat stee 127 1-minDS glans

20 fALatee 79 1-mm DS glass

21 flat, mel 89 1-mm DS _ glass

22 flat, steel 57 I-mm DS gasn

23 flat, steel 58 1-mw DS glass

24 flat, steel 103 1-mm DS glasS

25&~4 mode 69 0.5-mm Pent glass

26 " nged. ste! 153 0.6-mim DS glIMS

27 flat, sftel 64 0.6-mmn DS glasS

28 angled, steel 42 0.6-mm DS glass

29 angled, stel 39 0.6-mm DS glass

30 angled, stel 59 0.6-mm DS glass

Nall: DS -Deulw.( is m.ixplosive mic by do~DuPont Cotpnpui; it contains 63% by weight POWh, 8% itrocellulose

wan 9% acetyltributylidwsta. Its density was about 1.48 g/cm .

Padt. m ast Patuol~te (50% PE174/50% TNT) of density 1.67 5/cm'.

8



Table 3. Pressure, Strain Rate of Explosive, and Impact Simultaneity

Shot No. Pressure Strain Rate t Impact Simultaneity(GPa) (l/s) (ps)

1 0.39 0

2 0.40 0

3 0.47 0 12

4

5 0.35 35,000

6 1.31 0

7 1.24 0 15

8 1.07 31,000 _

9 1.25 36,000

10 - -

11 1.31 38,000 20

12 1.42 0

13 1.43 0 2

14 1.27 37,000 10

15 1.23 36,000 10

18 1.03 29,000 3

19 1.26 0 0

20 0.78 0

21 0.88 0 0

22 0.56 0

23 0.57 0 2

a This is for the strain rate calculated assuming a viscx'ity of 50,000 poise and a yield strength of 0.35 x 10P dyneslcm 2

for Detasheat.

9



Table 3. Pressure, Strain Rate of Explosive, and Impact Simultaneity (continued)

Shot No. Pressure Strain Rate' Impact Simultaneity

-(Gra) (/s) (Ps)

24 1.02 0 5

25 0.68 0 4

26 1.31 49,000 10

27 0.63 0 8

2 8 b 0.36 10,000 7

2 9 b 0.33 9,600 _

30 0.51 17,000

SThis is the smain rate ¢alculated a•svxmg a viscosity of 50,000 poise and a yield strength of 0.35 x 109 dynes/cra2

forDetasheet.

b For these shot. an IMdetector monitored asnall region of explosive at the edge of the inpact zone.

The desh lines in Table 2 indicate an absence of data due to failure of the arrival time circuitry used

to meawnr projectile velocity.

In Table 3, the dash lines indicate a lack of data for various reasons; failure of the velocity pin

circuitry, malfunctioning of the framing camera shutter or mistirning of the explosive light source used

to illuminate the explosive target.

3. RESULTS

As can be seen from the data in Table 3, many of our tests did not have good impact s?-ultaL.ity of

the flyer plate on the surface of the explosive target. Also, in many of the tests, we were not able to

observe the impact, due to experimental pioblems. For the impacts that we were able to observe, we did

no t see any obvious sign of explosive reaction such as light emission or the expulsion of reaction products

from the region of impact. In all cases, the explosive in the impacted region became darker in about

4-6 ps; after this, the darkness did no t appear to increase during the available time of observation, nbaut

15 ps. However the darkness did appear to increase with the impact pressure. Fo r some of the shots

(No. 14 vs. No. 19 and No. 18 vs. No. 24), we were able to compare shear and nonshear tests at pressures

which were nearly equal; the presence or absence of shear did not appear to have an effect on explosive

darkening.

10



For shot No. 25, the explosive target consisted of a 0.5-mm cast sheet of Pentolite explosive in which

the grain boundaries were very prominent. Upon impact at 0.68 GPa the grain boundaries were noticeably

darker than the rest of the explosive for several microseconds and then the entire impacted region became

uniformly dark.

Since we were not able to tell if the explosive darkening meant that reaction was occurring, we tried

to detect IR radiation by using a photovoltaic silicon photodiode that was sensitive to wavelengths from

the visible to the near IR (300 nm to 1,100 nm). Tw o longpass IR filters were used in tandem in front

of the photodiode in order to attenuate the visible light from the argon bombs by a factor of 10 billion;

the cut on wavelength was 785 nm. The filters and photodetector were shielded from stray light by

enclosing them within a phenolic tube which was pointed toward the impacted surface of the explosive

sample as shown in Figure 3. The photodetector viewed a small region on the edge of the impact area.

For shot No. 29, the argon bombs did not function and the photodiode did not detect any signal during

6 ms of observation. For shot No. 30, the argon bombs functioned and the photodiode detected a signal

but it corresponded to the turn on of light from the argon bombs before the flyer plate even impacted the

explosive target.

Several shots were. fired for which the rear surface (the surface facing the camera) of the explosive

was marked beforehand with fine lines using a permanent marker. The lines appeared to remain

undistorted during the time of observation, even though the impacted area of the explosive became dark.

This was true even at an impact pressure of 1.02 0Pa, sho! No. 24.

Examination of the debris recovered after the shot did not reveal any ,,idence of explosive reaction

"aýtving occurred. The flyer plate did not have any carbon residue or other indications of explosive

reactioi-.. The explosive within the impact zone was broken into small irregular fragments. The anvil was

generally shatte-4 into many small pieces. The projectile and most of the debris from the impact zone

enided up embedded in the rags within the catcher tank.

4. DISCUSSION

We were surprised that we were unable to detect any obvious sign of explosive reaction for Detasheet

since, in the paper previously mentioned (Boyle, Frey, and Blake 1989), we were able to cause Detasheet

to react under what appeared to be a milder stimulus, 0.2-GPa pressure and a shear velocity of 60 m/s.

11



The duration of those tests was about 500 ps, whereas the tests reported here woald be terminated when

release waves originating at the boundary of the flyer plate reached the axis, a time of about 15 ps. The

longer duration of those earlier tests may have allowed the explosive to reach temperatures required for

reaction. Also, in those earlier tests a cylinder of explosive was slid along a boundary of either steel or

explosive causing the explosive temperature to increase due to viscoplastic heating. The shear may havebecome more localized in those earlier tests due to greater thermal softening of the explosive at the peak

temperature region within the shear band. The concentration of shear motion in a narrow region would

increase the strain rate and the peak temperature.

In our current tests, if the strain rate is uniform across the target plate, the temperature increase in the

target plate can be expressed by the formula,

AT = (V [&l/dt]2 + Y [de/dt] ) t/pc, (5)

where

AT = temperatem increase (OC)

v = viscosity (poise)

d/dtt = strain rate (1/s)

t = time duration (s)

p = density (g/cm')

c = specific heat (ergs/g-0C)

Y = yield stress in shear (dynes/cm 2 ).

For the experiments reported here, the strain rate ol the explosive isa function of its thickness, viscosity,

and yield strength, as well as the component of the flyer plate velocity parallel to the explosive surface,

and the material properties of the flyer plate and anvil; this relationship is indicated in equations B4-1BI0

in Appendix B. Using this relationship, we computed the strain rates corresponding to a range of

explosive viscosities and yield strengths for shot No. 26 . We then used equation 5 to calculate the

corresponding temperature increase, assuming a time duration of 15 ps , an explosive density of

1.48 g/cm3, and a ,pecific heat of 1.25 x 107 ergs/g-*C. Figure 4 shows the temperature increase in the

explosive target as a function of its viscosity an d yield strength. It can be seen that, the calculated

temperature increase, over a wide range of viscosity and yield strength, is no greater than 11l60 C. We

would not expect to see evidence of explosive reaction in our experiment at such a low temperature.

12



200

180

160

Y. S. = 1.0 KBARS

140 Y. S. = 0.35 KBAR

1Y. S. = 0.0 KBARz

120Li

"Li 100 -

80

Li 60

4 0

20;

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40

00 -

-20000 0 20000 40000 60000 80000 100000 120000

VISCOSITY (POISE)

Figure 4. The temveaTwe increase in an gxplosive taImct Dioawe as a function of viscosityand Yield strength of the explosive. The sample thickness is 0.06 on. and thetransverse comoonent of the flyer plate velocity is 7.650 co/s.

_13



We can use Frank-Kamentskii's equation for the adiabatic explosion time (AMCP 706-180, 1972) to

calculate the temperature required to produce a thermal explosion in 15 ps. We used the following data

for PETN (Rogers 1975) for the required input parameters:

Specific heat 1.25 x W ergs/g-OC

Gas constant 8.31 x W ergs/g-mol-0 C

Early heat of reaction 1.26 x 1010 ergs/g

Frequency factor 6.3 x 1019/s

Activation energy 1.97 x 1012 ergs/g-mol

The calculated temperature for a thermal explosion time of 15 ps is 818 K, which corresponds to a

temperature. increase of 5250 C. This temperature increase is much higher than those calculated for the

parallel/oblique experiments. Taking 1160 C as the maximum calculated temperature increase for the

parallel/oblique tests, the time required for an adiabatic explosion would be 2.4 x 108 s.

In addition, the strain rate (and temperature increase) may have been limited by the explosive sample

sliding at one or both of the interfaces with the flyer plate and anvil. Th e surface of the glass anvil had

a commercial polish finish of 10 fringes per inch, and the steel target plate had a machined surface finish

with roughness of 16 pin rms. Any future tests should address the possibility of slippage at these

interfaces. A suggested approach w ould be to increase the traction by surface roughening. Also, the anvil

consisted of glass plies laminated together by polyvinyl butyryl plies. In order to avoid the possibility of

shear localization occurring in the polyvinyl butyryl, a single piece of thick glass could be used.

Th e steel flyer plate used in our tests had a yield strength of about 0.5 GPa, but we did not see any

evidence of yielding on the face of the recovered flyer plate. Such yielding, if present, would decrease

the impact pressure by a small amount. In order to avoid this possibility, a hardened steel flyer plate

should be used for future tests.

Th e most direct means of increasing the temperature of the explosive sample is to increase its strain

rate by increasing the velocity of the impacting projectile, decreasing the sample thickness, or doing both,

It is instructive to calculate the temperature increase that would be expected using the data of shot No. 26and varying the impacting velocity and the explosive sample thickness over a range of explosive

viscosities. The yield strength of the explosive is assumed to be 0.35 x 109 dynes/CM 2. Figures 5 and 6

show the calculated temperature increases for several sample thicknesses and impacting velocities.

14



600 i

VEL. = 153 M/SEC

VEL. = 114.75 M/SEC

S-------EL . = 76.5 M/SEC

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O0 - Io...... .. ..................

VISCOSITY (POISE)I

Figure 5. The temperature increase in an explosive target plotted as a function of the transve M.component of the flyer Dlate velocity and the explosive viscosity. Ile s nple thicknessis 0.06 cm , an d its yield strenytIh is assumed to be 0.35 kbar.

15



600

- THICK. =.015 CMTHICK. =.030 CM

*---THICK. =.060 CM500

zu400

Lii

C-)

cr-

300

10L..............

0

-2000 0 00 400600 0001000100

VICO IT (P IE

Figur 6.7etmeaueinfa in a 3)sv ae og wabo nofteM

thickness~~~ ~~~~~~~~~ an vicst,-ensepnn ftgfl~ agylIl I7f~a

and he xplgiy&Yieltengt isnswgW t DI .35hb-

100 I16



%I f* fin Wit Wr insti eta#41v' fatSio w~Itf wwtkmv0n of comnbined! pressurv/shcur. Using

Wa telblm4r4~n t et"I'd 1n#W hSit %ajoelv@ tied .tiwngt and viscosity, we caflculated A

tsr'nw,~ ~ ~ ~ ~ ~~11iuap1h *l;uJevoie ;iucrvane In wempruiure Is mucht* wea to ItSi VtSW ftijdtwt lot 0* 11"WtqJ1fou j4Wf1iiitIl.Ai~ijt~zmately 15 PA . and aslso

Emalf sa" L'J*wru~tv 0*newtne4 I-tpin

Ii*An IW t'i I4'4't*1 e01v t Mli

oLheflWhatt. 0 r MMu.,

It. WlS~tbfl'i



INTENTONALLY LEFr BLANK.

18



6. REFERENCES

Abou-Sayed, A. S., R. J. Clifton, and L. Hermann. "The Oblique-plate Impact Experiment." Experimental

Mechanics. pp. 127-132, April 1976.

Boyle, V., R. Frey, and 0. Blake. "Combined Pressure Shear Ignition of Explosives." Ninth Symposium

(International) on Detonation, OCNR 113291-7, vol. 1, Portland, OR , 28 Aug-I Sep 1989.

Halleck, P. M., and J. Wackerle. "Dynamic Elastic-Plastic Properties of Single Crystal Pentaerythritol

Tewanitrate." Journal of Apolied Physics. vol. 47, no. 3. 1976.

Kim, K. S., and R. J. Clifton. "Pressure-Shear Impact of 6061-T6 Aluminum." Journal of Applied

Mechanics, vol. 47, pp. 11-16, March 1980.

Li, C. H., and R. J. Clifton. "Dynamic Stress-Strain Curves at Plastic Shear Strain Rates of 1W sec1.Q"

Shock Waves in Condensed Matter, AIP Conference Proceedings No. 78, edited by W. J. Nellis et al.

Brown University, Providence, RI, 1981.

Pinto, J., S. Nicolaides, and D. A. Wiegand. "Dynamic and Quasi Static Mechanical Properties ofComp B and TNT." ARAED-TR-85004, U.S. Army Armament Research and Development Center,

Dover, NJ, November 1985. (AD-E401419)

Rogers, R. N. "Thermochemistry of Explosives." Thermochimica Acta, vol. 2, 1975.

U.S. Army Materiel Command. Engineering Design Handbook - Principles of Explosive Behavior.

AMCP 706-180, 1972.

19



INTE"TONALLY LEFT BLANK.

20



APPENDIX A:

DETAILS OF GAS GUN AND PROJECTILE

21



INMERMINALLY LEFT BLANK.

22



The gas gun used for these tests was machined from 4140 steel and tempered to 35 on the Rockwell

C scale. Th e barrel had the following basic dimensions:

length = 70 in

outside diameter = 7.750 inbore diameter = 5.940 in.

A 1/4-in x 1/4-in x 70-in keyway was machined along the bore of the barrel in order to prevent

rotation of the keyed projectile since rotation of projectiles having angled flyer plates could cause

nonsimultaneous impact to occur. The gun had a wraparound breech of approximately 1,044-in 3 volume;

the breech section was 24 in long and had an outside diameter of 14 in . Th e overall length of the

assembled gun was 91 in. The total weight of the gun was about 1,500 lb .

The projectile consisted of a polyethylene body to which the flyer plate was bolted. It had the

following characteristics:

body length = 12 in

body diameter = 5.925 in

flyer plate thickness = 2 in

flyer plate diameter = 5.75 in

total projectile weight = 15.4 lb to 22.9 lb .

Th e projectile had two O-rings (Parker 2-432) which served to seal against the high pressure nitrogen gas

contained in the wraparound breech as shown in Figure A-I. When a small pressure is introduced through

valve A, the projectile is displaced from its initial position and uncovers four large portholes connecting

the wraparound breech to the gun bore. The high pressure breech gas which dumps behind the projectile

causes it to accelerate rapidly. The O-rings were fitted against the gun bore with a 10% squeeze. For the

tests reported here, the lowest velocity was obtained with a breech pressure of 125 psi and the highest with

a breech pressure of 1,300 psi. We were not able to pressurize the breech beyond 1,300 psi due to

leaks-probably past the O-rings.

23



U))

0U

w IC

ccw

100

IcI900

24



APPENDIX B:

EVALUATION OF THE STRAIN RATE

25



Notation:

S1 = shear stress in projectile, dynes/cm 2

S2 = shear stress in target (explosive), dynes/cm2

s3 = shear stress in anvil, dynes/cm2

V = viscosity of explosive, poise

Y = yield strength of explosive, dynes/cm 2

01 = shear modulus of projectile, dynes/cm2

G3 = shear modulus of anvil, dynes/cm 2

C1 = elastic shear wave speed in projectile, cm/s

C3 = elastic shear wave speed in anvil, cm/s

Vt= initial component projectile velocity parallel to the interface, cm/s

V, = component of projectile velocity parallel to the interface after impact, cm/s

V3 = component of anvil velocity parallel to the interface after impact, cm/s

el = shear strain in the projectile, cm/cm

S= shear strain in the anvil, cm/cmr

T = thickness of the target plate, cm,

S2= shear strain rate in the target, s-

where

0, (steel) = 7.68 x 1011 dynes/cm2

G, (alum.) = 2.78 x 1011 dynes/CM2

G3 (glass) = 2.65 x 1011 dynes/cm 2

C1 (steel) = 3.12 x l&s cm/s

C1 (alum.) = 3.16 x 105 cm/s

C3 (glass) = 3.45 x IC cm/s.

To evaluate the strain rate in the target, we make the following assumptions:

(1) After a few reverberations of the wave back and forth acioss the target layer, theqhear in the

target plate is homogeneous; i.e., there is no strain localization. This assumption gives the lowest possible

strain rate. We will analyze this situation and will not consider the transient that exists before the

homogeneous state is attained.

27



(2) The stress and particle velocity anm continuous at the Interfaces.

(3) The projectile and the anvil respond elastically, so that

S1 = G1c1 (B1)

and

S3 =G (B2)

(4) The explosive obeys the following very simple constitutive relation:

S2 = Y + v i2 = Y +v (VI - V3)/ . (B3)

We recognize that real materials will have more complex behavior.

(5) We ignore heating of the layer and variations in the viscosity or the yield strength with

temperature.

With these assumptions, the transverse velocity (the component parallel to the interfaces) varies as

shown schematically in Figure B-1. A shock moves back into the projectile and reduces its transverse

velocity from V, to V1. A shock moves to the right in the anvil and increases its transverse velocity from

0 to V3 . Within the target layer, the velocity varies linearly from VI to V3. The shear strain in the anvil

is

V3

E3 3 (B4)

The shear strain in the projectile is

e Vt-VI (B5)

C1

28



Projectile Target Anvil

I I

V* I I

I Im

*> I IC I

V1 Elastic Wave

Distance (normal to target plate)

Figure B-I. Th e transverse velocity (the component parallel to the interfaces) in the flyer plate,explosive tarmet. and the anvil after impact.

Th e shear strain rate in the target is

'2 - (V - V3) / r. (B6)

At the interfaces, the stress is continuous, so the following equations hold:

GI(Vt- V 1)/C 1-v (VI-V 3)/T + Y, (B7)

and

G3 (V 3) / C3 = v (V 1- V3 ) r + Y. (B8)

29



Solving fo r V, an d V3 gives the following result:

V1U . VIY ("9)V+T4 -ZLCII2717

and

The viscosity Is unknown for thc cxplomlvcu t11t.1 wc uKcd (Wid 11W EoIIIiIuli jIVJvlstkn uvd IW4t to

almost certainly too simple to represent a real material), Novenlicleho, wt can mhake pot~ih pueIWwi Maht

the viscosity and calculate fth exultinX Ntrain rate, 1llolck an d Wackrile1 dien',ulilud 0 d(1Wa4021 b*PETN of 50,000 poise Ina shock wave experiment, '11fs could he used u. mn upjvrl bouh4 '11W )tI#J

strengt under pressure Isalso no t wcll known. lItIn clear dial the yield muvnph utndo, pr~o.vi It evfte

than ft~strength ftht Ismeasurd Inuncouiinwed uniaxia s)cxpefl'iuumz IltivNl- _& 4 -Witaa

determined a yield strength for compoul~tion 11 of stwut 0~1 libir. I).iig Ibewc vtolvet oif vi~wttooi en

yield strengith for Delruhe,:, we cani calculate 11alroimeii, fjoii 9qualltkI1 114 lIft), iniJ @etmnjei.4vit.

equation 5, for expdrvircn( 26, Uc cwiiputcd Ivinijcraue huinaitfI that *-ouhl. 1* &_ JIn I III#

950 C, Figure 4 hOKws the ,omputcd tcmnixruture IIn!96We fl I lplg oill tVl3~oO1~e114 jift)?14 It.ia

It can be seen that if yield xtrvn8tlt is heldcoi(nstant, Owey 14 s aviKIottIw vAlue W11101 11ýv IM, iglwif

lpossible tcmpcraututi,

11t1liuII P.M., owl 3. ..aufi )nwoii SYWia&.im, 4`1601 .Jb4 ~jasj.*aA i4d*%.d le.5 #age ho

2 Plnltu, J,. 5, NwdeIsIs, met' 1) A Wisoob-I ' aptoitpo '..sa 11104. Me-kil-4.. V.Vo.-Up WO V" a Lo Puti

ARAMI iM 354MWM,f15 Amyn~moaite. Me&suiot mistom4j.a~ pov 11l.y. fb~iD la0.., Iftlm~its I t..111.



Uttami I

hUIThut tgivwp

II



INtMNI(1NALLY L~PT IItLANK,

12



We can calculate the impact pressure produced when a flyer plate strikes an anvil. We assume that

the impact remains elastic. After impact, the pressure in the flyer plate and the anvil are equal at the

interface and the interface has a common particle velocity. Th e following notation a-,)lies:

Vn = normal component of flyer plate velocity, cm/s

u= interface particle velocity, cm/s

Pa= density of anvil, g/cm3

pf density of flyer plate, g/cm 3

Ua = elastic longitudinal wave speed in anvil, cm/s

Uf = elastic longitudinal wave speed in flyer plate, cm/s

P. = pressure in anvil, dynes/Cnr2

Pf = pressure in flyer plate, dynes/cm 2

Pi = interface pressure, dynes/cm2

Px = pressure in explosive, dynes/cm 2 .

After impact, an elastic wave of velocity U. propagates into the anvil and an elastic wave of velocity Uf

propagates into the flyer plate. The anvil undergoes a change in particle velocity (uj - 0), and the flyer

plate particle velocity undergoes a change (Vn - uj). By the laws of conservation of mass and momentum

across the elastic wave, we can write:

Pa = p1U. (uV 0) and Pf = pfUf (Vn- u). (Cl)

At the interface P. = Pf. Therefore we can write:

PsUatti = PfUf (Vn - ui).

This can be solved for ut:

U, = P(UVn / (PaU& + PtUf). (C2)

Then, since we assumed that P. = P1 = Pf = P. we can write:

Px - Pa - pAUapfUfVn / (p8 U8 + pfUf)- (C3)

The Impact of the flyer plate on the anvil is illustrated in Figure C-1, which shows the elastic equation

of state In the pressure-particle velocity plane.

33



P

FLYER PLATE, P= PFUF U

- -- ANVIL, P= P.U.U

U1 VN U

Figure C-I. hle elastic impact of the flyer plate on the anvil is shown in the pressure-panriclevelocity plane.

34



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£g2ie Organization Copis Organization

2 Administrator 1 CommanderDefense Technical Info Center U.S. Army Missile CommandATIN: DTIC-DDA ATIMN: AMSMI-RD-CS-R (DOC)Cameron Station Redstone Arsenal, AL 35898-5010Alexandria, VA 22304-6145 1 Co m n e

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Commander U.S. Army Tank-Automotive CommandU.S. Army Materiel Command ATTN: AMSTA-JSK (Armor Eng. Br.)ATMI: AMCAM Warren, MI 48397-50005001 Eisenhower Ave.Alexandria, VA 22333-0001 1 Director

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Records Management I Commandant2800 Powder Oill Rd. U.S. Army Infantry SchoolAdelphi, MD 20783.1145 ATTN: ATSH-WCB-O

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ATTN: AMSRL-OP-SD-TL, Aberdeen Proving GroundTechnical Library2800 Powder Mill Rd. 2 Dir, USAMSAAAdelphi, MD 20783-1145 ATTN: AMXSY-D

AMXSY-MP, H. CohenDirector

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No. of

HQDA (SARD-TRIMs. K. Kominos)

WASH DC 20310-0103

HQDA (SARD-TRADr. R. Chait)WASH DC 20310-0103

Adminisiator

Lckheed Missiles and Space Co.Org. 89-10, Bldg. 157ATIN: Y. ChooSunnyvale, CA 94088-3504

Aberleen Proving Ground

8 Dir, USARLATI'N: AMSRL-WT-T, T. Wright

AMSRL-WT-TB,

F. regoryW. Hillstrom

0. LymanJ. WatsonJ. Starkenberg

AMSRL.WT-TD, J. WalterAMSRL-WT-PE, D. Kooker

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