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47

Transcript of fas.org · we assume Bernoulli’s theorem applies (that is, that the jet pressure is large...

Page 1: fas.org · we assume Bernoulli’s theorem applies (that is, that the jet pressure is large compared to the target or jet material strengthsand that pressure is the same in the jet
Page 2: fas.org · we assume Bernoulli’s theorem applies (that is, that the jet pressure is large compared to the target or jet material strengthsand that pressure is the same in the jet

.An AfTlrmative Actiorr&ual’ Opporhsnity Employer

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PreparedbyLouiseCriss,GroupT-14

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DISCLAIMER

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This reposl was prepared as an accouart of work sponsored by an agency of the United States tivemment.Neither @e Lh@d States tivernment nor qty agency thereof, nor any of their empIoyeea, makes any

warranty, express or fmpfied, or assumes any legal Iiability”or responsibility for the accuracy, completeness,os Usefutnw of Py information, apparat ua, product, or process disclosed, or represents that its use would

not infringe privately owned rights. References hereti to any SIMIIC commercial product, proccaa, orservice by trade name, trademark, manufactures, or otherwise, does not necca&ifY constit ute or imply itacndomcment, rcco~endat ion, or favoring by the United States Cove.r%wmt or any agency thereof. The

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Page 3: fas.org · we assume Bernoulli’s theorem applies (that is, that the jet pressure is large compared to the target or jet material strengthsand that pressure is the same in the jet

Jet Penetration ofInerts and Explosives

Charles L. MaderGeorge H. Pimbley

Allen L. Bowman

J ““-r

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LosNamim Los Alamos National

UC-45Issued:

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November

.aboratorvLos Alamos,New Mexico 87545

ABOUT THIS REPORT
This official electronic version was created by scanning the best available paper or microfiche copy of the original report at a 300 dpi resolution. Original color illustrations appear as black and white images. For additional information or comments, contact: Library Without Walls Project Los Alamos National Laboratory Research Library Los Alamos, NM 87544 Phone: (505)667-4448 E-mail: [email protected]
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by

JET PENETRATION OF INERTS AND EXPLOSIVES

Charles L. Mader, George H. Pimbley, and Allen L. Bowman

ABSTRACT

The two-dimensional Eulerian hydrodynamic code 2DE,with the shock initiation of heterogeneous explosive burnmodel called Forest Fire, is used to model numerically theinteraction of jets of steel or tantalum with steel,water, and explosive targets.

The calculated jet velocity relative to the penetra-tion velocity into inert targets is a function of thesquare root of the target density divided by the jetdensity.

The calculated penetration velocities into explo-sives, initiated by a low-velocity jet, are significantlyless than for inerts of the same density. The detonationproducts near the jet tip have a higher pressure than thatof nonreactive explosives, and thus slow the jet penetra-tion. At high jet velocities, the calculated penetrationvelocities are similar for reactive and inert targets.

I. INTRODUCTION

The initiation of propagating detonations in PBX 9404 and PBX 9502 by

copper, aluminum, and water jets was modeled numerically in Ref. 1, using the

two-dimensionalEulerian hydrodynamic code 2DE.2

Studies of shock initiation by jets near the critical conditions contrast

with other shock initiation studies in that, for the latter, if detonation

occurred, it was because the initiating shock wave was of sufficient strength

and duration to build up to detonation. The propagating detonation was assured

by the large geometry. In near-critical jet initiation, however, a prompt deto-

nation of the explosive results, which builds to a propagating detonation only

if the shock wave produced by the jet is of sufficient magnitude and duration.

1

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The penetration velocities of projectiles interacting with explosives

initiated by the projectile are reported3 to be much lower than the penetration

velocities of inerts of the same density. This study examined projectile pene-

tration dynamics in inert

charge with a metal cone

jets can be approximated

appropriate dimensions.

The classic paper on

and reactive targets. Because jets formed by a shaped

contain small-diameter,high-velocity projectiles, the

by cylinders or balls of uniform velocity with the

jet formation and penetration by Birkhoff, McDougall,

Pugh, and Taylor4 describes what is called the “ideal” penetration velocity. If

we assume Bernoulli’s theorem applies (that is, that the jet pressure is large

compared to the target or jet material strengths and that pressure is the same

in the jet and target near the interface), then

0.5 pj(vj - VP)2= 0,5 Q?; ,

where p is density, V is velocity, j implies jet, t implies target, and p signi-

fies penetration.

We rearrange the expression to find the ratio of the jet velocity to jet

penetration velocity,

$=1+~~ .

P

We use this expression to determine the penetration velocity for a l.O-cm/ps

steel jet interacting with various

TargetSteelAluminumComp BWater

Bernoulli.’s theorem is for

fluid. For a compressible fluid,

exact only for a constant density

targets, as follows.

Penetration Velocity(cm/ps)

0.50.6280.6820.738

steady motion of an

the ideal penetration

incompressible uniform

velocity expression is

system; however, the experimental penetration

.

*

*

.

data from many studies of inert jets penetrating inerts are adequately described

using the ideal model.

2

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The penetrations of an aluminum target by an aluminum jet and of a steel

target by a steel jet were modeled using the particle-in-cell technique by

Harlow and Pracht.5 They concluded that their calculated penetration velocities

approached the ideal values.

Copper jet penetration into an aluminum target was calculated by Johnson6

using his two- and three-dimensionalEulerian hydrodynamic codes. His calculated

penetration velocity agrees with the ideal values.

The penetration velocity of a 13-mm-diam steel ball moving at various ve-

locities and impacting a 25-mm-thick cylinder of PBX 9404 or Composition B was3reported by Rice. The data were generated at Ballistic Research Laboratory by

R. Frey. Experimental data and Eulerian calculationsby Rice indicated that the

penetration velocity was markedly decreased, beyond the critical projectile

velocity for initiation of detonation, and was significantly less than predicted

by the ideal model.

This study examined the jet penetration of inerts and explosives by compar-

ing calculated and experimental projectile penetrations to determine the nature

of the process and the cause of the observed failure of the ideal penetration

model for explosives.

II. STEEL JET PENETRATING STEEL

Two PHERMEX radiographs of a steel jet7published. The steel jet was formed by a

60.O-mm-thick PBX-9404 hemisphere. The jet

penetrating a steel block have been

4.O-mm-thick hemishell driven by a

interacted with a steel block after

308 mm of free run from the center of the steel hemisphere.

The jet tip velocity was 18 mm/Ns and the jet velocity decreased approxi-

mately 1.3 mm/ps for each 10 mm of jet length. Radiograph 1185 was taken after

the jet had penetrated 45 mm of steel in 6 MS with an average penetration veloc-

ity of 7.5 mm/ps. Radiograph 1181 was taken after the jet had penetrated an

additional 35 mm of steel in 7.0 ps with an average penetration velocity of 5.0

mm/ps. The jet velocity decays from 18 mm/ps to 10 mm/ps after a run of 24 ft

in the air. The jet diameter is uncertain because of its diffuse boundaries in

the radiograph. The jet diameter

fuse along the length of the jet.

in our models.

The radiographs are shown in

increases and the jet interface is more dif-

We therefore examined 8- and 12-mm-diam jets

Figs. 1 and 2. Calculated density profiles,

with the experimental shock front and interface, are shown in Figs. 3 and 4.

3

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The 2DE computer code described in Ref. 2 was used to model the flow. Equation-

of-state parameters used for 347 stainless steel are the same as given in Appen-

dix B of Ref. 8.

The steel shock Hugoniot was described by Us = 4.58 + 1,51 U , where Us isP

shock velocity and U is particle velocity. The initial density of the steelP

was 7.917 ing/mm3and the Griineisengamma was 1.25. Elastic-plastic terms were

negligible, and tension was permitted only in the target.

The calculated profiles are sensitive to the jet description. The jet

initially has steel’s standard density, but the velocity gradient results in the

jet density decreasing with time.

The calculated pressures, densities, and vertical velocities near and

parallel to the vertical z-axis are shown in Fig. S at various times. Pressure

and velocity at the interface between the steel target and the advancing jet tip

are shown as functions of time in Fig. 6. Contours of pressure, energy, and

velocity in R and Z directions are shown in Fig. 7 at 6.o ps and in Fig. 8 at

13.0 ps.

The experimentally observed steel jet penetration into a steel plate ap-

pears to be adequately reproduced, considering the complicated nature of the

jet. The hole observed between the jet and target walls also appears to be sub-

stantially reproduced. The jet material appears primarily along the side of the

hole made in the target and in the splash wave. Reference 4 states that “care-

ful weighings have shown that a metal jet is captured by a metal target, which

loses no weight except a very small amount at the front surface.” Mautz has re-

ported that high-velocity steel jets penetrating steel remain partly on the tar-

get, and partly leave the target in a vapor or liquid form.

The observed agreement between the radiographs and numerical model suggests

that the important features of jet penetration are described by the fluid dy-

namics of the process. To examine the problem further, we simplify our jet to a

rod or sphere, initially moving with a uniform velocity.

III. STEEL ROD PENETRATING STEEL

Having demonstrated that steel target penetration by a steel jet of de-

creasing velocity can be modeled numerically, we next examine the penetration

physics of a simple system.

A 10-mm-diam steel rod with a 15-mm/ps velocity was modeled similarly to

the steel jet model described in Sec. II. The mesh cells were l-mm square and

4

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-3the time step was 4 x 10 Ms. The system was described by 50 cells in the

radial direction and 100 cells along the z-axis.

The calculated pressures, densities, and vertical velocities along and near

the vertical z-axis are shown in Fig. 9 at various times. Pressure and velocity

at the interface between the steel target and the upper tip of the rod are shown

as functions of time in Fig. 10. Contours of pressure, density, energy, and

velocity in R and Z directions are shown in Fig. 11 at 4.0 ps and in Fig. 12 at

8.0 PS.

The steel rod sends an initial shock pressure of about 950 GPa into the

steel target at a 16-mm/ps shock velocity and a 7.5-mm/ps particle velocity.

Radial motion of the steel target, and side rarefactions, decreased the inter-

face pressure to about 250 GPa, and the particle velocity remained at about 7.5

mm/ps. A diverging, approximately steady state profile developed near the

jet-target interface, which continued until the rod length was consumed. The

shock wave was supported by the higher pressure at the rod-target interface.

A steel rod of the same dimensions but with an initial velocity of 10 mm/ps

was modeled also.

The calculated pressures, densities, and vertical velocities along and near

the vertical z-axis are shown in Fig. 13

locity at the interface between the steel

are shown as functions of time in Fig. 14.

The steel rod sent an initial shock

at various times. Pressure and ve-

target and the upper tip of the rod

pressure of about 480 GPa into the

steel target, along with a 12.1-mm/ps shock velocity and a 5.O-mm/ps particle

velocity. The radial motion decreased the interface pressure to 100 GPa; the

particle velocity remained near 5.0 mm/ps for 18 ps, or a penetration distance

of 90 mm. A shock wave in the target, with pressure less than one-third of the

interface pressure, was supported by a

face.

The penetration velocity quickly

ity (half the initial rod velocity)

100-GPa pressure at the target-rod inter-

approached the “ideal” penetration veloc-

for a steel rod entering a steel target.

The initial high-pressure shock wave formed at the rod-target interface was

quickly degraded by side rarefactions and divergence to the “ideal” interface

pressure, P, of #pV~, whereas the particle velocity remained unchanged, as ex-

pected for jets and targets of the same material. The shock impedance relation-

= 1 + P~”~t/Pjusj)ship may be expressed as V./V where U~tJP

is the shock veloc-

ityandP=pUVtsp’

For jets and targets of the same ❑aterial, V = 0.5 Vj forP

5

Page 9: fas.org · we assume Bernoulli’s theorem applies (that is, that the jet pressure is large compared to the target or jet material strengthsand that pressure is the same in the jet

both the initial shock match across the interface and for the later penetration

after steady state is achieved; the pressure decreased from p U Vt St p to $pvz.P

The high pressure near the rod-target interface supported a lower pressure shock

wave that moved out into the target ahead of the rod-target interface with a

shock speed similar to the penetration velocity of the rod.

Iv. TANTALUM ROD PENETRATION

To examine the effect of different materials on the penetration process, we

modeled an unreported experiment performed by Campbell and Hantel at the Los

Alamos National Laboratory. They determined that, with an initial velocity of

7.3 to 6.6 mm/ps, the penetration velocity of a tantalum jet into a steel plate

was 4.0 mm/ps. The tantalum shock Hugoniot was described by U = 3.414 + 1.201s

uP’ p

= 16.69 mg/mm3, and y = 1.4.

In Table I, the calculated penetration velocity of the tantalum rod is

4.O-mm/ps for a 7.3-mm/ps rod, and 3.7 mm/ps for a 6.6-mm/ps rod. The 4.O-mm/ps

experimental penetration velocity, for a jet with a velocity between 7.3 and 6.6

mm/ps, is well reproduced by the calculations.

The good agreement between experiment and calculation for the tantalum jet

penetrating steel suggests that we can use the model to examine other systems.

System

Tantalumrod penetratingsteel

Tantalumrod penetratingsteel

Tantalumrod penetratingwater

Tantalumrod penetratinginertCompositionB

Tantalumrod penetratinginertCompositionB

Tantalumrod penetratingreactiveCompositionB

CALCULATEDAND IDEAL

Initial InitialRod Shock

Velocity Pressure

7.3 370

6.6 310

6.4 68

6.4 110

2.0 17

2.0 30

TABLS I

MODELPRESSURESARD Velocities

InitialParticle PenetrationVelocity InterfacePressureVelocity Calc.Final Ideal Calc.Final Ideal

4.2 4.0 4.33 80 74

3.8 3.7 3.91 60 60

5.5 5.2 5.14 13 13.2

5.0 4.6 4.85 20 20.1

1.7 1.64 1.51 2 1.97

1.8 1.37 1.51 6 1.97

. .aPresauresare in gigapascals,and velocitiesare in millimetersper microsecond.

,., .

6

Page 10: fas.org · we assume Bernoulli’s theorem applies (that is, that the jet pressure is large compared to the target or jet material strengthsand that pressure is the same in the jet

As predicted by the ideal model, the tantalum (p = 16.69 mg/mm3) rod at the

same initial velocity penetrates inert Composition B (p = 1.715 mg/mm3) faster

than steel, and penetrates water (p = 1.0 mg/mmJ) even faster. The ideal model

interface pressures and penetration velocities agree well with the numerical

results over a wide range of velocities and densities, except for the reactive

Composition B, where the interface pressure is three times greater in the calcu-

lation than in the ideal.

The pressure, density, and velocity in the R and Z directions are shown in

Fig. 15 for the tantalum rod with a 6,4-mm/ps initial velocity penetrating

steel, and in Fig. 16 for the tantalum rod penetrating water. A larger tip di-

ameter develops on the tantalum rod and makes a larger hole in the steel target

than in the water target. Pressure and velocity at the interface between the

upper tip of the advancing tantalum rod and the steel target are shown in Fig.

17, and between the tantalum tip and the water target in Fig. 18. The pressure

and velocity one-dimensional graphs along the tantalum rod (with a 2.O-mm/ps

initial velocity), and on into the Composition B target, are shown in Fig. 19

for the unreacted and detonated Composition B after 6,0 ps. The tantalum rod

interface pressures are larger and the interface velocities are lower for the

reactive case.

We examine the reactive case in detail in the next section.

v. STEEL BALL PENETRATION OF EXPLOSIVES

Rice reported~ the penetration velocity of a steel ball, 13 mm in diameter,

moving at varying speeds and striking 25-mm-thick cylinders of either PBX 9404

or Composition B.

We have modeled this system numerically, and we compared the results with

the experimental data of Frey. The Forest Fire2 description of heterogeneous

shock initiation described the explosive burn. The HOM equation of state, and

Forest Fire rate constants for PBX 9404 and Composition B, were identical to

those described in Ref. 2. The mesh was 0.5416 mm by 0.5 mm and the time step

was 0.005 ps. The computational problem was 78 cells in height and 20 cells in

width.

Figure 20 shows the experimental data and the calculated results of steel

ball interaction with PBX 9404 or Composition B. The ball velocity loss is de-

fined as the initial ball velocity less the penetration velocity. The agreement

7

Page 11: fas.org · we assume Bernoulli’s theorem applies (that is, that the jet pressure is large compared to the target or jet material strengthsand that pressure is the same in the jet

demonstrates that the model describes the important processes of explosive

penetration.

When the steel ball was penetrating inert or nearly inert explosive, the

penetration velocity could be described by the ideal model. When the ball

velocity was just sufficient to cause propagating detonation, however, the ob-

served and calculated penetration velocities were much less than predicted by

the ideal model. As the ball velocity was increased, the difference between the

actual and ideal penetration velocities decreased. A summary of the ball pene-

tration calculations is given in Table II.

TABLE II

BALL PENETRATION CALCULATIONS

Velocity@lm/ps)

Steel/Composition B 2.2

2.0

1.7

1.0

0.5

1.5

3.0

2.0

3.0

1.4

1.2

1.0

0.5

Steel/PBX 9404

State

Reacted

Late reaction

No reaction

No reaction

No reaction

No reaction

Reacted

No reactionpermitted

No reactionpermitted

Reacted

Late reaction

No reaction

No reaction

VelocityLoss

(mm/ps)

1.0

>0.8

0.5

0.25

0.10

0.30

1.2

0.5

0.80

0.80

>0.75

0.35

0.15

aV- ideal for Composition B is 0.682 (ball velocity).

v

&1.2

1.2

1.2

0.75

0.40

1.2

1.8

1.5

2.25

0.60

0.45

0.65

0.35

v

Id~ala

1.5

1.365

1.16

0.68

0.34

1.02

2.047

1.365

2.047

0.944

0.81

0.675

0.337

vlossIdeal

Q!!!!&Q

0.7

0.64

0.54

0.32

0.16

0.477

0.953

0.635

0.953

0.456

0.39

0.325

0.163

V; ideal for PBX 9404 is 0.674 (ball velocity).

8

Page 12: fas.org · we assume Bernoulli’s theorem applies (that is, that the jet pressure is large compared to the target or jet material strengthsand that pressure is the same in the jet

A plot of the interface pressure and velocity in the Z direction near the

z-axis, as functions of time, for 1.0- and 1.2-mm/ps balls interacting with PBX

9404 is shown in Fig. 21. The contours and one-dimensional graphs are shown in

Figs. 22 and 23. The 1.2-mm/ps ball results in prompt initiation of the PBX

9404, and the interface pressure is much higher and velocity loss greater than

for the l.O-mm/ps ball (which does not cause prompt initiation).

In Ref. 1 we showed that the Held experimental critical condition for prop-

agating detonation--the jet velocity squared times the jet diameter (V~d)--

adequately described the experimental and theoretical results. The steel ball

must present an “effective diameter” to the explosive. The critical ball ve-

locity for PBX 9404 shown in Fig. 20 is 1.14 mm/ps, The V~d for PBX 9404,

reported in Ref. 1, is 16.0; therefore, the ball has an effective diameter of

12.3 mm. This is, within the calibration error, not significantly different

from the actual ball diameter of 13.0 mm. The critical ball velocity for Compo-

sition B, shown in Fig. 20, is 1.8 mm/ps. The V~d for Composition B, reported

in Ref. 1, is 29; therefore, the ball has an effective diameter of 9.0 mm when

shocking Composition B.

Because the steel ball exhibits a complicated flow, we examined a simpler

system to demonstrate the essential features of the flow.

The ball was replaced by a steel rod of the same diameter, and rods with

velocities of 2.0 and 6.o mm/ps were calculated interacting with reactive and

nonreactive Composition B. The interface pressures and velocities near the

advancing upper tip of the steel rod, as functions of time, are shown in Figs.

24 and 25. A summary of the rod calculation is given in Table III.

The lowered penetration velocity of a projectile moving into detonating

(rather than nondetonating or inert) explosives is caused by the higher pressure

at the projectile-detonation product interface. The ideal model assumes that

the pressure at zero particle velocity is zero, which is correct for inerts;

however, for explosives the constant volume detonation pressure at zero particle

velocity is approximately 10 GPa for a slab of Composition B. In diverging

flow, the detonation product pressure at zero particle velocity is about 5 GPa.

The effect is not included in the ideal model, so it fails to account for the

velocity decrease.

If we assume that the ideal model is appropriate for the steel rod, and if

we set the calculated detonation product interface pressure, 5.0 GPa for the

9

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TABLE III

STEEL ROD PENETRATING COMPOSITION Ba

Initial ~ Penetration Velocityb

Interface PressurebCondition Rod Velocity Calc. Final Ideal Calc. Final Ideal

Reactive 6.0 4.0 4.09 18.0 14.4

Reactive 2.0 1.0 1.365 5.0 1.59

Inert 6.0 4.0 4.09 15.0 14.4

Inert 2.0 1.4 1.365 ‘“1.5 1.59

.

aIdeal penetration velocity is 0.682 (rod velocity) and ideal interface pressureis 0.8575 (penetrationvelocity)2.bVelocities are

2.O-mm/ps rod,

velocity. This

in millimeters per microsecond and pressures are in gigapascals.

equal to [~pj(Vj - VP)2], we estimate a 0.9-mm/ps penetration

is close to the 1.0 mm/ps calculated.

The relative difference between the ideal penetration velocity and the

calculated penetration velocity decreases with increasing projectile velocity;

the ideal model becomes better at higher projectile velocities, where the dif-

ference between the explosive reactive and nonreactive pressures (of about 4

GPa) becomes insignificant. In the next section we shall examine the effect of

projectile velocity on the penetration velocity in more detail.

VI. STEEL ROD PENETRATION OF PBX 9404

We have modeled a 16-mm-diam steel rod moving at velocities lower than

those necessary for initiating propagating detonation (1.0 mm/ps) in PBX 9404,

and at velocities great enough to penetrate the explosive faster than the deto-

nation velocity (8.8 mm/ps)o The study investigated the penetration velocity in

explosives throughout the range of possible jet velocities and examined the

steel rod and explosive interface pressure effect described in the previous

section. It also determined what would occur if the penetration velocity were

greater than the C-J detonation velocity.

The Forest Fire rate constants and the HOM equation of state used for

PBX 9404 were described in Ref. 2. The mesh was 2.O-mm by 2.O-mm square. The

problem was described by 25 cells in the radial direction

axial direction. The rod was 10 cells long and the steel

high. The time step for the calculation was 0.008 ps.

10

and 65 cells in the

target was 55 cells

Page 14: fas.org · we assume Bernoulli’s theorem applies (that is, that the jet pressure is large compared to the target or jet material strengthsand that pressure is the same in the jet

A summary of the results of the calculations is given in Table IV.

The interface or rod tip pressures and velocities as functions of time, for

a steel rod with a 15-mm/ps initial velocity penetrating PBX 9404, are shown in

Fig. 26. The contours and one-dimensional graphs are shown in Fig. 27. The

steel rod penetrates the PBX 9404 at 10.6 mm/Hs, and it forms a steady over-

driven detonation wave moving at the same velocity as the steel rod, and with an

overdriven effective C-J pressure of 100 GPa. The C-J pressure of PBX 9404 is

36.5 GPa and the C-J velocity is 8.8 mm/ps. The calculation demonstrates that

highvelocity jets cannot be used to destroy an explosive charge without initi-

ating an overdriven propagating detonation.

When the rod penetration velocity becomes less than the C-J detonation ve-

locity, the detonation wave moves away from the rod surface. To illustrate

TABLB IV

STEEL ROD PENETRATINGPBX 9404

InitialRod

Velocity

@.L@_

15.0

Final Calc.Penetration

Velocity(LQnlfps)

10.6

IdealPenetration

Velocity(~lvs )

10.117

IdealInterfacPressure %

__@YL

94.37

DivergingEffective

C-J Pressure(GPa)

90

InterfacePressure

(GPa)

DetonationVelocity(mfps)

10

Comments

Steady overdrive detonationwave

Steady overdrive detonationwave

Decaying wave moving fasterthan rod

Diverging detonation wave nmv-ing faster than rod

Diverging detonation wave aov-ing faster than rod

Diverging detonation wave mov-ing faster than rod

Diverging detonation wave mov-ing faster than rod

Diverging detonation wave nnv-ing faster than rod

Diverging detonation wave raov-ing faster than rnd

Diverging detonating wave mnv-ing faster than rnd

Diverging detonation wave movi-ng faster than rod

Nn detonation, decaying shnckwave

No detonation, decsying shockwave

No detonating, decaying shnckwave

100

13.0

11.0

9.0

9.2 8.768 70. B975

55

38

60

40

36

B.g

S.8

8.7

B.7

7.8 7.419 50.75

6.2 6.07 33.97

8.0 5.5 5.396 31 26.84 35

5.0 3.2 3.37 15 10.5 35 S.7

1.83.0 2.02 8 3.77 35 B.7

1.4 1.6862.5

2.0

1.5

1.0

0.7

0.5

7

6

5

5

0

0

0

2.6 35 g.1

1.1 1.35 1.7 35

35

35

8.7

8.7

8.1

0.6 1.01 0.9

0.25 0.67 0.4

0.5 0.47 0.2 .- ----

0.36 0.34 0.1 -- ----

0.3 0.22 0.20 0.04 -- ----

‘0.674 rnd velncity.

b0.922 (penetration ve10citY)2.

Page 15: fas.org · we assume Bernoulli’s theorem applies (that is, that the jet pressure is large compared to the target or jet material strengthsand that pressure is the same in the jet

this, Fig. 28 shows the interface or rod tip pressure and velocities as func-

tions of time for a steel rod with a 5-mm/I.Jsinitial velocity penetrating PBX

9404. Contours and one-dimensional graphs along the vertical z-axis are shown

in Fig. 29. The steel rod penetrates the PBX 9404 at 3.2 mm/ps. The detonation

wave proceeds at 8.7 mm/ps with a diverging effective C-J pressure of 35 GPa.

The interface detonation product pressure is 15 GPa, which is 4.5 GPa greater

than the ideal interface pressure at the rod tip of 10.5 GPa. As discussed in

the previous section, the ideal model assumes that the pressure at zero particle

velocity is zero, which is incorrect for constant volume detonation. A slower

penetration velocity results than that expected from the ideal model.

The effect of the 4-GPa additional interface pressure is most apparent when

the rod velocity just suffices to cause prompt propagating detonation. To il-

illustrate this, Fig. 30 shows the velocity as a function of time for a steel

rod with a 1.5-mm/ps initial velocity penetrating PBX 9404. Contours and one-

dimensional graphs are shown in Fig. 31. The steel rod penetrates the PBX 9404

at 0.6 mm/ps, which is 0.4 mm/ps slower than it would penetrate the PBX 9404 if

it were inert. The steel rod interface pressure is 5.0 GPa, which is 4 GPa

higher than the 0.9-GPa ideal interface pressure. Illustrating the importance

of this increased interface pressure upon penetration velocity, the calculated

penetration velocity is about the same for the 0.7-mm/ps

explosive does not decompose, as for the 1.5-mm/ps rod,

detonates.

VII. CONCLUSIONS

For engineering purposes, the initial jet penetration

inert can be estimated, using the shock-matching relationship,

steel rod, where the

where the explosive

2 ptu5t

v=1+—

Ppjusj “

velocity into an

Here, Vj is initial jet velocity, VP

is penetration velocity, p is density, Us

is shock velocity, j implies jet, and t signifies target. The initial shock

pressure can be estimated using P = Ptustvp” Final penetration velocity can be

estimated, using Bernoulli’s theorem, from

12

Page 16: fas.org · we assume Bernoulli’s theorem applies (that is, that the jet pressure is large compared to the target or jet material strengthsand that pressure is the same in the jet

> $P~=l+F.

P j

The interface pressure, P, at the jet tip can be estimated using

P = 0.5 ptv; .

When using a high explosive as the target, the

additional term, p*, and the Bernoulli equation for

0.5 pj(vj - VP)2 = 0.5 ptv; + p* ,

where we have determined p* to be approximately

studied.

pressure expression needs an

explosives becomes

4.0 GPa for the explosives

Obviously, these are only approximations and a more reliable

be obtained using the numerical methods described in this report.

velocity decreases significantly or the projectile length is not

than the projectile diameter, numerical calculations are necessary.

estimate can

If the jet

much longer

Even if the jet particle or projectile is no longer than the diameter, the

critical velocity for initiating propagating detonation can be estimated using

the projectile diameter and the Held critical V2d expression discussed in this

report and Ref. 1.

A jet with a penetration velocity greater than the

of an explosive results in an overdriven detonation wave

jet at a velocity near that of the jet.

The calculated penetration velocity into explosives

C-J detonation velocity

proceeding ahead of the

that are initiated by a

low-velocity jet is significantly less than for inerts of the same density,

Detonation products near the jet tip have a higher pressure than in inert mate-

rials of the same density, and thus slow the jet penetration more. The effect

is less important as the jet velocities increase.

Most significantly, if the jet diameter and velocity histories are known,

all the experimentally observed jet penetration behavior of metals or explosives

can be modeled numerically. Also, if the jet or projectile length is known, the

penetration depth and hole diameter may be calculated.

13

Page 17: fas.org · we assume Bernoulli’s theorem applies (that is, that the jet pressure is large compared to the target or jet material strengthsand that pressure is the same in the jet

ACKNOWLEDGMENTS

The authors gratefully acknowledge the contributions of James N. Johnson,

who explained why the initial shock particle velocity was identical to the

penetration velocity for targets and jets of the same material. They also

acknowledge the suggestions, contributions, and encouragement of L. W. Hantel,

A. W. Campbell, C. W. Mautz, D. L. Upham, and S. D. Gardner of the Los Alamos

National Laboratory; N. E. Hoskin, AWRE; and Peter R. Lee, RARDE.

REFERENCES

1.

2.

3.

4.

5.

6.

7.

8.

Charles L. Mader and George H. Pimbley, “Jet Initiation of Explosives,” LosAlamos Scientific Laboratory report LA-8647 (February 1981).

Charles L. Mader, Numerical Modeling of Detonations (University of Cali-fornia Press, Berkeley, 1979).

M. H. Rice, “Penetration of High Explosives by Inert Projectiles,” Systems,Science

GarrettTaylor,

Francis

and Software report SS-R-78-3512 (1977).

Birkhoff, Duncan P. McDougall, Emerson M. Pugh, and Sir Geoffrey“Explosives with Lined Cavities,” J. App. Phys. ~, 563-582 (1948).

H. Harlow and William E. Pracht, “Formation and Penetration ofHigh-Speed Collapse Jets,” Phys. Fluids ~, 1951-1959 (1966).

Wallace E. Johnson, “Three-Dimensional Computations in Penetrator-TargetInteractions,“ Ballistic Research Laboratory report BRL CR 338 (1977).

Charles L. Mader, LASL PH31RMEXData, Vol. III (University of CaliforniaPress, Berkeley, 1980).

Charles L. Mader and Milton Samuel Shaw, “User’s Manual for SIN,” LosAlamos Scientific Laboratory report LA-7264-M (September 1978).

14

Page 18: fas.org · we assume Bernoulli’s theorem applies (that is, that the jet pressure is large compared to the target or jet material strengthsand that pressure is the same in the jet

—...-—.

r .-. ———

. .=---- .

Fig. 1.Shot 1185. A steel jet formed by a 4.O-mm-thick steel hemishell, whichwas driven by a 60.O-mm-thick PBX-9404 hemisphere, penetrated a 304stainless steel block. The jet traveled for 35.57 ps. The steel blockwas 308 mm from the center of the steel hemishell. The radiographictime was 79.02 p.s.

15

Page 19: fas.org · we assume Bernoulli’s theorem applies (that is, that the jet pressure is large compared to the target or jet material strengthsand that pressure is the same in the jet

Fig. 2.Shot 1181. A 304 stainless steel block was penetrated by a steel jetformed by a 4.O-mm-thick steel hemishell driven by a 60.O-mm-thickPBX-9404 hemisphere. The jet traveled for 42.53 p.s. The steel blockwas 308 mm from the center of the steel hemishell. The radiographictime was 85.99 ps.

16

Page 20: fas.org · we assume Bernoulli’s theorem applies (that is, that the jet pressure is large compared to the target or jet material strengthsand that pressure is the same in the jet

I I I I

12

[

6.Ops

--- SHOT 1185

II

5

4

01234

Fig. 3.Calculated density profiles, after6.0 us of penetration, of a steelblock 110 mm long and 50@km wide,by an 8.O-mm-thick steel jet movingwith a tip-velocity that has de-creased to 12 mm/ps. The experi-mental shock front profile andtarget interface are shown for shot1185. The jet has penetrated 45 mmof steel. The density contourinterval is 0.5 mg/mm3.

12

tII

10

9

8

7

6

5

4

3

2

I

I I I I

13.ops

--–SHOT 1181

\

/

‘\ ,

\

4

0

Q

01234

Fig. 4.Calculated densi~y profiles after13 ps of penetration of a steelblock 110 mm long by 50 mm wide, byan 8.O-mm-thick steel jet movingwith tip velocity-that has decreasedto 7.75 mm/ps. The experimentalshock front profile and targetinterface are shown for shot 1181.The jet has penetrated 8.0 mm ofsteel. The density contour intervalis 0.5 mg/mm3.

17

Page 21: fas.org · we assume Bernoulli’s theorem applies (that is, that the jet pressure is large compared to the target or jet material strengthsand that pressure is the same in the jet

400 -

300 - /\

200 -/fb

Z-DIRECTION(13.0p8, — “10.OPS,— -—; 8.Ops,—--—;6.0pq----—-;’3.0ps,-----;2.0ps,———)

“~

———— ____ . >3t t I ) I 10.10 2.66 5.22 7.78 10.34 12.90

Z-DIRECTION(13.0us, — ;IO.OUS, — ——; 8.OLLS,-- —;6.Ops, ,3.0#s,------ ;2:ofLs,--—— )—. --— .

Z-DIRECTION

1000“

800 -

600 -

400 r

16

0.0 2.59 5.18 7.78 10.37 12.96

TIME (/LS)

I I I I

(13.0ps, —; 1“.ups,—---—; 8.Ops,—--—;6.Ops,—-—; 3.O@, ------;2.0ps,-— — )

Fig. 5.Calculated pressures, densities, andvertical velocities near and paral-lel to the vertical z-axis are shownat various times. The interfacecell between the jet and target islocated by a star.

18

00.0 2.59 5.18 7.78 10.37 12.96

TIME (~S)

Fig. 6.Calculated pressure and velocity atthe interface between the advancingsteel jet tip and the target areshown as a function of time.

10

. .

Page 22: fas.org · we assume Bernoulli’s theorem applies (that is, that the jet pressure is large compared to the target or jet material strengthsand that pressure is the same in the jet

.

..:. .... .. ..,. . . . . ,, .,.,,... . .. . . . . .. . . .. . . ..

Pressu]

.,

,1, :

~

. .. .

., ~, . . . . . . . . . . .,. . . . .. ,.

./..

U Velocity

Density

Fig. 7.

Energy

V Velocity

Pressure, density, energy, and U and V velocity $ontours are shown at 6.o ps forthe system shown in Fig. 3. The pressure contour interval is 50 GPa, the energycontour interval is 0.05 Mbar*cm3/g, and the velocity contour interval is 2 mm/ps,

Page 23: fas.org · we assume Bernoulli’s theorem applies (that is, that the jet pressure is large compared to the target or jet material strengthsand that pressure is the same in the jet

. .. .. . .. . .. .. .. .. . . .. .

. . .. . . . .. . . . . .. . . . .... .,.. .

Pressure

1“,.. ......:;) :

L

. .. .

EU Velocity

1“

Density

r

%

-4........

4?-’Energy

V Velocity

Fig. 8.Pressure, density, energy, and U and V ~elocity contours are shown at 13.0 US forthe system illustrated inenergy contour interval is

.!

20

~ig. ~. The pgess&e contour interval is 50 GPa.,the0.05 Mbar’’:rn3/g~and,the velocity interval is 2 mm/ps., .’. . . .

.

.

Page 24: fas.org · we assume Bernoulli’s theorem applies (that is, that the jet pressure is large compared to the target or jet material strengthsand that pressure is the same in the jet

1 1

‘“or 1!1 /jI

400II

11200 -

0.05 2.03 4.01 5.99 7.97 9.95Z-DIRECTION

( 8.0ps,— ;6.O~S*_--_;4.O~S,___ i2.0~S,--------i0,5~S,___ )

“~Fig. 9.

Calculated pressures, densities,and vertical velocities along andnear the vertical z-axis are shownat various times. The initialvelocity of the steel rod was15 mm/ps. A star indicates theinterface cell between the rod andtarget.

70-9.95

Z-DIRECTION( a.ops, _;6.0~S,___ i4.O~S,_--_--i

2.O~s,—- —;5. As,s)--—-)

0.05 2.03 4.01 5.99 7.97 9.95Z-DIRECTION

( 8.o/As,_i6.O~S,___ ;4.0//,s,------;2.”p8,—--—; ().5ps,-—_)

21

Page 25: fas.org · we assume Bernoulli’s theorem applies (that is, that the jet pressure is large compared to the target or jet material strengthsand that pressure is the same in the jet

1000

800

~

: 600

c

2m~ 400

n

200

0 I 1 I I

Fig. 10.I Calculated ~ressure and veloc-1

0.0 1.58 3.18 4.78 6.37 7.96 ity at the” interface between

TIME(/zs)the advancing steel rod tip(whose initial velocity was15 mm/ps) and the target areshown as functions of time.

“0.0 1.58 3.18 4.78 6.37 7.96

TIME(/As)

22

Page 26: fas.org · we assume Bernoulli’s theorem applies (that is, that the jet pressure is large compared to the target or jet material strengthsand that pressure is the same in the jet

I

Density EnergyPressure

Jl--,.....:..::.:;~:..”“ . . ; . . ...””-”” ---9

.: . . 0t . . .

i

:

U Velocity V Velocity

Fig. 11.Pressure, density, energy, and U and ~ velocity contours at 4.0 ps for a steelrod with a 15-mm/ps initial velocity penetrating a steel target. The pressure

contour interval is 50 GPa, the density contour interval is 0.5 mg/mm3, theenergy contour interval is 0.05 Mbar ●

cm3/g, and the velocity contour intervalis 2 mm/ps. The graph is 50 mm wide and 110 mm high.

23

Page 27: fas.org · we assume Bernoulli’s theorem applies (that is, that the jet pressure is large compared to the target or jet material strengthsand that pressure is the same in the jet

;..::.:..:.

~..>.:.:. :“

. . .. . . . . . . . . .“ . . . . . ----- .,. . . . . . ..:. %.. : ..-. . . . . .:”> . .

:. .::......

Pressure Density

..O

~ ~

‘.. .h:,’

;...;.:..~

....:...

..:.:.....:.

v.:.. ;:.. . . . . . . . . . . . . . .. . . .

. . ..:. “* –

.

Energy

U Velocity

Pressure, density, energy, and U and V velocity contours at 8.0 ps for a steel

V Velocity

Fig. 12.

rod with a 15-mm/ps initial velocity penetrating a steel target. The pressurecontour interval is 50energy contour intervalis 2 mm/ps. The graph is

24

GPa, the density contour interval is 0.5 mg/mm3, theis 0.05 Mbar ● cm3/g, and the velocity contour interval50 mm wide and 100 mm high.

.

.

Page 28: fas.org · we assume Bernoulli’s theorem applies (that is, that the jet pressure is large compared to the target or jet material strengthsand that pressure is the same in the jet

500] I I I I 1

Z-DIRECTION( 9.0#8, — i6.0~si z——; 3.0~s,_._i

Lops,-—--; o.5ps,------)

‘0.05 2.03 4.01 5.99 7.97 9.95

Z-DIRECTION( 9.OPS,—; 6.OjM, ———; O@,@;-—-;

I:op, ------ ; o.5p8,—--—)

N\

11

0 I\ >

0.05 2.03 4.01 5.99 7.97 9Z-DIRECTION

( 9.OPS,—— — ; 6.O/M, —.--—; 3.0ps, ___ ,2.0p9,—-— ;l.ops,— ;o.5pi,------)

1000“ I I i 1

800 -

~

? 600Uu

2fi 400 -“uCl_

200 –

o~0.0 3.50 7.18 10.76 14.35 I7.94

TIME (@)

-0.0 3.50 7.18 10.76 14.35 I7.94

TIME (~S)

Fig. 14.Calculated pressure and velocity atthe interface between the advancingsteel rod tip (with a 10-mm/ps initialvelocity) and the target as a functionof time.

5

Fig. 13.Calculated pressure, density, andvelocity one-dimensional-graphs alongthe steel rod (with a 10-mm/ps initialvelocity) are shown at various times.

25

Page 29: fas.org · we assume Bernoulli’s theorem applies (that is, that the jet pressure is large compared to the target or jet material strengthsand that pressure is the same in the jet

y

g

) ?.

.. .

.

J

... .. .. . .. .. .. . .. . .—. . . I. . . . . .. . .. . . . . . I. . ...0

. . . . .,

. . . . . . . .

. . . . . . . .

. . . . .

. . . .

. . .

.

.

Pressure

U Velocity

Fig.Pressure, density, and

Density

V Velocity

15.U and V velocity con-

tours at 6.0 IJSfor a 5-mm-radius tantalum rodwith an initial velocity of 6.4 mm/ps, pene-trating a steel target (40 mm high by 25 mmwide). The graph is 25 mm wide and 50 mm high.The pressure contour interval is 10GPa, thedensity interval is 0.25 mg/mms, and the veloc-ity interval is 0.5 mm/ps.

.

.

26

I

Page 30: fas.org · we assume Bernoulli’s theorem applies (that is, that the jet pressure is large compared to the target or jet material strengthsand that pressure is the same in the jet

r’.................Pressure

I

I

@--

. . . . . . . .. . J’

Density

U Velocity V Velocity

Fig. 16.Pressure, density, and U and V velocitv con-tours at 5.0 ps for a 5-mm-radius tantal& rod,with an initial velocity of 6.4 mm/ps, pene-trating a water target (40 mm high by 25 mmwide). The graph is 25 mm wide and 50 mm high.The pressure contour interval is 2 GPa, thedensity interval is 0.25 mg/mm3, and the veloc-ity interval is 0.5 mm/ps.

27

Page 31: fas.org · we assume Bernoulli’s theorem applies (that is, that the jet pressure is large compared to the target or jet material strengthsand that pressure is the same in the jet

400 -

300

200

100

‘oo~ ‘0r 1 I I I

8 –

6 -

4

2 -

o’I I I I 1

0 1.19 2.39 3.58 4.78 5.79

TIME (~S)

Fig. 17.

011 I I 1 I

o 1.19 2.39 3.58 4.78 5.97

TIME (/AS)

Calculated pressure and velocity at the interface between the advancing tantalumrod tip (with an initial velocity of 6.4 mm/ps) and the steel target are shownas functions of time.

80

t

wu3u-l

: 40mn

20

0 10 1.00 1.99 2.99 3.98 4.98

TIME (jAS)

10 I I I I

8 -

4 -

2 -

00

I I I I

1.00 1.99 2.99 3.98 4.98

TIME (/AS)

Fig. 18.Calculated pressure and velocity at the interface between the advancing tantalumrod tip (with an initial velocity of 6.4 mm/ps) and a water target are shown asfunctions of time.

.

.

.

28

Page 32: fas.org · we assume Bernoulli’s theorem applies (that is, that the jet pressure is large compared to the target or jet material strengthsand that pressure is the same in the jet

1 ( I I

0.0 ~0.05 2.03 4.01 5.99 7.97 9.95

0.20

J 0.15

g

g“ 0.10CJu?> 0.05

Z-DIRECTION

Nonreactive

I I I 1

0.0 I I I

0.05 2.03 4.01 5.99 7.97Z-DIRECTION

Calculated one-dimensional graphs2. O-mm/ps initial velocity) for ation, after 6.o p.s. The interface

Fig.near

0.3

05; 0.2

lx

2m# 0.1L

0.0

I I I I

0.05 2.03 4.01 5.99 7.97Z-DIRECTION

Reactive

0.20

:* (3.15EE

>

~ 0.10uCJ

w?> 0.135

0.00

19.

I J.

5 2.03 4.01 5.99 7Z-DIRECTION

9.95

7

the axis of the tantalum rod (with aComposition B target, with and without reac-cell is shown by a star.

29

Page 33: fas.org · we assume Bernoulli’s theorem applies (that is, that the jet pressure is large compared to the target or jet material strengthsand that pressure is the same in the jet

1.4%

I I I I I I I I 1 IEXPERIMENTAL oDETONATED

;* 1.2- 13-mm-diam[

“7❑

E STEEL BALL “UNDETONATED

; 1.0 -

[

❑IREACTIVE EOS,COMPB o ❑

VI CALCULATED ●REACTIVE EOS,PBX 94040~ o.8

AT 5ps ––IDEAL , A

>

!>2 ‘=1

1-= 0.60

9404

-1w 0.4>

COMP B

d<a

_J o#2●

m

oL-i1 I I I 1 I I I I 1 M-J

O 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0 2.2 3.0

INITIAL BALL VELOCITY (mm/ps)

Fig. 20.Initial ball velocity vs the ball velocitv loss.for a 13-mm-diam ste~lor Composition B-3.

1.00 1.99 3.00 3.98 4.98TIME (~S)

1.2 mm/ps

TIME (ps)

ball penetrating PBX 9404

2 ,0 .

c)

wm

25 -U’1uEL

o0 1.00 1.99 3.00 3.98 4.98

TIME (~S)

1.0 mm/ps

-o 1.00 1.99 3.00 3.98 4.9Q

TIME (HS)

Fig. 21.Axial interface pressure and velocity as functions of time between a steel ball(initially moving at 1.2 or 1.0 mm/us) and a PBX-9404 target. The l.O-mm/Usball velocity1.2-mm/ps ball

30

--- . .is too slow to cause prompt propagating detonation, whereas thedoes result in a propagating detonation.

.

.

Page 34: fas.org · we assume Bernoulli’s theorem applies (that is, that the jet pressure is large compared to the target or jet material strengthsand that pressure is the same in the jet

Z-DIRECTION

2.5

2.0

3.11

16.2-

‘E~ 124

z

~ 9.6“w

—n

,)

4.8-

1.0 r, I0.03 0.80 1.57 2.34 3.11 3.88

Z-DIRECTION

I.0-

0.5–

0. I I I0.03 0.80 1.57 2.34 3.!1 3.88

Z-DIRECTION

Fig’.22. -Pressure, density, U and V velocity, mass-fraction contours, and the pressure,density, and velocity one-dimensional graphs along and near the vertical z-axisat 4.5 ps for a 1.3-MM steel ball initially moving at 1.2 mm/ps penetrating PBX9404. The radial dimension is 16.25 mm and the axial dimension is 39.0 mm.

31

Page 35: fas.org · we assume Bernoulli’s theorem applies (that is, that the jet pressure is large compared to the target or jet material strengthsand that pressure is the same in the jet

\

~— ~==\>

<y

‘)

o

d...~........... ................................... ... .. .. .. .. ..........””

rressure

/’ /y

Density

.... .

. .

.. .. .. . .. ..

\.4&..:...“;”.” :.— .4 .

‘1.. (....U Velocity

.. . ... .. .. . . . . .. . . . .

.

.

,

.

V Velocity Mass Fraction

Fig. 22 (cent).

32

Page 36: fas.org · we assume Bernoulli’s theorem applies (that is, that the jet pressure is large compared to the target or jet material strengthsand that pressure is the same in the jet

25

20

5

I i I I

o~3.11 3.880.03 0.80 1.57 2.34

Z-DIRECTION

I.0

0.8

z

: 0.6vaaIL

0.2

0(

2.5 1 I I I

2.0-

1.5-

1.0-

0.5-

0 I I I I0.03 0.80 1.57 2.34 3.1I 3.88

Z-DIRECTION

1 I i

I I I I

13 0.80 1.57 2.34 3.11 3.88

Z-DIRECTION

Fig. 23.Pressure, density, and mass fraction contours and the pressure, velocity, andmass-fraction one-dimensional graphs, along and near the vertical z-axis, at 5.ops, for a 1.3-mm steel ball initially moving at 1.0 mm/ps penetrating PBX 9404.The radial dimension is 16.25 mm and the axial dimension is 39.0 mm.

33

Page 37: fas.org · we assume Bernoulli’s theorem applies (that is, that the jet pressure is large compared to the target or jet material strengthsand that pressure is the same in the jet

. . . .. . . .. . .. . .,..

.,.. .. ...... .. . . .. . . ..

. . . . . .4.,. .

Pressure

Fig.

Density

23.(cent)

Mass Fraction

.

34

Page 38: fas.org · we assume Bernoulli’s theorem applies (that is, that the jet pressure is large compared to the target or jet material strengthsand that pressure is the same in the jet

&’0

w(Y

7)(nwIYn

25

20

15

10

5’

0

I 1 I 1

.oJkmAhL—1.99 3.98 5.97 7.96 9.95

Nonreactive

1 I I 1

.0 ~

9.95

TIME (ps)

I I I I

40 -

0

k 30 -wc

z

K! 20ca

10 -

0 I I 1 10 1.99 3.98 5.97 7.96 9.95

2!

2.C

~

1.5

Lo

0.5

Reactive

I 1 I i

oo~9.95

TIME (ps)

Fig. 24.Interface pressure and velocity at the tip of a 6.5-mm-radius steelally moving at 2.0 mm/ps into reactive and nonreactive Composition B.

rod initi-

35

Page 39: fas.org · we assume Bernoulli’s theorem applies (that is, that the jet pressure is large compared to the target or jet material strengthsand that pressure is the same in the jet

80

~ 60

gwu3rJy40wwlxn

20

0

6

5

~

&

>1-G93w>s

2

I

I I I I

.0 [.00 1.99 2.99 3.98 4.98

TIME (~S)

Nonreactive

1 I I I

I I 1 I

0.0 I.00 1.99 2.99 3.98 4.98

TIME (/AS)

80

60

40

20

0

6

5

4

3

2

I

1 I I I I

~,0 1.00 1.99 4.98

TIME (/AS)

Reactive

I I 1 I

0.0 l-w 1.99 2.99 3.98 4.98

TIME (#S)

Fig. 25.Interface pressure and velocity at the tip of a 6.5-mm-radius steel rod initi-ally moving at 6.0 mm/ps penetrating reactive and nonreactive Composition B.

36

Page 40: fas.org · we assume Bernoulli’s theorem applies (that is, that the jet pressure is large compared to the target or jet material strengthsand that pressure is the same in the jet

.

Ew

wm

2u)w(rn

300

200

100

I 1 I 1 I

o~ ‘q,z~o 1.76 3.51 5.27 7.03 8.78 0 1.76 3.51 5.27 7.03 8.70

TIME (~S) TIME (~S)

Fig. 26.Interface pressure and velocity at the tip of a 16-mm-diam steel rod initiallymoving at 15 mm/ps penetrating“PBX9404.

Ag+-nY..............,........ . .. .. . . .. . . .

.. . . .,...,. . .. .. . .. .. .. .. .

. .. ...... .. .. . . .. . . . . . .

.

Pressure Density

Fig. 27.

Energy

,..

. .

.

.

I ●.

\...

U Velocity

Pressure, density, energy, U and V velocity and mass-fraction contours, and thepressure, density, and velocity one-dimensional graphs, along and near thevertical z-axis, at 8.8 ps, for a 16-mm-diam steel rod initially moving at 15mm/Ps penetrating PBX 9404.

37

Page 41: fas.org · we assume Bernoulli’s theorem applies (that is, that the jet pressure is large compared to the target or jet material strengthsand that pressure is the same in the jet

15

12

V Velocity Mass Fraction

0.10 2.66 5.22 7.78 10.34 12.90

Z-DIRECTION

400 -

300 -

200 -

‘Ot____L0.10 2.66 5.22 7.70 10.34 1:90

Z-DIRECTION

Fig. 27. (cent)

16.00 1 1 1 1

12.72 –

$

E 9.44 -E

>+Go 6.16 -

d>s

2.88 -

-.04 1 I I I

0.10 2.66 5.22 7.78 10.34 12.90

Z-DIRECTION

.

.

38

Page 42: fas.org · we assume Bernoulli’s theorem applies (that is, that the jet pressure is large compared to the target or jet material strengthsand that pressure is the same in the jet

.

*

.

.

J o.,~0.0 2.39 4.79 7.18 9.57 11.97 0.0 2.39 4.79 7.18 9.57 11.97

TIME (/AS) TIME (/LS)

Fig. 28.Interface pressure and velocity at th~ tip of an 16-mm-diam steel rod initially

moving at 5 mm/ps penetrating PBX 9404.

. .

.

.

..

.,..

Pressure

L

(---’%’

Density

.

Energy

.. .

... ..

..1

.

...

4..

U Velocity

Fig.Pressure, density, energy, U and V velocity and mass-fraction contours. and thepressure, density, and--velocity one-dimensional graphs, along and “near thevertical z-axis, at 12.0 ps, for a 16-mm-diam steel rod initially moving at 5mm/ps penetrating PBX 9404.

39

Page 43: fas.org · we assume Bernoulli’s theorem applies (that is, that the jet pressure is large compared to the target or jet material strengthsand that pressure is the same in the jet

. .

d

V Velocity Mass Fraction

Fig. 29. (cent)

c?~wK30-l(/3wIXa.

I I 1 t

60 -

40 -

20 -

0.00.10 2.66 5.22 7.79 10.34 12.90

9

6

3

c

Z-DIRECTION

I 1 I I

~

1)

10 2.66 5.22 7.79 10.34 12.90

Z-DIRECTION

[ I I 1

8.6

t

5.8 -

3.0 –

0.2 I I

0.10 2.66 5.22 7.78 10.34 I

Z-DIRECTION

40

.

Page 44: fas.org · we assume Bernoulli’s theorem applies (that is, that the jet pressure is large compared to the target or jet material strengthsand that pressure is the same in the jet

,

.

()~2.39 4.79 7.18 9.57 II .97

TIME (/AS)

. .

. .. .

.

. .. . . .

Pressure

/--’+[

L) —

/? ‘:;,. .’”.0“ ,’$’$, i}

k. /---

Density

Fig.

Fig. 30.Interface velocity ata 16-mm-diam steelmoving at 1.5 mm/ps9404.

..

Energy

31.

the rod tip forrod initially

penetrating PBX

---’-+!I

. ..

. .

.,

:it\{. ;

’11; i

U Velocity

Pressure, density, energy, U and V velocity, and mass-fraction contours and thepressure, density, and velocity one-dimensional graphs along and near the verti-cal z-axis, at 12.0 ps for a 16-mm-diam steel rod initially moving at 1.5 mm/Mspenetrating PBX 9404.

Page 45: fas.org · we assume Bernoulli’s theorem applies (that is, that the jet pressure is large compared to the target or jet material strengthsand that pressure is the same in the jet

‘i-

llc----,. .......:“1

V Velocity

l_-......Mass Fraction

Fig. 31. (cent)

_ 30

00.10 2.66 5.22 7.78 10.34 12.90

Z-DIRECTION

I I I I

9 –

G6 -

o~0.10 2.66 5.22 7.78 10.34 [2.90

Z-DIRECTION

3~

.

.

.

0.10 2.66 5.22 7.78 10.34 12.90

Z-DIRECTION

42

Page 46: fas.org · we assume Bernoulli’s theorem applies (that is, that the jet pressure is large compared to the target or jet material strengthsand that pressure is the same in the jet

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NTISPrimcode

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026450051.075

076.100101 125

126.150

A02

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US Department of Commerce

S28S POrI ROyal ROad

Springfk[d, VA 22161

MicroRche (AOI)

Pe.ge Range

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176.200

201.225

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276300

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