SIMULATION OF METEORQID-VELOCITY IMPACT BY USE F DENSE PROJECTILE

8/9/2019 SIMULATION OF METEORQID-VELOCITY IMPACT BY USE F DENSE PROJECTILE

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N S T E C H N IC L N O T E

-e=

w3

h

Y

n

3L:

c

SIMULATION OF

BY USE

F

DENSE

PROJECTILES

METEORQID-VELOCITY IMPACT

by Robert He M o ~ r ~ ~ o n

es

Research

Center

Fie

N A ~ I O N A L € R O N A U ~ I C SN D SPA CE A D ~ I N I S ~ R A T I O N W A S ~ I N ~ T O N ,

C

e A P R I L 1 9 7 0


2/35

1. Repor t

No.

NASA TN D-5734

SIMULATION OF METEOROID-VELOCITY IMPACT BY USE OF DENSE

PROJECTILES

2.

Governm en t Ac cess i on

No.

7.

Author(s)

Robert

H.

Morrison

Per fo rm ing Organ iza t io n Nam e and Add ress

NASA Ames Research Center

Moffett Field , Cali f., 94035

9 .

19.

Secu r i t y C lass i f . (o f t h i s repo r t )

Unclassified

12.

Sponso r ing Agency Nam e and Add ress

National Aeronautics and Space Administration

Washington, D.C. 20546

20 Secu r i t y C lass i f . (o f t h i s page )

21.

No. o f Pages 22. Pr ice *

Unclassified $3.00

34

115.

Supplementary Notes

3.

Rec ip ien t s Co ta log

No.

5 . R ep o r t D a t e

April 1970

6.

Per fo rm ing Organ iza t ion Code

8.

Per fo rm ing Organ iza t ion Repo r t

No.

A-3315

I O . Work U n i t No .

124-09- 15-02-00- 21

11.

Con t rac t o r Gran t No.

13.

Type o f Repo r t and Pe r iod Cove red

Technical Note

14. Sponso r ing Agency Code

16. A b s t r a c t

A technique

is

describe d for simulating the impacts of semi-infinite t arg ets by low-density, low-fineness rat io cylinders

at

meteoroid velocities by impacting high-density, low-velocity projectil es.

model forming the ba sis of the technique. The feasibility of the technique is experimentally investigated by sim ulat ing the impacts

of semi-infinite aluminum targ ets by polyethylene plastic cyl inders of various low-fineness ratios and the sa me velocity of

11.3 km/sec. The penetrations were simulated at lower velocities to within 10 percent by impacting aluminum, steel, nickel, and

copper projec tiles, but only to within 30 percent by impacting platinum projectiles.

In application

of

the technique, the impac ts of

semi-infinite aluminum targets by cylinders

of

polyethylene and porous aluminum (0.44 g/cmS)

at

veloc ities of 15 .2 and 22 km/set

respectively, were simulated.

Conditions for simulation are stated and embodied in a

17. Ke y Words

Suggested by Author(s)

Meteoroids

Hypervelocity Impact

Projectile

Simulation

18.

Dis t r ibu t ion S ta tem en t

Unclassified

-

Unlimited

For sa le

by

t h e C l e a r i n g h o u s e f o r F e d e r a l S c i e n t i f i c a n d T e c h n i c a l I n f o r m a t i o n

S p r i n g f i e l d , V i r g i n i a 2 2 1 5 1


3/35

SYMBOLS

A i

C

d

E

I

i

J

K

z

m

P

P

R

r

S

t

t l

t 2

U

U

V

X

area o f por t ion i o f i n t e r f a c e

speed of sound

diameter of cyl inder

s p e c i f i c i n t e r n a l e ne rg y

in te rf ac e between impacting mater ia ls

por t ion o f in t e r f ace ins id e boundary de f ined by po in t s o f in t e r s ec t ion

o f c y l i n d e r ' s r a d i a l r a r e f a c t i o n w it h i n t e r f a c e

impu ls e gi ve n t o t a r g e t ma t e r i a l i n

time t 2

by pressures ac t ing a t

p o r t i o n i o f i n t e r f a c e

constant

leng th o f cy l ind er

mass of cyl inder

pene t ra t ion

(maximum depth of crater) measured from undisturbed

t a r g e t s u r f a c e

pres s u re

ra re fa ct io n (head of ra re fa ct io n wave)

r a d i a l c o o r d i n a t e

shock wave

time

measured from instant of

impact

t ime f o r shock wave t o reach r e a r face of impact ing cyl inder

time a t which ax ia l r a re f ac t ion reaches in te r fac e

v e l o c i t y of one-dimensional shock wave r e l a t i v e t o und ist urb ed medium

mass ve lo ci ty behind one-dimensional shock wave re la ti ve t o

undisturbed medium

veloc i ty o f cy l inder a t impact

a x i a l c o o r d i n a t e

iii


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e

dimensionless parameter define d by equation

( 9 )

1 - I = r 7 - 1

P dens i ty

Subscr ip t s

Hug on i

o

t

t a t

e

i n i t i a l

s t a t e

p r o j e c t i l e o r cy l inder mate r ia l

r a d i a l d i r e c t i o n

t a r g e t

mate

r

i

a1

a x i a l d i r e c t i o n

impact case of low-density cyl ind er

impac t case o f s imula t ing p r o j ec t i l e

i v


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SIMULATION OF METEOROID-VELOCITY

IMPACT

BY

USE

OF

DENSE PROJECTILES

By Ro be rt H . Morrison

Ames Research Cen te r

SUMMARY

A technique i s desc r ibed fo r s imulat ing the impac ts o f sem i- in f in i t e

ta rg et s by low-density , low-f inenes s-ra t io cyl inders a t meteoroid ve loc i t i e s

by impact ing high-densi ty , low-veloci ty pro je ct i l es . Condit ions fo r s imula-

tion are stated and embodied in a model

forming the bas is of the technique.

The fe as ib i l i t y o f the t echnique i s exper imenta l ly inv est iga ted by s imulat ing

the impacts of se mi - in f in i te aluminum ta rg et s by polyethylene p l a s t ic cyl in -

ders of various low-fineness r a t io s and the same ve lo ci ty of 11.3 km/sec.

The penetrations were simulated a t lower v e l o c i t i e s t o wi t hi n

1 0

percent by

impacting aluminum, s t e e l , n ic kel , and copper pr oj ec t i le s , but only to wi th in

30 percent by impacting platinum pr oj ec ti le s.

In app l ica t ion o f the t ech-

nique, the impacts of sem i- i nf i n i t e aluminum ta rg et s by cyl inder s of poly-

ethylene and porous aluminum ( 0 . 44 g/cm3) a t vel oc it ie s of 15.2 and 22 km/sec,

respect ively , were s imulated .

INTRODUCTION

The simu latio n of meteoroid impact has , f o r th e most pa r t , been beyond

t h e c a p a b i l i t i e s of l igh t -gas-gun f ac i l i t i e s . The h ighe s t impact ve loc i ty

a t t a i n e d i n t h e s e f a c i l i t i e s , 1 1.3 km/sec, i s j u s t a t the lower end of the

meteoroid velocity spectrum of

11

t o 7 3 km/sec ( re f . 1 ) .

This v e l o c i t y ( r e f . 2)

was

obtained with a low-dens ity , p l as t i c cy l inder

th a t impac ted an aluminum ta rg e t . Ca lcu la t ions ind ica te th a t the in i t i a l

p ressure produced i n the t a rg e t ma te r ia l by t h i s impac t

i s

l e s s t ha n t h a t

produced by much slower, h igh er de nsi ty pr oj ec ti le s.

ges ts t ha t wi th the proper dimensions and ve lo ci t i es , h igher den si ty projec-

t i l e s cou ld genera te p ressure pu l ses

in the target mater ia l which would

approximate th at genera ted by the p l a s t i c c yl ind er impact ing a t a v e l o c i t y

exceeding 11.3 km/sec, and the pr oj ec ti le s thereby could sim ulate , t o some

degree, i t s impact damage a t p r e s e n t l y u n a t t a i n a b l e v e l o c i t i e s . In the same

manner, th e impacts of l ow-densi ty meteoroids a t higher ve loc i t i e s cou ld be

s imulated .

This observation sug-

A s

a s t e p t oward t h i s g o a l, d es ig n c r i t e r i a a r e h e r e i n pr op os ed f o r t h e

dimensions and ve lo ci t i es of dense pr oj ec t i le s t o s imu late the impacts of

low-density, low- fine ness -rati o c yli nde rs a t meteoroid ve lo ci t i es . The model

i n

which these c r i t e r i a are g iven and the re su l t s of experiments designed to


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t e s t the t echn ique a re p resen ted .

t i ve ly se mi -i nf in it e 2024-T351 aluminum tar ge ts impacted by aluminum, s t e e l ,

ni ck el , copper, and platinum cylin ders

a t

veloci t ies ranging f rom 4.41 to

8 . 3 5 km/sec.

P e n e t r a ti o n d a t a

are

inc luded fo r e f fec -

THEORETICAL

CONSIDERATIONS

Early Stages of Hypervelocity Impact

During the ear ly s tages of hyperveloci ty impact ,

much of th e pr oc es s

one-dimensional flowan be analyzed i n terms of h igh ly s im pl i f ie d f lows:

behind a normal shock and expansion-wave heads propagating from free surfaces

through mater ia l

a t

uniform pressure.

t a r ge t occurs dur ing th i s s imple .pa r t

o f

the f low, , i t should be poss ib le

t o def ine condi t ions f o r impact ,equivalence between pr oj ec t i le s of widely

d i f f e r e n t p h y s i c a l p r o p e r t i e s .

I f enough of the impulse g iven to the

.

The axisymmetric, hypervelocity impact of a s e mi - i n f i n i t e , t a r g e t b y a low-

f i n e n e s s - r a t i o c y l i n d e r i s depic ted

a t

t h e i n s t a n t o f impact i n f i g u r e

1.

The

cy l in der ' s ve loc i ty v , d iamete r d , l ength 2 and i n i t i a l d e n si t y

p o p ,

I

which in the genera l case i s d i f f e re n t ' f r o m ~ t h e n i t i a l d en s it y of t h e t a r g e t ,

pot , ar e ind ica ted . The orthogonal coordinate system

x

- r i s f i x e d i n t h e

ta r ge t wi th the x axis coinciding with th e axi s of th e cyl ind er. From th e

in s t an t o f impac t, the mate r ia l s o f bo th the cy l inder and the t a r ge t w i l l b e

compressed t o very high pre ssu res by shock waves.

exceeding the s t rengths of both mater ia ls , w i l l s t a r t a nonsteady, three-

dimensional compressible flow.

These p ressures , g re a t l y

The sa l i en t f ea t ure s of t h i s compress ib le f low at two ear l y t imes a f t e r

impact

are shown .in figure 2 , f o r a case where the speed of sound a t the

i n i t i a l impact (Hugonio t) p ressure i n the cy l inder mate r ia l i s l e s s t h a n t h a t

of the t a rg e t ma te r ia l . , .

In f i gure 2 (a ) the wave pa t te rn o f t h i s f low i n

a

cross - sec t iona l p lane

through the

x l

axis has been es t imated for a time soon af.t-er imp act. The

shock waves

between the mate r ia ls of the cy l inde r and ta rg et ,

compressing these respec-

t i v e m a t e r i a l s .

o f t h e r a d i a l r a r e -

fa ct io n waves, which s t a r t inward

a t

the ins tant of impact f rom the surface

of the cy l inder .

t h e r a d i a l r a r e f a c t i o n i n t h i s m a t e r i al p re ce de s t h a t i n t h e c y l i nd e r

material

along the in te rf ac e . Because pres sure waves are t rans mit t ed across the 1

in te rf ac e, expansion Mach waves ar e formed i n th e cy li nd er nla ter ial . However,

i n f i g u r e 2 , t h e c y l i n d e r' s r a d i a l r a r e f a ct i o n

i s

shown

as

though i t s propa-

gati on were unaff ected by thes e expansions.

impact i s gr ea te r i n th e cy lin der ma te ri al , Mach waves

a re genera ted in the

ta rg et mater i a l ins t ead . ( In s i mi la r mat er i a ls , no such waves are formed.)

A

r a d i a l ra re fa ct io n and th e ass oci ate d Mach waves form a boundary, in si d e o f

which the flow

i s

s t i l l one-dimensional and the two shock waves and the

Sp and S t . are shown prop agat ing away from the i nt er fa ce

I

Also shown a re th e hea ds. Rrp and R r t

Since the speed of sound in t he t ar ge t m ater i a l i s g r e a t e r ,

When the speed of sound a t

2


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i n t e r f a c e

are

pl an ar . Outside t h i s boulqdary , the f low i s three-dimensional

and the shock waves and interface

are

curved.

>

A t

a l a t e r t i m e , the shock

Sp

wi l l \ h a v e r e f l e c t e d from t h e c y l i n d e r ' s

r e a r f a c e as

a

ra re fa ct io n: The wave ,pat 'ter n .at t h i s t i me i s e s t ima t ed i n

f igure , Z ( b ) . Shown ,again

are

, t h e r a d i a l r a r e f a c

s

i n t h e t a r g e t m a t e r i a l,

which by t h i s t ime ar e , approaching the ing ge ne tm te d pos t of

the one-dimepsional flo.w,. Ins ide the r e . b y the ra di al expansion.

system, the ax ia l r a r e f a c t i o n ,h ea d , Rxp

The mate r ia l and wave motions o ccurr ing a long the , x , axis dur ing thesk

ea rl y stag es of the impact ar e b e t t e r shown in t he waye diagram .of f i gp re 3 . .

The shock wave prop agat es through th e cy li nd er and, upon enco unte ring

t h e c y l i n d e r ' s r e a r f a c e

a t

time t l i s r e f l e c t e d a s t h e a x i a l r a r e f a c t i o n

Rxp, which s t a r t s the i sen t ro p ic r e le ase o f th e mate r ia l from the Hugonio t

pressure. Subsequently, a t time

t 2 5

t h e a x i a l r a r e f a c t i o n o v e r t a k e s t h e

i n t e r f a c e I .

F o r

the f ineness ra t i os be ing conside red , th e ax ia l r a re fac -

t i o n a r r i v e s a t t h i s p o i n t b e fo r e e i t h e r o f t h e r a d i a l r a r e f a ct i o n s .

remains planar.

I t

Sp

'The cy l inder ve loc i ty v the wave, a r r i va l t imes

t l -

nd

t2.

may

a l l be r e la ted t o the impa\ct ing

flow paramet ers (se e appendix A). These paramete rs a r e th e speeds U and u,

r e l a t i v e ' t o t h e u n di s tu r be d medium,, of t h e s hock wave and t he - compressed

ma te ri al , respe+c$ively, and the sp ee d of sound CH, i n this compressed mate-

r i a l a t p r es su re

p ~ . . hese parameters, may be

calc ulat ed. for. various:. mate-,

r i a l s and any given press ure

a r e

l i n d e r . ' ~dimensions. and t h e one-dimensional

p ~ , - a s n d i c a t e d

i n

appendix B .

The

v = u p + u t (1)

where

. .

= U/( U -

u)

nv

The flow para met ers u, U , and CH must be eva lua ted fo r the mate r ia l s o f the

cyl in der (sub scr ip t p) and the ta rg et (subs cr ip t t ) a t th e same Hugoniot

pressure .

: . ,

3 .

Simulation Model

I t

i s

pos tu la ted th a t th.e in i t i a l pa r t .of the p ressure pu l se genera ted

i n a s e mi -i n fi n it e t a r ge t by a e hypq rvel ocit y'im pact of a low-den sity, low-

f in ene ss- ra t io cyl i nder can be s imulated and tha t t h i s impact can thereby be

simulated with the impact of a

s l o we r , h i g h e r d e n s i t y c y l i n d r i c a l p r o j e c t i l e

i f the followin g con dit ion s ar e met. The Hugoniot pr es su re p and the

H

3


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a r r i v a l time t 2 o f t h e a x i a l r a r e f a c t i o n a t t h e i n t e r f a c e

are

t o be t h e

same f o r b ot h cases. Furthermore, the

same

impulse J i s t o b e gi ve n t o

t h e t a r g e t

material

i n t h i s time by pressures ac t ing a t t h e p o r t i o n

i

of

the in te r fac e in s id e the boundary th a t i s d e l i n e a te d by t h e p o i n t s o f i n t e r -

s e c t i o n o f t h e c y l i n d e r ' s r a d i a l r a r e f a c t i o n wi t h t h i s i n t e r f a c e . To d e l i n -

ea te t h i s boundary, th e assumptions are made t h a t t he precedence of a t a r g e t ' s

r a d i a l r a r e f a c t i o n c au se s

a

n e g l i g i b l e r e d uc t i on i n t h e p r e ss u r e

a t

t h e i n t e r -

face

from the Hugoniot pr es su re

ra d i a l r a r e fac t ion , and tha t t h i s p recedence the re fo re has a n e g l i g i b l e

ef fec t

on the l a t t e r wave's propagation . Thus, the por tio n

i

o f t h e i n t e r f a c e i s

approximately planar and a t a cons tan t p ressure

The above cond it io ns f o r

s imulat ion may be wr i t t en , res pec t iv ely ,

as

pH

b e f o r e t h e a r r i v a l

of

t h e c y l i n d e r ' s

PH.

t 2 u = t2l.l

J = J

U

1 I

where the subscr ip ts 1 1 and

u

denote the impact cases of the lower density

c y l i n d e r and t h e s i mu la t i ng p r o j e c t i l e , r e s p e c t i v e l y .

The preceding conditions and assumptions are s u f f i c i e n t t o s p e c i fy t h e

v e l o c i t y ,

l eng th , and f ineness ra t i o o f a s i mu l at in g p r o j e c t i l e i n terms o f

these same qu an t i t i es f o r the low-density cyl i nder and the one-dimensional

flow parameters. The ve lo ci ty of t h i s p r o j e c t i l e i s der ived by subs t i t u t i ng

equa t ion (1) in to th e equat ion

u = u

t u

t u

which

i s

in pl ie d by th e condi t ion of equat ion

( 4 ) .

obta ined

i s

The veloci ty thus

v = v + u - u

U 1 I

PCJ P1-I

The length

o f

t h i s p r o j e c t i l e

i s

obt ain ed from equa tion s (Sa) and 3)

as

I t s

f i n e n e s s r a t i o

i s

der ive d from equat ion (6a) by

f i r s t

developing an

express ion fo r the impulse J

as

fo l lows. I f A i i s the area o f t h e p o r t i o n

i o f the in te r fa ce , the impulse J may be expressed

as

t 2

J =

pH i. d t

=

p H 1 2

i

d t

0

However, the area

Ai

is given by

4


9/35

Ai

=

7

(d - 2 c ~ ~ t )

S u b s t i t u t i n g t h i s e x p r e s s i o n f o r A i in to the one f o r J , performing the

in teg ra t io n , and rea r rang ing the res u l ta n t express ion y ie ld s

R

J

=

- p

t3

6

4

H 2 p

where

6 i s

a dimensionless parameter defined

as

r 1 2

1

+ -

e = l., l/up + 1/11HPCHP)(w) j

(9)

I f the l a t t e r express ion f o r

t i o n s (4) and (Sa) a re applied, equation (6a) becomes

J

i s subs t i tu ted and the cond i t ions of equa-

By use of th e id en ti ty of equat ion

(9), t h e p r o j e c t i l e ' s f in en es s r a t i o i s

where

equat ion (6b) .

i s re la te d t o the low-dens ity cy l inder ' s p rope r t i e s by

In summary, th e vel oci ty , length , and f inen ess ra t i o

of

a

c y l i n d r i c a l

p r o j e c t i l e t o s i mul a t e t h e impact o f a low-densi ty , low-f ineness-ra t io

cy l inder are given,

respec t ive ly , by the equa t ions

v = v + u - u

l

PO PlJ

c - .

5


10/35

and

1 .

GH =

U / U -

u)

I .

. ,

EXPERIMENTS

The experimental inv es ti ga ti on .consisted of two parts . , F i r s t , t h e

app l ic ab i l i t y o f the p receding s imula t ion re la t ionsh ips was determined by

simulat ing th e impact of th e previously mentioned pl a s t i c cyl inder of r e f -

erence 2 .

f i n en e s s r a t i o o f 1/3. . T examine somewhat-more gen era lly th e ap pl ic ab il i t y

of the s imulat ion techniqde, t h e impacts

of polyethylene cyl inder s wi th lower

fi ne ne ss r a t i o s and th e same ve lo ci ty (1'1.3 km/s'ec) were al so sim ulat ed. In

the second pa r t of th e exper imenta l in ves t ig at i on, an impact of th e 1 /3-

f ineness-ra t i io polyethylene cyl inder was s imulated a t

a higher. vel .ocity of

15.2

k m / s e c .

For

each s i f iu la t ioh ; the*per fe t ra t ion ( t a rg e t -c r a te r dep th )

so

obta ined was compared with that estimated from

The cylinder was polyethylene with a den sit y 'of 0 . 9 5 g/cm3 and a

1 / 4 v ~ 2 / 3

P/d = 0.34(Z/d)

( r e f . 3 ) , kh i c h i s app l icab le t o t he hyperve loc i ty impact of '2024-TZ51 alumi-

num by polyethylen e cyl ind ers with f i nen ess r a t i o s from 1/6 t o 1 .

To simula te the impact s i n t h e f i r s € pa r t o f th e exper imenta l inves t iga -

t i o n , t h e f ol lo w in g p r o j e c t i l e

mater ia l s

were us ed : 2024-T351 aluminum, AIS1

1018 s t e e l , pure n ic ke l, OFHC-copper, and pur e platinu m.

only OFHC copper was used. The ve lo ci t i es of the vari ous simulat ing proj ec-

t i l e s f o r yi el di ng Hugoniot pres sur es of 1.05 and 1.70 megabars and thus

simulat 'ing polyethylene impactin'g a t 11.3 and 15 ,2 :km/see, res peg tiv eIy , ' a re

l i s t e d i n & a bl e

1.

equat ion (7b) by su bs t i tu t i ng th e ve lo ci ty of polyethylene f o r v and tliie

va lues ca lcu la ted

as

indic ated i n appendix B f o r u and u .

. - _

For the second pa r t ,

The ve lo ci t i es were c a lc ula ted f o r each press ure from

P

PO PV

P r o j e c t i l e s o f t h e s e

materials

were machined with diameters near 5

mm

and var iou s low-fineness r a t i o s . The diamete rs and leng ths were measured t o

within 0 .06 and 0 .6 perce nt , re sp ec t i ve ly . ' The pr oj ec t i le s were then

launched, sabot-mounted,

a t

t h e r e q u ir e d v el o c it i e s. i n t h e b a l l i s t i c ra ng es

employed i n th e in ves t ig at i ons o f re fe rences 2 and 4.

these ranges were

equipped with r i f l e ba rr e l s , which impar ted spin t o the

pr o j ec t i l e s t o ensure a t t i tu de nea r ze ro ang le of a t t ack and separa t ion o f

th e segmented s a b o p . Spark shadowgraphs take n a t ,numerous stations on these

ranges provided okthogonal viewst of t h

gave condi t ion and a t t i tu de data .

and therefore

were

i n th e range found in re fer enc e 3, f o r which any anomalies

due t o angles. of a t t ack ar e outweighed by th e inh erent va r i a t io n i n c r a t e r

fo rm at io n. These shadowgraphs , toge the r wi th th e measprements f o r i n t e r v a l s

st an c? ; between th e s ta ti on s, - made poss$b41e i n each case a

of the impac t ve l oc i ty t o wi th in pe rceb t . I '

The l i g h t gas guns of

r o j e c t i l e s i n f l i g h t and th er eb y

The angles of at ta ck did no t exceed 5'

e _

I

.

6


11/35

The targets w e r e of the same

material

(2024-T351 aluminum) and s i z e

(10

x

10

x

5 . 1 cm) as those o f ' r e fe rences 2 and 3. The dep ths

of

t h e r e s u l -

t a n t c ra te r s were measured r e l a t i ve t o t h e u n d is t ur b ed t a r g e t f a c e t o wi t h i n

0 .6 percen t by an espec ia l ly adap ted d i a l ind ica to r .

RESULTS AND DISCUSSION

The per t i nen t da ta and the re su l t s o f the s imula t ion ' t e s t s a re g i v e n i n

t a b l e s 2 and 3, respectively.

(P/d), , corresponding t o th e ve lo ci ty

w,,

t o g e t h e r wi t h t h e d e n s i t y

length Z and fine nes s r a t i o [Z/d),,

i s

l i s t e d

f o r

each s imulzt ing projac-

t i l e . The ve lo ci ty v,,, lengt h

Z

and f inen ess r a t i o (Z/d) of the poly-

ethylene cy lin der whose pen etr ati on P,

was

simulated by

eact

p r o j e c t i l e a n d

t h e p e n e t r a ti o n of t h i s , p r o j ec t i l e normal ized wi th respec t t o tha t e s t ima ted

f o r the corresponding polyethylene cyl i nder

ti on , t h e maximum dev iat ion o f th e dimensionless pene tra tio n

'P/d'

f o r e ac h p r o j e c t i l e from

a

curve descri bed by'a n equation of t he form

P/d

=

Kv2i3

re la t ion between penetra t ion and impact veloci ty was shown t o apply fo r

hyperveloci ty impact up t o th e

11.3

km/sec i n ref ere nce 2 ,

dev ia t ion o f

were ob ta ined , shows th a t th i s r e la t i on adequa te ly descr ibes the d a t a

over.

t h e

ve loc i ty range t e s ted . In each case , the equa t ion

was

used t o est i mat e (P/d),

a t th e s imu lht i ng ve lo ci ty v,. The length

Z

and (Z/d),, were c a l c u l a t e d

by means of equa tio ns' (5b) and ( l o ) , r es pe ct iv el y; whereas th e normalized

) \

pene t ra t ion was calcu la ted from the- equat ion

In ta bl e 3 , the d imensionlkss pene ' t ra t ion

p o q

P,/P; .

are

a l s o l i s t e d : ' In addi-

i s given

This

A

nd f i t t e d to the d a ta by th e method o f

l e a s t

squares .

The, maximum

P/d, wi th in 3 percent f o r each case where sever a l data -p oi nt s

..

which is der ived by su bs t i tu t i ng equa t ions (5b) and ' (11) in to the iden t i ty

- ,

P,

(P/d), (Z/d),, 2

_ -

p, (P/d), (Z/d). z . ,

In using equati on (12) f o r t h e smallest f inen ess r a t i o aluminum pro ' je c t i le

and i t s corresponding 0 .11 8-f in eness ' ra t i o polyethylene cyl in der , i t was

assumed t h a t th e Z/d re la t i on of equa tion (11)

s t i l l

h e l d ,

? ,

F o r each s imula t ing p r o j ec t i l e , the normalized pene t ra t io n P,/Pb i s

p l o t t e d v er su s t h e f i n en e s s r a t i o

(Z/d),

c y l in d e r i n f i g u r e 4 .

Thi s fi g ur e and t a b l e 3 show t h a t th e 'aluminum, s teel , '

nicke l , and copper p r o j ec t i l e s , having f ineness

r a t i o s

'from 0,0816 t o

0 . 2 2 4 ,

s imulated wi th good accuracy ( t o wi th in 10 percent) th e penet ra t ib ns 'of t h e i r

corresponding polyethylene cyl in ders , having f inene ss ra t i os from 0.118 t o

of th e correspmdi ng .polyethylene

7


12/35

0.313.

s in ce the pene tra t i ons were deeper than those of t h e i r corresponding

polyethylene cylinders by as much as 30 percent.

However, poor r es ul ts were obta ined with t he p la t inum pr oj ec t i le s ,

The intpacts of th e st e e l , n ic ke l , copper, and platinum simula ting pro-

je c t i l e s cor respond to the p revious ly d i scussed case o f f i gur e

2 ,

where the

speed of sound

i n

t h e t a r g e t

material a t

high pressure

i s

g r e a t e r t ha n t h a t

o f the cy l inder

material ,

and t h e r e f o r e t h e r a d i a l r a r e f a c t i o n i n t h e t a r g e t

p re ce de s t h a t i n t h e c y l i n d e r a lo ng t h e i n t e r f a c e .

corresponding polyethylene cyl ind ers , the opposi te i s t r ue . The finen ess

r a t i o o f e ach s i mu la t i ng p r o j e c t i l e and i t s corresponding polyethylene cyl-

inder, however, was suf f ic ien t ly low tha t the ax ia l r a re fac t ion reached the

point on the axis

a t

t h e i n t e r f a c e be f or e e i t h e r of t h e r a d i a l r a r e f a c t i o n s .

For

the impacts of the

The poor res u l t s ob tained wi th the pla tinum pro je c t i l e s canno t be a t t r ib -

u ted so le l y t o experimental e r ro r s s ince these e r r o rs were no l a r ge r than

t h os e f o r t h e smallest f ine ness r a t i o aluminum pr oj ec t i le , which s imulated

cl os el y the polyethylen e impact. Nor

i s

t h e v a r i a t io n i n c r a t e r d ep th s,

as

represented by the

m a x i m u m

devia t ion of P/d from the f i t t e d curve , la rge

enough t o account fo r th e 20 t o 30 percent deeper pene tra t i on of p lat inum

s i n c e t h i s d e v i a t i o n was only

1

percent. Although a di f fe ren t equa t ion o f

s t a t e was used in c a lc ula t in g the one-dimensional f low parameters f o r p la t i -

num

(see appendix B ) , i t s

u s e a l s o i s not thought t o be so le l y respons ib le

f o r the much deeper pen etr ati ons .

Ra the r, the poor re su l t s ob tained wi th the pla tinum pr o j ec t i l e s a re

probably due t o the r ad i a l and ax i a l expansions o f p ro je c t i l e ma te r ia l be ing

much slower i n each of t hes e cas es subsequent t o time

expansion

i s

evident f rom table 4 where

it i s

shown th a t , desp i te se l ec t ion

of f ineness r a t i o and leng th t o dup l ica te the impulse

J

of the impact of

the 1 /3 - f ineness - ra t io po lye thylene cy l inder , the a rea

of

the one-dimensional

flow

a t

time t 2 i s much la rg er than in th e poly ethy lene ca se , The same

i s

t r u e f o r sim ulat ion with copper and aluminum, but t o a le ss er ext ent , The

slower ax ia l expansion, on the ot he r hand, i s evident i f one considers the

re f l ec t i on o f the a x ia l r a re fa c t ion from the in te r fac e , which must occur f o r

impacts of d is s i mi la r mater ia l s because of the acous t ic mismatch prese nt

the re .

nega t ive re f lec t io n o f the ax i a l r a re fac t ion , which , i n tu rn , causes the in i -

t i a l

pressure decay a t the por t ion

f o r th e polyethylene case where a pos i t ive re f lec t io n occurs . The p ressure

decay

i s

al so slower f o r simu latio ns with copper and aluminum, but again t o a

le ss er ex te nt . The much slower ra di al and ax ia l expansions i n the platinum

cause the shock pres sure in the aluminum ta rg et t o

be

s u s ta i n ed t o g r e a t e r

depths, thus producing gr ea te r pen etr ati ons . This suggests th e inadequacy of

t h e s im pl e c r i t e r i a f o r pr oj ec t i le d imensions when the physical prop er t ies of

the p r o j ec t i l e ma t e r ia l s d i f f e r vas t l y from those of the low-densi ty cy l in der ,

However, the use o f such p r o j ec t i l e ma te r ia l s i n s imula t ing a c tua l me teoroid

impacts t o develop

a

des ign c r i t e r io n would r es u l t i n an overes t imat ion o f

meteoro id pene t ra t ion a b i l i ty and, the re fo re , l ead t o a conservat ive des ign

fo r meteoro id p ro tec t ion .

t 2 .

The s lower radia l

The much g re at er ac ou st ic impedance of th e platinum causes a l a rge

i

of the in te rf ac e to be much s lower than

8


13/35

P r o f i l e s of t h e cra ters produced by the s im ulat i ng pr oj ec t i le s impacting

a t Hugoniot pr es su re s ne ar 1.05 megabar are d e p ic t e d i n f i g u r e 5 .

seen from the photographs, th e cra t e r shapes ar e more con ica l t han hemispher-

ica l , which

was

t h e r e s u l t o b ta in e d i n r e f e r e nc e

2

f o r the impact of th e h igh

speed po lye thylene cy l inder ( see f i g . 6 ) . However, i n comp'arison, t h e cra-

ters made by the p la t inum pr o j ec t i l e s have re la t i ve ly f l a t bo t toms.

cr a t er s f o r the aluminum, copper, and pla t inum pr oj ec t i le s of f in eness ra t i os

0 .224, 0 .151, and 0 .122, res pec t iv ely , (see f ig s . 5( a) , (d) , and (e)) nea r ly

s imulate the impact of the 1 /3-f i nene ss-ra t io polyethylene cyl in der of re f -

erence 2 . Their p r o f i l e s are compared in f i gu re 7 . Except fo r t he p la t inum

impact cra te r , t h e s e c r a t e r s are

very s im i l a r t o t ha t p roduced by the po ly -

e thy lene cy l inder .

A s

can be

The

The resul ts of t h e t e s t s ind ica te t he fe as ib i l i t y o f us ing s lower moving

bu t more dense p r o j ec t i l e s t o s imula te the impac ts o f sem i- in f in i t e t a r ge t s

by low-density , low -f ineness-ra t i o c yl in ders

a t

met eo ro id v e l o c i t i e s . I t i s

emphasized that the technique i s r e s t r i c t e d t o impa cts on s e mi - i n f i n i t e

t a r -

ge ts , but an analogous trea tmen t of th in -t ar ge t impact might prove us ef ul .

I n p a r t i c u l a r ,

th e techniq ue can be used f o r simu lat ing th e impacts of low-

fi ne ne ss -r at io cyl ind ers of polyethylen e and porous aluminum

a t

p r e s e n t l y

w a t t a i n a b l e met eo ro id v e l o c i t i e s .

I n t h i s a p p l i c a t i o n o f t h e t e c hn i qu e ,

th e impact of a 1/3- f ineness - ra t io

poly ethy lene cy li nd er a t 15.2 km/sec was

s imula ted by a copper p r o j ec t i l e .

The r e s u l t s a r e g iv en i n t a b l e 3 and f igure

8.

The s im ulated penetra t ion

agrees wi th th at e s t imated by equat ion (11) t o the same accuracy as t h a t

obta ined f o r the lower ve lo ci ty s imu lat io n. This agreement impl ies tha t the

vel oci ty exponent of t h i s equat ion appl ies t o impacts of polyethylene a t

ve lo ci t i es up t o 15 km/sec.

impact c r a t e r i n f i g u r e

8

i s more hemispherical than conical, which

i s

a

r e s u l t j u s t o p p os i t e t o t h a t o b t a i ne d f o r t h e l ower v e l o c i t y s imu l a ti o n .

I t i s

i n t e r e s t i n g t h a t t h e s ha pe o f t h e s imu la t ed

A s a fu r t he r appl i ca t ion of th e technique, th e impacts of porous a lumi-

num cyli nde rs with de nsi ty of 0.44 g/cm3 t h a t are s imulated by (1) the h igh-

ve loc i ty po lye thylene cy l inder o f r e f e rence 2 and (2) t he h ighe st ve lo ci ty

c o p p e r p r o j e c t i l e o f t a b l e

3

were determined. The impacts of p a r t i c le s with

th i s dens i ty a re o f in te re s t s i nce va r ious as tronomers have sugges ted dens i -

t i e s of about th i s value f o r cometary meteoroids ( r e f . 5) which a re though t to

be porous.

l eng th

and the ra t io o f t he pene t ra t ion t o the cube roo t o f th e

mass

(P/m1/3),, for

th e sim ulat ed porous aluminum cy li nd er s. These q u a n t i t i e s were c a l c u l a t e d

from the da ta fo r th e s imula t ing p r o j ec t i l e s by us ing the va lues o f t he one-

dimensional flow para met ers f o r th e porous aluminum as obtained from the

appendixes of re fe re nc es and 7 . Also l i s t ed i n t a b l e 5 f o r comparison i s

the ratio (P/m1/3),,

for the impact of semi-infinite aluminum by an aluminum

cyl in der wi th the same por osi ty and vel oc i t y as th e s imula ted cy l inders , bu t

wi th a f i n e n e s s r a t i o o f u n i t y . The r a t i o i n t h i s case was determined from

t h e t h e o r e t i c a l r e s u l t s o f r e f e re n c e 6 .

The resu l t s are given in table 5 , which l i s t s t h e v e l o c i t y

v,,,

2,

,

f ineness ra t io (Z /d ) ,,

,

th e d imensionless penetra t ion (P/d)

1 1

,

9


14/35

The ve lo ci t i es of t he porous aluminum pro je ct i l es , th e impacts of which

were s imulated by the referenced polyethylene cyl in der and t he copper proje c-

t i l e ,

repre sent gains of 59 and 95 perce nt , respe ct ive ly , over th e vel oci ty

of the refer enced cyli nde r. However, t he pen etr ati on simulated by copper

probably overest imates t h a t which would a ct ua ll y be produced by th e porous

aluminum cyl in der s in ce t he phys ical pro per t ie s of thes e two materials d i f f e r

v a s t l y . I n

f ac t ,

th e pene tra t i on s imulated by copper

i s

about 10 per cen t

g re a te r than th a t p re d ic ted by ex t rapo la t in g from

t e

pene t ra t ion s imula ted

these s imula ted pene t ra t ions i n de te rmin ing requ i red meteoro id p ro tec t ion fo r

spacecra f t shou ld l ead to a conservat ive des ign.

by polyethylene according t o th e re la t i on P/d

:

v2 3. Never theless , us ing

The ratios (P/m1/3),

f o r th e simulated porous aluminum c yli nde rs do

n o t n e c e s s a r i l y a pp ly t o i mp ac ts o f c y l i n d e rs o f o t h e r f i n e n e s s r a t i o s , b u t

t h e s e r a t i o s do a g r ee r a t h e r

well

wi t h t h os e o bt a in e d t h e o r e t i c a l l y f o r t h e

un it -f in en es s- ra ti o cy lin der s. The maximum di ff er en ce i s only about 10 per-

cent, which was obta ined f o r th e impact s imulated by copper ,

I f ,

f o r t h e

porous aluminum cylinders, (P/m1/3),

r a t i o , t h en t h e r e

i s

no shape

e f f e c t

f o r t h e s e c y l i n de r s

similar

t o t h a t

found f o r the impacts of polyethylene cyl inde rs i n reference

3.

i s indeed not a func t ion of f inen ess

CONCLUSIONS

The re su l t s o f the t e s t s i n d i c a t e t h a t t h e pe n e tr a ti o n s i n t o

semi-

inf in i te a luminum targets by polyethylene cyl inders of var ious low-f ineness

r a t i o s

impacting a t 11.3 km/sec were simulate d t o within 10 perce nt by t he

impacts a t lower ve lo ci t i es o f aluminum, s t e e l , n ick el , and copper projec-

t i l e s ,

but on ly - t o wi th in 30 percen t by th e impac ts o f p la tinum pro je c t i l e s .

From thes e re s u l t s

t

i s

concluded that the technique

i s

fea s ib le fo r simu-

la t i ng the impacts of semi - in f in i te ta rg et s by low-densi ty , low-f ineness-

r a t i o c y li nd e rs

a t

me te or oi d v e l o c i t i e s , w i t h in c e r t a i n l i m i t s . The

p r i n c i p a l l i m i t a t i o n seems t o be t ha t t he sound speed in th e s imula t ing

p r o j e c t i l e c a n n o t b e t o o small compared t o t he sound speed in th e cyl ind er,

the impact of which i s t o be s imula ted .

2024-T351 aluminum t a r g e t s by cy l in d er s of poly et hy le ne and por ous aluminum

(0.44 g/cm3)

a t

ve lo c it ie s of 15.2 km/sec and 2 2 km/sec, re sp ec ti ve ly , were

s imulated by t h i s technique.

The impacts of semi-infinite

Ames Research Center

National Aeronautics and Space Administration

Moffe t t F ie ld , C a l i f . , 94035, Nov. 5, 1969

10


15/35

APPENDIX

A

DERIVATIONS

The ve lo ci ty v can be rel at ed t o the one-dimensional f low parameters i f

the boundary condi t ions of equal pressur e and vel oci ty are ap pl ied on e i th er

s i d e of t h e p l a n a r i n t e r f a c e ( s ee f i g . 2 ) . These condit ions are

and

v - u p = u t

The

f i r s t

cond i t ion requ i res t ha t the

mass

v e l o c i t i e s

a t the same pressure

up and u t be evaluated

pH, and the second yie lds the r e l a t io n

v = u p + u t

(A31

f o r t h e v e l o c i t y .

The re l a t i ons fo r the a r r iv a l t imes t l and t 2 can be derived in a

manner

s imi lar

t o t h a t i n d i c a t e d i n r e f er e n ce 8 .

11


16/35

APPENDIX B

CALCULATION OF ONE-DIMENSIONAL FLOW PARAMETERS

The parameters of the one-dimensional flow behind

a

planar shock

wave

are

obta ined by app l ic a t i on of t he conservat ion laws of

mass,

momentum, and

energy acr oss t h i s wave. By choosing a coord inate sys tem f ix ed i n t he

un di st ur be d medium, one may de ri ve t h e famil iar Rankine-Hugoniot equations

where U and u are th e speeds , re la t i ve t o the undis turbed medium, of th e

shock wave and the shock-compressed

mater ia l ,

re sp ec ti ve ly . The symbols

p , p, and E r e p r e s e n t , r e s p e c t i v e l y , t h e p r e s s u r e, d e n s i t y, and s p e c i f i c

in t e rn a l ene rgy o f the mater ia l a t t he i n i t i a l s t a t e ( subsc r ip t 0 and a t

the shocked Hugoniot s t a t e (s ub sc ri pt H). For convenience, Eo may be

chosen t o be zero; and s in ce f o r hyperveloci ty impact

two equations may be approximated as

PH >>

po,

t h e l a s t

where th e def in i t io n of equat ion (Bl) has been subst i tu ted .

To so lv e f o r t h e f ou r unknowns 'H,

PH,

u, and

U a

four th equa t ion ,

the equa t ion-of - s ta te o f the mate r ia l , i s r e q u i r ed . I n t h i s r e p o r t , two

forms fo r t h i s equat ion were used fo r nonporous ma te ri al s . The f i r s t of

these

i s

the semiempi r ica l equat ion o f T i l l o t s on ( re f . 9) ,

where

values of the se constants for var ious mater ia ls a re l i s t e d i n t a bl e 6 , as

given by o r adapted from references

9

and 10.

a be st -f i t in te rp ol at io n between cal cu la ti on s from Thomas-Fermi-Dirac theor y

17 = p/po, 1 1 =

q -

1, and

a ,

b , A, B, and

Eo

are constants. The

This formulat ion represen ts

1 2


17/35

for very high pressures and exper imenta l data a t low pressures and i s

es t ima ted t o be accura te t o wi th in 5 perc ent of t he Hugoniot pres sure f o r

pressures below 5 megabars.

The second form of the equation of

s t a t e

(Enig,

r e f . 11) i s base d on th e p-u mirror-image approxim ation. This equ ati on,

( t h e n o t a t i o n f o r

S

i n r e f .

11

i s a) makes use of the l inear approximation

(Co and S are empirical constants) , wh'ich i s app lic abl e f o r many

materials

over a l a r ge p ressure range .

r i a l s and th e range of press ure s f o r which the y

are

app l icab le , as obta ined

from reference 1 2 , a re l i s t e d i n t a b l e 7.

The values of th ese const ants f o r var io us

mate-

The flow parameters may a l l be expressed i n terms o f the Hugoniot pres-

s u r e PH by equa tio ns, t h e convenience of which i s determined by the

equat ion of

s t a t e

used.

I f

T i l l o t s o n ' s e q u a t i o n i s used, t h e most convenien t

equat ions fo r these parameters are

where

sure. The

f i r s t

two equations are obta ined by sol vin g equations (Bl) and

(B2b).

sound,

c 2

= (ap/ap)s , t o equat ion

(B4)

and s u b s t i t u t i n g i n t o t h e r e s u l t

equa tion (B3b) and th e thermodynamic r e l a t i o n ( a E / a p ) s

=

p/p2.

CH

i s t he spee d of sound i n t h e shocked medium a t the Hugoniot pres-

The

l a s t

equat ion i s found by applying th e de f i n i t i on of t he speed of

The Hugoniot

13


18/35

pressure pH i n these equat ions

i s

give n by equa tio n (B4) as

pH

=

PH(PH,EH).

th i s equa tion fo r pH, rl i s o b ta in e d i m p l i c i t l y as nH

=

vH(pH). Therefore,

the f low parameters are ?unctions only of t he Hugoniot pre ssu re

However,

i f

equations (Bl) and (B3b) are s u b s t i tu t e d i n t o

CH =

cH(PH) (B9b)

I f

Enig 's equat ion i s used, th e most convenient equations f o r thes e parameters

are

Equation (B10) i s obt ain ed by sol vi ng equa tio ns (B2b) and (B6), whereas equa-

tion (B11) i s obta ined by app ly ing th e de f i n i t i on o f

c

t o equ ati on (BS) and

su bs t i tu t i ng in t o the res u l t equa tions (Bl ) and (B10).

For

the s imula t ion

t e s t s ,

h e one-dimensional flow para met ers were

cal cul ate d by usin g Til lo ts on 's equa tion f o r poly ethy lene, 2024-T351 aluminum,

AIS1 1018

s t e e l ,

nickel , and OFHC copper and by using Enig 's equation fo r

pla t inum.

parameters

were

obtained from the appendixes of references

6

and 7 .

of En ig ' s equat ion f o r p la t inum was necessa ry s ince the cons tan t s o f

T i l l o t s o n ' s e q ua t io n f o r t h i s material were not avai l able . The constants

used f o r polyethylene were adapted from those

given i n referen ce 10 for a

s l i g h t l y l ower d e n s i t y p o ly e th y le n e and a r e l i s t e d i n t a b l e

6 .

For

porous aluminum of de ns it y of 0.44 g/cm3, th e values of t he se

The use

I n a d d i t i o n , it

was

assumed t h a t t he equations of s t a t e f o r aluminum

and s t e e l al lo ys could be approximated by thos e f o r pure aluminum and pure

i ro n, resp ect ive ly . This approximat ion i s good i n t h e cas e of th e aluminum

a l l o y , s i n c e t h e v a lu e s o f

pH

=

1.000 megabar by us ing Eni g's equa tion

are

wi t h i n 2 percent of the cor-

respond ing va lues ca lcu la ted by us ing bo th th i s equa tion and th a t o f T i l lo t son

for pure aluminum.

u , U , and cH c a l c u l at e d f o r t h i s m a t e r i al a t

Using Enig's

equation t o ca lc ul at e th e one-dimensional f low parameters

f o r A l , F e ,

N i ,

Cu, and W

a t

p~

=

1.000 megabar gives values that agree well

with those ca l cul a te d by us ing Ti l l o t so n ' s equat ion. For each of thes e

mate-

r i a l s , th e values of u and th e values of cH, cal cul a te d by us ing the two

d i f f e r e n t e q u a ti o ns o f s t a t e , a g re e t o wi t h i n

1 perc ent and 3 per cen t,

14


19/35

respe ct iv ely . Furthermore , th e values of

U

agree t o wi th in 1 percent f o r

each

of

these materials except

F e ,

f o r which t he values agree t o wi th in only

6 percen t .

The agreement of these va lues provides confidence i n th e values

of th e parameters f o r P t , f o r which only Enig 's equation was used,

15


20/35

REFERENCES

1. Cosby, W i l l i a m A . ; and Lyle, Robert G . : The Meteoroid Environment and

I t s Effects on

Materials

and Equipment. NASA SP-78, 1965.

2 .

Denardo,

B .

P a t :

P ene t r a t ion o f P o lye thylene in t o S emi - In f in i t e

2024-T351 Aluminum up t o Ve l o c i t i e s

of 37,000 Feet Per Second.

NASA TN D-3369, 1966.

3. Denardo, B .

P a t :

P ro je c t i l e Shape Effects on Hypervelocity Impact

C r a te r s i n Aluminum. NASA TN D-4953, 1968.

4. Nysmith, C . Robert; and Summers, James L . : An Experimental In ve st ig at io n

of th e Impact Resi stan ce of Double-Sheet St ru ct ur es a t V e l o c i t i e s t o

24,000

Feet

Per Second. NASA TN D-1431, 1962.

5. Whipple, Fre d L . : On Meteoro ids and Pe ne tr at io n. J . Geophys.

Res.,

vo l . 68, no. 17, Sept .

1 ,

1963, pp. 4929-4939.

6. Bjork, R .

L . ;

Kreyenhagen,

K .

N . ; and Wagner,

M . H . :

Analyt ical Study of

Impact

Effects

as App li ed t o t h e Me teo roi d Hazard. NASA CR-757, 1967.

7 .

Ro se nb la tt , Ma rti n; Kreyenhagen, Kenneth N . ; and Romine, Dennis

W . :

Analytical Study of Debris Clouds Formed by Hypervelocity Impacts on

Thin

Pla t es .

F i n a l Te ch ni ca l Report AFML-TR-68-266, Shock

Hydrodynamics, Inc., December 1968.

8. Fowles, G .

R . :

At te nu at io n of t h e Shock Wave Produced i n a Solid by a

Fly ing Pla te . J . Appl. Phys., vo l. 31, no. 4, Ap ri l 1960, pp. 655-661.

9 . T i l l o t s o n , J . H . : Met a l l ic Equat ions o f S t a t e f o r Hyperve loci ty Impac t.

GA-3216 (AF29 (601) -47 59) , Gene ra l Atomic Div. o f G en eral Dynamics,

July 1962.

10. Walsh, J . M . ; Johnson,

W

E . ; Dienes, J . K . ; T i l l o t s o n , J . H . ; and

Yates , D . R . : The Theory of Hyp erv elo cit y Impa ct. Summary Repo rt

GA-5119 (DA-04-495-AMC-116

X ) ) ,

General Atomic Div. of General Dynamics,

March 1964.

11. E nig , Ju l iu s

W :

A Complete E , P , V ,

T ,

S

Thermodynamic Description of

Metals Based on the

P ,

U Mirror-Image Approximation. J . Appl. Phys.,

vol . 34, no. 4 ,

P t . 1 ,

April 1963, pp. 746-754.

1 2 .

Van Thiel, M . , ed . : Compendium of Shock Wave Data. S ec t ions A - 1 , A - 2 .

UCRL-50108, v o l s , I and 11, Lawrence Radiation Lab., U . of C a l i f . ,

Livermore,

C a l i f . ,

June 1966.

16


21/35


22/35

TABLE

2 . -

SUMMARY OF PERTINENT EXPERIMENTAL DATA

1

Round

I

aterial

Polye

2024-

E

r l e n e

5 1 A 1

,IS1

018 St e e l

N i

OFHC Cu

568

*

989

994

995

997

990

991

5-108

5-117

5-119

5-122

5.-123

5-124

5-125

5-126

5-127

5-203

5-114

5-115

5-116

5-197

5-213

5-214

J-109

5-110

5-111

5 - 1 1 2

5-259

5-198

5-205

5-206

SR- 19f

SR- 19;

SR- 191

SR-20(

5 - 2 1 1

5-249

5-251

5-207

5-209

5 - 2 1 0

P r o j e c t i l e

Diameter,

d ,

mm

5.702

5.075

5.075

5.072

5.075

5.072

5.075

5.080

5.090

5.085

5.080

5.362

5.080

5.105

5.080

I

4.821

i

4.811

4.821

4.811

5.090

c

4.559

Length,

z

mm

1.8

.411

.417

.417

.411

.818

.826

1.10

1.09

1.09

1.10

.20

.686

.688

.691

.460

.518

.533

.645

.650

.655

.665

.655

.729

.744

.739

.732

.732

.742

.726

.483

.475

.485

.551

.546

.554

Mass,

m ,

g

1.0453

.0233

.0233

.0232

.0230

.0467

.0469

.0616

.0611

.0605

.0615

.0613

.0616

.0610

.0610

.0614

.0752

.lo79

. lo75

.1209

.0812

.0917

.0953

. 1 1 2 2

.1102

. lo88

.1123

.1178

.1180

.1208

.1201

.1190

.1181

.1200

.1171

.2098

.2048

.2086

.1923

.1912

.1935

V e l o c i t y

km/sec

11.3

7.40

5.96

8.19

8.35

7.55

5.86

6.56

6.76

6.95

6.75

6.97

6.61

7.27

7.22

6.85

6.70

5.05

5.31

5.06

5.17

5.44

5.56

5.80

6.03

5.85

5.28

6.06

5.42

5.56

5.74

6.89

7.20

7.63

7.82

4.72

4.62

4.70

5.37

4.41

4.69

V,

Pe n e t r a t i o n ,

p ,

mm

7.54

5.23

4.57

5.56

5.69

6.50

5.44

6.38

6.55

6.81

6.68

6.73

6.40

6.96

6.83

6.66

6.88

7.11

7.29

7.49

6.30

6.83

7.14

7.87

7.98

7.75

7.24

8.28

7.75

7.92

8.08

9.27

9.52

9.88

9.88

9.35

9.02

9.27

9.12

9.42

10.2

P r o j e c t i l e

Mean

finenes

r a t i o

18


23/35

a c

N rl

rl c a

,+ rda

rd k \

E + J b

k a,

o c

za

0 0 0 0 d d 0 0 0 r l N M r l

r l d r l r l d d d d r l r l r l d d

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

m m N M N d L n r l W d d d d

d N O d r . r . m N u 3 d m d N

d N M M N N d N N M N M M

0

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

co a d

N b d

N

d \ D

. .

N

d r

rl

* L n

d N r l

N l n N

N

r l r l

. .

e D P

m u 3 m r . o ~ m r . w ~ ~ u 3 +

N M v) L n N d u3 m

0 0

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

r l r l d d d d r l d r l r l r l N N

b

O N

b m e

. .

. . . . . . . . . .

N

c o d

N

s'

M G E

c -

e

4

19


24/35

TABLE

5 . -

SI MULATED I MPACTS

OF

POROUS ALUM NUM

0.44 g/cm3)

CYLI NDERS

Vel oci ty,

vu

kmsec

18

22

Si mul at i ng proj ecti l e

Pol yeth-

yl ene

Length, Fi neness D mensi onl ess p/m/ 3)p, P/m1’3)p f or,

Z rat i o, penetrat i on, (z/d),, = 1,

cm g1/ 3

m Z/d),, P/d),

2. 5 0. 47

1.4

2.6 2.6a

2. 6 . 47 1. 8 3. 3 3. 0a

cmgi r

Fromtheoret i cal resul ts of reference 6

TABLE 6 . CONSTANTS

FOR

TI LLOTSON’ S EQUATI ON OF STATE

Pol yethyl ene

w

cu

Fe

A1

Be

Ti

N

M O

a

0 6

. 5

.5

.5

.5

. 55

. 5

.5

.5

. 4

.6

B,

Mb

0 .02

2. 50

1. 10

1.05

. 65

. 55

. 50

1.50

1. 65

. 50

.002

EO

a- cm3/ g

0.07

. 225

. 325

. 095

. OS0

. 175

. 070

. 090

. 045

. 025

. 07

Vormal densi ty,

P,, g/ cm3

0.92

19. 17

8. 90

7. 86

2.70

1.85

4.51

8. 86

10. 20

11. 68

. 95

Sources

Referene

9 and 1C

Assume

TABLE

7. -

EMPI RI CAL CONSTANTS

I N THE EQUATI ON

U = Co +

SU

[From ref. 1 2 1

Materi al

A1 2024

i ormal densi ty,

p0, g/ cm3

19. 17

8. 90

7.86

2. 71

2.785

8. 86

21. 43

Co, kmsec

4.005

3.958

3.768

5.38

5.355

4.646

3.646

Appl i cabl e pressure range,

Mb

1.268 0.395 - 2.074

1.497 .883 - 1.444

1. 655 . 43 - 1967

- 693- 1.972

1.345 .015 - 1.022

1.445 1. 009

-

1.491

1.535 . 322 - 2.718

1.35

20


25/35

E-

Figure l.- Axisymmetric, hypervelocity impact of semi-infinite target

by

low-

fineness-ratio cylinder of dissimilar material.

2 1


26/35

(a) At time soon after impact.

Figure 2.- Estimated wave pattern for axisymmetric, hypervelocity impact of

semi-infinite target by low-fineness-ratio cylinder (dissimilar material).

2 2


27/35

b)

At time soon after reflection of

shock

wave

Sp

from cylinder s rear face.

Figure 2.- Concluded.

2 3


28/35

t

X

Note: Not to scale

Figure 3 . - Wave diagram for material and wave motions occurring along

x a x i s .

24


29/35

2.0

I . 8

I . 6

I . 4

1.2

1.0

. 8

pcr

PP

. 6

. 4

. 2

0

- Simulating

projecti le

material

-

2024-T351

A I

-

AIS1

1018

Steel

A

N i

OFHC

Cu

b P t

-

Velocity,

V U ,

km sec

7.40

5 64

5.39

5.48

4.67

.I

.2 .3

.4

.5

(Z/dlp

Figure 4. Normalized penetration of simulating projectile versus fineness

ratio

of

corresponding polyethylene cylinder impacting at 11.3 km/sec.

25


30/35

z / d

= 0.081 0.161

v =

7.40

km/sec

..

0.2

I6

7.55

0.224

7.27

6.70

~ (a) 2024-T35I A I

5.31

(b) AIS1 1018 Steel

5.06

C ) N i

Figu re 5.- Impact

craters

i n 2024-T351 aluminum t a r g e ts produced by sim ula tin g

p r o j e c t i l e s a t Hugoniot pressures near 1.05 megabars.

26


31/35

z / d

= 0.0905

0.102

v

=

5. I7

km/sec 5.44

0.131 0.151

5.42

( d ) OFHC

Cu

0.0933 0.122

4.70

4.69

e ) Pt

Figure

5.-

Concluded.

2 7


32/35

Figure

6.-

Plaster replica (from ref.

2)

of impact crater in 2024-T351

aluminum target produced by 1/3-fineness-ratio polyethylene cylinder

at 11.3 km/sec.

28


33/35

1 d 0.224

( a

1 2 0 2 4 - T 3 5 1 A I

( b )

OFHC

Cu

v

= 6.70 km/sec

0.151

5.42

0.122

4.69

Simulating projec ti e

High -speed polyethylene cyl inder of ref. 2

---

Figure

7.-

Comparison of crater profiles.

29


34/35

30

I / d = 0.151

v

=

7 02

km/sec

Figure 8.- Impact crater i n 2024- T351 aluminum target produced by copper

s i mu l a t i n g p r o j e c t i l e a t Hugoniot pressure near 1.70 megabars.

NASA-Langley, 1970 2

A-3

3

15


35/35

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SIMULATION OF METEORQID-VELOCITY IMPACT BY USE F DENSE PROJECTILE