Kational Technical Information Service U. S. DEPARTMENT OF COMMERCE

AD-A014 142 NUMERICAL ANALYSIS OF PFOJECTILE IMPACT AND DEEP PENETRATION INTC EARTH~ MEDIA M. H. Wagner, et al California Research and Technology, I...
Author: Baldwin Morris
0 downloads 0 Views 4MB Size
AD-A014

142

NUMERICAL ANALYSIS OF PFOJECTILE IMPACT AND DEEP PENETRATION INTC EARTH~ MEDIA M. H. Wagner, et al California Research and Technology, Incorporated

Prepared forDe'ense.Nuclear Agency Army Engineer Waterwa ys Experiment Station August 1975'

DISTRIBUTED BY-

mJ7J

Kational Technical Information Service U. S.DEPARTMENT OF COMMERCE

T

RTRNISHED

C"

-'I-

OTIE

D.

QUALITYS AVAILABL.E COPY

Ac

01W.1r. L-i

R4

ri

NATIONAL TECHNICAL INFORMATION SERVICE

MPOT DOCUMENTATION PAGE

,ADINS?

s_wf _*r'_"W

W% 1 I"-a

I~.

k.,31

.

t*Or FIlttx#

I

19-

%

*ei

~

t*

4

'Pt

CTl%.

'~

L

,

o

ll*,

194

i AO

wl

RtI,. lr

A 1 i1

1

I*

* of PONT

-it i

.

I7 .

-

-

~

.~

A~~~~&t

Zi

0 0.

S a.

-

weta.*M

a.Ii, ___t_ All. St ,t '-t t@,* . *S

it7

I I

ir •

t

t, r,,.

:.t

.

I

,t

! ?,i fl r

* Soeli ,

'

I.

iC -

"

'.N'

V.

r,

.

Cl~f -'C't#l

. i

,*0 iS' ;" .

-

-C *

' it'.

'a;. .

l'o v

i

C'

;di | mt

-s. S

"* l,

i ",

'

iI

,

rlllt .

-DDC I

O

t

6

" C

s' Ortll. O

i

'.:,s

7"'r' r

*,~li fr 'l :i~a

r ''

".t+

]

t.vrev OD u

. .s r t

i "kit t

.n:

.t, i

f

es

t

, :,

or

nrm

ie

fid)

l

li.il

s

'ron-

of

-

O

:italyl..

, penetration

tC laSo ',i f

V,A oo"

of the t I,

dt'

e

'aur

i

ini itproit

'

I t'

.I

!Pe Pt'

t t It: itpori i ?4 a-

bwi" Iit tit Jut,

-r oArd r rn'tu j 1a.1i:1! A I'N a a_u.II ' out '.ta j'iu LJit . I thti '-, t: ha> t

M

I~~~

~~'

.

t

'

~

ttii at

I

i

:W

~

-'t t

~

4'e

i t i

Jdi rv cn ttI

va a

't

t i rs t _il .:tat, ia n *

of

I tI

-

Jr~ '

r.

~

A

- ;arr 4c t il J

fil

$ k It,

misk tA t'dI .

t.

tin.' 1,i

4 t c't' t!, pr it t ai I a'ad f.: -t vea I J

iart

ti

J1

t'1ft't

t'''

t' ehi' Vjt t t

*t

att

"I;a'atl *-pr4t

V' a

v-:e the

t4 , 1 t etnrit him t, t si.' pi aa'ttk i I e * tt'.a"t' r i.- t,!' t' h y, th~t. Jt t at'tniiug the :tt iti onl. Vt . tawlI de'pth, as

ap'l t~a -ati r-

t, prn

' on

tn-

t i'tu4

C'r:a.tlit

a~~ a

i nt c t iw I - t re'~ ~tL.

load-unload

iN nithitiJ for alleviating

dation foa' analy-i4

110

of' the

nature_

the rigid body' 'eiut

vroitect it ; th -,ia

which

pa met ica I approuth a, To aia iv:e the penietrart~ponN- a; .tt~aproblems. a' Id projetile

afiamy

deteta itid.

il

duting

hif''u'J

4p ate

a

Thu

essenti

h is t ory apied

z I- )figl Iavhstervt K'

ad

ajt ?u no

the Iant

V~ht

i on-

t, p

appA ienf I:y to a1mpIifyvIng,

;r~ttt 1dv.I

.ri!t

o-

we vrnt the

the no ,etip,

in

n t he fo()rLC

I

airI~ i fl itulit 1

on1

the connect ang section

n

*iam r u, ; t~ a~ tc -t

L a

imnali

The maxaimum

n~urrtel near

IT lt

or

tor thu balance

.auri-,t hr

tu ;itnetrat ion Qimitts.

n tie

,

ii -t

t-vc,

v.

Jt- #xI c ra t

rte;Uag

i nra'-nt

or

I x I inch.

It tt I pier'~-te

at i ng t niat

tn

auc

-:

thu

'Ia, ixt, fic

-w urI"t n bat

n

hi

q

for

layer .

'ilI

Wl

v' in-

at

the clantn

carried uut

hi>

into !ht

ihnev in

Aft, rxy.

It ital

n ot

ina Ref.

rriced

out for

the pi '3ettile penetrated

tame, 4

S.

trirou,,h

ir ii

cel I

sizv

th., t

in

eceLlcr it ion1

in t ht onT

.~in,

wCL 1- abohut

390 g's

in tie soili nd 44o g's

wati: I t;'

~~

ieorri~ihI e

;~~fan' ~ tvi'.

1hi

~

tpw

fin i~t.pos

(,r nL"

rigid-!,,oJy

in the

ini ted

t;

iK' i

in-0% :vtI criro ii..

:r

..

rvc4p*n

laver.

k,

w ith

hvste,

if ica I

:'r*''tii ac.

.i-

I st

~callv modelI thia

soi olut ions of deep penetrat ions ate o' for analyigtecmle n-

hi h.1:Lrtuna~tc ly,

into a soft it

earth tar-

i~s 'rot necessary

ion pr'icvsses- gcne:alliv

-rditi'rn,

i

cnarge only

-c. ing d' prt h w it h i n a hniog, reou:

~cbdu. rw

media,

target

tic

of

t'.rce loaidi

: on a projectile by

awtlyzing

just

pcriod and the pe(riods- Where the

etttcrrg different

htt:i ascd

gertlIog ic

4.he penctration dynamic

iti 1 re tsonA le accuracy

ari

ding nut and

snilut ion dcmonstratcs

: ir,:umstances,

c;. n teJtc~c th.-

trat

Ir;,

'In~ler th

and tix*

vn,trtonou;. interac-

conipit~cepcrtratiun in ordei to determine c)nidt in in deep penct iat ions, the target.

p;er.

inii

-'

1 '

it

oil ahead of the

CelY ':

:a Itigh-veloc ity projeLtile

,4(-t

solution, but

-'wdy

taktn to r.i

pectration

although thc

t rdton,f

a pli

tO hi'

itfcrencev ilt,

in the

rel ading hehav ior.

ai

i~2 ie.

!hc

cl i

trong!N

1"" 'tip

unl1

g rJ!

*r- i on o'ct r

the

ody and t-itzd-hody periutra-

the rigid

~

ti -111,cA'r

t -e

-

in

r ' sliI'-tantiaI I> allI'eviated hy using

h; c v

it

t.

i.r.lt

The aveage~

the force histo"v applied to the

;,

rted it,

t

lI ~

ar

he,.

probhlhfv due to the coi.:-er :oning

le ai I '>oc.

.

The nom-

%a-, _' x

ilatr~s t

ha Ie.

Er o f

.ii 4ut

t",e .

'L:;,I>

pr

S,

hlc Ji c cpancy betwvvyl decelerat iofl
thtI!

Lc

tti

6hi

rr

inJta

;d!ical

.

pr

1h,

I il NOnor

.1

tiolzn

iiv No

-1 so

2

at iori. Nolut ion-

p't irut

tw'

ight.

site p:rof i Ic cons isted of a

ol over shale. hcTc

Sue, of proper-

provided h.- Waterways

Exper-

ebve crzrven were fit by the hyster-

.

[05 ftfit

ina3trial Inidel!; which are

64"

lonv

12

-.

1

' ;i

t /se,:

00

1 .922-~ =129

Depth

1L,/ft

Depth (r)

(t't)

16.5.

c= 2.9501m/c - 12.2

1b/I t

Fl~~

~

~~~v

lo.II~ijtIz r Numrfl cal

IUI~l

44.1

28.35 34.43

4-"4 48 23 19.2

Dimensions in inches

Figure 2.

Peetrjtor Design

/

-

-

~ -

--

a

1

-a-

-

-~

-I

-

-

2:;

.1

*~I

t'*~

.t

~A ~a

-l

a -

~

*

-

'-

4

-

-~

-

.- ~

C

~

~

~o

-a,

.i~ I-.

O~

0 -

a

f

2:;

~

2: -

Lfl

-,

-?*

-B:;

0

*1~

a3

~ ~,

-

a

t-

-

.. t ~ a

1P~

Z

t

-

1

*S

-

0

-

0

-

-

-

-

-'

~ai

.

*

-

~)

1J3

-

-a-

7*

i

-a-

a

4~

D.

~L

.'f.

4.

-

.

0

.,

~

*

I.

~-* -

I a

a

£

-

-.

*I. -

-

--

-~

S -

a *1.

',,

*1 ~

a

-

-

-:

-

-

G~

-

-

-

q~

j

.-

-~

-,

-r.

a

-

-a.

-

-.

-

-e

-~ *-

-

*-.z

~

-.

-

r* *.~D

-

---

9

g

0-

'

.-

*

.

B

~,

~ -

-

-a

~

-*,

*z

-

.5 -

*= -.

.~,

~

0

a

U

.~-

-

1.. -

-

a

.- ~

~*

-

-

-

-

~J.a

described in Appendix A. Figures 3 and 4 show show the uniaxial strain load-unload paths provided by Wl-S,, together with the fits given by the models. [he models are seen to follow the WES curve quite well, with the exception of thu final'portion of unloading

in the ;tronglv hysteretic Layer 1. Figure S shows the -hear failure surfaces. (The upper plot gives the low prcs-ure region in detail.) Table I summarizes the site media properties.

10

VOiW (Josuie'

I

.~O -

-

Wes Rteprvsmntat ion-

.

0

Vwrtical Strain Fiv'ur# 3.

Uniaxia

3.0

. *

4.0

(Ln,;±neering)

St rain LOad-Lflload Paths for Lavetr I (Svi 1)

-Wrs

I

Representat ion

Void Closure

lit

800'-

a.

X

I.4

Vetia igue4

nailSri

Stan edUla

c.

(nineig ah

o

ae

Sae

800

400

-

----

~

200

200

400

800

600

S1500

I Laver 2

20

0

40 Pressure.

Figure

~.Shear raii1urv Stirlces ?.vr2

(Shai h.)

kat

for Layer 1 (Soil)

:ind

SECTION III COMPII1TAT IONAL METIIOD

3.1

lAVF-L CODlP

The NA\VL code was employed for these calculations. WAV.-L is a two-dimensional code %hich solves the equations of motion tor elastic-plastic bodies by means of a finiteditference Lagrangian-cell technique. The mathematical formulation is basically the same as that described by Wilkins. A sliding inttrface was used to allow penetration of the projectile thrr',gh the computational grid. For these calculations, the prtjectile/target interface *a- assumed to be frictionless. A lithostatic field in the soil was generated by pre'scribing initially compressed soil states. .3.2

GRID DECOUPLiN;

The sliding interface formulation in WAVE-L includes the capability for dynamically decoupling or unlocking the grid points whCn a prescribed dtc.upling or failure criterion is met. In a penetration problem, detoupling permits the cells initially attached to the axis to flow around the advancing nose shape, sliding along the interface. In these calculations, decoupling occurred when either the generalized plastic strain, ZP , in a cell adjacent to the axis, or tht tensile stress, -on normal to the axis (slide line) exceeded t ritical values. Generalized plastic strain is defined

as

14

a nd i1 A1 Tle t I " oIf thIte cum u I tiv"e pIa-t el -. :ient tindcr,,' :ntIt,It -Xp'.

J

is .il av-

sN

is~ tnY tv;,e

.

" deornat ion an

0 , aind thus

Of plas;tic stra InI is

it, T.':ed

ih,c: iti%.Il gencral i:ed plastic strain and tensile -,v lu.- s u t

tr o

.,.;er

I aind Liver

here: w

-p

nc

nc

. La

..

I

40 psi

R7oiI

Lavr 2 (shile) .013

,'uring

i.

-ve-io. Ity

,vn( ,rat ion,

the nose oten scparat: . the tangency point the.;

et

-

a n '-

normal .

moved as a free

towing arouti

tron the projectile before reaching

tnte no e and cylindrical body.

a.,

tr. the projecti le was no longer comlrcssive;

Whz n thi-

to the projectil(.

n .hih case

COMP!7TATtON OF STR!-I

boundary

the point, is

it again becomes attached

(Clo: ing of the void would general!v he

expected during the final

The pro)ectile

criterion' is met,

surfacc point and may subt(equently collide

with tht penetrator,

3.3

titC soi 1

.

ca Icu lIat ions, sep; rat ior o" a point could occtir when

the stres: i.e.,

12'1

stagtes of deep penetration.)

t

conttur

point:, spaced

along

ACr!i% is its

ON PROJECTILLI

dcfincd by a series of periphery.

plastic, or deformable projectile, these

(in an elastic-

boundary points

are corners of the cells used to d,s.z ibe the projectile.) Ihe projectil,,surface line constitutes a slide

line.

-;tre'LNCN a:c

ire tr-an-intteJ

I t ict i-i't rule.

th ii

oniv no+:,a i lInt.

tirtace

the

+++trtt'++-

I

icro-s

str#'-es

normilI

of the projectile

t:. eslide

line

accor-

F-or roth of the present cal atress applied to etch surface segment Referring to

iV determined is followr

the exadmple shown in the 'ketch below, the stre.ss compo'Irit' rn2: t

It: -

r directir

3, are compted at

trret

cells

tav

srgm'e.nt.

ceirfred qtat

to t*+' prtiv

hive the nc' t and

ti,,n

1.2

k,,A

to

-+_11 point at the or igin initially de-

coupled and to a'sign.zero point. - Pis

it

it

initial velocity to the soil

procedlire wa.. -ised in the rigid-body pcnetra-

.itition described in Section V. ILFORMABLL PRO+jECTIILi SnLJITION RESULTS The deformable-projectile penetration solution was

carried out until the nose was completely buried, with the ti , at about 20 inCheN dtpth. This took 0.837 msec. The computational grid, particle velocity field, and principal stress field at tKiN

time ate sho n in Figures 7 to 9.

20

04

0 'T-

~ .~.

~

4

"x"denotes material In cell has e~xperienced pl:'-, flow or failure SOrpAnIfe during soitir,

~

-4

211T

I

_ _ _ _ __

_

_

_

_

+

c,

O* ma. smO- t nceu

r

SITftsGnArgs~r 1610 99#.

urn If'

r.06

tf*f WIT

-

-~ I-~

. . **.

RAIU IN FigueR 8 i, i t

. . . . . . .

T3-24UE evr,,*Kd da

llootI ;-e I

n et

mIlo. Mgf-10 PCttm~tm 1W

C CCLZ tIil

0S

OF St PR.JICILE IT W?~ LMUTh 0 .001016

901L

see

co

00

.61

i

t

H:.

,v

t'.

o 0

0

coo

.

.

...

.

6.

-1

-

it*

.

P

.

k

IL

P.

10

5.I.20

. IN. ARIU 1. k' 4c.

0.37 %c *l 1Cs A

t

0i.

et

MSEC

pla stIic

fl ow or

t iIe ra. it

cefit

ilart

f.

A tolanic of t!,. ld.

lhe

rce'0

p aN? it 1,

'0nt ha'i

Je-torrnat ton

ti

n1.

3 pro ' ec-

1 radius has1

re 1% cia st ac

rid -

in

-15tj .

f :t Id plots AItained entefred th %

sI t

NolI

ex

-

the

the nose w it h thle body.

.t~i. it coillic t i it)

tht' Ipro je!-

the

outw~ird to abiout

uctti

in

fhas vXperienced

t -mv dur ing:

N-:lc

the rnse ttp, about

for ,It;.

A,

the symbol "x"

)

0i -ad ot

A -,(ret -- cf tht nit

at

ext endlin,

-tI

t:i,

th in aaal:a r

tt

ird tF:aguire

that nateri.i! in 'tint tell

a cellImxac

fasI

art1

t le IJvran

In

>uai I

from thi s

i s vgiven

solu-

irit Appen -

jit I '

Ific

initFigure-

it,

to tIl at a at t ragt I

dV

ueri!ll

I.N1h.

!?

hi

;eI-

tu

ctv it otti All.

Aftt-r

n

tht

*

J%,nami.

poet ra t a'on ,

athut t t

_1

)w

I '-

I,

;r

iloi:

it

hjstorre's of tfae ind resNulIt i ng

e, i vi: tc Iec

*and

depth oif penetra-

corfl' pondisng to o' intc hes of

-,c,

rag',

a Ct

prolect Ile are ,unnarj~ed

tccelerat iont

level had reached

Jill It to! persisted until the end of the towut S5 g*';. Jout ton, tic -patv Cie ftct that secpar at ion het hevr the oIi an I ;,ro t ,t I It. msecwh t i:t mndn

th ii;

first 6 inchetarict' t 'ift1.force and

1.1 t

ortc

thle I~

.. rgt

f(o I v~

'

n til

11

inches depth.

ap Itt d

by

thl. -oil

u

ttipl wet'c ot ri'cs

I

l a

~tru

ecct'Ieat iion

tnreractioo-, betweer!

of

zoning ind thr -trot.. lv hr -tertitc 'h flit Ig miodel u.cd t'dtf t ini

-4

IithI

to thle

the polm

Figuti

in the

Ilt are due

to

nature ul' the computational

tio- Iinit'

will be dacstIftrth'r

in

i.

Pai dom ina te aanpor-

whiach ;ire ;tpp.ateunt

'

a1bout

abouit

4. t i;l, iat

si

ttha t

lad niot oc t itartillt Ii

-on '!ac'

charac tt r of the unload.ar I -otv. This, problem

,tv'tion

with the rigid-

em r u m uwe-

,

c ug w. tg

a

0

0.002

.4

TIE6E

r -

!

.008

11m11101111 scene m aswOSU

ITWM or VTm

SW

i

m ue. tat. tLU IliS Sit

ud

0.

A

TIE

Li

ueII (26

Pu

t

eV

SE

o

v;TrDfral-iySlto

.

0.tt-

tce/"&

auiug

~.

iWOTIM

0.ffu0

I

acft

osM

0vumw . 0

0.4 Mti~fSVELPCVL

T

SS

0.9.

1 an

11,xJv so lit 141

-ursarr

I

F i iur

learF

it

st resses

ive

t Ihe peak compres

.i

ic roij tt I It.

i1 t

X'!,.tivfit:d

VI.

)t 'Wt to

( ol id

suriace

The peak %a uses x i da-hed cu rv&e. curv, I aid lIong it arc prub,.I': o)-ttr dtated dev to tie numericafll ! os:i Lit ton ),f t hto project ile, but tfhey --how in the oiria :t load i the locait ton ot cria 't;

I he night 4t

regions

in

ti lt rojuct ile. 4 inches

th" firt

in

art: cpericncd

s-t-v

otf rifc Jio-v t ip

Irt re%,

sca

and in t)a- thtin .anul|ar rtgion conne-.ting t()J.

i atsveIy tl modest comprcss ive t the waI I of the projcct i l . ii i t t , t rc>e!-, t ci, cd :)0'ar thc axis of the proLc e tt 1i- on I- t|ptr

te

ftli no-p %,ith

a- i

til,; n rt-

in

F ;gasrc 9. IvI .nu

prof ic')t

time>

c(IIsion

leftward compon-

bh the v- ctor%having

-hown

-

Just

rss

I

, vs distatce

de the proiject ale surfacr at 4S equence

ii-i

ipat :t,

after

owh 'iino

i

x..'.

+j',+a )/3

I

in

along the pt riphery of the projectile. of inlreasing ttres- along the pfojectile

the row of steel The progresis

seen.

All

after .1 ms c "how a sharp drop about' S in. At tatcir t imes, the meain nornal hajck f:--i the no'- ti p. of the profile. -,tie-N ped and bodY stre-

~

a~.l

ntcaT

thrliat)r'o

a

21)

jilthest.

~vs dai-tance 1aofiles at the

sion occur-

F igure

ILading stirface of the slug.

around its periphery.

txe-,

lb shows mean normal

along the projcctile axis.

erating force on tht cyl indrical

ported fiont

c')nnection huctween the nose

Tis

slug

is

Ten-

The dvcel-

being applied only

produces tension in

the unsup-

.irtact ;cvi.-ty

and displacement

histories were ob-

tained at several station,; in the soil and within the projectile.

fhee are available to interested readers in un-

published form at W11;.' 28

F-

-P.

4, .

-

.0

I

-

.4

I

I

I

-

A I-

~0

-.

~t

~J ?.

Q S

'a

A

I! II

Ii

U I

.4

r

S..,

-4

.1

f.J

(4A

~i1v

.4

~'

0

4.A4

C6

300

060 I

Z:

kT

40 c1

0 - r.i-2

-D

~ -t

.1

£~4 '

44

4

t-

rpo

ST-TT

Time (iset)

2.5

Depth of Nose Tip (in-) 6.33

4.264

I

.411

9.84

.837

20.03

D lstance from nose* rip

q

protetti

1.5

iLi

,

'-Plot

nean normLl stress ells

a.0

lud

1

-

;--

-

10

0

Figure 16.

--w-

....

-

On Ita

bdy (f1at}

Distanrce from Nose Tip,

Mean %or'nal

in.

Stres. Profiles Along Projectile Axis

32

1

-------- t

1040

20 .,xial

1

2

in this row of

a31l

-.

Axis

;E(C r IoN V RI c;II)- B¢)fY

OLIIT![

In a deep penetration, the target material undergoes large dictort;ons, while the projectile does not generally und'cr1..o anv .in

itf icant plat

ic deft),rmat in .

To anal, ze

the long t inLe proccs.es of deep project i 1,: peietra ion, including the projectile r-c;pon,;c, with a cor ,lete elastic-

ptlastic code solution -ould require an imi'rractical amount ,t computer t ime. This situation can be alleviated ht reat in:.z the pr,) %:ctiIea -; a

the soil

rigid body,

respinse and consequent

,hile anal.-ing

forces on the proj ect i le

surface using the regular elast ic - p

.t ic

the cd..

is

:t

The rigid-body as urmption

formulation of

.iu-tified so long

the proje~tile deformations -are not large enough to

significantly

interact with the target

response or pene-

tration dynamnic-. Th'e advantage of this approach is seen in considerations.

Zi;e folo!Wing

'Computational time is determined by the

totalnnher of cells and by the numer of integration cyc-es in a solution (i.e., thc total number of cell-cycles). The number of cycles is proportional to the reciprocal of the time step, whih in turn is set by the time it takes the fastest wave (generally a dilatatin:l or -ound wave) to cross the smallest cell dimension;

%tmx "

the projectil, as a rigid body, be reduced, (i)

-

ma c

mmn

By describing

the computational time can

since:

Larger cells can he iied (the sriall cells required to re:olve details of the projectile response are no longer needed)

33

2;

Longer t 'me step- van le u:.ed (both hucau'e of cth" ize

"aI .-ti

interior

h.d,

doc ; not prec lude analysis cf

1 apptroac ,t of trres,

the projcctil,.

loading historic,s

Vm-v

;Yv ha '.1

A; )

ho2 c, Von'i

.

imposed on the pr;-

1

This coupled tech-

, 1 yed on another i"ro

m.

; ai

,:ntour

Iht

.

foWr t he r i g id- body so-lutin i s of the penetrator peri-

'd w ;th a total of 33 latt ice points, IMc computational grid :n the in. intcrval . dlivided anto two pranc ipal regions, as shown in

at ;,

!-r,,r the prreble', axi,

-; o.itct

Ma ncrL.,1cd

lht- grid txended to a radius of 7

mtp-.

In tn, It retaA z

region,

the

vertic

al

inrUrtasing depth)

(ith-

'r .

a r"i x". iaa

ot? -v rt gio;

of synaetrv out to a

in., ani form zoning of 2 x 2- in. cells was 2Ai-tn. .adips., the ria! :one width was in-

- fm,.ead Ii

ftc in?

.

itself.

iv'-alt

ed in

3,1

tl

iut at :,,l

I agiare 1. rad itus,',.

ptenctr:ator

I

fti"a

r

zpawAl., t:ir.:t

it, tip

fvu, c--. s..

0.

con -cr'.vm;

a

It fL t ing thm

-otit

.a . ia t he def.rmahlut alrC

From the rigid-

ct are detcrrrine,. This information can then to "tr .;e" a deormable body anilysis of the stress

r-

cr,-

to projectile materia.aIl

:if

,o :- .d .

* itd hcc,:aa.e of tie lower sound a-- ,ciattd tuath soft earth mAter-

t - con: rated

'

ioin,

atct,ic

p

-

t .

o!

r cells,

umaa -- I

sptt

f 10

t

i'i

.

:\

in i01 steps until

cel!, , without

signi-

ion. ody case,

the K-line running the axis of the tarline was used along

Ut? pe,'nitrator cieritt ;ar and along -i

A:

rhis design for the

':o.

imattion:I

:one width

4-,ther AIide

34

NOW 00. SMO-4. 1:0t10W ow 0a____________

o CYCLE

(RRI

INl

WILS

U!

CM

0

C3

LL.

2.5

0

RADIUS Figulre 17.

Tnitial

(

I

5.0

FT nfig.rat

;--'n frr

P.g~iTd

Solution

SITE

1Kt

h'ti..datrv Ia twvrsaI tilt,

,N.Ji r ti,

iccommJ~'atu

t-1,

!I

11 I0

4%ilt

NIktII"J(''

O~li

m

Olifv

r;f:.fistp

A

J Ii':.d

p0

1i t

1V011;id

dJ I U

i

Ilet.

ta

.tfk

lt

o

the t

i-

in

int

1

I;k 1 .4 onI

t

ho!

:t t

i

i

!

dvIL t ions of dI celIlIs in

t niI

fronit

tt t tfi tilt

in

illfu

prlo

tech

t cnrd t !u

It)_ .h!etd

fr4I.

411

v

it

n'vo'v~ti

it'vi

I~

t.,t t I i'',

t '"

-inlMmit

r-

.sil

he

One plOt' a V

i :itv Ia;,(-

. ir'

dav t-

ite

;I lI

ierIa

deplthn1.

I Is.

pcne t

.1A

sho u

I'i t

toni

,

i

tnotcho>

J

1wri

ic

c t i Itc to viia ft'ct

r'':1I

122

uftit rscr .

t i

init

Y r;

t 1w

t

irmpr 4 i L

I igure Ii,

Remt.r'hcr

.

relat i.'e to

ud i -.ttarlI Id

1a11t t

h l'ijt

di A I

ftick

th1t

ionl

it

Jr at 4ioa

velI''1c it

andt

the

iad tit, i I vrtalic h'cd t K' hot tom of

it

I It

i~ilf't

tft tr

(,.I

41 lim, I

t,

t t I

I'

1and thiir

tie

ii.

it

I uigvr have any .

;rt-

t'c p) tilt?

At ;,tve

t .I k' 11I~ in

for a'' lit

-cct i I v

pzo'

!t

L14 iiii. no

on the ;antra

i:

It

;vt

t t-t a Iota I

itI'i t4. a

4l

W:

,

. it

t',

o

La''

4T id

,! It'

: titI Ic

aI rI ie, t

it

-

I Ito Ilit' s .irc t i-

'

l oi t

I J'

al111

t aI

3 and 4.

aNI'C, i it 1.1I!; decoupled forI

.,"

111

.

point

ice

it

ct

gids t

th!is

Refs

in

laitt

;1ro~i

r

Zt to,

the

of

oocr;At

(41

I,

.,thc ! l

a1t

)

!'

1la',~p lt'it

ht I~ Ii

at i .nlnrtt

us

in

id nean~III

oit1gi

and

l Ill

t hcn ur111

1

.t

.tir 'not' dfokn

JidJd I LI

0

w th

that

SO ilI.)

is

v of' cellI to trilV i

di

t h-

.7 f t

CXa

1j'-

g;Ir id,

-

Coo

I.IF

6.0i

it 1' !.~tf-2e

0

T7

rif

Betr~ It-~

C?7

inr'~tI

'ii*r~

t

2.0 s.

1

.84~E

t

14

i

4. 't

1 1> i

4

Iit

to

a

.cjtn

it

tdit.' Iicci vmid

ri

It

2I .

I j ll--

Ic

t

t

0

f

Ihejd s lt

.1 i ? 2'

t

-

k

d

of

vi.

i~

o it ti'flif

"a'

flu

,

iz t

Ud

I

Jt

t !tt. g

La~ I

fiv'i I

I41 .:;

U at!

gta a0t ;.1t

t, il I

I

t

PI

.

a

t

t It !'Ii

litds1 1-

If~

a

C

lftl j

ItfiT

;

I

la

tI t

1

'tt~- 3

ItI

;

I I1

11

I

.

tf

g

it t.

f!

I A'itv

l

I

t It

F-dc t'

t

tII

,I

pft

.t

j

cit!.,

A

t I oc

t~1tti

if ri. t:.i ui l , ,, l Iv ' l i,"

.-

tf~c%

I.,

I t

i.

ctII

;'1T-

ax;L t

n-

,itI I

i i

Il

zcatI hI

1

I

ka

i

c 'h

Ia.f .

-t! a t ,, I ('1 , i

int .i

3-

t lt.

t

I.

-

t.~~~

T

fi

t

&..

no! ';,

fi-gt id

;t

-1 Ut cCn

ONiI;I

. ;wt.g m

I

N, !,urO1-

: t-

h

:I

-,l fl

tat is

lit

!!

r!

tOI

l lI b

: II t

it bort v~

atli

ir

t

tbI1lt. 1t. t I, lit r t 2o 1!: st .wi tII i t'd Itd I t i n I!! i tI ca Io t', 1~. c i t cf ,s tht1 i! t In L It lit-J I"t 1> I t ti 1I e*t ttl Il' I' III a I t d t filit n ill c t kt1-' 'I griit vpna r ttCit it tl 1ht ;l ( t ,r ei lt + all.... i 'S c pt t t11 lf" 11'c.ic I a ti t. t.It z i. h Ii ~nt t m Cel a'vIt tilt c

tt3

1-1

.i

.|-- t It

the p..

ic

t

--I

IIir I

I I'. -1)t -r I i il

paI ra'1it

t

t 1Kl'1

7t, ILl}f

,.

" .I1"C.I

"-. 'vJ, i

, Iv I j

-

i ,lI

t*.

o' i"

t 11

I ,t -

1 It I

tO

t It il

t.'th1 i k t"a

lYr

i

oIf

F

-

~i

IIi

T

a

-

ORD tU! Figure

19.

(Iridl Cont ig-iror

aft~krkvz,39

T1

FT

T

5.76914 I SEC

*n witib Iro ject

.iat

11 .4 f t 1), pth-

F--tm

s"NN"noMP.

msmfe MwosmM

Sol/hl

tS~fc

4. RS

101 W

.

TTa

fiue2.Gi Souin

S4

* 199

ofgrtina rSciea

a

fRgdBd 21 et

O

4. u

CIL Ifoa ts craci a" ... . ...

.

p.

.

IgceuagLSv dVC-L clot

.

2.

:.



.

. .

° - ,

%%

.......-

a

..

RAOIUS cTr l'i

21

.

. .

.

.

11.5799 MSEC n. w!t it ........

gid B''dv

gL" ITI: Les 911 few*

lo

*.w

00a *

-

F

L

#L

F

04

N

A

'

IU

FT

T

*lvr p2

"I ic

-,4 22* * 1

9

45Z 9

1

il 9' 9it 9

e

4

1S

9 &

tZd 1WP1Srs fRgdBd h

ouin

lmnIP: f i. IU-4. IW

I

l

Piy

m

. w

wT to"3 U0ll

I

I

I

I

C'nml a, Ile. 617 8I

t

3--quare

grid

antd grid

I

.ivi'r I

", r

-. 4

0 4

.10.

,

"JO

*

I

1

0O.

2.

4.

I.

6.

6.

10.

TIME fISEC Figire 21.

Axial Force on Penetrator and Deceleration of Projectile v. rime, Rigid.Body Solution

43

I''I

12.

Cawe.:. 2Sync. me CncMsan.

AWi-

MOi.t- RIS-

SOO!Pavrr2-------ISWX

lot.

ff

)C UC

DETHF

I10

Fig-rp "a~t~ttfr - . l

'r. ad

ofPentratr.v

?-7

23 and 24 at early. timc: and at times after about (depths

below about

msec

13 ftj.

In the region beteen about

I and b.5 msec

(about

2-12 ft depth) , regular, much more severe oscillations lhese were apparently due to

at about o ktl: are .seen.

synchronous , amp I it yving interactions between iiature of the grid,

the discrete

the strongly hysteretic nature of the

loaiding iinloading-reloading cycle in

the material model,

and the gross distortions of the cells moving up the The initial

side. of the projectile. city iii the L.ver I modt

loading wave velo-

s ibout E40 fps.

'

Unlo.!ding

alw:i.s occurred at a much higher v( locity; (and reloading The gross distortion i.e., of the crdr of 6000-700IP fps. oi cells mov ing out and ;round the nose caused large ing-unloa,ii:g oscillation, apply ing

in

the few cell>, which wt re

ignificant axial forces to the nose.

sure profiles

load-

The pres-

in Figure 25 illustrate such oscillations.

I-or the reasons cited above, the Oscillations in the solution hetween about

I msec and 6.5 msec

(2 ft and 12 ft

in depth) are greatl'y exagRerated and should be disregai-Jud. Itowevt.r,, the average deceleration in this region ( 425 g's) Ahould '-t ill be fairly realistic.

And indeed it is seen

in

Figure. 23 and 241 that the average deceleration level drops only ahout lot (to about 390 g' s) when the sever, ,,;cillations go away with the introduction of the predeforn.ed, or canted grid.

Is thin dfra'p due to the grid geometry change

as ;uch, or to the el~miiation of exaggerated forces .the synchronous oscillations? grid canting was

in

Apparently the latter: the

introduced in a very gradual

fashion ahead

of the projectile, and it required only the very slight

43

U

--

__--

r

y ~-

-

-

-4----

I

-

I

i1~

-

~ aa ''a

t

.~

-

-

-

--

~-

4

-4--

4

-

-

0 -

4 4.-

4

4

--

A

'2. * II

'P

C

s

~

U!

/ / I

A"

C h~inge

i n gr i

inch. -

ie lou

synchronus

12.2'

( svv F~igure

t

in? eract ion!s.

I roppcd

to 300 i, ' ,

tilt dv,-lurat ion

L.Adicat ion ot

1int rodu

t i on of

ii Iu-t ra

tL'

1,-,celcr~tiun igurce-

2siI.I

u1;ied he?%c.f thti

veloc:I tyvV

t' I 'und

depth11.

the Pro i ect i Ic And target t ion is Oiown

27 and

-'S Kio

lable to

tilt

dececcerat ion ot

12- f t dept L.

440 9' %elocit v 3,JI0 g * s

I i gui e -'9

[nergy pairt i t ion ing hctween

dur ing thv c .Lr -. , of th is

s 6 lu.

3't).

, %. era 1 stat ions whi th in

The -e are a-a form at M~.S;.

I- igur.v

whi ch he-c obta i ned.

% Loc itv o and d isplacement

Stress, obta mned at

1

in Lavy r 2', and

increased ,to about

(A .ons;tant .

I fafter

av(ayr

thlt- predeto rmed gr id ) and

and iep t h hi .-tcrri -s. showh

in Liver 1.

Ir~.t ~IL~ ~2t~t. c-rre~~ue t)4

average

IveccI

the more acturate

as

Ivve

t'

nattv t te

rat ion

i

the >now)ther prof il

in the Laver WaS AS

thiV

rc.ard

few

as t he scvere o-,: i I

As son

it-re rt-Ju-.cA . t hc average dccel1 h

f ir st

to vi I

19~))

lat ion-

[hei

in thti

ieome r v w;i c h oc cu r i d

h is.tor ies khere

the target. mvd' a.

intecrested readers

in unp-tib i-;hcd

~1

2-

I

Li

I

-


W r...:j

a

I

.tV~

ta~ i

I i A't It -antcd,

hyteetit

c~je A& hat ri.r

nuJ w1,

myi

:_

pre-JeloI rmed g I id.

III

trofngly

At table ca~xre nevds to he takun

:i

to Ikp , .r it

-I

i,.

t h~e

poro!, i t

ma~t -t iaIi

m\

ting

in

and t he unload ing be-

~around

a

projecti

It

I. M. -I.

i~ik

nutt

h.Lti vatr 3t) W m; 11

2

I:. Nanr 1

M

hTrogi v:

.al

Xn - I v t i. a I

1~ ",

I w

-

Report on L.ight Armor

t uJd of uPewr.t Hdrotin.ai i c '-

t i Von Wtchan ics" I incMaty 19tb9

Desig

tc XiiIvrt i r a I sCtrojictii.

t;iJ PetrfVor.-tanct",

P p!

1fb

Sic-1 'cK

xd rodvn anics,

Inc.,

~.L.

Mliigptn, 'Pnc-trat ioni of' Proiect ilu into Continuous I a -th Med ia", st, fiP-U 11204 Satndaa Lab NAturies , May 1972 *

"Xi

*

rca! -\uil ; a!~~~~

f.

Ito, h. 'cr \n

".

rr

V

v-it'

I. tlkii'AlCtidlt ton of' Mast it -Plastvic 1:10W1 I~m-une Lvurvi it I thoratilry, * LCIL-'322 Rev. I1,

.

11 .u.ht cr, If. IL , ltrg, Nt' -"~l

I. I.

'1A \Iatl tII crt

Hi lt-(or i'-

"I lit#

.fIX \), -a ith Piett rat or Experimelnt iI i; V1, O)tober 19-4 L CRT R" &ot iX o>~

Kt %eihijgun, G. L. Lgquil, and W. S. lknaxi i-St rt,-us;K t in a Term inalI Pendc rait i on o f a Ilard La rthI i I t, 1ii rlutg nb-I !in pull Va t loll by WIS) 1 cl I t

I11 ItVV

14t-

i

fl

,

S.

P

etav-1

Experiment Stat ion,

,pt>1tcomptunicat I'st;

i.Li I 'I hLetrY o f PIIa>t i c i t>y, of

wi!ulb It 'litti I i]taF-ctc

1"I1.1 1

Xm,y

j

ion

Ox ford ,

19 50

and D)i splace t rt's-('s , VvtIoc i t Ies,. t ont rac t !IW-\39 - 7 - - -0007 Ma ' 19% *ug ? ecttol'

- va I Ch 1

'

au1

.\PVLNI I \ A

ttirni'~heJ h'- hi U'- m'g :ir'afldt InoduI'-

UI

ti~c 'two

for

%taturial i-Udvi"

lr\ SttI

X NiOr

hY -tV ct it

' I- f!t

C

-

6rui

) 1'e

%

1.nijd iri

f~d f k '

Ijeld iu Crv 'I I4V('

jn te

it t

hIas

t

>~~t

-IL

cn

equat ion:

o ne rg-

thio u td

t

I

a hY stcYeet ic

Fn bd e I

t it at u 1

dt;,

'u

mna

ei

on' osta n t

?

-eit-.

1.)ti,

a

ru1L

L; r t

ULtcI

II

low

t i c medel

rI ct I vp

A~

spc -

2

Jtvvcl

Iv pla-t ic

d~ I la-a~~c~tt

I

c la -t i c -

~!C' g

AfC 'ic

whc ,-

A

wehre

V'

I

1.. hd

ideai

itC

t iK Ce

I kk ii-'

1.ivi.

;ite

t ira i m arIa

t.

th

p o itt of void closure,

JduCCLd Irou

~t re'-s

thfe Iload ing

d i f f t-rnce v s

11t ret

~

Bvornd

cry I~ it,

t)

ld %:IO'-.ure, a well

p

u--

t

Aht

an

y

~ ~~

if

~

~

a

v

q

iIi

~I tJ)~ t ~

atj3ji

n

of

d

f

ott

o

tcu

v

(i-dr

11,

!,

rf

:

~

.t:m

X

tw

t-cqui

:

Sitn

a

t

I

I

cd

*

a ,

ed atpn

bhaVII

tit.

a nrg

1;5414,

P

e

l-d ecrtin

o

i.

h

d

n

I

load

Min

Gn unload

-7

loadoa

whe

N

B

(j4

.5

1

)dlh,

! I

. 2 5 e xp

I 7

Initial values of the bulk modulus, th,: shear modulus, the co-nstrained modulus, Poisson's ratio, and the dilatatior.aI sound speed from the model are: Bo = 4,237 psi

Vo = .2S

Go

c o = S42.6 ft/sec

2,542 psi

M o = 7,62t psi

A.1.4

Unloading Model

In the hysteretic region, w

K

valIi e of p rve:

to t he

"rori t he loading hy drosiat equja-

'led

at

yvalualudi

equal

~iflby:

"ohtai

P

,

VO Id c 10U!rc

I klre

k-

from

-

irto--ing a minimumn

l imited by p Si

ai i ! wre Su r fa.

A yivid Su'-.:d

de a

tunctIO

"heiv

r

icd

f

io.~(P) .3. I

uan fit I f alre

to the "

failure envelope

The Amw.t ion,~

lbx I:03I'

-8

Vxl

A

~4.$2b3xl1I

~

CAI 10

[1 sort,

i

I

.tr'~svK

and

I

e

-CXxi

Xvnr oTr r31tv I lo t -l.

U

vs pre,-

for un iaxial

strain

in I igure I in tht: text, and in

t .

isA

Figures

ttI~t 1) 1ix.

4

nat

jay- of state for

i ron was employed.*

I aind 4triength propet' ties, f or the t ii., pt~nnet ratoLNr here 'thlen aidded toc t he modelI. P.O ic-i

tr '

vi

I 74

-- - -- -

P-.4131x11f

stress-difference

trair,

13lx 1

are Mb.

vo I ume t r i c ->tra in

icsliowr, in

P

P24 P,

.

coimputed with the model, along With the

)Jt1!

1

%J

-

andI prc-.surt-

~L-cu~c A

t

on I' ad

tli-

!_or

to itt

Hevre tht

51'24311'

-

f oIlI ow i g 1prope r t itc,

The

densiw~ty

%ormn

K(I

,*hear rnOdulU'.,

.(Ish %ib

V

ril

asn'umcd to he constant

?~ t

~

qijittoo

ih

vi, i-ly

ion,

i tc~r(

of' tf-i

Pit~u~-

Hec

ten- lu

.

v'

-pue-uru I wuVi t ran, i! ion)

equat wfl

tulatei

,

at2

t

and

i-

it'

i eri

cuon.tarits a r c

WHO Mh~~ Nb18

II

it 711~

.~

b

is

[hec1bulIk

.

ti

lintited

ir'ret

t icai~; -; t by

to a

port ion of the pre-

tate of' it-on v:

psi)

N.4cornvt tit iona I

v

crIlit

P"t

',

hr '

111,ISO,=u

.

hith th

tr:

-'

.-

1 .204.xl 1'Psi)

A1i473

Y:

The shear mi~dulus ha a ivu

I 2.445x1(

.;3 %b

.:

vield strength,

':~.d'

1 489J lb/ft

7 .84 grn/cm

,

Hul1k Mnodulus.,

wt- re. ass unid:

covers~

the

-

a!

10

f'-i,,

-. 1

.F.u... N

-~

0

=

-

-

I I. 1-

-'-I

I

-~

-

'I

-

-

1~

*1

/

/

-~

*1 *1. Cd

-

/

.1

-

S

v-i

0

*

'f.

I-. -

*1~ I-

-Cd

I-

~

1.

1

*

I

L~A~~j

-

,l

tI -,ur i i

t,

lro-

100

Il

-

fl,

~

ol

V, ric i-jr~etrai L-ad:Jri~ladCure< fr

0

Laer

-1

f

ivdro- tat

'Volurrtr-i, igivA

nn 21?

Strain~

rod 1.rid ing 1hvii

t-at

for- Iavcr

I

F-

-

-

-

V

7

K

1~

1~

-z -t

£ U,

\

_

i~

V I -4-

-

'4

*

2

I lll

IT

II

Void Closure

1

0'

I

".I ..-

0't0

I))

t1(3

.

I

0,

I I

I.,

I

I. .

(I

l

l

0

I

I_

I

/I I)

.

I *I

/

.

I

/

0

I

i

I

I .t

0I(3

.(I(4

. fil5

.

O

(b

Volumetric Strain,.

A-(i.

llgire



.;

Hydrostaitic l.o:id-(Jnload Curves for Layer 2

APPNEND)IX

'u

0! S ORFI~ON,

1j )C

l-IILDE.!' PO> A part

-ef ics

t rAt

thu:

AND

PkIN~CIPAI. SU ESS

pl'ts

of

the

t it',

:anl

prinrciapal

pro -ivct ail

arid

-oil

it fl na it

it lith

'

3.F

rI

Fi

o

ii

.81

-

tiut'

Plot

I ont'Ioct\

toel

_)r.

-

S

II'-

t

1 (Rezone,

26K

ii- 8

119

11i- IvI

411. o

R

B1- 13

1-14

b3SS h>2

hIS In R 17

lS.6 8 3> 71 . VIC et'locity

12

i1-A19 1.

vector

faid

p - 20

jiluts shcw1

r:aratud(e of

the part icle' v4loc tv

In

stg

;at

each

the direction and 1litt

ice point

gria I

ft4' elt'd pilot-, t~~"li

a 11us

the dufur rtablu*

w n'. raFir

of

grid,

14

3i.

tiau

dunring

e 0C-2 t-

3.210

Irn

whi 1ch

-

.

128.1

t .rilIt

-

urc No.

RH-6

t~~t

strav

art.

V.it:,

____________~~~~

1,-

t orpata-t ional

a e'pwiue

prcpa-,J

It

SO!ITION

'!t)2A11[-Hi'

of ield

vt'ici

icl1e

fl,

F

*

f!

t1*

Tht- principal

coaaponients Of

t-

The mag~ni tude of the two pr inc ipal st re>-,es in the r-,. .1lane atrc plot ted in- thL ir correspond ing principal direc,t ions. 1h;, thi -d pr imc ipal strces (in tile azimuthal direct ion) i plottcd alIon4g thc l ine h -ect ing the other two p rInc ipalI d irect i ,I,;. 'ettors, po int ing to the right are tensile. Ans cxamplc of how a c:opressivv, to t!1o icif, st r ts tvnsor is plotted is s;kctcheid below:

:o- Compressive

'lens ile

Principal Stresses

~in r -z Plane Cell Coneti-.

.-

r

Pritcipal Stress in -Direction

!I

[he first 3-5)

tngures of the grid

three

(B-1,

show the initial entry of the penetratur A local rezont- is

4urface of the suil. in f-igure H-(, pe tt trator

(

Suggest Documents