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ELASTIC-PLASTIC WAVES IN UV0,2 URANIUM ALLOY
H. Bernier, P. Lalle
To cite this version:
H. Bernier, P. Lalle. ELASTIC-PLASTIC WAVES IN UV0,2 URANIUM ALLOY. Journal de
Physique Colloques, 1984, 45 (C8), pp.C8-273-C8-277. �10.1051/jphyscol:1984851�. �jpa-00224353�
J O U R N A L DE PHYSIQUE
Colloque C8, supplément a u n O 1 l , Tome 45, novembre 1984 page C8-273
ELASTIC-PLASTIC W A V E S I N UVo,2 URANIUM A L L O Y
H. Bernier and P. Lalle*
C.E. A., Centre d 'Etudes de Limeil-Valenton, B . P . n 27, 94190 Vi,iZZeneuve-Saint-Georges, France
*c.E.A., Centre drEtudes S c i e n t i f i q u e s e t Techniques d'Aquitaine, B.P. n o 2, Le Barp, 33830 Belin-Beliet, Franee
Résumé - Les ondes de d e t e n t e i s s u e s de l a f a c e a r r i s r e d ' u n p r o j e c t i l e , l o r s d e son impact s u r une c i b l e de même n a t u r e s o n t u t i l i s ê e s pour d é t e r m i n e r c e r t a i n e s c a r a c t é r i s t i q u e s dynamiques de l ' a l l i a g e d ' u r a n i u m UVo,2.
Dans l e domaine de p r e s s i o n c o u v e r t e x p @ r i m e n t a l e n e n t ( ~ 2 9 G P a ) , 1 a v i t e s s e au p r é c u r s e u r é l a s t i q u e e s t d ' e n v i r o n 3,45 kmis, e t l a l i m i t e é l a s t i q u e a ' h u g o n i o t e s t de 1,15 GPa.
La b a i s s e de p r e s s i o n d e r r i s r e 1 'onde de choc d ' i n t e n s i t é 20GPa (29GPa) débüte p a r une onde quasi é l a s t i q u e d o n t l a v i t e s s e e s t de 3,9 km/s
(4,2 km/s) e t l e s a u t de p r e s s i o n de 3GPa (3,7GPa).
A b s t r a c t
-
Release waves cûminy f r o m t h e back f a c e o f an u r a n i u a a l l o y p r o z e c t i l e i n a symmetric c o l l i s i o n a r e used t o e s t i a a t e sorne dynaiïiic c n a r a c t e r i s s i c s o f t h i s m a t e r i a l .I n t h e p r e s s u r e range e x p e r i n i e i i t a l l y covered ( 5 2Y GPa) t h e v e l o c i t y o f t h e e l a s t i c p r e c u r s o r i s a b w t 3,4.5 km/s, and t h e h u g o n i o t e l a s t i c l i m i t (HEL) -is 1,15GPa.
The p r e s s u r e decrease b e l i i n d t h e 20GPa 129GPa) shocl< wave b e g i n s w i t h a q l i a s i - e l a s t i c wave wliich v e i o c i t y i s 3,9 km/s 14,2 ::a/s), ana p r e s s u r e jumy o f 3GPa i3,7GPa).
Using an UVo,2 p r o j e c t i l e launched on an UVo,2 t a r g e t showing two s t e p s on i t s Face o p p o s i t e t~ t h e irapact one, cve r e c o r d , w i t h a P e r o t Fabry i n t e r f e r o r n e t e r , t h e v e l o c i t y o f t h e boundary s u r f a c e between t h e s e t v o steps and a t r a n s p a r e n t : a a t e r i a i ( w a t e r ) .
T n i s set-up i s i n t e r m e d i a t e betweeri t h o s e r e c e n t l y p r e s e n t e d by R. G. Mc Queen e t a i
Il]-
and C.E. M o r r i s e t a l [%]From t h e s e r e c o r d s we deduce f o r t ~ o d i f f e r e n t t h i c k n e s s e s o f t h e t a r g e t t h e v e l o c i t i e s o f t h e e i a s t i c - p l a s t i c r e l e a s e waves c o n i n g f r o m t h e bac/< f a c e o f t h e p r o j e c t i l e .
p r o j e c t i l e t a r g é t window
1 a
Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1984851
CS-274 JOURNAL DE PHYSIQUE
The shock inpeaance o f t n e t a r g e t b e i n g o r e a t e r t h a n t h a t o f t h e water, t h e schesiatic drawing o f t h e waves i s shown on f i g l b ( l a g r a n g i a n v e l o c i t i e s )
II
-
EAPERIIMENTAL SET-tiP11.7
-
The p r o j e c t i l e l a u n c h e rThe p r o j e c t i l e i s launched b y an e x p l o s i v e d e v i c e shown on f i g u r e 2 h e x o l i l a 1151 s l o o l 1151 bulfer l h i PMMAlPOl o r o i s c l i l s 18.1 a i r 1x1
P.W.
-d
l a r g s l l a , and e,ls h o r l i n e p i n s on ji 5 0 c i r c l e
F i g u r e 2
The d i s t a n c e X and t h e d i f f e r e n t t h i c k n e s s e s used i n o u r experinients a r e g i v e n i n Tabie 1 ( X has been chosen t a g e t a p l a t e a u on t h e V p ( t ) curve.
I l i
Copper 1 20 1 o,78j
1,521 -1
Table 1 11.2
-
The t a r g e tAs shown on f i g u r e 2, each s t e p o f t h e t a r g e t
-
deplateci UVo,2 uraniurn a i l o y-,
i s p a r t i a i l y covered w i t h a t r a n s p a r e n t n a t e r i a l ( w a t e r ) useci as winboh i n o r a e r t o r e c o r a t n e i i i o t i o n o f t h e i n t e r f a c e uranium-water t i u r i n g t h e shot.F o r an experirnent, t h e b e s t window j s t h e one h a v i n g t h e sane shock isipeciance as t h e t a r g e t . ù n f o r t u n a t e l y , i n o u r case, w a t e r i s f a r f r o g t h i s c o n d i t i o n . Sut we chose i t m o s t l y t o a v o i d s p a l l i n g i n t n e t a r g e t , anci because i t s v a r i a t i o n o f r e f r a c t i v e i n t i e x versus p r e s s u r ? i s Icnown f r o n H.C. P u j o l s ' d a t a [ 3 ] . I n t h e p r e s s ü r e range o f Our experiments, t n e c o r r e c t i o n t o i n t r o u a c e f o r u ( n a t e r i a l v e l o c i t y o f t h e i n t e r f a c e ) i s
=
0 3 5 giur i s t h e r e 3 1 v e l o c i t y , ui . t h e v e l o c i t y deUvced f r o z t h e i n t e r f e r o n e t r i c r e c o r d , i a s s u ~ i i n g vacuün i n s t e a d û f t r a n s p a r e n t window)
III - THE MEASUREMENT METMDS - 111.1
-
Chronometric p i n sTwo s h o r t i n g p i n s ( w i t h caps) i n c o n t a c t w i t h t h e f r o n t - f a c e o f t h e p r o j e c t i l e ( a t r e s t ) g i v e t h e b e g i n n i n g o f i t s m o t i o n .
Four o t h e r s h o r t i n g p i n s - t w o groups o f two f o r each t n i c k n e s s o f t h e t a r g e t - g i v e t h e t r a n s i t t i m e o f t h e shock wave i n t h e two p a r t s o f t h e t a r g e t .
The s i g n a l s d e l i v e r e d by t h e s e p i n s a r e r e c o r d e d on an e l e c t r o n i c d i g i t a l chronometer ( p r e c i s i o n +- 1 n s ) . ( s i x p i n s p e r s h o t ) .
111.2 - The P e r o t F a b r y v e l o c i r n e t e r T h i s apparatus has been d e s c r i b e d i n [4].
F i g u r e 3 shows t h e rough r e c o r d o f sfiot n o 2. Tne f o c a l l e n g t h o f t r i e l e n s l o c a t e d between t h e P.F. and t h e camera was 1000 mni, t h e d i s t a n c e between t h e p l a t e s o f t h e P.F. was 50 mm, t h e t i m e between markers 400 ns. The accuracy o f t h e measurement i s ' 7 m/s and? 10 ns.
I V - THE RESULTS --
I V . l - Shock v e l o c i t y i n t h e t a r g e t F i g u r e 3 I t i s o b t a i n e d by t h r e e ways :
a) t i i e s h o r t i n g p i n s l o c a t e d i n f r o n t - and on t h e b a c k - f a c e o f t n e t a r g e t g i ~ e t h e t r a n s i t t i m e f o r t h e t h i c k n e s s e s el and e
b ) t h e P e r o t Fabry v e l o c i m e t e r
-
g i v e s on th$ same record, t h e b e g i n n i n g o f t h e rno- t i o n o f t h e i n t e r f a c e t a r g e t - w a t e r f o r each t h i c k n e s s e and e.
The t i m e d e l a y between t h e s e two v a l u e s i s t h e t r a n s i t t i m e f o r t h e h o c k &ve t o t r a v e l t h e d i s t a n c e ( e 2-
el).C ) Knowing t h e shock p o l a r s o f t h e t a r g e t and water, t h e measurement o f ~ h e i n t e r f a c e t a r g e t - w a t e r v e l o c i t y g i v e s a l 1 t h e c h a r a c t e r i s t i c values o f t h e shock i n t h e t a r g e t .
I V .2
-
The t a r g e t - w a t e r i n t e r f a c e v e l o c i t y v s t i m e .The schematic diagram o f t h e waves i n Our experiments i s presented on f i g u r e 4.
The r e s u l t s o b t a i n e d - v e l o c i t y versus t i m e o f t h e i n t e r f a c e t a r g e t - w a t e r i n t h e experiments a r e shown on f i g u r e 5. The a r r i v a 1 t i m e s o f waves on t h e i n t e r f a c e a r e shown by arrows.
V - DATk ANALYSIS
V . l
-
E l a s t i c p r e c u r s o rTtie r e c o r d e d curves show t h a t t h e snock i n t h e t a r g e t i s preceded by an e l a s t i c p r e c u r s o r . Assu~ning t h a t UVo,2 a l l o y has a l i n e a r e l a s t i c b e h a v i o u r and obeys t o t h e Von Mises c r i t e r i o n , orle o b t a i n s 3,45 km/s f o r t h e e l a s t i c wave v e l o c i t y , 1,15 GPa f o r t h e h u g o n i o t e l a s t i c l i m i t , a m a t e r i a l v e l o c i x y o f 18 m/s, a compression r a t i o e ( = 1
-
V/Vo) o f 0.0052, a P o i s s o n ' s r a t i o v o f 0,19 and a y i e l d s t r e s s o f 0,851 GPa.JOURNAL DE PHYSIQUE
shock o r ++
F i g u r e 4
4.a
-
Diagram t ( x )-
4 . b V e l o c i t y vs t i m e o f t h e t a r g e t - w a t e r i n t e r f a c e1 , , , , , , , , , ,
.5
l i m e Ii s
F i g u r e 5
Diagrams V i t ) f o r t h e experiments 1 and 2
V.2
-
Quasi e l a s t i c r e l e a s e wavesFrom t h e records, t h e v e l o c i t i e s o f t h e quasi e l a s t i c and p l a s t i c waves vs p r e s s u r e are shown on f i q . 6. The dashed curve i s o b t a i n e d w i t h t h e assump- t i o n t h a t , i n t h e pressure-materi a l v e l o c i t y d i agram, t h e i s e n t r o p i c r e l e a s e curves a r e mirror-images o f t h e h u g o n i o t c u r v e . So, one o b t a i n s f o r t h e p l a s t i c wave q u a s i - e l a s t i c wave v e l o c i t y :
. _ s
,,,.... .F".
_....'. .... -
. .. T ,fi,
- -
, - + - ' ~ - p l a s t i c wave -
/
, / u s i n g t h e l i n e a r r e l a t i o n U=A+Bu between
t h e shock v e l o c i t y fU) and t h e m a t e r i a l v e l o c i t y ( u ) along t h e hugoniot. F o r UVo,2, t h e c o e f f i c i e n t s used f o r t h i s r e l a t i o n a r e A = 2,445 km/s. B = 1,665 w i t h
F i g u r e 6
From t h e r a t i o between l o n g i t u d i n a l cL and p l a s t i c cs waves, ( c L / s s = k ) ,
2 2
WC g e t t h e Poisson c o e f f i c i e n t u ( 0 = 3-k /3+k )
.
The Poisson r a t i o v a l u e so o b t a i n e d i s 0,40 f o r t h e maximum s t r e s s o f 20GPa, and 0,43 f o r 29GPa.Using t h e r e l a t i o n s between v e l o c i t y and s t r e s s jumps [5] , t h e c h a r a c t e r i s - t i c s of t h e quasi e l a s t i c waves a r e : v e l o c i t y 3,s km/s (4,2 km/s), p r e s s u r e jump 3GPa (3,7GPa) f o r a maximum shock pressure o f 2OGPa (29GPa).
We w i s h t o express Our thanks t o C. Segard and R. Audebal f o r p r e p a r i n g and making t h e experiments.
V I 1
-
REFERENCES1 R.G. Mc Queen, J.W. Hopson, J.N. F r i t z RS1.53.2.245 (1982)
-
J.M.Brown-
J.W. Shaner Proc APS Shock waves i n condensed m a t t e r Santa Fe 1983 - R.G. Mc Queen, J.N. F r i t z and C.E. M o r r i s Proc APS Shock waves i n conden- sed rnatter Santa Fe (1983).
2 C.E. M o r r i s , J.N. F r i t z , B.L. H o l i a n
-
Shock waves i n condensed m a t t e r 1981 AIP Conf.
3 H.C. P u j o l s P r i v a t e communication.
4 M. Durand, P. Laharrague, P. L a l l e , A. Le Bihan, J . Morvan, H.C. P u j o l s RSI 48.3.275 (1977)
5 J.R. Asay, L.C. Chhabildas, D.P. Dandekar JAP 51.9.4774 (1980)
