DUCTILITY AND FLOW RULE OF TANTALUM AT 20°C AND 500°C

(1)

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DUCTILITY AND FLOW RULE OF TANTALUM AT

20°C AND 500°C

J. Giannotta, G. Regazzoni, F. Montheillet

To cite this version:

J. Giannotta, G. Regazzoni, F. Montheillet.

DUCTILITY AND FLOW RULE OF

TANTA-LUM AT 20°C AND 500°C. Journal de Physique Colloques, 1985, 46 (C5), pp.C5-49-C5-54.

�10.1051/jphyscol:1985507�. �jpa-00224737�

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Colloque C5, supplkment a u n08, Tome 46, aoQt 1985 page C5-49

D U C T I L I T Y AND FLOW RULE OF TANTALUM AT 2 0 " ~ AND 5 0 0 ' ~

J.C. Giannotta, G. Regazzoni and F. Montheillet

~ c b l e des Mines de Paris, Centre de Mise en Forme des Matdriaux,

(UA

CURS 8 5 2 , GRECO Grandes De'forrnations e t Endomagernenti, Sophia A n t i p o l i s ,

06560 Valbonne, France

Hesum6

-

La d u c t i l i t e e t l a l o i de comportement du t a n t a l e o n t b t 6 B t u d i e e s

3 20 O C e t 500 O C dans l e domaine de v i t e s s e de deformation

-

2 x 1 0 ~ s-l.

On montre que l a d u c t i l i t 6 est e s s e n t i e l l e m e n t d e t e r m i n e e par l a s t a b i l i t e de 1 '6 l o n g a t i o n , q u i elle-m&me r 6 s u l t e d e s v a l e u r s d e s c o e f f i c i e n t s d ' 6 c r o u i s s a g e e t de s e n s i b i l i t e 3 l a v i t e s s e . A l a t e m p e r a t u r e ambiante, l ' a l l o n g e m e n t ?I l a r u p t u r e e s t une f o n c t i o n d e c r o i s s a n t e de l a v i t e s s e de d e f o r m a t i o n dans t o u t l e domaine e x p l o r 6 , t a n d i s qu'3 500 O C il

est

p l u s

e l e v e aux g r a n d e s v i t e s s e s que dans l e domaine q u a s i s t a t i q u e . Ce comportement e s t analogue 3 c e l u i du c u i v r e

P

20 O C , b i e n que l e s deux metaux a i e n t d e s s t r u c t u r e s c r i s t a l l o g r a p h i q u e s d i f f 6 r e n t e s .

A b s t r a c t

-

The d u c t i l i t y and flow r u l e of t a n t a l u m were i n v e s t i g a t e d a t 20 O C and 500 OC over t h e s t r a i n r a t e range 10-" 2 x 1 0 ~ s-'. I t was shown t h a t d u c t i l i t y is e s s e n t i a L l y determined by t h e e l o n g a t i o n s t a b i l i t y , which i n t u r n is c o n t r o l l e d by t h e s t r a i n h a r d e n i n g and s t r a i n r a t e s e n s i t i v i t y parameters. A t room t e m p e r a t u r e , t h e e l o n g a t i o n t o f r a c t u r e d e c r e a s e s o v e r t h e range of s t r a i n r a t e s i n v e s t i g a t e d , whereas a t 500 OC it is l a r g e r a t high s t r a i n r a t e s t h a n i n t h e q u a s i s t a t i c range. This l a t t e r b e h a v i o r is s i m i l a r t o t h a t of copper a t 20 OC, a l t h o u g h t h e c r y s t a l l o g r a p h i c s t r u c t u r e s a r e d i f f e r e n t .

I

-

INTRODUCTION

I t h a s been s u g g e s t e d t h a t t h e e f f e c t of s t r a i n r a t e on t h e e l o n g a t i o n t o f r a c t u r e is c l o s e l y r e l a t e d t o t h e c r y s t a l l o g r a p h i c s t r u c t u r e of t h e m a t e r i a l . A t room t e m p e r a t u r e , Kawata e t a l . /I/ have e s t a b l i s h e d t h a t d u c t i l i t y is l a r g e r a t high s t r a i n r a t e t h a n i n t h e q u a s i s t a t i c range f o r f c c m a t e r i a l s and c o n v e r s e l y f o r bcc s t r u c t u r e s . T h i s g e n e r a l t r e n d has been i l l u s t r a t e d by t e n s i o n t e s t s c a r r i e d o u t on p u r e copper and t a n t a l u m a t room t e m p e r a t u r e /2,3,4/. I n t h e p r e s e n t p a p e r , however, t h e u n i a x i a l t e n s i l e b e h a v i o r of t a n t a l u m is i n v e s t i g a t e d i n more d e t a i l a t both room t e m p e r a t u r e and 500 O C . Oue t o t h e high m e l t i n g t e m p e r a t u r e of t a n t a l u m (8,=2996 O C ) , room t e m p e r a t u r e (nD.09T ) c o r r e s p o n d s t o a "low t e m p e r a t u r e " t h e r m a l l y a c t i v a t e d r a n g e , whereas 500

n b ~

( - 0 . 2 4 ~ ~ ) f a l l s i n t o t h e s o c a l l e d a t h e r m a l range. The v a r i a t i o n s of d u c t i l i t y a r e d i s c u s s e d on t h e b a s i s of t h e observed s t r e s s - s t r a i n - s t r a i n r a t e r e l a t i o n s h i p s a s w e l l a s t h e o b s e r v a t i o n of t h e f r a c t u r e s u r f a c e s .

I 1

-

MATERIALS AND EXPERIMENTAL PROCEDURE

Two d i f f e r e n t shipments of t a n t a l u m were used f o r t h e e x p e r i m e n t s a t 20 O C and 500 OC. The former was a 99.80

X

p u r e t a n t a l u m , p r e p a r e d by powder m e t a l l u r g y , and t h e n r o l l e d and anne l e d . The specimens had a gage l e n g t h of 30

₉

mm and a s q u a r e c r o s s - s e c t i o n of 9 mm

.

The g r a i n s i z e was somewhat inhomogeneous, with an a v e r a g e v a l u e of 60 +m. On t h e o t h e r hand, t h e m a t e r i a l used f o r t h e t e s t s a t 500 O C was a

c a s t 99.90 X p u r e t a n t a l u m , which was f o r g e d and annealed. I t was s u b s e q u e n t l y

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C5 -5 0 JOURNAL DE PHYSIQUE

swaged and h e a t t r e a t e d . The s p e c i m e n s had a gage l e n g t h o f 15.7 nun and a c i r c u l a r

2

c r o s s - s e c t i o n of 5 nun

.

I t was assumed t h a t t h e d i f f e r e n c e s between t h e two k i n d s o f s p e c i m e n s would n o t a f f e c t t h e main t r e n d s of t h e m e c h a n i c a l b e h a v i o r .

The t e n s i o n e x p e r i m e n t s were p e r f o r m e d u s i n g an I n s t r o n machine i n t h e q u a s i s t a t i c s t r a i n r a t e r a n g e 6 h 6 5x10-1 s - l ) and an i m p a c t t e s t i n g machine o f t h e "cross-bow" t y p 5 d e y e l o p e d by t h e Commissariat 1 1 ' E n e r g i e Atomique a t h i g h s t r a i n r a t e s ( t

>

5x10 s- ). Due t o t h e h i g h f l o w s t r e s s o f t a n t a l u m ,

it

was n o t p o s s i b l e t o r e a c h s t r a i n r a t e s h i g h e r t h a n 2x10 s-' /5/. Fig.1 shows t y p i c a l l o a d v e r s u s

time d i a g r a m s o b t a i n e d a t v a r i o u s r a t e s and t e m p e r a t u r e s . The i n i t i a l peak o b s e r v e d a t 20 OC is a dynamic s t r a i n a g i n g e f f e c t ( F i g . l a ) / 6 / which v a n i s h e s a t 500 OC f o r t h e two t y p e s of t a n t a l u m ( F i g . 1 ~ ) . The i n t e r p r e t a t i o n of t h e dynamic t e n s i o n t e s t

r e q u i r e s some a s s u m p t i o n s /5/. The s t r a i n r a t e is d e t e r m i n e d by t h e r a t i o o f t h e mean t e n s i l e v e l o c i t y t o t h e i n i t i a l gage l e n g t h Lo, e.i. h

=

ALF/(AtFLo), where ALF is t h e e l o n g a t i o n t o f r a c t u r e and A ~ F t h e d u r a t i o n o f t h e test ( t h e o r d e r o f m a g n i t u d e o f A ~ F is s ) . A t t h e b e g i n n i n g of t h e t e s t , t h e d e f o r m a t i o n is inhomogeneous w i t h i n t h e s p e c i m e n ; i n t h e c a s e o f c o p p e r , however, it c a n , be c o n s i d e r e d a s homogeneous when t h e e l o n g a t i o n r e a c h e s a b o u t 10

X

/5/. The i n i t i a l peak o b s e r v e d on t h e d i a g r a m s a t b o t h 20 and 500 OC ( F i g s . 1 b , d ) h a s been g i v e n v a r i o u s i n t e r p r e t a t i o n s /2/: d i s l o c a t i o n dynamics, r e f l e c t i o n o f waves o r i n e r t i a e f f e c t s . I t s h o u l d be n o t e d . t h a t t h i s pea$ is v e r y l a r g e i n t h e case o f t a n t a l u m which is a h i g h d e n s i t y m e t a l (p=16000 kg/m ); t h i s s u p p o r t s t h e i d e a of an e f f e c t r e l a t e d t o i n e r t i a . T i m e F i g . 1

-

T y p i c a l l o a d vs. time t e n s i o n d i a g r a m s of t a n t a l u m s p e c i m e n s a t ( a ) 20 O C

and low i; ( b ) 20 O C and h i g h h; ( c ) 500 O C and low h and ( d ) 5UU O C and h i g h i. I 1 1

-

EXPERIMENTAL RESULTS

D u c t i l i t y . I n u n i a x i a l t e n s i o n , d u c t i l i t y can be measured by t h e t o t a l e l o n g a t i o n t o f r a c t u r e e F

=

A L F / L ~ and t h e e l o n g a t i o n t o f r a c t u r e o f t h e homogeneous p a r t o f t h e s p e c i m e n , i . e . eH

=

Ao/AH

-

1 where A. and AH a r e t h e i n i t i a l and f i n a l c r o s s - s e c t i o n s , r e s p e c t i v e l y . The e l o n g a t i o n eM c o r r e s p o n d i n g t o t h e maximum o f t h e t e n s i o n diagram is a l s o u s e f u l f o r d i s c u s s i n g t h e r e s u l t s .

A t 20 OC, t h e e v o l u t i o n o f t h e t h r e e e l o n g a t i o n s d e f i n e d above a r e v e r y s i m i l a r ( F i g .2). I n t h e q u a s i s t a t i c r a n g e , d u c t i l i t y d e c r e a s e s c o n t i n u o u s l y ; a t h i g h s t r a i n r a t e s , it is v e r y low, a l t h o u g h

it

seems t o s l i g h t l y i n c r e a s e w i t h s t r a i n r a t e . The r a t i o A ~ / A ~ o f t h e f r a c t u r e a r e a t o t h e i n i t i a l c r o s s - s e c t i o n r e m a i n s c o n s t a n t and e q u a l t o 0.01 o v e r t h e whole r a n g e of s t r a i n r a t e s . The f r a c t u r e s u r f a c e s , however, e x h i b i t a more b r i t t l e a s p e c t i n t h e dynamic r a n g e ( n o d i m p l e s ) t h a n a t low s t r a i n r a t e s ( a few d i m p l e s ) /4/. A t 500 OC, t h e r e is some s c a t t e r i n t h e r e s u l t s , a s it is commonly o b s e r v e d f o r d u h i l i t y measurements a t h i g h t e m p e r a t u r e ( F i g . 3 ) . N e v e r t h e l e s s , some c h a r a c t e r i s t i c t r e n d s c a n be deduced. A t low s t r a i n r a t e s , t h e t o t a l e l o n g a t i o n t o f r a c t u r e eF d o e s n o t v a r y s i g n i f i c a n t l y : eF = 35

L

( t h e v a l u e s o f d u c t i l i t y at t h e l o w e s t s t r a i n r a t e were a f f e c t e d by o x i d i z a t i o n ) . I n t h e dynamic r a n g e , eF a p p e a r s t o b e l a r g e r ( e F

-

42

%I,

and n o c l e a r v a r i a t i o n w i t h s t r a i n r a t e can be o b s e r v e d due t o s c a t t e r i n g . N e v e r t h e l e s s , t h e a v e r a g e v a l u e o f e F i n c r e a s e s s l i g h t l y w i t h s t r a i n r a t e . The v a r i a t i o n s o f eH and e h e x h i b i t

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I 1 I I I I I I

-

e~

TANTALUM

500°C

e~

-

A

e m

me

-

r*.

.

0

a.

.

-

- - -

.

8%

-

.

8 w

- - - -

L

t t

lo-"

lo-'

10-1

1

10 lo2

103 Strain

rate

s-'

(5)

C5 -5 2 JOURNAL

DE

PHYSIQUE

s i m i l a r t r e n d s w i t h i n t h e h i g h s t r a i n r a t e r a n g e . I t was c h e c k e d t h a t t h e difference i n t o t a l e l o n g a t i o n b e t w e e n t h e q u a s i s t a t i c and t h e dynamic domains is due " t o a n i n c r e a s e o f t h e n e c k l e n g t h . The l a t t e r i n c r e a s e s from 5 mm t o a b o u t 6 mm which i n d u c e s a n e l o n g a t i o n AL/Lo = 6.5 X n e a r l y e q u a l t o t h e i n c r e m e n t o f eF ( i . e . 7 X). The n e c k volume, h o w e v e r , r e m a l n s c o n s t a n t o v e r t h e whole r a n g e o f s t r a i n r a t e s . A l l t h e f r a c t u r e s u r f a c e s show a b r i t t l e a s p e c t , a l t h o u g h some r a r e d i m p l e s a r e p r e s e n t a t low s t r a i n r a t e s . The f r a c t u r e a r e a is v e r y s m a l l ( A ~ / A ~ 0.03 and 0 . 0 5 a t low and h i g h s t r a i n r a t e s , r e s p e c t i v e l y ) , which i n d i c a t e s t h a t t h e m a t e r i a l h a s a good " i n t r i n s i c d u c t i l i t y " , o r i n o t h e r words u n d e r g o e s l i t t l e damage d u r i n g s t r a i n i n g .

Flow r u l e . A t 20 OC, t h e s t r a i n h a r d e n i n g exponent n

=

a J n a / a l n a d e c r e a s e s w i t h d i n

4

t h e q u a s i s t a t i c r a n g e ( n

=

0.27 and 0.13 a t 10- and 10- s-', r e s p e c t i v e l y ) ; due t o t h e i n i t i a l peak and t h e low homogeneous e l o n g a t i o n , n was n o t d e t e r m i n e d a t h i g h s t r a i n r a t e s . On t h e o t h e r h a n d , a t 500 O C n 0.20 r e m a i n s c o n s t a n t o v e r t h e w h o l e

s t r a i n r a t e r a n g e .

A t room t e m p e r a t u r e and low s t r a i n r a t e s , t h e flow s t r e s s m e a s u r e d a t a g i v e n s t r a i n i n c r e a s e s s l o w l y w i t h E ( F i g . 4 ) a c c o r d i n g t o a power r e l a t i o n s h i p a

=

k-km, where k i s a c o n s t a n t and t h e s t r a i n r a t e s e n s i t i v i t y e x p o n e n t m d e c r e a s e s w i t h i n c r e a s i n g s t r a i n (:able I ) . I n t h e , dynamic r a n g e , f o r t h e above r e a s o n s , o n l y t h e e n g i n e e r i n g stress

=

FM/So c o r r e s p o n d i n g t o t h e maximum l o a d FM c a n be a c c u r a t l y d e t e r m i n e d . The stress (ZM)

-

s t r a i n r a t e r e l a t i o n s h i p c a n be r a t i o n a l i z e d a l t e r n a t i v e l y i n t h e form o f a power law ( T a b l e I ) o r a l i n e a r law

zM

=

uo

+

+E

,

which is o b s e r v e d a t h i g h s t r a i n r a t e s f o r many m e t a l s /2/. I n t h e p r e s e n t c a s e ,

uo

= 371 MPa and

p

=

0.092 MPa.s. The s t r a i n l r a t e s e n s i t i v i t y e x p o n e n t m

=

a l n a / a l n b t h e n i n c r e a s e s w i t h i (m = 0.110 a t 5x10' s-

,

m

=

0.271 a t 1 . 5 ~ 1 0 ~ s - I ) .

A t 500 OC, t h e b e h a v i o r o f t a n t a l u r n is well d e s c r i b e d by a power law o v e r t h e w h o l e s t r a i n r a t e r a n g e ( F i g . 5 ) . m = 0.020 is t h e n i n d e p e n d e n t of s t r a i n and s t r a i n r a t e ( T a b l e I ) . T a b l e I e!%) k(MPa.sm) m IV - DISCUSSION The t o t a l e l o n g a t i o n t o f r a c t u r e r e f l e c t s b o t h t h e s t a b i l i t y o f t h e e l o n g a t i o n a n d t h e " i n t r i n s i c d u c t i l i t y " , i . e . t h e s e n s i t i v i t y o f t h e m a t e r i a l t o damage, S t a b i l i t y i n t u r n i n c r e a s e s w i t h t h e r h e o l o g i c a l p a r a m e t e r s m and n , a s shown by v a r i o u s c r i t e r i a , w h e r e a s damage g r o w t h d u r i n g s t r a i n i n g is r e l a t e d t o t h e m i c r o s t r u c t u r e and t h e i n c l u s i o n c o n t e n t of t h e m a t e r i a l . A t 20 OC, d u c t i l i t y a p p e a r s t o be d i r e c t l y c o r r e l a t e d w i t h t h e p a r a m e t e r s o f t h e f l o w r u l e : i n t h e q u a s i s t a t i c r a n g e , m d o e s n o t depend on s t r a i n r a t e b u t n d e c r e a s e s s t r o n g l y w i t h i n c r e a s i n g E . The C o n s i d G r e c r i t e r i o n is a p p r o x i m a t e l y v e r i f i e d a t any g i v e n s t r a i n r a t e , and t h e v a r i a t i o n s o f eF, eH and el4 a r e v e r y s i m i l a r ( F i g . 2 ) . T h i s s u g g e s t s t h a t t h e d e c r e a s e o f d u c t i l i t y is a s s o c i a t e d w i t h t h e d e c r e a s e o f n. A t h i g h s t r a i n r a t e , t h i s t r e n d is a r r e s t e d , which is l i k e l y t o be due t o t h e i n c r e a s e i n s t r a i n r a t e s e n s i t i v i t y . However, t h i s e f f e c t may be e n h a n c e d by i n e r t i a ( s e e b e l o w ) .

A t 500 OC, t h e r h e o l o g i c a l p a r a m e t e r s m and n r e m a i n c o n s t a n t ; m

=

0.020 is l o w e r t h a n a t room t e m p e r a t u r e , s i n c e 500 O C c o r r e s p o n d s t o t h e a t h e r m a l r a n g e w h e r e a s

20 OC f a l l s i n t o t h e low t e m p e r a t u r e t h e r m a l l y a c t i v a t e d domain. The C o n s i d e r e 500 O C whole s t r a i n r a t e r a n g e 1 0 1 5 20 e M ( z M ) 240 251 257 219 0.02 0.02 0.02 0.017 20 OC q u a s i s t a t i c s t r a i n r a t e r a n g e 1 0 1 5 20 e M ( z M ) 339 339 339 275 0.053 0.040 0.033 0.028 dynamic r a n g e etvl(zM) 141 0.172

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Strain

rate

s

-'

600

2

500

Fig. 4

-

Logarithmic p l o t of flow s t r e s s o and engineering s t r e s s

$ =

FM/So a t

20 O C v s . s t r a i n r a t e h .

TANTALUM

2O0c

-

/

-

400

/ /

-

.

A / R

,300

Fig. 5

-

Logarithmic p l o t of flow s t r e s s o and engineering s t r e s s

zM

=

FM//SO

a t 500 O C vs. s t r a i n r a t e B (each point r e p r e s e n t s an average value).

4 / /

-

V)

200 -

10%

.

I I I 1 1 I I 1

250 ,200

I

10"

10'

1

10 lo2 10'

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C5-54 JOURNAL DE PHYSIQUE

c r i t e r i o n is again approximately v e r i f i e d , which a g r e e s with t h e ( r o u g h l y ) c o n s t a n t v a l u e s of eM and eH over t h e whole r a t e range. On t h e o t h e r hand, t h e e l o n g a t i o n t o f r a c t u r e is found t o be l a r g e r a t high s t r a i n r a t e s and t h e d i f f e r e n c e was a t t r i b u t e d t o an i n c r e a s e of t h e neck l e n g t h . I t h a s been shown r e c e n t l y t h a t i n e r t i a e f f e c t s can induce an i n c r e a s e of d u c t i l i t y a t high s t r a i n r a t e s /7,8/. The l a t t e r , however, seems t o be p r i m a r i l y due t o a l a r g e r e l o n g a t i o n of t h e homogeneous p a r t of t h e specimen ( e H ) , which was not c l e a r l y observed i n t h e p r e s e n t c a s e , such t h a t t h i s p o i n t remains open t o d i s c u s s i o n .

A remarkable f e a t u r e o f t h e d u c t i l i t y measurements a t 20 O C (Fig.2) is t h a t t h e e l o n g a t i o n t o f r a c t u r e of t h e homogeneous p a r t of t h e specimen ( e H ) is lower t h a n t h e e l o n g a t i o n corresponding t o t h e maximum l o a d ( e M ) . Although t h i s could be due t o an a r t e f a c t i n t h e dynamic range, s i n c e t h e measurements of eM a r e q u e s t i o n a b l e i n t h a t c a s e , it s h o u l d be concluded t h a t a neck begins t o grow b e f o r e t h e maximum l o a d is reached. Such e f f e c t is q u i t e unusual and would r e q u i r e f u r t h e r i n v e s t i g a t i o n . I t could be a t t r i b u t e d t o some p a r t i c u l a r f e a t u r e of t h e mechanical behavior of tantalum, e.g. second o r d e r e f f e c t s such a s t h e s t r a i n r a t e dependence of n and t h e s t r a i n dependence of m.

F i n a l l y , t h e power law s t r e s s - s t r a i n r a t e dependence observed a t both room t e m p e r a t u r e and 500 O C can be a s s o c i a t e d with t h e r m a l l y a c t i v a t e d deformation

mechanisms. A t 20 O C , t h e v e l o c i t y o f d i s l o c a t i o n s i n t a n t a l u m is thought t o be

c o n t r o l l e d by t h e overcoming of P e i e r l s s t r e s s e s / 9 / . A t 500 O C , on t h e o t h e r hand,

t h e b e h a v i o r of t a n t a l u m is comparable t o t h a t o f copper a t room t e m p e r a t u r e a t low s t r a i n r a t e s f o r which t h e c o n t r o l l i n g mechanism is t h e overcoming o f t h e d i s l o c a t i o n f o r e s t . I t should be noted t h a t t h e occurrence of t h e v i s c o u s d r a g i n t h e dynamic range, which o r d i n a r i l y l e a d s t o a l i n e a r s t r e s s - s t r a i n r a t e r e l a t i o n s h i p , is not c l e a r l y apparent i n t h e c a s e of t a n t a l u m w i t h i n t h e s t r a i n r a t e range p r e s e n t l y i n v e s t i g a t e d .

I n c o n c l u s i o n , t h e v a r i a t i o n s i n d u c t i l i t y o f t a n t a l u m appear t o be e s s e n t i a l l y c o n t r o l l e d by t h e flow r u l e . A s a r e s u l t , t h e e l o n g a t i o n t o f r a c t u r e can be very d i f f e r e n t a c c o r d i n g t o t h e c o n d i t i o n s o f s t r a i n i n g (e.g. 20 and 500 O C ) . Conversely, t h e v a r i a t i o n s i n d u c t i l i t y a t 500 O C a r e s i m i l a r t o t h o s e of copper a t 20 OC, although t h e s e m e t a l s e x h i b i t d i f f e r e n t c r y s t a l l o g r a p h i c s t r u c t u r e s .

ACKNOWLEDGEMENTS.

T h i s work was s u p p o r t e d by t h e CETAM (DTAT) under c o n t r a c t number 78-02-012. The a u t h o r s a r e i n d e b t e d t o Drs Ansart and Dormeval from t h e Commissariat 1 8 E n e r g i e Atomique (Centre de B r u y B r e s - l e - C h l t e l ) f o r t h e i r c o n t r i b u t i o n i n t h e e x p e r i m e n t a l program.

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