INTERNAL STRESS MEASUREMENT IN ALUMINIUM BY "DIP-TEST" METHOD AND CORRELATION WITH THE BORDONI RELAXATION EVOLUTION

(1)

HAL Id: jpa-00221068

https://hal.archives-ouvertes.fr/jpa-00221068

Submitted on 1 Jan 1981

HAL is a multi-disciplinary open access

archive for the deposit and dissemination of

sci-entific research documents, whether they are

pub-lished or not. The documents may come from

teaching and research institutions in France or

abroad, or from public or private research centers.

L’archive ouverte pluridisciplinaire HAL, est

destinée au dépôt et à la diffusion de documents

scientifiques de niveau recherche, publiés ou non,

émanant des établissements d’enseignement et de

recherche français ou étrangers, des laboratoires

publics ou privés.

INTERNAL STRESS MEASUREMENT IN

ALUMINIUM BY ”DIP-TEST” METHOD AND

CORRELATION WITH THE BORDONI

RELAXATION EVOLUTION

J. Chicois, A. Hamel, R. Fougères, C. Esnouf, Gilbert Fantozzi, J. Perez

To cite this version:

(2)

JOURNAL DE PHYSIQUE

c'oZZoque C5, suppZ6ment au noIO, Tome 42, octobre 2982 page C5-169

I N T E R N A L STRESS

M E A S U R E M E N T I N A L U M I

N I U M BY

I'D

I P-TEST" METHOD A N D

CORRELATION WITH THE BORDONI RELAXATION EVOLUTION

J . C h i c o i s , A. Hamel, R. FougSres, C. ~ s n o u f

*,

G. ~ a n t o z z i * and J. ~ e r e z *

Laboratoire de Me'taZZurgie e t Traitements Thermiques, B6t. 303

* ~ r o u ~ e drEtudes de M6tallurgie Physique e t Physique des Mate'riaux, E.R.A. 963 BZt. 502, I n s t i t u t National d e s Sciences AppZiqu6es de Lyon

-

69621

Vi

Z Zeurbmzne Cedex, France

Abstract.- The Bordoni r e l a x a t i o n appears only w i t h a s u f f i c i e n t v a l u e of s t r e s s g i v e n by t h e Par6 c o n d i t i o n . We have made a d i r e c t measurement of in- t e r n a l s t r e s s i n o r d e r t o know i t s e v o l u t i o n d u r i n g p l a s t i c deformation o r a n n e a l i n g . T h i s e v o l u t i o n i s compared w i t h t h e behaviour of t h e Bordoni r e l a - x a t i o n : v a r i a t i o n of t h e r e l a x a t i o n s t r e n g t h on t h e one hand and non l i n e a r p r o p e r t i e s on t h e o t h e r hand.

1 . I n t r o d u c t i o n . - It i s w e l l e s t a b l i s h e d t h a t t h e Bordoni r e l a x a t i o n s t r e n g t h i s r e - l a t e d t o t h e s t r e s s amplitude ( 1 ) . Indeed, t h e Bordoni peaks appear only when t h e Par6 c o n d i t i o n i s f u l l f i l l e d : ob2L = 2Wk (1) w i t h 0 = oi + u (ai i n t e r n a l , om ap-

m

p l i e d s t r e s s ) , L = d i s l o c a t i o n l e n g t h and 2Wk = double-kink n u c l e a t i o n energy. Du- r i n g p l a s t i c d e f o r m a t i o n o r a n n e a l i n g , t h e h e i g h t of t h e Bordoni peaks changes and t h i s change c a n b e due e i t h e r t o t h e v a r i a t i o n of d i s l o c a t i o n l e n g t h o r t h e v a r i a - t i o n of i n t e r n a l s t r e s s . T h i s second v a r i a t i o n i s o f t e n n e g l e c t e d . Thus, i s i s i n t e - r e s t i n g t o have a d i r e c t measurement of i n t e r n a l s t r e s s i n o r d e r t o know i t s evolu- t i o n d u r i n g p l a s t i c deformation o r a n n e a l i n g and t o compare w i t h t h e behaviour of t h e Bordoni r e l a x a t i o n . I n p a r t i c u l a r , we have s t u d i e d simultaneously t h e change of i n t e r n a l s t r e s s and t h e non l i n e a r p r o p e r t i e s of t h e Bordoni r e l a x a t i o n , which a r e c o r r e l a t e d w i t h t h e v a l u e of i n t e r n a l s t r e s s .

2. Experimental r e s u l t s i : i n t e r n a l s t r e s s

By d i p t e s t method, i n t e r n a l s t r e s s i s determined on p o l y c r i s t a l l i n e t h i n t u b e s of aluminium 99.999 %. The study i t s e l f i s concerned w i t h t o r s i o n a l c r e e p t e s t s . Maximum s t r e s s g r a d i e n t i s s m a l l e r t h a n 10 % of maximum a p p l i e d s t r e s s . The i n t e r n a l s t r e s s measurements a r e made w i t h a s p e c i a l t e s t machine, s u i t a b l e f o r t h i s t e s t t y p e ( 2 ) . The measurements of t h e c r e e p s t r a i n a r e c a r r i e d o u t w i t h a s p e c i a l s e n s i t i v e c a p t o r , f i x e d on t h e sample i t s e l f . T h i s a p p a r a t u s a l l o w s t o d e t e c t a s t r a i n v a l u e a s low a s 1

o - ~

(2). Samples a r e t h e n submitted t o an a n n e a l l i n g a t 525 K d u r i n g one hour a f t e r a c r o s s s e c t i o n r e d u c t i o n of 7 0 %.

Maximum c r e e p r a t e a r e p l o t t e d v e r s u s s u c c e s s i v e v a l u e s of t h e a p p l i e d s t r e s s i n f i g . 1. T h i s c u r v e p r e s e n t s two r a n g e s : t h e low s t r e s s range i s due t o a n a n e l a s t i c p r o c e s s and t h e high s t r e s s range i s l i n k e d t o a m i c r o p l a s t i c s t r a i n pro- c e s s . S i m i l a r r e s u l t s have been o b t a i n e d on i r o n carbon a l l o y s ( 3 ) . I n t h e high s t r e s s r a n g e , t h e s t r e s s corresponding t o z e r o c r e e p r a t e f o r d i f f e r e n t c r e e p s t r a i n v a l u e s i s determined. As i t w i l l %how below, t h e o b t a i n e d s t r e s s v a l u e s a r e v e r y

c l o s e d t o i n t e r n a l s t r e s s ones. The s t r e s s o b t a i n e d by e x t r a p o l a t i o n a t z e r o t o t a l c r e e p s t r a i n i s t h e i n t e r n a l s t r e s s which i s t y p i c a l of t h e mi.crostructura1 s t a t e of t h e specimen.

(3)

C5-170 JOURNAL DE PHYSIQUE

F i g u r e 2 r e p r e s e n t s t h e e v o l u t i o n of c r e e p r a t e dg a s a f u n c t i o n of a p p l i e d s t r e s s v a l u e s under unloading c o n d i t i o n s .

I n t h i s c a s e , t h e c r e e p s t r a i n , equal t o 3 . ~ 1 O - ~ , i s v e r y lower t h a n t h e p r e p l a s - t i c s h e a r s t r a i n (2.10-'). Assuming t h a t t h e e v o l u t i o n of a n e l a s t i c c r e e p r a t e law i s i d e n t i c a l under l o a d i n g and unloading c o n d i t i o n s , e r r o r v a l u e due t o t h e a n e l a s - t i c p r o c e s s is determined according a n a n a l y s i s method described elsewhere (4). In- t e r n a l s t r e s s +; i s always measured w i t h a p r e c i s i o n b e t t e r t h a n 2 %. I n t e r n a l s t r e s s v a l u e i s c l o s e d t o a p p l i e d s t r e s s one. I t i s i n good agreement with t h e f a c t t h a t thermal s t r e s s component i s v e r y weak i n aluminium a t room temperature. For a p r e p l a s t i c deformation of 2.10-', i n t e r n a l s t r e s s i s p l o t t e d v e r s u s t o t a l c r e e p s t r a i n ( f i g . 3 ) . T y p i c a l i n t e r n a l s t r e s s of t h e m i c r o s t r u c t u r e a s p e c t of specimen i s o b t a i n e d by e x t r a p o l a t i o n a t z e r o t o t a l c r e e p deformation. For s e v e r a l p r e p l a s t i c deformation, e v o l u t i o n of t y p i c a l i n t e r n a l s t r e s s e s i s shown i n f i g . 4. Moreover, f o r a 2 % p r e p l a s t i c s t r a i n , t h e v a r i a t i o n of i n t e r n a l s t r e s s e s with a n n e a l i n g tem- p e r a t u r e i s schown i n f i g . 5. The s t r e s s d e c r e a s e seems t o p r e s e n t two e v o l u t i o n ranges with t h e a n n e a l i n g temperature : one, between room temperature and 340 K, t h e o t h e r above. A t high a n n e a l i n g temperature, i n t e r n a l s t r e s s v a l u e t e n d s towards in- t e r n a l s t r e s s v a l u e o b t a i n e d b e f o r e p r e p l a s t i c deformation.

i.i : i n t e r n a l f r i c t i o n

F i g u r e s 6 and 7 schow t h e e f f e c t of a s t a t i c s t r e s s us on t h e i n t e r n a l f r i c t i o n s p e c t r a measured w i t h a v i b r a t i o n s t r e s s amplitude lower t h a n us. We observe t h a t f o r low p l a s t i c d e f o r m a t i o n t h e s t a t i c s t r e s s i n f l u e n c e i s s t r o n g ( f i g . 6) whereas, f o r important d e f o r m a t i o n , t h e Bordoni r e l a x a t i o n behaviour becomes l i n e a r ( f i g . 7 ) . F i g u r e 8 shows t h e e f f e c t of a n n e a l i n g on t h e non l i n e a r behaviour of t h e Bordoni r e l a x a t i o n . We c a n n o t e t h a t f o r h i g h temperature a n n e a l i n g , t h e Bordoni r e l a x a t i o n becomes v e r y s e n s i t i v e t o t h e amplitude of. t h e a p p l i e d s t r e s s .

3 . Discussion.- I n t e r n a l s t r e s s e s a r e due t o d i s l o c a t i o n s which a r e p r e s e n t i n t h e metal. The r e l a t i o n between i n t e r n a l s t r e s s r i and d i s l o c a t i o n d e n s i t y N i s g e n e r a l - l y given by t h e f o l l o w i n g r e l a t i o n :

r . = a f i (2)

with a a c o n s t a n t parameter. From t h i s r e l a t i o n , t h e i n t e r n a l s t r e s s e v o l u t i o n w i t h p r e p l a s t i c deformation i s given by :

T i

-

+

_i₀= a ( f i -

6)

₍₃

with T~~ and N o r e s p e c t i v e l y t h e i n i t i a l i n t e r n a l s t r e s s and d i s l o c a t i o n s d e n s i t y v a l u e s . However, t h e d i s l o c a t i o n d e n s i t y can be deduced from t h e a p p l i e d s t r e s s - p l a s t i c deformation c u r v e T, cp by t h e following r e l a t i o n (6) :

with A _da c o n s t a n t v a l u e .

Using a p l a n i m e t e r , t h e e v o l u t i o n of t h e d e n s i t y of d i s l o c a t i o n with p l a s t i c s t r a i n E i s determined from experimental (T

-

e p ) curve according t o r e l a t i o n ( 4 ) . T h i s evoyution c a n b e r e p r e s e n t e d by t h e f o l l o w i n g e x p r e s s i o n :

N

= N O

+

A' Em

d P (5)

w i t h m = 1.16. This r e s u l t i s i n good agreement with t h e ones found by o t h e r s au- t h o r s ( 6 ) and (7)

.

Assuming N >> N o , r e l a t i o n s (3) and (5) can be read a s f o l l o w s : ~ ~ - ~ ~ ~and = aN = A ' c m f i

(4)

n

T .

-

-ciO = K E with K a c o n s t a n t . P

n v a l u e i s equal t o 0.55 which i s near of receding v a l u e (m/2 = 0.58).

F i n a l l y , t h e s e r e s u l t s and t h e good o r d e r of magnitude of d i s l o c a t i o n d e n s i t y deduced from r e l a t i o n ( 2 ) ( e g ~ ~

=

cm-=) i n d i c a t e t h a t experimental r e s u l t s a r e c o h e r e n t .

On t h e o t h e r hand, t h e i n t e r n a l f r i c t i o n experiments show t h a t t h e Pard condi- tion (8) i s not s a t i s f i e d when t h e p l a s t i c deformation i s low ( f i g . 6) o r a f t e r an- nealing ( f i g . 8) because it appears o n l y a badly d e f i n e d peak without s t a t i c s t r e s s . The a p p l i c a t i o n of a b i a s s t r e s s of 5x10-= G r e e s t a b l i s h e d t h e Pard c o n d i t i o n and a

well-defined Bordoni peak appears c l e a r l y ( f i g . 6 and 8 ) .

However, a f t e r a n n e a l i n g , we o b s e r v e a n i n c r e a s e of t h e Bordoni peak a f t e r sup- p r e s s i o n of US : t h u s , t h e a p p l i c a t i o n of us m o d i f i e s t h e i n t e r n a l f r i c t i o n beha- v i o u r

.

For high p l a s t i c deformation, t h e Pard c o n d i t i o n i s always f u l f i l l e d and t h e e f f e c t of a b i a s s t r e s s i s n e g l i g i b l e ( f i g . 7 ) .

By comparison w i t h t h e i n t e r n a l s t r e s s measurements, we can deduce t h a t t h e non l i n e a r behaviour i s observed only when t h e i n t e r n a l s t r e s s e s a r e weak. But from t h e r e l a t i o n (1) and t h e experimental r e s u l t s , t h e Pard c o n d i t i o n i s s a t i s f i e d by s t r e s - s e s lower t h a n t h e i n t e r n a l s t r e s s measured by d i p t e s t ( ~ 5 x 1 0 - s ~ i n s t e a d of ~ 2 x 1 0 - k )

This r e s u l t can b e explained o n l y i f t h e i n t e r n a l s t r e s s e s d i s t r i b u t i o n i s t a - ken i n t o account. Indeed, such d i s t r i b u t i o n s have been observed by " i n s i t u " M.E.T. experiments (9). By d i p t e s t method, we measure t h e mean v a l u e of i n t e r n a l s t r e s s e s which can b e considered a s a "macroscopic" i n t e r n a l s t r e s s (10). On t h e o t h e r hand,

i n t e r n a l f r i c t i o n i s s e n s i t i v e o n l y t o t h e weakest " l o c a l " i n t e r n a l s t r e s s e s . This d i s c u s s i o n a l l o w s u s t o e x p l a i n t h e d i f f e r e n c e between t h e s t r e s s n e c e s s a r y t o f u l - f i l l t h e P a r 6 c o n d i t i o n and t h e i n t e r n a l s t r e s s deduced from t h e d i p t e s t . F u r t h e r - more, t h e f r a c t i o n of d i s l o c a t i o n s submitted t o low i n t e r n a l s t r e s s v a l u e s must de- c r e a s e when t h e p l a s t i c deformation i n c r e a s e s .

I n c o n c l u s i o n , we have observed a q u a l i t a t i v e c o r r e l a t i o n between t h e e v o l u t i o n of t h e i n t e r n a l s t r e s s e s and t h e behaviour of i n t e r n a l f r i c t i o n , e i t h e r a f t e r p l a s - t i c deformation o r a n n e a l i n g . Other experiments must be c a r r i e d o u t t o make more q u a n t i t a t i v e comparison between t h e s e r e s u l t s .

References

. ( I )

G . F a n t o z z i ,

W.

Benoit, C . Esnouf and J . P e r e z , Ann. Phys. F r . , 4 , 7 ( 1 979).

(2) A . Hamel, J. C h i c o i s , R. FougEres and M. T h g o l i e r , J o u r n a l of Physics E , Scien- t i f i c I n s t r u m e n t s , 2 p a r a i t r e .

(3) R. FougSres, A. Hamel and M , T h d o l i e r , Proceedings of ICSMA 5 , Aachen, W. Germany, 1 , 337 (1979).

(4) J. C h i c o i s , A. Hamel, R. FougSres and J. Perez, S c r i p t a Met., sous p r e s s e . (5) I. Kovacs and L. Zsoldos, D i s l o c a t i o n s and p l a s t i c d e f o r m a t i o n s , Pergamon

P r e s s , Oxford, p. 251 (1973).

( 6 ) R. W. Honeycombe, The p l a s t i c deformation of m e t a l s , Edward Arnold (1977).

(7) S. C e r e s a r a , H. Elkholy and T. F e d e r i g h i , Phys. S t a t . S o l . , 8 , 509 (1965). (8)

V.

K. Pard, J. Appl. Phys., 3 , 332 (1961).

(5)

JOURNAL DE PHYSIQUE

Fig. 2 : Evolution of t h e c r e e p r a t e v e r s u s a p p l i e d s t r e s s d u r i n g unloading of t h e sample by succes- s i v e s t e p s .

logi,bth creep rote

preplastic shear strain 2 10-' temperature 290 K

-6--

-7-

+---

inibl phstic strain +creep stram

I I

o

I 000 2000 x d 6

F i g . 3 : Evolution of t h e i n t e r n a l s t r e s s a s a f u n c t i o n of p l a s t i c s t r a i n d u r i n g a c r e e p t e s t .

preplastic shear strain 2 10-' _,+' ,'

4

.

+' test temperature 290 K + / # ,

-

,

.+'

2- 3- ,i + +/ '+

+/c---

---;fl 1-

+'---

+ 0 A & x

lo8

(c')

preplastic shear strain 2 temperalure I -,0.25 ,O ,425 ,o,S 0 -1-

Fig: 1 : Evolution of t h e logarithm of t h e maxlmal c r e e p r a t e a s a f u n c t i o n of t h e l o - -2- garithm of t h e a p p l i e d s t r e s s . P r e p l a s t i c s h e a r deformation b y t o r s i o n equal t o _-3- 2 ~ 1 0 - ~ , 5 1 ' 15

,

?

,initial +, + , creep stress

,

/ +, * ,,' /

:

/*

.'lanelastic component

+'

;"pccording to the First

,s:%(~~a) A%x104 F i g . 4 : I n t e r n a l s t r e s s and r a t i o

/,:

range of Figure 1

.

I+,/,

I

temperature 290 K

_-

of i n t e r n a l s t r e s s and shear modu- l u s v e r s u s p r e p l a s t i c s h e a r s t r a i n by t o r s i o n .

- 5

23

r I preplastit shew strain

0 ₄₅

(6)