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INFLUENCE OF EXTRUSION PROCESS PARAMETERS ON THE MECHANICAL PROPERTIES OF Al-Li-EXTRUSIONS

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HAL Id: jpa-00226552

https://hal.archives-ouvertes.fr/jpa-00226552

Submitted on 1 Jan 1987

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INFLUENCE OF EXTRUSION PROCESS PARAMETERS ON THE MECHANICAL

PROPERTIES OF Al-Li-EXTRUSIONS

G. Tempus, G. Scharf, W. Calles

To cite this version:

G. Tempus, G. Scharf, W. Calles. INFLUENCE OF EXTRUSION PROCESS PARAMETERS ON THE MECHANICAL PROPERTIES OF Al-Li-EXTRUSIONS. Journal de Physique Colloques, 1987, 48 (C3), pp.C3-187-C3-193. �10.1051/jphyscol:1987322�. �jpa-00226552�

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INFLUENCE OF EXTRUSION PROCESS PARAMETERS ON THE MECHANICAL PROPERTIES OF A1-Li-EXTRUSIONS

G. TEMPUS, G. SCHARF a n d W. CALLES

Vereinigte Aluminium-Werke AG, Leichtmetall-Forschungsinstitu~, B.P. 2 4 6 8 , 0-5300 Bonn, F.R.G.

ABSTRACT

The i n f l u e n c e o f t h e e x t r u s i o n process parameters and TMT on t h e mechanical p r o - p e r t i e s o f d i f f e r e n t L i t a l A (8090)-extrusions was i n v e s t i g a t e d . Strength was shown t o be i n f l u e n c e d l e s s by e x t r u s i o n temperature and r a t i o than by t h e ex- t r u s i o n aspect r a t i o (width/thickness) determining t e x t u r e . With i n c r e a s i n g ex- t r u s i o n aspect r a t i o t h e s t r e n g t h d e c l i n e s considerably. Depending on t h e homo- g e n e i t y o f s l i p d i s t r i b u t i o n t h e s t r e n g t h decrease can be c a l c u l a t e d w i t h excel- l e n t accuracy by t h e SACHS- o r the TAYLOR-model on t h e b a s i s o f a q u a n t i t a t i v e t e x t u r e a n a l y s i s .

1. INTRODUCTION

For t h e p r o d u c t i o n o f h i g h q u a l i t y A1-Li semiproducts ready f o r s e r v i c e i t i s e s s e n t i a l ca g e t knowledge o f t h e i n f l u e n c e o f t h e p r o d u c t i o n c o n d i t i o n s on t h e p r o p e r t i e s o f t h e semiproduct. As t h e r e a r e l i t t l e p u b l i c a t i o n s e s p e c i a l l y f o r e x t r u s i o n s [1,2], t h e purpose o f t h i s i n v e s t i g a t i o n i s t o determine t h e i n f l u e n c e o f t h e e x t r u s i o n process parameters on t h e t e n s i l e p r o p e r t i e s o f d i f f e r e n t l y shaped e x t r u s i o n s . As t h e s t r e n g t h o f AT-Li sheet and p l a t e m a t e r i a l i s known t o have a stronger s u s c e p t a b i l i t y towards t e x t u r e [3-61, t h i s t o p i c i s a p o i n t o f s p e c i a l i n t e r e s t i n t h i s i n v e s t i g a t i o n .

2. EXPERIMENTAL PROCEDURE

The e x t r u s i o n b i l l e t s ( 0 77 x 200 mm) were machined from r e c t a n g u l a r DC c a s t bars (300 x 900 x 2500 mm). The chemical composition o f t h e used L i t a l A - a l l o y (8090) i s given i n Tab.1.

Tab. 1: Chemical composition o f t h e L i t a l A a l l o y i n v e s t i g a t e d

The b i l l e t s were homogenised f o r 24h a t 550°C i n a i r and d i r e c t l y extruded on a 3.15 MN-press w i t h a 80 mm d i a . conta,iner. W i t h i n 2 min. t h e b i l l e t s were heated t o t h e e x t r u s i o n temperatures o f 400°C o r 450°C, which were always equal t o those o f t h e container. C i r c u l a r rods (0 16 mm), and d i f f e r e n t f l a t shapes were ex- t r u d e d ( e x i t speed Zm/min.). A11 e x t r u d a t e s were s o l u t i o n t r e a t e d f o r 30 min. a t 535OC, quenched i n water (20°C) and then s t r e t c h e d ( 2 %) immediately. A f t e r pre-aging (5d, 20°C) t h e e x t r u s i o n s were aged a t 185OC. A d d i t i o n a l l y t h e c i r c u l a r r o d was aged w i t h o u t preceding s t r e t c h . The t e n s i l e p r o p e r t i e s were determined i n e x t r u s i o n d i r e c t i o n .

The t e x t u r e measurements were c a r r i e d o u t on a f u l l y automatic and computer-con- t r o l l e d t e x t u r e goniometer 171. For each specimen f o u r incomplete d i f f e r e n t p o l e f i g u r e s {Ill), (2001, 12203, {113) up t o a maximum t i 1 t i n g angle o f 85O were

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1987322

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C3-188 JOURNAL DE PHYSIQUE

measured, from which t h e three-dimensional o r i e n t a t i o n d i s t r i b u t i o n f u n c t i o n s (ODF) were c a l c u l a t e d [8]. By t h e means o f i s o t r o p i c Gaup-type d i s t r i b u t i o n func- t i o n s t h e ODF were separated i n t h e s i n g l e components o f t e x t u r e and q u a n t i - t a t i v e l y evaluated [9].

3. RESULTS

3.1 I n f l u e n c e o f S t r e t c h on t h e A r t i f i c i a l Aging Behaviour F i g . 1 shows t h e dependence o f t h e mecha-

n i c a l p r o p e r t i e s o f t h e c i r c u l a r rods from 6 M aging t i m e a t 185OC w i t h and w i t h o u t MPO

s t r e t c h ( e x t r u s i o n temperature 450°C). A t 2 t h e beginning o f aging t h e s t r e n g t h values w i t h o u t s t r e t c h a r e higher than those f o r ,o 55m t h e s t r e t c h e d c o n d i t i o n . With i n c r e a s i n g

aging t i m e t h e s t r e n g t h f o r t h e unstretched Zbrn

c o n d i t i o n reaches a p l a t e a u f o l l o w e d by t h e R

peak s t r e n g t h . By s t r e t c h i n g , however, t h e s t r e n g t h i s c o n t i n u o u s l y i n c r e a s i n g t o i t s g3M

peak. Maximum s t r e n g t h i s achieved a f t e r

an aging time o f 30h f o r each treatment. zzoo A

The y i e l d s t r e n g t h R is higher by

25 MPa and t e n s i l e s t r e n g t h Rm by '

10 MPa due t o s t r e t c h i n g . A t t h e 100

beginning o f aging t h e e l o n g a t i o n values Trmted AGING TIME A drop f o r b o t h c o n d i t i o n s . Then f o r t h e

u k s t r e t c h e d r o d t h e e l o n g a t i o n remains F i g . 1: Age hardening curve (185OC) n e a r l y constant and then increases w i t h o f t h e c i r c u l a r r o d

overaging. For t h e s t r e t c h e d c o n d i t i o n

t h e e l o n g a t i o n e x h i b i t s a s l i g h t minimum and increases j u s t before t h e aging peak.

S t r e t c h i n g always r e s u l t s i n s l i g h t l y higher values of both s t r e n g t h and elonga- t i o n . Therefore i n t h e f u r t h e r i n v e s t i g a t i o n , a l l e x t r u s i o n s were s t r e t c h e d b e f o r e aging.

3.2 I n f l u e n c e o f E x t r u s i o n Parameters and Shape on t h e T e n s i l e P r o p e r t i e s

The s t r e n g t h o f d i f f e r e n t shapes ( c i r c u l a r and f l a t ) extruded a t 450°C and aged f o r 30h a t 185'C does n o t s y s t e m a t i c a l l y depend on t h e e x t r u s i o n r a t i o R ( F i g . 2 ) . For n e a r l y equal e x t r u s i o n r a t i o s i n t h e range from 1 : 22.3 t o 1 : 25.8 e.g.

600

oz

4 550

tsa I C

B = + Srn

d

V) Z Y C 0 3 = 450

W >

4 0 0 1 : ~ ~ 1:30 1:LO 1:50 1:60 1:70 1:80 1:90 EXTRUSION RATIO R

10 15 20 25

EXTRUSION ASPECT RATIO (WIDTH I THICKNESS) WIT Fig. 2: I n f l u e n c e o f e x t r u s i o n r a t i o F i g . 3: Strength Rp0.2, Rm VS.

R on s t r e n g t h Rp0.2, Rm e x t r u s i o n aspect r a t i o W/T

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t r u s i o n aspect r a t i o W/T o f w i d t h W t o thickness T. From t h e minimum W/T-ratio o f 1 (axisymmetric shapes) ( F i g . 3 ) t h e s t r e n g t h s t r o n g l y drops and i s s t i l l being reduced f o r W/T-ratios g r e a t e r than 10. T h i s r e d u c t i o n i s approximately by two times g r e a t e r f o r t h e y i e l d than f o r t h e t e n s i l e s t r e n g t h . Y i e l d s t r e n g t h d i f f e r s most between t h e c i r c u l a r r o d (W/T = 1 ) and the 65 x 3 mm f l a t shape (W/T = 21.7).

I n F i g . 3 t h e s t r e n g t h values o f t h r e e shapes extruded a t 400°C a r e given a d d i t i o - n a l l y . On a l e v e l 10-26 MPa higher than by e x t r u s i o n a t 450°C t h e y show t h e same W/T-dependency. I n order t o v e r i f y t h e i n f l u e n c e o f t h e W/T-ratio a t one

e x t r u s i o n t h e L-shape shown i n F i g . 3 was extruded a t 450°C. I t can be d i v i d e d i n s e c t i o n A ( t h i c k n e s s 12 mm, W/T = 1 ) and s e c t i o n B ( t h i c k n e s s 2 mm, W/T = 16, i f t h e e n t i r e w i d t h o f t h e shape i s considered). The s t r e n g t h values o f t h e s e c t i o n s A and B f i t very good t o the dependency o f Fig. 3. The e l o n g a t i o n values ( F i g . 4) a r e n e a r l y independent from t h e W/T-ratio and do n o t d i f f e r s i g n i f i c a n t l y f o r t h e

R 1:27

0 ~ 1 5 10 15 2 0 25

EXTRUSION ASPECT RATIO (WIDTH / THICKNESS1 W I T

6 0 0 25

MP0 Ye

d 5 0 0 2 0

N 0 m mc

4 0 0

I 15 g

W

DL r

- e

"

7 b u

7 3 0 0 0

Z 10 g

w *

r)

9 200 5

Y -

>

I

lo2 h 10)

Treated AGING TIME

F i g . 4: Elongation A5 vs. e x t r u - F i g . 5: Age hardening curve o f s i o n aspect r a t i o W/T s e c t i o n A and B (L-shape) two e x t r u s i o n temperatures. The i n f l u e n c e o f t h e s t a t e o f p r e c i p i t a t i o n on t h e W/T-dependency was determined by t h e age hardening curves o f t h e s e c t i o n s A and B ( F i g . 5 ) . As expected from t h e same W/T- r a t i o o f 1, s i m i l a r curves f o r s t r e n g t h and e l o n g a t i o n a r e observed f o r s e c t i o n A and t h e c i r c u l a r r o d ( F i g . 1 ) . I n s e c t i o n B, however, t h e peak s t r e n g t h i s reached 20h l a t e r and t h e s t r e n g t h i s always lower. There a r e a l s o considerable d i f f e r e n c e s i n t h e e l o n g a t i o n curves.

I . L ... l . . ... I . .

Solution ' lo0 10'

T r w t e d AGING TIME

Fig. 6: Strength d i f f e r e n c e between F i g . 7: Grain s t r u c t u r e o f s e c t i o n A and B vs. aging time s e c t i o n A ( a ) and B ( b )

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C3-190 JOURNAL DE PHYSIQUE

A t t h e begin o f aging t h e e l o n g a t i o n d e c l i n e s f o r t h e two sections. For s e c t i o n B i t remains n e a r l y constant up t o t h e overaged c o n d i t i o n . Section A e x h i b i t s lower e l o n g a t i o n values w i t h a minimum a f t e r 8h. Having reached i t s peak aged c o n d i t i o n t h e e l o n g a t i o n i s even s i g n i f i c a n t l y g r e a t e r than t h a t o f s e c t i o n B.

The d i f f e r e n c e o f y i e l d s t r e n g t h AR and t e n s i l e s t r e n g t h AR between s e c t i o n A and B changes w i t h aging t i m e ( F ~ B ? . ~ 6). A f t e r quenching andmin t h e overaged c o n d i t i o n the AR - and AR -values a r e lowest. With t h e begin o f agingAR increases r a p i d l Y 0 d d reache! i t s maximum (125 MPa) a f t e r 7h i n t h e underaggdm2 c o n d i t i o n . The d i f f e r e n c e s i n t e n s i l e s t r e n g t h AR a r e approximately h a l f o f those i n y i e l d s t r e n g t h . Compared w i t h t h e curve ?or AR the maximum i s l e s s pronounced and i s reached a f t e r a longer aging t i m e p0.2

(16h).

4.3 I n f l u e n c e o f M i c r o s t r u c t u r e

The m i c r o s t r u c t u r e s o f s e c t i o n A and B (30h 185OC) were examined by l i g h t and TEM microscopy i n order t o determine t h e reason f o r t h e s t r e n g t h d i f f e r e n c e s . I n t h e c e n t r e o f s e c t i o n A and B (Fig. 7 ) t h e r e i s an as-extruded m i c r o s t r u c t u r e w i t h pancake-shaped g r a i n s i n s e c t i o n B due t o t h e g r e a t e r W/T-ratio. A t t h e o r i g i n a l g r a i n boundaries a f i n e r e c r y s t a l l i s a t i o n has s t a r t e d w i t h t h e r e c r y s t a l l i s e d volume f r a c t i o n s l i g h t l y g r e a t e r i n s e c t i o n B. The r e s u l t s o f t h e TEM-examination show t h e subgrains t o be equal i n s t r u c t u r e and s i z e . There are a l s o no d i f f e r e n - ces i n t h e s t a t e o f p r e c i p i t a t i o n - T h e f l a t t e r g r a i n s i n p a r t B and t h e h i g h e r degree o f r e c r y s t a l l i s a t i o n a r e u n l i k e l y t o cause t h e remarkable d i f f e r e n c e i n s t r e n g t h .

4.4 I n f l u e n c e o f Texture

The { I l l ) - p o l e f i g u r e s taken from t h e c e n t r e o f s e c t i o n A and B d i f f e r consider- a b l y ( F i g . 8). According t o i t s axisymmetric deformation s e c t i o n A shows a pro- nounced <111>+<100> double f i b r e t e x t u r e .

F i g . 8: { 1 1 l ) - ~ o l e f i g u r e s o f s e c t i o n A ( a ) and B ( b )

Due t o t h e predominantly plane deformation t h e t e x t u r e o f s e c t i o n B i s s i m i l a r t o t h a t achieved by r o l l i n g . The volume f r a c t i o n s o f each t e x t u r e component and t h e background were determined from t h e ODF's (Tab. 2 ) . The double f i b r e t e x t u r e ( s e c t i o n A) i s composed o f 75 % i n <Ill> d i r e c t i o n and o f 22 % i n <loo> d i r e c - t i o n . I r r e s p e c t i v e o f s l i g h t d e v i a t i o n s from t h e given i d e a l o r i e n t a t i o n , i n s e c t i o n B t h e t h r e e t y p i c a l r o l l i n g t e x t u r e s S, Bs and Cu predominate w i t h a t o t a l amount o f 65.9 %. For each t e x t u r e component t h e o r i e n t a t i o n f a c t o r s Ms and Mt resp. were c a l c u l a t e d , which r e l a t e y i e l d s t r e s s a and c r i t i c a l r e s o l v e d

shear s t r e s s rc : Y

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TAYLOR-factor. According t o t h e SACHS-model [ l o ] p l a s t i c deformation occurs as s i n g l e s l i p i n t h e {Ill} <110> s l i p system w i t h t h e minimum f a c t o r Ms, i .e. t h e maximum SCHMID-factor m. The TAYLOR- model [Ill, however, i s v a l i d f o r m u l t i - s l i p i n a t l e a s t f i v e independent {Ill} <110> s l i p systems. I n Tab. 2 t h e f a c t o r s Ms

Section A Section B

<uvw> Mi% Mt Ms Component { h k l } <uvw> Mi% Mt Ms

<Ill> 75 3.67 3.67 S 11233 <634>

<loo> 22 2.45 2.45 Bs { O l l } <211>

Background 3 3.07 2.24 Cu {112} <Ill>

Goss/Bs { O l l ) <511>

- {138} <751>

- (111) <112>

cube^^ {025} <loo>

Background

-- - - .-

Mean-Value

Mt, Ms 3.38 3.36

Tab. 2: Volume f r a c t i o n M i , TAYLOR-factors Mt and SACHS-factors Ms f o r t h e t e x - t u r e components.

and Mt are given f o r l o a d i n g i n e x t r u s i o n d i r e c t i o n <uvw>. Except f o r the <Ill>

and <loo> o r i e n t a t i o n s t h e M t - f a c t o r s a r e g r e a t e r than t h e Ms-factors, because i n t h e case o f m u l t i - s l i p l e s s favoured s l i p systems must be a c t i v e t o m a i n t a i n c o m p a t i b i l i t y a t t h e g r a i n boundaries. The Mt and Ms f a c t o r s a r e equal f o r t h e

<Ill> and <loo> o r i e n t a t i o n s , because 6 and 8 s l i p systems resp. have t h e same Ms-factor, thus s u f f i c i e n t e q u i v a l e n t s l i p systems-being a c t i v e f o r t h e v a l i d i t y o f t h e TAYLOR-model. The mean o r i e n t a t i o n f a c t o r s Ms and mt -balanced-with t h e volume f r a c t i o n - a r e n e a r l y equal f o r s e c t i o n A. I n s e c t i o n B Ms and Mt d i f f e r considerabl and t h e y a r e lower than i n s e c t i o n A,especial l y f o r t h e SACHS-model .

The higher #t and As values o f s e c t i o n A a r e due t o t h e h i g h volume f r a c t i o n (75 %) o f <Ill> o r i e n t a t i o n s w i t h t h e h i g h e s t M t and Ms f a c t o r s a t a l l . For t h e same c r i t i c a l resolved shear s t r e s s i n both s e c t i o n s t h e d i f f e r e n c e o f t h e y i e l d s t r e n g t h AR PO. 2 r e l a t e d t o t h e y i e l d s t r e n g t h o f s e c t i o n A [R p0.2 ( A ) ] can be

30

% 25

=? - 2 0

d E? -+

=qs a

10

3

Treoted AGING TIME

F i g . 9: Strength d i f f e r e n c e r e l a - Fig. 10: S l i p d i s t r i b u t i o n ( a ) t e d t o "A" vs. aging t i m e and p r e c i p i t a t i o n ( b )

o f s e c t i o n B (2h 185OC)

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C3-192 JOURNAL DE PHYSIQUE

c a l c u l a t e d from Rs and i t w i t h eqn. ( 1 ) :

SACHS: A RpO. 2/Rp0. (A) = 26.2 % TAYLOR: D RpO. 2/Rp0. (A) = 7.7 %

These models d e s c r i b e extreme c o n d i t i o n s w i t h t h e SACHS-model as t h e upper and t h e TAYLOR-model as t h e lower l i m i t f o r t h e r e l a t i v e d i f f e r e n c e i n y i e l d s t r e n g t h P r i n c i p a l l y t h e r e l a t i v e s t r e n g t h d i f f e r e n c e ( F i g . 9 ) shows t h e same dependency from aging time as t h e mere s t r e n g t h d i f f e r e n c e ARp0.2.

I n t h e underaged c o n d i t i o n (2h aging t i m e ) t h e maximum o f 27 % i s achieved. A f t e r quenching o r overaging t h e values a r e lowest (12 %, 15 % resp.).

F i g . 11: S l i p d i s t r i b u t i o n ( a ) F i g . 12.: S l i p d i s t r i b u t i o n o f

and p r e c i p i t a t i o n ( b ) s e c t i o n B ( s o l u t i o n t r e a t e d ) o f s e c t i o n B (150h 185OC)

5. DISCUSSION

The a p p l i c a b i l i t y o f e i t h e r t h e SACHS- o r t h e TAYLOR-model depends on t h e pre- dominant slip-mode, which was determined by TEM-analysis o f deformed and n o t deformed s e c t i o n s o f t h e f a i l e d t e n s i l e specimens ( s e c t i o n B ) .

For t h e underaged c o n d i t i o n (2h 185OC) s l i p occurs on s i n g l e , v e r y pronounced s l i p bands (Fig. 10a). T h i s inhomogeneous s l i p d i s t r i b u t i o n i s a t t r i b u t e d t o t h e s p h e r i c a l , ordered and coherent 6 ' (A13Li)- p r e c i p i t a t e s ( F i g . l o b ) e a s i l y shear- a b l e by d i s l o c a t i o n s . Once s l i p i n t h e system w i t h t h e lowest SACHS-factor has s t a r t e d and c u t 6 ' - p r e c i p i t a t e s , t h i s p r i m a r y s l i p plane i s weakened and f u r t h e r s l i p i s b e i n g concentrated on i t l e a d i n g t o t h e observed f o r m a t i o n o f s l i p bands [12]. Therefore t h e r e l a t i v e s t r e n g t h d i f f e r e n c e i n t h i s c o n d i t i o n must be c a l c u l a t e d by SACHS, which i s c l e a r l y confirmed by t h e experiment. A f t e r over- aging (150h 185OC) t h e s l i p d i s t r i b u t i o n i s completely homogeneous ( F i g . l l a ) due t o t h e p a r t l y coherent S'(A1 CuMg) l a t h s besides 6 ' - p r e c i p i t a t e s a c t i n g as obstacles t o d i s l o c a t i o n movgment ( F i g . l l b ) . They a r e bypassed on o t h e r (secondary) s l i p systems w i t h t h e n e c e s s i t y o f m u l t i - s l i p [4,13].

A f t e r quenching s l i p i s a l s o homogeneous ( F i g . 12), as t h e 6 ' - p r e c i p i t a t e s a r e t o o small t o be d e t e c t e d and t o cause inhomogeneous s l i p [14]. The homogeneous s l i p i s o b v i o u s l y caused by m u l t i - s l i p . For t h e quenched and t h e overaged condi- t i o n t h e low r e l a t i v e d i f f e r e n c e i n s t r e n g t h t h e r e f o r e agrees w e l l w i t h t h e c a l - c u l a t i o n according t o t h e TAYLOR-model.

(8)

Compared w i t h e x t r u s i o n temperature and r a t i o t h e s t r e n g t h o f L i t a l A-shapes s t r o n g l y depends on t h e e x t r u s i o n aspect r a t i o ( w i d t h / t h i c k n e s s ) W/T which

- changes t e x t u r e

- reduces s t r e n g t h w i t h shapes g e t t i n g f l a t t e r ( i n c r e a s i n g W/T)

- b r i n g s about a s t r e n g t h d i f f e r e n c e between axisymmetric and f l a t shapes, which i s g r e a t a t t h e begin o f aging and low a f t e r quenching and i n t h e overaged c o n d i t i o n .

As t h e t e x t u r e - s t r e n g t h r e l a t i o n s h i p i s described by t h e SACHS-model f o r s i n g l e s l i p and by TAYLOR f o r m u l t i - s l i p , t h e s t r e n g t h d i f f e r a n c e can be c a l c u l a t e d on t h e b a s i s o f a q u a n t i t a t i v e t e x t u r e a n a l y s i s w i t h good agreement

- by SACHS f o r t h e inhomogeneous s l i p d i s t r i b u t i o n - a t t h e begin o f a g i n g

- by TAYLOR f o r t h e homogeneous s l i p d i s t r i b u t i o n a f t e r quenching and i n t h e overaged c o n d i t i o n .

ACKNOWLEDGEMENTS

T h i s work was sponsored by t h e BMFT. The t e x t u r e a n a l y s i s by J. H i r s c h ( I n s t i t u t f u r Metallkunde, RWTH Aachen) i s g r a t e f u l l y acknowledged.

REFERENCES

[ 11 N.C. Parson and T. Sheppard i n : "Aluminium-Lithium A l l o y s 11", ed.: T.H.

Sanders, J r . and E.A. Starke, TMS-AIME, Warrendale, PA (1984) 53.

[ 21 N.C. Parson and T. Sheppard i n : "Aluminium-Lithium A l l o y s I I I M , e d . : C.Baker e t a l . , The I n s t i t u t e o f Metals, London (1986) 222.

[ 31 M. Peters, K. Welpman and T.H. Sanders, J r . , Proc. 3 r d Conf. o f E-MRS on Advanced M a t e r i a l s R & D f o r Transport, ed.: R.J.H. Wanhill e t a l . , Les B d i t i o n s de physique, Les U l i s (1986) 63.

[ 41 P.J. Gregson and H.M. Flower, Acta M e t a l l , 2 (1985) 527.

[ 51 M. Peters, J. Eschweiler and K. Welpmann, S c r i p t a Met., 20 (1986) 259.

[ 61 S. Fox, D.S. Mc Darmaid and H.M. Flower, Conf. Aluminium Technology 1986, The I n s t i t u t e o f Metals, London (1986) 72.1.

[ 71 J. Hirsch, G. Burmeister, L. Hoenen and K. Lucke i n : 'Experimental Techniques o f Texture Analysis", ed. : H. J . Bunge, DGM-Verlag (1986) 63.

[ 81 H.J. Bunge "Mathematische Methoden der Texturanalyse" Akademie Verlag B e r l i n (1969).

[ 91 J. H i r s c h and K. Lucke i n : " T h e o r e t i c a l Techniques o f Texture Analysisl',ed.:

H. J. Bunge, DGM-Verlag (1987).

[ l o ] E. Sachs, Z . Verein Deutsch. Ing. 72 (1928) 734.

[ll] G . I . T a y l o r , J. I n s t . Met. 62 ( 1 9 3 q 307.

[12] K . Welpmann, M. Peters, T.H. Sanders, J r . , Aluminium 60 (1984) 735 and 846.

[ I 3 1 W.S. M i l l e r , M.P. Thomas, D.J. L l o y d and D. Creber, Mater. S c i . and Techn. 2

(1986) 1210.

[14] K. V.- J a t a and E.A. Starke, J r . , M e t a l l . Trans. A. Z A (1986) 1011.

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