INTERNAL FRICTION STUDY OF STRAIN AGING IN ALLOYS

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INTERNAL FRICTION STUDY OF STRAIN AGING IN ALLOYS

R. Schwarz

To cite this version:

R. Schwarz. INTERNAL FRICTION STUDY OF STRAIN AGING IN ALLOYS. Journal de Physique

Colloques, 1985, 46 (C10), pp.C10-207-C10-214. �10.1051/jphyscol:19851047�. �jpa-00225431�

JOURNAL DE PHYSIQUE

Colloque CIO, supplément au n012, Tome 46, décembre 1985 page C10-207

Materials Science and rechnology Division, Argonne National Laboratory, Argonne, IL 60439, U.S.A.

Abstract - Interna1 f r i c t i o n measurements were used t o study s t r a i n aging

i n

m r y s t a l s of

AR-Mg

and

Cu-AR

alloys as a function of temperature and

aging time. In t h e x s e n c e ofdeformation-generated vacancies, sol ute segregation t o dislocations s t a r t s a t 200 and 300

K,

respectively. Excess vacancies were generated

i n

pure

&

and AR-Mg alloys by in-situ pl a s t i c deformation at 120

K.

With increasing tëiiïperature, solute segregation t o dislocations s t a r t s

i n

these alloys at 200

K,

as

i n

the absence of excess vacancies. The excess vacancies become mobile in pure

^AR

and in the

At-Mg

alloys at 250

K.

I t i s concluded that the i n i t i a l locking of disloca€Tons by solutes occurs through a rearrangement of solutes near the dislocation cores and that

i n

&-Mg alloys, def-ormation-generated vacancies have l i t t l e or no effect in

t h =

process.

1

- INTRODUCTION

In alloys w i t h a low dislocation density, a significant contribution t o the flow s t r e s s arises from the interaction between dislocations and solutes. In substitu- tional fcc alloys this .interaction i s weak, typically of 0.1 - ^{0.2 eV.} Therefore, the flow stress,

^T,

should decrease monotonically

w i t h

increasing temperature.

This T-T dependence i s not observed. .a

&-Kg

alloys, for example, for T < 250 K, dz/dT <

O,

as expected. However, f o r 250 <

T

< 600

K, T

increases

w i t h

increasing temperature (see Fig. 2b). In other alloys, and over

T

regimes of similar widths, T(T) shows a plateau (i.e.,

d ~ / d T =

O ) , the height of which increases rapidly with i ncreasing sol ute concentration. For even higher temperatures, dz1dT is agai n negative. The athermal flow s t r e s s region has received considerable attention Ill,

b u t

a satisfactory explanation for

i t

has yet t o be formulated.

(1)

Work supported by the U.S. Department of Energy.

( 2 ) Present address: Center f o r Materials Science; Los Alamos National Laboratory;

Los Al amos, NM

87545.

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:19851047

(30-208 JOURNAL DE PHYSIQUE

From a microscopic p o i n t o f view, t h e s o l u t e environments t h a t the d i s l o c a t i o n s 18see11 d u r i n g p l a s t i c deformation can be o f t h r e e types: (a) s t a t i s t i c a l , when t h e s o l u t e s are d i s t r i b u t e d a t random, as i n t h e r e s t o f the a l l o y ,

when t h e s o l u t e c o n c e n t r a t i o n near t h e d i s l o c a t i o n s d i f f e r s (usul!l)j-ghat

i n t h e r e s t o f t h e a l l o y , and ( c ) mobile, when t h e s o l u t e s d i f f u s e f a s t and are able t o f o l l o w moving d i s l o c a t i o n s ~ o r more o f these environments can i n - fluence t h e f l o w stress, depending on the r e l a t i v e values o f time constants c h a r a c t e r i z i n g t h e k i n e t i c s o f d i s l o c a t i o n motion and o f s o l u t e d i f f u s i o n t o d i s - l o c a t i o n s .

It i s now f i r m l y e s t a b l i s h e d t h a t f o r s o l u t e environments (a) and (b), t h e d i s l o c a - t i o n s move d i s c o n t i n o u s l y . They spend times tw a t r e s t , w a i t i n g f o r t h e r m a l l y a c t i v a t e d breakaway events, and times tr, where tr

<<

tw, running between

r e s t p o s i t i o n s . I f N i s the number o f l a t t i c e spacings between r e s t p o s i t i o n s , a d i s l o c a t i o n spends a time tr/N i n the v i c i n i t y o f any given l a t t i c e s i t e . On t h e o t h e r hand, t h e s o l u t e m o b i l i t y i s c h a r a c t e r i z e d by a time per atomic jump, tS.

A comparison between these c h a r a c t e r i s t i c times allows f o r a c l a s s i f i c a t i o n o f the d i s l o c a t i o n dynamics i n t o t h r e e regimes: (1) At low temperatures, tw

<<

tS and tr/N

<<

ts, and the d i s l o c a t i o n s always i n t e r a c t w i t h a s t a t i s t i c a l s o l u t e en- v~ronment. ( 2 ) At intermediate temperatures, tw

>>

^{tS and tr/N}

<<

^{tS, and}

t h e d i s l o c a t i o n s break away from 'segregated

'

sol u t e environments, but g l id e through ' s t a t i s t i c a l ' environments. ( 3 ) At h i g h temperatures, (tr/N)

>

t,, and t h e d i s l o c a t i o n s move i n a v i s c o u s - l i k e manner, dragging along a cloud o f solutes.

The models t h a t have been advanced t o e x p l a i n t h e "plateau" i n t h e f l o w s t r e s s can be c l a s s i f i e d according t o whether t h e y invoke s t a t i s t i c a l o r se r e ated s o l u t e d i s t r i b u t i o n s . The models i n v o k i n g f i x e d s o l u t e s a t t r i b u t e th*to n a t u r a l f l u c t u a t i o n s i n t h e sol u t e d i s t r i b u t i o n ; f o r sol u t e concentrations above a few p e r - cent, and f o r moderate temperatures ( i .e. low applied stresses), groups o f

obstacles may behave as single, broad, e f f e c t i v e obstacles 121 o r as l i n e a r b a r r i e r s o r troughs 131. I n both cases t h e a c t i v a t i o n energy f o r d i s l o c a t i o n breakaway exceeds t h a t f o r s i n g l e solutes, thus g i v i n g a more athermal f l o w stress.

The models i n v o k i n g mobile s o l u t e s a t t r i b u t e t h e "plateau" t o t h e l o c k i n g o f t h e d i s l o c a t i o n s by d i f f u s i n g s o l u t e s 14-71. I n these models, t h e l o c k i n g a t tempera- t u r e s t h a t are f a r t o o low f o r s o l u t e d i f f u s i o n through t h e l a t t i c e i s explained i n terms o f an enhanced s o l u t e d i f f u s i v i t y i n t h e d i s t o r t e d l a t t i c e regions near the d i s l o c a t i o n cores.

Amplitude-Dependent I n t e r n a 1 F r i c t i o n (ADIF) i s w e l l s u i t e d f o r studying s o l u t i o n hardening i n a l l o y s . Contrary t o macroscopic f l o w s t r e s s measurements, i n ADIF t h e d i s l o c a t i o n s are o n l y forced t o overcome t h e weak obstacles (solutes). and n o t the strong ones ( o t h e r d i s l o c a t i o n s , p r e c i p i t a t e s ) . Thus, w h i l e t h e f l o w s t r e s s has c o n t r i b u t i o n s from s o l u t i o n hardening and s t r a i n hardening, ADIF m a s u r e s o n l y t h e e f f e c t s o f solutes. An added advantage o f t h e ADIF method i s t h a t the measurements do n o t change t h e I1state" o f the specimen, and hence repeated experiments can be conducted using t h e sarne specimen i n order t o examine t h e e f f e c t s o f v a r i o u s thermal o r mechanical treatments.

Theory 181 and computer modelling 191 show t h a t i n a l l o y s , t h e applied s t r e s s amplitude z0[6,] which r e s u l t s i n a value

&,,,

o f the ampl itude-dependent

decrement i s p r o p o r t i o n a l t o t h e solution-hardening component o f t h e f l o w stress,

7., I n s e c t i o n 2 we present measurements o f zo[Gm] i n annealed a l l o y s i n g l e c r y s t a l s o f CU-& and Al-Mg. I n s e c t i o n 3 we i n v e s t i g a t e t h e inf.luence t h a t excess vacancies ( i x r o d u c e d

6 y

p l a s t i c deformation a t 120 K ) have on t h e t r a n s i t i o n from t h e ' s t a t i s t i c a l ' t o t h e 'segregated' regimes.

II

-

STRAIN AGING I N THE ABSENCE OF EXCESS VACANCIES

C h a r a c t e r i s t i c d i s l o c a t i o n k i n e t i c s times t, and tr were defined i n s e c t i o n 1.

S t r a i n aging occurs when solutes segregate t o arrested d i s l o c a t i o n s d u r i n g tw.

Therefore, a m a n i n g f u l m a s u r e o f t h i s e f f e c t i s the s t r e s s necessary t o remove a d i s l o c a t i o n from the s o l u t e environment t h a t develops a t temperature T a f t e r a

waiting time. ta. This quantity can be derived from o o [ ~ ] measurements pro- vided the solute environment at t = O resembles t h a t encountered by a dislocation when i t becomes arrested during a macroscopic flow s t r e s s t e s t . In the ADIF t e s t s we create t h i s environment by forcing the dislocations, f o r a s u f f i c i e n t l y long time, i n t o an o s c i l l a t o r y motion of amplitude much larger than t h a t used during the subsequent measurements of a0[6,] as a function of aging time. This i n i t i a l - ization i s explained in d e t a i l in /IO/ and

/ I l / .

Figure

1

shows ao[6,] measurements as a function of temperature and aging time in a Cu-0.2 at.%

ILe

single crystal 1101. These measurements are interpreted as follows: The time-independent, T-dependent, heavy curve on the l e f t gives t h e s t r e s s ( a r b i t r a r y u n i t s ) at which dislocations break away from s t a t i s t i c a l solute environments. The time-indepen'dent, T-dependent, heavy curve on the r i q h t qives the s t r e s s at which the dislocations break away from a f u l l y se reqated solute environnent, 1.e. an environnent t h a t i s in thermodynamic e g u h i t h the r e s t of the alloy. The f i v e thinner curves (including the one labeled ' f r e e decay') give the t r a n s i t i o n between these two extremes for fixed aging times. In t h i s context, the ' f r e e decay' curve must be associated with an aginq time

t a - ~ o - ~ s /IO/.

Figure 2 ( a ) shows o,L6,] as a function of temperature and aging time in an

An-1 at.% M g single crystal /7/. These e a r l y measurements were obtained before the development of the f a s t data acquisition system necessary t o measure the "free decay' curves /IO/. Figure 3(b) shows the T-dependence of the c r i t i c a l resolved shear s t r e s s in AR-1.1 at.%

Mq

c r y s t a l s deducet fromlflow s t r e s s measurements a t the constant t e n s i l e s t r a i n r a t e of 4.17 x 10- sec- /12/.

A

comparison between Figs. 3 ( a ) and 3 ( b ) show t h a t u0[6,] measurements give a good measure of the macroscopic flow s t r e s s . Furthermore, t h i s comparison suggest t h a t f o r

240 <

^T

< 600K, the time tw during which the dislocations are arrested are of the

order of seconds. Similar tw values have been estimated for macroscopic flow a t s t r a i n r a t e s of the order of

~ O - ~ S . /3/

0 1 l I i i i i i ~ ~ ~

O .

200

400

600

800 1000 TEMPERATURE ( K I

TEMPERATURE (KI

Fig.

1

- Temperature dependence of uoL6,] in a

Cu

- 0.2 a t . %

AR

single crystal f o r f i v e d i f f e r e n t aging times.

Fig.

2

- ( a ) T-dependence of 0,[6~] in an AR - ^{1 a t}

^.%

^{M g} single crystal f o r

d i f f e r e n t aging times. ( b ) T-dependence of the

CRSS

from flow s t r e s s

t e s t s at a s t r a i n r a t e of 4.17

x

1 0 ' ~ sec-' ( a f t e r Asada e t al., /12/).

CIO-210 JOURNAL DE PHYSIQUE

Figures 1 and 2(a) show t h a t t h e s o l u t e environment near t h e d i s l o c a t i o n s chanqes from s t a t i s t i c a l t o se r e , ated a t a temperature Tl t h a t i s independent o f aqinq time. r u r t h e r m e a s u ï d k $ b T O / show t h a t Tl i s also independent o f s o l u t e concen- t r a t i o n . From t h e measured d i f f u s i v i t y o f AL i n Cu /13/, and o f Mq i n Aa /14/, i t f o l l o w s t h a t these changes cannot occur by s o l u t e d i f f u s i o n through t h e l a t t i c e . The l a r g e discrepancy between t h e s o l u t e d i f f u s i v i t i e s deduced from mechanical t e s t s and those measured d i r e c t l y has been known f o r many years i n connection w i t h t h e Portevin-Le C h a t e l i e r e f f e c t . F o l l o w i n q a suqqestion o f C o t t r e l l /15/,

researchers /16,17/ have a t t r i b u t e d t h e h i g h s o l u t e d i f f u s i v i t y i n mechanical t e s t s t o t h e excess c o n c e n t r a t i o n o f vacancies t h a t i s li k e l y t o e x i s t i n p l a s t i c a l l y deformed a l lo y s . This expl a n a t i o n cannot be assumed o p e r a t i v e here because, f o r t h e p r e s e n t l y a p p l i e d c y c l i c stress, t h e d i s l o c a t i o n s are presumably g l i d i n g over s h o r t distances, overcoming o n l y t h e s o l u t e s and n o t draqging jogs along.

Even i f s o l u t e d i f f u s i o n through t h e p e r f e c t l a t t i c e i s absent, a simple r e d i s t r i - b u t i o n o f t h e sol u t e s w i t h i n t h e d i s t o r t e d l a t t i c e r e q i o n near t h e d i s l o c a t i o n cores can change a p p r e c i a b l y t h e breakaway s t r e s s . The l a c k o f Debye-type r e l a x a t i o n peaks i n t h e temperature dependence o f t h e amplitude-independent

decrement (see Fig. 4 i n 1101) suggests t h a t t h e s o l u t e displacements are p r i m a r i l y i n d i r e c t i o n s perpendicular t o the core. A mode1 f o r t h e s o l u t e r e d i s t r i b u t i o n w i t h i n t h e cores was presented e a r l i e r / I O / . It i s based on t h e assumption t h a t i n t h e d i s l o c a t e d c r y s t a l , as t h e s o l u t e approaches t h e d i s l o c a t i o n core, i t sees not o n l y a decrease i n t h e ground-st'dte energy, b u t also a decrease i n t h e energy d i f f e r e n c e , AU, between t h e ground s t a t e and t h e adjacent saddle p o i n t s . It i s thus l i k e l y t h a t near t h e core, AU becomes s u f f i c i e n t l y small t o a l l o w f o r

t h e r m a l l y - a c t i v a t e d s o l u t e jumps i n t o lower energy p o s i t i o n s , thus incrementing t h e d i s l o c a t i o n - s o l u t e b i n d i n q energy. Furthermore, successive s o l u t e jumps would a l l o w t h e d i s l o c a t i o n s t o become s t r a i g h t i n response t o t h e i r own l i n e tension.

This e f f e c t has indeed been observed i n AL-0.1 at.% Mq a t 300 K / I O / and i n Cu-0.2 at.% Aa a t 491 K /9/. The complete s t r a i g h t e n i n g o f t h e d i s l o c a t i o n s , w i t h o u t a d e t e c t a b l e increase i n t h e amplitude-independent decrement, i s f u r t h e r evidence t h a t t h e sol u t e s move perpendicul a r l y t o t h e cores.

III

-

STRAIN AGING I N THE PRESENCE OF EXCESS VACANCIES

I n f c c a l l o y s , where s o l u t e t r a n s p o r t occurs b y vacancy-assisted d i f f u s i o n , vacan- c i e s are thought t o p l a y an i m p o r t a n t r o l e i n t h e aqinq k i n e t i c s . The h i q h ampli- tude c y c l i c s t r a i n , although s u f f i c i e n t t o f r e e t h e d i s l o c a t i o n s from segregated solutes, cannot c r e a t e p o i n t d e f e c t s through t h e dragqjng o f d i s l o c a t i o n jogs.

Thus, i n order t o study t h e e f f e c t s o f excess vacancies by i n t e r n a l f r i c t i o n , these must be introduced by p l a s t i c deformation. For t h i s , t h e i n t e r n a l f r i c t i o n

apparatus was m o d i f i e d (Schwarz and Funk, unpublished), a l l o w i n g us t o bend t h e v i b r a t i n g reeds i n s i t u a t 120 K. Because t h e reed has a t h i n n e d r e q i o n (see Fig. 1 i n /IO/), t h e bending causes p l a s t i c deformation o n l y w i t h i n t h i s region, which i s t h e same t h a t c o n t r i b u t e s t o the energy losses measured by ADIF.

Curve A i n Fig. 3 shows t h e 6(u0) dependence i n an undeformed AL-0.1 at.% Mg c r y s t a l a t 128K. Curve B i n t h i s f i g u r e shows 6(aO) f o l l o w i n g p l a s t i c deforma- t i o n . The p l a s t i c s t r a i n near t h e surface o f t h e thinned r e g i o n i s estimated t o be 0.02. As t h e r e s u l t o f p l a s t i c deformation, t h e r e i s an increase i n 6 i and a de- crease i n t h e value o f u0 a t which 6 becomes amplitude dependent. 60th e f f e c t s can be r a t i o n a l i z e d i n terms o f t h e generation o f d i s l o c a t i o n segments free of seg- regated s o l u t e s . The two s h o r t h o r i z o n t a l l i n e s c u t t i n g curves A and B i n Fig. 3 show a decrement l e v e l 0.005 higher than t h e corresponding 67 values. The i n t e r s e c t i o n o f these l i n e s w i t h curves A and B d e f i n e t h e stresses

a,[6, = 0.0053, shown by the arrows on t h e abscisa. The f o l l o w i n g measurements describe t h e T-dependence o f 6 i and o f uo[Sm] i n s i n g l e c r y s t a l s o f AL,

AR-0.1 at.% Mg, and Al-1.0 at .% Mg. The u0[6,] measurements for .aging t i m e o f 60 s were taken using a decrement-time histogram s i m i l a r t o t h a t shown i n Fig. 10 o f /IO/. A mass spectrographic a n a l y s i s o f t h e pure AL sample revealed about 10 ppm Fe, w i t h a l 1 o t h e r i m p u r i t i e s a t concentrations below t h e 3 ppm l e v e l

.

0 . ~,

,:,:

~ ~

" , -

1 ^, ~

^{, ,}

^,

, ^{, ,}

..

^{. x xrr xxxx../}

i

94 -3 -2 -1

LOG (CO)

TEMPERATURE (K)

F i g . 3

-

Decrement versus s t r e s s amplitude i n AR

-

0.1 at.%Mg a t 128 K before (crosses) and a f t e r ( c i r c l e s ) p l a s t i c deformation.

Fig. 4

-

T-dependence o f t h e amplitude independent decrement i n pure AR f o l lowing p l a s t i c deformation a t 120 K. Crosses: measurement d u r i n q i n c r e a s i n q T;

c i r c l e s and t r i a n g l e s : measurements d u r i n g decreasing T.

111.1 Measurement of 6 i

Figures 4 and 5 show 6 i ( T ) measurements i n pure AR and i n AR-0.1 at.% Mg

c r y s t a l s , r e s p e c t i v e l y . Measurements i n Al-1 at.% Mq are very s i m i l a r t o those i n Fig. 5 and are thus n o t shown here. For each f i g u r e , t h e sample was p l a s t i c a l l y deformed a t 120 K and 6 i was measured d u r i n g t h e continuous h e a t i n g (crosses) and subsequent c o o l i n g ( c i r c l e s ) a t t h e r a t e o f 150 K l h r . L e t t e r s have been added t o these f i g u r e s i n order t o f a c i l i t a t e t h e i r discussion. However, before d i s c u s s i n g these r e s u l t s i n greater d e t a i l , we need t o summarize t h e t h e o r e t i c a l

i n t e r p r e t a t i o n s o f t h e 6 i ( T ) curves.

For a d i s l o c a t i o n d e n s i t y A i n t e r a c t i n g e l a s t i c a l l y w i t h a 2 f i x e d p o i n t - o b s t a c l e c o n f i g u r a t i o n , the Granato-Lucke t h e o r y p r e d i c t s 61 ^.:ABIK

,

where B i s t h e v i s - cous damping and 1/K i s an e f f e c t i v e compliance. A d d i t i v e c o n t r i b u t i o n s t o 11K of i n t e r e s t here are ( l / K ) ~ o o p ^12, a r i s i n g from t h e bowing o f d i s l o c a t i o n segments o f length R between f i x e d obstacles, and (l/K),bS R, due t o t h e compliance of t h e d i s l o c a t i o n - o b s t a c l e i n t e r a c t i o n . Thus, t h e s e n s i t i v i t y o f 61 t o p o i n t d e f e c t s a r r i v i n g at d i s l o c a t i o n s decreases as t h e defect c o n c e n t r a t i o n increases.

For a constant d i s l o c a t i o n density, t h e T-dependence o f 6 i i s determined by t h a t o f B(T) and K(T). If the s o l u t e s are f i x e d i n the l a t t i c e , 61 r e f l e c t s t h e T- dependence o f B(T), which, except f o r very low temperatures, increases l i n e a r l y w i t h i n c r e a s i n g T. The dashed l i n e s added t o Figs. 4 and 5 represent t h i s i n - crease, f o r d i f f e r e n t values o f A / K ~ . The non-zero 61 i n t e r c e p t a r i s e s from energy losses i n the sample holder.

The data f o r AR-0.1 at.% Mq i n Fig. 5 w i l l be discussed f i r s t . F o l l o w i n q p l a s t i c deformation a t 120 K, 61 has a r e l a t i v e l y h i g h value. With the increase i n T, 6 i shows d i p s and r i s e s which i n d i c a t e changes i n t h e environment o f p o i n t d e f e c t s surrounding t h e d i s l o c a t i o n s . These changes commence a t -125 K ( p o i n t a), where 6 i ( T ) changes from a l i n e a r increase t o a plateau, and end a t -275 K.

Once t h e &-Mg a l l o y has been heated t o t h i s temperature, t h e 6 i ( T ) curve has t h e shape i n d z a t e d by t h e open c i r c l e s , which remains unchanged f o r f u r t h e r increases o r decreases i n T. This shape i s u s u a l l y found i n annealed a l l o y s .

C10-212 JOURNAL DE PHYSIQUE

Fig. 5

-

T-dependence o f the amplitude independent decrement i n AR

-

0.1 at.% Mg f o l l o w i n g p l a s t i c deformation a t 120 K. Crosses and c i r c l e s denote measurements d u r i n g i n c r e a s i n g and decreasing temperature, r e s p e c t i v e l y . Fig. 6

-

T-dependence o f a0[6,] f o r an aging time o f 60 s i n AR

-

^{1 a t .% Mg.}

Crosses and c i r c l e s denote measurements during i n c r e a s i n g and decreasing temperature, r e s p e c t i v e l y .

I n Fig. 5, t h e p l a t e a u (a-b) i s a d e v i a t i o n from the expected l i n e a r increase ( r - a ) and thus denotes t h e f i r s t a r r i v a l o f p o i n t d e f e c t s t o t h e d i s l o c a t i o n s . The r a t e a t which t h e d e f e c t s a r r i v e increases r a p i d l y a t p o i n t (b). The a r r i v a l o f these d e f e c t s stops a t 220 K ( p o i n t c). The slope o f (c-d) i s steeper than t h a t o f t h e dashed curve ( r - c ) suggesting t h a t f o r 220

<

T

<

250 K, some o f t h e p r e v i o u s l y a r r i v e d d e f e c t s leave t h e d i s l o c a t i o n o r coalesce, thus i n c r e a s i n g t h e value o f

n.

A d d i t i o n a l p o i n t d e f e c t s segregate t o the d i s l o c a t i o n s w i t h i n (d-e). At p o i n t (e), t h e 6 i ( T ) curve j o i n s t h a t c h a r a c t e r i s t i c o f aged a l l o y s . No a d d i t i o n a l aging stages are observed f o r T

>

275 K i n the 6 i ( T ) curves o f %-Mg a l l o y s . This i s c o n t r a r y t o t h e i n f o r m a t i o n provided by the C T , [ ~ ~ ] measurements ( t o be

described l a t e r ) which show a d d i t i o n a l aging stages.

The 6 i ( T ) measurements i n pure AR (Fig. 4) were more d i f f i c u l t t o o b t a i n because i n A l , t h e 6(ao) curve becomes amplitude dependent a t extremely low oo values.

Even working a t t h e l i m i t s o f s e n s i t i v i t y o f Our instrument, we were unable t o conf i d e n t l y reach t h e amplitude-independent region. Nevertheless, t h e 6 i (T) curve f o r pure An has c l e a r signatures, some which d i f f e r from those seen i n t h e 6 i ( T ) curves f o r t h e AR-Mg a l l o y s . The most important d i f f e r e n c e i s t h e absence i n pure An o f stage ( b f c ) . This i m p l i e s t h a t stage (b-c) i n the a l l o y s i s due t o the l o c k i n g o f t h e d i s l o c a t i o n s by solutes o r by vacancy-solute complexes. We can

also i d e n t i f y stage (d-e). Because t h i s stage i s seen both i n pure AR and i n the AR-Mg a l l o y s , we a t t r i b u t e d i t t o t h e segreqation of vacancies t o t h e d i s l o c a t i o n s . E n t r a r y t o the 6 i ( T ) curve f o r the AR-Mg alloys, t h e 6 i ( T ) curve f o r pure AR

shows a d d i t i o n a l s t r u c t u r e f o r T

>

3% K (beyond p o i n t e ) . I n the alloys, a t T = 325 K the d i s l o c a t i o n s are already locked by solutes t o such an extent t h a t a d d i t i o n a l p o i n t defects, a r r i v i n g a t higher temperatures, do not give measurable changes i n 6 i ( T ) . On the other hand, i n the AR c r y s t a l , a t , T = 325 K t h e d i s -

locations are o n l y locked by vacancies. These leave t h e d i s l o c a t i o n s o r coalesce d u r i n g stage (e-O). 6 i ( T ) i n pure A l begins t o decrease at 450K ( p o i n t O ) w i t h t h e a r r i v a 1 t o t h e d i s l o c a t i o n s o f t r a c e i m p u r i t i e s d i f f u s i n g through t h e bulk.

I n order t o determine whether the peaks i n 6 i ( T ) , such as (e-O-p) i n Fig. 4 or (c-d-e) i n Fig. 5, were caused by Debye-type r e l a x a t i o n s , t e s t s were performed whereby the sign o f dT/dt was reversed a t s p e c i f i c p o i n t s along these stages. One such a r e v e r s i b i l i t y t e s t , performed i n AR around T = 485K i s shown i n Fig. 4. It was e s t a b l i s h e d that, w i t h the exception o f stage (e-O) i n pure AR, none o f t h e anneal i n g stages i s r e v e r s i b l e .

II 1.2 Measurements o f uo[6,,,].

F i g u r e 6 shows t h e T-dependence o f ao[6m = 0.0051 f o r an aging time ta = 60 s i n an Al-1 at.% Mg c r y s t a l . The decreases (b-c) and (d-e) i n Si, seen i n Fig. 5, correspond t o t h e increases (b-c) and (d-e) i n u0L6,J, seen here. These two stages were discussed previously. The u [6,] versus T curve shows a d d i t i o n a l aging stages, s t a r t i n g a t 360 K ( p o i n t f y and 560 K ( p o i n t h). I n AR-0.1 at.% Mg, t h e o v e r a l l T-dependence o f u0[6,] i s s i m i l a r t o t h a t o f Fig. 6 (Schwarz and Funk, unpublished), b u t the minima a t ( f ) and (h) are not seen. This suggests t h a t stages ( f - g ) and ( h - i ) are due t o an increase i n t h e amout o f solutes i n s o l u t i o n f o l l o w i n g the d i s o l u t i o n o f Mq p r e c i p i t a t e s near aged d i s l o c a t i o n s ( f o r T

>

360 K) and i n the bulk ( f o r T

>

560 K). This i n t e r p r e t a t i o n , although h i g h l y speculative, agrees w i t h Our e a r l i e r d e t e c t i o n by ADIF o f Mg p r e c i p i t a t e s i n AR-1 at.% Mg. a t 331 K, but no evidence o f p r e c i p i t a t e s i n the same sample a t T = 585 K 171.

I V

-

DISCUSSION AND CONCLUSIONS

The aim o f the present i n t e r n a 1 f r i c t i o n studies i s t o achieve a b e t t e r understand- i n g o f s t r a i n aging i n a l l o y s at temperatures t h a t are too low f o r b u l k s o l u t e d i f - f u s i o n . I n p a r t i c u l a r , we want t o i n v e s t i g a t e whether the l o c k i n g o f d i s l o c a t i o n s by sol utes moving through d i s t o r t e d l a t t i c e regions near d i s l o c a t i o n s can expl a i n t h e so-called ' p l a t e a u ' i n t h e T-dependence o f the flow stress. A f u r t h e r issue of i n t e r e s t i s the r o l e of deformàtion-generated vacancies i n the aging k i n e t i c s . The f i r s t s e r i e s of measurements were performed i n undeformed a l l o y s ( s e c t i o n I I ) . These t e s t s show t h a t t h e solutes are mobile near d i s l o c a t i o n s cores a t tempera- t u r e s as low as 200 K i n AR-Mq a l l o y s , and 300 K i n Cu-AR a l l o y s . The second s e r i e s o f measurements ( s e c t i o n III ) were performed AR-Mg a l l o y s p l a s t i c a l l y de- formed a t 120 K. These t e s t s show t h a t the vacancies g z e r a t e d by p l a s t i c deforma- t i o n have l i t t l e e f f e c t on t h e e a r l y stages o f s t r a i n aging. The arguments f o r t h i s conclusions are as f o l l o w s : Figure 4 shows t h a t i n pure AR, the bulk of t h e deformation-generated vacancies become mobile a t 250 K ( p o i n t d). This value agrees w i t h t h a t deduced from isochronal annealing peaks observed i n AR a f t e r quenching

/la/.

However, i n the AR-Mg a l l o y s , s i g n i f i c a n t l o c k i n q o f d i s l o c a t i o n s occurs between 190 and 220 K (sta@ b-c i n Figs. 5 and 6). Therefore, t h i s stage, which i s not seen i n pure AR, must be associated w i t h s o l u t e motion by an

i n t e r s t i t i a l - l i k e mechanism. Certainly, t h i s can o n l y occur near the d i s l o c a t i o n cores.

The deformation generated vacancies g i v e l a r g e r signatures i n t h e T-dependence of 6 i than i n the T-dependence o f 00[6,] f o r ta = 60 S. I n

9 -

^{1 a t % Mg,}

t h e o v e r a l l shape of t h e 0,[6~] versus T curve (Fig. 6) i s approximately the same f o r i n c r e a s i n g and decreasing T, except f o r a v e r t i c a l displacement. This displacement occurs m o s t l y i n stage ( h - i ) , which we a t t r i b u t e t o t h e segregation of s o l utes t o unaged d i s l o c a t i o n s , f o l lowing the thermal d i s o l u t i o n o f Mg

CIO-214 JOURNAL DE PHYSIQUE

r r e c i p i t a t e s . I n agreement w i t h t h i s i n t e r p r e t a t i o n , t h e uoL&,,,] versus T curves i n A l

-

0.1 at.% Mg (Schwarz and Funk, unpublished), measured d u r i n g i n - c r e a s i n g and decreasinq T runs, do n o t show t h e v e r t i c a l d i s p l acement seen i n Fig.

6 f o r t h e more concentrated a l l o y . We thus conclude t h a t i n AR-Mg a l l o y s , and f o r s t r a i n s o f t h e order o f 0.02 o r less, t h e r o l e o f d e f o r m a t i o n q e n e r a t e d vacancies on s t r a i n aging i s minor. S u b s t a n t i a l l o c k i n g o f t h e d i s l o c a t i o n s occurs by s o l u t e motion w i t h i n t h e d i s t o r t e d l a t t i c e surroundinq t h e d i s l o c a t i o n cores a t

temperatures about h a l f those needed f o r s o l u t e d i f f u s i o n i n t h e bulk. F u r t h e r - more, t h i s m o b i l i t y allows the d i s l o c a t i o n s t o s t r a i g h t e n i n response t o t h e i r l i n e tension. The thermal l y - a c t i v a t e d breakaway of a d i s l o c a t i o n from a dense l i n e a r d i s t r i b u t i o n o f solutes, as opposed t o the random d i s t r i b u t i o n i n a plane T Ô G T a t lower T, i s one o f t h e e x p l a n a t i o n s proposed f o r t h e ' p l a t e a u ' i n t h e f l o w s t r e s s 131. The present measurements show how t h i s l i n e a r d i s t r i b u t i o n may form i n t h e absence o f long-range sol u t e d i f f u s i o n .

The ADIF measurements o f t h e k i n e t i c s o f s t r a i n aging by s o l u t e m i g r a t i o n near t h e d i s l o c a t i o n cores suggests t h a t t h e solution-hardening component o f t h e f l o w s t r e s s increases w i t h aginq t i m e as 1101

where c i s t h e s o l u t e concentration, zo(c,T) i s t h e flow s t r e s s i n t h e absence o f s o l u t e segregation, AT(c,T) i s t h e s a t u r a t i o n value o f t h e l o c k i n g stress, and tc i s a t i m e constant p r o p o r t i o n a l t o t h e s o l u t e d i f f u s i v i t y near the d i s l o c a t i o n cores. This equation has been used t o e x p l a i n the negative value o f t h e s t r a i n r a t e s e n s i t i v i t y o f t h e f l o w s t r e s s 1191 and, more r e c e n t l y , t o e x p l a i n t h e ampli- tude o f s t r e s s s e r r a t i o n s o f t h e t y p e Portevin-Le C h a t e l i e r 120,211.

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