On the plastic behaviour of concentrated CuMn single crystals

Scr~pta

MIiTAI.LURGICA

Vol.

ON THE P L A S T I C

14, pp. 923 - 928, 1980 Printed in the U.S.A.

BEHAVIOUR

Th.

OF C O N C E N T R A T E D

Wille

and Ch.

Cu-~n

Pergamon Press Ltd. All rights r e s e r v e d .

SINGLE C R Y S T A L S

Schwink

I n s t i t u t A fur Physik, T e c h n i s c h e U n i v e r s i t M t D - 3 3 O O B r a u n s c h w e i o , Fed. ReD. G e r m a n y (Received

June

5, 1980)

Introduction Solid s o l u t i o n h a r d e n i n ~ and the easy qlide staqe of d e f o r m a t i o n of c o n c e n t r a ted fcc alloys have been the o b j e c t of a l r e a d y many i n v e s t i q a t i o n s (cf. reviews (I-3)). The most i n t e n s i v e l y i n v e s t l q a t e d C u - b a s e d systems, like Cu-Al (4-9), Cu-Ge (10-13), C u - G a (10,11) and C u - Z n (14,15), have a s t a c k i n q fault e n e r q y (SFE) w h i c h c o n s i d e r a b l y d e c r e a s e s for h i ~ h e r c o n c e n t r a t i o n s of the alloyed e l e m e n t (16). C h a r a c t e r i s t i c p r o p e r t i e s of these alloys as the a p p e a r a n c e of c o a r s e slip bands i n d i c a t i n q o r e d o m l n a n t planar alide and a o r o n o u n c e d inhomoq e n e i t y of slid have been d i s c u s s e d as to be s t r o n g l y influenced or even caused by the d e c r e a s e in SFE r e d u c i n q the p r o b a b i l i t y of cross slid p r o c e s s e s (cf.2~. The i n t e n t i o n of the p r e s e n t work is to test this view and to i n v e s t i g a t e the role of SFE r e ~ a r d i n ~ the p l a s t i c b e h a v i o u r of alloys by s t u d y l n ~ a C u - b a s e d s y s t e m in w h i c h the SFE of c o p p e r is not or not a p p r e c l a b l v c h a n q e d bv alloyinq, w i t h o u t a s i m u l t a n e a u s d i m i n u i t i o n of the s o l u t i o n h a r d e n l n ~ effect. This seems to be the case for Mn as a l l o y i n ~ element where the SFE is r e p o r t e d to d e c r e a s e o n l y very s l i a h t l v with a l l o v i n a (16), at least for c o n c e n t r a t i o n s below 1Oat%Mn(17). Ni as solute even raises the SFE of c o p p e r in a c c o r d a n c e with the t h e o r e t i c a l s u ~ q e s t i o n that here the p r e s e n c e of empty d - s t a t e s results in an i n c r e a s e of the SFE (18,19). But, as the s o l u t i o n h a r d e n i n q effect of Ni is m u c h lower than that of Mn we d e c i d e d for the C u - M n s y s t e m which, moreover, until now has been I n v e s t i q a t e d with respect to its flow stress only in the d i l u t e a l l o y ranae (20). We used for our studies sln~le c r y s t a l s o r i e n t e d for sln~le slid (Schmld factor 0.49) w i t h a M n - c o n c e n t r a t i o n b e t w e e n 3.3 and 7.7 at% Mn. All samples were h o m o q e n i z e d for 24 hours at about 60 K b e l o w their m e l t l n a point, then annealed for 4 - 6 hours at 690 K and s u b s e a u e n t l y q u e n c h e d to 240 K. Samples w i t h less than 2 at% Mn do not show a LHders band in staqe I, their mode of d e f o r m a t i o n c h a n a i n q a r o u n d this c o n c e n t r a t i o n . W e will c o n s i d e r this point more c l o s e l y in a f o l l o w i n q paper (21). Critical

resolved

shear

stress

(crss)

and a c t i v a t i o n

parameters

The crss, ~oi of C u - M n samples i n c r e a s e s b e t w e e n 77 - 300 K with i n c r e a s i n ~ Mnc o n c e n t r a t i o n and d e c r e a s e s steeply with i n c r e a s i n a t e m o e r a t u r e (Fiq. I). Both findinas are typical for c o n c e n t r a t e d fcc alloys (I-3), thouqh q u a n t i t a t i v e l y the h a r d e n i n q effect of Mn exceeds that one of o t h e r e l e m e n t s llke A1 (7-9), Ga (Io,11), Ge (11,13) and Zn (14,15) (cf. Fiq. I). The d e p e n d e n c e of ~ o on the M n - c o n c e n t r a t i o n is s h o w n in Fiq. 2 in a loq ~ o - log c - DIot. For compar is o n w i t h t h e o r i e s (cf. (1)) d a s h e d lines i n d i c a t e ci/2- and c 2 / 3 - d e p e n d e n c i e s . As r e p o r t e d a l r e a d y for C u - G e a l l o y s (cf. (13)) also the C u - M n alloys obey for h i a h e r c o n c e n t r a t i o n s m o r e c l o s e l y a c l / 2 - r e l a t i o n s h i D than the c 2 / 3 - L a b u s c h law (22).

0036- 9 7 4 8 / 8 0 / 0 8 0 9 2 3 - 0 6 5 0 2 . 0 0 / 0 C o p y r i g h t (c) 1980 Pergamon Press Ltd.

924

FLOW OF Cu-Mn CRYSTALS

50 ~

Vol.

~0 ":

\\o

-

/13 /

n

/0/0"

o/

9,3 - - -

10

/ / /

10 "-.

~ 295 K

o/O

20

20

a/

n4~

~n/

MPa

Cu M

8

77K

50

~o

14, No.

/

/

/

-~-

/

!u20_at%Zn

/

/ /.

C20 Cb

.1" /

/

/I//"

l

T K FIG.

c

I

FIG.

T e m p e r a t u r e d e p e n d e n c e of the crss for C u - M n (o). For c o m p a r i s o n curves for C u - 7 . 3 a t % G e and C u - 3 O a t % Z n (both from (13)).

a t % Mn 2

Double l o ~ a r i t h m i c plot of the d e p e n d e n c e of the crss, ~ O, on c o n c e n t r a t i o n of Cu-~n for two temperatures.

F o l l o w i n g w e l l - k n o w n p r i n c i p l e s a t h e r m o d y n a m i c a l a n a l y s i s of the ~Zfo(T)-curves yields v a l u e s for the c h a r a c t e r i s t i c a c t i v a t i o n parameters: average free activation enthalpy, ~-~o, d e n s i t y of o b s t a c l e s in the glide plane, Nz, and athermal c o n t r i b u t i o n to the flow stress, ~ o The basis for the a n a l y s i s is always an A r r h e n i u s e q u a t i o n for the strain rate: = ao exp -

f( ~ s ' & C o ' N z )

'

(I)

kT where f is a d i m e n s i o n s l e s s function a d d i t i o n a l l y d e p e n d i n g on the e f f e c t i v e stress on a d i s l o c a t i o n , ~s, w h i c h is the d i f f e r e n c e b e t w e e n the applied stress, N o , and the a t h e r m a l stress ~ o c o r r e c t e d for the T - d e p e n d e n c e of the shear modulus ~(T) :

%

:

-

(T)i (Ol

(2)

The choice of d i f f e r e n t p o t e n t i a l s for the i n t e r a c t i o n b e t w e e n d i s l o c a t i o n and o b s t a c l e s (23) influences the function f, but not a p p r e c i a b l y the r e s u l t i n , act i v a t i o n parameters. T a k i n g Seeger's p o t e n t i a l (24) one gets as a first approximation:

o12/3

X%

T

2/3

where C and To are functions of the a c t i v a t i o n parameters, essentlallv. The e q u a t i o n s a t i s f a c t o r i l y d e s c r i b e s the t e m p e r a t u r e d e p e n d e n c e of the crss and yields via C and T o by a graphic e v a l u a t i o n EPJo and Nz, if some choice for T ~ o is made guided by the c o n s i d e r a t i o n that only a finlte ~ o yields a t e m p e r a t u r e d e o e n d e n c e of ~ w h i c h is not u n r e a s o n a b l y large (23). Table I shows these results for four alloys t o g e t h e r with the scatter caused by the u n c e r t a i n t i e s in ~po.

Vol.

[4, No.

8

FLOW OF Cu-Mn

Table

925

CRYSTALS

I

Activation parameters A--Go, N z as d e t e r m i n e d from thermal a c t i v a t i o n a n a l y s i s for C u - M n a l l o y s a c c o r d i n g to egu. (3), e v a l u a t e d for a ranoe of most p r o b a b l e a t h e r m a l stresses, T~o, in each case. Nz is c o m p a r e d w i t h the a v e r a q e areal d e n s i t y of Mn~atoms, NMn = c a t ' 4 / ( ~ ' b 2) (Cat = atomic c o n c e n t r a t i o n ) . ~)uo

T

O~°

[at%]

[MPa]

[K]

[ ".Pa ]

3.3

6-8

3.8

Nz/NU n

Z"juo/ '~o

10 -3

77

30.9

0.9-1.2

9-11

O.8-I .O

O.19-O.26

16.6

1.2-1.5

2- 3

O.2-N.3

0.36-0.48

77

32.8

0.8-0.9

22-24

295

18.1

1.2-1.5

2- 4

I .6-I .8

O. 24-0.30

O.2-0.3

0.44-0.55

77

42.8

0.8-0.9

38-47

2.0-2.5

O.28-0.33

295

22.5

0.9-1.0

14-18

0.7-0.9

0.53-0.62

77

49.8

0.7-0.8

81-1OO

3.0-3.7

O. 28-O. 32

295

23.8

0.8-0.9

32-47

I .2-I .8

O. 59-0.67

12-14

7.7

[eV]

[m-2 ]

295 8-IO

5.5

Nz. IO 14

GO

CMn

14-16

The i m p o r t a n t c o n c l u s i o n s that can be drawn are: I) The ~ o - v a l u e s , v a r v i n q with CMn from 0.7 - 1.2 eV for 77 K and from 0.8 - 1.5 eV for 295 K, are of nearly ,the same m a g n i t u d e as those d e t e r m i n e d for Cu-Ge alloys and C u - 3 O a t % Z n (23). 2) The ratio of the o b s t a c l e d e n s i t y to the a v e r a g e areal d e n s l t v of single Mnatoms, Nz/NMn, is smaller than 5.10-3 for all alloys. That shows that as in oth e r fcc alloys i n v e s t i q a t e d not sinqle atoms but qroups of them act as obstacles (7,12,13,23,25). 3) The r a t i o b e t w e e n the p r o b a b l e a t h e r m a l stress and the crss, ~ o / ~ o , is found to i n c r e a s e w i t h s o l u t e c o n c e n t r a t i o n from about 20% to 30% ~ o r T = 77 K, and from 35% to 70% for T = 295 K. S i m i l a r values were found for C u - G e and C u - Z n (23).

~°°t

FIG.

%oi ~o i

,/o

,

i"

°/

~o --~°/

//

""

.¢/

.''"

T= 295 K

.-.."

20: __o~-~°~

O,5 o,1'

'

o,2 "

'

~,0 k'3

"

o,

"~'

'

,9

o.'5 .....

15 0,6

3 and FIG.

4

Strain h a r d e n i n ~ curves up to fracture (arrows) for C u - 7 . 7 a t % M n (o) and C u - 3 . 8 a t % M n (o) at T = 295 K (Fiq. 3) and T = ~7 K (Fig. 4) o = 1.16 I0-~ s-1. The curves for oure copnet (-.-, 99.999%) are taken from (27), that for C u - 3 O a t % Z n (---) from (15). For C u - 7 . 7 a t % M n , 295 K, the end of the L¢Iders reoion is indicated by an arrow.

0.7

= In I/1o FIG.

3

926

FLOW OF Cu-Mn

CR Y S T A L S

Vol.

14, No.

FIG.

4

8

.of-

Y20 !

YO0

s

,

T M~

/

0

,'/

80 /

/

O/

0

Q,

01 '

0/./." .'"

60

e~ -

°

_

°

w ~

-l"

i

ee

"

0,.5

o~

012

~o

o~s

o~$

o14

Strain

8 . . . .

,.,.s

0,6

=lnl/Io

hardenina

.

_

0,'7

curves

The c o m p l e t e strain h a r d e n i n ~ curves d r a w n for 295 K (Fig. 3) and 77 K (Fig. 4) show the w e l l - k n o w n e l o n g a t i o n of staae I by a l l o y i n g b e s i d e the solute h a r d e nina. At the b e a l n n i n ~ of d e f o r m a t i o n for O ~ 6 = in i/i o & O.I~ a LSders band is p r o p a a a t i n a a l o n a the crystal. A f t e r w a r d s i r r e a u l a r l y spaced strona slip bands are v i s i b l e on the crystal surface , i.e. slip is n r o c e e d l n q r a t h e r inhom o q e n e o u s l y with planar glide as also o b s e r v e d for p o l y c r y s t a l l i n e C u - 2 O a t % M n (26) . A l r e a d y at the end of staae I, where the h a r d e n i n , rate starts to increase, d o u b l e cross slip p r o c e s s e s set in abundantly. C o n s e q u e n t l y , d u r i n a the followina second stage of d e f o r m a t i o n the normal staae II - w o r k h a r d e n i n , p r o c e s s e s of pure c r y s t a l s and the work s o f t e n i n ~ p r o c e s s e s due to d o u b l e cross sllp s u p e r p o s e r e s u l t i n a in a smaller but c o n s t a n t work h a r d e n i n a rate for the second stage than o b s e r v e d for sta~e II of pure copper. This i ~ m e d l a t e l y can be seen from Fias.3 and 4. A l l o y systems in which d o u b l e cross slip sets in only after d i s t i n c t stage I I - h a r d e n i n a have a somewhat smaller work h a r d e n i n ~ rate in sta~e II, too. That is e x p l a i n e d by H i r s c h (28) by the p r e s e n c e o~ the f r i c t i o n stress leadinq to a smaller f r a c t i o n of s e c o n d a r y to primary d i s l o c a t i o n densities. The a c t i v a t i o n v o l u m e as d e t e r m i n e d inq account of F r i e d e l ' s relation):

from

stress

relaxation

experiments

V = ~ kT d i n ( - ~ ) d~ shows

a dependence

T ab l e 2 gives temperatures.

on stress

the c o n s t a n t s

which

(4)

can be very well

R and S d e d u c e d

(and tak-

described

by V = - ~

from the e x p e r i m e n t s

P

.

for d i f f e r e n t

A d i s c u s s i o n of the c o m b i n a t i o n of s o l u t i o n and strain h a r d e n i n g in the second stage w h i c h starts from linear a d d i t i v i t v o~ stresses (29) uses with a d v a n t a a e these results (cf. similar c o n s i d e r a t i o n s for C u - N i in (30)), but is not further r e p o r t e d here.

Vo[.

14,

No.

8

FLOW OF Cu-,Xln CRYS'IAI.S

Table

2

The c o n s t a n t s R and S d e s c r i b i n ~ the the a c t i v a t i o n volume, V = P / ( ~ + S ) , r e l a x a t i o n e x n e r i m e n t s for two Cu-)~n c o ~ p e r and C u - 1 O a t % N i for c o m p a r i s o n T EEl

77

295

c [at%~In]l

R [IO -21

J]

, 40

S [~"Pa]

45~±

927

2o

stress d e p e n d e n c e of as d e t e r m i n e d from stress alloys. Data for pure from (30). c [at%Ni]

~ [Io -21

,73

O

330

o

S [ ~Ipa]

3.8

350~

7.7

32o J

60~

le

276

37

3.8 7.7

2 O O O ~ ± 400 18OO |

90 ~ ± 30 60 I

O 10

885 1020

37

O

At hiqh strains the ~ ( a ) - c u r v e s c a l c u l a t e d for single slin bend d o w n w a r d s (dashed parts). This is the result of ~lide on the c o n j u g a t e slid system evidenced by the a p p e a r e n c e of c o r r e s D o n d i n ~ Slid lines. The stress w h e r e a b u n d a n t d o u b l e cross slin sets in is smaller for Cu-Mn than for C u - G e (cf. (11)), if alloys with the same c o n c e n t r a t i o n o--~ solutes are comnared. This is in full a c c o r d a n c e with the much s t r o n g e r d e c r e a s e of the SFE in Cu-~e than in Cu-Mn with alloyinq. S u m m a r i z i n a , the strain h a r d e n i n ~ curves for C u - M n reflect the typical solid s o l u t i o n h a r d e n i n ~ P h e n o m e n a as well as the small chan~e of the SFE with alloyin~ as c o m p a r e d with the SFE of pure copper. Conclusions T a k i n ~ t o q e t h e r the results r e p o r t e d we qet the r e m a r k a b l e s t a t e m e n t that the o b s t a c l e p a r a m e t e r s and the slip p h e n o m e n a of c o n c e n t r a t e d C u - ( 3 - 8 ) a t % M n - a l l o y s w i t h a n e a r l y c o n s t a n t SFE w h i c h equals that of pure Cu are very similar to those of o t h e r c o n c e n t r a t e d c o p n e r alloys with a much lower SFE. In the latter case one u s u a l l y araues that the small SFE renders cross s l i p p i n ~ of screw dislocations difficult, c o n s e q u e n t l y c o n c e n t r a t e s the slid n r o c e s s e s to few slid p l a n e s and favours p l a n a r ulide. A m i c r o s c o o i c c o n s e q u e n c e is the formation of larqe d i s l o c a t i o n qroups as o b s e r v e d by TEM in C u - A I ( 4 - 6 ) , Cu-Zn (31) and Cu-Ge (32) and by slid line replica in C u - G a (8,10). I n h o m o ~ e n e o u s qlide in C u - M n needs a d i f f e r e n t e x n l a n a t i o n . Cross slip of screw d i s l o c a t i o n s can be impeded not only bv a small SFE c a u s i n ~ a large d i s l o c a t i o n s p l i t t i n q but also by a f r i c t i o n a l stress. This m e c h a n i s m was first s u g g e s t e d to our k n o w l e d q e by C h r i s t i a n for fcc alloys and also for bcc c r y s t a l s (33,34). Recently, B l o c h w i t z et al. (35) p r o p o se d for fcc Ni-Fe cross slid to be h i n d e r e d by a c o m b i n e d atomic s i z e - s h e a r m o d u l u s interaction, and K a r n t h a l e r and SchH~erl (36) p r o v e d in a rather d e t a i l e d study the d o m i n a t i n ~ i n f l u e n c e of friction as c o m p a r e d to the SFE by c o m p a r i s o n of strain h a r d e n i n ~ b e h a v i o u r and d i s l o c a t i o n s t r u c t u r e (via TEM) of pure Ni (SFE hiah) , N i 3 - F e (SFE hi~h) and C u - 1 5 a t % A l (SFE low). In a simple q u a l i t a t i v e p i c t u r e f l u c t u a t i o n s of the o b s t a c l e d e n s i t i e s w h i c h inc r e a s e for h i ~ h e r solute c o n c e n t r a t i o n s (33) will impede d i s l o c a t i o n m o t i o n differently in d i f f e r e n t parts of the crystal. With i n c r e a s i n ~ solute c o n c e n t r a tion and c o n s e q u e n t l y i n c r e a s i n ~ o b s t a c l e d e n s i t y the easy ~lide re~ions will d i m i n i s h until, finally, slip p r o c e s s e s set in only at a few s t r e s s - f a v o u r e d positions e.~. near the qrips of the tensile specimen. Then the d e f o r m a t i o n nroceeds in a L~ders band w h e r e the p r o p a g a t i o n of ~lide occurs by cross slip ind uc e d and s u p p o r t e d by internal s t r e s s e s and external torque (31,37,38,39). Q u a s i - p l a n a r qlide p r o c e s s e s will be c o n c e n t r a t e d to the zones of less impeded qlide w h e r e more or less sharply bound qlide bands appear. F u t u r e work will have to c h e c k and imnrove this view and to ask for the scope of i n f l u e n c e of the f r i c t i o n m e c h a n i s m also in the low S F E - a l l o y s as stressed in (36).

928

FLOW OF Cu-Mn CRYSTALS

Vol. 14, No. 8

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Acknowledaement The authors are very grateful to Prof. Neuh~user for reading the manuscript and helpful comments.