Stress equivalence of solution hardening

Scripta METALLURGICA

Vol. 6, pp. 807-814, 1972 P r i n t e d in the U n i t e d States

P e r g a m o n Press,

Inc.

S T R E S S E Q U I V A L E N C E OF S O L U T I O N H A R D E N I N G

Z.S. B a s i n s k i , R.A. Foxall and R. P a s c u a l * of Physics, N a t i o n a l R e s e a r c h Council, Ottawa,

Division

(Received June

Most t h e o r i e s y i e l d stress and single

of s o l u t i o n h a r d e n i n g

and c o n c e n t r a t i o n b a s e d

solute

atoms

(see

30, 1972)

involve

oi" a d i s l o c a t i o n

(i) for review).

segment

ing out u n t i l it b e c o m e s associated with

and m a g n e s i u m

depend d i r e c t l y

solute

atom and the s u b s e q u e n t

solute

atom.

atom.

In this note

equivalent,

i.e.

s m a l l e r than the crystal volume

data on alloys b a s e d on copper,

it is dependent

on the c o n c e n t r a t i o n

of solute,

of solute

atoms.

authors'

experiments

of solid s o l u t i o n h a r d e n i n g ;

it does not

and that the a c t i v a t i o n volume

on copper and s i l v e r alloys

The m a t e r i a l s gold,

Johnson-Matthey,

3mm x 3mm square

Cominco,

plane

(l[I).

[II0] towards The crystals

the c r o s s - g l i d e

faces

i n t e r s e c t i n g these in the c o p p e r alloy

copner,

99.9999%;

cross-section

single

gradient

and then cut into 6.25

6-10 ° from

inves-

d e s c r i b i n g these

(2).

A.S.& R.,

silicon,

99.999%;

Pechiney,

aluminum,

extra pure;

99.998%.

moulds by c o o l i n g in a v e r t i c a l l0 -4 Torr,

of a d e t a i l e d

and

The

Procedures

used were as follows:

indium and silver,

nickel,

are part

of papers

in more detail w i l l be p u b l i s h e d shortly Experimental

silver

of s o l u t i o n har-

on stress but

The data on m a g n e s i u m alloys

a series

bow-

The a c t i v a t i o n volume

of the d a t a on s i l v e r alloys have b e e n taken f r o m the literature.

experiments

is the

is the break-

f r o m a single

tigation

was

models

p i n n e d by the next

contain a large n u m b e r

some

in these

are a n a l y s e d to show that the t h e r m a l b e h a v i o u r

d e n i n g is stress

may

Implicit

the

a dislocation

of d i s l o c a t i o n movement

this event must be a p p r e c i a b l y

c o n t a i n i n g one solute

a relationship between

on the i n t e r a c t i o n b e t w e e n

a s s u m p t i o n that the unit a c t i v a t i o n event away

Canada

crystals were grown in s p l i t - g r a p h i t e

furnace u n d e r a vacuum of b e t t e r than

cm lengths.

The o r i e n t a t i o n

[211] and one of the

c o n t a i n e d very little

showed that

surfaces.

in m a n y

crystals was about

*Now at Centro A t o m i c o B a r i l o c h e ,

S.C.

substructure.

crystals

The average d e n s i t y

Etch pits

on

there were no s u b - b o u n d a r i e s of g r o w n - i n

3 x l0 ~ cm -2. de B a r i l o c h e ,

807

of the crystals

faces was the c r o s s - g l i d e

forest

dislocations

This high degree Pcia.

de R. Negro,

of Argentina

808

STRESS EQUIVALENCE

perfection results about

OF SOLUTION

in a y i e l d stress

HARDENING

for b o t h pure

Vol.

c o p p e r and pure

s i l v e r of

20 g . m m -2 at r o o m t e m p e r a t u r e . The s p e c i m e n s were d e f o r m e d in t e n s i o n at a s t r a i n - r a t e

Frequently

during deformation

this and 2 x 10 -5 sec. -I. from d e c r e a s e s

the s t r a i n - r a t e was

Values

in s t r a i n - r a t e .

strain-rate

in stress,

A~, were always

taken

=(kT÷lnq \ A~ ' / T

v the

of the change

of 2 x I0 -~ sec.-:

changed instantaneously between

The data will be e x p r e s s e d e i t h e r as the acti-

v a t i o n volume

or

6, No. 9

sensitivity

Results C o p p e r Alloys Figure

i illustrates

y i e l d stress,

Go,

the r e l a t i o n s h i p b e t w e e n

for c o p p e r alloys

2 illustrates

of several

298°K.

Figure

between

78 and 298°K on the y i e l d stress

the data for all the alloys

the d e p e n d e n c e

For example, despite

the points

stress

Stress tures

i.e.

s t u d i e d in detail

and s t r a i n - r a t e

identical

Figures

It is obvious that of solute.

Thus

for the alloys

dependence

flow stress was o b t a i n e d

of d e f o r m a t i o n

over a wide range of t e m p e r a -

initial

respectively

flow stress

The t e m p e r a t u r e

from t e m p e r a t u r e

over the whole

for alloys w i t h i d e n t i c a l

of s o l u t i o n har-

of solute.

of the initial

shortly

stu-

of s o l u t i o n h a r d e n i n g are

3 and 4 i l l u s t r a t e

of s o l u t i o n h a r d e n i n g .

of w h i c h will be p u b l i s h e d

thermodynamics

dependence

at all w i t h the c o n c e n t r a t i o n

e q u i v a l e n c e has b e e n

of the initial

in y i e l d stress

the d a t a c o r r e l a t e well w i t h the amount

correlate

c o r r e s p o n d i n g to two levels

the details

smooth curve.

in c o n c e n t r a t i o n .

and s t r a l n - r a t e

for some of the dilute alloys.

the t e m p e r a t u r e

v, and

In each of the three plots

the data and the c o n c e n t r a t i o n

the factor of 25 d i f f e r e n c e

equivalent,

volume,

for C u - 0 . 1 9 % Ag and Cu-5% Ni lie close to each o t h e r

died, b o t h the t e m p e r a t u r e d e n i n g but do not

of the d i f f e r e n c e

at 78°K.

fall on a single

no such c o r r e l a t i o n exists b e t w e e n

activation

systems d e f o r m e d at 78°K and

(2).

cycling experiments,

Figs.

temperature flow stress,

for alloys

dependence

3 and 4 show that the

range

down to 4.2°K are

independent

of t h e i r

composition. The a n o m a l o u s up to about

50°K

increase

(Fig.

and Cu-Ge and Cu-Ni

in i n i t i a l

3) has b e e n o b s e r v e d in alloys

(5).

increasing temperature

of Cu-Zn

(3), Cu-Ag

This b e h a v i o u r has b e e n s t u d i e d in some detail

dilute alloys b a s e d on copper, dilute

flow stress with

silver and gold

alloys b a s e d on the noble metals.

(4) for

(2) and appears to be t y p i c a l

of

Vol.

6, No.

9

STRESS EQUIVALENCE

OF SOLUTION HARDENING

809

I0 ~ A O.OI%AI,(o) O O.05%Ag(,~) B 0.0.5 e O.l%Ao C 0.1 S O.19%Ag

A

COPPER ALLOYS

D 025

E F G H i K L M

0.5 1.0 1.4 1.8,5 2.s 4.6 5.6 7.4 N 9.2 P I1.0

El \ C 0

104 hi

oA

3

~

o

D. ~Q

~

0 >

v

298°K

~

7 0

T 0.5%AI OJ%A(~(~)

U 5.6%Al 0.34%Aq V 0.5% Si (<>) W 10% Si Y 5% Ni ((~)

~.[

F-

w_

78 ° K

< 103 - ~9

"~,,u P

Y ~

~o~ N P

10;20

i

I

I

IO0

I000

3000

YIELD STRESS g.mm -z

Copper

alloys.

Stress

FIG. i of the activation

equivalence

volume

at 78 and 298°K.

/u

2000

P

IOOO

H / K

COPPER ALLOYS

e~

GY/° ,T,~

700

'EE d~ 600 GO (/)

E

\

,,t 500

E

I--Do

if)

]o ~oo C o

~

B/

Zo

~---J 300

_~ 200

,/ ~_o

~

~

.

C u - 0 . 5 % AL (a) Cu-O.1%AQ (o) Cu-O 5 % S i ( v )

I

I

ioo IOOO YIELD STRESS (co)AT 78°KgmmT 2

I

3000

I

I

J

I00

200

300

i

4OO

TEMPERATURE °K

FIG. 2 FIG. 3 Copper alloys. Stress equivalence of t~e Copper alloys. The temperature dependifference in stress between 78 and 298 K. dence of the initial flow stress for Notation same as in fig. i. alloys corresponding to two levels of solution hardening.

810

STRESS EQUIVALENCE

OF SOLUTION HARDENING

Vol.

6, No. 9

0.12

FIG. 4 Copper alloys. The temperature dependence of the strain-rate sensitivity of the initial flow stress for the alloys compared in fig. 3.

O.IC

T

F o.oB E E d~

..--.~o.o6 b~

--IF-

0.04

Q02 Cu-O.l% Ag (o)

0

,

I

50

i

I00

I

~

I

I

[

150 200 250 TEMPERATURE °K

300

t

350

I

400

A O.Ol%ln(o) B 0.05% C 0.1% D 0,2% E 0.5% F 1.0% G 2.5% H 4%

5x104 l

ALLOYS

=~ ,o,I

% ~ o C~

N 0.25% Sn(e] P 0.5% O 0.6% R 10% S 20% T i0% Au(a) U 20%Au

T 0,28% In(o)

. ~ ~ E o

.J

J 0.45% K 0,95%

z

_o

T 298°K

F-

FIG. 5 Silver alloys. Stress equivalence of the activation volume at 78 and 298°K. The data for Ag-Sn alloys and the Ag-In alloys I, J, K were taken from (6).

103

I

20

I00 YIELD STRESS cjmm?z

I

I000

Vol.

6, No.

Silver

9

STRESS

The t h e r m a l

behaviour

also.

Ag-A u

been

have

data

drawn

from

stress

combined

the

for the

both

three

directly

for A g - 0 . 2 5 %

factor

HARDENING

811

with

published

systems

with

the

Sn and

data

compared solute

Ag-20%

for

the

systems

results.

correlate

based

on the

very

Ag-ln

with

in view

of the

and (6).

lines

for the

cop-

off the y i e l d

stress

the

stress

on the

dependence

well

is Ag-ln

and Ag-Sn

to points

In p a r t i c u l a r

strikin~

alloys

systems

As o b s e r v e d

and s t r a i n - r a t e

content.

Au is

silver

data

corresponding

experimental

temperature

in

authors'

f r o m values

of the

the

hardening

6 the

but

do not

similarity

in the

difference

of a

of 80 in c o n c e n t r a t i o n .

Magnesium

Alloys

Figure magnesium possible data

5 and

derived

scatter

alloys,

correlate

of solution

In Figures

(6) were

through

per b a s e d

data

OF SOLUTION

Alloys

equivalent

The

EQUIVALENCE

7 illustrates

alloy

systems

complications

to a single

is stress

to a given

Unfortunately, to i n v e s t i g a t e stress

due

curve

equivalent,

responding

the

dependence

(7 - ii);

limit

to s t r a i n - a g e i n g

shows

that

despite stress

there

of o o ( 7 8 ) - O o ( 2 0 0 )

an u p p e r

the

large

effects.

temperature

differences

is i n s u f f i c i e n t

strain-rate

stress

equivalence

of the

of the

temperature

dependence

would

be

The

solute

for

chosen

excellent

dependence

in the

the

volume

was

fit

of the

several

to avoid of the

yield

stress

concentration

cor-

level.

equivalence

tivation

on Oo(78)

of 200°K

stress

equivalent

sensitivity

activation

volume,

indicates

data

but

available

the

strongly

observed

that

the

ac-

also.

Discussion The

results

mal p r o p e r t i e s alloy

systems

of stress

based

usual

If the

activation and

for

system.

number may

made

process,

the

If we

assume

interacts

planes,

average

atom is e a s i l y

silver

and many

to be

and

magnesium.

contained

a, of the

that

ther-

consequence the

interac-

is in c o n t r a d i c t i o n

a uniform

involved

to

n is sometimes

of i n t e r a c t i o n ,

occupied

solute

in the unit

considerably

on its two

plane

important involves

(assuming

varies

range

atoms

slip

This

of the

for various

hardening.

in v

5 show

stress

possible

solute

One

of the n u m b e r

I and

hardening

equivalence

of stress

process

atoms.

of s o l u t i o n

in figs.

shortest

stress range

activation

solute

atoms

only with

area,

shown

a wide

as an i n d i c a t i o n

data

the

established over

in theories

solution

dislocstion

have

the unit

n of solute be t a k e n

a particular

the

is that

a dislocation

assumption

distribution)

above

hardening

on copper,

equivalence

tion b e t w e e n the

described

of s o l u t i o n

very

large

from system i.e.

that

to

the

immediately

adjacent

effectively

by a solute

given by a = b2~

where volume

c is the

atomic

corresponding

concentration

of solute.

to d i s l o c a t i o n - s i n g l e

Therefore

solute

atom

the m a x i m u m

interactions

activation

will

be

812

Vol. 6, No. 9

STRESS EQUIVALENCE OF SOLUTION HARDENING

I000

,Q

SILVER ALLOYS L 0 . 0 5 % Sn M 0 . 0 8 % Sn

E E

~-~ u

A

I/

OJ

No ,oo

eM

I

/

bo

,/ 1020

Silver alloys.

I I I00 I000 YIELD STRESS (o"o) AT 7 8 ° K g.mm.-2

FIG. 6 Stress equivalence of the difference in stress between 78 and 298°K. Notation same as in fig. 1.

IOOC MAGNESIUM ALLOYS

B -~" L~,°o,/'''° ""~ /P

8

~1oo

V A/

£~"

bo

P 1.5%Lilo ) Q 4.5% R 6.0% S 11.8% T 15%

u O.l%cdl,,)

~ 02.;2. • ~

v o,%

Z O.O06%Zn (=) J 0.019%

E

/ j / /

W 2.4% Y O.O03%Th(•) Z 0.049%

K 0 .0 5 4 ~o

/a

L 0,15% M 0.258% N 0.45%

I/

/

,bo

A 0.49% In(o ) B 1.0% C 2.06% D 40% E 0.;>4% AI(e)

F O.Sg"/.

• Z Y/I

T

~J

31oo

' K)O0

YIELD STRESS(Oo)AT 78"K g.mm:"z

' tSO0

FIG. 7 Magnesium alloys. Stress equivalence of the difference in stress between 78 and 200°K. The sources of data are as follows: Mg-AI(7!, Mg-Cd(8), Mg-ln(7), Mg-Li(9), Mg-Th(10) and Mg-Zn(7).

Vol.

6, No.

9

STRESS E Q U I V A L E N C E

OF SOLUTION

HARDENING

813

V

= ab. s of v s w i t h the o b s e r v e d values of v for the systems A g - A u and A g - S n

Comparison

shows that n for Ag-20% Au Ag-0.25%

Sn

(G ° = 272 g. mm. -2) is only about

454 g.mm. -2) about

10.

(G o = 306 g.mm. -2)

is about 230 w h e r e a s

The m i n i m u m value

for C u - 0 . 0 1 %

is about 17.

n for Cu-0.19%

of n o b s e r v e d

AI d e f o r m e d at 50°K.

Single

in this

at very

regime.

Another responsible

low c o n c e n t r a t i o n s W o r k on this

important

consequence

for the stresses

i n c l u d i n g the a n o m a l o u s on the noble

metals,

3 and 4 w h i c h

show that

to c h a r a c t e r i z e

available

provide

strong evidence

alloys

a very

the initial

varies

are not

other

that

gion may reflect

deformation

that alloys w i t h i d e n t i c a l at t e m p e r a t u r e s Therefore

data

3 and 4

thus provides

c o n s i d e r e d to consist

(12).

Although

large a c t i v a t i o n volume

in this t e m p e r a t u r e

range,

ob-

the p l a t e a u reassociated

the data show

c o r r e s p o n d i n g to the p l a t e a u

such as r e c o v e r y

equivalent

at any t e m p e r a t u r e

plays

region.

at all t e m p e r a t u r e s

or s t r a i n - a g e i n g . and solute

only an indirect

The m a g n i t u d e atoms which role in the de-

of the h a r d e n i n g b e h a v i o u r .

of the p a r t i c u l a r

hardening

is f r e q u e n t l y

i n t e r a c t i o n b e t w e e n the d i s l o c a t i o n s

In c o n c l u s i o n ,

ponsible

such d e t a i l e d

the data in figs.

s o l u t i o n h a r d e n i n g near 0°K have i d e n t i c a l h a r d e n i n g

of c o m p l i c a t i o n s

for the stress

termination

Although

range

of s o l u t i o n hardening.

region

only s l i g h t l y b e l o w the range

of the p a r t i c u l a r accounts

is s u f f i c i e n t

w o u l d be o b t a i n e d also for the

the h a r d e n i n g may be c o n s i d e r e d stress

absence

in figs.

the latter b e i n g equal to the stress

little more than the very

activated

is most evident

Stress e q u i v a l e n c e

at any t e m p e r a t u r e

"plateau"

range studied,

at one t e m p e r a t u r e

range.

g e n e r a l p a r a m e t e r for the d e s c r i p t i o n

is that the m e c h a n i s m s

even in the high t e m p e r a t u r e

stress e q u i v a l e n c e

t a i n e d in the high t e m p e r a t u r e

more

o b s e r v e d for alloys b a s e d

c o n s i d e r e d here,

component,

is o b t a i n e d

interactions

may not be obeyed

temperature

This

little with temperature.

The s o l u t i o n h a r d e n i n g

the present

work shows

interaction between

for s o l u t i o n h a r d e n i n g

should be b a s e d on models

dilute solutions)

by a single p a r a m e t e r

and predict of stress.

that

a single m e c h a n i s m ,

the d i s l o c a t i o n s

and solute

in close packed metals. in w h i c h

the i n t e r a c t i o n b e t w e e n a d i s l o c a t i o n very

related.

flow stress

for all the alloys

of a t h e r m a l and an a t h e r m a l

in the

over the whole

over the w h o l e t e m p e r a t u r e

with t h e r m a l l y

equivalence

the entire t h e r m a l b e h a v i o u r ,

in w h i c h the stress

equivalence

(G ° =

is only

i) are e x p e c t e d to become

at low t e m p e r a t u r e s

must be i n t i m a t e l y

l, which

atom-dlslocation

for

in progress.

of stress

observed

behaviour

S i m i l a r l y n for Cu-5% Ni

so that stress

is c u r r e n t l y

the value

Ag (G ° = 390 g. mm. -2)

so far is about solute

(for w h i c h n is e x p e c t e d to be much s m a l l e r than important

ii00 w h e r e a s

Theories

independent

atoms,

the unit a c t i v a t i o n process

and many solute

atoms

is res-

of s o l u t i o n involves

(except p o s s i b l y

a h a r d e n i n g b e h a v i o u r which

in

is c h a r a c t e r i z e d

814

STRESS EQUIVALENCE OF SOLUTION HARDENING

Vol.

6,

No.

9

Acknowledgements The authors

wish to thank Mr. J.W.

growing the single construction Duesbery

crystals,

and maintenance

for valuable

of apparatus

discussions.

port of the International

Fisher

Mr. J. Broome

for his invaluable

and Mr. J. Riddell and Mrs.

Dr. Pascual

Atomic Energy

in in

S.J. Basinski

acknowledges

Agency,

assistance

for assistance

Vienna,

and Dr. M.S.

the financial

and the National

sup-

Research

Council. References I.

T. Suzuki, Second International Conf. on the Strength of Metals and Alloys (Pacific Grove, California) 237. The American Society for Metals (1970).

2.

Z.S. Basinski,

3.

R.E.

4.

Z.S. Baslnski and D. Dove, Cambridge (1960).

Fifth

5.

K. Kawada and I. Yoshizawa,

J. Phys.

6.

R.H. Hammar, 708 (1967).

7.

A. Akhtar and E. Teghtsoonian,

8.

H. Scharf,

9.

A. Urakami, M. Meshii and M.E. Fine, Second International Conf. on the Strength of Metals and Alloys (Pacific Grove, California) 272. The American Society for Metals (1970).

Jamison

R.A. Foxall

and F.A.

R.A.

E.D.

Sherrill,

Strahl

P. Lucac,

and R. Pascual,

M. Bocek

W.F. Sheeley, 693 (1959).

Levine

ii.

A. Akhtar and E. Teghtsoonian,

12.

P. Haasen,

Japan

4, 197 (1956).

International Soc.

Japan

and A.A. Hendrickson,

I0.

Trans.

Acta Met.

to be published.

Phil.

Mag.

Inst. Metals

31, 1056

(1971).

Trans.

Japan Inst. Metals

Z. Metallk.

Nash, Trans.

Acta Met.

on Crystallography,

9,

25, 897 (1972).

and P. Haasen,

and R.R.

Congress

59, 799

Am. Inst. Min.

173 1339

9, XL (1967).

(1969).

(1968).

Engrs.

215,