Comments on “Solid solution softening in B.C.C. alloys”

Seripta

METALLURGICA

V o l . 3, pp. 5 3 1 - 5 3 6 , 1969 Printed in the United States

Pergamon

Press,

Inc.

COMMENTS ON "SOLID SOLUTION SOFTENING IN B.C.C. ALLOYS" RAM B. ROY AB Atomenergi, Studsvik, Sweden

(Received

April

25,

1969;

Revised

May

27,

1969)

Solution softening in b.c.c, metal alloys has been observed in many instances eg. in Fe-Cr, Horn et al. (I) , Ta-Mo, Ta-W, and Te-Re, Mitchell and Raffo (2) , in Te-Re, Raffo and Mitchell (3)

Na-W, Harris (4) and in W-Re, Raffo (5) .

The main characteristics of this

phenomenon is that it occurs mainly at small concentrations (%1 to 4 %) and at low temperatures (although there are exceptions, W-Re, Raffo(5)}. Increasing concentration and temperature restores the normal solution hardening behavior.

The exact mechanism of this phenomenon is

not clearly understood although it has been speculated by the above-mentioned authors that the effect may be due to the local lowering of the Peierls barrier for the nucleation of double kink on a screw dislocation in the vicinity of the alloy atoms if the Peierls mechanism is operative and/or alternatively the solute atoms near a dissociated screw dislocation facilitate the constriction of partials if the dissociation-recombination mechanism is operating.

The key assumption in the above model is that the experimentally observed shear

stress, Oc, in the alloys can be separated into two parts, namely, o

c

= G

p

+ ~ , where o a p

is finite in the unalloyed metal and is identified with the Peierls stress and o a is zero in the pure metal and identified with the solution hardening effect,

o

decreases with the P

concentration but o a increases and at low concentrations, the decrease in o p predominates over the increase in o a and hence the observed solution softening effect.

Furthermore, in

this model, the absence of solution softening with increasing temperature and concentration is attributed to the accompanying decrease in the Peierls barrier. However, an inconsistency arises if one compares the prediction of the theory with the experimental results.

A decrease in o

with composition will depend critically on the P

effectiveness with which the solute atoms destroy the periodicity of the solvent matrix which

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COMMENTS ON SOLID SOLUTION SOFTENING IN B.C.C. ALLOYS

i n t u r n d e p e n d s upon t h e d e s p a r l t y b e t w e e n t h e r e s p e c t i v e systems f o r which e x p e r i m e n t a l d a t a e x i s t atoms differ from~l.2

Vol. 3, No. 8

atomic diameters.

For t h e a l l o y

t h e a t o m i c d i a m e t e r s o f t h e s o l v e n t and s o l u t e

% in the case of Fe-Ni (6) to ~I0 % in Fe-Pt (6)

Fe-Pt alloy is not any stronger than in Fe-Ni alloys.

but the effect in

For intermediate cases eg. in W-Re (5)

with a size difference ~2.5 % the effect is much stronger than in Nb-W (4) wlth a size difference ~ 4 . 1 % . Furthermore, the temperature variation of Pelerls stress is only mild and follows the temperature variation of the shear modulus (7) , and therefore the preponderance of g

a

over g

p

at higher temperatures should not be simply attributed as due to the lowering of Pelerls barrier st these temperatures. In an alternative stress ( g )

model presented here, it will be assumed that the observed yleld

of the alloy can be separated into thermal g(th) and athermal U(ath ) components

and the solution softening is supposed to occur mainly due to the lowering of g(th) term. Solution softening is possible only when the decrease in U(th) term predominates over the increase in U(ath ) term due to solutlon hardening. It is suggested that the solute solution softening effect observed In 6.c.c. alloys is due to the modulus difference between the solvent and soiute atoms.

Flelscher (8) was first

to point out the importance of the so called modulus effect in alloy hardening.

In this

theory the individual atoms in the alloy are considered to be the sources of hard and/or soft centres depending upon the relative values of the elastic moduli of the solvent and solute atoms in their pure state.

The stress field around a dislocation (Including the screw

dislocations as shown by Chow (9)) interacts with the Indivldual fleld of the solute atoms in such a way that a dislocatlon is locally attracted towards the softer atom and repelled from the harder ones, the strength of the interaction being proportional to 1-2 where r is the r

shortest distance between the dislocation and the solute atom, (cf. strength of the size effect~,

y being constant for motion on a sllp plane).

type of interaction

requires

a knowledge o f ~ t ~ c

t h e s h e a r modulus r e s p e c t i v e l y f o r most o f t h e a l l o y s , AS

and A~

and ~ c

and c t h e c o n c e n t r a t i o n .

A quantitative appreciation of this ) where B end ~ a r e t h e b u l k and (~)

h o w e v e r , f o r v e r y low c o n c e n t r a t i o n s

b e t w e e n t h e s o l u t e and t h e s o l v e n t atoms i n t h e i r

and (

( 0 . 1 - 2 . 0 %) t h e d i f f e r e n c e s pure state

a p p r o x i m a t i o n as a measure o f t h e s t r e n g t h o f t h e modulus e f f e c t . their

respective

are not available

w i l l be t a k e n i n

These v a l u e s ,

alon E with

atomic diameters are presented in table 1 for various alloy systems.

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SOFTENING

IN B . C . C .

ALLOYS

533

TABLE I x)

Alloy

AUll i0 dynes~ cm

ASII l0 dynes~ cm

Predicted effect

Experimental observation

Fe-Cr

+ 3.37

- 0.96

Weak?

Yes (weak?)

Fe-A1

- 5.54

- 8.85

No

- (see the text)

Fe-Ni

- 0.56

+ 0.75

Weak

Weak

Fe-V

- 3.49

-

No

- (see the text)

Fe-~

+ 4.h0

+ 9.14

Yes

Yes

1.18

Ta-Mo

+ 5.64

+ 6.49

Yes

Yes

TaW

+ 9.1~

+11.47

Yes

Yes

Ta-Nb

- 3.17

- 2.60

No

No

B-b-W

+12.31

+i~.07

Yes

Yes

x) The ~ and B values have been taken from Smithells, Metals reference book, Butterworths, London, ~, 708, 1967

It will be assumed that if both A8 and Ap are positive the dislocation solute-atom interaction is repulsive and if the A8 attractive.

In the case A8

be regarded as uncertain.

and Ap

and Ap

terms are negative the interaction is

are of opposite sign, the sign of the interaction will

It is readily seen from table i that the repulsion is stronger

for Fe-Mo, Fe-W, Ta-W, Ta-Mo and Nb-W while the attraction is predominant in Fe-V, Fe-AI and Ta-Nb.

The uncertain cases are Fe-Cr and Fe-Ni.

At low temperatures the screw dislocations in pure b.c.c, metals are trapped and lie straight along

< iii>

direction in the Pelerls valley.

atoms, however, may modify this situation.

Addition of substitutional solute

In the case of repulsion (AS and A~, positive)

dislocations will be kinked due to solute-dislocation

interaction and small segments of dis-

locations will bow out of the Peierls valley part way up the saddle point.

The location of

these bow-outs are expected to be preferred sites for double kink nucleation in the Peierls mechanism (because of the decreased stress needed for kink nucleation). such bow-outs will be proportional to b / f - ~ i n concentration)

The spacing i of

the glide plane (C, being the solute

and in the limit when i-- ip, where ip is the length of kink segments in the

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SOFTENING

IN B . C . C .

Peierls model, a situation may arise where O(th) (alloy)
ALLOYS

(pure metal).

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At low

concentrations and temperatures it is possible that the decrease in O(th) may far exceed the increase in O(ath ) and the observed yield stress of the alloy may actually lie below the yield stress of the pure metal.

At high concentrations, however, where i <
are expected to be difficult and the aforementioned argument will be no longer valid.

In

concentrated alloys, therefore, solution hardening is expected even at lower temperatures. In the case of attraction (AB and AB, negative), the alloy atoms are attracted to the dislocations and bow-outs are not possible, and therefore dislocations remain straight at all concentrations.

In the absence of bow-outs, a decrease in O(th)

(alloy) is not expected

and solution hardening should prevail at all concentrations. In concentrated alloys, however, there is another possibility.

In certain alloy systems

the dislocations may be actually dissociated into partials due to lowering of the stacking fault energy by solute additions. for a perfect dislocation, O

c

= O

Because the Peierls potential for partials is smaller than p

+ O

a

as suggested by previous authors and solution

softening at low concentrations can occur because o p


At temperatures where the nucleation of double-klnd ceases to be the controlling mechanism of deformation in b.c.c, alloys, both harder and softer solute atoms are expected to induce solution hardening at all concentrations. The alloy systems in table 1 have been examined in terms of the above-mentioned hypothesis.

The definite cases are labelled "yes" or "no" indicating if solid solution softening

is possible or not.

The boarder cases are labelled "weak".

It is seen from table i that the

predictions of the p~esent hypothesis is reasonably in accord with the experimental observations except in the case Fe-V and Fe-AI.

Nunes (I0) has reported solution softening in

polycrystalline Fe-AI and Fe-V systems but his results are based on the lower yield point involving large dislocation motion whereas the prediction of the present hypothesis is applicable to solution softening effect on the proportional limit of the alloys.

Furthermore,

both V and A1 show considerable affinity for the interstitial impurities and therefore a true measure of solution softeningeffect of C and N in the specimen.

in Fe-V and Fe-AI cannot be measured in the presence

This condition was apparently not fulfilled in Nunes experiment.

A further complication may arise in the case of monocrystals because of the orientation dependence of the yield stress.

Unless monocrystals of identical orientations are used for

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each alloy system, a true measure of the alloy effect is not possible.

ALLOYS

535

Similarly, tension

and compression tests might give opposite results. In summary, solution softening at lower temperatures and low concentrations occurs through the intervention of the alloy atoms on the thermally activated process controlling the low temperature deformation.

This is achieved by decreasing the thermal fluctuation

energy for the nucleation of double kink in Pelerls process.

At higher concentrations this

is not possible. At higher temperatures (le. above the critical temperature T ) where the controlling c mechanism is not a thermally activated process, the normal behavior of solution strengthening is expected at all concentrations.

References 1.

G.T. Horn et al., JISI, 201, 161, 1963

2.

T.E. Mitchell and P.L. Raffo, Cand J. Applied Physics h5, 10h7, 1967

3.

P.L. Raffo and T.E. Mitchell, Trans. AIME, 2h2, 907, 1968 B. Harris, Phys. star. Sol. 29, 383, 1968

5.

P.L. Raffo, J. Less-common metals, 17, 133, 1969

6.

H.H. Kranzlein et al., Trans. AIME, 233, 6h, 1965

7.

D. Guyot and J.E. Dorn, Cand. J. Phys. hS, 983, 1967

8.

R.L. Fleischer, Acta Met. 9, 996, 1961

9.

Y.T. Chow, Acta Met. 13, 251, 1965

I0.

J. Nunes, JISI, 20h, 371, 1966