The effective stress component of the yield stress of dilute BCC solid solutions at low temperature

Vol.

SCRrPTA METALLURGICA

4, pp.

Printed

73-76,

PerRamon

1970

in the United

Press,

Inc.

States

THE EFFECTIVE STRESS COMPONENT OF THE YIELD STRESS OF DILUTE BCC SOLID SOLUTIONS AT LOW TEMPERATURE Shin Takeuchi The Institute for Solid State Physics, The University Minato-ku, Tokyo, Japan

of Tokyo

( R e c e i v e d O c t o b e r 4, 1969; Revised December 11, 1969)

It has commonly been observed in bcc metals that the yield stress becomes less dependent

on temperature with the addition of a few percent of substitu-

tional solute atoms

(1).

Even the solid solution softening effect has often

been reported to occur at low temperatures perature dependence

of the yield stress,

the yield stress ~y at low temperatures shown in FIG. l, i.e., the athermal temperature

(2).

In the discussions

it seems to be generally accepted that can be resolved into two components

component

ci as extrapolated

plateau of Oy-T curve and the remaining thermal

are sometimes

called the internal

The above resolution

stress and the effective

of the yield stress, however,

when the low temperature

deformation

of the tem-

is controlled

as

from the high

component stress,

~*.

They

respectively.

would not be appropriate by the double kir~ formation

mechanism. Although the origin of °i or the solid solution hardening temperatures interaction

is not understood

clearly,

effect at higher

it may probably be mainly the long range

stress between the dislocation

and the solute atoms

(3,4).

The long

range internal stress on a slip plane due to solute atoms may be periodic dimensions,

changing its sign by nature from place to place.

in two

Its wave length

will be of the order of the mean distance of the solute atoms on the slip plane. Yielding at low temperature of dislocations. movement,

is controlled by the thermally

According to the double kink mechanism

activated motion

of the dislocation

the dislocation velocity is determined by the rate of the formation of

double kinks on screw dislocation,

which is the function of the effective

In dilute alloys with the concentration ing conditions will be satisfied:

ol the order of one percent,

Firstly,

stress

the follow-

the activation length of the double

kink formation is comparable with the wave length of the long range interaction stress field.

This is based on the facts that the observed activation volume of

the deformation process at low temperature

is of the order of lO in the unit of

b 3 (5), where b is the strength of the Burgers vector,

and that the average dis-

tance of the solute atoms just below and above the slip plane is also of the 73

74

YIELD STRESS OF DILUTE BCC SOLID SOLUTIONS

order of lO in b in an alloy with the concentration Secondly,

Vol.

4, No.2

of one atomic percent.

the extent of the kink motion is much larger than the wave length.

This is because the short range interaction tional solute atom is, in general, kink formation,

energy of a kink with a substitu-

much smaller than the energy of the double

resulting in much larger rate for the kink to pass through the

solute atom than the rate of the formation of double kinks. Under the above two conditions, processor

the double kink formation in an elementary

dislocation motion must take place where the long range stress

assists the formation as shown in FIG. 2.

The similar argument that a solute

atom may aid in the formation of a double kink has originally been made by Weertman

(6).

As a result,

the effective

stress that contributes

to the forma-

tion rate of the double kinks or the rate determining process of the dislocation movement is never the subtracted value but rather the added one of the applied stress and the long range internal stress. sisted by the long range stress, stress relevant

Of course,

the kink motion is re-

but this resisting stress and the effective

to the formation of the double kinks are independent

of each

other. In conclusion,

it is incorrect

bcc solid solution as the effective as the considerable

to regard the conventional

o ~ value in dilute

stress for the double kink formation,

part of °i is attributable

so far

to the long range internal stress

due to solute atoms.

pure bcc metal

~1 '*

~

Applied stress

solid solution

Internal

..,,..

o t

stress

double kink

Temperature FIG. 2

FIG. 1 Resolution of yield stress into two components, ~i and ~*.

Double kink formation under periodic internal stress field.

I~EFEI~NCES lo

2.

For example; S. Takeuchi, H. Yoshida and T. Taoka, Inst. Metals 9, 715 (1968). For example; T. E. Mitchell and R. L. Raffo, and also Ref. 1.

Suppl. to Trans.

Japan

Canad. J. Phys. 45, 1047

1967)

Vol. 4, No,

2

YIELD STRESS OF DILUTE BCC SOLID SOLUTIONS

75

3.

E. F. Mott, Imperfections Sons, New York (1952).

in Nearly Perfect Crystals,

4.

J. Friedel, Dislocations,

p. 382. Pergamon Press, Oxford (1964).

5.

H. Conrad, The Relation between the St~acture and Mechanical Properties of Metals, p. 475. H.M.S.O., London (1963).

6.

J. Weertman,

J. Appl. Phys., 29, 1685 (2958).

p. 173. Joh~ Wiley &