Some observations on the microstrain characteristics of silver

LETTERS

TO

for a quench from -40°C to -17.5%. For comparison, the results for a quench downward in temperature from 0°C to -17.5% are also shown. In Fig. 4 the average relaxation rate was obtained from the initial slope of the anelastic strain curve and thus is proportional to the volume. averaged vacancy concentration.(l) Comparison of the two annealing curves in Fig. 4 shows (within an experimental error of roughly a factor of two) no differences in the rate of approach to equilibrium after subsaturation and supersaturation of vacancies. This is in agreement with f.c.c. resultsc2)and suggests that the same step is rate-limiting in the process of vacancy formation as in that of vacancy decay. This

is shown

in Fig.

4

I

I _‘0

B Ng

n rxlWN-OuENCHED

/

0*

c-

- 17.5.

- -

EOUIUBIWM *T-IZs

VALUE c

0

COMPUTED

VALUE

0

EXP.

VALUE

c

I

-_-_-

UP-OUENCHEO

- 40e

c--

17s

ee

c

u 0

0

100

200

300

Annsolinp

400

SO0

600

Tima ISSC)

Pm. 4. Vecency formation and decay curve8 for a specimen up-quenched and down-quenched to - 17~5°C. 7 is proportional to the volume averaged vacancy concentration.

The author is grateful to F. M. Monroe for experimental assistance and to B. S. Berry for making available experimental results prior to publication. J. R. COST Metallurgy

Department

ScientiJic Laboratory Ford Motor Company Dearborn, Michigan

References 1. B. S. BERRY, to be published. 2. J. R. COST, Acta Met. 11, 1313 (1963). 3. J. LULAY end C. A. WERT, Acta Met. 4, 627 (1956).

4. J. R. Cosr, Proc. Int. Conf. on Lattice Defects in Quenched Metals. Academic Press Inc., New York. To be published. 5. A. S. NOWICE and B. S. BERRY, IBM J. Re8. Dev. 5,297, 312 (1961). 6. H. I. AARONSON and D. J. SCHMATZ, to be published. 7. A. S. NOWICK and R. J. SLADEK, Actu Met. 1, 131 (1953). 8. E. S. WAJDA, G. A. SHIRN and H. B. HUNTINOTON, Acta Met. 8, 39 (1955). 9. G. S. KAXATH, R. S. CRAIQ and W. E. WALLACE, Trans. Anaer. In&. Min. (MetalE.) Engrs. 227, 26 (1963). * Received November

30, 1964.

THE

EDITOR

551

Some observations on the microstrain characteristics of silver* The purpose of this note is to present some results on the effect of substructure on the microstrain characteristics of polycrystalline silver which aid an understanding of the physical nature of the microstrain region. Tensile specimens of gauge length 1 in. and cross sectional area of 0.08 in. x 0.30 in. were prepared from cold rolled (100 % reduction) 99.9 % purity silver. Measurements of the microscopic yield stress (the stress to produce a permanent strain of 2 x 1O-6 in/in) and the rate of strain hardening in the microstrain region were made at room temperature with the Tuckerman optical strain gauge, using the load-unload technique previously described”). The specimens were tested in the cold rolled condition and also after two series of annealing treatments, one at a temperature (170°C) which produced recovery and recrystallization without appreciable grain growth and the other at a temperature (600°C) which produced considerable grain growth. The nature of the variationsin substructure and grain size accompanying the annealing treatments were determined using optical and transmission electron microscopy. The average grain size of the cold rolled silver was 50 #IA. Transmission electron microscopy of thin films prepared from the cold rolled bulk specimens revealed a high density of dislocations within a grain with the characteristic cell structure described by Bailey and Hirsch t2). The high density arrays were very unstable in the electron beam and annealing twins (Fig. 1) readily formed during examination. Annealing bulk specimens at 170°C produced significant changes in the microstructure of silver with annealing twins becoming readily apparent after a treatment for 2 hr and steadily increasing in number with longer times at temperature. Localized grain growth only became significant after an anneal at 170°C for 40 hr. On annealing the specimens at 600°C considerable twin and grain growth occurred. After an anneal for 45 min the average distance between grain or twin boundaries was ~200 p and after an anneal for 20 hr the average distance had increased to ~1200 p. Electron microscopy indicated that an anneal at 600°C produced a relatively low density distribution of dislocations within a grain, as in Fig. 2. Dislocation movement could be induced under the electron beam and long ribbons of stacking faults were created by the separation of partial dislocations (Fig. 3).

552

ACTA

METALLURGICA,

VOL.

13,

1965

FIG. 1. Annealing twins in cold rolled silver.

x 20,800

Fra. 2. The disloec&on distribution in silver after an anneal at BOO*Cfor 4 hr. x 10,700

LETTERS

Micro&rain specimens jected

measurements

were made on as-rolled

and on specimens

to annealing

The microscopic was detected

(approximately hardening

had been

sub-

at 170°C and 600°C.

THE

1800 psi) purity.

for

polycrystalline

The subsequent

could well be represented

silver

rate of strain by a parabolic

at an almost

annealing

treatment

in the microscopic

2 hr reduced proximately remained

(Fig. 4) plot. the

An anneal at 170°C for

microscopic

450 psi,

yield

although

at approximately

cold rolled condition.

the

stress slope

to

ap-

dald$Js

the same level as in the

Continued

annealing

at 170°C

(i) The after

significant

a relatively

complete observed material.

departure

from

the

parabolic

relation

for the cold rolled and 170°C annealed The microscopic yield stress after 2 hr

for a 170°C anneal.

The subsequent

20 hr at 600°C the first plastic flow was detected the range 750-1250

psi and was followed

in

by gross

at 170%

(2 hr) and

any further observations

that

recrystallization

dependence

of

taking

that

stages

seems

reasonable

it appears throughout

at 170%.

would

yield

be expected

Hence

stress

a

solely

to produce

a

rather than the discontinuous

change observed experimentally. shown

appreciable

place

microscopic

variation

occurred continued

silver.

treatment

the

on recrystallization continuous

is

in annealed

the entire annealing

Bailey and Hirschc2)

a large energy of annealing that

release occurs

of cold

rolled

to the onset of recovery. the

marked

in

silver,

reduction

It in

microscopic yield stress can also be related to a recovery process. The exact nature of such a process cannot presently be formulated

but is likely to depend

on a relaxation of the long-range stress fields associated with the high density dislocation arrays.

rate

of strain hardening progressively decreased and rapid yielding occurred above 1200 psi. After an anneal for

time

the optical

which they attributed

anneal at 600°C ranged from 650 to 900 psi, which represented a small increase in value over that measured

short

did not produce

the early

cold rolled silver at 600°C resulted in a

this

increase

in the microscopic

From

changes in either the microscopic Annealing

reduction by annealing

changes.

have

rate of strain hardening.

Hence

annealing

for 4,20 and 40 hr did not yield any further significant yield stress or the

stress.

a significant

yield stress.

yield stress affected

FIG. 3. Slip traces and some extended dislocations x 14,000

stress-strain

constant

produced

These results lead to several interesting conclusions:

stress of approximately

This value is appreciably lower than reported t3) by Koppenaal and Parikh

553

EDITOR

yielding

yield stress of the cold rolled silver

900 psi (Fig. 4).

of comparable

which

treatments

at a tensile

that previously

TO

by

(ii) Although the microscopic yield stress is reduced a 170°C anneal, the rate of strain hardening

remains approximately

constant.

This suggests that

the area swept out by a mobile dislocation is not significantly altered. Such a deduction is interesting

ACTA

554

METALLURGICA,

in view of the apparent reduction in the available area within a grain by the formation of annealing twins. It indicates that dislocation movement is likely to be initially restricted by the finer scale obstacles provided by the dislocation cell walls within a grain, rather than by the grain boundaries. (iii) An anneal at 6OO’C for 20 hr produces a surprising increase in the microscopic yield stress to a value equal or slightly larger than that of the cold rolled condition. As at this temperature considerable dislocation rearrangement and annihilation occur, it seems likely that the increase in microscopic yield

2,0~-_

IS00 -

z ::

GIO00 2

-

soo-

0-1 0

I

2

3 [PLASTIC

4

5 STRAIN

GOLD

ROLLED

o

AS

A

AFTER

2 HRS

x

AFTER

3/4

o

AFTER

20

’

6

’

7

AT 17O.C

HR AT 600.C HRS

’

8

AT 600%

’

9

’

IO

1

(x t&6inlinl]“2

FIG. 4. The effect of annealing on the micro&rain characteristics of silver.

is due to either an alig~ent of disloeatio~ into a stable, low-energy eonfiguration or to a reduction in dislocation number to the point at which From the nucleation effects become important. nature of micro yielding observed for this condition, it appears that dislocations start to move at a stress at which they can continue to move relatively freely through the matrix. This is in contrast to the behavior produced by the other heat treatments where it is likely that dislocation movement is activated over a range of stress due to the relative heterogeneity of the dislocation structure. In the true meaning of the term, the specimen annealed at 600% for 20 hr does not contain a unique microstrain region as the curve in Fig. 4 continued in a like manner to a strain beyond the macroscopic yield point. Thus it seems that some measure of heterogeneity in the dislocation eon~guration is a prerequisite for a distinct microstrain region in silver. (iv) Previous investigations of the microstrain region of polycrystalline beryllium(l~*) have shown several points of difference with the predictions of the general theoryr5) which describes the dependence of stress

VOL.

13,

1965

microstrain (E) on the stress o and grain size (D) of polycrystalline metals by:

(1) where K is a constant, p is the density of dislocation sources and og is the stress to activate the first dislocation sources. This relation was derived from the simple physical model of Frank-Read sources generating dislocations which move freely across the grain, with the only barriers to dislocation motion being provided by the grain boundaries. The present results on silver afso suggest that the physical nature of the microstrain region is more complex than that represented by equation (1). The parabolic stress-strain relation was only observed in silver specimens containing an appreciable substructure within a gram. In specimens where the ideal condition required by equation (1) of a negligible substructure was created, a parabolic plot was not observed and gross yielding occurred. Consequently dislocation interactions rather than simple dislocation pileups appear likely to be the cause of the parabolic stress-strain relation in silver. The dependence between microstrain and grain size predicted by equation (1) was previously experimentally confirmed’5) over only a limited range (~3). Over the wider range (-24) examined for silver it appears that the dependence is not as predicted by equation (1). It can also be concluded that in general the use of annealing treatments to vary grain size is not ideal, in view of the complicating changes in substructure which may also occur. The able experimental assistance of K. V. Vuori is gratefully acknowledged. The author is also indebted to Dr. C. H. Li, Dr. J. A. Sartell and Dr. R. J. Stokes for useful discussions and to Dr. J. N. Dempsey, Director of Honeywell Research Center, for his continued interest and permission to publish. W.

BONFIELD

Research Center Hopkins, Minnesota ~~~~~wel~

References 1. W. BONFIELD and C. H. LI, Acta Mot. 11, 685 (1963). 2. J. E. BAILEY and P. B. HIREKXI, Phil. Ma@. 5, 485 (1960). 3, T. J. KOPPENAAX,and N. M. PARIKH, Trans. Amer. Inst. Min. (MetaZZ.)Engm 334, 1173 (1962). 4. N. BROWN and K. F. LUEENS, Acta Met. 9, 106 (1961). 5. W. BONFIELD and C. H. LI, Acta M& 12, 677 (1964).

* Received November 3, 1964.