On mechanical twinning in single crystals of vanadium

ON

MECHANICAL

TWINNING J.

W.

IN

SINGLE and

EDINGTONt

R.

CRYSTALS E.

OF

VANADIUM*

SMALLMANS

Single crystals of vanadium have been deformed in compression along the [Ill] direction at 77°K. The specimens deformed initially by twinning on the (121)[il l] and the (211)[ill]-twin systems; but, twinning on the (iZl)[ill] system was usually preferred after about 6% strain. If specimens which had been prestrained to 10 0A compression were aged for 15 min at 100°C and re-strained at 77°K deformation continued by twinning, but at a stress 20 percent lower than the final stress attained during the prestrain treatment. On ageing at 100°C for longer times, this stress difference decreases in magnitude until after 3 hr ageing at 100°C re-straining at 77°K produces a true stress-strain curve which is a continuation of that obtained during the prestraining treatment. The change in stress after short ageing times at 1OO’C is explained by the relaxation of long-range stresses built up during prestraining at 77°K. The gradual decrease in the stress difference is explained in terms of gradual pinning of the incoherent twin boundaries by diffusing impurity atoms. FORMATION DES MACLES MONOCRISTAUX

MECANIQUES DANS DE VANADIUM

LES

Des monocristaux de vanadium ont QtB deform& en compression suivant la direction [ill] 21 77°K. Les Bohantillons se dbforment d’abord par maclage dans les syst&mes (121) [ill] et (211) [ill]; cependant le maclage suivant le syst&me (121) [ill] apparait plus volontiers apr& une d&formation d’environ 6 %. Sides 6chantillons prbd8form6s de 10 % en compression sont viellis 15 min. PL100°C et redhform& 8,77”K, la dbformation se continue par maclage, mais pour une contrainte inf&ieure de 20 % & la contrainte finale Si l’on vieillit B 100°C pendant un temps plus long, cette atteinte lors du traitement de p&d&formation. diff&enoe de contrainte diminue, et ap& un vieillissement de 3 h. & lOO”C, une nouvelle deformation 8. 77OK conduit B une courbe tension-d&formation qui prolonge celle obtenue au tours du traitement de pr6d6formation. La modification du niveau de contraintes observee apr&s un vieillissement de courte durbe & 100°C s’explique par la relaxation des contraintes & grande distance form&es au tours du traitement de pr& dbformation it 77°K. La disparition graduelle de la diff&ence de contraintes s’explique par un blocage progressif des joints de macles non cohbrents, par la diffusion des atomes d’impureti?s. UBER

mcmmscHE

ZWILLINGSBILDUNG

IN VANADIUMEINKRISTALLEN

Einkristalle aus Vanadium wurden vei 77°K durch Kompression entlang [ll l]-Richtung verformt. Die Proben verformten sich anfiinglich durch Zwillingsbildung in den (El) [ill]und (211) [ill]Zwillingssystemen. Oberhalb etwa 6 % Dehnung war jedoch gewiihnlich Zwillingsbildung im System (El) [il I] bevorzugt. Nach einer Vorverformung van 10 % Kompression und 15 Minuten Anlassen bei 100°C erfolgte die Weiterverformung bei 77°K weiterhin durch Zwillingsbildung, allerdings bei einer urn 20 % kleineren Spannung gegeniiber der bei der Vorverformung angelegten Endspannung. Nach liingerem Anlaasen bei 100°C wird diese Spannungsdifferenz kleiner; schliel3lich erhiilt man nach dreistiindigem Anlassen bei 100°C bei der Weiterverformung bei 77°K eine wahre Verfestigungskurve, die eine Fortsetzung der Verfestigungskurve fiir die Vorverformung ist. Die Iinderung der Spannung nach kurzen Anlal3zeiten bei IOO’C wird erkliirt mit der Relaxation van weitreichenden Spannungen, die wiihrend der Verformung bei 77°K entstanden waren. Der allmiihliche Abfall des Spannungsunterschiedes wird mit der schrittweisen Verankerung inkoharenter Zwillingsgrenzen durch diffundierende Verunreinigungsatome erkl&rt. 1. INTRODUCTION

Mechanical

followed

twinning is a common mode of deforma-

by ageing

at higher temperatures,

tion of the b.c.c. transition metals at low temperatures.

low-temperature been previously

However,

results of a series of compression

it has been shown that prestraining

u-iron(l) and niobium(2) at room temperature twinning

on restraining

theless, if prestrained room temperature,

at low temperatures. specimens

further

both

inhibits Never-

single crystals treatment

deformation

2.

at low tem-

Although

it has been shown

that

polycrystalline

cylinders

13, JULY

1965

WORK

to produce

compression

and 0.25 in. in length.

1. Impurity content of the vanadium single crystals ppm

17, 1964. t Metal Science Group, Battelle Memorial Institute, Columbus, Ohio 43201, U.S.A. 3 Department of Physical Metallurgy, University of Birmingham, England. VOL.

EXPERIMENTAL

0.10 in. in diameter

TABLE

* Received November

METALLURGICA,

above.

Table 1 was spark machined

deforms by twinning at low temperatures,(3)

the effect of prestraining at 20°C on deformation at low temperatures has not been examined. Furthermore, the effect? of prestraining at twinning temperatures,

ACTA

tests carried out on

using the prestraining

A single crystal of “three-pass” electron-beammelted vanadium containing the impurities shown in

peratures then proceeds by twinning.(l) vanadium

of vanadium,

outlined

are aged just above

on the

properties of b.c.c. metals has not reported. This paper describes the

765

C

0

N

Pb

Cu

Fe

Mg

Ag

100

300

700

10

1

20

1

1

ACTA

766

METALLURGICA,

The cylinders were finished on the fine range of the spark machine and a surface layer, O.Ol-in. thick, was removed by electropolishing under the conditions described previously.(4) Compression tests were carried out on a hard-beam tensile machine at a strain rate of 8 x 1O-4 set-l using a compression jig attachment with “Sintox” compression plungers. Specimens were aged in situ on the tensile machine in an oil bath maintained at 100 f l”C, and a small stress (about 10 percent of the elastic limit) was maintained on the specimen during ageing in order to prevent re-alignment of the specimen. The surface of some specimens was photographed at various stages of testing. In these experiments, a small stress was maintained on the specimen by clamping the compression jig closed before its removal from the tensile machine for specimen photography. 3.

RESULTS

The compression axis of all the specimens was close to [ill], and deformation occurred by simultaneous twinning on the (i%)[ill] and (2ll)[ill]-twin systems. However, after some 6% strain, one twin

no8

VOL.

13,

1965

system-namely, (iZl)[ill]-was usually preferred. A typical stress/strain curve for a crystal tested in compression at 77°K is shown in Fig. l(a). It has been found that crystals prestrained either 3 percent or 10 percent in compression at 20°C deform by twinning on subsequent deformation at 77°K. However, the general level of the stress/strain curve is much higher, as shown in Fig. l(b). If a specimen is strained 10 percent at 77°K before straining 3 percent at 20°C and then immediately re-strained at 77”K, deformation still proceeds by twinning, but the stress level is again higher than it was during the previous test at 77°K (see Fig. 2, curve A). A similar specimen tested in the same sequence, but aged for 30 minutes at 100°C after the deformation at 2O”C, also twins on retesting at 77°K. In this case, twinning occurs at a high stress level, but not as high as that for the specimen tested in the same sequence without the ageing treatment (see Fig. 2, curve B). These results show that a prestraining treatment at 20°C does not prevent subsequent twinning at 77”K, but that ageing at 100°C after prestraining at 20°C promotes twinning. However, in order to eliminate the differences in the dislocation arrangement which

-----7r

.-.

5 PERCENT

FIG. l(a). A typical true-stress/strain curve for a vanadium single crystal, compressed along a [ 11 l] direction up to 20 % strain.

STRAIN

10

Ibl , ,

l5

20

25

FIG. l(b). A typical true-stress/strain curve for a vanadium single crystal, prestrained at 20°C (curve A) and re-strained at 77°K (curve B).

EDINGTON

AND SMALLMAN:

MECHANICAL

TWINNING

OF

VANADIUM

767

crystals were each prestrained 3 percent at 77’K, photographed, given either an Al or A2 ageing treatment, and then restrained 2 percent and 6 percent, respectively, at 77’K before photographing again. In each case, well over half the surface of the crystal was photographed. Careful comparison of photographs showed that on re-straining after 15 min ageing, the twins created during the prestrain treatment had both lengthened and thickened (see Fig. 4). Nowever, after 210 min ageing, many new twins were present after re-straining, whereas the twins formed during prestraining had only thickened very slightly (see Fig. 5). It is clear, therefore, that an Al-ageing treatment makes the propagation of preformed twins easier compared with the prestrained crystal, whereas an A2-ageing treatment promotes the creation of new twins rather than the propagation of preformed twins. 4. DISCUSSION

FIG. 2. A typical true-stress/strain curve for & crystal, compressed in steps of 10 ‘A strain--&& at 77”K, second at ZO”C, third at 77”K, curve A. Curve B is for a crystal tested in the same sequence, but aged at 100°C for 15 miu after straining at 20°C.

deformation at 77°K and 20°C is known to produce,(5) it was decided to carry out both the prestraining and the re-straining treatments at 77’K. Such a prestraining approach also allows an accurate estimate to be made of the effect of ageing on the mechanical properties at 77°K because the stress levels for the prestrained and restrained material can be compared directly. The behavior of single crystals of vanadium prestrained 10 percent at 77*K, aged at IOO’C for periods of time ranging from 15 min to 9,980 min, then restrained at 77°K is shown in Fig. 3. It can be seen that the initial flow stress, o,, after ageing for short periods of time, is about 20 percent lower than the final stress, oP, before unloading at t$he end of the prestrain treatment. However, with increasing ageing time, the stress difference (oP - on) decreases until after 180 min ageing at 100°C the stresses, o, and aR, are comparable. Indeed, the stresses remain comparable even after ageing times of up to 1 week. For ease of reference, the ageing times described above have been designated Al for ageing times of up to 180 min and A2 for longer ageing times. To understand this effect, it is important to know if new twins are being created or if twins which are already present are being propagated on re-straining after these ageing treatments. Consequently, two

It is interesting to compare the results of these experiments with the known strain-ageing behavior of polycrystalline vanadium(“) for deformation at 20°C. In the latter case, the lower yield stress on re-straining is always greater than the maximum stress reached in the prestrain treatment, even after only 15 min ageing time at 1OO’C. Furthermore, the maximum increase in the lower yield stress is about

FIG. 3. Typical true-stress/strain curves for crystals prestrained 10 % at 77”K, aged for periods of time of up to 9980 min at lOO”C, then retested at 77°K.

768

ACTA

METALLURGICA,

VOL.

13,

1965

FIG. 4(a). Single crystal, prestrained to 3 % strain at 77°K

x 100.

FIO. 4(d). Same area after ageing for 30 min at IOO‘W, then restraining to 8 further 2% strain at 77*K. Note general twin thickening and the movement of Twin A from Position B to C x 100.

4,000 psi and occurs after 5,000 min ageing at 100°C. This increase is about 8 percent of the lower yield stress of the fully annealed material. In contrast, in the present experiments, the stress at which deformation begins on re-straining at 77°K after short ageing times at 100°C is about 18 percent lower than the maximum stress reached during prestraining. This stress difference gradually decreased until, after 180 min at IOO°C, it no longer exists. Let us first consider the behavior of these crystals after Al ageing. The experiments have shown that an ageing treatment of 15 min at 100°C makes it much easier to propagate the twins already present in the material. To understand this phenomenon, it is necessary to know why a twin stops propagating during initial deformation. There are a number of reasons why a moving deformation twin stops; for example, the resolved shear stress on a twin may drop below the shear stress required to propagate the

twin. This can occur if twins are nucleated in a region of a high local stress, such as a crack. However, this mechanism is not expected to be important, since no cracks are observed on these specimens and the surface preparation is expected to remove any marked stress concentration. The twin may also meet an obstacle such as another twin through which it is unable to propagate. However, careful observation of twin/ twin intersections shows that twins on one system do not act as barriers for twins on the other. Indeed, Smith et a1.f’) have shown that twins on these particular twin systems can propagate across one another quite satisfactorily. It is also possible that a twin stops propagating because it has lowered the stress on the twin plane operating as a result of its formation on that twin plane. However, it is difficult to see how a short ageing time of 15 min at 1OO’C would cause such a stopped twin to begin to propagate again at a lower stress level.

EDINGTON

ANIl

SMALLMAN:

MECHANICAL

TWINNING

OF

Fro. 5(a). Single crystal, prestrained to 6 % strain at 77°K.

VANADIUM

769

x 100

FIG. 5(b). Same area after ageing for 210 min at 100°C then restraining to a further 4 “/pstrain at 77OK. Note the absence of twin thickening and the large numbers of new twins; note also twm boundaries at A, B, and C which have not moved. x 100

A more probable

reason for (a) the stoppage

twin during prestrain,

of the

and (b) its propagation

at a

elapse for noticeable experiments

stress relief to take place.

Indeed,

show that if ageing takes place at 20°C

lower stress after ageing, is the presence of long-range

instead of lOO”C, it is only after 180 min ageing time

stress fields in the crystal

that there is a measurable

which contribute

to work

hardening by making it difficult to move dislocations. Such long-range

stress fields are expected

to be much

larger at 77°K than at 20°C because of the large distortion-associated-deformation twinning.(*) At the low temperature, up

during

high stress concentrations

deformation

because

they

can build cannot

be

for twinning on re-straining min ageing difference

the twins produced during the prestraining treatment will grow at a lower applied stress than was necessary before. Thus, deformation will continue at a lower stress level. Thermal fluctuations would be important in the stress-relief process, so a period of time would

at 20°C is necessary

in stress level equivalent

to bring

about

a

to that produced

by 15 min ageing at 100°C. It

can

be

assumed

that

the

stress

relaxation

described above is governed byan equation of the form

relieved by slip, since oi for slip is large.c3) However, as the temperature is raised, the friction stress decreasesc3) so that slip can take place to relieve the As a result of the general long-range stresses. relaxation of the long-range stresses in the crystal,

lowering of the stress levels Moreover, 1400 at 77°K.

(UP- @R) At where up -

=Aexpg,

oE = the stress difference on re-straining At = the time interval at the absolute ageing temperature T A = a constant k = Boltzmann’s constant, and Q = the activation energy for process.

the

ACTA

770

The

above

thermally

kinetic

values

activated

process

value is in reasonable

are

consistent

with

with Q = 0.3 eV.

agreement

a

This

with the value

0.2 eV which has been associated ment of dislocations

METALLURGICA,

of

with the rearrange-

ruption

hypothesis

of deformation

13,

outlined

at 77°K

above.

Inter-

by deformation

locked after 3 hr ageing at 1OO’C. Thus, it is expected boundaries treatment

in twins

further deformation. about

ageing at 100°C brings

stress relief as described

above,

leading

to a

of the stress/strain curve, as shown in Fig. 2, curve B. Dislocation rearrangement is not expected

lowering

to be important ageing

in the previously

experiments(@

reported

where prestraining

new twins

The gradual decrease in the value of the (up -

crR)

term for ageing times up to 180 min is interpreted the

boundaries

gradual

by diffusing

not the incoherent described

pinning

of

solute

atoms.

twin boundaries

by Sleeswyk,(l@

incoherent

in

twin

Whether

or

are dissociated

as

segregation

of solute atoms

such as carbon and oxygen to the twinning dislocations will be expected segregation shown’@

to occur

in a similar

to slip dislocations.

that slip dislocations

Now

manner

to

it has been

in vanadium

prestrain

will be created

while very

of prestrain twins should occur.

is in agreement

with the observations.

This

ACKNOWLEDGMENTS

The authors wish to thank Professor for

the

provision

Development Kingdom

are fully

of

laboratory

and Engineering

Energy Authority

strain-

are comparable.(3)

of

the

little thickening

G. V. Raynor

facilities

Group

and

the

of the United

for financial support.

REFERENCES

is carried

out at 20°C because the values of (TVat 20°C and 100°C

terms

all the incoherent

during

at

stresses are increased by this

However,

treatment formed

will be locked by a few carbon atoms, and

20°C increases the flow stress for twinning because the values of the long-range

1965

that after an AB-ageing

consequently

in cr-iron.cs)

It is possible to explain the results shown in Fig. 2 on the stress-relief

VOL.

H. COTTRELL, Nature, Lond. 167, 954 (1951). 2. C. J. MCHAROUE, Trans. AIME 224, 234 (1962). 3. T. C. LINDLEY and R. E. SMALLMAN, Acta Met. 11, 361 (1963). 4. J. W. EDINGTON and R. E. SMALLMAN, Amt. J. Inst. Metals 8, 8 (1963). 5. J. W. EDINGTON and R. E. SMALLMAN, Acta Met.; to be 1. A. T. CHURCHMAN and A.

published.

6. J. W. EDINGTON, T. C. LINDLEY and R. E. SMALLMAN, Acta Met. 12, 1025 (1964). 7. S. W. J. SMITH, A. A. DEE and J. YOUNG, Proc. Roy. Sot. A121, 477 (1928). 8. D. HULL, Fracture ofSolids, p. 477 Interscience Publishers (1961). 9. H. G. VAN BUEREN, Imperfections in Crystals, p. 377. North-Holland

Publishing

Comoanv ( 1961). 10: 7Ok (1962j.

10. A. W. SLEESWYK, Acta get.