A yield phenomenon in face-centered cubic single crystals

A YIELD PHENOMENON

IN FACE-CENTERED P. HAASENt

A.

and

CUBIC SINGLE CRYSTALS*

KELLY1

A small yield-point effect is found during interrupted tensile tests on single crystals of pure aluminum and nickel. The effect is most marked at low temperatures. Experiments have been carried out to determine the conditions under which the effect ocours, and these are correlated with those of other workers. It is concluded that the phenomenon is unlikely to be a strain-aging effect. An explanation is sought in terms of dislocation rearrangements during unloading. UN PHENOMENE

PLASTIQUE

(YIELD)

DANS LES MONOCRISTAUX

A FACES CENTREES

CUBIQUES

Un “yield point” peu prononce a et& observe au tours de tractions interrompues sur des monocristaux d’aluminium et de nickel pur. C’est aux basses temperatures que l’effet eat le plus marque. Des experiences ont Bte r&ah&es pour determiner lea conditions dans lesquelles il apparait et elks ont Bte cornpar& avec celles d’autres chercheurs. On conclut qu’il eat peu probable que les phenomenes soient en relation aver le vieillissement de deformation et l’on propose une explication en fonction des rearrangements des dislocations lors de la liberation des Bprouvettes. STRECKGRENZENEFFEKT

BE1 KUBISCH-FLACHENZENTRIERTEN

EINKRISTALLEN

Bei Unterbrechung der Zugverformung wurde an Einkristallen aus reinem Aluminium und Nickel ein kleiner Streokgrenzeneffekt gefunden. Der Effekt ist am deutlichsten ausgepragt bei tiefen Temperaturen. Es wurden Versuohe ausgeftihrt, um die Bedingungen festzustellen, unter denen der Effekt auftritt. Diese werden mit den Ergebnissen aus anderen Arbeiten in Zusammenhang gebracht. Auf Grund der Befunde ist es sehr unwahrscheinlich, dass es sioh um einen Reckaltenmgseffekt handelt. Auf der Basis einer Umordnung der Versetzungen w&rend des Entlastens wird eine Erklarung ftir den Effekt vorgeschlagen.

1. INTRODUCTION

Recently Lange and Liickeu) reported the existence of a small, but measurable, yield point in the stress-strain curves of single crystals of pure aluminum when these were restrained at room temperature after prior deformation and aging at the same temperature. Blewittt2) found the same effect in copper single crystals deformed at 78°K. The phenomenon was more marked when the annealing was carried out at 300°K, between tests at 78’K, than when the aging was done at 78°K. Similar effects have been found by other workers. Stokes and Cottrell@) mention an effect in aluminum deformed at 9O”K, and Noggle(4) has also found it in this metal deformed at 78°K. Diehl(@ made quantitative measurements of the effect in copper single crystals deformed and aged at room temperature. In similar material, at the same temperature, Cupp and Chalmers(6) obtained delayed yields, which they interpret as indicating a yield point. The present authors have investigated the same effect in single crystals of nickel and aluminum deformed at 2O”K, 78”K, 90”K, and room temperature. * Received June 19, 1956. t Institute for the Studs of Metals, University of Chicago. i Metallurgy Department, Northwestern University, Evanston, Ill. ACTA

METALLURGICA,

VOL.

5, APRIL

1957

The purpose of this paper is to point out that the effect seems to be of general occurrence in single crystals of pure face-centered cubic metals, deformed at low temperatures, and to discuss possible explanations. Fig. 1 illustrates the effect diagrammatically. A crystal is strained to the point A on the stress-strain curve and is then unloaded. On reloading, a small amount of plastic flow may occur before the stress corresponding to the point A, (aa) is reached, but the reloading curve passes above oa and then returns to the stress-strain curve expected from a continuation of the curve obtained prior to unloading. It is with this increase in stress (Au) that the present work is concerned. 2. EXPERIMENTAL

DETAILS

Single crystals of aluminum were produced by the strain-anneal method from material of nominal purity 99.992% presented by the British Aluminium Co.5 These were of gage dimensions 0.1 x 0.3 x 2.0 in. Nickel single crystals of rod shape, 2.0 in. long and 0.090 in. in diameter, were grown from the melt. 3 These crystals were grown and part of the experimental work on aluminum was carried out while one of the authors (A. K.) was with the Department of Physical Metallurgy, The University, Birmingham. 192

HAASEN

KELLY:

AND

A YIELD

PHENOMENON

Test 1. A specimen

193

was strained at a temperature

T,, unloaded

to a small stress of about

(to maintain

alignment),

100 g mm-2

and then further

strained

at T,. Test 1A. A test under the same conditions as Test 1, but without The

unloading

specimen

between straining operations.

was thus

aged

stress at Tl.

under

Test 2. A specimen was strained at a temperature T,, unloaded and annealed in situ at a higher temperature T,, and then retested at T,. Test 3. A specimen was deformed T,, unloaded, the temperature at Tl.

test continued

Test 4. A specimen c

STRAIN

at a temperature

lowered to T,, and the

was strained at a temperature

T,, unloaded,

the temperature

test continued

at T,.

raised to T,, and the

FIG. 1. Illustration of the yielding phenomenon.

These J.M.

were 890).

examined

of 99.98%

purity7

In addition,

some

Matthey

crystals

were

which had been grown from commercially

phre material

(99.4%

Ni).

The orientations

crystals were found by X-ray in Fig. 2.

(Johnson nickel

The aluminum

in a hard-beam

specimens

tensile-testing

machine

see-l.

at a strain machine

The nickel crystals were

deformed only in the latter type of machine. was carried out at a variety

Straining

of temperatures:

78”K, 90”K, and at room temperature The temperatures

/

-40

were deformed

rate of 5 * 10e5 see-l and in a pendulum-type at a rate of -IO-*

of the

methods and are shown

20”K,

(289”-300°K).

lower than room temperature

were

obtained by immersing the specimens in liquid hydrogen, nitrogen, and oxygen. Four main types

of experiment

were carried out.

These may be described as follows: EXTENSION FIG. 3. Part of a load-extension curve for crystal A5 deformed at 90’K.

Whenever

a yield-point

tity measured

effect was found, the quan-

was that denoted

Aa measures the maximum obtained N30. All. /

/

@NIO

ON31

1.

of the curve

before and after reloading.

ca,ses where recovery found

Aa in Fig.

on reloading from that found by joining the

curves obtained .N22

by

divergence

by

producing

In those

occurred between tests, Aa was backwards

the smooth

curve

obtained after a few per cent strain following reloading. Au is always

the maximum

difference

in resolved

shear stress and 0 is the resolved shear stress. 3. RESULTS FIG. 2. Orientation of the crystals examined. A = aluminum, N = nickel. 7 According to our analyses after fabrication.

A large number of tests have been carried out. results

may

conveniently

be

described

headings of the experiments. Test 1. Part of an experimental

curve

under

The the

obtained

194

ACTA

METALLURGICA,

VOL.

5,

1957

(3

*AT

90°K

x AT

300’

K

0 AT Zoo K

Bra. 4. Variation of Ad with u for aluminum crystals. a = Crystal A10 tested at 300°K. b ;T-.Crystal Al tested at 90°K. c = Crystal A20 tested at 20°K. uel = critical shear strers.

300Acr gm mm-* 250-

200-

l50-

too -

50-

0

i III 012345 “el Fro. 5. Variation

I

I

I

of Au with

I

I

I

IO

I

I

i

(r kg mme2

u for four nickel

crystals

Ii

15

I

l

tested at 20°K.

I

]

/ 20

1

j

J

uel = critical shear stress.

1 25

HAASEN

300-

KELLY:

AND

A YIELD

PHENOMENON

II

II 15

195

ACT

gm mmw2

250 -

200 -

150 -

100 -

0.

I

I

012345

I

I

FIG. 6. Variation

from an aluminum

II

1, with

A plot of ho

points

I

IO

I

CT kg mmm2

I

I

I

I

20

I

I

I

I

2 ,

of Ao with (T for two nickel crystals teated at 300”K, 78”K, and 20°K (N5, N14).

of Test

under the sslme conditions The following

II

I

single crystal deformed

to the formulation shown in Fig. 3.

I

according

T, = 9O0K, is

against

G obtained

is shown in Fig. 4, curve b.

should be noted.

No effect is

observed for small values of o. No dependence

of Ao

shear stress.

When

cr exceeds

a, -

5 kg mm-s,

Aa

increases with CF. The curves in Fig. 6 show the variation

of ho with

o for two crystals of nickel deformed at room temperature, 78°K

and 20°K.

A qualitative

behavior is found at all temperatures

similarity

of

and the magni-

on aging time was found for times from 1 min (the

tude of the effect at a given flow stress depends little

shortest possible) up to several hours. In aluminum de-

on temperature.

Although

formed

with increasing

temperature,

at room

temperature

a smaller

effect

found-curve

a, Fig. 4. One aluminum

was deformed

at 20°K and the results are plotted

was

crystal (A20) in

curve c, Fig. 4. These are generally similar in trend to those obtained One crystal

This may be due to an orientation

of the magnitude

of Ao, but no system-

of this has been made for aluminum. u for four nickel

of widely differing orientation,

deformed

at

The general trend of t,he results is similar to

that found for aluminum, with the difference that a small and constant value is found for small values of o-no

yield

A large number of crystals were tested at 78’K and shown in Figs. 5 and 6. No time dependence

Fig. 5 is a plot of Aa against 20°K.

because the rupture stress of the crystal is attained.

(A2) deformed

at 90°K failed to show

point was ever found

at the critical

of an

increase of Ao with a is limited at room temperature

at room temperature.

atic investigation crystals,

somewhat

the observation

at the other two temperatures.

any effect at all. dependence

cr,, decreases

magnitude

All gave similar results to those of the

of Aa could be found at any temperature

for aging times between 6 min and 10 hours.

Test 1A. This test was carried out on nickel crystals at 20”K,

78”K,

and room

varying aging times.

temperature

In twenty-six

for widely

cases out of thirty

no effect was observed within the accuracy of measurement (10 g mm-2), even at the highest stresses attainable.

In four cases a small, and it is thought spurious,

effect’ was found.

Unloading

of 10%

between

tests

IQ6

ACTA

METALLUROICA,

gives a small effect. It seems necessary to reduce the load by more than 50% for a test of type 1A to become atestoftypel. ‘&st fA was carried out on aluminum crystal 20 at 20°K. NO yield point was observed. “rest 2. Nickel crystals deformed at 78OK, annealed for several hours at 3OO”K, and retested at 78’K, show values of Ao larger by a factor of 2 to 3 than those observed in test 1 at 78’K. The general shape of the Ao versus (I ‘curve is similar for tests 1 and 2, but AG rises more rapidly at high stresses in test 2. The value of A.o is also. increased in aluminum crystals on annealing at 300°K between tests at 90°K. A typical value of Ao of 17 g mm-a found in a crystal aged at 90°K was increased to 27 g mm-a on aging at 3OQ’K between tests at 9O’K. Test 3. Nickel specimens show a much larger yield point when the second deformation is carried out at a lower temperature. Thus, Aa at 78°K after a roomtemperature prestrain to a low flow stress is about LOOg mm-s, while it is about 25 g mm-2 in a constanttemperature test (type 1 at 20°K, 7PK, or 300°K). There was no sign~cant difference between the value of Au found on straining at 78’K or 20°K after de. formation at room temperature. The measurements in this type of test show an unusually large scatter. For stresses in excess of CQ= 11 kg mm-s, Ao increases with o in a manner similar to that found in test 2. Aluminum specimens were strained at room temperature and then further deformed at 90°K. Llnder these conditions no anomalous yielding was observed at 90°K. However, stray-hardening at 90°K after prior deformation at room temperature is very rapid and possibly masks any effect. Stokes and Cottrell(sj reported an effect at 90°K after prior deformation at 300°K if a specimen was deformed at 90°K before the deformation at 300°K. Examination of their curves shows that the effect is only observed under these conditions if the strain increment at 300°K is small. Test 4. Nickel crystals were deformed at 78”K, the temperature raised to 3OO”K, and the test continued, No anomalous yielding was observed until the tiow stress at 78°K exceeded 3.8 kg mm-e; Ao then increased with o. This test cannot be carried out on aluminum crystals, since “work softening” occurs (7,s) and corn--Ï pletely masks any ef’l?ect. The small values of AG (see Fig. 7) obtained in this test on nickel are not due to a work-softening elect, since the ffow stress is changed by equal amounts on raising and on lowering the temperature between 300°K and 78°K.

VOL.

5, IQ87

350-

A@ gm mm-2 3OO-

250-

0

012345

I

I

I

I1

Q kg mme2

IO

I1

FIG. 7. Xchematio diagram showing v&&ion CTfor differsnt types of t&s on nickel orptals.

I

15

of Aa with

The experimental findings are summarized in Fig. 7 for the various types of test carried out on nickel crystals, The curves are drawn approximately to scale for Tl = 78°K and T, = room tem~ratu~, for a crystal having an orientation in the center of the unit triangle. Since the results for alumina are qualitatively similar to those for nickel, the curves for tests 1 and 2 serve to illustrate the type of variation found in this metal in the same temperature range, bearing in mind that ACTis immeasurably small for small o. A number of other experimental facts may now be cited. In ahuninum the flow stress measured at 90°K recovers on annealing at 3OO’K. However, test 2 on aluminum shows a larger value of Aa than that found in test 1. Removal of a surface layer of the specimen by ele~tro~o~~s~ at 300°K during the experiments of type 2, while leading to a larger reduction of the flow stress than simply annealing, does not affect the value of Ao. ~mmer~ia~y pure nickel cry&ala show a less marked effect than the crystals of high purity. For instance, in a test of type 3, Ao was 25 g mm-s at (I -+ 2 kg mrnm2for two crystals (N-19) of commercially pure nickel tested at 78°K and 20*K, compared to 100 g rnrnmain similarIy oriented crystals of the pure

HAABEN

AND

KELLY:

material. The values of Aa found for nickel crystals were not changed by a prolonged anneal iu hydrogen or a prolonged decarburizing treatment followed by a vacuum anneal. We shall summarize here the results of other workers. DiehY5) investigated the effect in copper at 300°K according to the formulation of our test 1. Aa was found to increase linearly with o except for stresses near the critical shear stress, where no effect was found. The slope of the Ao against cr curve decreased from 1.6% to 0.7% at high stresses (when the stressstrain curve becomes concave to the strain axis). BlewiW) has reported experiments of types 1 and 2 on copper single crystals with T, = 78°K and T, = 300°K. Few figures are given, but no effect was found for stresses of less than o - 4.0 kg mm-2 in the experiments of type 2, and much larger stresses were attained in an experiment of type 1 at 78’K before the effect was noticed. These results, together with those of Diehl, are quite consistent with the stress and temperature dependence of AC summarized for aluminum and nickel in Fig. 7. Noggle(@ performed an experiment of type 2 on alum~um crystals with T, = 78°K and T, = 3OO’K. From his curves it can be seen that Aa increases with o, the ratio being ~1*2~/~. This is in good agreement with the values found in the present work. Cupp and Chalmers’@ deformed copper single crystals at room temperature by stepwise loading and found a delay of some seconds between the application of a load increment and the resumption of plastic flow. They interpret this as indicative of a yield point developed by aging under load. The difference in the method of testing in Cupp and Chalmers’ experiments and those described here prevents a direct comparison. 4. DISCUSSION

In view of the similarity of the results obtained from experiments on a number of metals, it seems reasonable to seek a general explanation. The experimental findings may be summarized as follows: A. In interrupted tensile tests on face-centered cubio single crystals a small yield point is found when the resolved shear stress exceeds a certain value. The magnitude of the effect (Ao) increases with the flow stress (a). B. The specimen must be aged under a reduced load in order to show an effect. C. A o is increased on aging at temperatures greater than hhe testing temperature. D. The effect is less marked at higher tempera2-_(lZPP.)

A YIELD

PHENOMENON

197

tures of testing, i.e. 300”K, but is relatively insensitive to temperature at low temperatures (9O0K, 2O’K). E. Within the accuracy of the experiments carried out here, Aa is independent of time of aging, for times greater than a few minutes, at temperatures from 20°K to room temperature. The original discussion of this effect is due to Blewitt,(a) who attributes it to strain-aging and specifically to the formation of Cottrell atmospheres and consequent locking of the dislocations by vacancies produced during plastic flow. This explanation has also been advanced by Noggle.(*) Cupp and Chalmers(Q suggest that their effect may be explained by the locking of dislocations by a substit,utional solute or hydrogen present as an impurity. The strain-aging hypothesis is attractive, since it appears to agree qualitatively with a number of the present observations (notably A, C, and D) if it is assumed that the number of point defects present in the material increases with increasing deformation. The features of a tensile test usually taken as criteria for the existence of a strain-aging effect leading to dislocation locking are:t9) (1) A fall in load at the beginning of plastic deformation, (2) The absence of an effect on immediate retesting, (3) The return of the fall in load after a suitable aging treatment. In the present case it must be assumed, regarding (I), that the locking is insufficiently strong to produce a drop in load in most experiments and regarding (2), that the migration of point defects to dislocations takes place so rapidly that this criterion cannot be observed. This explanation has very serious difficulties when the nature of the possible point defects responsible for locking is considered. Table 1 shows the times for various defects to move one interatomic distance in aluminum, nickel, and copper at 20°K, 90”K, and 300°K. The activation energy for the motion of vacant lattice sites has been taken as onethird that for self-diffusion(lO) and for vacancy clusters as one-tenth of thisol) (both of these are minimum estimates). Do in both cases is taken as 1 cm2 see-‘. For hydrogen diffusion the values are taken from the literature.(ls) It, is seen that vacancies are quite immobile at 90°K and that clusters are immobile at 20°K. Hydrogen, the most mobile impurity, cannot be responsible for an effect at temperatures much less than 90°K. Even if a point defect be present with an activation energy for motion of 0.1 eV, it would be quite immobile at 20X, where the effect is found in nickel and aluminum. The strain-aging hypothesis is also inconsistent

ACTA

198

METALLURGICA,

TABLE 1. Times for various defects to migrate one interatomic distance in aluminum, copper, and nickel at 20”K, 90”K, and 300°K. Figures for activation energy for selfdiffusion from references( lf3), ( 17). For hydrogen diffusion (12).

Type of defect

Metal 1 Single vacancy

2 Vacancy cluster

3 Interstitial hydrogen

90

20

2 x 10-n 3 x 10’0 00

10-18 2 x 10-a 3 x lo’@

$ oc)

300

7 x 10-S

(Temperature OK) Al

cu

300

lo= co Ni

300

16s co

:8

with finding

B,

experiments(rai4)

since

10’9 7 x IO-5 108’

No figures available

10-B

2 x 10-n

1%

l&’

in conventional

strain-aging

aging under load leads to increased

values of the upper yield point, but never to a decrease. The absence of a time dependence a range of temperature an explanation

from 20°K

of the effect over to 300°K

in terms of strain-aging

VOL.

6, 1957

In aluminum deformed at and above room temperature the intersection of dislocations makes no contribution to the flow stress.(‘) Yet a yield-point effect has been observed in the present experiments and by Lange and Liicke. (l) Thus, process (a) cannot be generally responsible for the yield point. Processes (b) and (c) may both anchor the relaxing dislocations on unloading.* One expects the anchoring to be more effective the closer the dislocations are spaced, so the yield point should increase with increase of flow stress, as is observed. A rise in temperature while the specimen is unloaded will make dislocation rearrangement easier and hence increase the yield point. However, if widespread recovery occurs, one expects mutual annihilation of dislocations to lead to a state of lower elastic energy than does dislocation rearrangement. Hence the yield point should be reduced at higher temperatures, as is found in the case of aluminum. With this model the reduction of the effect found in impure nickel may be understood by supposing that dislocation rearrangement is less easy due to the presence of impurities. This last point could be checked directly by measuring the reverse plastic flow as in the experiments of Thompson, Coogan, and Rider.05)

makes

very unlikely

ACKNOWLEDGMENTS

and suggests to the present authors that the effect is

a result of the rearrangement of dislocations during unloading rather than a thermally activated migration of point defects to dislocations. A similar idea has been proposed by Diehl.c5) The salient feature of the effect is that some irreversible process occurs during unloading of the specimen and that this does not occur if the dislocations are merely brought to rest, since no yield point is found if the load is fully maintained during aging. In this condition the applied stress is approximately balanced at the position of any dislocation by a back stress due to other dislocations in the lattice. Although, on unloading, the dislocations are under the full action of the back stress, only a small amount of reverse plastic deformation occurs.(r5) The present authors believe that most of the dislocations anchor themselves during unloading, and that this process of anchoring, which prevents reverse plastic flow, is also responsible for the yield-point effect on reloading. There are three possible mechanisms for the hindrance of dislocation motion in pure-metal crystals. These are: (a.) the generation of jogs and point defects by dislocations intersecting other dislocations, (b) the formation of sessile dislocations, (c) the elastic interaction of dislocations.

The authors would like to express their thanks t,o Professor C. S. Barrett for helpful discussions Professor

L. Meyer for his assistance

ments using liquid hydrogen. to Mr. K. K. Ikeuye crystals.

and to

in the experi-

They are also indebted

for growing

the nickel

single

One of us (A. K.) thanks the Managers of

the I.C.I. Fellowship

at the University

Fund for financial support while

of Birmingham. REFERENCES

1. H. LANC+E and K. L~~CKE Z&l. fiir Met&k. 2. 3. 4. 5. 6. 7. 8. 9. 10.

44, 183 (1953). T. H. BLEWITT Phys. Rev. 91, 1115 (1953). R. J. STOKES and A. H. COTTRELL Acta Met. 2, 341 (1954). T. S. NO~QLE Ph.D. Thesis, Illinois (1955). J. DIEHL Ph.D. Thesia, Stuttgart (1955). C. R. CWP and B. CHALMERS Acta Met. 2, 803 (1954). A. H. COTTRELL and R. J. STOEES Proo. Roy. Sot. A 288, 17 (1955). Phil. Mug. [8], 1,835 (1956). A. KELLY R. E. SMALLMAN, G. K. WILLIAMSON, and G. ARDLEY A& Met. 1, 126 (1953). J. W. KAUFFMAN and J. S. KOEHLER Phys. Rev. 97, 555 (1955).

* The small value of Au in the initial stage of plastic deformation (easy glide) where sessile dislocations should not yet be formed indicates the importance of process (b). Further evidence for this may be seen in the recent observation of Diehl and Rebstocku*) that plastic twisting of a copper crystal during an interruption of a tensile test produces a large yield point on reloading.

HAASEN

AND

KELLY:

in Handbuch der Physik Vol. VII, 1, 383, Springer, Berlin (1955). 12. C. J. SMITHELLS Metals Reference Book Vol. II Butterworths, London (1955). 13. A. N. HOLDEN and F. W. KUNZ J. App. Phya. 23, 799 (1952). 14. H. W. PAXTON J. A33p. Phys. 24, 104 (1953).

11. A. SEEQER

A

YIELD

PHENOMENON

199

15. N. THOMPSON, C. K. COOGAN, and J. G. RIDER J. Inst. Met. 84, 73 (1955). 16. A. S. NOWICK J. App. Phys. 22, 1182 (1951). 17. R. E. HOFFMAN, F. W. PIKUS, and R. A. WARD J.

Metals 8, 483 (1956). 18. J. DIEHL and (1956).

H.

REBSTOCK

2.

LNaturforsch,

lla,

169