TEMPERATURE DEPENDENCE OF THE YIELD POINTS IN IRON*

N. BROWN? and IX. A. EKVALLt

Hetween 300’ anti 90°K the elastic limit, and the anelastic limit were measured in polycrystalline irons wit,h 0.0014 and 0.012 per cent interstitial impurities using a high sensitivity extensometer. The elast’ic limit was independent of temper&me but depended on purity. The anelastic limit depended on tem- perature and impurity content8. but t,he decrease in temporat,ure dependence wit,h decreasing amount of impurity indicated that an ultra-pure iron should show no temperature dependence of t,he anelastic limit as measured with a high sensit,ivity ext,cnsometer. These rest&s do not, support the existence of a tern- pcrat~ure dependent, Peierls-Nabarro force in iron.

The iarge temperat,ure dependence ordinarily associated with t,hr marroscopie lneasur~ments of the yield point was shown to be associated with the rate of work hardening in the mi~rostrain region i.e. botwcen our anelastic limit and the macroscopic, yield point. The rate of work hardening in the micro- strain region increases markedly with deereasmg t,emperature. It was concluded that t.hermally activated cross-slip would determine the temperature dependence of the macroscopic yield point if im- purities rould be completely eliminated.

INFLUENCE DE LA TEMPERATURE SUR LES LIMITES ELASTIQUES DU FER

La limita Blastique et lalimite inelastique ont et& mesurees entre 300” et 90°K dans dcs fors polycristallins presentant 0,0014 eb 0,012 pour-cent, d’impuret& interstitielles, au moyen d’un extensometre de haute sensibilit,& La limite Blastique a et& trouvde independanto de la temperature, mais depend de la purete. La limite inelastique dPpend de la temp&ature et du pourcent,age d’impuret&, mais l’influence dbrois- Sante de la temperature pour des poureentages deeroissantes d’impuret& indique qu’un fer ultra pur ne doit pas montrer d’influenee de la temperature sur la limite elastique mesur&e it l’aida d’un extensometre t&s sensible. Ces resultats ne confirment pas l’existence d’une force de Peierls-Nabarro d&pendant de la temperature dans le fer. Les auteurs montrent que l’influenoe importante de la temp8rature normalement associee aux mesures mecroscopiques de la limite Blastique, ext en relation avec la vitesse de durcissement par deformation dans la region de microdeformation, c.&.d. entre notre limite inelastique et la limite elastique macroscopique. La vitesse de durcissement par deformation dans la region de microdeformation augment,e sensiblement lorsqu’on diminue la temperature. Los auteurs concluent quo seules des devia- tions de dislocatzions a&i&es thermiquement determinent I’influence de la temp&ature SW la limit,e &.stique macromopique, pour autant que les impure& puissent etre @limi&es compl&temenD.

TE~~PERATURABH~~GIGKEIT DER ST~~CKGRENZEN VOW EISEN

Mit Hilfe sines hochempfindlichen Extensometers wurden an polykristallinen Eisenproben mit 0.0014 und 0.012 Prozent Zwischengitter-Verunreinigungen ewischen 300” und 90°K die Grenzen des elastischen und des anelastisohon Bereichs gemessen. Die elastische Grenze war unabhiingig van der Temperatur, hing aber vom Reinheitsgrad ab. Die anelastische Grenze hing van Temperatur und Verunreinigungsgehalt ab, aber die Abnahme der Temperaturabhiingigkeit bei abnehmender Menge an Verunreinigungen deutete darauf hin, da6 bei ultra-reinem Eisen die anelastischo Grenze, mit einem hochempfindlichen Extensometer gemessen, keine Temperaturabhiingigkeit zeigen sollte. Diese Ergeb- nisse unterstiitzen nicht die Existenz einer temperaturabhiingigen Peierls-Nabarro-Kraft in Eisen.

Die starke Tenlperat~abh~ngigk~it. die gewahnlich mit makroskopischen Messungen der Streck- grenze verbunden ist, hang& wie sieh zeigen l&t, ~usamme~ mit dem Ve~estigun~sanatieg im Gebiet der ~~ikro.Dehnung, d.h. zwischen unserer anelastischen Grenze und der makroskopischen Streckgrenze. Der Verfestigungsanstieg im Gebiet der Mikro-Dehnung nimmt mit abnehmender Temperatur betracht- lich zu. Es wird gesehlossen, da6 nur thermisch aktivierte Quergleitung die Tempereturabhangigkeit~ der makronkopinchen Streckgrenze best)immt, wenn man Vrrunreinigungen viillig ausschliefien kann.

I. INTRODUCTION

No general agreement exists concerning the cause of

the large temperature dependence of the yield point

of b.c.c. high melting point metals. These metals

show a difference in yield point between room temper-

ature and that of liquid nitrogen which is on the order

of 50,000 lb/n?. Since this value is very large when

compared to f.c.c. and h.c.p. metals, a great deal of

interest has been generated on the subject. A recent

review by Conrad(l) covers the various viewpoints

which exist, for explaining the ~mperature dependence.

At the present time there are essentially the following

four opposing viewpoints : (1) interstitial impurities,

(2) Peierls-Nabarro force, (3) thermally activated

cross-slip, and (4) jogs. The impurity argument is

based on the strong interaction between interstitia.ls

and dislocations as first pointed out by Cottrell and Bilby.@) The P-N-F argument was put forth by

Heslop and Petchc3) who, after eliminating the effect, of

grain size, prior strain, and had supposedly eliminated

the effect of impurities, were left with no mechanism

but t,hat. of the innate resistance of the lattice. They,

* Received March 2, 1962. however, did not completely eliminate the effect, of

t University of Pennsylvania, Philadelphia, Pennsylvania. impurities because the lowest impurity levels were

ACTA METALLURGICA,VOL.lO, NOVEMBER 1962 1101

1102 ACTA METALLURGICA, VOL. 10, 1962

still greater than that necessary for complete satur- ation. Conrad and Schoeck(4) tried to eliminate the

effect of impurities by measuring the temperature

dependence in the unlocked state by deforming an impure iron at’ a low t,emperature and then cycling the temperature in a region where diffusion was nil. They showed that the temperature dependence of this un-

locked stat’e was greater than for the locked state, but

still there remained a large temperature dependence ; so they also suggested that a frictional stress or P-N-F was

the cause. Schoeck and Seegerc5) had calculated that

no temperature dependence should be produced by random interstitial impurities and therefore favored

the P-N-F. Basinski and Christian@) did strain rate

cycling experiments and also suggested the P-N-F.

However, Smith and Rutherford”) using very high purity iron and Lawley et aZ.@) using high purity

molybdenum showed that the temperature depend-

ence down to liquid nitrogen temperature could be decreased by purification. However, L-V-M found

that the temperature dependence between liquid nitro-

gen and liquid helium temperatures was essentially

independent of purity.

The drag of jogs was suggested by Schoeck’“), but

the lack of the temperature dependence with respect to prior strain would seem to contradict his argument.

The cross-slip mechanism has been suggested be-

cause iron and iron silicon alloys are known to cross- slip extensively and because edge dislocations move

more readily than screws as shown by Low and Guard,uO) and Stein and Low.oi)

In bhe present investigation, a more direct method

was used to test the idea of a temperature dependent

P-N-F by measuring the stress at which the first

movement of dislocations (microyielding) could be detected. The effect of impurities was also tested by

using high purity iron in a condition where the dis-

locations were unlocked. Although there are many reasons to believe that a direct measure of the P-N-F

in iron may not be possible because there always exists lengths of dislocation (kinks) which lie across the

energy valleys of the crystal, one may at least expect that some temperature dependence of the movement of kinks would exist if the lattice friction is so sen- sitive to temperature.

In order to appreciate the present experimental approach, it is useful to illustrate the type of yield points that can be observed. Previous work by Roberts and Browno2) describes in detailthephenome- non of microyielding. The yield points illustrated in Fig. 1 are for iron, but the general aspects have been observed in single crystals and polycrystalline metals such as Zn, Al, Ag, Cu, a-brass and steel. The

FIG. 1. Type of yield points in iron.

annealed or aged state shows a high initial elastic limit

which also coincides both with the proportional limit

and the stress which produces a permanent strain

upon unloading. Iron and steel and sometimes even

zinc single crystals show an upper and lower yield point followed by a region of flow where the stress

after an appreciable plastic strain is called the flow-

stress. Once the specimen has received a permanent strain, the dislocations are unlocked from the solutes

that have segregated during annealing or aging so that

upon reloading a new elastic limit, (TV, results. oE is the stress at which a loop is observed upon loading

and unloading as shown by curve d in Fig. 1. oE rep-

resents the first detectable movement of dislocations.

oE is truly the elastic limit because t’he loops repre-

sent an energy loss. In a series of loading and unload-

ing tests at increasing stress amplitude, a stress a, is

observed at which the loop is open (curve h, Fig. 1) (a permanent strain occurs). This stage of yielding is

called a, because it represents the limit of anelasticity. a, is generally about the same as the stress at which a

deviation from linearity can be measured and is the

same as what is usually called the proportional limit.

Actually, stress and strain cease being proportional when loops are observed, but one is unable to measure

the deviation from linearity usually associated with the so-called proportional limit. Finally beyond o, there is a region of rapidly decreasing work hardening

until the region of macroscopic flow is reached where the corresponding stress is called the flow stress. The region between a, and the macroscopic yield point is usually taken to be the region of microyielding for the case of annealed or aged material. However the very initial movement of unlocked dislocation begins at oE. Although all yield points depend upon the sensitivity with which strain is measured, for a given sensitivity,

BROWN AND EKVALL: YIELD POI?;TB IN IRON 1103

bE’ and IS&~ represent different stages in the yield pro-

cess and in general exhibit a different dependence on temperature, prior strain, and impurities.

II. EXPERIMENTAL

Two purit,ies of iron were used. The high purity iron was zone refined at Battelle. The chemical eom- positions in weight, per cent follows :

Material C N 0 H Others __ .._._ - K 0.011 0.001 O.O34 0.002 0.161 (mostly

Xi and CU) __-

Zone refined 0.0012 0.0002 0.0029 0.00005 0.011

The K material was furnaced cooled from 700% and the ZR material from 5BO’C. The final grain size was about 0.1 mm. The zone refined material was also tested in the as-swaged state. The tensile specimens had a 1 in. gage length and g in. dia. The machining was done with particular care to insure straightness. All specimens were electropolished prior to t,esting.

The method for determining microyielding was used in another investigation by Lukens and Brown.(l3) The specimens had special ball and socket grips to minimize bending. The oxtensometer consisted of two parallel concentric rings whose capacitance was meas- ured by a Fielden Proximity meter. The strain signal from the capacitance meter and the st,ress signal from the Instron load cell were fed into a Moseley X-Y recorder. Since the basic observations were based on deviations from linear behavior, it was particularly important to make certain that the basic set up is linear and reversible over the load range of the investi- gation. A heat, treat,ed alloy steel specimen witah the same shape as the test specimen was extended up to stresses of 50,000 lb/in2 at, various strain sensit!ivities as determined by the capacitance meter settings, and it behaved in a completely linear fashion for a,11 strain sensitivities and loads that were used in the present investigation. A large number of calibra,tion checks showed that deviations from linearity corresponding to dislocation st~rains as low as 4 x 1OW were detect,- able. A t,ypicaI test last,ed about 20 see during which time the t,emperat,ure change was about 0.02”C.

III. THE FIRST STAGE OF YIELDING (ig

A. Procedure

In order to observe (rE it was necessary to prest,rain the annea.led or a.ged state. cE wa.s measured at temperatures of 300”, 200*, and 90°K. The strain rates were varied from 0.05 to 0.10 per minute. The amount

01

Strain

Frc. 2. Typical data for determining CTS.

of prestrain varied from 10W4 to 5 x 1OW in initially annealed material. The swaged material had the above prestrains superposed on the swaging strain which is estimated t’o be about 40 per cent after the final pass. Typical data are shown in Fig. 2 where oE occurred at a load of 400 lb. At least seven determinations were made of aE at a particular temperature and for a given specimen. The same specimen could be used over t,he ent8ire t,emperature range. Two specimens of each type of material were used. From the data in Fig. 2, aE was determined by two methods: one method was simply a direct observation of when a loop could be detected and the second was to plot the stress amplitude of a loop versus its area with @E being the stress obtained by extrapolation to zero area. Both methods gave the same value of aE. It, was also found t#hat t,he shape of the hysteresis loop did not, change during the ma.ny cycles of loading and unloading. Since the hysteresis loops are only observed after a prior plastic deformation, there seems little doubt that they are connected with t’he movement) of dislocations.

There was also the possibility t,hat. magnetoelast,ic damping was making an appreciable cont,ribLltion t,o the hysteresis. To check this ~~o~ibilit~y, a specimen was wrapped in a solenoid with an applied field of 200 Oe. Many tests were made with and without the magnetic field. and it was found that bhe magnetic field did not perceptibly change the size of the hyster- esis loops. This result is consistent with the other invest,igations which show that the internal frict,ion associated with magnetoela,stie damping is at least an order of magnitude less than that, associated with these loops. In these tests pi ix on the order of 0.05

1104 ACTA XETALLURGICA, VOL. 10, 1962

and it is amplitude dependent as expected for dis-

location damping. More details on the internal friction

aspects of this type of hysteresis loops are in a paper

by Roberts and Brown.(14)

B. Results on oE

The results are quite clear in that oE is independent

of temperature, strain rate, and t&he amount. of pre-

strain. Only the impurity level affectSed oE as shown

in Table 1. TABLE 1. a~ (1000 lh/in2) .-. -- _-._ .._I_

Material 300°K 200°K WK -- -

K 11-14 11-14 11-14 _-.-

ZR 3-s 5-5 3-B ._ --

ZR and waged 4-5 3-F 4-6

The spread in a given value of oE represents the

accuracy with which oE can be measured. The differ-

ence in oE between the swaged and unswaged ZR

material is not considered to be significant at this time.

The lack of a temperature dependence of gE has also

been observed in zinc and al~lminum.

In common with all definitions of a yield point, oE

depends on the strain sensitivity at which it is meas-

ured. It would at first seem that gE has no particular

significance because it decreases as the sensitivity of

the extensometer increases and it is completely unob-

servable when the sensitivity is too low. However, CT~

is meaningful because, as one makes the sensitivit,y

greater and greater and greater, 5E asymptotically

approaches a non-zero limiting value which is char-

acteristic of a given metal. By using a fixed strain

sensitivit,y, relative values of 5, may be obtained for

different materials or for the same material under

different conditions. In so far as a direct measure-

ment of stress is concerned, (rE represents the smallest

stress at which the movement of a large number of

dislocations can be detected directly.

oE truly represents a frictional stress because it is

the stress level which must be exceeded before appre-

ciable dislocation movement is possible. Since the

area of the hysteresis loop represents a loss of energy

by friction. then as pointed out by Roberts and

Brown’12) the value of the frictional stress can be

determined from the slope of the curve of loop area vs.

loop width. Frictional stresses which are determined

in this fashion agree with the value of oE.

There is another totally different measurement of

the frictional stress in iron which also agrees with our

value of (TV. Carrin~ton et &. measured the curvature

of bowed dislocations under the electron microscope.

They obtained a frictional stress using the relation-

ship, CT = Gblr. They found, in terms of the resolved

shear stress, values of the frictional stress of about

5600 lb/in2 for their purest iron whose purity was

somewhere between our ZR and K material. Our

results varied from 1.5-7000 lb/in2 if we consider the

maximum shear st,ress in order to make both results

comparable. Considering the accuracy ofboth methods

the agreement is encouraging,

oE is t’he stress to move the most mobile part of the

dislocat’ion array. We ca’nnot say whether kinks or

edges are moved by Dhe stress, ox. It is suggested

that, edges move easily because the observation of dis-

locations in iron by Low and Guard(lo) shows that

edges move more readily than t,he screw dislocat,ions.

Most> likely kinks also move at the stress 5E but their

contribution to t,he strain may be quite small. Ran-

dom impurities affect oE in a temperat,ure independ-

ent way. Schoeck and Seeger c5) have presented a

theory for t,he strengthening by interstitial atoms and

this strengtlleniIlg is temperature independent,.

Their equat,ion is

a5 - = 65 kg/mm2 per at,. % of solute e ac

where o is the resolved shear stress.

For our ZR material this represents a strengthening

of 2200 lb/in2 which is about one-half the observed

value of Go;. Thus, it appears that even if we had zero

impurities, 5E would still be about 2000 lb/in2. We

attribute t,his residual value of 2000 lb/in2 to the innate

resistance of the b.c.c. lattice to the movement of edge

dislocations. Workwithothermetalsof impurities com-

parable to those in iron show that 5E varies greatly

with crysbal structure. For example in 99.999% Zn

and 99.99 Al, oE is about 1 and 300 lb/in2 respectively.

Both of these values are much different than the

2000 lb/in2 value for iron. There seems to be little

doubt that. the type of crystal lattice plays a large

part in determining the lowest stress at which dis-

1ocat)ion movement can be detected by the direct

method employed here. In other words the innate

resistance of the iron lattice is appreciable in iron but

it does not exhibit the large temperature dependence

associa.ted with t#he macroscopic yield point. Thus,

we will now investigate a, which is the next stage in

yielding in order to determine t#he source of the tem-

perat’ure dependence.

IV. THE SECOND STAGE OF YIELDING 0~

A. P~oct?durP

5’A was measured in the locked and unlocked states.

Locking was produced by aging t,he specimen at 125°C

BROWN AND EKVALL: YIELD POINTS IN IRON 1105

Frc. 3.:Temperat,ure cycling experiment for determining o_,+

for 20 min. The locked state exhibited the usual

upper and lower yield point. After Go was measured

at a particular temperature, the same specimen was

aged again, and t,hen o, was determined at another

~mperatu~. Each de~rmination of aA produced

ver*y little workhardening compared to the change in

strength associated with the change in temperature.

At all times the load on the specimen was never relaxed

completely in order to maintain alignment so that

accurate relative changes in a, could be obtained as a

function of the temperature.

o,, for the unlocked state was obtained by prestrain-

ing at a temperature below -30°C and then cycling

the temperature in order to determine Us. Figure 3

shows the procedure for determining a, where o;a in

the unlocked state was determined after a measure-

ment of crA in the locked state. Sometimes bs was

determined by measuring deviations from the linear

portion of the loading curve and at other times from

the stress which would produce an open loop. Both

methods gave about the same result. Figure 4

Strain

FIQ. 4. Typical data for determining GA.

shows typical data for determining u_~ at a particular

temperat,ure.

The variat.ion of Go with temperature is shown in

Fig. 5. The locked state gave the greatest! ternperatll~

dependence. For the unlocked state the temperature

dependence depended upon purity. It should be

pointed out that prestrains of about 10m4 to 5 x low2

had no effect, on the temperature dependence in agree-

ment with Conrad and Schoeck.(*) Swaging had a

small effect on the temperature dependence so that

although moderat,e deformatior~s do not affect the

t,emperat,ure dependence an extremely large amount

does have an effect.

C. Discussion on a,

The results on the large temperature dependence of

the locked state is consistent with the findings of

Conrad and Schoeek(4). The explanation is simply

_.

% (C+N) 80 -

o-Locked-O.012

n-Unlocked-O.012 .-

.-Unlocked-O.0014

c-Swoged-0.0014

0 100 200 300 400 5(

T. K

u 10

FIG. 5. Te~~perature dependence of o;a for various materials and state of locking.

that the dislocations are strongly pinned by the inter-

stitials. Most likely at the 0.012 per cent impurity

level the interstitials have pinned the dislocations by

precipitating in the form of carbides and nitrides.

Thus, we can say that the usually observed form of

impurity pinning causes the greatest temperat,~lre

dependence.

For the unlocked state the data indicate that with a sufficient increase in purity, the temperature depend-

ence of o, could be reduced to zero. It appears that

a further increase in purity by an order of magnitude

would eliminate most, of the 15,000 lb/in2 increase in

Go between 300” and 90°K. At 300°K ‘51 was 15,000 lb/in2. This increase of

10,000 lb/in2 over the value of crE is interpreted as the

great,er stress to move screw dislocations. Thus screws

1106 ACTA METALLURGICA, VOL. 10. 1962

experience a greater lattice resistance than edges, and they also interact more strongly with random im- purities than do the edges so that the temperature dependence is enhanced.

V. MACROSCOPIC YIELDING

The large temperature dependence that is usually observed is associated with measurements of the flow stress. Since it appears that zero temperature depend- ence would occur with an ultra pure material when yielding is observed from the microstrain viewpoint, the transition from microyielding to macroyielding should be explored. Figure 6 shows the stress strain curves for the K material in the unlocked state for the region between a, and the usually measured flow stress. For the 90°K curve a, ww about 50,000 lb/inz. The important point to be observed is the extended region of high work hardening before the flow stress is reached. At the flow stress the rate of work hardening is about the same as at room temperature. At higher tempera- tures the stress-strain curve bends more rapidly be- tween ad and the flow stress; t.his fact indicates that the work hardening in the microstrain region decreases with increasing temperature. A large temperature dependence of the flow stress will be observed whereas the microyield point a, shows a much smaller tempera- ture dependence.

Once impurit,ies are eliminated, it appears that the temperature dependence of iron is not associated with the temperature dependence of the innate lattice resistance, P-N-F, but it depends on the increased rate of work hardening in the microstrain region.

60 -

-

3.6x@ 0

6

FIa. 6. Stress-strain curves at various temperatures for material.

K

._ ,”

IO s

2

FIG. 7. Idealized stress-strain curves for an ultra-pure iron at two temperatures.

Kehos) has observed by electron microscopy that the dislocation array formed at low ~mperatures is rather straight and uniform and it becomes more tangled in the form of cells at higher temperatures. Consequently it appears that dislocations do not change their slip plane as readily at low temperatures, This means that cross slip does not occur as readily so that greater work hardening results in the microstrain region. By analogy with f.c.c. metals, the region between 5A and the flow stress is comparable to stage II hardening, but the hardening is so intense that this region cannot be separated from the elastic region in a macroscopic stress-stain test.

VI. SUMMARY

It is convenient to summarize the results of this investigation by drawing an idealized stress-st.rain curve for an ultra-pure b.c.c. material at. a high and low temperature (Fig. 7). The region from O-stress to 5E is purely elastic. At 5E the edge dislocations move. oE depends on impurity level and the P-N-F but not temperature. From 5E to 5, the edge dislocations move anelastically. At 5, the screw dislocations move. oh will only vary with temperature if impurities are present because the screws interact strongly with impurities in accordance urith Cottrell and Bilby.(2) Between o, and 5= the screw dislocations cross slip and the material work hardens. At high temperatures

BROWN AND EKVALL: YIELD POINTS IN IRON 1107

cross-slip occurs readily so that the dislocations can

interact and form tangles which reduce the rate of

work hardening via a reduced internal stress field. At

the low temperature cross-slip is more difficult so that

the dislocations are more uniformly distributed (simi-

lar to a pile up) and greater work hardening is observed

in the micro&rain region. Finally, the stress becomes

so high that if the specimen does not fracture, the

dislocations can cross slip and either move out of the

crystal or interact with other dislocations so that

the internal stress field is not increased further.

It is concluded that in the absence of impurities (1)

the stress to first move all dislocations in iron is inde-

pendent of temperature (2) that the temperature

dependence of the macroscopic yield point is associated

with a high rate of work hardening in the microstrain

region. Probably the dependence on temperature of

the rate of work hardening in the microstrain region

depends upon the thermal activation of cross-slip.

ACKNOWLEDGMENTS

Dr. J. M. Roberts, K. F. Lukens, R. C. Ku and J. L.

Rutherford were most helpful during the course of

this research. Dr. P. B. Hirsch provided many stimu-

lating discussions. The zone refined iron which was

produced by the Battelle Memorial Institute was made

available by the American Iron and Steel Institute,

The iron was processed to rod by the courtesy of John

Kiszka at the Frankford Arsenal.

The support and encouragement from the Office of

Naval Research is gratefully acknowledged.

REFERENCES

1. H. CONRAD, J. IronSt. Inst. 198, 364 (1961). 2. A. H. COTTRELL and B. A. BILBY. Proc. Phus. Sot. A 62. y

49 (1949). 3. J. HESLOP and N. J. PETCH, Phil. Mug. 1, 866 (1956). 4. H. CONRAD and G. SCHOE~K, Acta Met. 7. 791 (1960). 5. G. SCHOECK and A. SEEGER, Acta. hfet. 7; 495 (1959). 6. Z. S. BASINSKI and J. W. CHRISTIAN. Amt. J. Phvs. 13.

u --,

299 (1960). 7. R. L. SMITH and J. S. RUTHERFORD, Trans. Amer. Inst.

Min. (Metall). mgrs. 209, 857 (1957). 8. A. LAWLEY. J. VAN DEN SYPE. and R. MADDIN. J. Inst.

Met. in press. 9. G. SCHOECK, Acta Met. 9, 382 (1961).

10. J. R. Low and R. W. GUARD, Actn Met. 7, 171 (1959). Il. D. F. STEIN and J. R. Low, J. Appl. Phys. 31, 362 (1960). 12. J. M. ROBERTS and N. BROWN, Trans. Amer. Inst. Min.

(Metall.) Engrs. 218, 454 (1960). 13. K. F. LUKENS and N. BROWN, Acta Met. 9, 106 (1961). 14. J. M. ROBERTS and N. BROWN, Acta Met. 10,430 (1962). 15. A. S. KEH, United States Steel Research Report No. 908

(1960).