The effect of stacking fault energy on the plastic deformation of polycrystalline Ni-Co alloys

THE

EFFECT

OF STACKING FAULT ENERGY ON THE PLASTIC OF POLYCRYSTALLINE Ni-Co ALLOYS* C. K. L. DAVIES,?

V.

SAGARt:

and

IX. N.

DEFORMATION

STEVENS?

The deformation aharaeteristiosof a series of polycrystalline Ni-Co alloys have been studied by measuring activation, volume flow stress, Cottrell-Stokes ratio (CSR) and work hardening rate in the temperature range 4.2 + 480 K. The alloys contain O-70 per cent cobalt and have a range of stacking fault energy (SFE) from 240 - 10 mJjm*. The relative oontributions of short range (7, + TV)and long range stresses (7~) to the total flow stress (T) have been estimated. In the initial stages of a stress-strain curve (E < 0.06) short range stresses determine the flow stress; whereas at iarge strains the long range stresses are the dominant part. The CSR is obeyed approximately only at large strains. The magnitude of 7~ is determined by the ease with which cross-slip takes place, being easier at higher temperatures and for higher SFE alloys. The degree of cross-slip determines the rate of work hardening. INFLUENCE

DE

L’ENERGIE DE FAUTE D’EMPILEMENT SUR LA PLASTIQUE DES ALLIAGES Ni-Co POLYCRISTALLINS

DEFORMATION

Lea cara&&istiques de la deformation d’une aerie d’alliages Ni-Co poiycristallins ont et& &udi&es par des mesures du volume d’aotivation, dela contra&&e plastique, dn rapport de Cottrell et Stokes et du taux de consolidation antre 4,2 K et 480 K. Les alliages contie~ent de 0 &70 % de cobalt et leur energiede faute d’empilement psut varier de 240 a 10 mJ/mr. Les contributions relatives des contraintes a courte distance (7, + TV) et des contraintes a longue distance (7~) a la contrainta plastique tot& (7) ont 6te Bvaluees. Dens les premiers stades d’une eourbe aontrainte-deformation (E < 0,06), les contraintes a oourte distance ont une part pmponderante dans la contrainte plastique, alors que pour lea deformations importantes, ce sont les contra&es Q longue distance qui predominent. Les r4sultats ne suivent approximetivement le rapport de Cottrell et Stokes que pour des deformations importantes. L’amplitude de 7~ est determinee par la facihte avec laquetle it se produit un gliasement devil, celm-ci Btaut plus facile aux temperatures Blev&~s et pour les alliages dont l’energie de faute d’empilement est Blevee. L’importance des gliasements d&i& determine le taux de consolidation. DER

EINFLU6

DER STAPELFE~L~RENERUIE VON POLYKRISTALLINEN

AUF DIE PLASTISCHE Ni-Co-LEGIERUNGEN

VERFORMUNG

Die Verformungseigenschaften einer Reihe polykristelliner Ni-Co-Legienmgen wurden anhand der Messung des Aktivierungs-volumens, der FlieOspannung, des Cottrell-Stokes-Quotienten (CSR) und der Verfestigung im Temperaturbereioh zwisohen 4.2 K und 480 K untersucht. Die Legierungen enthalten O-70 % Kobalt und ihre Stapelfehlerenergie (SFE) liegt zwischen 240 und 10 mJ/me. Die relativen Beitriige der kunreichenden (rr + ri) und weitreichenden (7~) Sparmungenzur Gesamtfliel3spannung (7) wurden abgesehatzt. Am Begmu der Verfestigung (E < 0,06) bestimmen kurzreiohende Spanmmgen die Flie0spammng; bei grogen Abgleitungen dagegen dominieren die weitreiahenden Spamumgen. Der CSR wird nur bei gro&m Abgleitungen nahezu erftillt. rs wird dadumh bestimmt, wie leicht Quergleitung s~ttfinden kann; Que~leit~g erfolgt leichter bei hijheren Temperaturen und in Legierungen mit gr&erer SFE. Das AusmaP der Quergleitung bestimmt den Verfesbigungskoeffizienten.

I. INTRODUCTION AND EXPERIMENTAL PROCEDURE

Considerable work has been csrried out on the plastic deformation of single crystal pure metals and alloys(i) in an attempt to determine the effect of stacking fault energy (SFE) on the deformation processes. The main effect of SFE has been shown to be on the stress necessary to initiate thermally activated cross-slip of screw dislocations at a given temperature and strain rate.(i) This stress being larger for materials of low SFE. Thermally activated cross-slip occurs only at large strains on the stress-strain curve of single crystals and results in a continuously decreasing rate of work hardening. It is not clear at * Received January 2, 1973: revised April 9, 1973. t Department of Materials, Queen Mary College, London, El 4NS. $ Now at: University Engineering Department, Cambridge, Enghmd. ACTA

METALLURGICA,

VOL.

21, OCTOBER

1973

what stage this process occurs on the stress-strain curves of polycrystalline metals and alloys.(*-” It is now generally agreed that the thermally activated inte~ection of forest and glide dilutions is the rate controlling mechanism in msny face centred cubic metals and alloys at low temperatures.(r*2+9) The thermal component of the flow stress, TV,therefore, depends on both the separation of forest dislocations (L) and the width of the extended dislocations, i.e. rs = cl&r4

(I) where cc1is ELconstant. The width of the extended dislocations will depend upon the SFE, being larger for lower SFE alloys. The density of forest dislocations will depend on the extent of cross-slip which will become more diffioult for lower SFE alloys. The magnitude of r$ will therefore depend on stacking fault energy.

1343

ACTA

1344

METALLURGICA,

The nature and origin of the athermal component of the flow stress (7*) has long been a subject of controversy. Seeger’l) has suggested that rG is long range in nature and results from dislocation pile-ups (TV). Basinskifs) and Saada(2) have suggested that TV is short range in nature and arises mainly from elastic interactions between forest and glide dislocations (ti). If both of these processes contribute to the athermal component of the flow stress (T& we may write:(‘) 7 = 7, + 7i + 7L.

(2)

Since 7g and ri both depend on L, becomes

equation

7=- ; + 7L

(3)

TABLE 1. Materiels

TOco+

45 co+ 32 Cot 21 cot Xi*

21, 1973

Activation volumes were measured as a function of plastic deformation at various temperatures as was the flow stress. The experimental activation volume is defined as V,

&!!$

which is related to the actual activation volume V = xLb

(5)

v = #Ve

(6)

by the relation”0)

(2)

where a is a constant. As the ease of cross-slip will determine both the number of dislocations in a pile-up and the density of forest dislocations the magnitude of ri and TV will therefore depend on the SFE. The present work investigates the effect of SF% on the deformation processes in polycrystalline N-Co alloys in the temperature range where long range diffusion cannot play a significant role in the deformation processes (i.e. below 0.25 T,). The stress (T)strain (E) curves and the rate of work hardening (&/a&) were determined to investigate the role of cross-slip during plastic deformation. Cottrell-Stokes ratios were measured as a function of temperature and strain to determine the relationship between the thermal (TV)and athermal (T@) parts of the flow stress.

Code name of the material

VOL.

where x is the activation distance, T the test temperature and k is the Boltzmann constant. Measu~men~ of the activation volumes and hence L together with values of the total flow stress (T) enabled the separate contributions to the total Aow stress due to long range (TV) and short range stress (T, + TV)to be determined by using equations (2) and (3). 2. EXPERIMENTAL

METHOD

The composition, purity and the SFE@) of the materials used in this work are given in Table 1. The alloys were vacuum cast, then forged and hot rolled to cylindrical rods. Cylindrical specimens of 0.3 cm diameter with threaded ends were machined from the rods. The specimens were then heat treated tZoproduce a regular grain size of approximately 9 X low5 m (Table 2). and their composition

Composition Symbol

c,

\I’ h 7 r

Iii (mass %)

CO (mass %)

29.85 53.62 67.02 i7.82 99.80

69.85 45.81 32.30 21.58

* Metals Research-Melbourn, t Cobalt Information-Chichester

(pTs”m) 60 70 770 70 50

Roy&on, H&s. House, 278/282

Si (ppm) 10 50 50 50 10

Stacking fault) energy

Mg (ppm) 2: z:

90 60 50

10

11:

High Street, High Holborn,

(pE)

@J/m9

TJD ND ND XD ND

10 90 150 190 240

London WCl.

TABLE 2. Heat. treatments

Heat treatments

flatwid

1h 1h 1h 1h 1h 1h 1h 1h i h

at at at at at at at. et at

1363 K in Argon atmosphere 973 K + 0.10 pre-strain 1273 K in vacuum 973 K -+ 0.10 pre-strain 1273 K in vaouum 973 K -+ 0.10 pm-strain 1223 K in vacuum 973 K + 0.10 pre-strain 1173 K in vacuum

Average number of grains per mm 11.0 11.5 10.4 10.0 12.0 -

DAVIES

et al.:

EFFECT

OF

STACKING

FAULT

ENERGY

ON

PLASTIC

DEFORMATION

1345

(b) Measurement of stress and strain All the tests were carried out on an Instron Universal testing machine at strain rates of 2.5 x 10” s-l and 5 x 1O-5 s-l. The specimen extension and hence the strain was measured on the specimen gauge length using a linear variable differential transducer (LVDT) . The apparatus has been described in detail previou~ly.(~~~~)The force and hence the stress was measured using the standard Instron load cell and both the extension and the force were continuously recorded on a three pen Rekadenki recorder. The test specimen temperature was obtained by either immersion in liquid helium, liquid nitrogen, a mixture of ethyl alcohol and solid carbon dioxide, or by immersion in temperature controlled ,baths of iso-propane, ethyl alcohol or silicone oil. The temperature was maintained to fl K.@) (G) Differential tests The Cottrell-Stokes ratios (CSR) were measured by determining the ratio of the flow stresses 7(Tl)/7(T,) at two temperatures for a constant structure. The change of temperature was effected in about 15 min and it was therefore necessary to unload the specimen before making a temperature change to minimize the effect of thermal recovery. The CSR was determined as a function of strain at temperatures of 77 + 480 K. The tests were carried out at a strain rate of 5 x 10m5

01

0

08

‘!TRAIN TENSILE

The experimental activation volumes (7, = ki3 In ijar) were determined by instantaneously changing the cross-head speed by a factor of t,en. The nominal strain rate 5 x 10m5s-l was changed to 5 x 104 s-l and back in an interval of 0.01 strain. Activation volumes were measured as a function of strain at temperatures of Si -+ 480 K. The activation volume and the flow stress were measured as functions of temperature for a constant, structure for two alloys (Ni-21Co, Ni-45Co) by differential strain rate and differential t,emperature tests.19) The experiments were carried out, over a temperature range of 4.2 -+ 298 K. The measurements were made for two deformed stat.es (a) and (b) corresponding to strains at 298 K of approximately 0.06 and 0.20. s-1.

(a)

.04

.00 TENSILE

-I2

.I6

.20

-24

-20

STRAIN

FIG. 1. Stress-strain curves at 298 Ii and d = 2.5 x 1W3 * 1.

I

28

FIQ. 2. Stress-strain curves for Ni-21Co at i = 5 x 1O-5 s-1.

3. EXPERIMENTAL

0

24

RESULTS

Stress-strain curves

Stress-strain curves for a temperature of 298 K and a strain rate of 2.5 x 1O-3 s-l are shown in Fig. 1. The flow stress for a given strain can be seen t,o increase with increasing cobalt cont’ent in the alloy. The rate of work hardening decreases with increasing strain more rapidly for alloys containing progressively less cobalt. Stress-strain curves determined over the temperature range 4.2 -+ 480 K show similar effects. The effect of temperature of deformation on the stressstrain curve of Ni-21Co is shown in Fig. 2 for tests

ACTA

1340

0

METALLURGICA,

xl0

VOL.

200 TEMPER

AT%

Fra. 3. Temperature dependence of the yield stress (o,)-corre&ed

carried out 8t 8 strain rate of 5 x IO4 s--l. The flow stress for 8 given strain c8n be seen to increese with decreasing temperature. The rate of work hardening decretlses with increasing &rein more rapidly for tests carried out at progressively higher temperatures. Stress-str8in curves for the alloys Ni, Ni-32Co, Ni-45Co and Ni-7OCo show similar effects. Tests were c8rried out at 8 strain rate of 2.5 x 10” s-l or 5 x 1O-6 s-1, While the effect of strain rate is small, the slower tests, in gener81, result in &lower flow stress at 8 given strain for all temperatures and alloys. The temperature dependence of the yield stress (corrected for the variation of the shear modulus with temperature) is shown in Fig. 3. The temperature dependence of the yield stress increases with decreasing cobalt content. Analysis of the stress-strain curves showed that all the curves can be represented by a polynomial of the second degree of the form E = A, + A,a + A,u2

21,

T\K

1973

400

500

for the variation of shear modulus.

SFE}. The rate of chenge of activation volume with strain at 8 given temperature is greater for alloys of lower cobalt content (i.e. higher SFE). (c) Cottretl-Stokes ratios The Cottrell-Stokes ratio is plotted as a function of strain for alloy Ni-21Co in Fig. 5. It, can be seen that st 811 temperatures the CSR only becomes constant after considerable strain. The strain at which the ratio becomes 8pproximately constant increases with decreasing temperature and decreases for higher SFE alloys. (d) Constant structure Cests Activation volumes for & constant structure are plotted 8s 8 function of ~mper8ture in Fig. 6 for the

(7)

where G is the applied tensile stress. A linear plastic hardening range w8s not observed on any of the stressstrain curves even at strains around 0.01. (b) Activation volumes The veriation of activation volume with strain for alloy Ni-21Co is shown in Fig. 4. The variation of activation volume suggests that at any temperature the density of forest dislocstions increases 8s deformation proceeds, the rate of increase being greater at, higher temperatures. This may be the result of increased activity on the secondary slip systems due to increased thermal activation. The variation of activation volume with strain 8s 8 function of tern.. perature shows similar effects for all the alloys. The activation volume for a given temperature and strain is greater for alloys of lower cobalt content, (i.e. higher

Fra. 4. Activation volume (5’) vs strain (E) for Ni-21Co.

DAVIES

et aZ.:

EFFECT

OF

STACKING

FAULT

b-

ENERGY

ON

PLASTIC

DEFORMATIOK

1347

d(298K) - 0.0

.

_ d(395K) d296K)

-70 0

95

40 TENSILE

.I5

I .25

*20

STRAIN

FIQ. 6. Cottrell-Stokes ratio vs strain (E) for Ni-2lCo.

deformed states (a) and (b). The activation volume decreases more rapidly with temperature for deformed state (a) (E 11 0.06) than for deformed state (b) (E N 0.20). Activation volumes for higher cobalt alloys are generally smaller than those for the lower cobalt alloys. The temperature dependence of the flow stress for deformed states (a) and (b) are shown in Fig. 7. The flow stress at a given temperature is always greater for the higher cobalt alloy. The curve for the deformed state (a) becomes near horizontal at 420 K for alloy Ni-21Co but continues to decrease for alloy Ni+GCo. The curves for both alloys have a similar form but the curve for the higher cobalt alloy is extended to higher temperatures before the flow stress becomes temperature independent. The alloys deformed to state (b) (E N 0.20) show a much smaller proportional change in flow stress over the temperature range studied than that observed for deformed state (a) (E !Z 0.06).

two

14

DEFORMED

STATE

ra OE 12 6

I

OO

I

100 TEMPERATURE

200

300 T\K

FIG. 6. Variation of activation volume (1.) with temperature at constant structure for Xi-LICI.

4. DISCUSSION

AND

CONCLUSIONS

We shall attempt to determine the respective contributions of the short range stresses (To + TJ and long range stress (rL) to the total flow stress (7) and then explain the effect of SFE on the plastic deformation of Ni-Co alloys using this information. (a) Existence

Of hZ$I

9Unge

8tW88e8

(TL)

If we substitute equation (5) into equation (3) the total flow stress (T) is given by (8) It has been shown(11) that x does not vary significantly with strain hardening at a given temperature and abz is therefore approximately constant. If there are no long range stresses (i.e. 7L N 0) then the flow stress (T) at a given temperature should be linearly related to the reciprocal of the activation volume (l/V). The curve should cross the 7 axis at TV, the yield stress. A plot of flow stress versus the reciprocal of the activation volume for two alloys is shown in Fig. 8. A straight line is not observed and the graph becomes increasingly curved with increasing flow stress. This suggests that long range stresses exist and that TL increases more rapidly than ( Ts $ Ti) with increasing strain. The graphs become more curved as the temperature of deformation decreases which suggests that the contribution of T= to the total flow stress (T) increases with decreasing temperature. The graphs also become more curved with increasing cobalt content (i.e. decreasing stacking fault energy) which suggests that the contribution of TV to the total flow stress (T) increases with decreasing stacking fault energy.

ACTA

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METALLURGICA,

VOL.

21.

1973

#

230.120-

I

0

200

100

300

400

600

500

T\K

FIQ. 7. Temperature dependence of the flow stress at constant structure for Ni-2lCo

320

-

I

NI-JSCo

240

-

I

298

In

I60

80

Ni-2ICo

K

J -

1

0.5

and Xi-46Co.

1

I.0

30

2.0

55

50

40

7’ \ Io=m’

Fm. 8. Shear stress vs the inverse of the activation volume (l/V).

The existence of long range stresses is also implied by the variation of the Cottrell-Stokes ratio at small strains when r”(T,) > T’(T2) -T’(T~) T”(T,) where 7” > 7’. Substituting equation becomes

Since both 7i and 7, depend on the density of forest dislocations we may write TiV = CI7lln(TA

(9)

TV’ = Cp,‘(T2).

(11)

and also (2) in (9) the inequality

T,“( Tel + pi” + TL” > T~‘(TJ + pi’ + 71,’ T,‘( T,) + TV’ + TV’ . T,“(T,) + 7i” + TL”

or”

= Q,“(Tz)

T,‘(T,) = %,‘(T& (10)

where C, > 1.

(12)

DAVIES

et al.:

EFFECT

OF

STACKIKG

FAULT

Combining inequality (10) and equations (11) and (12) it can be shown that

fz: TiW/Ti). Equation (13) suggests that the long range stresses (TV) are increasing at a faster rate than the short range stresses (T, + To). It can therefore be seen that both the Cottrell-Stokes ratio data and the activation volume data suggest the existence of long range stresses. (b) ContT~b~t~o~of the short range stresses (TV+ q) and the long range stresses (q,) to the total jlow stress (T) We shall now attempt to determine the relative magnitude of the stresses arising from interactions with forest dislocations (TV+ TJ and that due to long range stresses (TV). These can be calculated from equation (3) if the values of a and L are known for each alloy at a given temperature. The value of I/ can be calculated from equation (5) if the activation distance x is known as the activation volume has been determined experimentally. The activation distance (x) at a given temperature can be calculated from the constant structure tests if it is assumed that the 7[G(O)/G( T)] vs temperature curve becomes horizonta1 at 420 K for alloy Ni-21Co and at 500 K for aIIoy Ni45C0, Fig. 7. At these critical temperatures (Z’,) the activation distance (x) becomes greater than the equilibrium width of an extended dislocation and the temperature dependent part of the flow stress (T8) becomes zero. It is also assumed that the activation distance at 4.2 K is equal to b. The activation distance zzat any temperature f !P) is given by (11) x(T) = b &)

[T8;~~&j*‘3.

@*I

ENERGY

ON

PLASTIC

DEFORMATION

The dependence of z(T) on (7,)lj3 results from the dependence of L(T) on Ts which occurs due to dislocation bowing. x(T) can now be determined using values of 7, calculated from Fig. 7 and from measured activation volumes at constant. structure (Fig. 6). The values of L at a given temperature and &rain are then calculated from equation (5) (V = xLb) using the measured activation volumes (l?ig. 4). The values of l/L so determined are plotted against. shear stress in Fig. 9 for alloy Ni-21Co. Values of (l/L) are numerically equal to the square root of the forest dislocation density. Dislocation densities as a function of stress can therefore be calculated for alloys Ni-2lCo and Ni-@Xo, and the values at 95 MN/m2 and 298 K are 1.04 and 2.56 x 101*/m2 respectively. These values compare very favourably with the value of 0.42 x 101*/m2 for pure Ni determined by thin film electron microscopy by Lin and McLean(12) at the The dislocations same stress and temperature. densities increase with decreasing SFE. If it is assumed that at the yield stress (TJ the long range stresses are negligible then equation (3) becomes 1 -

0L*

Ty=a

(15)

4

The values of Q for a given temperature can then be determined from Fig. 9 and from equation (15). These values are given in Table 3. The values of (TV+ TV)and 7~ can now be determined from

(16)

(7, $_ Ti) = : 7~

=

7 -

(T,

+

Ti).

Figures 10 and 11 show the variation of long range stresses (Q) and short range stresses (T, + To as a function of strain for two alloys at two ~mperatur~. In all cases the rate of increase of long range stresses

4

i

1

0

L

80

lb0

SHEAR

1349

STR%

(MN/m2)

320

400

FIU. 9. Shear stress vs the reciprocal of the separation of forest dislocations (l/L) for Xi-ZlCo.

ACTA METALLURGICA,

1350 TABLE

3. Values of aI Values of a1 (N/m)

Temperature

21 co

45 co

77 K 196 K 298 K

2.76 2.64 2.7

2.7 2.64 2.28

(TV) with strain is greater than that for short range stresses (TV+ TV). However, &,/as decreases more rapidly with strain (E) than does a(T, + 7,)/a&. The rate of decrease is more rapid at lower temperatures and for the lower cobalt alloy (i.e. higher stacking fault energy alloys). It is clear that the CSR cannot be constant at strains up to 0.10 as the long range stress (7J is increasing much more rapidly in this region than the short range stress (7, + TJ. However, at later stages on the stress strain curve it is possible that the CSR is constant as &la& decreases. This is borne out by the CSR data in Fig. 5. It can also be seen from Figs. 10 and 11 that the CSR will not become constant until larger strains, at lower temperatures or for higher cobalt alloys (lower SFE). This is seen to be so for the CSR data. (c) Dislocution

structure contributing

to short and

long range stresses

The exact dislocation structure contributing to short range and long range stresses cannot be identified from the mechanical tests performed here, nevertheless some conclusions may be drawn. It has been shownol) that the thermally activated intersection of forest and glide dislocations is the rate controlling mechanism in Ni-Co alloys at low temExperimental and theoretical 7, vs peratures. temperature curves have been determined and are

VOL. 21, 1973

shown to be in excellent agreement.“‘) The thermal component of the flow stress, rg, will therefore depend on the width of extended dislocations and will increase with decreasing SFE (higher cobalt contents). This also results in the flow stress temperature curves (Fig. 7) only becoming horizontal at higher temperatures for lower stacking fault energy alloys. Values of 7, have been calculated from the flow stress temperature curves and can be compared with the measured values of (TV+ TJ in Figs. 10 and 11. The value of the athermal short range stress component (TV)is found to be between 2 and 3 times the value of the thermal stress component (7,). Calculations have been made to determine the three main dislocation interactions which contribute to athermal short range stresses (71)(13-15) The resuhing flow stress from these sources is given by 7i = a,Gb/L where as is a constant equal to 0.1, 0.4, or 1.0. Values of a2 have been calculated using values of l/L from Fig. 9 and values of 7i determined from Figs. 5, 10, 11. The values lie between 0.1 and 0.2. These low values of as suggest that repulsive elastic interactions bet,ween forest and glide dislocations are the main contribut,or to the short range stress (TV) as as N 0.1 for this process. (12) There is, however, another possible source of short range stresses. This is the formation of constrictions in widely dissociated dislocations as suggested by Cousland. (ls) The constriction energy in low stacking fault energy materials may be t,oo high to be supplied by thermal fluctuations even at, high temperatures. It may, therefore, always be necessary to partially constrict a dislocation with the applied stress. Although in principle this stress will be temperature dependent, the dependence at high

280

240

cI

*OS

.I6

.24 SHEAR

-32

-40

-48

STRAIN

FIG. 10. Long range (TV)and short range stresses (TV+ TV)as a function of strain for Ni-21Co.

DAVIES

et al.:

EFFECT

FAULT

ENERGY

ON

PLASTIC

DEFORMATION

1351

1

0 FIU.

OF STACKING

*OS

-16

-24 SHEAR

-32

.40

48

STRAIN

11. Long range (7,) and short range stresses (7, -+- 7,) as a fun&ion of strain for Ni-45Co.

temperatures may be so small that it appears temperature inde~ndent. Before trying to identify the source of long range stresses it is important to examine the role of erossslip in the deformation processes. As mentioned earlier, the variation of long range stresses with strain as a function of SFE and temperature seems to suggest that cross-slip controls the magnitude of long range stresses. This possibility is also suggested from the way the Cottrell-Stokes ratio varies at. different temperatures. The CSR only becomes constant when thermally activated cross-slip slows down the rate of increase of long range stresses. This will take place at progressively lower stresses as the temperature of deformation is increased. This is borne out by the present results. The increasing non-linearity of the stress-strain curves with strain also suggests that cross-slip is taking place to a greater extent as the applied stress inMore positive evidence for cross-slip, creases. however, comes from the variation of the rate of work hardening with temperature and SFE. It is expected $_ c- 170 MN\m’

that at a given T&, the dislocation structure contributing to long range stresses is the same at all temperatures, for all materials. However, as a specimen with this structure is deformed, cross-slip will occur more easily when the temperature or the stacking fault energy of the material is high. Accordingly, the rate ,of work hardening will be lower at high temperatures and in high stacking fault energy materials. To examine these effects the rate of work hardening at a given TV is shown as a function of temperature in Fig. 12. The value of TV was chosen to ensure that extensive cross-slip is taking place in each specimen. As predicted, this figure shows that the rate of work hardening decreases with increasing temperature and with increasing stacking fault energy. The role of cross-slip discussed, supports the pile-up theory of long range hardening. (‘) Hazzeldine and Hirscho’) and Kronmulleros have calculated the long range stresses exerted by various types of dislocat,ion pileups. They have shown that the maximum opposing stress is about 60-80 per cent of the total flow stress. The relative magnitude of long range stresses in Figs, 10 and 11 would then suggest such pile-ups contributing to long range stresses. (d) Stress--&rain curues

t

OO

t

m

I. 300

xx) TCWERATLIRE

T\K

Fra. If. Variation of work hardening rate as & fun&ion of temperature.

The temperature dependence of the yield stress is shown in Fig. 4. In general the yield stress is greater for alloys of lower SFE. The curves become approximately horizontal only at higher temperatures as the stacking fault energy of the alloy decreases. The value of the yield stress is determined largely by the value of the thermal component of the flow stress (I#). The value of T, increases with increasing activation distance x and hence increases with decreasing SFE. The rate of decrease of r, with t~emperature will be

1352

ACTA

METALLURGICA,

much more rapid for high stacking fault energy alloys resulting in a horizontal curve at much lower temperatures as observed (Fig. 3). Following yield, the long range (TJ stresses will increase more rapidly than the short range stresses (r8 + T&, (Figs. 10 and 11) resulting in a variation of the CSR with strain at low strains (Fig. 5). However, at strains of less than 0.06, (TV+ T{) will be the main contributor to the flow stress. This is seen to be so, as the flow stress of a specimen deformed to a strain of 0.06 at 298 K and then re-tested at 77 K is the same as the 0ow stress of a specimen deformed to a strain of 0.06 at 77 K (Figs. 2 and 7). The activation volume (V) of the two specimens is also equal (Figs. 4 and 6). The activation distance (5) must be equal for both specimens as they are deformed at the same temperature and stress and hence the dislocation structure must be similar for both specimens. This suggests that extensive cross-slip does not occur at strains of 0.06. When specimens are deformed to larger strains arL/& decreases continually with increasing strain (Figs. 10 and 11). At some point the CSR will become approximately constant as a(7, + 7,)/a& does not decrease so rapidly with increasing strain. The rate of decrease of ar,/as is more rapid at higher temperatures and for higher stacking fault energy alloys (Figs. 10 and 11). This results in the CSR becoming approximately constant at lower strains for higher temperatures of deformation and for higher stacking fault energy alloys. At large strains the long range stress (TV) is the major contributor to the flow stress. This is seen to be so, as the flow stress of a specimen deformed to a strain of 0.20 at 298 K and then ret,ested at 77 K is much lower than the flow stress of a specimen deformed to a strain of 0.20 at 77 K (Figs. 2 and 7). The activation volumes of the t,wo specimens are similar (Figs. 4 and 6). This suggests that the values of 7J for the two specimens are similar and that~the difference in flow stress arises due t,o a difference in the values of rl;. The flow stress on any &ress-strain curve (Figs. 2 and 3) at a given strain can be seen to decrease with increasing temperature of deformation and with decreasing SFE. The rate of work hardening can also be seen to decrease with increasing temperature of

VOL.

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1973

deformation and with decreasing SFE (Figs. 2, 3 and 12). The flow stress on the early part of the curve is determined largely by 7, which will decrease with increasing temperature or with increasing SFE as the activation distance (x) decreases. The flow stress on the later parts of the curves is determined largely by (rL). The value of rL depends on the extent to which cross-slip takes place as does arJ& the major contribution to the work hardening rate. Cross-slip will take place more easily at higher temperatures and in higher stacking fault energy materials, resulting in both lower flow stresses and lower rates of work hardening (Figs. 2, 3 and 12). ACKNOWLEDGEMENTS

The authors would like to thank the Science Research Council for financial support for this work and the Rutherford High Energy Laboratory for the use of their liquid helium mechanical testing facility. Thanks are also due to the Cobalt Information Service and International Nickel Ltd for providing the nickelcobalt alloys; to the National Physical Laboratory, Delta Manganese Bronze Limited and Enfield Rolling Mills Limited for forging and rolling some of the material, and finally to Professor E. H. Andrews of the Materials Department, Queen Mary College for provision of research facilities. REFERENCES A. SEEKER and S. MADER, Electron 1. H. KFLONMULLER, Microscopy and Strength of Cly8t&.8, p. 665, edited by G. THOMAS and J. WASHBURN. Interscience (1963). 2. S. K. MITRA and J. E. DORN, Trans. Mel. Sot. AIME. 337, 1016 (1963). 3. P. FELTHAM and G. J. L. COPLEP,Acta Met. 8,642 (1960). 4. F. W. J. L. PAR~ETER, Ph.D. Thesis, Oxon (1962). 5. 2. S. BASINSKI, Phil. Mag. 4, 771 (1959). 6. P. R. THORNTONand P. B. HIRSCH, Phil. &fag. 8, 738 (1958). 7. H. KRONMULLER and A. SEEOER, J. Phys. Chem. Solids 18. 93 (19611. G. &ADA, A& Met. &,I66 (1961). :: V. SA~AR, Ph.D. Thesis, Queen Mary College, London (1971). 10. G. B. GIBBS, Mat. Sci. Eng. 4, 313 (1969). 11. C. K. L. DAVIES, V. SAQAR and R. S. STEVENS, Phys. Status Solidi, to be published. 12. T. L. LIN and D. MCLEAN, Met. Sci. J. 2, 108 (1968). 13. G. SAADA, Acta Met. 8. 200 (1960). 14. J. P. HIRTH, J. a$. Phye. $2, 760 (1961). 15. J. FRIEDEL. Dislocations 222 f19641. golidi 37, 159 (1970). 16. S. McK. CO~~LAND, Phys. S&k. 17. P. M. HAZZELDINEand P. B. HIRSCH, Phil. Mag. 15. 121 (1967). 18. H. KRONMULLER,Moderne Probleme der Metallphysik. p. 152, edited by A. SEECER, Springer (1965).