Deformation enhanced grain growth in a superplastic Sn-1% Bi alloy

DEFORMATION

ENHANCED GRAIN GROWTH Sn-1 % Bi ALLOY* M. A. CLARKt

and

T.

H.

IN A SUPERPLASTIC

ALDEN?

A Sn-1% Bi alloy has been studied to determine the effect of euperplaatio deformation on the grain growth kinetics. Using both con&ant oroashead speed and oreep teats, the gram size wee measured as a funation of deformation time and etrain over a wide range of strain rates. It was found that duriug deformation. oonsiderable increases in the grain growth ratea ooourred when oompared to static ratee. The effeot was most pronounced at intermediate strain rates iu the high &rain rate-sensitivity region. The euggeeted me&a&m for enhanoed growth involves the production of excess vacancies in the grain boundary region, leading to increased boundary mobility. AUGMENTATION

DE LA VITESSE DE CROISSANCE DES DANS UN ALLIAGE SUPERPLASTIQUE

GRAINS PAR Sn-l%Bi

DEFORMATION

On a Btudie un alhage Sn-l%Bi pour d&arminer l’influenoe de la deformation superplaatique cur la cinetique de oroiesenoe dea grains. A l’aide d’essais de fluage et d’emais de deformation B vites6e oom~tante, la taille des grains a 6% mesur& en fonction de la deformation et de ea dur&, pour un large domaine de vitemea de deformation. Lea aut.eum obmrvent au ooum de la d6formation. dos aooroiammente oonsid&ablee des viteaaea de aroiesanca den grains par rapport aux viteesee statiques. L’effet le plus important a Bt6 obeerv6 pour le4r vitemes de d&formation interm6diairea dana le region de forte eensibilite a la viteam de d6formation. Le m&ax&me propoe6 pour oe phenomene est bau6 aur la produotion de laaunes en exo&s au voiainage des joints de grains, oe qui entraine une mobiliti acorue des joints. DURCH

VERFORMUNG BEGUNSTIGTES KORNWACHSTUM PLASTISCHEN Sn- 1 y. Bi-LEGIERUNG

IN EINER

SUPER-

An einer Sn-1% Bi-Legierung wurde der EintluB einer euperplastimhen Verformung auf die KornWaohatumskinetik untersuoht. In Krieohversuohen und Verformungsverauohen bei konstanter Geschwindigkeit der Kri&.alleiuspannung wurde die Krongr6De als Funktion der Verformungszeit und Dehmmg fur einen grogen Bereioh der Dehngesohwindigkeit gemeasen. Dabei wurde naohgewieeen. da3 daa Kornwaohstum w&hrend der Verformung im Vergleiuh rum im statimhen Waohstum erheblioh gr6Oer ist. Der Effekt ist bei mittleren Abgleitgemhwindigkeiten Be&oh starker GesahwindigkeitaabhengiBkeit am stark&en ausgepr&t. Der fur dieaes vemt&rkte Wachstum vorgesahlagene Mechanismua geht von der Erzeugung von VbemchuOleerstellen im Korngrenzenbereiah aus, die zu einer erh6hten Bewegliohkeit der Korngrenze fiihrt.

INTRODUCTION

Because of the high homologous temperatures required for superplasticity, growth of the matrix grains or second phase particles frequently occurs during the deformation. A number of investigators(1-17) have also noted that the kinetics of coarsening are enhanced by deformation; i.e. the grain size in a deformed specimen is larger than in a specimen held for an equal time at the deformation temperature. No theoretical explanations for this enhancement have been published. To obtain super-plastic extension at a high strain rate, a small grain size must exist not only prior to but during deformation. Thus, a study of the grain growth kinetics during superplastic deformation is of both theoretical and practical interest. For relative simplicity a single phase superplastic alloy was chosen, namely Sn-1 oABi.(m) Two further advantages of this alloy are: * hived Ootober 16, 1972; revised January 29, 1973. t Depertment of MetaRT The University of British Columbia, Vanoouver 8, B. ., Canada ACTA

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1. Annealing and deformation can be performed at room temperature which corresponds to a high homologous temperature (0.6 Tm) 2. Normal grain growth in dilute Sn-Bi alloys has been studiedo@) and theoretically discussed.(“) EXPERIMENTAL

High purity (99.999%) tin-l % bismuth was air melted, chill cast into 1 in. diameter ingots and then homogenized in air for 7 days at 13O’C. After being machined to 0.94 in. diameter, the ingots were back extruded at 0” or 20% to either 0.160 in. or 0.033 in. diameter rod which was quenched and stored in liquid nitrogen. Before mechanical testing, eaoh specimen was annealed for 20 min at room temperature. For large elongations, tensile specimens were machined on a jeweller’s lathe, otherwise the material was tested as extruded. All testing and annealing was done at room temperature. Deformation was done in tension using either constant extension rate in an Instmn machine or constant stress in a creep machine. The creep stress was kept

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constant within f5 per cent by removing periodically a small portion of the load. Creep strain w&smeasured from the movement of two scribe marks on the specimen. Stress-strain rate relationships were determined directly by rate change tests in the Instron or from the initial slope of the strain-time curves for the creep teats. Alternating tension-compression tests were performed using a strain range of 2 per cent. Total strains were about 40 per cent. Specimens were prepared for etching and examination using diamond knife ultramicrotomy(21) which produced an almost distortion free surface. To reveal the grain boundaries, one of two etchants was used: (1) 2% HCl in ethyl alcohol or (2) 5 cm3 HCI, 2 gm ferric chloride, 30 cm3 of water and 60 cm3 of ethyl alcohol. Grain size (D) was measured on the photomicrographs using the intercept method(2e) with a 10 cm circumference circle. At least 320 intersections were counted for an accuracy of better than f7 per cent at, the 95 per cent confidence level. Since little grain elongation was detected in the longitudinal direction (Fig. I), most size measurements were done on transverse sections. Grain size and type distributions were also determined. The type of a grain was defined as the number of sides evident in a planar section. The method of Johnson(23) was used to measure size distributions. The grains were grouped into classes according to the definition : A = 2p (1) where A is the mean planar area (,u~) of a grain belonging to class P which takes integral values 20. The area limits of each class are given by 2P;t1f2. At least 900 grains were counted for each distribution. RESULTS

Stress-strain

rate curves

The alloy displays a high strain rate sensitivity (m = d log a/d log 8) region characteristic of superplastic material as well as a low sensitivity region at high strain rates (Fig. 2). There is also some indication of a decreased rate sensitivity at very low strain rates. The maximum value of m is approximately 0.45 at B = 10-2/minute. At this strain rate, the maximum sample elongation is 300 per cent but without appreciable grain elongation of individual grains (Fig. 1). Processing variables such as extrusion ratio and temperature have a small effect on the position of the u-B curve but the basic shape is unchanged. Both low extrusion temperature and low extrusion ratio (0.150 in. dia.) shift the curve horizontally to the left.

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I TENSILE AXIS

I

FIG. 1. Longitudinel section of Sn-1% Bi Mmple after 300 per cent elongation.

@ain gmwth with static annealing On a log-log plot the grain size (D) vs time curve for static annealing is S-shaped (Fig. 3). Processing variables have little effect on the grain size-time curve; points for both 0.150 in. and 0.083 in. die rod are plotted in Fig. 3. The straight line portion of the experimental curve was drawn using regression analysis to the equation: D = atn (2) where D is average grain diameter (,u) t is annealing time (min) a, n are constants. The analysis yielded a = 0.105 p/(min)” and n = 0.46. The growth can also be represented over most of the time range by an equation O2 -

0,2 = a2t

(3)

with B, = 1.8 p and a = 0.067 p/(min)l’2, where D, is a constant equivalent to an “initial” grain size. Equation (3) has been termed a “theoretical curve” (Fig. 3) because it adequately describes the growth of cells in a soap froth when the driving force is considered to be the reduction in surface energy.(a) Grain growth during deform&m To determine the effects of deformation on the grain growth kinetics, a series of samples were strained at various initial strain rates and to various strains and the grain size (in transverse sections) was measured

CLARK

AND

ALDEN:

GRAIN

GROWTH

IN

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ALLOY

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100 D STRAIN TEST A

RATE

INDIVIDUAL

CHANOE

CREEP

TESTS

i

101

I

ro-6

I

IO -5

IO4

I

1

IO -3

IO -2 i

FIG. 2. Stress-strain

rate data

1

I

IO -I

I

I IO’

Imin-‘I

for Sn-1%

Bi at room temperature.

---

-LXICaIYLnTAL

cuI)vc

l~CORCllCU CURVE

zP-*

b I IO

a?f

WInI

6~~08Tj+l?

I

I

I

I

100

IO00

10000

100000

TIME

Fro.

I4p.

hid

3. Grain size vs time during static annealing

immediately after testing. For strain rates >lOas/ min, In&on tests were used with the 0.150 in. dia. material and for rates
at room temperature.

size. Excluding the two highest strain rates, deformation appears to shift the annealing curve upward without, changing appreciably the value of the exponent “n.” The extent of the upward shift decreases with decreasing strain rate. The change in grain size with strain was studied using these zame teats. The relative grain size increase was defined as AD/DA, where AD was the

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IO 9 6 7

6 0

Y

0

GTATIC

A

ANNEALING

x 0

I .I0

I

I

I’0

IO TESTING

TIME

0.1 -2 ‘0 -3 2110

I

I

100

1000

i

(mln)

FIG. 4. Grain size vs time during tensile deformation

at different

strain

rates.

20

t

A

Fxo. 5. Grain size vs time during creep deformation

difference between the deformed grain size D, and the a~eibled grain size D_4after the same time a5 required for the deformation. By plotting AD/D, rather than r>, itself versus strain, the complication of increased BA with the longer deformation times required at the lower strain rates is eliminated. The relationship between AD/D, and strain appears to be linear (Figs. 6 and 7). The slope of these lines is a measure of the degree of enhancement of grain growth by strain. This slope at first increases, then decreases with decreasing strain rate between l/min and 2.5 x 10-s/min. It is

r (mh’l 7~10~

v

2.10-•

0

1110

-4 -5

.

&7x10

0 0

-5 1110 I.6dO -6

8t different strain

rates.

highest at strain rates in the high rate sensitivity region (EIO-s/min) (Fig. 8). Alternating tension-compression deformation produced a slightly larger grain size enhancement than deformation in tension alone. A sample strained 38 per cent in tension at 7 x IO-*/min had a grain size of a 3.3 p and a AD of 0.65 p. The tension-compression sample strained for the same length of time and to the same total strain but with a net strain of only 2 per cent had a grain size of 3.7 p and a AD of 1.0 p. After deformation ceases, the grain size continues to

CLARK

AND

2.0

-

I.0

-

GRAIN

ALDEN:

GROWTH

IN

A SUPERPLASTIC

i

8

ALLOY

1199

hlii’)

I.0

A 04

0

20

0

40

00

SO TRUE

100 W

STRAIN

-2

x

10

0

rr1d3

I20

I40

160

FIG. 6. Relative grain size ohenge vs r&rein during tensile deform&ion.

I

Ol

I

IO

0

TRUE

I

%AIN

w

30

‘0

Fra. 7. Reletive grein size ahange va strain during oreep deformation.

increase with time of annealing but at a much slower rate than during deformation (Fig. 9). 8&t! and typ distributions Type distributions were determined for a sample deformed 14 per cent at an initial strain rate of 2.7 x 10d/min and compared to the distribution in a scunple annealed statically for the deformation time (Fig. IO).

Although there is a small difference in the two distributions both are essentially of the log-normal form typical of annealed materials.c”) A grain size distribution wa8 determined for the same deformed sample and compared to the size distribution of an annealed sample of equivalent mean grain size (Fig. 11). Once again both curves are of the typical log-normal form.

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A

CREEP

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FIG. 8. Slope of relative grain size change-strain curves vs strain rate.

IO_

s8‘I8-

6 8w

4 i-

2-

I

I

IO

100

IO00

l0,000

I

oqpoo

Imid Fm. 9. Grain size vs time during and after deform&ionat 6 = lo-*/min. TIYC

DISCUSSION It has been shown that deformation of the Sn-1 % Bi alloy does produce an increase in rate of grain growth; deformation in the superplastic strain rate region acts to increase the value of a in the equation D = at".The relative grain size enhancement (AD/ DA) increases linearly with strain and is dependent upon strain rate, the enhancement being greatest for the superplastic strain rates. However, the shape of the grain type and size distributions are unaffected by the deformation. Before discussing these observations theoretically, s brief review of some characteristics of superplastic deform8tion is appropriate. Deform&ion in a high

strain rate sensitivity region is accompanied by large amounts of grain boundary sliding and grain rotation.(ll*ls) The grains retain their equiaxed shape(ll) and are almost dislocation free after large amounts of elongation.(s*ls) Activation energies in the superplastic region are low,(@u of the order of the activation energy for grain boundary diffusion. These characteristics are consistent with a theoretical model in which the strain rate is controlled by the rate of grain boundary sliding. Because of the importance of grain boundary sliding and grain rotations in superplasticity, the possibility exists for grain “coalescence”@r) to occur during deformation. Grain boundaries in a single phase metal exist because of different crystallographic orientations of

CLARK

AND

GRAIN

ALDEN:

GROWTH

IX’ A SUPERPLASTIC

A---A

ANNEALED

MEAN 5.74

STAl DEY I.99

5.78

I.02

ALLOY

% O-DEFORMED

: .’

‘k \\\\ 4, \

:

O

:

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I

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t

2

3

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4

5

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a

6

IO

II

12

0

I

2

3

4’

5 @RAIN

6

7

-A

6

I4

(Deformed to 14 per cent strain at

FIG. 10. Grain type distribution for annealed end deformed structures. i = 2.7 x 10-6/min.)

A-

I3

ANNEALED

S

IO

II

12

CLASS

Fm. 11. Grain size distribution for annealed end deformed structures of equivelent mean grain size. (Deformed 14 per cent 8t i = 2.7 x 10~‘/min.)

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the grains (Fig. 12a). If one of the adjacent grains rotates (Fig. 12b) in a direction so that the misorientation is eliminated (Fig. 12~) then the boundary itself will be eliminated and the two original grains will have coalesced into one. After coalescence, some local migration of the surrounding boundaries will probably occur (Fig. 12d). It is clear that this mechanism is capable of producing an increased grain size as a result of deformation. The amount of sliding and grain rotation and hence the number of coalescence reactions should increase continually with strain. Consequently the amount of grain size enhancement should also increase with strain as was found experimentally (Figs. 6 and 7). The effects of strain rate (Fig. 8) are also consistent with the mechanism3 has been found”” that the percentage of the total strain due to grain boundary sliding reaches a maximum at the strain rate of maximum “m”. Thus for a given amount of strain, the amount of grain rotation and the grain size enhancement should reach a maximum in the superplastic region (Fig. 8). The results of the alternating tension-compression experiment are less evidently in agreement with the coalescence model. In this experiment, the grains are likely to oscillate about their original position instead of undergoing large rotations, and thus fewer coalescences should occur. The model then predicts less enhancement of the grain growth in the tension-compression test, contrary to experiment.

n)

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Extensive operation of a coalescence model could affect the shape of the grain type distribution curve since, for example, a coalescence between a 6-sided and a ‘i-sided grain will produce one g-sided grain, thus decreasing the relative frequencies of 6 and 7 type grains and increasing the frequency of the g-sided type. Detailed calculations(2s) have, in fact, shown that considerable changes in the form of the distribution curve would be required to produce the measured grain size enhancements by the coalescence mechanism. The type distributions aft’er deformation were, however, similar to the undeformed distributions (Fig. 11). For these two reasons, it is concluded that, the grain coalescence mechanism is unlikely to be the cause of the grain size enhancement. In view of the similarities of the size and the distributions in deformed and undeformed samples as well as the existence of a common grain growth lavs (D = at”), it is probable that during deformation the grains increase in size by normal processes of grain growth; viz. boundary migration driven by a lowering of surface energy leading to the growth of large grains and the disappearance of small. The grain size enhancement must then be due to an increase in the boundary migration rate a during deformation. For normal grain growth it has been shown thaP*~)

OF. ONE

b) ROTATION GRAIN

.j

AFTER

COALESCENCE

.dAFTER

DOUWDARY

ADJUSzyIII(T

FIG. 12. The grain ooalseoenoe meohanism.

CLARK

AND

ALDEN:

GRAIN

GROWTH

where M is the mobility of the rate determining step, dF/dx is the gradient of free energy per atom across the boundary in the direction of boundary migration, and dD/dt is the rate of change of the average grain diameter. Since in dilute Sn-Bi alloys growth is impurity controlled,(lB*N) the mobility is related to a diffusion coeiiicient by the equation’N) ni

M=v kT where Di is the diffusion coeacient for the impurity atoms in a distorted region close to the grain boundary, k is Boltzmann’s and

constant,

T is temperature.

In a fully recrystallized material, the driving force or free energy gradient will be the reduction in grain boundary surface energy so thatt20)

Thus deformation could increase either the mobility or the driving force and produce a grain size enhancement. Deformation could alter the driving force by: 1. Introducing strain energy in the form of dislocation pile ups at the boundary or triple points, 2. Introducing result of sliding, or

steps at the sample surface as a

3. Producing elongated grains. All of these processes could encourage local boundary migration; however, it is not obvious that they would lead to an overall increase in grain size. Enhanced mobility requires only that deformation increase the diffusion coefficient of the Bi atoms in the region close to the boundary. Strain enhanced diffusion has been a subject of considerable controversy in the literature. Several investigatons(31”6) have reported large increases in self diffusivity after deformation, but these results have been challenged on theoretical and experimental grounds.(37-39) The effects of deformation on the grain boundary diffusivity have not received widespread attention. Bhat and Vitovec(“) studied the diffusion of zinc in copper with superimposed fatigue straining and found some increased diffusion along grain boundaries which, they postulated, might be due to damage resulting from grain boundary sliding. Blackburn and Brown(“) measured

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the grain boundary diffusion coefficients of Ag diffusing in covpet bicrystals. Tests on static and sliding boundaries showed a slight increase (30 per cent) in grain boundary diffusivity when the boundaries were sliding. Thus there is some experimental evidence to suggest that grain boundary sliding might increase diffusion coefficients in or near the grain boundary region. Models of grain boundary sliding which involve shear in the boundary region caused by glide and climb of dislocations could perhaps produce an excess of vancancies. However, since the exact mechanism of sliding is still not clear,‘42) we will not propose a detailed model of the excess vacancy production. Instead, we shall assume that grain boundary sliding does produce an excess of vacancies in the boundary region and describe a simple model for mobility enhancement based on this assumption. If the production rate of these excess vacancies is proportional to the strain rate and annealing rate of vacancies is proportional to the excess vacancy concentration, then the equation governing the vacancy concentration is(*) dn, = K,i dt -

n,K2 dt

(7)

where n, = atomic fraction of vacancies due to strain K, = constant, such that K,d is the rate of vacancy production B = strain rate K, = constant dependent upon the nature of the vacancy sinks. Integration

of this equation yields : K 12, = 2 8(1 -

exp (-K,t))

(8)

2

where t is the time to reach a value of strain at the given strain rate. If diffusion takes place by a vacancy mechanism, the diffusivity is proportional to the total atomic fraction of vacancies.tU) Thus the diflusivity in a strained system will be proportional to (n, + n,,) where n, is the equilibirum vacancy concentration. According to equations (4, 5 and 6). M dF

dD -= dt

-=kTD’ dx

D’k” (9)

where k” is a proportionality constant. When the vacancy concentration is in thermal equilibrium, Di CCn, and dD -= dt

2k’n D

(10)

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where k’ = k”lkT is a constant at constant temperature. This equation integrates to D2 -

0,” = 2k’nJ.

(11)

Equation (11) has the same form as equation (3) which describes the experimental static grain growth of Sn-1 % Bi. If however, excess vacancies are generated the growth rate is given by

(12) Substituting for n, from equation (8)

dD

-=

k’

2 C(1 -

exp (--K,t))

+ 12,

2

(13)

at

B

Integration of this equation gives the grain size variation with time during deformation:

K 1- 2 i

exp (-K2t)

)I ’

K,

h’2

(14)

If values of the various constants can be estimated, this equation can be used to calculate theoretical grain size vs time curves during deformation at various strain rates. An approximate value of n, of 10ee was obtained fromt”) n, =

exp - +J$

(14

where AH,, the activation energy for formation of a vscancy, is 11.8 kcal/mole.(&) k’ can then be determined from the value, a, for the theoretical unstrained grain growth curve (equations 3 and 11) . The constant K, will depend upon the nature of the vacancy sinks in the material. The most effective sink in this case will probably be the grain boundary. Girifalco and Grimes(a) have shown that for a plate-like sink: K2=3=20,exp

L”

(

AL) RT

(16)

where D,, is the vacancy diffusion coefficient, AH, is the activation energy for vacancy motion = 15.7 kcal/mole(45’ Do is the frequency factor for vacancy diffusion = 9.7 cme/sec(46) and L is the perpendicular distance from the sink. An accurate value for the distance L cannot be determined

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without knowledge of the detailed mechanism of the boundary shear process that produces the vacancies. A value of L = 100 A was taken as an estimate which yielded K, = 103/min. To determine K,, values of B, t and 6 for one experimental point were inserted in equation (14) along with the values of the other constants. The theoretical curves were thus constrained to pass through only this point and could be used for comparision with experimental points at other strain rates. The point chosen was D = 4.7 p at t = 100 min and f = 10-2/ min which gave K, = 4.1 x 10M3. Barry and Brown’47) estimated K, = 10m3 for strain enhanced bulk diffusion. Grain size-time curves for several strain rates, calculated from equation (14) are shown in Fig. 13. Experimental points from Figs. 4 and 5 and the unstrained annealing curve are also shown for comparison. Agreement of the experimental points with the theoretical curves is satisfactory. Theoretical AD/nA vs strain curves were computed by substituting the time required to reach a given value of strain into equation ( 14). Agreement is good for t < lO”/min (Fig. la), and the trend to lower slopes with decreasing strain rate (Fig. 8) is predicted. In the model, the reason for this decreasing grain growth enhancement is the decreased production rate of vacancies at the lower strain rates [(dn,/dt ai). For g > 10-3/min the model predicts a greater enhancement that that experimentally observed (Fig. 14). At these higher strain rates t,he value of “m” is lower (Fig. 2) indicating that the mode of deformation is changing and less grain boundary sliding occurs.(ll) To incorporate this effect in the model, K, must, decrease as the fraction of the total strain accomplished by sliding decreases. Predictions of the annealing behaviour after deformation can also be made. When excess vacancies are no longer produced K1 equals zero. The excess vacancies that were present at the end of the deformation will continue to influence the grain growth until they anneal out. If the deformation ends at time t,, the excess vacancies present, nzl, will be given by: K n 21 = 2 .@(l -

exp (-K,t,)).

(17)

2

The loss rate of the excess vacancies is given by:

dn, -at

-nJC,.

(18)

Integration of this equation yields : n, = nZl exp k2(tl - t)

(19)

CLARK

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I

I?;

I

I

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GROWTH

TINEhn)

A SUPERPLASTIC

I

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1205

ALLOT

1

10000

1000

Fra. 13. Comparison of theoretical and experimental grain size vs time during deformation curves.

EXPERIW POINTS 8

I.0

x lo-2 0 20

40

60 TRUE

80 STRAIN N

100

I20

E.16’ 140

FIG. 11. Comparison of theoretical and experimental relative grain size change vs strain curves.

where 5 is the atomic fraction of excess vacancies at time t after deformation ceases. Substituting equation (19) into equation (12) gives dD -= dt

k’(?& exp

(&Vl

D

-

t)

+

n,)

Da -

D,” = Lk’n,(t - tl) 2k’nZI -

(20)

If D,, is the grain size at, time t,, integrat,ion of this equation gives the time dependence of the grain size r

after deformation :

(1 -

exp (K2(tl - t)).

(21)

+,

A curve was calculated5 from this equation with t, = 120 min and D, = 4.6 ,u after deformation at B = lo-z/min. When compared to the corresponding

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experimental curve (Fig. 9), the theory correctly predieted the sharp transition in the curve after deformation. The results of the tension-compression experiment are also consistent with the diffusivity enhancement . . model. Reversal of the stress dlrectlon should &Ill produce a grain size enhancement as long as excess vacancies

are being generated

by the sliding boundary.

Experimentally the stress reversal had little effect on the grain size enhancement produced. Thus the diffusivity

enhancement

model

is consistent’ with

all

the experimental results on the Sn-1 % Bi alloy and appears capable of explaining the grain size increase effect associated with superplastic deformation. REFERENCES 1. W. A. BACKOFENand S. W. ZEER, Trans. ASM 61, 300 (1968). 2. W. B. MORRISON, Trans. Am. In&. Min. Engrs. 2&,2221 (1968). 3. T. H. ALDEN and H. W. SCHADLER,Tran.8. Am. Inat. Min. Engra. 242. 825 (1968). 4. R. KOSSOWSKY and J. H. BECHTOLD, Westinghouse Research Paper 67-lF7. Solid p. 3. (1967). P. CHAUD~~BI,Acta Met. M, 1777 (1967). 8: C. M. PACKER, R. H. JOHNSON and 0. D. SHERBP, Trans. Am. In&. Min. Ibgr8. %!& 2485 (1968). 7. R. C. COOK,M.Sc. Thesis, University of British Columbia (1968). 8. 11. W. HAYDEN, R. C. GIBSON, H. F. MERRICK and J. H. BROPHY, Trans. ASM 60,3 (1967). 9. H. W. HATDEN and J. H. BROPHY, Trans. ASM 61, 542 (1968). 10. J. H. BROPHY,R. J. LINDIN~ERand R. C. GIBSOX, Tram. ASM 88, 230 (1969). 11. T. H. ALDEN. Acta Met. 15.469 (1967). 12. M. J. STOW&L, J. L. ROBI&TSON‘and &. M. WATTS, Met. Sci. J. 8,41 (1969). 13. D. LEE, Acta Met. 17,1057 (1969). 14. D. LEE, Met. Trans. 1, 309 (1970). and D. LEE, Trans. Am. Inst. Min. 15. W. A. BACKOFEPI’ Engr8. 289, 1034 (1967).

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16. W. A. BACKOFES. G. S. MARTY and S. W. ZEHR, Trans. Am. Inat. Nin. Engrs. 343, 329 (1968). 17. W. B. MORRISOX.Trans. ASM 61, 423 (1968). 18. T. H. ALDES, Trans. Am. Inst. Min. Engrs. 236, 1633 (1966). 19. E. L. HOLXES and W. C. WISECARD, J. Inat. ,Ilet. 88.468 (1959-60). 20. P. GORDOK,Trans. Am. Inat. Xin. Engra. %27,699 (1963).

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24. R. L. FULLMAxp Metal Interfaces. *SM (lg51).

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