Viscous creep in Pb—9 Sn

Materials Science and Engineering, 14 (1974) 169--177 © Elsevier Sequoia S.A., Lausanne -- Printed in The Netherlands

Viscous Creep in Pb--9 Sn* K. LINGA MURTY Department of Me tallurgy, The University of Newcastle, N.S. W. 23 08 (Australia) (Received April 23, 1973; in revised form July 3, 1973)

Summary High-temperature creep has been studied in Pb--9Sn solid solution alloy in the stress region o f 3 × 10 - 6 - - 4 × I O - ~ G using doubleshear type specimens at temperatures near the melting point. A composite plot o f the dimensionless parameters "~ kT/DGb versus T/G indicated viscous creep behaviour at stresses below about 1.8 × 1 0 - 5 G . The temperature dependence of the steady-state creep-rate yielded values of 21.15 + 3.67 kcal/mole and 25.01 +_ 1.16 kcal/mole for the activation energies of creep in the low and high stress regions respectively. These values are in essential agreement with that for self-diffusion in pure lead. It is suggested that the present creep data are explicable in terms of a single creep mechanism based on Weertman's viscous-drag model for high-temperature creep in solid solution alloys.

I. INTRODUCTION At high temperatures (usually above 0.75TM, TM in deg K) metals exhibit Newtonian viscous deformation where the steadystate creep rate is directly proportional to the applied stress. Nabarro 1 and later Herring 2 postulated the diffusional creep mechanisms where the deformation is due mainly to the exchange of vacancies from one side of a grain *The experimental work described here was carried out while the author was associated with the late Professor John E. Dorn at the Inorganic Materials Research Division of the Lawrence Berkeley Laboratory of the University of California at Berkeley and was supported by the United States Atomic Energy Commission through the facilitiesof I.M.R.D.

to another in a fine grained specimen under stress. This Nabarro--Herring creep is perhaps the best understood of all the creep phenomena 3 and is predominant in metal specimens which either are very 'small' (i.e. large surface to volume ratio, e.g. wire or foil type specimens) or consist of very fine grains. In general this type of creep is important at very high temperatures (near the melting points) and at very small applied stresses. At present there exist a number of examples which exhibit Nabarro--Herring creep: Au, Ag, Cu, Ni, Fe, A1, etc. 3 ,4; in all cases either thin wires or foils are used. Coble s modified Nabarro-Herring model by considering the vacancy exchange through the grain boundaries and obtained good correlation with some experimental data on viscous creep at lower temperatures, down to 0.75T M . As far back as 1957 Harper and Dorn 6 noted in bulk samples of poly and m o n o crystalline aluminium that the steady-state creep rate is directly proportional to the applied stress at stresses smaller than about 10-SG; G = shear modulus. In addition t h e y observed that the activation energy for creep in this low stress region is roughly equal to that in the high stress region where Weertman-type 3,7 dislocation climb model is believed to operate. But their experimental creep-rates were found to be about 1000 times those predicted by Nabarro--Herring model. The fact that the single crystals also yield results identical with those from the polycrystalline samples ruled out the possibility of the Nabarro--Herring creep. The appearance of significantly large primary creep, the uniformity of strain in the b o d y of the grains and across their boundaries 6 , and the recent observation of sub-grain boundaries in crept

170 samples 7 in this stress region add to the above to refute the Nabarro--Herring mechanism as the dominant mode of deformation in this viscous creep region. None of the proposed theories explains these experimental findings. Recently Muehleisen et al. 7 repeated and confirmed Harper and Dorn's findings 6 while Murty et al. s - ~ o reported similar behaviour in A1--3Mg, lead, tin and both poly and mono crystals of aluminium using bulk double shear type specimens in lieu of the tensile specimens used by others quoted above, thus indicating the generality of the Harper--Dorn creep. Murty et al. attributed this creep phenomenon, the so-called Harper--Dorn creep, to the modified versions of the glide of jogs on screw dislocations and/or the climb of saturated edge dislocations s,, 0 Experimental studies of the creep processes at these very low stress levels are of immense importance in design considerations. Generally materials are subjected in service at these levels and below, and 'blind extrapolation' from the studies of creep processes at higher stresses can be disastrous, due mainly to the contribution of the diffusion creep and more severely of the Harper--Dorn creep. The present work is carried out to further record viscous creep in other materials, arid P b - 9 S n solid solution is chosen to compare these findings with the viscous behaviour in A1--3Mg solid solution alloy s, pure lead 9, etc. The recent experimental findings on the microstructural details in crept Fe--3% Si are utilized in analysing the present results in the light of various theories of diffusion controlled creep. As will be clear later a single creep mechanism in collaboration with these substructural details may explain the deformation characteristics in the present alloy in the whole stress range (~ 3 × 10-6G - 3 . 5 × 10-SG) employed here.

II. EXPERIMENTAL ASPECTS Pb--9% Sn alloy was cast, from 99.999% pure lead and tin supplied by the United Mineral and Chemical Corporation, into ingots of 7/8-inch diameter rods. Double shear type specimens were machined from these rods. These specimens were annealed in situ for a minimum of 3 hours at a temperature above the planned test temperature, usually between

530 ° and 540 °K which fixed the grain size at 0.25 + 0.14 cm.. Creep tests under constant load, which turns out to be con~stant stress for the particular geometry of the specimens, were conducted on a machine originally of a design by Murty and Dorn. This machine is suitable for creep studies down to shear stresses of about 2.0 p.s.i. (or loads of ~ 0.45 lb.) and shear strain rates of 2 × 10 -9 sec -1 s. The tests were carried out in a stirred silicone oil bath and the temperatures were controlled to + 1 deg K. The length changes were monitored continuously with a Daytronic type LVDT and a strip chart recorder, and are measured with an accuracy of + 5 × 10-Sin. The main advantages of the present specimen geometry are that the constant stress conditions are achieved w i t h o u t any special arrangement of levers or springs, and also that uniform elongations and constant steady-state creep rates are observable to shear strains beyond 0.80 thereby making it possible to obtain a relatively large number of stress-cycles on a single specimen s '1

III. EXPERIMENTAL RESULTS In this section the various experimental results obtained in the course of the present investigation will be described. At the outset it should be noted that the characteristics of the high-temperature creep are best represented by the following phenomenological equation 3 DGb

'

where A is a constant and D is the appropriate diffusivity. The temperature (T), the shear stress (r), the steady-state strain-rate (q,), the temperature compensated stress (r/G, G is the shear modulus) and the non-dimensionalized shear strain-rate ( ~ k T / D G b ) are tabulated in Table 1. In evaluating ~ k T / D G b , we used D = 0.995 exp

_

25~650 cm 2 / s e e , RT

(2)

corresponding to the volume self-diffusion in pure lead ' 2 (1) T h e stress d e p e n d e n c e o f the strain-rate Figure 1 is a plot of ~ k T / D G b versus r / G

and clearly depicts that the strain-rate is lin-

171 TABLE 1 Experimental data on Pb--9Sn

T

7"

(°K)

(p.s.i.)

z/ (sec -1 )

543 533 533 533 531 531 531 528 528 533 533 501 503 503 503 489 489 502

10.01 7.01 4.22 3.26 5.53 11.55 11.55 7.02 7.02 25.15 20.80 19.66 24.19 20.00 19.66 24.47 20.00 33.25

1.975 X 8.971 X 6.503 × 4.455X 4.975× 1.918 x 1.267 X 8.966 × 8.752x 1.941 x 8.202 x 1.182 x 3.631x 1.349 X 1.178 X 1.672 × 7.004 X 8.881X

* D = 0.995 exp (--25,650/RT)

~G10 -a 1 0 -9 10 -9 10 -9 10 -9 10 -8 10 -s 10 -9 10 -9 10 -7 10 -s 10 -s 10 -~ 10 -s 10 -8 10 -s 10 -~ 1 0 -~

1.127 X 7.772 X 4.681 X 3.616X 6.108X 1.271 X 1.271 × 7.722 × 7.722X 2.787 x 2.306 x 2.075 x 2.560x 2.117 X 2.081 × 2.537 X 2.074 x 3.514X

"~kT* DGb 10 -s 10 -5 10-5 10 -6 10 -6 10 -s 10 -s 10 -6 10-5 10 -s 10 -s 10 -s 10 -s 10 -s 10 -s 10 -5 10 -5 10 -5

cm2/sec.

Pb - 9 S n Do • 0,gg5 em21s.,

I

4O .,,.j a

2O

0

10

20

30

10s (~/G) Fig. 1. Stress dependence o f the steady-state strain-rate p l o t t e d as ~hT/DC-b vs. T/G.

3.822 X 2.555 x 1.852x 1.269X 1.534 × 5.919 × 3.891 x 3.119 x 3.043 × 5.553 X 2.336 X 1.295 × 3.642 × 1.354 X 1.184 X 3.191 X 1.338 X 9.316 X

10 - I s 10 - i s 10 -15 10 - i s 10 -15 10 - I s 10 - i s 10 -15 10 - I s 10 -14 10 -14 10 -14 10 -14 10 -14 10 -14 10 -14 10 -14 10 -14

172 "T

I

I

I

I

I

cl. Y "7 ( D

Pb - 9 Sn

QJ UI

10.6 B

m

l

Viscous Creep Region 1

I

1.82

1

I

I

1.861 I000 ,o K

1.90

T Fig. 2a. The temperature dependence of the creep rate plotted as In ~ T / r vs. 1 / T in the viscous creep region. The slope of the line yields 21.15 _+ 3.67 kcal/mole for the activation energy for creep.

'

I

'

I

'

Pb - 9 S n "

25

10-7 "i ca 5 in

-8 10 High S t r e s s Region

16

1.9

2D 2.1 100(3 , OK-1 T Fig. 2b. in ~ vs. 1 / T in the high stress region. The slopes of the lines yield 26.46 ± 0.76 and 26.86 +- 1.87 kcal/mole for the apparent activation energy for creep at constant stresses o f 25 and 20 p.s.i. early related to the applied stress for stresses below about 2 X 10-SG. The data extrapolated to zero strain-rate for zero applied s t r e s s . I t is t o b e n o t e d t h a t i f t h i n p l a t e l e t s o r wires are used a back stress due to surface

tension effects had to be subtracted from the applied stress to make a correlation between the observed strain-rates and stresses 6 . The s c a t t e r in t h e p r e s e n t d a t a is n o t a p p a r e n t from Fig. 1 owing to the condensed scale ne-

173

cessitated for the entire set of data* to be represented on a single linear plot. But the details may be found in a log--log plot shown later and also in Table 1 from which it is clear that the scatter in the data at low stresses is quite large compared with that in the high stress region. Because of the small loads and strain-rates involved the scatter is unavoidable. At higher stresses the creep-rate rapidly increases with the stress and the data here are in agreement with the earlier findings by Weertman in his microcreep studies in Pb--Sn and other solid solution alloys ~3

(2) The temperature dependence o f the creeprate To determine the activation energy for creep the temperature dependence of the creep-rate is evaluated in the regions below and above the knee (Fig. 1) in the stress dependence of the strain-rate. In the viscous creep (low stress) region, the creep rate is given by 8 z/ = A 1 T / T exp (-- Q c / R T ) ,

(3)

where A I is a constant, Qc is the activation energy for creep and R T has the usual meaning or; 0 ln-~ T To utilize the complete set of data presented in Fig. 1 In (~/T/r) is plotted versus l I T in Fig. 2a and the slope of the resulting straight line yielded a value of 21.15 -+ 3.67 kcal/mole for the activation energy. Within the experimental accuracy this value is comparable with that for self-diffusion in pure lead and may be regarded as essentially equal for all practical purposes. In the high stress region 'ln~ versus l I T ' is plotted as shown in Fig. 2b at constant stresses of 20 and 25 p.s.i. Some d a t u m points were directly taken from Table I and the rest were obtained from an extrapolation of the data at stresses near 20 or 25 p.s.i. The corresponding slopes yielded values of 26.86 + 1.57 and 26.46 + 0.76 kcal/mole respectively at 20 and 25 p.s.i, for the apparent activation energy for creep. These values are corrected for the temperature variation of the shear modulus following Murty et al. ~4, using * T h e d a t u m at T = 3.514 × 10-SG c o u l d n o t be s h o w n here b u t is i n c l u d e d in t h e d o u b l e log p l o t t o follow.

Qc=z~H+RT

(n--1) d d i~n+ G l

1 ,

(5)

where AH is the apparent activation energy and n is the stress exponent. In the present case the correction term was found to be -1.65 kcal/mole or Q~I = 25.01 kcal/mole. The superscript II refers to the high stress region. This value is in excellent agreement with that for volume self-diffusion in pure lead.

IV. D I S C U S S I O N

In the present section the experimental results on Pb--9Sn described in the previous section are compared and correlated with the predictions by theories of diffusion controlled creep. Before discussing these correlations, the microstructural features accompanying creep deformation, especially the stressdependence of the dislocation density, reported on other metals will be described. MuehleisenT,l s found that the dislocation density in crept aluminium is independent of the applied stress for stresses below about 3 × 10-6G. At high stresses it has been established from the data on other metals that the dislocation density increases as the square of the applied stress 3 . These observations were already utilized in explaining the Harper--Dorn creep in aluminium and other metals 8 - 1 o. 15 The recent experimental study by Stang I 6 on the substructures developed in crept Fe--3% Si solid solution alloy indicated that at stresses below ~ 1.9 × 10-SG the dislocation densit y tends to be independent of the applied stress and reaches a constant value given by x/pb=1.84×

10 - 5 ,

T ~ 1 . 9 × 10 - 5 G

while an extrapolation at the high stress end coincides with the earlier work on the same material by Barrett I 7 and L y t t o n Is , and in that stress range T2

p - - - , r >

1 . 9 × 10 - 5 G

(8)

~2G2b2

with a = 0.94. Figure 3 shows the data of Stang, Barrett (820°C} and L y t t o n plotted in terms of nondimensional parameters In x/p b versus In r/G. We utilize this set of data on the dislocation density in our present analysis,

174

"1;/G lo"

e

10-13

s

lo "s

s

10-~

'

I

'

I

Present Doto(Pb-9~)~ /

--.--I~raMK~sm g /

s

Jf 10-1~

_ 1o.4

t

S

/

_ /~-

/

iS

Cy

10-1$ . / ~

stong _.~ Lytton ~/Borrett

_JJ

......

-S

Ext ropolotion j 10"s

lO 4

$

lO-S

s

10-4

S 10-$

Fig. 3. The stress dependence of the steady-state creep rate in Pb--gSn plotted as In Z/kT/DGb vs. In r/G (top). Included here are the theoretical trends predicted by the drag mechanism using the stress dependence of the d i s l o c a t i o n d e n s i t y in Fe--3Si (bottom) p l o t t e d as ~/p b vs. riG. Included here are the data of Stang ] 6, Barrett (at 820 ° C) ] 7 and Lytton ] s m a i n l y because t h e transitional stress r c (~ 1.9 X 10-SG) is in g o o d a g r e e m e n t w i t h t h e k n e e (r c ~ 1.8 X 10 -s G) observed in t h e present creep d a t a (Fig. 3). I n c i d e n t a l l y this clearly shows t h a t t h e k n e e in the creep d a t a is associated w i t h t h e m i n i m u m stress n e e d e d f o r the dislocation multiplication. T h e present value o f ( r / G ) c is in r e a s o n a b l e a g r e e m e n t w i t h t h e b o w - o u t m e c h a n i s m ] 0,2 ] a c c o r d i n g t o which (~/

= 2v~b=3.68X

10 - 5 .

(7)

c

It is u n f o r t u n a t e l y unavoidable t o d r a w conclusions f r o m t h e d a t a on a d i f f e r e n t material owing t o t h e lack o f the s u b s t r u c t u r a l inform a t i o n in the present system. S o m e justificat i o n for the present p r o c e d u r e h o w e v e r m a y be f o u n d f r o m t h e c o r r e l a t i o n s o f t h e c r e e p p r o p e r t i e s o f various metals 3 . In addition, p r e l i m i n a r y e x p e r i m e n t a l results ] 9 o n t h e s u b s t r u c t u r e d e v e l o p e d in A1--5Mg c r e p t in tension in this region indicate similar t r e n d s as in F e - - 3 Si. F o r c o m p a r i s o n with the viscous c r e e p behaviour in o t h e r materials t h e present low

stress d a t a o f P b - - 9 S n are p l o t t e d as f k T / D G b versus T/G along with t h o s e 10 o n A1, Sn, Pb, Ag and A1--3 Mg (Fig. 4). T h e line repres e n t e d as H a r p e r - D o r n is t h e m e a n o f t h e d a t a o n A1, Pb, A1--3Mg and Ag. It is t o be n o t e d t h a t the slopes (A) o f the lines in Fig. 4 are slightly d i f f e r e n t f r o m t h e earlier r e p o r t e d ones s ,] 0 w h e r e A values c o r r e s p o n d i n g t o t h e e x p e r i m e n t a l value o f n ( a r o u n d u n i t y ) obt a i n e d f r o m double-log plots are given. Since a slight variation in n is r e f l e c t e d as a relatively large change in A and since it is established t h a t in this stress range ( H a r p e r - - D o r n region), f ~ r 1, t h e values o f A are t o be comp u t e d with n = 1 or b y making linear plots as in Fig. 4. T a b l e 2 summarises t h e values o f A for the e x p e r i m e n t a l n, and A w i t h n = 1 f o r all these materials. It is clear t h a t P b - - g S n is singled o u t f r o m t h e rest in t h a t it deviates much more from the mean or Harper-Dorn line*. In s o m e cases 20 Bingham t y p e expression was f o u n d t o be applicable, i.e. ~ ~ (r -*Tin is excluded from the discussion since it e x h i b i t s an e x c e p t i o n a l behaviour (large n and A) in the high stress region also w h e r e climb creep is believed to be operative.

175

40

1

I

I

Horper- Dorn ( A . L.23,104' ) 30

A

~I~2o v

% 10

A L ~ 0

5

10

15

20

~o6 ( x/o ) Fig. 4. Linear plots of Z/kT/DGb vs. riG for various metals in the viscous creep region. t o ) . T h e p r e s e n t w o r k o n P b - - g S n a s w e l l as t h e e a r l i e r w o r k b y M u r t y e t al. o n A I - - 3 M g , A1, P b a n d S n 8 - 1 ° c l e a r l y s h o w s t h a t t h e data extrapolate to zero strain-rates at zero applied stress. I t is c u r r e n t l y w e l l e s t a b l i s h e d t h a t c r e e p i n s o l i d s o l u t i o n a l l o y s is c o n t r o l l e d b y v i s c o u s drag due to solute locking of dislocations according to which s,13 DGb = 2pb2

"

(8)

Assuming that the dislocation density varies w i t h t h e a p p l i e d s t r e s s as i n d i c a t e d i n F i g . 3 we note that the above equation predicts ~ ,Gk T D b

_ 2.26 (~) a '

~ ~ 2 × 10 -SG

(9) and _- 0.

0 × 10-

o

,

•

.

In general, solid solution alloys such as the present one exhibit stress exponents between

TABLE 2 Values of A for various metals

Metal

n

A (from exptl, n)

A (with n = 1)

Pb--9Sn Sn Ag Pb

0.99 0.94 1.00 0.97

3.31 7.24 6.60 2.88

3.35 1.48 6.60 4.18

A1

1.07

5.05 × I0 -I1

3.98 x I0 -I1

AI--3Mg

0.91

1.39 × 10 -11

2.14

× × × ×

10 -1° 10 -11 10 -11 10 -11

X × X X

10 -1° 10 -1° 10-' 1 10 -11

X 1 0 -11

Reference Present M o h a m e d , Murty and Morris (a) ZilingC°) Mohamed, Murty and Morris(a) Harper and Dorn(c) Barrett, Muehleisen and Nix (d) M o h a m e d , Murty and Morris (a) Murty, M o h a m e d and Dorn (e)

A H _ D = 4.23 × 10 -11 (a) See reference 10. Co) K.K. Ziling, Fiz. Metal. i MetaUoved., 15 (1963) 584; also see reference 10. (c) See reference 6. (d) See reference 7. (e) See reference 8.

176

I

At 10 4s

o Burton a Harper ond Dorn

-

~1Hohomed, Murty and Morris

Muehteisen •~. ¢-~

lo-w

°

\ |

0.1

,

I

,

1.0

I

,

10

d

mm

Fig. 5. G r a i n size dependence of the c o m p e n s a t e d s t r a i n - r a t e depicting the transition f r o m H a r p e r - - D o r n region t o N a b a r r o - - H e r r i n g region as t h e grain size decreases. T h e datum shown as filled triangle (A) c o r r e s p o n d s t o single crystal w i t h d e q u a l t o d i a m e t e r o f t h e gage section. ( r = 2 x 1 0 - e G )

3 and 3"5 at stresses around 10-4G 13. The trends predicted by eqns. (9) are shown in Fig. 3 along with the experimental data, and it is clear t h a t while the high stress data are in essential agreement with the theory the experimental creep rates fall within a factor of 2 from the predicted line at low stresses. Thus it seems as if the entire set of the present experimental data is explicable by a single mechanism invoking the transition in the stress dependence of the dislocation density at a stress of ~ 10 -s G. Earlier, several authors attempted to explain Harper--Dorn creep in A1 and other metals in terms of the models based on the glide of jogged screw dislocations 6 , s a s , climb of isolated saturated edge dislocations ~0,1 s ,21 and a balance between the generation and annihilation of gliding dislocations 7. All these models, with the assumed stress independent dislocation density, again yield results in agreement with the present experiments in the low stress region. It is more conceivable that in the present system the viscous drag due to solute locking controls creep in the entire stress range since it is already established that this model explains the creep properties in the high stress region, and thus no change in the operating mechanism is needed to explain the low stress data. At the stress levels of the present work the diffusion creep mechanisms such as the

Nabarro--Herringl ,2 and Coble s make at most negligible contribution to the overall creep-rates. For the grain size of the present samples {0.25 cm) indeed ~ e x p t . ~ 810~N--H a n d ~expt. ~ 104~Coble • We note here that these mechanisms operate in parallel with the viscous drag and Harper--Dorn mechanisms, and thus if the grain size of the samples is made sufficiently small one should be able to observe a transition from one to the other. Indeed the recent work by Burton 22 on A1 does much to show this as depicted in Fig. 5. Here again we had to combine Burton's results on thin platelets of aluminium with the other sets of data 6 ,7,23 to observe the predicted transition. Burton's measurements are in reasonable agreement with Nabarro-Herring predictions and depict the required d-2 d c Harper--Dorn creep should be observable.

ACKNOWLEDGEMENTS

The author is grateful to the late Prof. J.E. Dorn for inculcating in him the basic ideas of the present research and for the short but invaluable guidance. Acknowledgements are due to Prof. J.W. Morris, Jr. and Mr. F.A. Mohamed of the University of California for

177

some valuable discussions, and to Prof. E.O. Hall for a critical reading of the manuscript. Thanks are due to Prof. W.D. Nix of the Stanford University for providing a copy of the thesis b y Stang and to Mr. D. Grivas for carrying out part of the metallography. The financial support of the Australian Institute of Nuclear Science and Engineering through a post-doctoral fellowship at the University of Newcastle is gratefully acknowledged.

REFERENCES

1 F.R.N. Nabarro, in Strength of Solids, Phys. Soc., London, 1948, p. 77. 2 C. Herring, J. Appl. Phys., 21 (1950) 437. 3 J.E. Bird, A.K. Mukherjee and J.E. Dorn, in D.G. Brandon and A. Rosen (eds.), Quantitative Relation Between Properties and Microstructure, Israel University Press, 1969, pp. 255--342. 4 H, Jones, Mater.Sci. Eng., 4 (1969) 113. 5 R.L. Coble, J. Appl. Phys., 34 (1963) 1679. 6 J.G. Harper and J.E. Dorn, Acta Met., 5 (1957) 654; also J.G. Harper, L.A. Shepard and J.E. Dorn, Acta Met., 6 (1958) 507. 7 C.R. Barrett, E.C. Muehleisen and W.D. Nix, Mater. Sci. Eng., 10 (1972) 33. 8 K. Linga Murty, F.A. Mohamed and J.E. Dorn, Acta Met., 20 (1972) 1009. 9 F.A. Mohamed, K.L. Murty and J.W. Morris, Jr.,

Met. Trans., 4 (1973) 935. 10 F.A. Mohamed, K.L. Murty and J.W. Morris, Jr., Harper--Dorn Creep of Metals, L.B.L. Rept. No. 1158, September, 1972, presented at John E. Dorn Memorial Symposium, Fall Meeting AIME, Cleveland, Ohio, October, 1972. 11 D.M. Schwartz, J.B. Mitchell and J.E. Dorn, Acta Met., 15 (1967) 485. 12 J.W. Miller, Phys. Rev., 181 (1969) 1095. 13 J. Weertman, Trans. AIME, 218 (1960) 207. 14 K. Linga Murty, M. Gold and A.L. Ruoff, J. Appl. Phys., 41 (1970) 4917. 15 E.C. Muehleisen, The Role of Structure in Newtonian Deformation of Metals, Ph.D. Thesis, Standford University, 1969, unpublished. 16 R.G. Stang, High Temperature Creep in Fe--3% Si, Ph.D. Thesis, Stanford University, 1971, unpublished. 17 C.R. Barrett, Trans. AIME, 239 (1967) 1726. 18 J.L. Lytton, The Role of Preferred Orientation on the Elastic and Plastic Properties of Metals at High Temperatures, Ph.D. Thesis, Stanford University, 1962, unpublished. 19 K. Linga Murty, unpublished research and work in progress. 20 A.U. Karim, in J. Burke and V. Weiss (eds.), Ultrafine Grain Metals, Syracuse University Press, 1970, p. 295. 21 J. Friedel, Dislocations, Pergamon Press, 1964. 22 B. Burton, Phil. Mag., 27 (1972) 645. 23 J.W. Morris, Jr., F.A. Mohamed and K.L. Murty, Harper--Dorn Creep in A1, L.B.L. Rept. No. 830, April 1972, Phil. Mag., to be published.