High-temperature deformation mechanisms in superplastig ′n-22Al eutectoid

HIGH-TEMPERATURE M.

L.

DEFORMATION MECHANISMS Zn-22Al EUTECTOID*

VAIDYA,t$

K.

LINGA

MURTYtP

and J.

IN SUPERPLASTIC E.

DORNtll

The temperature and the stress dependences of steady-state strain-rates in Zn-22Al eutectoid were studied by tensile and creep testing using double shear type specimens in a normalized stress (r/G) range of 55 x lo-’ to -5 x 10-3. The stress dependence of the strain-rate revealed three drstinct regions with stress exponents of 0.87 f 0.12, 1.99 & 0.15 and 3.73.k 0.17. The activation energv for deformation obtained in the regrons I and II was identified as that for grainboundary diffusion whiie that found in the region III was approximately equal to the self-diffusion value. The experimental results in the employed stress range obeyed the following phenomenological equation. g

= /l8”

(;)”

($

From the experimental values of the creep parameters it, nr, c( and A, the mechanisms of deformation are identified. Dislocation climb and Coble creep were found to be the controlling mechamsms in the regions III and I respectively. The present results in the region II are m close agreement with the predictions based on Ball-Hutchison model for superplast,icity, and the models based on gram boundary sliding yield stram-rates about 250 times the experimental values. MECANISMES

DE DEFORMATION A TEMPERATURE ELEVEE L’EUTECTOIDE SUPERPLASTIQUE Zn-22Al

DAKS

L’intluence de la temperature et de la contrainte sur lea vitesses de deformation en regime permanent, ont Bte Btudiees dans l’eutectoide Zn-22Al par des essais de traction et de fluage effect&s dans le domaine de contraintes normalisees (r/G) sit& entre 5 . lo-’ et 5 . 1O-5 environ, sur des Bohantillons du type cisadlement double. L’etude de I’influence de la contra&e sur la vitesse de deformation met en evidence trois regions distinctes, au les exposants de la contrainte sont respectivement 0,87 rt 0,12, 1,99 i. 0.15 et 3,73 f 0,17. L’energie d’activation pour la deformation obtenue dans les regions I et II correspond it la diffusion intergranulaire, alors que pour la region III elle est approximativement egale 8, la valeur d’auto diffusion. Les resultats experimentaux suivent dans le domaine de contra&es utilise l’equatlon phenomonologique suivante: g

= A(i)”

(;)”

($

Les mecanismes de deformation sont identifies a partir des valeurs experimentales obtenues pour les parametres de fluage n, m, a et A. Les auteurs trouvent que les mecanismes correspondant aus regions III et I sont respectivement la montee des dislocations et le fluage de Coble. Les resultats obtenus pour la region II sont en tres bon accord avec les previsions domees par le modele de Ball-Hutchison pour la superplasticite, tandisque les modeles bases sur le glissement aux joints de grains donnent des vitesses de deformation environ 250 fois plus grandes que les valeurs experimentales. HOCHTEMPERATUR-VERFORMUNGSMECHANISMEN Zn-22Al-EUTEKTOID

IM SUPERPLASTISCHEN

Die Temperatur- und Spannungsabhiingigkeit, stationilrer Abgleitgeschwindigkeiten im Zn-22X1Eutektoid wurden in Zug- und Kriechversuchen untersucht. Die Messungen wurden an Doppelscherproben in einem normalisierten Spannungsbereich (r/G) zwischen -5 x 10-r und -5 x 10-X durchgeftihrt. Die Spannungsabhiingigkeit der Abgleitgeschwindigkeit zeigt drei ausgepragte Bereiche mit Spannungsexponenten van 0.87 & 0,12, 1.99 + 0,15 und 3,73 f 0,17. Die in den Bereichen I und II gemessenen Aktrvierungsenergie ist gleich der Aktivierungsenorgie der Korngrenzendiffusion: die fur Bereich III bestimmte Aktivierungsenergie ist gleich dem Selbstdiffusionswert. Die im untersuchten Spannungsbereich gewonnenen Ergebnisse gehorchen cler folgenden phanomenologischen Gleichung:

Mit Hilfe der experimentellen Werte der Kriechparameter n, m, a und A wird der Verformungsmechanismus identifiziert . Im Berelch III bzw. I ist Versetsungsklettern bzw. Coble-Kriechen der bestimmende Mechanismus. Die fur Bereich II vorliegenden Ergebmsse sind in guter Ubereinntunmung mit den Vorhersagen des Ball-Hutohison-Modells der Superplastizitiit. Die vom Korngrenzengleiten ausgehenden Modelle hefern Abgleitgeschwindigkeitcn, die etwa das 250-fache des experimentellen Wertes betragrn.

* Received March 23, 1972; revised February 20, 1973. t Inorganic Materials Research Division, Lawrence Berkeley Laboratory, University of California. z Permanent Address: Dept. of Metallurgy, Indian Institute of Technology, Kanpur, India. QPresent Address: Dept. of Metallurgy, University of Newcastle, N.S.W., 2308 Australia. 11Materials Science, College of Engineering, University of California, Berkeley, California. Deceased September, 1971. ACTA

METALLURGICA,

VOL.

21, DECEMBER

1973

1. INTRODUCTION

There had been a number plastic

behavior

of various

trial-applicability Recent amount 1615

of studies on the superalloys

both from indus-

as well as fundamental

reviews(l-3) of literature

on superplasticity available

viewpoints.

reveal the vast

on this subject.

Most

1616

ACTA

METALLURGICA,

of the experimental data had been confined to the amourns of neck-free deformation and their relation to t’he strain-rate sensitivity index, m (= a In cr/ a In i). Systematic studies of the strain-rate dependencies on the stress and the temperature in a wide range are needed to get an understanding into the micromechanics of the deformation characteristics. Recent survey and analyses(*) clearly indicate the lack of experimental data to check the theoretical predictions, especially at extremely low stresses. Even the available data at low stresses are not unambiguous because nonuniform deformation renders t,he actual stress values doubtful. Superplasticity is commonly referred to extensive uniform tensile deformation due to rapid increase in the stress with the strain rate. This is analogous to extensive uniform tensile deformation due to rapid increase in the stress with the strain whenever this occurs in high strain-hardening materials at low temperatures, while superplasticity is confined to fine grained (ml-10 pm) materials at elevated temperatures and reasonably low strain rates. Until recently no particular mechanism of deformation is inferred to apply the description “superplasticity”(2). However Bird et ~2.c~) categorized superplasticity as a mode of deformat,ion with the steady-state strain-rate being proportional to the square of the stress and inversely to the square of the grain size, and the activation energy for flow being equal to that for the grain boundary diffusion. t5) From their analyses of the deformation characteristics in terms of the dimensionless parameters, namely BkTIDGb vs a/G (6: strain rate, D: diffusivity, G: shear modulus, b = Burgers vector, c: tensile stress and kT has the usual meaning), they could divide the available stress range into 3 parts. (1) high stress region where a dislocation mechanism such as “dislocation climb” operates.(s) (2) intermediate stresses where “superplasticity” is observed, and (3) low stress range where a stressdirected vacancy diffusion mechanism such as Nabarro-Herring@-lo) or Cobleol) creep contributes predominantly. Thus predicted trends are depicted in Fig. 1. None of the suggested theories can explain all the currently available data on superplasticity. Avery and Backofen”) suggested the possibility of Nabarro creep in a Pb-Sn alloy. But strong evidence from recent experimental work(**25) refutes the required n = 1 stress dependence. Packer and Sherbyo2) analysed the low stress data of Avery and Backofen using an empirical relationship of the form

(1)

VOL.

21,

1053

.

.

bl . ,_

Fro. 1. Predicted trends of deformation mechenisms in a super-plastic material. Comparison of mechanisms controlled by Coble, Superplastic and dislocation Climb creep at low, intermediate and high stress regions.“’

where K is a constant and d is the grain size, and they obtained an improved agreement. Gifkins et uZ.‘~~*~~) analysed their data on Pb-TI alloys using the semitheoretical relationship :

where D, is the grain boundary diffusivity. The estimated rates were too slow to account for the experimental data. A studied review of the available data indicates a more satisfactory correlation with u2 dependence in lieu of al dependence.(*) Such correlations suggest either BkT m=KG

o2 0

b2 d> 0

K’ G2 00

s

(34

or ikT -= D,Gb

b2 ’

(3’4

depending on whether the activation energy is that for self-diffusion or grain boundary diffusion. Bird et aZ.‘d4) analyses of the data on Zn-Al(S) and PbSn(‘) reveal that the constants K and K’ in the above equations differ by four orders of magnitude and also that the latter equation with the grain-boundary diffusivity gives a better correlation. It is to be noted that the equation 3(b) is essentially that given by Ball and Hutchison.(5) The basis for equation 3(b) and the underlying assumptions have already been reviewed by Bird et cd.(*)

VAIDYA

et al.:

DEFORMATION

MECHANISMS

Although a reasonable correlation between theory and experiments is observed at high and moderate stresses (i .e . “Dislocation Climb” and “Superplasticity”’ regions), various inconsistencies were noted at lower stresses. Some of the earlier investigations indicate(6) that dislocation climb may control the deformation at low stresses. However, the data at low stresses indicated strong grain size dependence of the strain rate, an observation inconsistent with a climb mechanism. It is more likely that at these low stresses the deformation mechanism is stress-directed vacancy migration. In a re-evaluation of Ball-Hutchison data’s) on Zn-Al eutectoid as well as Avery-Backofen data(‘) on Pb-Sn eutectic, Bird et al.(4) proposed that Cobleol) creep may be the dominant mechanism at these extremely small stresses. Unfortunately none of the existing data extend to low enough stresses to prove their point unequivocally. The motivation thus of the present research was to; (1) work with Zn-Al alloy of eutectoid composition; (2) obtain experimental data on steady-state strainrate as a function of stress in a wide range of stress levels-creep tests for low stress data while Instron tests for high stresses, and achieve high precision in the mechanical data by using double shear specimens thereby avoiding non-uniform deformation;oe) (3) to investigate the grain size dependence of the strain rate; (4) to study the ~m~rature dependence of the deformation rate and determine the activation energies for flow in all the regions covering the available stress range; and finally (5) to correlate the experimental findings wit.h the theoretical expectations and demo~trate the proposed transitions from comb-controlling to superplastic and then to Coblej Nabarro creep regions as lower stresses are encountered. 2. EXPERIMENTAL PROCEDURE Zn-22 % Al alloy was prepared from 99.999 % pure Zn and Al. The alloy we melted in a graphite crucible and chill-cast in a water cooled mold of 14 in. dia. The ingots were hot rolled at ~320°C to $ in. dia. and double-shear specimens of the shape and dimensions as in Fig. 2 were prepared from the rolled stock. The machined specimens were solution treated in an argon atmosphere at 375’C for 15 hr. They were then quenched to ice temperature where spontaneous decomposition produced very fine equiaxed grains of the two phases of the eutectoid. Annealing treatments at 265°C for various times yielded the following grain sizes : (i) 6 hour anneal--d = 1.19 & 0.32 pm; (ii) 2 days2.36 f 0.26 pm; (iii) 2 weeks-3.60 f 0.26 ,um; and (iv) 5 weeks-4.62 & 0.28 ,um.

IN

SUPERPLASTIC

Zn-22Al

1617

Thrrnccouplt *ells

____-_-_

_____-___

FIG. 2. Drawing of the double-shear type test specimens.

The grain sizes were determined from the electron micrographs of the surface replicas as the mean linear intercept (Z) and converted to average spatial grain diameter (d) using the relationship d = 1.75 t.15) The prepared specimen8 were tested in an Instron testing machine(1a) or a creep machine, originally of a design by Murty, at constant load which turns out to be constant stress for the particular configuration of the specimen. An electrically heated oil bath stirred by bubbling argon was used to obtain temperature8 above the room temperature. The temperature8 were monitored with Chromel-~umel thermocouples and were maintained constant to fl”. To obtain the low stress data, creep tests were conducted and the samples were crept at a constant load (stress) until the steady state was reached and then the load was changed, and again waited until it was clear that the steady state rate was obtained before changing the load again. The length changes were monitored by a Daytronio LVDT and the length measurements were accurate to 15 x 10e5 in. The Instron data were obtained by differential strain-rate tests at a constant ~m~rature as described by Vandervoort et aZ.(15-16) By utilizing the double shear type test specimens uniform elongations and constant steady-state strain-rates were observed to shear strains beyond O&0.(17) 3. EXPERIMENTAL RESULTS The specimens of the four different grain sizes were tested in a temperature-range from 175 to 250°C in both an Instron testing machine, and a creep machine for strain-rate8 smaller than, or of the order of, 10e5 se&. Following is an account of the various experimental observations. (i) Xtrees dependence

of the strain-rate

Figure 3 is a double-log plot of the steady-state strain-rate as a function of the stress at a constant temperature of 250%. There exist three distinct regions with constant stress exponents. The extension of each region depend8 on the grain size of the specimen. While there is a strong grain size dependence in

ACTA

1618

M~TALL~RGICA,

VOL.

21,

l l

1973

Zo-22A1 r, m 10 Wqcnt) 500 (W3xnIIJ

i

r, psi

Fra. 3. Double-log plot of the steady-state shear strainrate vs the applied shear stress at 260°C.

regions I and II the data obtained on all samples merge into a single line at high stresses. The least squares analyses of the data yielded values of 0.87 & 0.12,2.03 4 0.08 and 3.51 & 0.18 for the slopes in the regions I, II and III respectively. The values of the stresses at which the transitions occur from regions I to II and II to III depend upon the grain size, and the smaller the grain size the higher are the values of these transition-stresses. Both Instron and creep data were gathered for region II. Only Instron data were taken in region III and only creep data in region I. The differential strain-rate tests in the region III indicated large transients. In the region II these transients were very short, and often the steady states were reached soon after the change in the cross-head speed. The creep curves in the region II revealed either very brief or no primary creep range. In most cases steady-state creep-rates were attained almost immediately upon loading. On the other hand in region I steady-stat.e creep was always preceded by reasonably long transients, the extent of these transient creep regions being dependent on the stress level. (ii)

Grain size dependence of the strain-rate

The strain-rate seems to be independent of the grain-size in the region III (Fig. 3). Further confirmation of this is given in the next se&ion. Figure 4 is a plot of the logarithm of the strain-rate vs the logarithm of the grain size in the regions I and II at stress-levefs of 10 and 609 psi respectively at 250°C. The resulting straight lines indicated d-zJ@~e~azand d-l~sg~~zs dependencies of the strain-rates in the regions I and II respectively.

Fro. 4. Dependence of the strain-rate on the grain size. Double-log plots yield lines with slopes qua1 to 2.50 & 0.32 and 1.69 -& 0.29 respectively in the regions I and II.

(iii) Temperature dependence of the strain rate To determine the activation energies for flow, the temperature dependence of the steady-state creep-rate was studied in all the three regions. Figures 5 (a-c) are plots of “In @+-’ vs l/T” and the resulting activation energies from the slopes of these straight lines are found to be 17.8 f 0.2 kcal/mole, 18.9 rf_-0.3 kcal/ mole and 28.8 -& 0.3 kcaljmole respectively in the regions I, II and III. These values for the aetivat,ion energy may be compared with that for volume selfdiffusion in pure zinc (24.3 kcal/mole)~18) and aluminium (33.0 k~al/mole),~~B~and with those for grain boundary diffusion in zinc (14.0 kcal/mole)(sO) and in aluminium (16.5 kcal/mole).t From the recent work of Hassner@r) on the grain-boundary diffusion of Zn in Al-Zn alloys at a constant temperature of 340°C for various concentrations of Zn, a value of 13.2 kcaljmole is inferred for the activation energy for grain-boundary diffucion in Al-78 An if Do is assumed to be unity. Ball and Hutchison(5’ obtained a value of 15.45 kcal/ mole for the activation energy in the superplastic region and this value has to be compared with the present one in the region II. 4. DISCUSSION

The phenomenological equation applicable for hightemperature diffusion-controlled creep was given by t Assuming

that H, = #Ho.

SAIDTA

REFORMATIVE

et al.:

MECHANISMS

XX S~~~RF~AST~C

AH 2 28.8k

AH = 1718 k Cal / mole

0

IdI1.90

36

1619

Zn-SfAl

Cal /mole

5

I

1.95

I

I

I

200

2.05

2JO

1000

OK“

-7-l

I

I

I

2.15

2.20

2.25

IO””

1.90

I 1.95

I 2.00

I 2.05

I 2.10

I 2.15

I 2.20

2.25

q

FIG. 58. Arrhenius plot of the logarithm of the strain-rate vs l/T in the region I.

FIQ. 5c. Arrhenius plot of the temperature oompensated strain-rate plotted as In 3Qair w l/T in the region III.

Bird et Qt.(*)to be t

I

I

I

I

1

I

4

2n - 22 Al

1.90

I.95

2.00

2.05 9,

2%

2.15

220

i”, 0

(4)

where D is the appropriate diffusivity, either volume self-diffisivity or grain-boundary diffusivny. In alloys the appropriate diffusivity is inter or chemical diffusivity I),* D,* D (5) sllOg= (NBDA* + ~~D~*)~

Region Il AH = 18.9 k Cal /mole

!Dl~!

jkT =A DGB

2.25

OK-’

Fru. 5b. The temperature dependence of the steady-state strain-rate in the region II plotted aa In $ CT VB l/T.

where N, and N, are the atomic fractions of A and B atoms in &binary AB ahoy, D* is the tracer diffusivity and j is the correlation factor. As shown in the earlier section the activation energy for creep in the regions I and II turned out to be near to that for grain-boundary diffusion while that in region III was equal to the mean of the activation energies for self-diffusion in zinc and aluminium. The paucity of data in the literature on diffusivities in the ahoy makes accu&e ~o~elation disrupt. Thus the identi~~~tion of the exact diffusion coefficient or the diffusing species is at present not possible. To make a master plot of the data covering the entire stress range, equation 4 is rewritten as (6)

ACTA

1620

METALLURGICA,

VOL.

21,

1973

16

2

FIG. 6. Plot of “ln pkT/D&b vs In r/G “depicting the grain size dependence. In the regions I and II, datum points obtained at various temperatures for the four grain sizes were shown while in the region III, the data obteined at different temperatures for only the largest grain-size were plotted for simplicity.

where a = 0 for the regions I and II while a = 1 in the region III. Figure 6 is a plot of “ln jkT/D,Gb vs In r/G” and the data obtained on specimens with different grain sizes at various test temperatures (175, 200, 225 and 250°C) are plotted. For simplicity the data obtained in the region III at different temperatures are shown only for a single grain size of

4.6 pm. It is to be noted that the trends observed here are akin to the predictions made by Bird et uZ.(@ as shown in Fig. 1. To reveal the effect of the temperature on the transition from regions II to III, In pkT/ D,Gb is plotted as a function of In r/G in Fig. 7 for two different grain sizes (3.6 and 4.6 ,um). Included here are also the theoretical trends, expected in the region

-0

IO”-

-

IO

lo”-

-

IO

-

IO

-II

-12

42

&” b

i!kL

-13

_,FbGb

IO -

-

IO

IO”-

-

IoH

I$ -

-

IO

4

Fro. 7. Plot of “ln fkTID,CJb vs In r/Q” for two grain size values, d = 4.0 pm and d = 3.0 pm Ft various temperatures showing the transition from region II to region III. Theoretkal predictions based on the dislocetion climb model for the different temperatures were shown in the region III for comparison with the experimental results.

VAIDYA

et al.:

DEFORMATION

MECHAN

III based on the climb-model, with A = 6 x lo’, n = 4.5, m. = 0 and a = 1 in equation 6 above, applicable for high-temperature creep in pure zinc and aluminium.(4) It is assumed that the diffusion frequency factor (D,) is the same for self-diffusion and grain-boundary diffusion, and DID, = exp (-HJRT). The three different regions depicted in Fig. 6 are analysed in the following. Region I. This region extends from stresses of the order of 10-s G to lower and a strong grain size dependence of the strain-rate is noted. The approximate linear stress-dependence of the creep-rate suggests a diffusion mechanism by vacancy exchange, either Nabarro-Herring(s*lO) or Coble.(ll) The fact that the activation energy for flow is approximately equal to that for grain-boundary diffusion argues for the Coble mechanism. Further support of the operation of Coble mechanism in this region is obtained through the grain-size dependence of the creep-rate as well as the factor A. The experimental value for A was found to be 55 f 25 compared to 150 predicted by Coble model. The experimental value for m was determined to be 2.50 f 0.32 in comparison to 3 predicted by this model. It appears from these observations thus that the Coble mechanism controls the deformation in the region I. Region II. The analysis of the experimental data at the four different temperatures in this region indicates that the strain-rate is proportional to ,1.29~.15/&.69&-0.29 and the activation energy for deformation mai be identified as that for grainboundary diffusion. These findings are in line with the Ball-Hutchison modeP5) for superplastic deformation. As shown in the review paper by Bird et CL?.(~) most of the experimental data available on superplastic creep do correlate with an equation of the form 6kT -= D,Gb

KL G 00

2

b”’ ii

,mm2

.SMS

IN

SUPERPLASTIC

Zn-22Al

1621

proposed grain-boundary sliding as a deformat,ion mechanism during creep and noted that r2 dependence of the creep-rate may be observed at intermediate stresses while r1 and r4 at low and high stress regions. Although the trends predicted by Langdon are qualitatively identical to the present ones, they however are much different in details. His model for creep due to grain boundary sliding predicts $kT mb=

b1 4) ;i

72

(8)

0G

with ,!? = 6 and D is either lattice or grain-boundary diffusivity depending on the circumstances.(23’ This model yields strain-rates which are about 250 times the experimental values. It should be noted that several workers(22*2Q) believe that the exponent n in equation (6) is temperature dependent. If this were ‘true then the activation energy for deformation could not be determined as is done in conventional creep, and here in Figs. 5. As revealed in the present work n is not a continuous function of the temperature or the stress (except in the transitional regions such as between II and III in Fig. 7), but n takes on constant values over certain regions of r/G, such as those depicted in Fig. 6. Indeed the data presented by Nicholson to show that n is a continuous function of temperature may be replotted in terms of pkT/D,Gb and -r/G (Fig. 8). It is

0 a 0 0

473 436 396 361

Doto d Nutlolla”

(7)

where K is a numerical constant. The present results yield a value of 302 & 216 for K and 1.69 & 0.29 for m in the above equation. The Ball-Hutchison model predicts values of -200 and 2 for K and m respectively. Such an agreement notwithstanding, microstructural observations(22l argue against such a mechanism for superplasticity. Whereas the BallHutchison model requires dislocation pile-ups and motion of dislocations through the grain-interior (at least in some grains if not in all), “marker-experiments” of Nicholson’22) indicate that there is little or no dislocation activity in the grain interior. None of the presently proposed theories explain these experimental observations. In a recent paper Langdonc22)

t

,dl66 10-6

i 10-5

10-4

W-'

r/G FIG. 8. Data of Nuttsll taken from reference 21 plotted as “ln jkTID,Clb vs In r/Q” to show that n IS not a continuous function of temperature in the “Superplastlc” region. As is clear from this plot, the data at various temperatures coelesced into a single line in the stress range ~6 x 10-s G to wlO-* G and start deviating into separate lines as the ‘climb’ region is approached at higher stresses.

ACTA

1622

METALLURGICA,

VOL.

21,

1973

clear from this analysis that t,he data at different temperatures merge into a single line with a value of 2 n - 22Al 2 for n while they start deviating at high stresses as conventional creep (climb creep) region is approached (cf. Fig. 8). These results are in close agreement with the recent flndingst on the deformation kinetics in Pb-Sn eutectic.(%) It appears from the above that a model for superplasticity must explain and predict the following : +J kT DbGb (1) the strain-rate is proportional to (~/d)2 ; (2) the activation energy for deformation is equal to that for grain-boundary diffusion; (3) the constant A has a value of ~200; and (4) there is no dislocation activity in the interior of the grains.@2) Region III. As noted earlier there is no apparent grain-size dependence of the strain-rate in this region and the activation energy for creep is about 1.7 times 10” 10” 1o-’ t,hat observed in regions I and II. This value is equal ‘/G to the mean of the activation energies for volume FIG. 10. Comparison of the experimental results obtained for the two grain-size values, 1.2 pm and 4.6 I’m. with the self-diffusion in zinc and aluminium. The experitheoretical lines obtained from various creep models. mental results in this region are plotted in Fig. 9 as In jkT/DGb vs In r/G. The least squares analysis of Such a stress-dependence in addition to t’he approxithese datum points obtained on specimens of all mate equivalence of the activation energy for flow in grain-sizes yields the following relation this region and that for self-diffusion suggests a dislocation model such as climb@) of edge dislocations. 7 3.73io.17 gb = (1.36+,2:,9,2)x106 G (9) The experimental value for A of 1.36 x lo6 supports 0 such a contention. The experimental data on high I I’ temperature creep in pure metals yield a value of 6 x 10’ for A when climb model is applicable.‘*) It Zn - 22Al thus appears that climb of dislocations controls the d,lrm . 1.2 deformation in this region. To summarize the above observations, In j&T/ D,Gb was plotted vs In r/G in Fig. 10 for the extreme grain sizes (1.2 and 4.6 pm). The experimental results are shown by dashed lines. The datum point’s are not shown for simplicity and the details may be found in Fig. 6. To compare the experimental results with various theories, the theoretical curves expected from Nabarro-Herring,tB*lO) Coble,(ll) Ball-Hutchison,t5) grain-boundary sliding (Langdon), dislocation climb(**s) as well as viscous glide(*J6) mechanisms are also plotted in Fig. 10. Also included herein are the theoretical lines predicted by the NabarroHerringc5) mechanism in subgrain@) as well as the Nabarro-Burdeen-Herring mechanism based on the climb of dislocations from Bardeen-Herring sources. FIG. 9. Experimental data in the region III plotted as Table 1 summarizes the parameters obtained through In jkT/DQb vs In r/a. The composite plot of the data on the different grain sizes yields a value of 3.73 & 0.17 the various diffusion-controlled creep models along with for the stress exponent. those found in the various regions in the present work. It is clear from Fig. 10 that Coble, “Superplastic” and t It is interesting to note that in the superplastic region m Pb-Sn eutectic the deformation parameters K, 7t and m were Climb mechanisms operate in the regions I, II and found to be 259, 1.95 and 1.79”s’ compared to the present III respectively. In addition the contribution to values of 302, 1.99 and 1.69 for Zn-22 Al. I

I

VAIDYA

et al.:

TABLE 1. Creep parameters

DEFORMATIOS

MECHANISMS

IX

SUPERPLASTIC

1623

Zn-22dl

CL,m, n and -4 in t,he empirical equation

g& = A($)”(g)’ (gy obtained Mechanism

in the present experiments

by various diffusional creep t,heories rl

?%

m

a

Region I Region II Regio? III

and those predicted

2,50 f 0,32 1,69 5 0,29 0

087 & 0,12 l,QQ + 0,15 3,73 & 0,17

55 + 25 3y2sq216 I,36 io;B; i s 10’

2

1

21

Nabarro-Herring

1

Coble

0

3

1

160

Superplastic

0

2

2

200

Grain-BoundarySliding Climb

0 1

1 0

2 4

6 6 x 10’

: 1

0 o* 2t

3”

;$

::

Glide Nabarro-Subgrain Nabarro-BardeenHerring

: 5

* With 6/6 = 0.1(7/G), here 6 = mean aubgrain diameter. t With d = 6 = mean subgrain diameter, here c? is independent 2 Assuming D, = D,, here D, = dislocation core diffusivity.

fi1* 12’ ” 1f?r(hl4O/n7) 7,4 x 10-e

Reference Present study on Zn-22Al Nabarro’@’ Herring’1o1 Coble’ll’ 1Ball and Hutchisont5’ Langdon’ p31 Bird et al.“’ Weertman’*’ Bird et al.“’ Murty ef .1.(x6’ NabarrolP5) 1

of the applied stress.“*)

tat&e ReZation Betweea Properties and ~~crostract~re, the deformation-rats in Zn-22 Al of the other edited by D. G. BRAXDON and A. ROSEN, p. 255. Israel mechanisms which may simultaneously be operating University Press (1569). Sci. J. 3, 1 (1565). 5. A. BALL and M. M. HUTCHISON, 2CfetaE is negligible in the stress range from 5 x lo-‘G to 6. E. W. HART, Acta Met. 15, 1545 (1567). 5 x 104G. Even though the predictions based on 7. D. H. AVERY and W. A. BACKOFES, Trans. ASIII, 58,551 (1565). Ball-Hutchison model agree quantitatively with the * Phy8. 26, 1213 (1555). 8. J. WEEB!rXAN, J. a&. ex~rimen~l results in the superplastic region, 5. F. R. N. NABARRO, Rept. of conf. on the Strength of So&da, p. 76. The Physical Society (1948). microstructural evidence argues against such a model 10. C. HERRING, J. appl. Phys. 21,437 (1550). and it appears thus that there exist,s at present no 11. R. L. COBLE, J. appl. Phys. 54, 1675 (1563). completely satisfactory theory of superplastic de- 12. C. M. PACKER and 0. D. SHERBY, Trans. AS2If 00, 21 (1567). formation. 13. R. C. GIFKIXS, J. In&. dletals 95, 373 (1967). ACKNOWLEDGEMENTS

This work was supported by the United St.ates Atomic Energy Commission through the Inorganic Materials Research Division of the Lawrence Berkeley Laboratory of the University of California, Berkeley. One of the authors (KLM) is thankful to Professor J. W. Morris, Jr. for his interest in the present work and for a critical reading of the manuscript. Acknowledgments are due to Mrs. E. Burns for preparing the manuscript. MLV wishes to acknowledge the KanpurIndo-American Programme under USAID for financial support. REFERENCES 1. E. E. UNDERWOOD, J. Metala 14, 514 (1562). 2. R. H. JOHNSOX, Metal Mater. 4, 115 (1970). 3. G. J. DAVIES, J. W. EDIXGTON, C. P. CUTLER and Ii, A. PADMANABFKAN, J. Mat. Sci. 5, 1051 (1571). 4. J. E. RIRD, il. K. MUXL~ERJEEancl J. E. DORX, &anti-

5

14. R. C. GIFKINS, J. Am. Ceram. Sot. 51, 65 (1568). 15. R. R. VANDERVROOT, A. Ii. MC~HERJEE and J. E. DORX, Traras. ASM 59,530 (1566). 16. K. LINQA MURTY, F. A. MOHAXED and J. E. DORK, Scte Met. QQ.1009 (15721. and J. E. DORS, Acta 17. D. M. S&WAR~Z, J: B. MITCHELL Met. 15, 485 (1567). 18. G. SRIRN, E. S. WAJDA and H. B. HUNTINGTOS. dcta Met. 1. 513 (1553). 19. J. J. SPOKA$ and C. P. SLIGHTER, Whys. Rev. 113, 1462 (1965): also T. S. Lusnv and J. F. >lURDOCS, J. appl. Phys. 88, 1671 (1562). 20. E. S. WAJDA, Acta Met. 2, 184 (1954). A. HASSNER, Isotopenpra& 5, 148 (1565). fi: R. B. NICHOLSON, m the International Materials Sym. posium, University of California. Berkeley ( 197 1). 23. T. G. LANODON, Phil. Hag. 22, 685 (1570). 24. D. J. DINOLEY. Scanning Elect~os Mieroacopy Conference, p. 325. Chicago (1570). 25. K. LINDA MURTY, D. GRIVAS and J. W. MORRIS, JR., Deformation characterlstlcs of superplest,tc Ph-Sn eutectio, L.B.L. Report, University of l’ahfornia (1572), to be published. 26. F. R. N. NABARRO, Phil. .&fag. 16,231 (1567).