Deformation mechanisms in h.c.p. metals at elevated temperatures—II. Creep behavior of a Mg-0.8% Al solid solution alloy

Deformation mechanisms in h.c.p. metals at elevated temperatures—II. Creep behavior of a Mg-0.8% Al solid solution alloy

ACU mrrdl. OOOI-6160.82 Vol. 30. pp. I I57 to 1170. 1982 DEFORMATION MECHANISMS IN H.C.P. METALS ELEVATED TEMPERATURES-II. CREEP BEHAVIOR Mg-OX”,/...

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.ACU mrrdl.

OOOI-6160.82

Vol. 30. pp. I I57 to 1170. 1982

DEFORMATION MECHANISMS IN H.C.P. METALS ELEVATED TEMPERATURES-II. CREEP BEHAVIOR Mg-OX”,/, Al SOLID SOLUTION ALLOY SURESH

061147-14$03.00,0

CopyrIght C 1981Pergamon Press Ltd

Printed in Great Brltaln. All nghts reserved

S. VAGARALIt

and TEREXCE

AT OF A

G. LANGDOS

Departments of Materials Science and Mechanical Engineering. University of Southern California. Los Angeles. CA 90007. U.S.;\. (Received

13 Augur

1981;

in rerisedfornl

9 December

I9YI)

Abstract-Experiments were conducted to determine the creep behavior of a 5lg-0.8”” Al solid solution alloy over the temperature range from 473 to 810 K. The results show the occurrence of three different mechanisms, with the creep process dependent on the testing temperature and stress level. In the lower temperature range. up to -600-750 K depending on the stress. the behavior divides into IWOregions: (i) at the lower normalized stresses, the activation energy for creep is _ 140 k 10 kJ mole-‘. there is a very small or no measurable instantaneous strain, there is a very brief normal or inverted primary stage of creep, the stress exponent is s 3.0. there is extensive basal slip. and the substructure consists of a random distribution of dislocations; (ii) at the higher normalized stresses. the activation energy for creep is _ 140 k IO kJ mole-‘, there is a measurable instantaneous strain. there is an extensive normal primary stage, the stress exponent is -6.0. and the substructure consists of well-defined subgrains. The data are consistent with viscous glide at the lower stresses (class A behavior) and a transition to dislocation climb at the higher stresses when the dislocations break away from their solute atmospheres. From measurements of the critical break-away stress, the solute-dislocation binding energy is estimated as -0.14 k 0.03 eV. In the higher temperature range. above -600-750 K depending on the stress, there is a measurable instantaneous strain, a normal primary stage of creep, the activation energy is -230 + 15 kJ mole-’ and decreases with increasing stress, the stress exponent is -4.0. and there is extensive non-basal slip. This behavior is consistent with the cross-slip of dislocations from the basal to the prismatic planes. and the constriction energy is estimated as . 160 k 10 kJ mole-‘. RbumGNous avons &udie experimentalement le fluage d’une solution solide Mg-0.8”; AI entre 473 et 810 K. Nos risultats ont mis en ividence trois mecanismes diffkrents. dont I’activite dipend de la temperature de I’essai et du niveau de la contrainte. Aux basses tempkratures. jusqu’h 600-750 K er.viron selon la contrainte, on observe deux domaines: (i) pour les contraintes normalisies Ies plus faibles, I’energie &activation du fluage est de i’ordre de 140 2 10 kJ mole- ‘. il y a une diformation instantanee trts petite ou non mesurable, un tr& bref stade primaire normal ou inversk, I‘exposant de la contrainte est de I’ordre de 3,0, le glissement basal est tr& actif et la sous-structure consiste en une rkpartition aleatoire des dislocations; (ii) pour des contraintes normalisCes suptrieures. I’energie &activation du fluage est de l:ordre de 140 5 10 kJ mole- ‘, la d&formation instantanke est mesurable, il y a un large stade primaire normal. I’exposant de la contrainte est de I’ordre de 6,0 et la sous-structure consiste en sous-grains bien pcfinis. Les r&hats sont en accord avec un glissement visqueux pour les faibles contraintes (comportement de classe A) et une transition vers une montee des dislocations aux contraintes plus fortes, lorsque les dislocations se detachent de leurs nuages de solutC. Nous avons estime I’energie de liaison solut&dislocation g 0.14 k 0.03 eV. B partir de mesures de la contrainte critique de dtcrochement. Pour les temperatures les plus Clevkes, au-dessus de 6W750 K selon la contrainte. la diformation instantanke est mesurable, il y a un stade primaire normal, l’tnergie d’activation est de I’ordre de 230 k 1’5kJ mole-’ et elle dtcroit lorsqu’on augmente la contrainte. I’exposant de la contrainte est de i’ordre de 4.0 et le glissement non-basal est trts actif. Ce comportement est cohCrent avec le glissement d&G des dislocations du plan de base dans les plans prismatiques; I’inergie de constriction est estimCe & 160 + 10 kJ mole-’ environ. Zusammenfassung-Das Kriechverhalten der Mischkristall-Le_pierung Mg-0.8”b Al wurde im Temperaturbereich 473 bis 810 K experimentell untersucht. Die Ergebmsse zeigen. daB drei verschiedene Mechanismen auftreten, .bei denen der Kriechprozess von der Versuchstemperatur und der Spannungshiihe abhiingt. Bei niedriger Temperatur (bis -750 K je nach Spannung) ist das Verhalten in zwei Bereiche aufgeteilt: (i) bei geringen normalisierten Spannungen betrtigt die Kriechaktivierungs-energie _ 140 + 10 kJ mole-‘. eine unmittelbare Dehnung ist sehr klein oder nicht meDbar. eine erste Stufe primIren Kriechens ist sehr klein und normal oder invertiert. der Spannungsexponent betrggt -3,0. starke Basisgleitung tritt auf und die Substruktur ist aus zuftillig verteilten Versetzungen aufgebaut; (ii) bei hiiheren normalisierten Spannungen betrlgt die Aktivierungsenergie _ 140 k 10 kJ mole-‘, die unmittelbare Dehnung ist meobar, ein ausgeprlgter normaler Primzrgleitbereich tritt auf. der Spannungsexponent betrlgt -6.0 und die Substruktur besteht in wohldefinierten Subkorngrenzen. Die

t Now at Department of Chemical and Nuclear Engineering, University of California, Santa Barbara, CA 93106. U.S.A. 1157

1158

VAGARALI

AS0

LANGDON:

DEFORiMATION

IN H.C.P. METALS-II

Ergebn,isse sind konsistent mit viskosem Cleiten bei niedrigen Spannunpen (Klasse-A-Verbalten) und einem Lbergang zu Versetzungsklettern bei hiiheren Spannungen, wenn sich die Versetzungen van ihren V~runreinigungs~olken IosreiBen. Aus der kritischen Losrei~spannung WI sich die ~indungsenergie zu -0.1-t z 0.03 eV abschltzen. Bei hoher Temperatut. oberhalb 600-750 K je nach Spannuna. tritt eine mel3bare unmittelbare Dehnung auf. ein normales primlres Kriechen. Die AktivierungseneTgie betrlgt 5 230 I 15 kJ mole-’ und wird geringer mit ansteigender Spannung. der Spannungsexponent ist -4.0 und ausgepragte Nicht-Basisglitung liegt var. Dieses Verhalten ist vertrlglich mit der Quergleitung von Verserzunoen aus der Basis- in orismatische Ebenen. Die Einschniirenergie IPBt sich zu _ 160 + 10 kJ mol;- ’ abschLtzen.

1. INTRODUCTION It is now recognized that the creep behavior of metallic solid sofution alloys divides into two distinct classes [l. 21. The first type, termed class M (Metal type) [3], has characteristics which are similar to pure metals, inciuding a stress exponent close to 5, a normal primary stage of creep, and the formation of an internal subgrain structure. The second type, termed class A (Alloy type)[3], behaves differently to pure metals, with a stress exponent close to 3, either an almost instantaneous steady-state behavior or a very brief normal or inverted primary stage, and the formation of a substructure consisting of an essentially uniform distribution of dislocations. Class M behavior is generally attributed to a recovery process involving dislocation climb, whereas class A behavior is attributed to a viscous drag process in which the glide of dislocations is restricted due to the presence of solute atom atmospheres. Although these two types of behavior are well supported by experimental results on several f.c.c. solid solution alloys, a lack of detailed creep data has so far prevented a similar approach in other crystal systems. The present work was designed to provide information on the creep behavior of an h.c.p. solid solution alloy. In general, the creep properties of h.c.p. metals are rather poorly documented at the present time, despite the widespread use of Mg-based alloys in nuclear reactors. An earlier report, designated part I [4]. described the results obtained from a detailed investigation of the high temperature mechanical properties of pure magnesium, and this paper describes a similar investigation of the Mg-O.8 wt% Al solid solution alloy. This alloy, known as ‘Magnox AL80,’ is used extensively as a canning material in nuclear fuel elements.? A very brief review of the published information on creep of the Mg-O.S% Al alloy is given in the following section, and the experimental program and results are described in detail in the subsequent sections.

2. CREEP

BEHAVIOR

OF Mg-W%

Al

Harris and Jones [7] prepared a detailed compilation of much of the early creep data obtained on Mg-O.SXAl in the nuclear canning program. From

* Detailed reviews of the development and performance of magnox in reactor fuel elements have been given by Eidred et ni. ES] and Harris [IS].

this analysis, it was concluded that, over the temperature range of about 400 to 800 K, the activation energy for creep (- 134 kJ mole-‘) is essentially equal to the value for lattice self-diffusion in pure magnesium ( z I35 kJ mole- t [8]) at all stresses. and the stress exponent, n, decreases from -7.0 at high stresses (a 2 154MPa) to -3.5 at intermediate stresses (0.6 MPa 5 0 5 15.4MPa) and to _ 1.0-1.5 at low stresses (a 5 0.6 MPa). The creep regime with n 2 3.5 was tentatively attributed to viscous glide behavior (class A), and the low stress regime uith n z 1.0-1.5 was attributed to Nabarro-Herring diffusional creep [9, IO]. More recently, it was concluded that Mg-0.83, Al deforms by Nabarro-Herring diffusional creep at low stresses and temperatures above _ 650 K f - 0.7 r,. where r, is the absolute melting pointt and by Coble diffusional creep [l I] at low stresses and temperatures below -650 K (121. However, these extensive compilations of data are based primarily on tests performed in the homoiogous temperature range of -0.5-0.7 r, and no evidence has been presented to indicate a change in the deformation mechanism in Mg-O.87; Al at reasonably high stresses and temperatures above -0.7 I,. By contrast, it was shown in part I(43 that the creep behavior of polycrystalline magnesium at stresses above the diffusional creep regime may be divided into two distinct regions: at temperatures up to + 60&750 K depending on the stress level, the activation energy is T 135 + 10 kf mole-’ and is equal to the value for lattice self-diffusion in magnesium, the stress exponent is -5.2, there is extensive basal slip, and the behavior is consistent with control by disloabove cation climb; whereas at temperatures -600-750 K, the activation energy increases to _ 220 f 10 kJ mole-’ and depends on the stress level, the stress exponent is -6.0, there is extensive non-basal slip, and the behavior is consistent with the cross-slip of dislocations from the basal to the prismatic planes. To date, a similar change in mechanism with increasing temperature has not been reported in any h.c.p. solid solution alloy. Accordingly, the present experiments were undertaken with two objectives: first, to provide a direct comparison between the behavior of a magnesium solid solution alloy and the pure metal; second, to investigate whether there is also a change in the deformation mechanism in Mg-O.87; Al at high temperatures.

VAGARALI 3. EXPERIYvIENTAL

ASD LANGDON:

DEFORMATION

PROCEDURE

Rods of the Mg-O.8 wt’, XI alloy. 14.3 mm in diameter. were obtained from Magnesium Elektron. Inc. The rods were produced by a two-stage hot extrusion and a semi-quantitative spectrographic process, analysis is given in Table 1. Tensile specimens were machined from the rods with gauge lengths of either 19.1 mm for testing on an Instron machine or 25.4mm for creep testing under conditions of constant stress. Prior to testing, each specimen was annealed at 513 K for 4 hours under a steady flow of argon gas of 99.99”, purity to give an average grain size, ti. of 240 k 15 {tm. For metallographic observations by optical microscopy, some specimens were also prepared with two parallel. flat, elsctropolished surfaces. The specimens were tested either on an Instron machine operating at a constant rate of cross-head displacement or on a constant stress creep machine. The tests were performed in air at temperatures up to 673 K and in argon gas of 99.999”); purity at higher temperatures. The testing temperature was maintained constant to + 1 K and the strain was continuously monitored in the creep experiments to an accuracy of kj x IO-“. Full details of the experimental conditions. and a schematic diagram of the creep testing facility, were given in part I [4]. Following creep testing, several specimens were cooled rapidly under load for substructural examination by transmission electron microscopy. Sections having a thickness of -0.5 mm were cut from the gauge length using a precision wafering saw, and these sections were carefully ground to a thickness of -0.1 mm using ISO. 320, 400 and 600 grit silicon carbide papers. Each section was electropolished using a stainless steel cathode and a continuously-agitated solution of 1 part nitric acid and 2 parts methanol. The polishing temperature was maintained below -4O’C by immersing the bath in a mixture of dry ice and acetone. Thin foils, obtained by the window technique. were examined at up to 125 kV. 4. EXPERI&lENTAL 4.1

IN H.C.P.

1159

METALS-II

Table 1. Semi-quantitative spectrographic analysis of \lg-O.V,~ Al

Element

ppm

AI Be

5300 60

Ca Fe

cj0 30 30 <80 loo

Mn Si Zn

instantaneous strain and an extensive normal primary stage. The various types of creep curve are illustrated by the plots shown in Fig. I of the logarithmic strain rate, h, vs the total strain, E, for tests conducted at four different stress levels at an absolute temperature. x of 573 K. At the two lowest levels of applied stress. cr, the primary stage is very brief and either inverted (8.2 MPa) or normal (12.0 MPa). As the stress level is increased, the normal primary stage extends to higher strains (15.6 MPa), until ultimately it occurs over strain ranges of _ 157; (25.2 MPa). The very brief primary stage obtained on the Mg-0.8~,;\I alloy at the lower stress levels contrasts with the observations reported earlier for pure magnesium where there was always an extensive normal primary stage except at high temperatures and very low stresses ( -2 MPa at 773 K) in the diffusional creep regime [4].+ Essentially similar results were obtained with Mg-O.dS;Al over the entire temperature range, with the exception that there was a measurable instantaneous strain and no evidence for an inverted primary stage at high temperatures, even at the lowest stresses used experimentally.

Id2

I

I

I

I

I

RESULTS

Simpe ofthe creep curves

Creep tests were conducted over the temperature range from 473 to 803 K. At the lower temperatures and low stresses, the shape of the creep curves was typical of class A behavior: there was a very small or no measurable instantaneous strain on application of the load. and then a very brief primary stage which preceded steady-state flow. The primary stage was inverted at the very lowest stresses (i.e. the creep rate increased to the steady-state value). At the lower temperatures and high stresses, there was a measurable + Compare. for example. the plots shown in Fig. 1 for Mg-0.8”, Al with the corresponding plots shown in Fig. 2 of part I [4] for pure magnesium at the same testing temperature.

.ul

Fig.

I. Strain rate vs strain for specimens tested at 573 K at four different

stress levels.

1160

VAGARALI

AND

LANGDON:

DEFORMATION

IN H.C.P. METALS-II

4.3 Temperature dependence of the creep rate Temperature cycling tests were performed at constant stresses over the temperature range from 473 to 803 K. As in the earlier work on pure magnesium [4], the activation energy, Q, was estimated from the relationship

Q-

Fig. 2. Strain rate YS strain showing the effect of stress cycling at 623 K. 4.2 Stress dependence of the creep rate

Isothermal stress cycling tests were performed in the temperature range from 523 to 803 K. X typical result is shown in Fig. 2 for a testing temperature of 623 K and stresses from 4.20 to 9.80 ivlPa. Using this procedure, the steady-state creep rates were determined at several different stresses. and it was found that, as indicated in Fig. 2, the measured steady-state rate was independent of the cycling history. The results from a number of tests conducted at different temperatures are shown in Fig. 3, logarithmically plotted as steady-state strain rate, .& vs applied stress. cr. The data show that there is a significant variation in the stress exponent with stress and temperature. In the low temperature range, from 523 to 623 K (open points in Fig. 3), the datum points lie on two straight lines with slopes of either -3.0 at the lower stresses or -6.0 at the higher stresses, and the transition stress delineating these two regions decreases with increasing temperature. In the high temperature range, from 673 to 803 K (closed points in Fig. 3), the stress exponent is -4.0. In practice, there is some scatter in the experimental data, and there is an indication of a slightly higher stress exponent at the two highest testing temperatures of 773 and SO3K. This scatter is probably due to concurrent grain growth during the test, because of the close proximity to the annealing temperature of 813 K. Concurrent grain growth tends to introduce an essentially continuous decrease in the measured creep rate, as illustrated in Fig. 4 for two tests conducted at 773 K. Since there was relatively minor primary creep under these testing conditions at very low stress levels, the decreasing creep rate was unambiguously associated with grain coarsening. Furthermore, the extent of grain growth was substantial in the slowest tests at 773 and 803 K: for example, the specimen tested at 773 K with 0 = 1.65 MPa exhibited an initial grain size of z 24O~tm and a final grain size of _ 1500 pm at E r 2OS,. In an attempt to avoid these problems, the datum points shown in Fig. 3 at the two highest temperatures were recorded at low total strains.

R In(i2 G;- ’ T2$,G1-

’ T,)

(1)

(Tz - T,);T,T,

where R is the gas constant. tt and i2 are the strain rates immediately before and after a small change in temperature, AT from T, to T2. and G, and G3 are the values of the shear modulus at temperatures T, and T2, respectively. The shear modulus at each absolute temperature, T; was obtained from the relationship for pure magnesium [13]: G = (1.92 x 10” - 5.6 T)MPa.

(2)

Using this procedure, it was found that the activation energy was reasonably constant in the temperature range from _ 473 to _ 623 K, but there was an increase in the activation energy at the higher testing temperatures. A typical temperature cycling sequence at the lower temperatures is shown in Fig. 5: the temperature was changed periodically by about 25’ within the steady-state region, and the values of Q were estimated from equation (1). The results of these experiments are shown in Fig. 6, plotted as the average value of Q obtained in each test against the mean testing temperature, ‘I: This

1

I,,,111

Mg-0.6%AI d = 240pm

0523

-

4.0 0 l

8 A

623 673 723 773

_

5 .r)

lb L

1

toI IO

I

1.0 Q

MPa)

Fig. 3. Steady-state strain rate vs stress for specimens tested over a range of temperatures from 523 to 803 K.

inc:easing stress in the higher temperature range. Tunis trend u;fj confirmed by preparing Fig. 8 irom a series of measmements of Q oier a range of stresses at 750 and 773 K.

r 0

IO-’ 0

(MPU)

I.65

2.50

0

I

I

4

e

I

12

I

& (Y.!

I6

I

I

20

24

I

23

Fig. 4. Strain rate YSstrain showing the effect of concurrent grain growth during two tests at 773 IL

shows that the activation energy is _ I40 i 10 kJ mole-’ at temperatures from about 473 to 623 K. but the activation energy increases at higher temperatures up to -22Oi ljkJmole_’ at SOOK. There is considerable experimental scatter at the highest temperatures. and this is attributed to the problems of concurrent grain growth. To confirm the increase in activation energy with increasing temperature, a single specimen was subjected to a series of incremental temperature increases, each of about 2S”, over the temperature range from 593 to 743 K at a stress of 6.4 MPa. The result is shown in Fig. 7, and the estimated values of Q are consistent with the data shown in Fig. 6. Ciose inspection of the results indicated that the activation energy was independent of stress in the lower temperature range but that. as noted earlier for pure magnesium [3], the value of Q decreased with plot

4.4.1 Oprid microscap,~. Very extensive basal slip \vas kisibls on the polished surfaces of the specimens tested at tem~ratures up to 623 K. An exampie is shown in Fig. 3 for a specimen deformed to a strain of 6”, at 573 K with a stress of S.2 XlPa. There was also evidence of grain fragmentation at these lower temperatures, as indicated in Fig. 9 by the abrupt changes in the direction of the basal slip lines and or by the sharp changes in contrast within a single grain. At the higher temperatures. above about 723 K, there was very extensive non-basal slip, as shown in Fig. 10 for a specimen tested to a strain of lo”,, at 773 K under a stress of 8.0 MPa. The transition from predominantly basal to nonbasal slip in Mg-O.S”, Al with increasing temperature is similar to earlier observations on pure magnesium [3. l-t]. 1.42 ~rffns~il~.~.~i~~z eircrron micrOscq_v. Several specimens were examined by transmission electron microscopy. In the low temperature regime. below ~623 K, and at lower stresses where n 1 3.0. there was a random distrib~ltion of distocations and no evidence for the formation of subgrain boundaries. .An example in this region is shown in

Fig. 11 for a specimen

tested to a

strain

of IO”, at 573 K under a stress of 11.5 MPa. However. at high stress levels at the same testing temperature, in the region where n = 6.0. there was clear

evidence for subgrain example

formation

under these conditions

during is shown

creep.

r\n

in

Fig. I2 for a specimen tested to a strain of W& at 573 K at a stress of 25.2 MPa. In the high temperature regime, above 2773 K, there were some isolated but well-defined sub-boun-

daries and many free dislocations. boundary

formation

is shown

Xn example

of sub-

in Fig. 13 for a speci-

kJ

Fig. 5. Strain rate vs strain at 8.4 MPa showing the determination of the activation energy from abrupt changes in temperature.

Fig. 6. Averaqs value of the activation energy ior creep YS the mean testing temperature in temperature c?_clingtests.

116’

to-

10

IOT

” .IJ

Id

i IO

Fig. 9. Photomicrograph oia specimen test-,d to a strain of 6”,> at 573 K and 3.2 \lPa. showing cxtensiLc basal shp 2nd grain fragmentation.

j I

I AT325

26

23

25

26

25

M&l - 0 8 % Al

IO

I 20

t I5

I IO

I 5

c =6.4tdPo d =240~lm I I 25 30

E (%I

Fig. 7. Strain rate vs strain shouing the increase in activation energy with increasing temperature for a specimen tcstcd at 6.-i XI Pa.

men tested to a strain of lo”,, at of 2.5 UPa.

773 K under

a

stress

Isothermal tensile tests were performed at a nominal strain rate of 2.2 x 10-Js-’ at the higher temperatures from 675 to 800 K. The results are shown in Fig. 14, plotted as true stress vs true plastic 300

I

I

I

I

strain. E,, for four different test temperatures. ‘As in pure magnesium C-l], these curves shon- that there is negligible strain hardening at temperatures above _ 700 K. and a plateau or constant Ro\t stress is then attained at plastic strains of _ Zoo, Using these stressstrain curves. Fig. 15 was constructed to show the variation of How stress with temperature at true plastic strains of I”,,. 2”,. and at the plateau stress. 4.6 Tire wriwrim

colrrrwfor

The activation volume for creep was determined by stress change experiments at constant temperature. in which the stress was decreased by small increments (of the order of 0.0%0.15 o) at regular strain intervals and the creep curve was recorded on a hi_ehly espanded scale. The apparent activation volume. I’*, was calculated from the relationship (3)

I

where f is the shear strain stress ( =CT21.

Mq-0.8%

0

creep

rate and r is the shear

Al

d =240pm CO-

Ol

0

T(K) D

750

0

773

/

I

I

I

I

I

2

4

6

8

IO

12

o-

(MB)

Fig. 3. Activation energy for creep vs stress at high temperatures. showing the incrcass in activation energy with decrease

in

stress.

Fig. IO. Photomicrograph of a specimen tested to a strain of IO”, at 773 K and 8.0 >LfPa. showing extensive non-basal . s11p

Fig. Ii. Transmission &ctron mi;ropraph ol a specimen tested !J ;I strain of itI”, at 573 K and 1 I.5 SlPa. jho\vinp :! random distribution ol di&xations.

The variation of I” with strain is shown in Fig. 16 for tests under two different conditions in the high temperature regime: k‘* is expressed in units of h’ where h is the Burgers vector (3.2 x IO-‘” m for mapnesium). The results show that I.* is essentially independent of strain at the lower stresses. Lvhereas at the higher stresses there is a gradual decrease in Y* with increasing strain to a constant value in the steadystate region of creep. The \alues of I’* were deterinined under stead!state conditions over a temperature range from 73 to 810 K. and the results are shoan in Fig. 17. These data show that V* is essentialI>- independent of temperature. but there is a sharp drop in the value of I’* with increasing stress from > 15OOh’ at g < 3 MPa to 10 MPa. The present results on Mg-U.Y”,Al. including the magnitudes of L’*. are similar to earlier observations on polycrystalline Mg [4] and Mg single crystals oriented for prismatic slip[lj].

5. DISCCSSIOZ

.An important jimilaritk between the results on Mg-OY,, AI and those reported for pure magnesium in part I [1] is the increase in activation energy with increasing temperature (Figs 6 and 7). This trend is typical of h.c.p. metals. including Cd [16]. Zn [17] and Zr [i 31. The increase in xtibation energy may be further contirmed by rcpiotting the data in Fig. 3 in a form which is normalized through the standard relationship fdr high temperature creep

where k is Boltzmann‘s constant. D, is a frequenq factor. and .-i, F and n are constants. Using equation (41, the data acre normalized to a temperature of

d=240ym i = 2.2~10-4sT(K)

A---I 5

0 D

675 72i

A

773

0

800

I IO

Ep (Y.)

Fig. il. Transmission

electron micrograph of a specimen at 573 K and 15.1 XlPa showing subgain formatlon.

teskzd to a strain of l5’,

Fig. 14. True stress bs true plastic strain for specimens deformed at a nominal strain rate of 2.2 x 1iY’ S- ’ at temperatu:ss in the range of 675 to 500 I;.

!

I

mj - 0 a-k A:

d=

241,

yin

i = 2.2‘10-4s-’

0

600

700

Plolcou

900

900

T :lci

Fig. 15.Flow stress vs tsmpcmture at true I”,, and 2”,, and at the plateau

plastic stress.

str;fins

ot’

523 K by plotting the logarithmic normalized strain rate. E(G, G5,,i”-‘(7Y523t LS the reciprocal of the absolute temperature. 1,‘7: The resutt is shown in Fig. IS. covering stresses in the range from 3.0 to 32.0 XIPa. This plot therefore confirms that. over the ranges of stress and temperature covered esperimentali~. the creep behavior of Mg--OX’,, Al is controlled by two ditlerent mechanisms upcrating independently [lo]. At low temperatures. the activation energ! is constant and equal to I40 r IO kJ mole-‘. Hoivever. there is a transition to a new mechanism at the higher temperatures. and this transition occurs over the temperature range from 600

to ‘50 K such that the :ransition r&es piace at hiz&er temperatures as the stress level is decreased_ fn the hiyh temperature region. the activation energ>- is of the order of 230 5 I5 kJ mole-‘. but there is a slight dependence on stress which is risible in Fig. lS because the four lines in this region (for stresses from 3.0 to lO.O\fPal are not quite parallel. In fact. the slopes of the lines increase slightly with decreasing stress. and this is consistent with the increase in Q uith dscrea4ny stress shown in Fig. 8. The experimental results therefore divide into two distinct types of behavior, as under: I 1I .At the lowr temperatures. up to - 600-750 K depending on the stress level. there is a very small or no measurable instantaneous strain at low stresses. thw is a bet-h brief normal or inverted primary stage preceding stead>-stat? tiow at the lo\\tr stresses and an cstensi\s normal primary stage at the higher stresses. the xtivation energy is constant and equal to I-IO f 10 kJ mole-‘, the stress exponent is -2.0 but increases to -6.0 at high stresses. there is very extensive basal slip. and the substructure consists either of a random dtstribution oidislocations when II 1 3.0 or of Lvell-detincd subprains u-hen N L 6.0. (2) At the higher temperatures. above - 600-750 K depending on the stress level. there is a measurable instantaneous strain. there is a short normal primary stage of creep. the activation energy is of the order of ‘30 2 IS kJ mole-’ and decreases slightly with an increase in stress level. the stress exponent is -1.0. there is ebidsnce for very extensive non-basal slip, and the substructure consists of some isolated but wlldefmsd sub-boundaries and many free dtslocations. The deformation mechanisms occurring in Mg-OY, Al in these t\vo regions of fiow are considered in the following sections.

2ooo1 zax

/

I

Mg-08% PI

-I

d ‘24Op.m Hq-0

8% PI a

i(K) 723

0 0

773 810

f

d*240rm ISOO-

-i

n e

IOOO-

;

500-

i

01

I

I

0

IO

5 c

Fig.

16. .Appar:nt acti\atian volume Yj strain ferent experimental conditions.

for two dif-

Fig.

17. .Appar:nt

activation tures irnm

-I 15

(MPo)

tolumc vs SITCSSfor tempera73 to SIO K.

VAGARALI

AND

LANGDON:

DEFORMATION

T (KI -1 IO-,

800

750 (

700 I

650 I

6co 1

5% I Mq-0.0%

5y Al

d 324Opm Q MPo)

Id’-

0 =230tl5

Q’l40tlO

LJ moi’

0 + * . 0 8 0 0

3.0 5.0 7.0 10.0 IS.0 20.0 25.0 32.0

kJ ml-’

Id/T

(K’)

Fig. 18. Normalized strain rate vs the reciprocal of absolute temperature for stress levels from 3.0 to 32.0 MPa.

5.2 Lower temperature behavior Depending on the level of the applied stress, this type of behavior extends from -473 to - 750 K. The results from the temperature cycling tests

shown in Fig. 6 and the normalized creep data plotted in Fig. 18 are mutually consistent in this region, and they both indicate an activation energy which is independent of stress and equal to - 140 + 10 kJ mole-‘. This value is very close to the activation energy of _ 135 k 10 kJ mole-i reported earlier for the creep of pure magnesium over the same temperature range [4]. and also to the value of c 134 kJ mole- * obtained by Harris and Jones [7] from an analysis of creep data for Mg-O.8%Al. It is also similar to the activation energies for both lattice self-diffusion in magnesium ( - 135 kJ mole- ’ [83) and the chemical interdiffusivity of aluminum solute atoms in magnesium (- 143 k 10 kJ mole-’ [ZO]). The transition in stress exponent from -3.0 at low

t Reference to Fig. 3 shows that the transition stress of 15.4 MPa reported by Harris and Jones [‘I] is within the range of transition stresses observed at temperatures from 513 to 623 K. $ Nabarro-Herring diffusional creep [9. IO] was also observed in pure magnesium in part I[?]. with a grain size of 80pm at a temperature of 773 K and stresses below -2.5 MPa. This testing condition is on the lower limit of the present experiments, and the larger grain size used in the present work (24O~m) would tend to displace the upper limiting stress for diffusional creep to even lower values.

IN H.C.P. METALS-II

1165

stresses to -6.0 at high stresses suggests the occurrence of two creep mechanisms operating independently. These exponents are quite similar to the values of s 3.5 and _ 7.0 reported by Harris and Jones [7] for creep of Mg-0.8y/;,Al at intermediate and high stresses, respectively. However, the present results indicate that the transition stress between these two regions decreases slightly with increasing temperature. as shown in Fig. 3, whereas Harris and Jones [7] concluded that the transition occurred at 15.4 MPa irrespective of the operating temperaturet. In addition. Harris and Jones 173 reported Nabarro-Herring diffusional creep [9, lo] at c 5 0.6 MPa but, as indicated in Fig. 3, this stress level is significantly lower than the lowest stress used in the present experiments:. The regions with n E 3.0 and n = 6.0 are now considered separately. 5.2.1 Stress regime with n 2 3.0. The experimental results in the region where n c 3.0 provide strong evidence that creep of the Mg-O.80/oAl solid solution alloy occurs by a viscous glide process as in class A behavior. The various points of agreement with this mechanism include not only the stress exponent of -3.0 but also the lack of a significant instantaneous strain upon loading, the very brief normal or inverted primary stages of creep (Fig. l), and the internal observations of a uniform distribution of dislocations and a lack of subgrain formation (Fig. 11). To examine this mechanism in more detail, it is necessary to consider the three models which have been proposed for viscous glide in solid solution alloys. In the theory of Weertman [21], it is assumed that edge dislocations pile up due to the mutual interaction between dislocations of opposite sign on adjacent but parallel slip planes. Ultimately,the resulting back stress stops the operation of the dislocation sources. and this stress is relieved, so that another dislocation loop is generated at each source, by the climbing together and annihilation of the leading edge dislocations in each pair of pile-ups. Thus, the motion of dislocations occurs as sequential glide and climb processes, and the slower of these two processes is the rate-controlling mechanism. In solid solution alloys when glide is slower than climb, the steady-state creep rate is given by e=

n(1 - p)aI 6A’G’

(5)

where p is Poisson’s ratio and A’ is a constant which depends on the dislocation-solute interaction controlling the glide process. When glide is restricted by the presence of solute atmospheres around the dislocations, the dislocationsolute interaction developed by Cottrell-, and Jaswon [22] leads to A, = e2cb5G’ --ET

where e is the solute-solvent

(6)

size difference, c is the

1166

VAGARALI

AND

LANGDON:

DEFORMATION

Mq-08%AI d = 240pm

I

IN H.C.P. METALS-II

assisted by the line tension of the dislocations. As subsequently developed by Bird er al. [25], this model leads to a steady-state creep rate which is given by dGb

3

( )O u

c=o.18 kT c .

(9)

Thus, the significant feature of this model is that it predicts a creep rate which is independent of the solute concentration and the solute-solvent size factor. In addition, the model applies strictly only to very dilute solute concentrations. To check the predictions of these three models, the datum points shown in Fig. 3 in the low temperature regime of 523 to 623 K (open points) were replotted in the logarithmic form of ikT/dGb vs a/G, putting e = - 0.1373 [26] and taking 0’ as the chemical interdiffusivity of aluminum in magnesium [20] : D’= 1.2 x IO-‘exp(-143,000jR~mZ lO-4

10-3

10-z

U/G

Fig. 19. Normalized strain rate versus normalized stress for temperatures from 523 to 623 K.

concentration of solute atoms, and d is the chemical interdiffusivity of the solute atoms. Putting p = 0.34 and substituting equation (6) into equation (5) gives

The theory of Takeuchi and Argon [23] is also based on the Cottrell-Jaswon interaction but in this case it is assumed that there is a homogeneous distribution of edge dislocations. By considering the rates of dislocation multiplication and annihilation, the steadystate creep rate due to dislocation glide is given by

It is interesting to note that the creep rates given by these two models [equations (7) and (8)] differ by a factor of < 3 despite significant differences in the basic assumptions incorporated into the development of the mechanisms. The third model is based on the concept, first suggested by Friedel[24], of the diffusion of solute atoms t Equations (7) and (8) contain an additional temperature term in the form of (T/G)‘: over the limited temperature range of 523-623 K, the variation in this term has a negligible effect on the positions of the theoretical lines in Fig. 19. : The similarity in behavior may be app:eciated by a comparison of Fig. 19 which plots ikvDG6 vs u/G for Mg-O.BP/;AI and Fig. 14 of part I [4] which plots akT/DGb vs o/G for pure Mg.

s-r.

(10)

The result is shown in Fig. 19, and all of the experimental points now lie on a single line of slope c 3.0 at low stresses but with an increase in slope at c/‘G 2 10e3. Figure 19 shows also the predicted creep rates for the theories of Weertman [Zl]. Friedel[24], and Takeuchi and Argon [23], as given by equations (7j, (9). and (S), respectively?, and the composite experimental data reported by Harris and Jones [7] for Mg-O.8% Al with a grain size of z 200 pm. Within the region where n 1: 3.0, the present results are in excellent agreement with the data of Harris and Jones [7], but the experimental creep rates are over an order of magnitude lower than the predictions of the three theoretical models. 5.2.2 Stress regime with n = 6.0. There is a sharp deviation from the behavior with n 1 3.0 at high stresses; the stress exponent in this region is nominally -6.0 (Fig. 3) and the activation energy is again c 140 + 10 kJ mole-’ (Fig. 18). A similar trend was reported earlier for pure magnesium [4], where n = 5.2 in the low temperature region and there was a deviation to higher values of n at o/G 2 1.3 x lo-‘. The latter results were interpreted in terms of a dislocation climb process at low stresses when n 2 5.2, and a breakdown in power-law creep at the higher stress levels. At first sight, the similarity between the present results and those reported earlier for magnesium [4] suggests that the deviation from linearity at high stresses may be due again to power-law breakdown& However, closer inspection suggests that this interpretation is incorrect for three reasons. First, Sherby and Burke [l] showed that power-law breakdown occurs at values of i/D which are very close to 10gcm-Z for a wide range of materials. For pure magnesium, D may be put equal to the value for lattice self-diffusion in magnesium [8] : D = 10e4 exp( - 135,OOO/RT)m’ s-r.

Thus,

g/D = lo9 cm-’

is

equivalent

(11) to

VAGARALI

AND

LAXGDON:

DEFORMATION

$k?Y’DGb 2 2 x 10-s at 323 K. and the latter value is

consistent with the deviation from linearity for pure magnesium shown in Fig. 14 of part I [4]. However. for the Mg-O.SP; Al alloy, this value of 2;D, when combined with the appropriate value of D’from equation (10). is equivalent to &7?fiGb c 1 x lo-* at 523 K, whereas the deviation from linearity shown in Fig. 19 occurs at normalized strain rates which are at least two orders of magnitude below this calculated value (CkT’bGb e lo-lo). Second. it has been suggested that, in solid solution alloys in which dislocation glide is restricted by the presence of solute atmospheres, there will be an upper limiting stress at which the dislocations pull away from their atmospheres [24,27]. Depending on the associated stress level, therefore, this may give rise, in solid solutions, to a transition from viscous glide to dislocation climb with increasing stress. The present results are consistent with this concept because of the marked change in substructure as the stress level is increased at a constant testing temperature. In the low stress regime, when n = 3.0. there is a uniform distribution of dislocations which is consistent with viscous glide (Fig. 11); but at high stresses, when 11= 6.0. there is subgrain formation which is consistent with dislocation climb (Fig. 12). Furthermore, although no attempt was made to take detailed measurements, the subgrains observed in the region with n : 6.0 are of the anticipated size for the experimental stresses. For example, the average subgrain size, i, is usually given by [ZS, 28) i.!‘b = <(CT/G)-’

(12)

where < 1 20. For cr = 25.2 MPa and a temperature of 573 K, as shown in Fig. 12, equation (12) is equivalent to i. z 3-4fim. Third, following the theory of Friedel[24J, the dislocations break away from their solute atmospheres at a critical breaking stress, crb,which is given by

w;c *b = Sb3kT

Ii67

IN H.C.P. METALS-II

sium, AV, = 8.2 x 10-30m3 [.?S]. so that, with p = 0.34, the value of W, is of the order of -0.21 eV (-20 kJ mole-‘). Thus, the theoretical value of Ct;, calculated from equation (14) is in reasonable agreement with the value estimated rather crudety from the experimental variation of fib with temperature. It is therefore concluded that the creep behavior of Mg-0.8% Al in the lower temperature region is consistent with viscous glide at the lower stresses when n z 3.0, but that there is a transition to control by dislocation climb at the higher stresses when the dislocations break away from their solute atmospheres. It should be noted that the nominal stress exponent of _ 6.0 at the higher stresses in Mg-O.87; Al is reasonably similar to the value of n =r 5.2 obtained in pure magnesium in the dislocation climb region C-11.In addition, the similarity in activation energy between the glide and climb regions in Mg-O.87; Al is attributed to the very small difference between the activation energies for chemical interdiffusion of aluminum solute atoms in magnesium in the glide regime (- 143 k 10 kJ mole-’ [ZO]) and lattice self-diffusion magnesium in regime in the climb ( - 135 kJ mole- ’ [S]). As in pure magnesium [a]. it is anticipated that there will be a breakdown in powerlaw behavior at even higher stress levels. 5.3 Higher temperature behavior Depending on the level of the applied stress, this type of behavior occurs at temperatures above -&JO750 K. The major features in this region are microscopic evidence for very extensive non-basal slip and an activation energy which is significantly higher than the values for either lattice self-diffusion in magnesium or the chemical interdiffusion of aluminum solute atoms in magnesium. Both the evidence of nonT (K) 22,

600

750

5:0

50,0

(13)

where &, is the binding energy between the solute atom and the dislocation. Using the data shown in Fig. 3 at the four lowest temperatures, Fig. 20 shows the transition stress, eb, between n : 3.0 and n 2 6.0 as a function of the reciprocal of temperature. The four experimental points fall on a straight line and, from equation (13). the slope of this line is equal to W,%;‘jb3k. so that the solute-dislocation binding energy is estimated as c 0.14 * 0.03 eV ( - 14 f 3 kJ mole-‘). Alternatively, the value of W, may be calculated from the theoretical expression (241 (14) where AV, is the difference in volume between the solute and solvent atom. For aluminum in magne-

1.5

1.6

1.7 1.8 103/T (K -‘I

1.9

2.0

Fig. 20. Transition stress between the stress exponents of - 3.0 and -. 6.0 vs the reciprocal of absolute temperature.

1165

VAGXR.+LI ASD LANGDON:

DEFORMATION

basal slip and the high activation energy are similar to earlier observations on pure magnesium [4]. and other points of similarity include the rapid variation of How stress with temperature (Fig. 15) and the stress dependence of the apparent activation volume for creep (Fig. 17). The behavior of pure magnesium at the higher temperatures was analyzed in terms of glide-controlled or cross-slip mechanisms for slip on the non-basal planes [4]. and a similar approach will be employed in the present analysis; a more detailed description of the various deformation processes is given in part I [4]. The glide-controlled mechanism of Gilman [29] assumes that dislocation motion is limited by lattice friction on the non-basal planes. The activation energy for this process, Q, varies with stress according to the expression Q = Qk + a/Jo

(15)

where QI, is the energy of formation of a singte kink and q is a constant. The activation energies obtained for creep by temperature cycling over the range from 723 to 800 K (Fig. 6) and those estimated from the stress cycling experiments in the higher temperature region (.Fig. IS for (r = 3.0-10.0 MPa) were plotted against the reciprocal of stress, l/a, as shown in Fig. 21. The datum points from temperature cycling reveal an essentially linear dependence on l/a at high stresses, and the slope of the line is 225/a kJ mole- ’ where Q is in MPa. Extrapolation of the line to l/g = 0 gives an activation energy for kink formation of Qlr 2 160 & 10 kJ moIe_ i. This value is very much higher than the energies usually associated with kink formation in metals (Qk z 20-40 kJ mole-’ [30] 1,so that the glidecontrolled mechanism of Gilman [29] is an unlikely process for creep of the Mg-O.8%Al solid solution alloy at high temperatures. An alternative glide-controlled mechanism, developed by Weertman [Zl). is based on the overcoming of the Peierls stress on the non-basal planes by the nucleation and propagation of a double kink. In this case, the activation energy varies linearly with stress through the expression Q = Q&l - rct,‘2rLp)

IN H.C.P.METALS-II

From Fig. 8. the experimentai activation energy at 0 = 0 is Qe T 235 f 10 kJ mole-‘. Taking G = 1.3 x 10’ MPa at 773 K. and b = b’, the value of 7p is calculated from this model as _ 5.3 x IO’ MPa. This value is unreasonable because it exceeds the shear modulus. In addition, it is possible to calculate the theoretical value of tp from the expression [32]

= -Z- exp( -(*) rp (1 - !4

(18)

where

bi is bi = 3.7 x lo-I”

the interplanar spacing. Putting m for the (lOi0) prismatic planes in magnesium, equation (18) gives r,, 2 lOmJ G. Thus, the value of TVcalculated from equation (17) is not consistent with the double kink mechanism. In addition, the high experimental values of the apparent activation volume, of the order of 5 500-1700 b3 (Fig. 17). are aIso inconsistent with this m~hanism~~ In the cross-slip mechanism of Friedel[33], a basal screw dislocation recombines over a sufficient length that it is able to cross-slip on to the prismatic plane. The shear strain rate is then given by [34] ZflfR’)“’

;i= N ‘*L A*b”vr’ exp SFR (

(20)

rbkT

where N, is the number of screw segments of dissociated dislocations on the basal plane per unit volume, L, is the total length of each segment, A* is the area swept out per unit activation, v is the Debye frequency, f is the energy per unit length of an undissociated dislocation, R is the recombination energy per unit length, and L’, is the formation energy for a constriction. It follows from equation (20) that, at constant temperature, (21)

(iMPa)

Q

xx)2olo

I

I

54

i

2

3

i

I

I

(16)

where r is the shear stress, rp is the Peierls stress, and Qo, the activation energy for the process, is given byC311

h’q

where b’ is the separation between the Peierls hills.

-O.W.Al

T =723-600K

t The true activation volume, V: is related to the apparent activation volume, V*, by [4] V = li* - mk7j?

(19)

where m is a stress exponent having a value of 2.5 for the double kink mechanism. The values of 2.5 k’lh are -- 100-400 b’ for the experimental conditions used for Ms~-0.8”,

Al.

cl

01

02

0.3 I/O-

0.4

0.5

0.6

0.7

(MPo-'1

Fig. 21, Activation energy for creep vs the reciprocal of stress at temperatures from 723 to 800 K.

AND

V.4GARALI

LANGDON:

DEFORMATION

IN H.C.P.

1169

METALS-II T (K)

I

I

I

I

600

900

-f-f- 107

Mg-O.BXAI

d = 240pm

700 I

I

Y

650 I

600 I

Mq-O.E%AI d = 240j.m ,i s 2.2‘10-4

-IO 2 (2Fw

I.1

I

I

I

I

1.2

1.3

1.4

I3

103/T

b

0.4 l/T2

Fig. 22. True

(MPa-2)

from equations (3) and (19). noting that the stress exponent is m = 2 for the cross-slip mechanism in equation (20), equation (21) is equivalent to 2kT _ v = 2(2i-R’)‘,” r’b

(22)

Figure 22 shows a plot of the true activation volume, V* - ZkT/r, vs l/r’, using the data from Fig. 17. The experimental points lie on a straight line having a slope which is given by 2(2fR3)“’ ---= b

5 x 1O-‘6 MPa2 m3.

b L’,

1 -=

TT

from equation

bk 2(2I-R3)“’

In

lMultiplication of equations (23) and (25) gives a value for the constriction energy in Mg-O.Soi, XI of Lrc 2 160 i 10 kJmole-‘. This value is very similar to earlier estimates for the constriction energy in pure magnesium (4 135 2 10 kJ mole- ’ [4]. _ 147 kJ mole-’ [15], and s 133 kJ mole-’ [35] ). The estimate of Li, may be further checked by noting that, from equation (20), the activation energy for the cross-slip mechanism is given by

(23)

IV L A*b”v

’ ’

Si-Rj

(2j-‘R3)l”

=

(20) it follows that

bC:

bklnr

+

-

(K-l)

2(21-R3)1’2T’

= 5.3 XIPa- ’

2(2TR3)=

Q

.4lternatively,

I 1.7

from 675 to 800 K (Fig. 15) and putting : = a.‘2+. From equation (24) the slope of this line is given by

and,

5

I I.6

_

Fig. 23. Plot of [ljrT - bk In r,(ZfR’)*] vs 1 T using the flow stress data at a true plastic strain of l.O”, for temperatures from 675 to SO0 K.

0.6

activation volume vs VT’ for temperatures from 723 to 810 K.

~/’

s-1

(24)

When the shear strain rate is constant, the first term on the right of the equality in equation (24) is constant. Thus, the cross-slip mechanism requires a linear variation between [I/TT - bk In 7/(2TR3)*] and l/?; and this is shown in Fig. 23 using the flow stress data at a plastic strain of 17; for temperatures

t In part I [4], the equivalent data for pure magnesium were plotted as l;‘rT vs l/7: thereby ignoring the small variation with applied stress contained in the second term on the right of the equality in equation (24). This simplification is not acceptable for the Mg-O.89,41 alloy because of the smaller value estimated for 2(2rR’)‘,,h [i.e. Z(ZTR’)*/b is equal to 5 x 10ez6 MPar m’ in Mg-0.8”, Al and 1.9 x 10ez5 IMPa’ m’ in pure magnesium].

u,

+

2(y3)’ 2

(26)

so that Q = Ii, when 1’~ = 0. From Fig. 21. the extrapolated value at l/a = 0 is L-<1 160 + 10 kJ mole- r. which is in excellent agreement with thz value of LI, obtained by data analysis. It is therefore concluded that. as in pure magnesium [4]. the deformation behavior of the Mg-0.8%Al solid solution alloy at the higher temby the peratures, above c 600-750 K, is controlled rate of cross-slip of screw dislocations from the basal to the prismatic planes. Further support for the occurrence of this mechanism is provided by- the observations of very extensive non-basal slip at high temperatures (Fig. 10) and the presence of some isolated but well-defined sub-boundaries (Fig. 13). 6. SUM;CIARY

AND

COSCLUSIOSS

(1) The deformation behavior of a ~l_O.S”~ Al solid solution alloy was investigated in the temperature range from 473 to 810 K. The results show that

1170

VAGARALI

A\ND

LANGDON:

DEFOR,MATION

the creep of Mg-O.S”;Al is controlled by separate mechanisms acting independently in the lower and higher temperature ranges. Depending on stress. the transition in creep behavior occurs over the temperature range from -600 to 750 K, with the transition temperature increasing as the stress level is reduced. (2) In the lower temperature range, up to _ 600-750 K, the behavior divides into two regions: (i) At the lower normalized stresses, the activation energy is independent of stress and equal to _ 140 k 10 kJ mole-’ : this is in excellent agreement with the value for chemical interdiffusion of aluminum solute atoms in magnesium. At these stress levels, there is a very small or no measurable instantaneous strain, there is a very brief normal or inverted primary stage of creep, the stress exponent is -3.0, there is evidence of extensive basal slip. and the substructure consists of a random distribution of dislocations. The behavior is interpreted in terms of viscous glide in which dislocation movement is restricted by the presence of solute atmospheres (class A behavior). (ii) At the higher normalized stresses. the activation energy is again _ 140 + 10 kJ mole-‘. there is a measurable instantaneous strain, there is an extensive normal primary stage of creep. the stress exponent is -6.0. and the substructure consists of well-defined subgrains. This behavior is interpreted in terms of a transition to dislocation climb at the higher stresses when the dislocations break away from their solute atmospheres. From measurements of the critical breakaway stress, the solute-dislocation binding energy is estimated as -0.14 + 0.03 eV. (3) In the higher temperature range, above -600-750 K, there is a measurable instantaneous strain, a normal primary stage of creep, the activation energy is c 230 f 15 kJ mole- ’ and decreases slightly with increasing stress, the stress exponent is -4.0, there is very extensive non-basal slip, and the substructure consists of free dislocations and some isolated but well-defined sub-boundaries. The behavior in this range is interpreted in terms of the cross-slip of dislocations from the basal to the prismatic planes, and the constriction energy is estimated as s 160 + 10 kJ mole- ‘. Ackno&dgemenr-This work was supported by the United States Department of Energy under Contract DEAMO3-76SFOO113 PA-DE-ATO3-76ER1040S.

REFERESCES 1. 0. D. Sherby and P. M. Burke, Prog. Mater. Sci. 13, 325 (1968). 2. F. A. Mohamed and T. G. Langdon, ;Icra metall. 22, 779 (1974). 3. P. Yavari, F. A. Mohamed and T. G. Langdon. clcra metall. 29, 1195 (198 1).

1s H.C.P. METALS-II

4. S. S. Vagarali and T. G. Langdon. .&rd merull. 29. 1969

(1981). 5 V. W. Eldred. J. E. Harris. T. J. Heal. G. F. Hines and A. Stuttard, Physical Merallurgy of R~‘acror Fw/ Elremenrs (edited by J. E. Harris and E. C. Svkes). D. 341.

The Metals Society, London (1975). ’ ‘- r 6. J. E. Harris. Microstrucrural Science (edited by E. W. Filer, J. M. Hoegfeldt and J. L. McCall), Vol 4. p, 4j. Elsevier. New York (1976). 7. J. E. Harris and R. B. Jones. Report So. RD;B R.144. C.E.G.B. Berkeley Nuclear Laboratories (1963). 8. P. G. Shewmon and F. Xv. Rhines. Truns. Am. Inst. Min. Engrs 200, 1021 (195-t). 9. F. R. N. Nabarro, Reporr of a Conference on Srrrnqrh of Solids. p. 78. The Phisical-Society. London (1948i. . 10. C. Herring. J. aDo/. Phrs. 21. 437 (19501. 11. R. L. Cobie. J. hip/. P&s. 34, 167Y11963). 12. G. F. Hines, V. J. Haddrell and R. B. Jones, Physictd Merallurg.v of Reactor fuel E:lemenrs Iedited by J. E. Harris and E. C. Sykes). D. 72. The Metals Societv. I London (1975). . ’ 13. L. J. Slutsky and C. M. Garland, Ph_~s. Rec. 107, 972 (1957). 14. R. B. Jones and J. E. Harris. Proceedings of the Joint ln~ernational Conference 011 Creep. Vol. 1, p. 1. The Institution of Mechanical Engineers. London (1963). 15, P. W. Flynn, J. Mote and J. E. Dorn. Trans. Am. InsI. ,Lfin. Engrs 221, 1148 (1961).

16. J. E. Flinn and S. A. Duran. Trolls. .dm. Imr. .Ifiu. Engrs 236, 1056 (1966). 17. W. J. McG. Tegart and 0. D. Sherby. Phil. .ilag. 3, 1287 (1958). 18. A. J. Ardell and 0. D. Sherby. Trmrs. ilm. Itlst. .Clin. Engrs 239, 1547 (1967). 19. T. G. Langdon and F. A. Mohamed. J. clusrrtr/asian fnsr. Merals 22, 189 (1977).

20. G. Moreau. J. A. Cornet and D. Calais. J. iVuci. Marer. 38, 197 (1971). 21. J. Weertman, J. appl. Ph.vs. 28, 1185 (1957). 22. A. H. Cottrell and M. A. Jaswon. Proc. R. Sot. A 199, 104 (1949). 23. S. Takeuchi and A. S. Argon, Acra meru[l. 24. 883 (1976). Pergamon Press, Oxford 24. J. Friedel, Dislocations. (1964). 25. J. E. Bird. A. K. Mukherjee and J. E. Dorn, Quanritatioe Relation Between Properties and .Microstructure (edited by D. G. Brandon and A. Rosen), p. 255. Israel Univ. Press. Jerusalem (1969). 26. H. W. King. J. Mater. Sci. 1. 79 (1966). 27. J. Weertman. Rate Processes in PIasric Deformation of Marerials (edited by J. C. bf. Li and A. K. IMukherjee), p. 315. American Society for Metals. Metals Park, Ohio (1975). 28. S. Takeuchi and A. S. Argon. J. Maw-. Sci. 11. 1542 (1976). 29. J. J. Gilman. J. appl. Phys. 36. 3 195 ( 1365). 30. J. E. Dorn and S. Rajnak. Trans. Am Inst. Min. Engrs 230, 1052 (1964). 31. A. Seeger. Phil. Msg. 1, 651 (1956). 32. J. P. Hirth and J. Lothe, Theory of Dislocations. McGraw-Hill, New York (1968). . 33. J. Friedel, Internal Stresses and fatigue in Metals (edited by G. M. Rass’weiler and W. L. Grube), p. 220. Elsevier, Amsterdam (1959). 34. J. E. Dorn and J. B. Mitchell. High-Srrengrh hfarerials (edited by V. F. Zackav). - o. . 510. John Wiley, New York (1965). 35. K. Milifka. J. cadek and P. Ry9, dcta metall. 18, 1071 (1970).