The Portevin-Le Chatelier effect in an Al-Mg-Si alloy

THE

PORTEVIN-LE

CHATELIER P.

G.

EFFECT

IN AN

Al-Mg-Si

ALLOY*

McCORMICKt

The nature of the Portevin-Le Chatelier effect in an Al-Mg-Si alloy was investigated. At high strain rates, 2 > 1O-s min-‘, and room temperature, the periodic locking form of serrated flow was observed, which resulted from repeated Liider’s bend initiat.ion and propagation along the speoimen gauge 1engt.h. Each Ltider’s band was found to initiate in the same region of the specimen &nd propagate along the gauge length in the s&me direction. Measurements of the Luder’s strain, FL, indicated that EL was proportiomd to the total strain and independent of the strain rate. Both sL and the Liider’s flow stress were observed to increase along the gauge length. The resulting strain gradient along the specimen increased linearly with strain. Measurements of the temperature and strain rate dependence of the critical strain for serrated flow, so yielded an activation energy of 0.64 eV and a strain exponent of 1.6 in the Ham.Jaffrey equation. At low strain rates unlocking serretions were observed, which were characterized by a negative strain rate dependence of Ed. EFFET

PORTEVIN-LE

CH~TELIER

DANS

UN

ALLIAGE

Al-Mg-Si

L’ameur a etudiir la nature de l’effet Portevm-Le Chatelier dans un alliage Al-MgSi. Pour des vitesses de deformation &levees, E > 1O-s min.-1, it temperature ambiante, l’ruuteur a observe la forme periodique de la courbe hechuree qui resulte de la formation repetee des bandes de Liider et de leur prop&gation sur la longueur de l’eohantillon calibre. Chaque bande de Liider semble se former dans la mbme region de l’eohantillon et se propager sur sa longueur dans la meme direction. Des mesures de la deformation de Liider, sL, montrent que Q. est proportionnelle ii la deformation totale et independante de la. vitesse de deformation. Les ttuteurs ont observe que ss et la, contrainte de Liider augmentent en meme temps sur toute la longueur de ~~ch~ntillon calibrct. Le gredient de deformation resultant le long de l’echantillon augments lineairement avec la deformation. Des mesures de le variation de la deformation critique e, avec la temperature et la vitesse de deformation pour la courbe de traction hachuree, donnent une energie d’activation de 0,64 eV et un exposant de la deformation de 1,6 dans l’equation de HamJeffrey. Pour les vitesses de deformation faibles, les auteurs ant observe des hachures non periodiques, caracttrisees par une variation negative de F, avec la vitesse de deformation. DER

PORTEVIN-LE

CHATELIER-EFFEKT

IN

EINER

Al-Mg-Si-LEGIERU~G

Die Natur des Portevin-Le C~telier-~ffektes in einer Al-~g-Si-Legierung wurde untersueht. Bei hohen Dehngeschwindigkeiten (e > 1O-3 min-1) und bei Raumtemperatur wurde die periodische Blockierung des diskontinuierlichen FlieBens beobachtet, die eine Folge der wiederholten Ltidersbandbildung und -ausbreitung entlang der Probe wsr. Alle Liidersbiinder entstanden in demselben Probenbereich und breiteten sioh in derselben Richtung entlrtng der Probe rms. Messungen der Liidersbanddehnung EL ergaben, da6 so proportional zur Gesamtdehnung und unabhilngig von der Dehngesehwindigkeit war. Sowohl so als auoh die Ltiders-FlieBspannung nahmen entlang der Probe zu. Der sich daraus ergebende Gradient der Dehnung entlrtng der Probe nahm linear mit der Dehnung zu. Messungen der Abh~ngigk~it der kritischen Dehnung fur diskontinuierliches FlieBen, EC, von der Temperatur und Dehngesehwindigkeit erg&m eine Aktivierungsenergie von 0,64 eV und einen Spannungsexponenten in der Ham-Jrtffrey-Gleichung von 1,6. Bei kleinen Dehngeschwindigkeiten wurden Losrei3prozesse beobachtet, die durch eine negative Abhiingigkeit der Griilje BL von der Dehngeschwindigkeit charakterisiert waren. 1. INTRODUCTION

The occurrence of the Portevin-Le Chatelier effect (serrated yielding) is generally ascribed to the effect of dynamic strain ageing on macroscopic plastic flow. Dislocations moving through the lattice can interact with solute atoms, forming dragging solute atmospheres when,@)

where vd is the dislocation velocity, D is the solute diffision coefficient and I,, is the effective radius of the atmosphere. In substitutional alloys a critical plastic strain, s,, is required for the onset of serrated flow, which is generally observed in the temperature xange 0.2-0.4T,. Recent work@-6) has shown the existence of two types of serrated yielding, characterized by both the * Received September 23, 1970.

t School of Metallurgy, University Kensington, N.S.W., Australia. ACTA

METALLURGICA,

VOL.

of New South Wales,

19, MAY

1971

463

form of serration, as evidenced on a stress-straiu curve, and the strain rate or temperature dependence of the critical strain, eO. At low and intermediate temperatures or high strain rates in the serration range, E, is found to increase with increasing strain rate and decreasing temperature. In this region the solute mobility, which is initially insufficient to form atmospheres, is increased by vacancy production during deformation while the dislocation velocity decreases, allowing the locking condition [equation (I)] to be met at E,. Expressing the vacancy concentration-strain relation as C,aP and the dislocation density-strain relation as pcr.8, Cottrellu) and Ham and JafYrey@’ have shown that equation (1) may be expressed as

where A is a constant and Eea is the effective activation energy for solute migration. Similar expressions for the critical strain have been derived by Worthington

ACTA

464

and Mukherjee

and Brindley”) dislocations

are effectively

formation plication,

as evidenced

et aZ.(*) At

locked

requires dislocation

to or below

VOL.

19,

1971

F, the

further

de-

and multi-

on a stress-strain

curve by an

by a discontinuous

the level of the curve.(7*gs10)

Such serrations

are called locking

originate

from

the

locations.

In

addition

produced

by

deformation,

supersaturations

and

breakaway

abrupt rise in flow stress followed fall back

METALLURGICA,

locking to

have

as they

serrations

of initially vacancy

mobile

dis-

concentrations

quenched-in

also been found

vacancy

to influence

the strain at onset of serrated flow.c2) At high temperatures often

found

and

increasing

and low strain rates,

to increase

with decreasing

temperature.(2~4~5~8*11-14)

region the form of serrations the locking increase

in that,

yield drop.

in this

Although

region,

In

this

to differ from

at least initially,

in flow stress is observed

continuous done

serrations

is found

E, is

strain rate

no

prior to the dis.

little work has been

it has been is low enough

shown

that

initially

the

dislocation

velocity

for the

dislocations

to be aged from the start of deformation.(3)

The serrations appear to be due to the breakaway multiplication termed that

of initially

unlocking

each

initiation The

aged dislocations

serrations.

unlocking

occurrence

serrations

in

an

previously.(5)

of

both

flow

in

alloy

paper the

and

and are

corresponds

locking

and has

describes

strain rate and temperature serrated

locking

to

the

band.

Al-Mg-Si

This

Load-elongation curve exhibiting serrations (i: = 0.1 min-I).

Thomas(14) has shown

serration

of a local Liider’s

FIG. l(a).

unlocking been

noted

effects

of

on the characteristics

of

same

the

alloy.

observations

on the effect of repeated

propagation

on the uniformity

Experimental Liider’s band

of deformation

are

also reported. 2. EXPERIMENTAL

A

commercial

6063 Al

METHOD

alloy,

having

composition

of 0.7% Mg and 0.4%

this study.

Constant

were

conducted

on

cross-head 3/16 in.

a nominal

Si was used

speed tensile diameter

in

tests

specimens

with a gauge length of 2 cm using an Instron testing machine. The specimens were annealed at 500°C for 1 hr and were either quenched

furnace cooled prior to testing. 0.04 mm. Testing temperature mersing the specimen

into water at 20°C or The grain size was was varied by im-

in appropriate

low temperature

baths. In some tests an extensometer affixed the specimen was used to measure strain.

onto

3. RESULTS

3.1 Characteristics of serrated yielding The form of serrated flow in this alloy has been briefly discussed elsewhere.c5) At strain rates greater

FIG. 1 (b). Load-elongation curve exhibiting serrations (d = 10-3min-‘).

than 2.5 x 10e3 min-l locking

serrations

unlocking

at room temperature,

were observed.

A typical

periodic force-

elongation

curve is shown in Fig. l(a) for a quenched

specimen.

In addition

parameters

have

been

to the critical used

to

strain, F,, two

characterize

these

serrations ; the strain occurring between successive serrations, cs, and the stress drop, Ao, associated The strain between with each periodic serration.

: PORTEVIS-LE

hIcCORMICK

CHATELIER

15-

A0

EFFECT

IS

465

Bl-Mg-Si

I

10-

-0

x ti

GAUGE LENGTH

l2 cu. ., I. 5-

I

I

I

.05

.lO

.15

e FIG. 2. The effect of strain and gauge length on the strain between successive periodic locking serrations, ~~ (B = 0.1 min-I).

.05

0

.I5

.lO

E serrations,

successive

ey, was

linearly with increasing

found

strain, independent

men gauge length as shown in Fig. 2. of AO with strain is shown in Fig. 3. Fig. 1, the yield drop for each periodic may

be divided

into

to

two

increase of speci-

The variation As shown in serration,

components;

FIG. 3. The

smooth

effect of strain and temperaturc serration magnitude.

portion

in Fig. 5.

of the stress-strain

The strain occurring

Ao,

each Liider’s

the discon-

extensometer,

band through

on the

curve as shown

during the passage of

the gauge length

of the

F~‘, was found to increase linearly with

tinuous increase in flow stress prior to the yield drop, ho,,

and the displacement

elongation

of the level of the force-

curve accompanying

each serration,

The increase in ha with increasing due to the increase

in AC,.

A(J,.

The discontinuous

flow

stress rise, ha,, was not found to increase significantly with

strain

after

the

first few

100 -

strain is mainly

serrations,

and

110 -

at

large strains AC, decreased to zero. In a separate set of tests an extensometer to the gauge measure

length

strain.

of the specimen

A typical

attached

was used

force-elongation

to

curve is

shown in Fig. 4. From the stepped form of the curve it may be seen that once serrated yielding is initiated all

subsequent

deformation

passes of Liider’s the specimen.

bands

It may

along

occurs

via

repeated

the gauge

length of

also be seen that

the flow

stress increases during the propagation of each Liider’s band along the gauge length and that a discontinuous flow stress rise accompanies the passage of successive Luder’s bands through the same region of the specimen. Measurements of the average Luder’s to

flow stress as a function

coincide

with

the

of strain were found

extrapolation

of

the

initial

100 -

M-

I

I

I 025

.o,o

I I,

WI

Elongation(cm.) FIG. 4. Typical load-elongation extensomet,er measurements

curve obtained (B = 0.1 min-I).

from

ACTA

466

METALLURGICA,

total strain in close agreement with the measurements of E,. At strain rates less than 2.5 x 1O-3 min-l the serrations initiated as unlocking serrations as shown in Fig. l(b). After several per cent strain periodic locking serrations were observed superimposed on the higher frequency unlocking serrations. The stress drops associated with the unlocking serrations were found to be constant at small strains and the strain period between successive serrations increased with increasing strain.

VOL.

19,

1971

Ii’ -

ru” Ii’,

. QUENCHED n

FURNACE

COOLED

FIG. 6. Strain rate dependence of the critical strain F, for quenched and furnace cooled specimens.

shown in Fig. 7. For the furnace cooled specimens e, is independent of strain rate at small strains, but increases with increasing strain rate at large strains. The strain rate was found to have a negligible effect on the serration stress drop, AG, for strain rates up to 0.5 min-l. At higher strain rates Aa decreased significantly with increasing strain rate and at the highest strain rate used (2.5 min-l) the serrations

I

I

I

11

.Ol

“““’

1’

e

.02 QUENCHED a I

FIG. 5. Stress-strain curve for B = 0.13 mine’. Stress values after onset of serrated yielding are the average Liider’s gow stress.

“IN:’

15 -

3.2 Effect of strain rake The effect of strain rate on the critical strain for the onset of serrated yielding, Ed, is shown in Fig. 6 for both quenched and slowly cooled specimens. The transition from positive to negative strain rate dependence of .sCwas found to occur at the same strain rate as the transition from locking to unlocking serrations. Both the quenched and furnace cooled specimens exhibit a similar strain rate dependence of E, in the positive region; the curve for the furnace cooled specimens being displaced to lower strain rates. The value of m + ,8 in equation (2) for both the quenched and furnace cooled specimens is 1.6. The previously reported value of 2.7t5) is incorrect. The strain between successive serrations, E,, was found to be independent of strain rate over a strain rate range 10-L1 min-l for the quenched specimens

nO Y

ui,‘O

5-

L

I

I

I

.OS

.lO

.I5

E FIG. 7. The effect of strain rate on the strain between successive periodic locking serrations, E., for quenched and furnace cooled specimens.

McCormick

:

PO~TE~I~-Lo

C~ATELIER

EFFECT

IN

467

Al-&Ig-Si

became somewhat irregular. The strain rate dependence of the flow stress and rate of work hardening, is shown in Fig. 8. The form of the curves suggests three regions of differing strain rate dependence. For strain rates less than 2.5 x 10e3 min-l, in the region of unlocking behaviour, both the flow stress and the rate of work hardening increase with decreasing strain rate. For d between 2.5 x 10e3 min-l and 0.5 min-l both are reasonably constant, and at high strain rates, i > 0.5, the flow stress increases while the work hardening rate decreases significantly with increasing strain rate. The high strain rate

i

I 3.4

I

I

I

3.5

3.6

3.7

I /T

I

I

3.8

3.9

X IO’ (LK-‘)

FIG. 9. The temperature

dependence

of cc.

E, and Ao+ is shown in Figs. 10 and 3. With decreasing temperature the rate of increase of both E, and Au with strain is decreased. 3.4 Luder’s band initiation and strain distribution Frr,. S(a). Strain

rate

dependence

flow stress.

of the

I per

cent

In light of the force-elongation curves (Fig. 4) obtained using an extensometer to measure elongation, a further set of tests were carried out in which an extensometer having a gauge length of I cm was

15 -

FIG. 8(b).

The effect of strain rate on work hardening. /

region corresponds well with the decrease in A@ at high strain rates.

’ 23.5-C i). 9.0 *a l

3.3 Eflect of temperature The temperature dependence of E, measured at a strain rate of 10-l min-r in the locking region is shown in Fig. 9. The apparent activation energy calculated from equation (2) using m + /3 = 1.6 is 0.64 eV. The effect of temperature on values of

I 0

I

t

I

I‘ .05

I,

3.0 ‘I

r-14.5

”

*

I

I .lO

I

t

I

I .15

E Fro. 10. The effect of temperat,ure on the strain between successive periodic serrations, sl.

ACTA

468

~~~TALI~U~GIC-~,

positioned either 1 cm from the top or 1 cm from the bottom of specimens having a gauge length of 6.5 cm. By measuring the time delays from the yield drop to the start of deformation within the gauge length of the extensometer and from the end of the deformation to the next yieId drop, it was determined that each Luder’s band initiated in the same region at an end of the specimen and hence successive Liider’s bands traversed the specimen in the same direction. It should be noted that care had to be taken in attaching the ext,ensometer t,o the specimen to avoid triggering the Liider’s bands at the knife edges. On comparing the Ltider’s band strain for the two extensometer positions, it was found that a greater strain occurred near the end of the specimen where the Liider’s bands terminated, than where t,hey initiated. In Fig. 11 the strain measured at each end of the specimen is plotted as a function of the cumulative number of Liider’s bands which have traversed the specimen. The end to end variation in strain was found to increase linearly with the mean strain from zero to a vaiue of 0.5 per cent after a mean strain of 8 per cent as shown in Fig. 12. The strain variation was also exhibited in reduction in area measurements along the gauge length of specimens after straining as shown in Fig. I3 for various mean strains. It is seen that, the end to end strain variation increases with the mean strain, becoming quite appreciable at mean sOrainsof 15-20 per cent. I

I

1 .06 -

w .04-

* TO?

I 0

1

2

I 4

L

I

I

I

t

6

8

10

12

14

LijDER’f

1 ‘16

I 18

BANDS

FIG. 11. The strain occurring at each end of the gauge length plotted as a function of the cumulative number of Liider’s band passes.

I

VOL.

1

19,

I

.02

1971

I

I

I

I

.06

.04

I

I

.08

z Pm. 12. The effect of strain on the end to end strain difference. 4. DISCUSSION

4.1 Locking serrations The periodic locking form of serrated yielding observed in this study at high strain rates is similar to that reported earlier by RusseWg) in copper-tin alloys (Russell type A serrations) and others.(2~8~10J5) The form of the extensometer force-elongation curve in Fig. 4 shows quite clearly the d~cont~uous nature of plastic flow after the onset of serxated yielding. Similar results have also been obtained by Muntz and Macherauch(l”) in a-brass, using an extensometer technique to measure strain-time curves during serrated flow. As proposed originally by ~u~ell,(9~ each serration corresponds to the initiation of a Liider’s band which then propagates along the length of the specimen. Once the Liider’s band reaches the end of the specimen further deformation occurs by the initiation of a new Liider’s band, as evidenced by the rapid rise and discontinuous fall in the flow stress. The rapid rise of the flow stress, the agreement between the measurements of E, and Ed’, and the independence of E, and ssr on the gauge length and strain rate indicate that strain

PORTEVIN-LE

MCCORMICK:

CHATELIER

EFFECT

IX

Al-Mg--Si

469

The Liider’s strain and the Ltider’s band velocity are related a&‘) E&V& = 2I 0% The dislocation velocity at the Liider’s front may be expressed as(‘) Vd zzz - 6 P&b

(6)

where pL is the mobile dislocation density and i, is the local Ltider’s strain rate. The Liider’s strain rate may be expressed in terms of the applied strain rate as

where w is the effective band width. Hahn(18) has shown that vt z vd, thus from equations (5)-(7) EL = bwp&

I

’ 0.8

DISTANCE

I

I

I

3.1

5.4

7.7

ALONG

GAUGE

LENGTH

(CM)

FIG. 13. The w&a&n in strain aclong the specimen gauge length for various meen strains.

agoing occurs very rapidly behind the propagating Ltider’s band. If zt&is the Liider’s band velocity and 7 the time required for ageing, the ext,ent of the unaged region behind the Liider’s band is wLr.(16) It appears then that V&T
tst

If pL is assumed to be a constant fraction of the total dislocation density, pL = fp, where p increases with strain as p = C&P (9) then Ed,may be expressed as a function of the total strain as eL = b~~C&~ w If 6 N 1 as is often observed,(2*6*1g) equation (10) predicts an approximately linear increase of Ed with strain independent of specimen gauge length as observed in Figs. 2 and 7. It may be argued that equation (9) may not hold after the onset of Liider’s flow, however the measurements Ham and Jaffrey@) indicate that the occurrence of serrated ilow does not influence the dislocation density-strain relation. Soler-Gomez and Tegart t2) found a linear relation between E& and strain and /3 = 0.95 in gold-indium alloys. RusselP found E~UEin a copper-tin aIloy and Ham and Jaffrey(@ determined /3 = 1..17 for the same alloy using both pre-strain and dislocation density meas~lrements. It thus appears that, the increase in eL with strain results from the increase in the mobile dislocation density with strain. An interesting feature of Liider’s flow in substitutional alloys is that each Liider’s band propagates along the length of the specimen under an increasing flow stress. Worthington and Brindley”) have suggested the increasing flow stress is due to work hardening in an unaged region behind the Liider’s band. The form of the force-elongation curves in Fig. 4 indicates, however, that the rising flow stress is directly associated with the Liider’s strain. Furthermore, it is difficult to rationalize why

ACTA

470

METALLURGICA,

any deformation would occur behind the Liider’s band if the Liider’s band can propagate at a lower stress. For the first Liider’s band the increasing stress could be due to the band front encountering increasingly aged regions as it propagates aIong the specimen. This, however, would not apply to subsequent bands. The increasing flow stress could also be due to increased drag on the LGder’s front as a result of progressive ageing along the gauge length. The Liider’s strain also increases along the specimen in the direction of band propagation, as shown in Fig. 11, It is apparent that as a result of the strain gradient there will be an internal stress gradient along the gauge length due to the increase in the aged-in dislocation density. The internal stress gradient would then cause an increasing Liider’s stress along the specimen, and the Liider’s strain gradient along the gauge length would be increased with the passage of each band along the gauge length. As shown in Fig. 12, the strain gradient along the specimen increases linearly with strain, suggesting that the increasing stress at least after the passage of the first few Liider’s bands is due to the dislocation structure rather than progressive ageing of the Liider’s front.

VOL.

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of soluute in soh&ion in the furnace cooled specimens.‘9j The activation energy for serrated flow, Em = 0.64 eV, measured from the temperature dependence of cc is in reasonable agreement with recent measurements in other aluminium base alloys.(4p8) The activation energy for vacancy migration in aluminium is 0.75 eV,(22) while the solute binding energies for both Mg and Si are 0.2 e-57(23*s)It is possible that interaction between Mg and Si atoms occurs, lowering the effective vacancy-solute binding energy. The relative strain rate insensitivity of the flow stress and the rate of work hardening at intermediate strain rates is a common feature in aluminium alloys tested at room temperature.(13*25z26) This insensitivity is also reflected in the independence of ANTon strain rate and the coincidence of the extrapolated pre-serration portion of the stress-strain curve with the Liider’s stress-strain measurements in this region. concentration

The occurrence of unlocking serrations and the negative strain rate dependence of E= at low strain rates is well documented.(z-5,8~11-14) In this region the flow stress and the rate of work hardening also 4.2 Effect of strais rate and temperature increase with decreasing strain rate. Since Charon locking serrations neck’s@) calculations indicate that the mobile dislocaThe value of m + 0, 1.6, measured from the straintion density is aged from the start of deformation, it rate dependence of E, for both the quenched and the appears that dislocation immobilization during strainslow cooled specimen is somewhat lower than that ing is necessary to explain 6he increasing strain measured in previous studies. Experimental values required for dislocation unlocking as the strain rate is of m, p and m + @ for substitutional alloys are sumdecreased. marized in Table 1. It is seen that m N 1 and p N lThomas(14) has correlated successive unlocking 2.5 giving 11~+ @ f;’ 2-3. Theoretical predictions of m serrations with the observation of parallel band are in the range 1.25-2.(2**21) The reason for the low surface markings associated with discontinuous value of m + /3 measured in this study is not known, Liider’s band propagation in a quenched Al-Mg alloy. particularly since the same value was obtained for At low strain rates it is apparent that only discontinboth the quenched and the furnace cooled specimens. uous Liider’s band motions is possible due to rapid If ,Br2f 1 as indicated from the Liider’s strain measureageing of the Liider’s front. The presence of periodic ments, the value of m, m Y 0.6, appears to be anomalocking serrations superimposed on the unlocking serlously low. It was not possible to measure the in. rations indicates, as observed by Thomas,(3) that dedividual values of m and @ using the IEam-JaffreycQ formation proceeds by the repeated discontinuous pre-strain method because of the presence of large motion of Liider’s bands along the gauge length of the yield points on restraining. The displacement of t#he specimen. s,-g curve for the furnace cooled specimens above that 5. CONCLUSIONS for the quenched specimens is due to the decreased 1. The oceurrenee of locking and unlocking serraTABLE

Alloy Gu-SXl CS-Sn Au-In Cu-Zn Al-Mg-Zn -

1.

Experimental v&es m

B

1.03

1.17

1.19

0.95

0.88

2.45 ~_~

of YB,8 and m + p m i- B

~-~

2.Y3.1 2.14 2-3 3.33

Reference 6.9 15 2 10 8

tions is characterized by the strain rate dependence of the critical strain, Ed. 2. Periodic locking serrations are associated with the repeated initiation and propagation of Liider’s bands along the specimen gauge length. 3. The rate of strain ageing behind the Li.ider’s band is very rapid.

MCCORMICK:

PORTEVIN-LE

CHATELIER

4. The increase in the Liider’s strain with increasing total strain is due to the increase in dislocation density with strain, 5. The increase in the Liider’s flow stress during band propagation is primarily associated with the development of the strain gradient along the gauge length during deformation. 6. The activation energy for serrated yielding is 0.64 eV and the value of the strain exponent is 1.6. 7. At low strain rates the serrated flow is characterized by repeated discontinuous Liider’s band motion. 6. ACKNOWLEDGEMENTS

The author would like to thank Professor E. 0. Hall and Dr. C. M. Sellars for valuable discussions. 7. REFERENCES 1. A. H. COTTRELL,;phiZ.Msg. 74,829 (1953). 2. A. J. R. SOLEB-COMEZand W. J. McG. TE~QART,PhiZ. Mag. 20, 495 (1969). 3. W. CHAR,NOCK,Phil. Mag. 20, 427 (1969). 4. B. J. BRINDLEY and P. J. WomHmaToN, Acta Met. 17, 1357 (1969).

EFFECT

IX

Al-Mg-Si

471

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