Hardening of pure magnesium by lattice defects

HARDENING

OF PURE J.

M.

MAGNESIUM

IL4MPSHIREt

and

BY LATTICE D.

DEFECTS*

HARDIES

Comparison of the flow stresses of pure magnesium in the as-quenched and quenched-and-aged conditions with that of air-cooled material indicates a temperature-independent strengthening effect on quenching that is greatly increased by subsequent aging. The absence of visible lattice defects from the quenched materials prompts explanation in terms of opposition to the motion of slip dislocations bv the atomic distortions associated with individual vacancies or small vacancv clusters. The hardening during aging, on the other hand, is accompanied by the precipitation of prismatic loops of dislocation on b-al planes and is explicable in terms of dislocation bowing of slip dislocations between such pinning points. Subsequent softening then simply occurs because of evaporation of vacancies to sinks. DURCISSEXEST DU JIAGSESIUM PUR PAR DES DEFAUTS RETICULAIRES des contraintes d’ecoulement plastique du magnesium pur tremp6, et trempe et vieilli. et de celles du materiau refroidi B l’air met en evidence un effet de durcisscment au tours de cet effet augmente nettement si on effectue un la trempe, qui est independant de la temperature; vieillissement ulterieur. L’absence de defauts visibles dens le reseau des materiaux tremp& suggere que les distorsions atomiques. dues aux lacunes individuelles ou aux petits agglomerats de lacunes. s’opposent au mouvement des dislocations de glissement. D’autre part, le durcissement au tours du vieillissement est accompagne d’une precipitation de boucles prismatiques de dislocations sur les plans de base, qui peut btre expliquee par une courbure des dislocations de glissement entre les points d’epinglage. L’adoucissement qui en resulte est alors simplement dn a la migration des lacunes vers les puits.

La comparaison

VERFESTIGUNG

VON

REINEJI

1L4GSESnTZII

DURCH

GITTERDEFEHTE

Em Vergleich der FlieBspannungen von reinem, abgeschrecktem und abgeschrecktem und angelassenem Magnesium mit der FlieDspannung von luftgektihltem JIeterial zeigt einen temperaturnnabhangigen Verfestigungseffekt nach dem Abschrecken, der durch das nachfolgende Anlassen noch stark zunimmt. Die Abwesenheit beobschtbarer Gitterdefekte im abgeschreckten >Iaterial fiihrt zu der E&l&rung, da9 die mit individuellen Leerstellen oder kleinen Leerstellenagglomeraten verbundenen atomaren Verzerrungen als Hindernisse fur die Versetzungsbewegung auftreten. Die Verfestigung beim Anlassen ist andererseits begleitet von der Ausscheidung prismatischer Versetzungsringe auf Basisebenen und kann so e&art werden, da0 sich die Gleitversetzungen zwischen diesen Hindernissen ausbeulen. Sachfolgende Entfestigung ist dann eine Folge der Wanderung von Leerstellen zu Senken.

1. INTRODUCTION

strengthening effect of quenched-in defects w&s first demonstrated by Maddin and Cottrell,(l) Kenny and Burn found an increase in both the strain-hardening coefficient and the critical resolved shear stress of quenched single crystals of magnesium. Furthermore, they reported a further increase on aging at 100°C and a subsequent decrease if aging was prolonged. No accompan_ying electron metallography was carried out in either case but a mechanism based upon the jogging of dislocations by lattice vacancies in the quenched materials was proposed. .&tempts have since been made to correlate hardening effects kth observed lattice defects in aluminium (Westmacott ;t3) Hardie and M.ichael(~~), aluminium-magnesium (Crivelli-Visconti and Greenfield ;t5) Hardie and Xichael(4)), copper (Galligan and Washburn ;@I Davidson and Galligan(7)) and gold (Poshida et oZ.(*)) but no such correlation has previously been attempted for magnesium or its alloys. 0 tg) observed no dislocation Lally and Partrid,e loops in quenched magnesium foils but did observe Some

>-ears

after

the

* Received July 20, 19i3; Revised November 5, 1973 t Nom at the Corporate Laboratories of the British Steel Corporation Sheffield. ‘$ Department of 1Ietallurgy and Engineering Jlaterials, The University of Sewcastle upon Tyne. ACT-4 1\LETALLURGICA, 10

VOL.

22, JIAY

1954

657

loops on subsequent aging. The present investigation was conceived as an attempt to correlate the change in flow stress with the latt.ice defects observed in bulk samples of magnesium when quenched and aged. As in the earlier wok on aluminium, heat treatment of thin foils was generally avoided because it gives structures which are not representative. 2. EXPERIMENTAL 2.1 Fabrication

METHODS

and heat treatment

Magnesium of 99.95% purity was melted under flux and sprinkled with sulphur during pouring to keep oxidation to a minimum. The cast material was extruded at 360°C to 4.75 mm dia rod and then cold-drawn to 4.32 mm wire. The drawn wire could then be given a controlled recrystallisation anneal before testing. Tensile specimens with threaded ends and a gauge length of 25.4 mm having dia 3.1i5 mm were machined directly from the wire. Quenched specimens were compared directly with those cooled in air after the same heat treatment. Heat treatment before quenching was accomplished in a sealed furnace which had a few per cent of sulphur dioxide added to its atmosphere to promote formation of a protective coating on the specimens and so combat more extensive oxidation. Specimens

6.3

ACTA

METXLLURGICA,

jvere suspended in the furnace on t,hin nire t-hat could be fused at. the end of the heat-t,reatment period and the specimens quenched by t,he free-fall technique. Uncertainty about the effective quenching temperature and initial cooling rate was minimised by having the quenching tank secured to the bot.tom of t,he sealed furnace. The reproducibility and effectiveness of quenching were confirmed by subsequent results. The soaking time before quenching xvas an ample 30 min and the quenching medium was an ice-water mistute. After quenching, specimens were either given a controlled aging treatment at an elevated temperature or tested immediately, even though it ~‘~1s verified that aging up to 1 hr at room temperature produced no measurable change in properties. Aging treatments were carried out in a fluidized-bed furnace and careful control of time at the aging temperature achieved by means of a thermocouple embedded in the centre of a control specimen. &win sizes were maintained as closeIy as possible t,o 0.10 mm dia but corrections were applied for variations in individual specimens by means of a Hall-Petch criterion, the applicability of which was first confirmed over a range of grain sizes. Again the flow wit.h air-cooled values, stresses \vere compared i.e. 10 = flow stress after heat treat.ment - flow stress aft,er air cooling. 2.2 Flow stress measurements Tensile tests were performed on a hard machine and load-elongation curves recorded autographicatiy. Because of t.he absence of a sharp yield in the stressst,rain curves obtained, a 0.1 per cent offset criterion was adopted for expressing flow stresses.

To avoid bhe use of quenched foils for observation of defect,s, 1 mm thick discs were cut from wire of tensile specimen dimensions after completion of heat treatments. By attaching these to a brass block Kith double-sided sellotape, they could be polished mechanically (on both sides) to a final thickness of 0.95mm and then removed by prolonged soaking in Chemiclene. The resultant discs were Ohen electropolished in a 1 :A solution of nit,ric acid in methyl alcohol, at room temperature and a potential of 2V. Immediate washing in methyl alcohol and dr*ying produced good clean foils. All foils were esamined in a J.E.M. electron microscope operating at 100 kV, using a f 20’ t,ilt.ing stage and always obtaining a diffraction patt.ern corresponding to each micrograph. Jieasurements of loop

VOL.

‘22,

1974

densities and sizes were carried out lvith the basal plane perpendicular to the electron beam, i.e. the orientation of the foil was chosen so as to give reasonably circular loop images, and as closely as possibb to t, were the two beam condition. Foil thicknesses, method and loop determined by the slip-trace densit,ies, X1 calculated from : x = npt

(1)

where n x-as the number of loops observed in an area A, and t lay in the range 20004000 8. The number and size of loops was determined from the photographic plates (magnification N 9000 x ) by projection on a screen at a further magni~cation of N 17. Loop densities were determined from measurement of ten areas (from two or three foils) for each specimen condition, All loops obserrecl lay on the basal plane and were of the +[2043] type, and mean diameters were determined from measurements across the line of no contrast of 60-120 loops. The probable error of the mean varied from 1.7 to -7.4 per cent for loop diameter measurements but, because of the smaller number of measurements, was 2.9-6.2 per cent for loop densities. 3.

RESULTS

3.1 Quenched magnesium Despite a measurable hardening effect (as compared with air-cooled specimens) when quenched from temperatures above 600°C (Fig. I), pure magnesium specimens contained no observable dislocation loops. When, however, quenching of thin foils was examined, structures similar t,o those obtained by Lally and ,

$

12.4

w cc t v)

g

12.0

ii I c o

il.6

OUENCHING

TEMPERATURE

lc

Frc. 1. Variation of the 0.1 per cent flov xre83 of pure magnesium with quenching temperature.

HAMPSHIRE

AND

HARDIE:

HARDESISG

OF

PURE

XAGSESIUY

BY

LATTICE

DEFECTS

6.59

FIG. 2. Complex dislocation structure in magnesium quenched in the form of thin foil.

Partridge(g) were produced (Fig. 2). The obvious conclusion is that structures such as the latter are produced by strain, whether this arises from the quenching of t.hin foils or the absorpt,ion of hydrogen. The hardening of quenched magnesium increases markedly as the quenching temperature increases over 500°C and, since the fraction of vacant lattice sites present in t.he magnesium will likewise increase over this temperature range, t.he obvious inference is that the increasing defect concentration promotes the increasing hardness increment, even t,hough the actual defects producing the hardening have not been observed.

0

100

200

300

TEMPERATURE

400

‘C

FIG. 3. Effect of 10 min isochronal aging on the flow stress increment for magnesium quenched from 525%.

3.2 Effects of aging The effects of bot,h isochronal and isothermal annealing on the %omstress of material quenched from 525’C were examined. The isochronal curves (Fig. 3) show a spectacular increase in %om stress from t,he original value of 11.85 kgf/mm* to a peak at about 16O”C, followed by a sharp drop towards the mean air-cooled value (11.53 kgf/mm*) at higher t.emperatures. Isothermal aging (Fig. 4) also results in a rise in %ow stress to a peak and a softening after prolonged aging. Both the rate of hardening and the speed of the competing soft,ening process increase at higher aging temperatures, xvitiththe result that the peak strength achieved decreases for aging t.emperatures above 1iO”C. The concurrent variations in densit;v and size of precipitated loops (Fig. 5) indicate that both closely follow the manner of change observed in %ow stress. It seems, therefore, that aging quenched pure

A, R-COOLED

10

1 0

I

40

80 AGING

120 TIME

160

mlnutel

FIG. 4. Isot,hermal aging curves for magnesium quenched from 505’C _ .

magnesium at low temperatures promotes condensation of dispersed vacancies to gire collapsed discs which anneal out at higher temperatures. The loops of dislocat,ion so formed (Fig. 6) appear to be responsible for a spectacular strengthening effect which likewise disappears as vacancies evaporate from loops.

ACTA

660

l

I

XETALL’L’RGIC.~,

‘0

/

-1

/

\

0’0 / 1

0

100 AGING

I

I

200

300

TEMPERATURE

lc

1 5

I

-I

I: 09 3. 3

FIG. 5. Variation of number and mean size of precipitated dislocation loops with isochronal aging.

VOL. 22, 19i4

pork should preclude retention of a very large concent,ration of single vacancies and therefore, even after quenching from the lowest temperatures, vacancies should be largely in the form of clusters. This itself complicates any hypothesis for the mechanism of hardening since the size of the clusters is indefinable. However, t’he relationship between the theoretical vacancy concentration at the quenching temperature-calculated from the ent.ropy and energy of vacancy formation determined by Xairy et uZ.‘~O)and the increment in flow stress is linear (Fig. 7). (It should be noted here that the theoretical vacancy concentration at BWC, 2.6 x 10-j, compares well with that estimated as present. in loops after a specimen quenched from this temperature is aged at liO’C, i.e. 1.5 x lO-j-even though some vacancies are known to be lost to sinks during the aging treatment. In fact these figures indicate about 25 per cent loss of vacancies during quenching.) The optimum fit to the experimental results appears to be given by a modification of the equation derived by Peteh(“) for the force acting on a dis. lo&ion as a result of carbon and nitrogen atoms with mean separation A. The equation obtained by int,egration of the Cottrell expression for the interaction energy between a solute atom and a moring dislocation reduces to Aa=-

86GA& 7r

Fro. 6. Dislocation loops observed in 8 thin foil prepared from a pure magnesium mire quenched from XYC and aged for 5 min at 170°C.

1. DISCUSSION

r3 11 In % 011

(2)

for introduction of a distortion he into a lattice of atoms of radius r. Since In (A/&-) varies by a factor of two only over the range A = 20r t.o 200r, a random distribution of vacancies (i.e. atomic distortions) in

OF RESULTS

Two distinct hardening phenomena may be clearly distinguished in quenched magnesium specimens. The quenched material, which has no observable dislocation loops present, is hardened in comparison with air-cooled mat.erial but aging, which results in precipitat,ion of visible dislocation loops, produces a much more striking increase in flow stress. 4.1

Hardening

by dispersed vacancies

The quench-hardening of magnesium, in the absence of risible dislocation loops, must somehow be interpreted in terms of dispersed vacancies. The concentration of the latter will obviously increase rapidly at. temperatures approaching the melkg point of magnesium, and so does the strengthening effect-until incipient fusion occurs at grain boundaries. The size of specimen quenched in the present.

0

2 VACANCY

4 CONCENTRATION

6

8 x10’

FIG. 5. Variation of the flow stress increment with the theoretical vacancy concentration at the quenching temperature.

H_LXPSHIRE

HARDESISG

.AX~ HXRDIE:

OF PUKE

ma.gne~iunt nhcre there are 1.3 x 10ZO(= a) atoms/ mm3 gives 1 -13 = nC,, and hence d6G A& r%C,hl IG = 7

l

(3)

3$zC,)‘~”

of vacancies present. where C,. is the concentration This represents t$he observed linear dependence of of vacancies into clusters 10 upon C,. Aggregation \viII of course not only affect AE, the degree of atomic distortion. but will also prevent t,he dispersion of such distortions being adeyuat.ely represented by -1 as calculated above. Despite the inadequacy of available information about the state of aggregation of vacancies and the distortion introduced by thetn to the crystal structure, reasonable to investigate the it is nevertheless degree of correlation that ma? be achieved between theor!- and experiment, assuming a loss of -35 per cent. of vacancies during quenching and that G for magand r = 1.6 x 1Wi mm. nesium is 1iSO kgf/mm? Theoretical estimates of the fract,ional atomic volume of a racancin the noble metals have produced values ranging from 0.4 to O.tj,‘l” but there remains a great deal of uncertaint,J- about values for specific Good agreement, between observed and metals. calculated values of A.a for quenched magnesium are obtained using AF = 0.1 (Table 1) and the 1. Comparison of the increase in flow stress due to a vacancy dispersion calculated from (3) with that observed in quenched pure magnesium TABLE

Quenching temperature

Theoretical v*cancy concentration X 105

lo%,

Al7 from (3) A& = 0.1 kgf/mm”

.j25

2.626

5.0

0.46

.55U ___ 3‘3 5911

3.892 5242 6.964

2.9 3.9 5.2

0.64 0.52 1.06

Observed Aa ligf/mm” 0.31 0.70 0.91 1.16

disagreement introduced by employing higher values of AE would obviously be at least partially nullified by allowing for t,he aggregation of vacancies (and resultant increase in 11) that is inevitably present. 4.2 Hdening

by prismatic loop.~

Magnesium quenched from 62X does not show very pronounced strengthening by quenched-in defects until it is aged at temperatures above ambient and the marked st,rengthening that then ensues is obviously related to the simultaneous formation of prismatic dislocation loops-no doubt due to the collapse of vacancy discs TV-henthey exceed a certain size.

JIAGXESIIX

BY

L;\TTICE

DEFECTS

661

Most models offering an explanation of hardening by such dispersed obstacles to the movement of dislocations across slip planes (usual+ applied to cubic mat,eriaIs tith multiple slip SF-stems) are based on the mechanism of bowing between certain pinning points suggested by Oro\l-an,(*Z’ n-here T the shear stress necessary to more the dislocation is given by Gb r=s.

The major variations in approach concern the computat.ion of 11, the average length between pinning points but it is generalIF assumed that

(51) although k varies from 0.5 (Westmacott. et .6.(14’) to 2.S (Foreman”5)). If the hardness increment Aa is taken as 4~. then combination of (4 with 5) gives:

Despite his different approach to the problemobtaining an expression for the stress acting on a moving dislocation as a result of tetragonal distort,ions, Fleische+) also obtained a stress increment that was effect,ively proportional to (,v(z)l,‘“, where 11 is the diameter of a vacancy disc and S the concentration of such discs per unit volume. He assumed that a dislocation loop introduced a tetragonalkjstrain of 1.0 and t,hat 3 of the loops Kere effective to obtain a relationship equivalent. to (6) nith k = 1.9. A plot of the flow st,ress increment, ha, due to the prismatic loops that appear on aging magnesium quenched from EZY’C, against (Sd)“’ gives a reasonable relationship (Fig. S), although there appears to be pronounced deviation at the highest value of AG. The best general fit between theory and observations is only achieved by employing k = 0.09 in (6)-a value considerably smaller than that previously proposed. It might, however, be argued that this is because more effective hardening arises from the location of the loops formed during aging on the basal planes that are also the principal slip planes. The deviation at higher values of A?rodoes appear greater than would be espect.ed from esperiment,al error and, if the agreement between theory and esperiment is examined closely (Table S), it may be seen that high estimates of hardness increment are associat,ed with loop diameters below 1.7 x 10V4 mm, whereas low estimates occur with larger loops. In other words, large loops seem to promote more effective hardening than small loops for a given dispersion. This is demonstrated clearly by the

measurements

on specimens

aged for 2 min at 13FC

and for 10 min at MW.

0

OO

a a 0

l

3. The correlation between flow stress increment and the function (Xd)“? for magnesium aged after quenching from 5Zi’C.

FIG.

TABLE

2, Comparison

of observed flow stress increments with those cttlculoted from (6), using k = 9.09. for magnesium quenched from 525’C and aged at various temperatures

Loop densi:>-

-Aging Time min. ., 10 30 60 10 10 10 10

Esamination, in an electron microwope. of thin foils prepared from quenched and aged tnaterials after some plastic deformation in the wire form. reveals not, only the generally increased den&y of dislocations but also a pronounced tangling around the original prismatic loops that, formed from quenched-in defects (Fig. 9) and this is consistent with hardening due to Orowan bowing of disloc&ions pinned by t,he prismatic loops. Indeed, were it not for the complete absence of precipitate from foils of undeformed material, the structure might be mistakenly interpreted as dislocation-pinning by precipitate particles. Futher eridence that, condensation of racencies to produce collapsed loops and evaporation of -vacancies from these loops to sinks at higher temperat.ures are the basis of the competing hardening and soft,ening processes seen in isothermal annealing curves is provided by the act,irat.ion energies of the latter processes derived by the cross-cut method. The

Temperature ‘C

mm-3

Ii0 lit) 1iO 170 120 “40 300 340

i 10-J 1.’ _. d 17.5 16.0 14.’ 13.“ 16.3 12.3 9.9

rms Loop dia

Objerl-cd 117

Calc&tel.i la

lO-* mm

kgf/mm’

knfjmm’

1.69 1.99 1.56 1.74 1.26 1.56 0.59 0..59

3.29 7.3s 4.40 3.15 1.w 2.18 1.4; 1.05

2.89 3.67 3.30 3.09 2.54 3.14 1.65 1.50

softening process was studied at 1X and 2WC because the first process (hardening) is orer in a rery short time at these temperatures. On the other hand, temperatures of 110 and l-WC \vere found useful for studying the harclening, because softening effects are then negligible. The act,iration energy thus calculated for t.he hardening process KS 0.52 = 0.01 eV/atom: which agrees well with the value of 0.5 eV/atom measured by BeererG’) for the migration of racanties in magnesium. The softening at higher temperatures had an activation energ- of 1.22 + 0.3 eV/at,om and compares reasonably with bhat for self-diffusion in magnesium (1.39 eV/atom) measured by Shen-mon and Rhines. (Is1 It, is also in reasonable v-ith the values associated with the an-

ageement FIG. 9. Dislocation-loop interactions in a flail of magnesium that had been previously and aged.

deformed quenched

nealing of resisriri@ b-y Beerers(17) - 1.54 2 0.17 eV/atom, and Lery et rrl.‘ls) - 1.3 = 0.2 eV/atom.

EAMPSHIRE

4.3 Temperature

H_iRDESISG

ASD HAiRDIE:

independence

OF PURE

of hardening

Hardening resulting from the long-range interaction of moving dislocations with elastic dist,ortions of the lattice (as proposed for the hardening by dispersed vacancies) and hardening attributable to Orowan bowing between dislocation loops (as postulated for the aged materials) would both be expected to make a temperature-independent contribution to the flow stress. It was therefore not surprising that, in flow stress measurements between 57 and 373 Ii, air-cooIed, quenched and quenched-and-aged materials all exhibited a similar linear decrease of about 65 per cent, over t,his range (about 0.2 per cent per K). 5. CONCLUSIONS (1) The hardening of pure magnesium increases as the quenching temperature is increased above 500°C, until incipient fusion leads to a rapid decrease. (2) This increment in flow stress has been related to the concent,ration of vacancies present at the quenching temperature and reasonable fit obtained to a model depending on the obstruct,ion of dislocation motion by the presence of atomic distort,ions, using the model applied to interstit,ial solutes by Petch.(“) (3) The much greater contribution to st,rengthening t.hat arises when prismatic loops of dislocation form during aging (presumably due to the collapse of discs of condensed vacancies) may be interpreted in terms of Orowan bowing of dislocation segments pinned by the precipitated loops. (4) The hardness increment produced by this process is about 20 t.imes that predicted for f.c.c. lattices but t,his may be because the dislocation loops responsible for the pinning form on basal planes in magnesium and these are the principal

Y_iGSESIL-31

BP

L_ITTICE

DEFECT8

663

slip planes, i.e. the effect,ireness of the loops is greater than would occur Fv-ith a random dispersion. (5) There is some evidence that larger precipitated loops of dislocation cause more effective hardening than small loops. ACKNOWLEDGEMENTS

The authors are grateful to the Ministr? of Aviation Supply for financial support for the xork and t,o Magnesium Elekt,ron Ltd. for the supply of magnesium and technical advice about melting, casting and heat treatment. They also appreciate numerous discussions with their colleagues and the helpful advice and criticism of Professor Petch. REFERENCES 1. R. MADDIS and A. H. COTTRELL,Phil. Xag. 46, 735 (1955). 2. N. S. KE?*XY and A. A. BCRR. Trans. Net. Sot. AIXE 224,629 (1962). 3. K. H. WESTXACOTT,Phil. Xag. 14? 239 (1966). 4. D. HARDIE and .I. D. XICHAEL, Phzl. Mug. 23,319 (1971). 5. I. CRI~ELLI-VISCONTIand I. G. GREEXIELD, J. appl. Phys. 39,2845 (1968). 6. J. GALLIC+AX and J. WASEB~RS, Phil. Xag. 8.1455 (1963). 7. J. L. DAVIDSOS and J. >I. GALLIGAS, Phi/a. S’tatzcs Solidi 26, 345 (1968). 8. S. YOSHIDA, 11. KIRITAXI, Y. DEGUCHIand S. KAXIGAKI, Truna. Jap. Inst. Metals 9, (supp. 83) (1966). 9. J. S. LALLY and P. G. PARTRIDGE,Phil. Mzg. 13,9 (1966). 10. C. JLURY, J. HILLAIRETand D. SCH~LKHER, Acta -Vet. 15, 1528 (1967). 11. S. J. PETCH, Acta Net. 3, 186 (1955). 12. J. TAKAMZRA, Physical metallurgy, edited by R. W. Cahn, p. 881. Sorth-Holland, Amsterdam-London (1970). 13. E. OROWAX, Symp. on internal &eaaeS in metal8 and alloye, p. 451. In3titute of Metals (1948). 14. K. H. WESTMACOTT,C. W. FO~TA~N, and R. J. STIRTOS, Acta Net. 14, 1628 (1966). 15. A. J. E. FORENAX, Phil. Hag. 17, 353 (196s). 16. R. L. FLEISCHER,B&z Met. 10,835 (1962). 17. C. J. BEEVERS,Acta Xel. 11, 1029 (1963). 18. P. G. SHEWMOS and F. X. RHIXES, Ttuns. AIDE 290, 1021 (1954). 19. V. LETT J. HILLAIRET, D. SCHUUCHER, G. REVEL and T. CHAUDRON, Rep. internat. conf. on vacancies and intefstitials in metals, Jiilich-Conf.-2, p. 782 (1968).