The hardening of metals due to an increase in the stability of subgrain boundaries

THE HARDENING OF METALS DUE TO AN INCREASE IN THE STABILITY OF SUBGRAIN BOUNDARIES M. M. MYSHLYAEV Institute

of Solid State

and 1. M. ARISTOVA

Physics, Academy of Sciences of the U.S.S.R.. Chernogolovka Moscow

District.

142432

U.S.S.R.

and V. A. LIKHACHEV A.F. IotTe Physic+Technical

Institute, Academy of Sciences of the U.S.S.R., Leningrad, U.S.S.R.

(Received 21 September

1973; in reciseti,form

28 Juiy 1977)

Abstract-The results of mechanical and electron microscopic investigations related to the principal characteristics and the mechanism of hardening of metals during rapid cooling of limited duration during the creep process arc reported. The effect of various factors (structural state of metals, temperature, loading and time regimes of hardening) on the degree of hardening is investigated. The stability of the hardened state of metals and the effect of hardening on the thermoactivation parameters of creep are studied. It is established that hardening arises due to an increase in the stability of subgrain boundaries. The stability is ascribed to the formation near the sub-boundaries of dislocation loops and stacking fault tetrahedra resulting from coalescence of point defects generated during deformation. R&sum&-On prbente les rCsultats d’essais mdcaniques et d’btudes au microscope &ctronique sur lq caract&tiques principales et Ie mbcanisme de durcissement des mCtaux par un rcfroidisscment rapide de duree limit& au tours du fluage. On ttudie I’influence de divers facteurs (&at structural des m&aux, temptrature, rCgime de charge et duree du durcissement) sur I’importance du durcisscment. On ttudie egalement la stabilitt de l%tat durci et I’effet du durcissement sur les param&es d’activation thermique du tluage. On montre que le durcissement provient d’une augmentation de la stabilitb des sous-joints de grains. Cette stabilitt provient de la formation, au voisinage des sous-joints, de boucles de dislocations et de tCtra&res de fautes d’empilement provenant de l’agrtgation des dtfauts ponctuels produits au tours de la d&formation. Zosammenfissong-Es werden Ergebnisse mechanischer Messungen und elektronenmikroskopischer Untersuchungen mit Beziehung zu den haupt-siichlichen Merkmalen und der Verfcstigungsmechanismus von Metallen, die wiihrend des Kriechprozases fiir eine begrenzte Zcit rasch abgekiihlt wurden, dargelegt. Es wird der EinfluD verschiedener Faktoren (struktureller Zustand des Met&s, Temperatur, Belastung und Zeitbereiche der Verfestigung) auf den Verfestigungsgrad untenucht. Die Stabilitlit dcs verfestigten Zustands dcs Metalls und dcr EinfiuD der Verfestigung auf die Parameter der therm&hen Aktivierung des K&hens werden studiert. Es wird festge-stellt,da!3 die Vcrfestigung von einer Stabilittlts-

zunahme da Subkorngrenzen herrllhrt. Die Stabilitit wird der Bildung von Versetzungsringen und Stapelfehlertetraedern Grenzen durch das Zusammenlagem zugeschrieben.

in der N&he der von wiihrend der Verformung erzeugten atomaren Defekten

INTRODUCI‘ION Earlier work [l] has described the hardening behav-

iour of metals during steady state creep, due to very rapid cooling of limited duration. The schematic drawing in Fig. 1 explains the experimental procedure for achieving such effect. Here, the “OAC” curve corresponds to creep at constant temperatures T and stress u. The “AB” portion of the curve corresponds to deformation of specimens subjected to sharp cooling from T to To at instant tI. Similarly, the reverse increase in temperature from To up to T at instant t2 should result in recovery of the previous creep rate, i.e. should produce a curve parallel to the “AC”. As the experiments have shown however, deformation

usually occurs in accordance with the “BD” curve. This curve, which under certain condition may have a transient stage, is characterized by a significantly lower steady state creep rate. Characteristic feature of this hardening is described in Ref. 1. The decrease in the rate of creep due to a temporary cooling under load can be significant, e.g. there may be a reduction by a factor of 100. The present communication deals with the results of the detailed investigation of the above mentioned phenomenon. The creep tests were carried out using, basically, polycrystals under torsion and uniaxial tension. In the tensile experiments flat specimens (50mm x

453

454

MYSHLYAEV ef ul.:

THE HARDENING

OF METALS BY SUBGRAIN

BOUNDARJES

Table 1. Regimes of annealing deformation and hardening for materials investieated kIneaiing

Deformation regime prior hard.

Hard regime

treatment T 7, (“C)

d (kg/mm’)

::: g

100 100 80 1:

1.3 2.7 2.0 20

90 90 150 250 340 170 200

zI:+ 5.8t 9.ot

600* 850*

3.0 1.0 1.0 30 3’0 3:o 1.0

850* 850* 600 11W

1.0 1.0 3.0 1.0

200 200 232 200

247 29.5t It

11W 6OO*

30 1.0 1.0 1.0

417 200 200 400

54t 15.5

::;

54t 15.7

0.35. 0.10

267 100 100 20$

180

4.0

1.1

150

Materials

(a,)

ct

Al 99.99%

500 500 500 500 500 500 500 830 %*

3.0

AI 99.5% At 99.3% Al 98.8% A8 99.990/, Ag 99.92% Fe (0,03o/,C) cu 9997% cu 99.7% Cu +2.50/, Al

Cu + 5.00/.Al cu +41% at Zn Ni 99.93% Ni 99.3% +40% Co Ni +60% Co DJBAT (91.3% Al; 4.5% Cu; 0.5% Fe; 0.5% Si; 0.3% Zn)

11W 11W aged

s 1:.2t

( 1&s,

(2,

(;)

2

Designation in Fig. 2

3.6 1.8 0.87 0.90 7.2

20 20 20 20 20 20 20 20 220 20 135 20

17 17 96 17 17 18 18 120 2.0 17 2.0 18

2.7 6.4 7.5 7.0 5.0 3.0 3.4 7.5 7.7 5.0 2.9 4.0

18 21 12 11 16 13 4 14 1 17 8 7

20 20 20 100

z

27 20 3:2

2 5 20 10

: 2:3

;

1.9 130

3 15

3.0

19

1::: 240 6.8 9.3 :!!

2:9 lt8 0.66

36 20 10 2.0 10 17

2.0

* In vacuum, the rest in air. t Tension, the rest torsion. $ CooIitt8 within the furnace.

21Smm x O.ISmm . ..0.75rnm) were used. Solid and tubular cyliidrical specimens were subjected to torsion; their length was SO-7Omm. Solid ~pecirnens were 4 mm in diameter, the inner diameter of tubular specimens was 7mm and their outer diameter was 10mm. Before the tests, the specimens were annealed in the regimes represented in Table 1. The error of me~~ernen~ of deformation was 2 x 1O’3%. The temperature was controlled with an accuracy of f l”C, and heating and cooling of the specimens was usually done at a rate of about l”C/s. The microstructure of the specimens was investigated in JEM-150 and JEM-120 electron microscopes. R~ERi~R~AL

related hardening, since deformation associated with all the stages of the hedging treatment did not, as a rule, exceed 0.0020/,. In order to understand the physical nature of hardening, detailed investigations were carried out in

RESULTS

1. Mechanical tests The typical creep curves of the annealed and hardened specimens are represented in Fig. 2. The ordinate and abscissa represent the same parameters as depicted in Fig. 1. The particular test conditions, hardening. regimes and other data are tabulated in Table 1. As is seen from the curves in Fig. 2, the rate of creed of all the metals investigated decreased markedly after the hardening treatment: the ration go/&= n (where &,, i- are the rates of the steady state creep prior to and after hardening, respectively) reached values up to IO*. Such an effect can, in no way. be associated

with

an ordinary

deformation

+2 Time,

t

Fig. 1. Schematic drawing of the hardening treatment. Creep of the specimen at temperature 7’ and stress n prior to (OAC) and after (BD) hardening.

MYSHLYAEV et

THE HARDENING

id.:

0E’ METALS

BY SUBGRAlN

N

BOUNDARIES

17

Fe +O.O3%C

15

Nl+60%co

I3

A1 99.3’/.

435

c =: 2; “, m

12 Al 99.5%

&ii

ii

AL 99.3%

7

C&s.7%

6

Ni+40%Co

“, 0; _.. .. sf ZE =a t5p

$2

9

r!

qan n2d

5

Cu+S%

4

Al 9&B=/.

80”

2

Cu+2.6%Al

cid

I

Ag 99.92%

0

0.6 2.0 6.0

500

for for IO.0 for looq for Time, 1.0

4.0

A(.

curves:8.9,13,14,16,17,l8.l9,20~2~ curves: l,2,3.4,6,7,10,11,12 curve : 5 curve

: 15

h

Fig. 2. Creep curves of materials in the initial and hardened states (for details, see Table 2). On all the curves related to the initial state and on curves 2, 3, 5, 6, I, 13, 14 only the steady state of creep is shown for hardened specimens. order to understand the conditions under which harThe effect of the magnitude of the temperature dening arose, and also the e&ct of various factors jump during cooling from the constant temperature on the degree of hardening. The experimental results level, on the hardening behaviour, is illustrated by are given below. curve 2 in Fig. 4, showing the degree of hardening The experiments showed that hardening occurred of 99.30/, pure aluminium versus the lower temperaonly at deformational temperatures below a certain ture. It was also noted that very strong tooting did critical temperature (T,,) which is about 0.4-0.45 T,,, not cause hardening, i.e. curve 2 in Fig. 4 must have where Tm is the melting temperature given in K. Figure 3 shows to degree of hardening as a function of the mean temperature T,, of the cycle Eqecially the effects of the TAT,,, = Tf T,/2T,. upper and lower temperatures of the cycle on the degree of hardening were studied. For that purpose, \ \ in the first case the lower temperature was held con\ \ stant and in the second ease it was the upper one, I (+)-Al 99.99% It turned out that hardening within the temperature 2 (of-h 99.97% range less than critical prominently increased as the 3 (X)-Al 99.3% 4 (A I- A9 99.92% tipper temmture of the cycle increased while the 5 (of-OfBAT lower temperature remained constant. Hardening disappeared when the test temperatures passed through _IX&f-x ---a--0.5 0.6 the cri$ical temperature. For aluminium 99.3”/e pure Avcroge homolopus temperature, 7&./7, this is illustrated by curve 1 in Fig. 4. In these experiments, the stresses producing creep were selected in Fig. 3. Hardening as a function of the mean homologous temperature of the cycle for several metals under torsion such a way that the rate of the steady state creep (for all the metats T - To = 30”).The external stress was of the initial specimens should be 4.1 x ~O-‘S-~ at seiected to be such that hardening was similar for various all temperatures of deformation. materials.

456

MYSHLYAEV

et al.:

THE HARDENING

OF METALS

BY SUBGRAIN

BOUNDARIES

J.0

N P.0 1.0 0

10

00

40

“A..

-2--A

6 -

I

UpPer t~~oiure,

lCtfor curve 1)

Lower

V 1% I

0 I 0 I 0

L

0

tG$erature, I 60 Time, h lfor

20 Cootinp rote, 1

TIE,

min I 0

2.0 Creep

curve 2)

curvZO3.4

40 lC/rein I 40

(for

I

f 60 curve 5) I 60

( for curve 61 4.0

6.0

strain, % (for curve 7)

Fig. 4. The e&t of hardening conditions on the degree of hardening in Al. l-Effect of the upper temperatureof the cycle. 2-FSect of the lower temperatureof the cycle. 3, 4-E%ct of ageing time at the lower temperature.Curve 4 relates to the case of extension et 3.8kg/mm*. 5-Eff& of the cooling rate, 6-E&t of the unloading time for aluminium 99.S%.7--Effect of the preceding deformation by creep. In all the cases except those speciaIly pointed out, 99.3% alumininm was used under torsion. The upper and the lower temperatures were 80 and WC, respectively. Ageing at the lower tem~at~e was 17 h and the stress was 2.0 kg/mm2 for the external fibre. a maximum. For instance, nickel sharply cooled from 400°C down to 20°C did not harden after 79 h ageing, At the same time, at the tower temperature of 27O*C, a 2.5-fold hardening arose after 16 h ageing. A series of experiments on ~umini~, copper nickel of various purities, their alloys and several other materials showed that hardening occurred only when the ageing of the specimens under load at the lower temperature exceeded a certain characteristic time. The incubation period depended on the experimental conditions and the material used. Thus, in aluminium 99.3% pure, the incubation period was about 5min at the lower temperature of 20°C. Under analogous conditions, in nickel, the incubation period was several days. Nickel, however, hardened after l-2h ageing at 210°C. Armco iron and brass strongly hardened after 1.5 h ageing at 20°C. It is of importance to note that after the incubation period was over, ageing at the lower temperature was followed at first by very rapid, then, gradualIy diminishing increase in the hardening level. Eventually a “‘saturation” in the degree of hardening was reached. Figure 4 (curves 3.4) shows the corresponding curves for aluminjum subjected to torsional and tensile deformations.

Occurrence of the hardened state was found to be close& associated with the cooling conditions. Hardening of all the materMs used was obtained only upon rapid cooling. The critical rate of cooling below which no hardening was observed depended on the material and experimental conditions. As is shown by curve 5 in Fig 4, for aluminium 99.3% cooled from 80°C down to 2O*C, it was about O.lYC/s. It is seen from the figure that cooling at a rate exceeding O.W/s did not increase the hardening level. It shall be mentioned’ that even when the specimens were cooled within the furnace, the rate of cooling could be higher than the critical one. Furthermore, preservation of the unha~en~ state required an extremely slow cooling, often during several days. The rate of the subsequent heating from Te to T did not affect the degree of hardening The external stress and the nature of its alteration at various creep stages and during the hardening treatment decisively affected the hardening IeveI. In order to obtain the hardened state, the presence of an external stress was required both during creep prior to cooling of the specimens and when they were cooled and aged ‘at the lower tem~rature. No hardening was obt!ined if there was no load on the sample at the lower tem-

MYSHLYAEV c, crl.: THE HARDENING perature. The same was true also when at the lower temperature. the sign of the stress (even for a short duration) was opposite to that which was used during the preceding creep tests. If prior to cooling the specimens were unloaded during the time r, and then were loaded again and immediately cooled, the rise of hardening was the stronger the shorter time T was (curve 6 in Fig. 4). The effect of the magnitude of the external stress on the degree of hardening has been also studied. The hardening was stronger the higher the applied stress was. This tendency, however, displayed itself differently in various materials. Thus, in 99.37” pure aluminium subjected to creep under torsion at 80°C and cooled down to 20°C for 17 h, hardening was

n N 8.4 at 3.0 kg/mm’ but did not exceed n N 2 at stresses less than 2.5 kg/mm’. At the same time in aluminium 99.5%, hardening under the analogous conditions was practically independent of the magnitude of the external stress. As the experiments showed, the degree of hardening depended on the stage of creep at which the hardening treatment was carried out. In all cases it did not arise at the beginning of creep. In the middle of the first stage, however, hardening became noticeable, and by the initiation of the steady state creep it reached a maximum level that, subsequently, was practically independent of the preceding deformation.

OF METALS BY SUBGRAIN

BOUNDARlES

It took place despite the fact that the strain during creep (including the first stage) was generally rather small compared with the instantaneous strain during loading. In Fig. 4 curve 7 illustrates hardening versus the preceding deformation by creep for 99.3% pure aluminium. No qualitative difference was observed in hardening in torsional or tensile specimens. In several cases, however, (for instance, in aluminium 99.3%) the degree of hardening was less at tension than that at torsion though the test conditions and the regimes of hardening treatment were equivalent. The experiments with several materials under torsion showed that hardening of the specimens

depended on the operating load applied at the preceding stage of creep. If the reversed loading was applied to already hardened specimens, no hardening occurred. This effect is illustrated for instance, by curves l-4 in Fig. 5. Note, too, that the rates of the steady state creep for curves 3 and 4 are analogous and coincide with the rate of the steady state creep corresponding to curve I. The problems associated with anisotropy of hardening are described in detail in Ref. 2. It has been found that the degree of hardening can be increased by repeating the hardening treatment (curves 1, 2 in Fig. 6) and by employing higher annealing temperature and/or annealing time (Table 2). Hardening was sufficiently stable at all tempera5

Time,

h (for

curves

1.4)

Fig. 5. The effect of the reversal in sign of stress and plastic deformation on the curves of creep of unhardened (1.5) and hardened (26) aluminium specimens under torsion. 3, 4-curves of creep of 99.5% pure aluminium at 80°C and 20 kg/mm’ after the reversal in sign of stress at the steady state stage of creep for the initial (1) and hardened (2) states. Hardening was obtained by ageing at 20°C during 96 h. 7, I-curves of creep of 99.3% pure aluminium at 80°C and 3.0 kg/mm2 for the initial (7) and hardened (8) specimens that were subjected to active deformation by torsion (10%) towards creep at the points corresponding to the points D and G on curves 5 and 6, respectively. 9, lo-same for specimens subjected to a momentary loading of the reversed sign at the instant, corresponding to the points E and F (at the time E and F the stress was reversed, after 30s it was reestablished).

A.M. 26/3--

‘i

457

458

MYSHLYAEV et al.:

THE HARDENING

OF METALS BY SUBGRAIN

BOUNDARIES

Table 2. Hardening of aluminium 988% as a function of the annealing treatment (tensile tests at 90°C and 5.8 kg/mm’; lower temperature 2OC, 1.8 h ageing at 20°C) $

B

Annealing

5 6.0

Time(h)

T (“C) . 74.0 'Z

oao.c B5 2.0co

:: =& 2.0

8 's :: LO- " B 0"

2 3 3 1.5 3

300 300 400 500 500

r D

tures below the critical one. Above this temperature it was removed by annealing, whereas the annealing critical temperature approximately coincided with the hardening critical temperature. Curve 3 in Fig. 6 shows the effect of the annealing temperature on the post annealing hardening in aluminium. It is seen that the complete annealing of hardening occurred from approximately 150°C. The hardening process showed stability against the influence of deformation by creep. Hardening remains even after an appreciable extent of creep deformation (curves 2,4 in Fig. 7). It shall be emphasized; however, that weak hardening ‘disappeared during creep. This is illustrated by curves 5,. 7 of Fig. 7.

-* *o 2 4 6 Number of hardening operation cycler(for curves1,2) I I I 1 0 IS0 250 300 Annealing tempemturc. r: (for curve 3 1

Fig. 6. 1.2-the degree of hardening as a function of hardening treatment cycles. for 99.97% pure Cu and 99.3% pure aluminium under torsion. l-99.97% pure Cu; upper temperature = 17WC, lower temperature = 13O”C, external stress = 9.2 kg/mm*, ageing time = 4 h (at 13O“C). 2-99.3x pure Al; upper temperature = 83”C, lower temperature = 13°C. external stress = 3.5 kg/mm’, ageing time = 17 h (at 13°C). 3-Post-annealing hardening of aluminium specimens (99.3yd as a function of the annealing temperature. Torsion at 80°C and 2.0 kg/mm2.

/

I

I h (for I

Time,

Time:’

I 1.2

8.0

I.0

I

1.5 1.7 2.5 2.7 3.4

2.0 h (for

h (for

curves

1.2) I

I

10 curves

4.0

I

3.4)

20 curves 5.6.7)

Fig. 7. Curves of creep of weakly and strongly deformed specimens under torsion. I, 2-for aluminium (99.5’2;) at 8o’C and 3.2 kg/mm* in the, initial state (I) and after hardening (2) obtained after 84 h ageing at 20 C. 3. 4, S-for nickel at 400°C and 21 kg/mm* in the initial state (3) and after hardening at 170” during 16 h (4) and at 20°C during 79 h (5). 6, ‘I-for nluminium (99.3’%,) at 80°C and 2.0 kg/mm* in the initial state (6) and after IOmin ageing at 2O’C (7).

MYSHLYAEV

et af.:

THE

HARDENING

A striking example or hardening stability was shown by the specimens subjected to rapid plastic deformation. It is well-known that under normal conditions such deformation gives rise to strong work hardening and hence to a decrease in the rate of creep. This can be deduced by comparing the courses 01”curves 5 and 7 in Fig. 5. In the same figure, curves

OF METALS

BY SUBGRAiN

BOUNDARIES

459

a cellular structure with complex networks of dislocations of high density both in the cell boundaries and in the cell interior. An example of such a defect structure is shown in Fig. 8(a). In alloys, compared with

pure metals, the dislocation density in the boundaries and in the volume of the cells was much higher and increased as the amount of an alloying element in6 and 8 show the effect of active deformation on the creased. In Cu-5 wt.O/, AI and Ni-60 wt.% Co, the behaviour of the hardened specimens. In contrast to disIocation density was so high, that continuous disIocation networks were observed. During the primary the previous case the hardened specimens subjected stage of creep dislocation redistribution occurred in to active deformation at first showed the behaviour of an accelerated deformation and then reached the the specimens in such a way that dislocation-free areas appeared which were disoriented subgrains. rate of creep characteristic to the hardened state. The steady state stage of creep was characterized Finally, it shall be mentioned, that rapid active defermation of the reversed sign in relation to that at by a prominent subgrain structure. Practically no diswhich the hardening treatment was performed, com- locations were in the subgrain interiors. For all the pletely eliminates hardening (curve 10 in Fig. 5). metals but aluminium, the subgrain boundaries were Moreover. a momentary reversal of the sign of the rather dense irregular dislocation networks of the applied stress also eliminates hardening although the type shown in Pig. 8(b). Aluminium crystals at the extent of the strain during such reversal is small (less steady state stage were characterized by the subgrain structure with boundaries generalfy formed by hexagthan 0.1%) and despite the fact that in the unha~en~ specimens (curve 9 in Fig. 5) this procedure does not onal, rarely quadrangular dislocation networks or affect the steady state creep. In the following series uniform dislocation cell walls. The subgrains were about 3 pm in sixe and the average spacing between of experiments on 99.3% aluminiurn, the creep pardislocations in boundaries was about 0.1 pm. The ameters of the specimens in the initial and hardened micrograph of one of such subgrain boundaries is states were studied. The specimens in the hardened shown in Fig. 8(c). Polygonization of the structure state were subjected to torsion under the conditions corresponding to stable hardening. In both states the was more prominent in the specimens subjected to higher annealing temperature and/or longer annealing rate of the steady state creep vvas stress and temperatime. It should be noted that in the microstructure ture dependent in the following way: of all investigated metals (except annealed aluminium) <=Aexp(-q)(I-$J (1) at various stages of the creep deformation, diilocation loops were observed, but they were scarce. In Ag specimens corresponding to the steady state creep, Here the constant A = 10” s-r, U = 1.2eV and single large stacking fault tetrahedra were observed. T, = 0.7 x lo3 K were practically independent both In one hand, after the hardening treatment the subof the initial state of material and of the hardening grain structure typical of the steady state creep level. The coefficient y alone appeared to be structure remained the same as before the hardening treatment. sensitive. It responded to both factors and decreased On the other hand, an additional characteristic feaupon hardening by a factor of 1.5. These experimental ture of the structure of hardened specimens was the results are described in detail in Ref. 3. presence of numerous dislocation loops in subgrain 2. Electron microscope investigations boundaries and near them. The loops were 100-500 A in size, their average density was about lo9 cm- ‘. The The initial state of cylindrical specimens was charnumber of regions containing dislocation loops and acterized by the subgrain structure, whereas, the specimens annealed at lower temperatures or for the loop density in them increased as the degree of hardening increased. For instance, in aluminium shorter time had more complex dislocation structure. specimens strongly hardened under torsion, loop-free In general the grains of flat aluminium specimens and, subgrain boundaries were rarely observed; instead also, of all silver, copper, nickel, Cu-AI and Niio boundaries containing numerous dislocation loops specimens contained a small number of single dislocawere often present. The subgrain boundaries were distions. Sometimes, in individual grains there were tantorted in the region that contained the loops. This gled dislocation networks. Plastic deformation of the specimens during the loading process caused a could be seen clearly in aluminium specimens. The higher the density of the loops was, the more complex marked complication of the structure. As a result, the were the boundaries. In the subgrain interiors (far transient or primary stage of creep in torsion of aluminium was characterized by subgrains with bounfrom the boundaries), as a rule, no dislocation loops daries formed by complex dislocation networks and were observed. Sometimes, regions were observed with a considerable dislocation density in the subwhich contained loops and a small number of dislocagrain interior. In aluminium deformed in tension, and tions, which can be interpreted as subgrain bounalso, in Cu, Ni, Si, Cu-Al, Ni-Co, t~mination of daries. In some cases, disrocation loops did not surloading and initiation of creep were characterized by round the boundaries but were Iocated at one side.

460

MYSHLYAEV er al.:

I-HE HARDENING OF METALS BY SUBGRAIN BOUNDARIES

Fig. 8. Dislocation structure of specimens corresponding to different states. (a) in silver at the initial stage of creep under tension; (b) the same, in the steady state stage; (c) a subgrain boundary in aluminium in the steady state stage of creep under tension; (d) loops in hardened aluminium (torsion); (e) stacking fault tetrahedra in hardened silver (tension); (f) in aluminium subjected to the reversal in sign of the loading.

In hardened Ag specimens and in Cu-2.5 wt.% Al, Cu-5 wt?A Al and Ni-60 wtP/, Co, in subgrain interiors and in regions near them stacking fault tetrahedra were observed in addition to dislocation loops, as illustrated in Fig. g(d) [4]. Analysis of dislocation loops was done for aluminium specimens by the technique described in the Ref. 5. The inv~tigation of numerous dislocation loops showed that they were always prismatic and lying in { 110) planes, { 111} planes and in planes located between them (i.e. in planes that correspond to the subsequent rotation of a ( t 10) plant (or { 111:) against the (110) direction until it coincides with a f 1I I j (or {I IO)) plane. In the case of torsion itIf the analysed loops were of the vxancy type [6]. In the

case of tension, the majority of loops were of the interstitial type [7]. If the hardening treatment was carried out under conditions in which no’ hardening occurred, no noticeable increase in the number of dislocation loops or stacking fault tetrahedra was observed; they were scarce. Thus, loops were practically absent in unhardened aluminium specimens. This was pa~icularly true, in specimens sharply cooled on the steady state stage from temperatures above critical down to room temperature, and unloaded after a very long ageing time at this temperature. It was also true in specimens that were slowly cooled within the furnace at steady state conditions and untidy after a tong ~~~c~llgtime at 20°C. Loops were practically absent in the specimens that although

MYSHLYAEV

et cd.:

THE HARDENlNG OF METALS BY SUBGRAIN BOUNDARIES

hardened were subsequently annealed at tcmpcraturcs above the critical temperature. As was noted above, the steady state creep was characterized by polygon structure. We investigated the response of this structure to the reversal in sign of thk loading in torsion. It was shown [2] that the application of a stress of the reversed sign (in relation to that at which the subgrain structure was formed) caused the destruction of the subgrain boundaries, and gave rise to numerous regions with high dislocation density where no subgrain structure was observed. An example of such structure in aluminium is represented in Fig. 8(e). If the specimens were further subjected to a creep test, then, over a period of time, the subgrain structure formed again, analogous to its formation in the annealed specimens during the process of the initial creep. The newly-formed subgrain structure occurred independently of the sign of the applied stress. DISCUSSION OF THE EXPERIMENTAL RESULTS 1. The nature of hardening Before discussing a possible nature of hardening, we mention several facts resulting fro& mechanical and electron microscopic data. 1. The only structural element observed in the hardened specimens were dislocation loops and stacking fault tetrahedra. If no such defects arose (for’instance, during the hardening treatment in the temperature range above critical temperature) or, if they were eliminated by annealing, then hardening either did not occur or it was removed, respectively. 2. For hardening to take place, a polygon&d structure produced by deformation is needed. Hardening was absent in the absence of polygonized structure and disappeared if the polygon&d structure was eliminated (due to application of 6 stress of reversed sign). The degree of hardening was higher, the more prominent the polygonisation, the more regular and dislocation structure of the subgrain boundaries, and the higher the density of loops and tetrahedra in the boundaries were. In view of the above mentioned observations, the most probable mechanism of hardening can be an increase in the stability of the subgrain boundaries due to formation of dislocation loops and stacking fault tetrahedra. The principal possibility of dislocation pinning and, therefore, hardening induced by these defects, is widely known. Therefore, in this presentation it is necessary only to demonstrate that loops and tetrahedra were the main reasons for the observed hardening. Arguments in favour of this hardening mechanism arise both from qualitative and quantitative considerations; first, because no other structural elements beside loops and tetrahedra were observed in the hardened specimens; second, because of the reasons given below.

461

If a moving individual di$ocation is assumed to o+ercome the stress field of the loop, the effective counteracting stress must, within an order of magnitude. be equal to Afltir,,,: /?Gh/l; Q,

(2)

where G is the shear modulus, h is the Burgers vector, i)n is the loop density related to the unit area of the subgrain boundary, /I = 0.5. By assuming for aluminium p. 2 IO9 loop/cm’ in the average, we obtain Au,,, 2 1.2 kglmm’. On the other hand, it follows from equation (1) that in order to maintain also the initial rate of creep in the hardened state, the specimens have to be loaded by an additional stress Au x ao(yo - 7,)/y, where cr,, is the stress causing the rate of creep of unhardened specimens, yO, y,, are the values of the y coefficient in (1) prior to and after hardening, respectively. Then, by using the experimental data (yO/yI I 1.5) we obtain for the particular test conditions (00 z 2 kg/mm’)Au = 0.9 to 1.8 kg/mm’, i.e. Au is close to Au,~~ If more dislocations are assumed to be present between the loops (as in alloys containing fine-dispersed precipitates) the effective additional stress coincides with (2) at /? * 1.0. In other words, this mechanism approximately explains the increase in hardness. Evidently, the real inhibition to dislocation motion by loops will be further strengthened if dislocations directly interact with loops. Under these conditions, additional pinning will appear due to dislocation reactions in the nodes resulting either in the formation of new dislocation segments or in dislocation annihilation in places of interactions. Let us now consider the efficiency of subgrain boundary pinning by loops as a whole. It can easily be shown that the boundary located in the field of stress a, experiences an effective pressure produced by the stress peIl z (b/a,J a, where acff is an effective spacing between dislocations in a boundary. If this stress is produced by loops formed during the hardening treatment then, in order to retain the initial rate of creep it has to be compensated by the corresponding increase of the external stresses. The effective pressure on the boundary produced by loops P” can be estimated by considering that loops interact only with closely located dislocations because the stress produced by loops decreases with spacing r to a value no less than 1/2r2. At the given assumptions p. z f11Gb2p,, from which for the effective additional stress, we obtain Au,,, = BIGba.rtp. = BlGbp,p; ‘12,

(3)

where pI is the dislocation density in subgrain boundaries, & z 0.5. By assuming, in accordance with the experimental data acll = 0.1 pm in the case of aluminium, we obtain Auelf z 0.4 kg/mm2, i.e. a value close to the experimental one. Among the two mechanisms of hardening by loops considered here, the second one associated with the subgiain boundary

462

MYSHLYAEV

er cd.: THE

HARDENING

OF METALS

pinning seems to be the most probable. In fact, if in the first case only the density of dislocation loops is of importance, then in the second case the dislocation density in the boundaries is of importance, too. In accordance with Ref. 3 the efficiency of the hardening activity of loops must be less for materials where the dislocation density is higher in the subgrain boundaries. This is in agreement with the experimental results. The considered mechanism of an increase in the boundary stability explains several basic characteristics of hardening. Thus, an increase in the degree of hardening with increase in temperature and’ time of preliminary annealing of specimens (see Table 2) can result from an increase in stability of the polygonized structure arisen during creep. The effect of prelimin& deformation (curve 7 in Fig. 4) and the effect of reversal in sign of the applied stress (Fig. 5) are associated with the formation in the first case and with the destruction in the second case of the subgrain [2,3,7]. Finally, presence of the annealing critical temperature (curve 3 in Fig. 6) can be explained by the dissolution of loops or tetrahedra at high temperatures. It has to be noted that the experimentally obtained critical annealing temperature coincides with the annealing temperature of the loops, which for all the metals, is about 0.45 T, [83.

Two different mechanisms for the formation of dislocation loops and stacking fault tetrahedra are known to exist. They can arise either directly from dislocations (for instance, due to dislocation reactions) or due to point defects coalescence. Referring to loops in aluminium that were investigated in detail in the present work, it can easily be seen that the most likely reason of loop formation must be coalescence of vacancies (in the case of torsion) or of interstitial atoms (in the cast of tension). It is difficult to explain the observation that’the loops in alumini~ were of vacancy type or of interstitial type only, solely in terms of mechanism of loop formation. It has to be noted that loops and tetrahedra arose at the lower temperature of the hardening treatment when there is no defowatioti and, hence, no dislocation movement. Besides, the hypothesis concerning loop formation directly from dislocations presents a severe probtern when trying to interpret the detailed kinetics of occurrence of the hardened state. Thus. we consider the mechanism of point defect coalescence in detail. In terms of the given model, loops arise due to super-saturation with point defects resultin from rapid cooling. The characteristic time 50 Z L$D for point defect coalescence into discs depends on the characteristic diffusion length Lo and the diffusion coefficient of vacancies or interstitial% D. By assuming L, equal to the typical spacing between loops, i.e. to the spacing between coalescence centres. we find, that in alurninil~n~ r0 P IO*s for the vacancy mechanism [9]. This value is close to the experimentally observed incubation period of alu-

BY SUBGRAlN

BOUNDARIES

minium hardening (see curve 3 in Fig. 4). The other characteristic time of the order of 104 s (Fig. 4) corresponds to L, z 1 pm. This time can be associated with vacancy diffusion towards loops at. distances comparable with subgrain sizes. Subgrains having just these sizes were typical of the structure of the hardened specimens. The experimental data represented in this work permit the“~timation of the lower limit of concentration (c) of point defects remaining in a specimen by the initiation of coalescence process. In fact, this concentration can be given as

1

2Gb4 d,k~, +Q, (4) E where d is the mean grain size, d, is the loop diameter, al is the characteristic spacing between the atoms, Cb is the equilibrium concentration at the coalescence temperature T,,. Her,e, the first term takes into account the number of defects required for the f&nation of loops, the second considers a change’ in their equilibrium concentration due to the effects of the dislocation line curvature [9] and the third (cl) considers the defects which disappear in other sinks. At the normal temperatures of coalescence for all large-size loops the second term can be ignored compared with the first term. Thus, in al~ini~, by assuming T,~:OOK, d,z:& dz3pm, pn s fOg loops/en?, we obtain the value of about 2.5 x 10q6 for the 6rst term, and of only lo-’ for the second even in the case of vacancies. (The activation energy of vacancy formation in aluminium is assumed to be 0.8eV [9].) If loss of defects in the other sinks is ignored, then, the value of the first term gives the quantity characteristic of the initial cohcentration of defects. A very important conclusion results from the above estimation: point defects that have coalesced into loops cannot be of thermal nature. For instanoe, in aluminium at lO@‘C,the thermal ,equilibrium concentration of vacancies approx~ately equals to 1O’g, which is by 3 orders of magnitude less than that estimated above. For interstitials, this difference has, naturally, to be greater. From this it can be concluded that these point defects are related to deformation process. Let us estimate the concentration of point defects produced during plastic deformation. If deformation occurs due to the movement of dislocations, then, the rate of generation of point defects is approximately equal to [lo] c=

3tWGl d

+c0exp

dc - = a&* dt

= a&C,

(5)

where p is the mean dislocation density, b is the effective Burgers vector, i is the mean dislocation velocity, ( is the rate of deformation, a0 < 1 is a coefficient considering the fraction of the non-conservative moment. If the effective lifetime of defects equals IO 5 then in the steady state regime of creep the excess concentration of point defects will be AC =.dc/ dfT = a&r. This relation contains the criterion for

MYSHLYAW’

ct cd.: THE HARDENING

the principal possibility of the effect of the above mechanism, since the coeflicient a0 must satisfy the requirement a0 < 1. In fact, here, all the values but a0 are estimated rrom the experiment. A deviation from the equilibrium concentration is estimated from the data of sizes and concentrations of loops. The rate of deformation is measured directly in the experiments. The time T can be determined from the curve G in Fig. 4. For the mostly typical conditions for aluminium under torsion, .5 P lo-‘s-l, AC z 2.5 x 10-6, T 2 10’s. Then, a0 z lo-‘, which is quite acchecking

ceptable and satisfies the criterion a,, < 1. Thus, it follows from the above data that in aluminium, loops could be formed due to coalescence

of point defects (at the lower temperature) produced in the process of the preceding steady state creep (at the upper temperature). For other metals, the experimental data were incomplete and specific analysis of the nature of loops and tetrahedra was not undertaken. It can, however, be concluded that the observed secondary defects (loops and tetrahedra) arise from the same cause. One comes to this conclusion upon comparing the facts concerning the behaviour of aluminium on the one side and of the other metals on the other side, and, also, the facts associated with the qualitatively similar character of the structural changes accompanying the process of hardening in all the materials. The validity of the mechanism discussed is confirmed by fundamental characteristics of the effect of hardening. Thus, the presence of the critical hardening temperature (Figs. 3 and 4) is explained by the fact that it is impossible to obtain the needed concentration of point defects in the vicinity of subgrain boundaries due to high diffusional mobility of defects. The final velocities of point defect migration also hinder the attainment of a critical value of excess vacancies and interstitial atoms. Hence the requirement of a sufficiently high rate of cooling in the hardening treatment which is in agreement with the experimental data (curve 5 in Fig. 4). Similar considerations permit to understand the effect of the extent of temperature drop on hardening. The lack of hardening during cooling down to low temperatures (curve 5 in Fig. 7) is associated with inadequate diffusion. Unfortunately, at present, it is very difficult to explain the consequence of the loading factor on the cooling stage and on further ageing at a lower temperature. Also, it is not clear why vacancies are formed in torsion and interstitial atoms in tension. One could, however, assume that occurring of interstitial loops and lack of vacancy in specimens under tension are associated not with the type of point defects existing at the moment of cooling, but with the effect of the stress state on the process of loop formation. In fact, it can easily be seen that in the field of tensile stresses u, a prismatic dislocation loop is subjected to a radial component of the F, force equal to F, = a& ub, where b is the Burgers vector of a dislocation forming a loop, aXXis the direction cosine

OF METALS BY SUBGRAIN

BOUNDARIES

463

that characterizes the rotation of the chosen system of co-ordinates against the “natural” system of CO_ ordinates oriented by the s axis along the tensile axis, where b > 0 for an interstitial loop and b < 0 for a vacancy loop. Since afxd > 0. all interstitial loops undergo radial “tension” and vacancy loops undergo “compression”. Therefore. one can assume, that the lack of vacancy loops is simply associated with the impossibility of their growth in the field of tensile stresses. The same logic, however. lcads to the conclusion that in torsion a purely prismatic loop will be subjected to a radial force F, = -2a,,a,,ob whose sign is not determined unequivocally since the product of the direction cosines axraxy can be either more or less than zero. Therefore, it has to be concluded that the type of loops is determined by the type of point defects. CONCLUSIONS 1. Results of an investigation of the effect of hardening of metals that arise during very rapid cooling of limited curation during the process of creep are given. 2. It is stated that hardening arises due to an increase in the stability of subgrain boundaries by dislocation loops and stacking fault tetrahedra forming near them. 3. It is’shown that loops and stacking fault tetrahedra form due to coalescence of point defects (vacancies and interstitial atoms) that are generated during the creep process. Ackmowledgemenrs-The author expresses

his sincere appreciation to Professor A. Mukherjee and Professor 0. D. Sherby for their interest and for the general help extended during the preparation of this paper.

REFERENCES 1. G. V. Vladimirova, V. A. Lilchachev, M. M. Myshlyaev and S. S. Olevskii, Dokl. Akad. Nauk S.S.S.R. 188. 1034 (1969). 2. V. A. Likhachev, M. M. Myshlyaev, S. S. Olevskii and T. N. Chuchman, Fiz. metal/. Metallooed. 37, 1279 (1974). 3. G. V. Vladimirova, V. A. Likhachev, M. M. Myshlyaev and S. S. Olevskii, Fiz. metall. Metafloued. 31, 177 (1971). 4. k. G. Myshlyaev and S. S. Olevskii, Probl. Prochnosty 3, 24 (1975). M. M. Myshlyaev, S. S. Olevskii, I. M. Atistova and V. M. Shpeizman, Fiz. metall. Metalloved. 37, 1013 (1974). 5. P. B. Hirsch, A. Howie, R. B. Nicholson, D. W. Pashley and M. Y. Whelan, Electron MicroscoDvof Thin Crvs_ rals. Butterworths,.London (1965). . . W. L. Bell and G. Thomas, Phil. Msg. 13, 395 (1966); Phys. Status Solidi 12, 843 (1965); L. R. France and M. H. Loretto, Proc. R. Sot. (A)JW, 83 (1968); Phil. Mug. 19, 873 (1969). 6. M. M. Myshlyaev, S. S. Olevskii, L. V. Vladimirova and V. A. Likhachev. Dokl. Akad. Nauk S.S.S.R. 191, N 5, 1022 (1970). 7. M. M. Myshlyaev, S. S. Olevskii, S. R. Maksimov, V. A. Likhachev and G. V. Vladimirova, Phys. Starus Solidi (A) 7, 325 (1971).

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THE HARDENING

8. A. Ball and R. E. Smallman, Am tnetuN. 14, 1349 (1966); M.‘. Doyama, ht. Conf. Lattice De$ws in ~uenc~~ Met&s. Argonne National Laboratory, 15-17 June (1964). Academic Press, New York (1965); S. Yosbkia, M. Kiritani and Y. Shimomura, ibid.; J. Silcox and M. J. Whelan, PM. &fag. 5, I (1960).

OF METALS BY SUBGRAIN

BOUNDARiES

K, i-l. Westmacott, R. S. Barnes and R. E. Smallman, Phil. Mug. 7, 1585 (1962); J. 1. Lutton, K. U. Wcstmaeott and L.C. Potter, Two. A.I.M.E. 233, 1757 (1965). 9. J. Friedel, 5~~f~~tio~. Pergamon Press, Oxford (1964). 10. A. N. Cottrefl, LXslocations and Plastic Flpw in Crystuls. Clarendon Press, Oxford (1953).