The work-hardening of Cu-Fe alloy single crystals containing iron precipitates

THE

WORK-HARDENING

OF C&Fe ALLOY SINGLE IRON PRECIPITATES*

K. MATSUURAt,

CRYSTALS

CONTAINING

and K. WATANABEt

M. TSUKAMOTOt

Some Cu-Fe alloys, which contained the spherical y-iron precipitates, were tensile-tested between 77°K and room temperature and the dislocation structures were observed by an electron-microscope to examine the effect of iron particles on the work-hardening of the alloys. In addition, the y_* transformation of iron particles induced by plastic deformation was examined by magnetic measurements. The extent of region of easy glide was decreased with decreasing deformation temperature and increasing particle size. This was closely associated with the strain-induced transformation of iron particles. The lower the temperature and the larger the particle size the more rapidly the transformation occurred, being accompanied by the generation of dislocations. It was concluded that the strain-induced transformat,ion stimulated the activation of secondary dislocations near the particles and so the beginning of stage II. ECROUISSAGE

DES

MONOCRISTAUS D’ALLIAGES DES PRECIPITES DE FER

Cu-Fe

CONTESAYT

Des alliages Cu-Fe contenant du fer y pr6cipit6 sous forme spherique ont Qt.5soumis a des essais de traction entre 77°K et la temperature ambiant.e. Les structures de dislocations ont QtB examinbes au microscope Qlectronique pour Qtudier l’influence des particules de fer sur 1’Ccrouissage des alliages. En outre, la transformation y --, a des particules de fer, induite par la deformation plastique, a Btt5Btudib par des mesures magn6tiques. L.&endue du domaine de glissement facile diminue quand la temperature de deformation diminue et quand la taille des particules augmente. Ceci est Btroitement li6 8, la transformation des particules de fer induite par la dhformation. La transformation se produit d’autant plus rapidement que la temp&ature est plus basse et la taille des particules plus grande; elle est accompagn6e par la creation de dislocations. Les auteurs concluent que la transformation induite par la deformation favorise l’aotivation de dislocations secondaires et, par consequent, acct%%re le dbmarrage du Stade II. DIE

VERFESTIGUNG

VON

Cu-Fe-EINKRISTALLEN

MIT

EISES-AUSSCHEIDUNGEN

Einige Cu-Fe-Legierungen mit kugelfijrmigen y-Ausscheidungen wurden zwischen 77°K und Raumtemperatur im Zugversuch verformt. Zur Untersuchung des Einflusses der Eisenteilchen auf die Verfestigung wurde die Versetzungsstruktur in den Proben elektronenmikroskopisch untersucht. AuDerdem wurde die durch die plastische Verformung induzierte y-a-Umwandlung der Eisenteilchen mit Hilfe magnetischer MeDmethoden analysiert. Mit abnehmender Verformungstemperatur und zunehmender TeilchengrCiDe nimmt die Liinge des Bereiches I (easy glide) ab. Die spannungsinduzierte Unwandlung von Eisenteilchen hlngt eng damit zusammen. Je tiefer die Temperatur und je grdl3er die Teilchen sind, umso schneller erfolgt die Umwandlung, die mit der Erzeugung von Versetzungen verbunden ist. Die SchluOfolgerung daraus ist,, da13 die riktivierung sekundiirer Verset,zungen in der N&he der Teilchen und somit. das Einsetzen der Bereich IIVerformung durch die spannungsinduzierte Umwandlung stimuliert wird.

1. INTRODUCTION

The recent studies on the work-hardening crystals have

of copper showed

hardening

appears

the stress-strain particles

alloys

that

the

containing

oxide

region

quasi-parabolic

in the initial

curves

of part

particles

of stage

is small (
it occupies

the whole stress-strain

microscopy

showed the rows of prismatic density of dipoles.

curve.

deformed

into

of

harden-

the volume fraction

of the crystals

Ashby

I of

when the volume fraction

ing extends

dislocations were observed particles.(6*7)

of single

Electron stage I

dislocations

loops were also observed

containing

small alumina

in a-brass

particles.(4)

were shown to be consistent

alloys

These features

with the cross slip mecha-

nism as proposed by Hirsch.c5) On the other hand, in alloys with large oxide particles the secondary * Received August 22, 1972; revised December I, 1972.

t Faculty Japan. ACTA

of Engineering,

XETALLURGICA,

Hokkaido

VOL.

University,

21, AUGUST

Sapporo,

1973

punching the

prismatic

of pure copper

or single phase alloy.@)

of

copper

explained

On the other

parabolic particles.

been

of primary

dislocations.@) of

similar

alloys

f.c.c.

to those

containing

cobalt

showed

of single-phase

the region of stage I was long it was not so steep and not

like those of the copper alloys with SiO, The difference in behaviour of copper-

cobalt and copper-oxides 1033

non-

has

dislocations(6*g) and

the copper

precipitates

crystals.(6’ Although and slightly curved,

with

above

by the interaction

hand,

curves

alloys

as mentioned

the geometrically-necessary

stress-strain

them from the “SW

which were formed in the

loops,(3) the secondary

semi-coherent

de-

for the compatible

dislocations”

particles

theoretically

which were formed

“geometrically-necessary

and distinguished

work-hardening

deforming

at the

particles by cross-slip, secondary

of matrix,

deformation The

and they lie along lines drawn from the particles in the direction of the primary Burgers vector.“l.“) The combined structures of prismatic loops and Orowan

slip and prismatic formation

tistically-stored

loops, helices and a large

These are all primary

called the dislocations,

at the nondeforming

dislocations”

until

to be generated

alloys was ascribed to some

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1034

METALLURGICA,

shearing of the cobalt particle by the glide dislocations. In the present work, the work-hardening of copper alloys containing y-iron precipitates has been studied, which might be expected to be similar to that of the copper-cobalt alloy. According to the copper-iron phase diagram, the equilibrium precipitate is bodycentered a-iron with small amounts of copper in solid solution below the eutectoid temperature of about 835°C. However, it has been found that a metastable f.c.c. y-phase, which is coherent with the copper matrix; precipitates from the supersaturated Ephase on ageing, and several works have shown that the y-iron precipitates are instantly transformed to the a-iron by cold work.(1e-13). Easterling et ~2. studied the transformation of y-iron precipitates to a-iron by plastic deformation from electron microscopy and magnetic measurements and concluded that discs of martensite were formed across the y-iron precipitates by the dislocations which passed through the precipitates during plastic deformation.(l4-1s) It was also found that some y-a transformation occurred during easy glide but that it was most rapid at the beginning of stage II. Woolhoused7) studied the loss of coherency of y-iron precipitates due to neutron irradiation and tensile deformation, and showed that the coherency was lost due to the interaction with the interstitial dislocation loops which were produced by neutron irradiation or by the cross slip mechanism of glide dislocations due to either of Hirschcs) or Gleiter.(ls) The purpose of the present work is to examine the work-hardening and the dislocation structures of alloys with such iron particles. It will be shown that the effect of iron particles on the work-hardening is different from that of both the hard oxide particles and the soft cobalt particles mentioned above. 2. EXPERIMENTAL

METHODS

Copper-iron alloys were melted in vacuum from O.F.H.C. Cu (99.99%) and electrolytic Fe (99.9%). Alloys of the following compositions were prepared: Cu-0.44 wt. % Fe, Cu-1.10 wt.% Fe and Cu-1.50 wt. % Fe. Single crystals 3 mm square were grown from the melt in the graphite moulds by a modified Bridgeman technique. After homogenization in vacuum at lOOOY! for 4 days, these were solution heat-treated again at 1000°C for 3 h, air-cooled and aged at 700% for 4 hrs and 4 days respectively. Tensile specimens of gauge length 40 mm were then cloth-polished and finally electropolished. Tensile tests were carried out at room temperature, 208°K

VOL.

21, 1973

and 77°K at a strain rate of about 3 x lO-P/sec. Specimens for electron microscopy were sectioned from tensile specimens either parallel or perpendicular to the primary slip plane by acid cutting. The sections principally examined were (lli) sections parallel to the primary glide plane, (101) sections normal to the primary Burgers vector and (i21) sections normal to the primary glide plane and parallel to the primary Burgers vector. Slices about 1 mm thick were sectioned by acid cutting and chemically clothpolished to a thickness of about 0.2 mm. These were dished by jet polishing and then finally electropolished in an electrolyte of ethanol (6): nitric acid (1) kept at about -3O’C. The specimens were examined in a H-U 12 electron microscope at 100 kv. Saturation magnetization was measured on a Cu1.l wt. % Fe alloy at room temperature by using Sucksmith method to determine the amount of ferromagnetic iron developed during deformation. Specimens for the magnetic measurements were cut from tensile specimens perpendicular to the tensile axis. 3. RESULTS

3.1. Precipitates Specimens air-cooled from solution temperature showed a fine dispersion of spherical particles with the lobe contrast arising from coherency strain, which suggested that the particles were the y-precipitates coherent with the matrix. At ageing at 700°C for 4 h, the particles grew and still showed the lobe contrast as shown in Fig. l(a). However, it was observed in the specimen aged for 4 days that some large particles with radius exceeding about 700 A lost the lobe contrast and emitted tangled dislocations or prismatic dislocation loops from their interfaces. The examples are seen in Fig. l(b). The prismatic loops appear to be punched into the matrix as particles are lost during the thinning operation, These particles might be interpreted as semicoherent y-precipitates which lost the perfect coherency. However, these might also be considered as the a-iron, which were transformed from the y-iron being accompanied by the generation of dislocations. Unfortunately, the structure of the precipitates couid not be determined as the diffraction pattern of the precipitates was not obtained. Hereafter, such particles showing no lobe contrast will be called incoherent particles. The mean diameters, volume fractions, and mean planar spacings of precipitates in each alloy are tabulated in Table 1. The mean diameters were obtained from electron microscopy and the volume

MATSUURA

et al.:

WORK-HARDENING

OF Cu-Fe

ALLOY

SINGLE

CRYSTALS

1035

3.2. Stress-strain curves

Fxo. 1. (a) Coherent iron particles in a (k-1.5% Fe alloy aged 4 h at 700°C. g: operating reflexion.

3.2.1. Small coherent particles (Aged for 4 h). The stress-strain curves of the alloys with small coherent particles, which were aged 4 h at 7OO”C, were quite similar to those of a-brass crystal~,~~) as seen in Figs. 24. The alloys initially deformed by the propagation of a Liiders band. The deformation by Liiders band became more pronounced with increasing solute content. After the Liiders band covered a whole surface of the specimen, the extended region of easy glide with a slightly parabolic work-hardening occurred in the stress-strain curve. Despite the difference between the orientations of the alloys, it can be seen that the extent of easy glide at room temperature increases with the solute content, and with the volume fraction of particles. This was also observed in the Cu-Co alloys containing semi-coherent cobalt particles.(2) The alloys showed a clear overshoot phenomenon; slip bands on the conjugate system came out suddenly from one end of the specimen at the end of overshoot, and the bands propagated to cover a whole surface of the specimen. So the shear stress-shear strain curves were calculated on the assumption of single glide on primary system until the end of overshoot, after which single glide on the conjugate system was assumed to occur. So the discontinuities, shown by the dotted portions, appeared in these stress-strain curves due to the overshoot. The overshoot defined as the ratio r,/r,, varied between about 1.l and 1.2, where rl, and r8 were the shear stress on the primary slip system and the conjugate slip system respectively, and it tended to increase at lower temperature. The overshoot also appeared to increase with solute

FIG. 1. (b) Coherent and incoherent iron particles in a Cu-1.5% Fe alloy aged 4 days at 700°C TABLE 1. Size and distribution of iron particles. f: particle volume fraction, 2R: mean particle diameter, D: mean planar particle spacing given by R(2~/3f), and 3: effeotive mean planar particle spacing given by D - 2R. Alloy

Ageing

Cu-0.4%

Fe

Cu-1.1%

Fe

Cu-1.5%

Fe

4 4 4 4 4 4

h 8t 700°C days 8t 700°C h at, 700°C days 8t 7OO’C h at 700°C days at 7OO’C

f(%) 0.15 0.15 0.91 0.91 1.42 1.42

2R(A)

D(P)

B(r)

260 900 300 1060 360 1100

0.46 1.68 0.23 0.81 0.22 0.67

0.43 1.49 0.20 0.70 0.18 0.56

fractions were calculated from the compositions of alloys and the equilibrium phase diagram. The solubility of iron in e-phase (copper matrix) and copper in a-iron at 700°C were taken as 0.35 at % and 0.42 at % respectively.(Na21)

I

I

I

0.5

I

1.0

I

I

I.5

Shear strain Fro. 2. The stres+rain curves of Cu-0.4% Fe alloy aged 4 h and 4 days at 700°C respectively.

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METALLURGICA,

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curves at 77’K, as marked with “e.h.” in Figs. 3 and 4. Such anomalous hardening was not observed in the stress-strain curves at 208°K or room temperature. The stress-strain curves of the Cu-0.4 wt. % Fe alloy with large particles were similar to those of the same alloy with small coherent particles but showed a shorter extent of easy glide and a larger workhardening rate in stage II than the latter (Fig. 2). 3.3. Di.slmzth

structures

Dislocation structures were examined only in the Cu-1.5 wt. % Fe alloy. 3.3.1. Small coherent particles

I

I

I

0.5

1.0

Shear

I I.5

strain

Fm. 3. The StF3%-&~8in CIU!"~S Of CU-1.1% Fe 8llOy aged 4 h and 4 days at 700°C respectively. conbmt, although a systematic variation with solute content was not clearly found possibly clue to the different orientations of crystals tested. It would be worth while to note in the stressstrain curves of Cu-1.1 wt. % Fe and Cu-1.5 wt. % Fe alloys that the extent of easy glide is the shorter, the lower the deformation temperature is. Such temperature dependence of the extent of easy glide is in contrast to that observed in pure metals and solid solution alloys.(24*25) The Cu-0.4 wt. % Fe alloy showed a normal temperature dependence of easy glide similar to pure copper or the solid solutions. 3.2.2. Large particles (Aged for 4 days). The Cu-1.1 wt.% Fe and Cu-1.5 wt.% Fe alloys aged for 4 days, which contained large particles, showed a small extent of easy glide and little or no overshoot (Figs. 3 and 4). The extent of easy glide in both alloys also decreased with decreasing temperature in the same way as in the alloys with small coherent particles. The stress-strain curves were similar to the parabolic hardening of the copper alloys with oxide dispersions of about 1% volume fraction except for the small region of easy glide. So it is difficult to decide whether the region of rapid hardening after easy glide should be regarded as stage II or as a part of the parabolic hardening. It is shown later that the region of rapid hardening is more like stage II of pure copper than parabolic hardening. An anomalous excess work-hardening was observed in the initial part of rapid hardening of stress-strain

A. Stage I (region of easy glide). General dislocation structures of the alloy with small particles were similar to that observed in the Cu-Co alloys.@) Figure 5 shows the structure for the (llf) section parallel to the primary slip plane when deformed at room temperature. The main features of the structure were the primary dislocations attached to the particles, the dipoles and the dislocation loops around the particles as indicated by a mark A. These loops appear to be the prismatic loops which are produced by the cross slip mechanism.(5Js) Many particles are attached by the dislocation lines or loops and show a complicated contrast even under the same type of reflection as in Fig. 1. These structures show that the glide dislocations by-pass the particles by Orowan’s mechanism or the cross slip mechanism at least in the initial stage of deformation. Figure 6 shows the

1

I

I 1.0

I

0.5

Shear

I

I.5

strain

Fm. 4. The StIW8-Str8in ourves of Cu-1.6% Fe 811OJ’ aged 4 hand 4 d8ye at 700°C respectively.

MATSUURA

Fro. 5. Cu-1.5% Fe deformed to stage I (1 IT) section parallel direction.

et al.:

WORK-HARDENING

alloy, aged 4 h at 700°C and at R.T. Shear strain (E) = 0.27. to primary slip plane. S.D.: slip g: operating reflexion.

st.ructure for the (101) section deformed at 77’K, where the primary dislocations are only seen faintly in residual contrast. Secondary dislocations are not observed in this stage of deformation. Some particles appear in a uniform dark contrast, which are interpreted as being transformed to an incoherent state losing coherency by interaction with matrix dislocations during plastic deformation. The general dislocation structure after deformation at 77°K was quite similar to the structure after room temperature deformation except that a larger proportion of incoherent particles was observed. B, Transition region from stage I to stage II. The general dislocation structure was similar to that in

Fro. 6. Cu-1.5% Fe alloy, aged 4 h at 700°C and deformed to stage I et 77°K. e = 0.26. (101) section showing many incoherent particles with dark contrast.

OF

Cu-Fe

ALLOY

SINGLE

CRYSTALS

1037

stage I. Rows of prismatic loops or helical dislocations aligned in the direction of the primary Burgers vector were more frequently observed in the transition region than in stage I and the local occurrence of secondary dislocations was recognized. Figure 7 shows the dislocation structure in the (i21) section which is perpendicular to the primary slip plane and parallel to the primary Burgers vector, where (111) reflection occurs and so the primary dislocations are invisible. It shows that some secondary dislocations begin to operate locally. The secondary dislocations marked with A appear to begin to extend from the incoherent dark particles. It was observed that with increasing deformation more particles were transformed to the incoherent state and that more transformation of particles took

Fro. 7. Cu-1.5% Fe alloy, aged 4 h at 700°C and deformed to the transition region from stage I to stage II at R.T. E = 0.69. (721) section showing occurrence of secondary dislocations, where primary dislocations are invisible.

place by deformation at 77’K than at room temperature. C. Xtage II (region of rapid hardening). When deformed to stage II, rows of prismatic loops or helices were not clearly recognized possibly due to the occurrence of secondary dislocations and instead of them it showed the cell-like structure as shown in Fig. 8 for the (101) section. However, the cellstructure was not well developed as in pure copper and the dislocations were rather homogeneously distributed. It is seen in Fig. 8 that the secondary dislocations occur in many regions and originate the cell-structure on a fine scale. Tilting experiments showed that most of the secondary dislocations belonged to the conjugate system.

1038

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1973

were primary secondary dislocations were contained in the tangles as at B (Fig. 10(b)) and these tangles were formed by the interaction of primary glide dislocations with the secondary ones. Deformation at 77’K resulted in the dislocation structure similar to that produced at room temperature. The structure for the (101) section is shown in Fig. 11. It is seen from the figure that a large proportion of particles are transformed to the incoherent State.

B. Stage II (region of rapid hardening). The tangles around each particle extended further to link together end form the cell-structure in stage II as shown in Fig. 12. It is seen that the primary dislocations along [i21] are arrested by the secondary dislocations extending from the particles. The above dislocation structure is very similar to that observed around large silica particles in a deformed copper-silica alloy by Brown and Stobbs.c6) Tilting experiments showed that these secondary dislocations had Burgers vectors contained in the cross slip plane. It is seen from the comparison of Figs. 8 and 12 that the cell structure is larger in scale and more well-defined in the alloy with large particles than in one with small particles. 3.4. Coherent-incoherent 8. Cu-l.Sq& Fe alloy, aged 4 h at 700°C and deformed to stage II at R.T. E = 0.10. (101) section Showing the undeveloped cell-structure formed by secondary dislocations of conjugate slip system. FIG.

Many particles appeared in dark contrast and seemed to be transformed to the incoherent state.

transformation of particles

It has been observed in this investigation that more particles lose the lobe contrast, or coherency and appear in a uniform dark contrast, often generating the dislocations, with increasing deformation. This was interpreted as the particles transforming to an incoherent state, losing coherency with the matrix.

3.3.2. Large particles A. Stage I and transition region from stage I to stage II. The dislocation structure in stage I was similar to those shown in Figs. 5 and 6 for the small particles, except the dislocation tangles around the incoherent dark particles. The prismatic loops and helices were more frequently observed in the transition region than in stage I, as shown in Fig. 9. The tangled dislocations were generated around each particle and connected with each other in some local regions. It is seen in Fig. 10(a) for the (i21) section that the tangled dislocations join up between neighbouring particles (region A or B) and it is also seen that the tangles in the direction of the primary Burgers vector appear to originate from the interaction of the glide dislocations with the rows of prismatic loops or helices as seen at A. Tilting experiments showed that although most of the dislocations seen in Fig. 10(a)

Fm. 9. Cu-1.5% Fe alloy, aged 4 days at 700°C and deformed to the transition region from stage I to stage II at R.T. E = 0.29. (1lI) section showing rows of prismatic loops s,nd helices.

MATSUURA

et al.:

WORK-HARDENING

OF &-Fe

ALLOY

SINGLE

CRYSTALS

1LO39

FIG. 10. (a) Same as Fig. 9. (I21) seotion showing the i&era&ion of glide dislocations with row8 of prismatio loops or helices (A) and with seoondary dislocations (B); (b) Same area as a region marked in Fig. 10(a). Only secondary dislocations are visible here.

The fraction of incoherent particles with dark contrast was counted in the photographs of (101) sections, since the primary dislocations appeared in faint residual contrast for the (101) section and so the effect of contrast of primary dislocations was less than in the other sections. The dark particles attached to the dislocation tangles, as at B in Fig. 11, were counted as incoherent ones. Although in this case the lobe contrast might be masked by the contrast from the tangled dislocations, the presence of tangles strongly suggests that the particles are incoherent. The results shown in Fig. 13, anyway, might be

considered to show the change in the fraction of incoherent particles qualitatively rather than quantitatively. It is clear, however, that the lower the deformation temperature and the larger the particle size, the more rapidly the particles are transformed to an incoherent state. It also shows that the coherentincoherent transformation becomes rapid at the transition from stage I to stage II. This is in agreement with the results of magnetic measurements and electron microscopic observation by Easterling et aZ.(l*J5) In the present study, magnetic measurements were done on a Cu-1.1 wt. % Fe alloy. The

1040

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METALLURGICA,

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1973

Aged4 doyr

0.4 06 Shear strain

0.2

0.8

1.0

FIG. 13. The increase of fraction of incoherent particles by deformation. Cu-1.6% Fe alloy.

11. Cu-1.5% Fe alloy, 8ged 4 deys at 700°C 8nd deformed to the transition region from stage I to stage II 8t 77°K. E = 0.15. (101) section. Lsrge particles (B) appear to be wholly transformed to incoherent stete, while smsll ones (A) to be pertially transformed 8s dark bands. Fm.

results are shown in Fig. 14 together with the stress-

strain curves. They show that the amount of a-iron or martensite increases rapidly at the end of stage I and the transformation occurs more swiftly when the particle size is larger and the deformation temperature lower. The saturation magnetization, expected when all the precipitates are transformed fo a-iron, is estimated to be about 1.74 Gauss per gram of alloy, based on the amount of precipitated iron determined from the phase diagram. So the results of magnetic measurements are semi-quentii&ively similar to the results of Fig. 13. From this agreement, it appears that most of the incoherent particles with dark contrast are a-iron or martensite transformed from the

coherent

y-iron.

presented

by

According to the photographs Easterling and Weathery,(ls) and

Woolhouse,(17) the incoherent or semicoherent

particles

of y-phase appear to lose the lobe contrast showing the uniform dark contrast.

without

Easterling et al. observed that, alternating dark and light bands were formed along a (110) direction of the matrix in the y-iron particles when the Cu-2 or 1 wt. % Fe alloy was deformed.(l4-1s) They inferred that these dark bands represented discs or laths of martensite separated by retained austenite, and that these were nucleated by matrix dislocations passing through the particles. In the present investigation, it is seen in Fig. 11 that fine dark bands are formed

_____

1.74

.

-deformed

at RT.1

I.5

Aged 4 hrs. ---

deformed

at 779

Aged 4 hrs. --‘deformed

at RTk

1.0

$ t B ;; 5

0.5

0.5

Shear

FIQ. 12. Cu-1.50/b Fe 8lloy, aged 4 days at 700°C and

deformed to stage II at R.T. (101) section showing the formation of cell-structure by the interaction of prim8ry dislocations with secondary dislocations. E = 0.55.

1.0

I.

strain

Fro. 14. The chenge of saturation magnetizetion of Cu-1.1% Fe alloy by deformation at room temperature and the stress-strain curves. The saturetion megnetiz&ion is expected to be about 1.74 Gauss per grem of alloy when 811 the precipit8tea transform to ferromagnetic a-iron. The doublets of points show the values measured on two slices which are cut from each speoimen. 7: shear stress, MS: saturation magnetizcrtionper gram of slloy.

MATSUURA

et al.:

WORK-HARDENING

along the intersection with the (111) plane in the smaller particles as A, while the larger particles as B show a uniform dark contrast, emitting dislocations . The dark bands appear to be the laths of martensite as observed by Easterling et al. So the above observation suggests that the larger particles showing a uniform dark contrast have been instantly transformed to the martensite as a whole, while the smaller particles have been partially and gradually transformed. 4. DISCUSSION

4.1. Region of easy glide

OF

Cu-Fe

ALLOY

SINGLE

CRYSTALS

1041

The value is about the same as that of pure copper or a-brass. This means that the iron particles are not non-deforming and Orowans loops, prismatic loops and secondary dislocations are not so much formed in easy glide since the work-hardening is not markedly affected by the presence of iron particles. The above prediction appears to be consistent with the observations made on the alloy with small particles, in which only a few loops are seen around each particle in the region of easy glide. So most of dislocations are expected to pass through the particles during deformation in easy glide. The presence of a few prismatic loops around each particle, as shown in Fig. 5, suggests, however, that some glide dislocations by-pass the particles during deformation. The change of yield stress with the effective planar particle spacing D was in agreement with that expected from‘Orowan’s relation modified by Ashby, i.e.

It has been found that the stress-strain curves of the copper alloys with non-deforming particles, such as silica or alumina, show a stage I of temperaturedependent, steep and quasi-parabolic work-hardening, which comes from the interaction of glide dislocations with the rows of prismatic loops or the secondary dislocations around the particles.(l-4) In the present 2R alloys with iron particles, the region of easy glide or rV=r,+0.84K$ln--rr,+$ (1) stage I did not show such steep and quasi-parabolic r hardening, although it was slightly curved for the alloys with small particles. As shown in Fig. 15, the .where r, is the yield stress of the matrix, G is the rate of work-hardening was nearly independent of shear modulus of the matrix, b is the Burgers vector, t,emperature and the magnitude was 0.5-1.0 x low3 G r is the effective core radius of about 2b and K is unity for the present alloys irrespective of the size of particle. for an edge dislocation and 1 - v for a screw dislocation (v is the Poisson ratio). D is the effective mean planar particle spacing and is given by D - 2R, where D is the mean planar spacing of the particles. The yield stresses are plotted in Fig. 16 according to the above relation, which shows that the Orowan’s . n m relation is nearly satisfied. From these and the low work-hardening rate of the 6 *-, eI t easy glide region, it is concluded that the first few dislocations, which move on the slip plane and enAped 4 days counter the particles at the initial stage of deformation, by-pass the particles by Orowan’s mechanism or cross slip mechanism and then the subsequent dislocations shear the particles by collapsing the inner x loops, keeping a few loops around them. This process E ; Br P will perhaps cause the transformation in some of the particles. Another process has been suggested by Woolhouse: the particles (~320 A in dia.) need at the most two loops to relieve the coherency completely Cu-30XZn (in one direction) and once coherency is lost, the glid-e ing dislocations, no longer repelled by the misfit cu ,I stress field, can cut through the particles. 300 100 200 In the alloy with large particles the dislocation Temp. “K structure appears to be complicated due to the tangled dislocations formed around the incoherent FIG. 15. Temperature dependence of work-hardening rates in stage I (81) and stage II (011) for Cu-Fe alloys, particles. However, the same thing as mentioned copper and a-brass (after Mitchell et aZ.‘lB’) 0: Cu-0.4’36 above is assumed to occur in the small region of easy Fe, X: Cu-1.1% Fe, 0: Cu-1.5qb Fe.

=e

l

==-QL_2k

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“E E \

2 c

I.*

I

I

I

I

I

2

3

A/d,

I 4

kg/mm2

Fro. 16. The change of yield stress (TJ with the effective mean planar particle speaing (b). The dotted lines shown by T, end T# sre the by-pess stresses given by equetion 1 for edge 8nd screw dislocation respectively. A = 0.84K((%/2) In (2R/I) (see text).

glide of this alloy because of the low work-hardening rate. 4.2. Transition from stage I to stage II The extent of easy glide region, E~~,was largely controlled by the particle size. The alloys with small particles showed a large extent of the easy glide region and with these alloys the overshoot phenomenn was evidently observed, while those with large particles showed a small extent of the easy glide region and no overshoot. It is inferred that the operation of local secondary slip leading to stage II is ditlicult in the former alloys and the reverse is true in the latter. Another interesting point about the easy glide region is the temperature dependence of gII. It is well known that in pure copper and the solid solutions the extent of the easy glide region gets longer as the deformation temperature is decreased. This has been interpreted as due to the larger stress required to operate the local secondary slip at the lower temperature.‘24*25) In the present alloys except for the Cu-0.4% Fe alloy, the extent of the easy glide region was shorter the lower the deformation temperature was. The stress, rII, at the end of the easy glide region was little changed in the Cu1.1% Fe alloy, or showed a tendency to decrease in the Cu-1.5% Fe alloy with lowering temperature. While in the Cu-0.4 % Fe alloy which contained a small amount of particles the stress increased at lower temperature, as in pure copper. It can be concluded that above a volume fraction (>l *A) the critical stress

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necessary for the local secondary slip decreases with lowering temperature. The electron microscopic observations and especially magnetic measurements showed that the fraction of the particles transformed to the incoherent aphase was rapidly increased at the transition region from stage I to stage II and that the transformation got faster as the deformation temperature was lowered and the particle size increased. So it is inferred from this together with the behaviour of ~~~mentioned above that the transition from stage I to stage II is closely associated with the straininduced transformation of iron particles. The transformation of particles was often accompanied by the generation of tangled dislocations, and sometimes prismatic loops, as observed in the undefomed alloy with large particles. The tangles were observed to be formed around the incoherent particles during the plastic deformation of the alloy with large particles. The tangles contained the secondary dislocations and they extended from each particle to form the cell-structure in stage II. So it is inferred that the initially coherent particles are transformed to the incoherent state with the generation of tangled dislocations during plastic deformation and the dis. locations generated act as the sources of secondary dislocation, stimulating the beginning of stage II. The same situation is also expected to occur during the plastic deformation of the alloy with small particles. However the rate of the strain-induced transformation was small compared with that of the large particles and the generation of dislocations from the incoherent particles was not so evidently observed as in the large particles. Therefore, in the case of small particles, some of the secondary dislocations, as seen in Figs. 7 and 8, might also originate from the grown-in dislocations, which have been introduced during the growth of crystals from the melt or during the subsequent heat treatment, although the density of grown-in dislocations is small (
MATSUURA

et al.:

WORK-HARDENING

So, the homogeneous distribution of primary dislocations, which is associated with the fine distribution of small particles, would not be effective to operate the secondary sources and would result in the delay of the beginning of stage II. Furthermore, the overshoot phenomenon suggests that the small particles raise the yield stress for slip on secondary systems as do solute atoms in the a-brass alloys. This and the homogeneous distribution of primary dislocations should result in a larger extension of the easy glide region in the alloys with small particles than in pure cooper. 4.3. Extra work-hardening and stuge II (region of rapid hardening) The number of incoherent a-phase particles increased rapdily in the transition region from stage I to stage II. Therefore, the dislocation tangles around the incoherent particles should also increase rapidly from this region. Furthermore it might be expected that the primary dislocations find it difficult to pass through the incoherent a-phase particles. Easterling and Miekk-ojao4) observed in thin foils that moving dislocations were traversing coherent particles, whereas their movement was effectively hindered by fully transformed particles. Therefore, a part of the tangled dislocations around the incoherent particles might be due to the geometrically-necessary dislocations which are formed for the compatible deformation of regions surrounding non-deforming particles. The rows of prismatic loops or the helices were also observed more often in this region than in the region of easy glide. Therefore, it is expected that the parabolic hardening due to the prismatic loops or the secondary dislocations, which has been confirmed to occur in stage I of copper alloys with oxide particles, begins to occur from the transition region in the present alloys. In fact, the anomalous workhardening was observed in the initial region of stage II when the alloys with large particles were deformed at 77”K, but not when deformed at room temperature. It has been found that the parabolic hardening of stage I in the copper alloys with oxide particles is strongly dependent on temperature and there is a marked recovery effect around room temperature. From these the authors would like to believe that the anomalous work-hardening observed in the alloys with large particles is caused by the dislocation tangles, which are generated by the transformation of particles, and the geometrically-necessary dislocations including the prismatic loops, helices and tangles. In the later stage of rapid hardening, the effect of these dislocations is masked by the statistically-

OF Cu-Fe

ALLOY

SINGLE

CRYSTALS

1043

stored dislocations and the work-hardening shows the usual character of stage II similar to that of pure copper and the solid solutions as mentioned later. In the alloys with small particles, the number of incoherent particles increased more slowly with deformation than in the alloys with large particles. So the effect of hardening due to the dislocation tangles around the incoherent particles and the geometrically-necessary dislocations will gradually appear in the stress-strain curves. This may be a reason that we can hardly see an anomalous hardening in the stress-strain curves. The stress-strain curves of the Cu-1.1 % Fe and Cu-1.5 % Fe alloys with large particles seem to be quasi-parabolic except for a short region of easy glide. So the work-hardening after easy glide might be considered to be of the same nature as the quasiparabolic hardening which has been observed in the copper alloys containing oxide particles at a volume fraction above about 1%. However, the hardening rate of the region shovcing rapid and nearly linear work-hardening was little dependent on temperature except for the anomalous extra-hardening and it was about the same as that of stage II of pure copper or a-brass as shown in Fig. 15. These facts show that the region of rapid hardening should be considered as similar to stage II of pure copper or the solid solution, but not as a part of the parabolic work-hardening seen in the copper alloys with non-deforming particles. The contribution of the dislocation tangles generated by the transformation of particles and the geometrically-necessary dislocations would be important only in the region of extra-hardening, which has appeared in the initial region of rapid hardening. 6. SUMMARY

1. The stress-strain curves of Cu-Fe alloys with small iron particles showed a large extent of the easy glide region and an evident overshoot phenomenon, while those with large iron particles showed a small extent of the easy glide region and no overshoot. 2. In spite of the low work-hardening rate of the easy glide region, the yield stress was given by Orowan’s relation. The main features of the dislocation structure in the easy glide region of the alloy with small particles were the primary dislocations attached to the particles, the primary dipoles and the prismatic loops around each particle, and the structure of the alloy with large particles was complicated by the tangled dislocations around the particles. 3. It was inferred from the above that the first few dislocations bypass the particles by Orowan’s mechanism or the cross slip mechanism at the initial

1044

ACTA

METALLURGICA,

of deformation and after that the subsequent dislocations shear the particles. 4. It was found in the Cu-1.1 wt. % Fe and Cu-1.5 wt. oAFe alloys that the extent ofthe easy glide region was shorter, the lower the deformation temperature was. 5. The initially coherent y-iron particles were transformed to an incoherent state, probably uiron, by plastic deformation. The strain-induced transformation occurred rapidly at the end of easy glide and it was faster as the lower the deformation temperature and the larger the particle size. 6. The transformation of the particles was accompanied by the generation of tangled dislocations, which contained secondary dislocations and extended from each particle with deformation to form the cellstructure in stage II. 7. The dependence of the extent of easy glide region on particle size and temperature, mentioned in 1 and 4, was ascribed to the strain-induced transformation of particles, which stimulated the activation of secondary dislocations near the particles and so the beginning of stage II. 8. An anomalous work-hardening was observed in the initial region of stage II when the alloy with large particles was deformed at 77°K. This hardening would most likely be caused by the dislocation tangles generated due to the transformation of particles and the geometrically-necessary dislocations-prismatic loops, helices and tangles. However, t,he region of rapid hardening (stage II) in alloys with large particles should be considered to be similar to stage II of pure copper or the solid solutions, but not as a part of the parabolic hardening seen in the copper alloys with non-deforming particles. stage

ACKNOWLEDGEMENTS

The authors wish to thank Professor T. Takeyama, Professor M. Maeda and Dr. M. Sato for the laboratory

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facilities made available, and Mr. T. Hapashida and Mr. M. Kitamura for the assistance in performing the experiments. REFERENCES 1. R. EBELINC and M. F. ASHB~, Phil. Mag. 13, SO5 (1966). 2. F. J. HUMPEREYS and J. R. MARTIS, Phil. Nag. 16, 927 (1967). 3. P. B. HIRSCH and F. J. HTXPHREI.S, Pm. R. SOC. (London) A318,45 (1970). 4. F. J. HUMPHREYS and P. B. HIRSCH. Proc. R. Sk. (London) A318, 73 (1970). 5. P. B. HIRSCH, J. Inst. Met. 86, 5 (1957). 6. L. M. BROWN and W. M. STOBBS. Phil. Mag. 23, 1201 (1971). 5. W. M. STOBBSand L. M. BROWS, 4th European Regional Conference on Electron Microscopy, Rome, p. 413 (1968). 8. RI. F. ASHBY, Phil. Mag. 14, 1157 (1966); Ibid 21, 399 (1970). 9. K. TANAKA, K. NARITA and T. MORI, Acta Met. 20. 297 (1972). 10. F. BITTER and A. R. KA~;FMAXS, Phys. Rec. 56, 1044 (19391. 11. 6. S. SMITH, Age Hardening of Metals, p. 186 (1940). 12. J. M. DENNEY, &lo Met. 4, 586 (1956). 13. J. B. NEWKIRK, Trans. Am. Inst. Min. Engrs 209, 1214 (1957). 14. K. E. EASTERLIN~ and H. M. MIEKK-OJA, Acta Met. 15, 1133 (1967). 15. K. E. EASTERLIN~ and P. R. SWANN, The Mechattimn of l%&e, Transformaliona in Crystalline Solids, p. 152 16. I?. E.‘EASTERLING and G. C. WEATHERLY, Acta Met. 17, 845 (1969\. 17. G. k. W&OLHOUSE, 2nd Int. Conference on Strength of Metals and Alloys, Asilomar, California, p. 573 (1970). 18. H. GLEITER, Acta Met. 15, 1213 (1967). 19. W. SUCKSMITH,Pm. R. Sot. (London) A170. 551 (1939). 20. M. HANSEN, Conatilulion of Binary Alloys, p. 580. McGraw-Hill (1958). 21. H. A. WRIEDT and L. S. DARKEX, Trans. Am. Inat. Min. Engra 218, 30 (1960). 22. T. E. MITCHELL 8nd P. R. THORNTON, Phil. Mag. 8, 1127 (1963). 23. M. F. AOHBY, Proc. Second Bolton Landing Conference on Oxide Dtiperaion Strengthening, New York, p. 143. Gordon and Breach (1968). 24. J. GARSTONE,R. W. K. HONEYCO~~BEand G. Gmmmnf, Ada Met. 4. 485 (19561. 25. A. SEEOER: J. &E&L, 5. MADER and H. REBST~~K, Phil. Msg. 2, 323 (1957). 26. J. W. STEEDS end P. M. HAZZLEDINE. Faraday Sot. 38, 103 (1964). 27. J. W. STEEDS, Pm. R. Sot. (Lo?hdon) A292, 343 (1966).