Magnetomechanical behaviour of nickel and cobalt, particularly during fatigue deformation

MAGNETOMECHANICAL BEHAVIOUR OF NICKEL AND COBALT, PARTICULARLY DURING FATIGUE DEFORMATION* R. S. CARMICHAEL? Polycrystalline rods of nickel and cobalt have been subjected to torsional plastic deformation. The variation of the magnetic characteristics of coercive force, initial saturation remanenoe, and strainacquired remanence were observed. The dependence of these properties on the structural condition and state of internal stress of the material is explained by considering the particular mode of plastio deformation. Thii is assooiated with the differences in dislocation slip behaviour in cobalt, with one slip plane, and nickel, with four planes. The response of a multidomain configuration of magnetic domains, and thuz of the bulk magnetization, is intimately associated with strain-induced changes in the crystalline structure. The magnetomechanical effects are particularly well indicated during reverse loading. Initial fatigue straining gives pronounced and anomalous variations in the magnetio charaoteristics. COMPORTEMENT

MAGNETOMECANIQUE DU NICKEL ET DU COBALT AU COURS D’ESSAIS DE FATIGUE

EN PARTICULIER

Des barres polyoristallines de nickel et de cobalt ont Bte soumises a une deformation plastique en torsion. L’auteur a Btudie la variation des caraotiristiques m&aniques: champ coercitif, remanence initial0 et remanence acquise sous deformation. L’intluence, sur ces propri&&., de la structure et de l’etat de tension existent dans le materiau eat interIn&&s en considerant le oaractere particulier de la deformation plastique. Ceci eat asso& aux differences dans le oomportement du glissement des dislocations dans le cobalt, aveo un plan de glissement, et dans le nickel, avec quatre plans de glissement. La reponse d’une conflguration multidomaine des domaines magnetiques, et, par suite, de la magnetisation dens la mase, eat associee intimement aux variations de la structure oristalline induites par la deformation. Lea effets magnetomecaniques apparaissent de fapon particulierement nette durant la diminution de la charge. La deformation initiale resultant des essais de fatigue produit des variations importantes et anormales des oaracteristiques meoaniques. DAS MAGNETOMECHANISCHE VERHALTEN VON NICKEL UND BESONDERS WFiHREND DER ERMUDUNGSVERFORMUNG

KOBALT,

Polykristalline Nickel- und Kobaltstiibe wurden in Torsion plastisch verformt. Die Anderungen der Koerzitivkraft, der Sattigungsremanenz und der verformungsbedingten Remanenz wurden beobachtet. Abhangigkeit dieser Eigenschaften von der Struktur und den inneren Spannungen des Materials wird e&l&t, indem die besonderen Verformungsmechanismen betrachtet werden. Diese hangen mit den verschiedenen Gleitverhalten des Kobalts (eine Gleitebene) und dss Nickels (vier Gleitebenen) zusammen. Die Reaktion einer Vieldomitnenkonfiguration magnetisoher Domiinen und somit der Gesamtmagnetisierung hangt eng mit spannungsinduzierten iinderungen der kristallinen Struktur zusammen. Die magnetomechanisohen Effekte treten besonder deutlich bei Ermiidung auf. Einsetzende Ermiidungsverformung hat ausgepriigte und anomal gro6e Variationen der magnetischsn Eigenschaften zur Folge.

1. INTRODUCTION

There interest

is considerable in the interaction

mechanical

behaviour

parameters

encountered

character varying

of

materials

degrees.

such magnetic

scientific

in the associated and

of magnetic

in magnetic

commercial

properties

materials.

and

magnetic

Many

structure-sensitive

to

changes

It is desirable to be able to relate

of defects,

with

METALLURGICA,

VOL.

17, MARCH

properties,

present.

of irreversible

such as remanence

brought about by applied stress,

The change in magnetization

alteration

1969

of the strains

caused by the appli-

cation of stress is termed inverse magnetostriction,

* Received March 19, 1968; revised June 24, 1968. t Department of Physics, Faculty of Engineering Science, Osaka University, Toyonaka, Osaka, Japan. Experimental work conducted while in Department of Earth and Planetary Sciences, University of Pittsburgh, Pittsburgh, Pa. ACTA

in magnetic

and coercivity,

effects to the internal state of a crystal,

and redistribution

and magnitude

There is a need for an interpretation

and changes produced in that state by deformation.04) These changes will consist of the creation, annihilation,

The presence of exter-

stress will give an observed

behaviour which is very dependent upon the

configuration

in the study of the magnetic are

stress fields.

nal, and localized internal,

261

or

piezomagnetism. Matteuci’s) was probably the first to examine the effect of mechanical stress on ferromagnetic metals. A recent study(s) of aspects of the magnetomechanical

behaviour

plastic fatigue deformation

of nickel subjected

to

has lead to an interpreta-

tion of other early work by Naga0ka.c’)

The latter’s

ACTA

262

METALLURGICA,

work included an interesting induced self-reversal of magnetization. The present paper is concerned with an extension of the investigation of nickel, with new tindings for cobalt. The magnetomechanical behaviour may be explained with a structure-sensitive model relating the response of a multidomain magnetic configuration to changes in the internal stress state. The model has been outlined in connection with magnetomechanical behaviour of the ferrimagnetic mineral magnetite,@) and may now be applied here to nickel and cobalt. The magnetizations of both nickel and cobalt are sensitive to stress, because of their large magnetostriction. The magnetic parameters investigated as a function of the deformation are coercive force (H,), strainacquired remanence, change of an initial saturation isothermal remanent magnetization (IRM), and change in a pre-existing strain-induced remanence. Of particular concern is deformation by reversing the sense of loading, i.e. fatigue. In fatigue, changes in the internal structure are pronounced, and give The marked and interesting magnetic effects. magnetic behaviour of nickel and cobalt is significantly different, but the variations are readily interpreted by considering the structural dissimilarities and corresponding different modes of deformation of the two materials. 2. EXPERIMENTAL

TECHNIQUES

2. I Samples and apparatus The metal rods are described in the Table 1. All are polycrystalline. The deformation is measured in terms of the rod’s outer-fibre shear strain (circumferential displacement/deformed length), expressed as a TABLE 1. Description of nickel and cobalt rods Nickel rods Characteristic $tYg?)

Cobalt rod

A

B

E

99.999 0.5005 7.72

99.999 0.6005 7.73

99.5 0.4755 7.70

Length (cm) Maximum torsional deformation: Twist (degrees) 160 Outer-fibre 11.7 shear strain (%) Field for defor_::;> mation (oe)

160 11.7 1.3

160 11.1 1.3

99.6 0.473 7.70 120 8.3 1.3

percent. The actual length of rod free to deform in torsion was 6 cm for all samples. All the rods were initially annealed to soften them mechanically. The coercive forces were reduced from 24 to about I Oe, and 88 to 12.8 Oe, for the nickel and cobalt respectively. These terminal values are in accord with those given by Kersten.(2)

VOL.

17,

1969

Torsional deformation was applied using a shop lathe fitted with two chucks which gripped the sample rod. The ambient field between the chucks was 1.3 Oe, and was axial and fairly uniform. Measurements of remanence and coercive force were taken on a ballistic magnetometer, constructed by Prof. K. Kobayashi. 2.2 Experimental method Torsion is convenient to produce plastic deformation because the shape of the rod is not changed, as would be the case for tension or compression. Thus the demagnetizing factor remains constant. Repeated cycles of torsion over a given strain interval permit readily reproduced experiments. In addition, the strain is uniformly distributed along the length of the rod. The sample was twisted by rotating one calibrated chuck with respect to the other, through a measured number of degrees. For the determination of the magnetization produced by torsional deformation of a rod, account must be taken of the IRM acquired when the rod is placed in the field of the lathe. Since the samples are demagnetized prior to each strain increment step, this IRM can be measured. There is also a pressure remanent magnetization (PRM) acquired by the ends of the rods in the process of severe gripping. Both the IRM and end-PRM are superimposed on the change in magnetization of the central deformed section of the rod. The latter moment will be denoted twist remanent magnetization (TwRM) here, to distinguish it from the endPRM component. The total remanence after a deformation step is thus “TwRM + IRM + PRM”. 3. EXPERIMENTAL

OBSERVATIONS

3.1 Coercive force The change in coercive force with cyclic deformation for nickel rods A and E is shown in Fig. 1. For rod A [Fig. l(a)], the bulk coercive force of the annealed rod was 1.1 Oe. With severe gripping, the H, of the end sections rises to about 14 Oe. The rod’s bulk H, is then 5.8 Oe. It increases at a decreasing rate with unidirectional deformation. With cyclic torsion, the rod continues to harden magnetically, the H, tending toward a limiting value of about 24 Oe. Results for rod E [Fig. 1(b)] are similar. The behaviour during the initial stage of reverse twisting for both rods is anomalous. An immediate increase is followed by a marked decrease. By 3% reverse strain, the coercivity is again increasing monotonically. Figure 2 shows the variation of H, for the cobalt rod. The response to fatigue is different from that of the nickel rods. There is an immediate decrease in H,,

CARMICHAEL:

MAGNETOMECHANICAL

VARIATION Nickel TORSION

40

0

Rod

COERCIVE

A

120

OF

Ni

Rod

E

Nickel

Hc (0.) 25 c

160

Co

263

L.CYCLE, __O__

TORSION

(degreea)

AND

FORCE (b)

COLE L*2_,__

00 TWIST

OF

BEHAVIOUR

0

L,-

I

40

00 TWIST

120

160

(degrees)

Fra. 1. Variation of coercive force (H,) with cyclic torsional deformation. Nickel rods A and E.

followed by a gradual increase. The limiting value for this interval of 8.3% strain appears to be about 40 Oe. 3.2 Initial saturation remnence If a nickel rod is given an initial saturation IRM and then progressively deformed in a small field, the behaviour shown in Fig. 3 for rod A results. The gripping of the end sections decreases the bulk remsnence somewhat. All further change is due to VARIATION

OF

COERCIVE

Cobalt TORSION H, (oe)

FORCE

Rod CYCLE

3.3 Acquired rernanence

I--

I

I

I 0

20

40 TWIST

60

60

The remanence decreases torsional deformation. uniformly. It reaches a limiting value of 40 e.m.u. after a twist strain of 3%, when twisted from either end of the total strain interval. This is about onequarter of the value of initial saturation IRM. If the rod is placed in the lathe so that the lathe field of 1.3 Oe opposes the sense of initial IRM, the limiting value of remenence is about -40 e.m.u., i.e. directed in the sense of the reversed field. The same treatment for the cobalt rod is illustrated in Fig. 4. The decrease in remanence is much less rapid. The value after a strain of 8.3% is about twothirds the value of the initial saturation IRM.

100

I 120

(degrors)

FIG. 2. Variation of coercive force with cyclic torsional deformation. Cobalt rod.

Consider now the remanent moment acquired, over successive deformation intervals, from a demagnetized condition at the start of each strain increment. Figure 5(a) shows the acquisition of total moment for nickel rod A. The external field throughout the experiment was 1.3 Oe. The experimentallydetermined variation of the IRM and end-PRM components is shown as dotted lines. Both reach limiting values as the torsionally deformed region of the rod hardens mechanically and magnetically. By the end of “Torsion Cycle l”, the IRM induced from the field of 1.3 Oe is 0.15 e.m.u., and the endPRM is 7 e.m.u. With these two components subtracted from the total moment, the “isolated TwRM” moment results, shown in Fig. 5(b). The shape of the curves is reminiscent of those for coercive force (cf.

ACTA

264

METALLURGICA,

TORSION After

INITIAL Nickel -Linr

VOL.

17,

SATURATION Rod

1969

I.R.M.

A

Torsion Cycle Reldtoc)

3 4

-o-

-a-

+ 1.3 - 1.3

1) End8 Grippod.$.

TWIST

(degrees)

40

I60

SO

n

-3 -SO

FIG. 3. Change of an initial aeturetion IRM with deformation of nickel rod A. field in opposite sense of initial remenence.

TORSION After

INITIAL Cobalt

-Llnr

20

TWtST

1

Fkld (00)

4

40

I.RM.

Rod

Torslon Cyck

-o-

0

SATURATION

Negative field denotes

1.3

60

SO

(degrees)

100

120

J

FIQ. 4. Change of an initial saturetion IRM with deformation of cobalt rod.

CARMICHAEL:

MAGNETOMECHANICAL

REMANEKE

ACQUIRED Fran Nickel

(cl)

TORSICN CYCLE

1.w I

Ni

AND

Co

266

Rod A

MOMENT

2 0 -----

(ml

OF

DEMAGNETIZED STATE

(bl

TwRM+lRM+PRM

MOMENT

BEHAVIOUR

TwflM

only

TORSICN CYCLE

‘o2 ---Q-a I

‘“1 40..

_w------IO

_,-’ --.-__.-._

I

c__&#meIRY 40

0

80 TWIST

120

160

(dogreer)

0

40

80

I 120

160

TWIST (dognot)

FIG. 6. Acquisition of remanence in nickel rod A over successive strain interwds, in external field of 1.3 Oe. Rod demagnetized before each increment. (a) Total 8cquired moment, TwRM + IRM + PRM. (b) TwRM component alone; IRM and PRM subtracted.

Fig. 1). The limiting value of the moment is about 40 e.m.u., the same as that in Fig. 3. Results for the Cobalt rod are shown in Fig. 6. The curves are for the TwRM component alone. As for the nickel, the IRM and end-PRM attain

REMANENCE ACQUIRED Rorn DEMAGNETIZED STATE Cobalt Rod

’

_

2 --

e--

TORSION CYCLE (emu)

3._ 7 t

0

v : 20

40 TWIST

60

80

Kx)

3.4 Pre-existing remanence Figure 7 shows the results of subjecting nickel rods to successive strain increments, with the moment not being demagnetized at each stage. The deformation therefore acted on the total remanence remaining after the previous deformation step. An initial sharp drop in remanence on fatiguing is followed by an increase. The moment stabilizes after a reverse strain of about 3%, as before. The shape of the curves for nickel is quite different from that for acquired remanence (cf. Fig. 5). On the other hand, those for the effect of deformation on pre-existing remanence for cobalt are the same as those for acquired remanence.

TwRM only

MOMENT

limiting values by the end of Cycle 1; 0.12 e.m.u. and 1 e.m.u. respectively. The limiting value of total acquired remanence, including IRM and PRM, for this strain interval is about 7 e.m.u. This is 3.7% of the value of saturation IRM’. The shape of the curves is again similar to that for the coercive force (cf. Fig. 2).

I

4. DISCUSSION

I20

4.1 Mechanical behaviour during plmtic deformation

(dogroes)

FIG. 6. Aoquisition of remsnence in cobalt rod over successive strain intervals, in external field of 1.3 Oe. Rod demagnetized before each increment. Acquired TwRM component alone; IRM and PRM subtracted.

All the strain noted in the experiments here was that remaining after the sample rod was removed from the lathe. It represents plastic deformation, except for the small central core of the rod which was

ACTA

266

METALLURGICA,

TORSION Nickel

With

PRE-EXISTING

Rod B

17,

1969

REMANENCE Nickel Rod

lb)

E

MOMENT

MOMENT

-o-

TORSION

--O--TORSION

20

VOL.

40

CYCLE

2

CYCLE

3

SO TWIST

,

TORSION

120

160

0

40

60 TWIST

(drgrrrr)

CYCLE

4

I20

IS0

(drgrow)

FIG. 7. Change in pm-existing moment by torsional deformetion, in field of 1.3 Oe. (a) Nickel rod B; interval Il. 7 %. (b) Nickel rod E ; strain interval 11.1 Oh.

strained

elastically.

Unidirectional

cold

hardens

the material

mechanically,

because

increased density and interaction The strain-hardening larger the

yield

point

material

exhibits

Bauschinger

effect@) The yield

mechanical

softening

then resumes directional pheres

“fatigue point

strain-hardening

of dislocations

dislocations

of pairs of opposite secting to

new

sign.

and

mechanically

uni-

softening

is

atmosReversed distri-

Further,

some

With the presence of intercross slip of dislocations

cobalt

such a material

slip

planes

will

has one slip plane,

favourably

orientation

of

softening

in

The

endures less with continued

dislocations

slip systems.

fatigue.

can be created

strain,

on many

There is an essential difference,

fore, between the fatigue-induced

In the former, to a single set of

slip planes ; in the latter, they can establish three-dimensional

network

more there-

mode of structural

effectively

further assist in dispersing defect accumulations. Hexagonal-close-packed

stresses during

are limited

by the combination

softer

principal

dislocations

leads to more widely

slip plane systems,

more

as the material

on strain-hardened

can be annihilated

are

and nickel.

fatigue

buted defects on existing slip planes.

which

in cobalt

of dislocation

had been created

are those

with respect to the changing

deformation

slip planes during the pre-reversal working. motion

and

with continued

The

latter

oriented

This

stress is reduced.

with the dispersion

which

or the

Lubahn

The

because

deformation,

softening”,

is transitory,

deformation.

associated

by a progressively

In reversed

(see, for example,

Felgar(l”)).

of the

of structural defects.

is accompanied stress.

working

strain

because

of

a more

intersecting

slip planes. 4.2 Response of magnetic characteristics to structural deformation The response of the coercive force and moment

for

nickel were interpreted@) of these parameters internal

in terms of the dependence on strain-induced changes in the

stress state.

The new results reported

for nickel, and all those for cobalt, in the same manner. mechanical

here

can be explained

Magnetic hardening accompanies

hardening

in

multi-domain

materials

that being the basal (0001) plane. In such a material, the immediate reversed motion of dislocations with

because of the increased hindrance movement. The uniform increase

fatiguing

first half of Cycle 1 in Figs. 1 and 2 is phenomeno-

is followed

eventually

by the reconstitution

of pileups on the same set of slip planes. Facecentered-cubic nickel, however, has four sets of {Ill} slip planes. Some mobile dislocations can thus trsnsfer to new, more relatively unworked slip planes.

to domain wall of H, for the

logically similar to the behaviour of the stress-strain curve. The pinning of domain walls by interaction with defect

stress fields(**ll) will be most effective

when

CARMICHAEL:

MAGNETOMECHANICAL

defects are accumulated into localized pileups. When the defects are dispersed, the coercive force should decrease. In nickel (Fig. 1) an unusual behaviour results in initial fatigue. Although the material is mechanically softer because of the reduction in internal stress concentrations, it is magnetically harder. The new appearance of defects in previously lessstrained regions acts to effectively immobilize walls which were previously unimpeded. There is thus an initial increase in coercivity. This is followed by magnetic softening between 1 and 3% reverse strain in Fig. 1, The softening is due to continued reduction of the magnitude of stress concentrations, and annielation of some defects with the massive i~te~ction of new and old slip systems. The fluctuation in coercive force is relatively large because the domain pattern is strongly influenced by the presence of defect pileups and their alteration. The width of, for example, a 180” domain wall in nickel is about 1500 A(” f1*12)-larger than the inter-dislocation spacing. In cobalt (Fig. 2), the coercive force decreases with initial fatigue, as would have been anticipated with the strain softening caused by dispersing of dislocations. The magnetic softening is not p~noun~. The domain wall width is now less than the interdislocation spacing. A 180’ wall has a thickness of about 120 A,tcf*12,13)The mechanical softening accompanying reversed motion of defects does give the domain pattern increased mobility, however. There is a dispersing of dislocations on a number of parallel slip planes in regions of stress concentration. With strain-softening, some domain walls can relax more in response to demagnetizing-field energy. The coercive force will decrease, as witnessed in Fig. 2. The behaviour of nickel is not duplicated because of the absence of dislocation oross slip. After the softening phase in both nickel and cobalt, the Ho increases monotonically with continued deformation and hardening. It is noted that the transition to hardening is much more gradual in cobalt. This is because complete softening must occur on the single set of slip planes before renewed strain hardening sets in. In nickel, slip and hardening can occur on new planes, with the pie-fatigue slip plane systems in a state of residual hardening. It was noted that an initial saturation IRXdeoreased with deformation (Fig. 3 for nickel, Fig. 4 for cobalt). This is related to the structure-sensitive response of a magnetic multidomain pattern.@) For the nickel rod, a limiting value of remanence is attained. This

BEHAVIOUR

OF

Ni AND

Co

267

occurs by about 3% reversed strain, which corresponds to the end of the region of pronounced fluctuation in the coercive force. The limiting value represents the stabilized moment remaining after sufficient deformation has acted in concert with external field energy tending to increase the remanence, and demagnetizing energy tending to reduce it. The comb~ation of these energies in the period of domain instabi~ty during deformation results in the equilibrium limiting value. The same value is noted for acquired remanence (Fig. 5). The less rapid decrease in moment for cobalt (Fig. 4) is explained by the more spatially restricted rearrangement of dislocations. There is thus a less effective influence on giving the domain pattern increased mobility during straining. In addition, cobalt has uniaxial magnetic anisotropy with a single axis of “easy” magnetization, whereas nickel has ‘four easy axes. Thus cobalt has essentially only 180’ domain wall motion, and the walls are readily pinned by the presence of defects. Nidkel has 70.5’ and 109.5” walls also. These am encouraged to move directly by the stress acting during deformation. This gives the total domain pattern more mobility. Some domains may also rotate their magnetization by 70.5’ to eir~umvent a large stress barrier such as that due to a dislocation pileup. The curves for strain-induced moment acquired from a demagnetized state (Fig. 5 for nickel, Fig. 6 for cobalt) are similar to those for coercive force. They reflect the same magnetomecha~~l effect. The movement of dislocations gives the domain configuration more mobility. When the material is magnetically softest, at a reverse strain of about 3% for nickel and about 2% for cobalt, there is a condition of low internal stress in the material. The magnetoelastic energy associated with dislocations is more uniform in distribution. The domain pattern thus yields a smaller, more energetically favoured, remanence. For the case of localized defect accumulations, as for the work-hardened state, the magnetoelastic energy variation is large and pins a larger residual moment. If the fatigue deformation acts on a pre-existing moment (Fig. 7), there is an immediate decrease in remanence. The relaxation of the internal stress state allows the metastably-pinned moment to respond to dema~etizing energy, and decrease in magnitude. With continued unidirectional deformation, the stress state regains its pre-fatigue condition, and the moment created during the transitory deformation process is again immobilized. This is true for both nickel and cobalt.

268

ACTA

METALLURCICA,

5. CONCLUSION

A variety of experiments on nickel and cobalt indicate the interaction of magnetic properties end plastic deformation. The behaviour of the two materials exhibits differences. However, a structure sensitive model previously outlined for magnetomechanical effects in magnetitet8) provides a consistent explanation for all aspects of the behaviour of all three materials. Both-nickel and cobalt reveal large changes in some magnetic characteristics during fatigue deformation. Fatigue is particularly illustrative of the relationship of a structure-dependent internal stress state to magnetic properties such as ooercivity and remanence. This may have useful and interesting application in new uses for such magnetic materials. ACKNOWLEDGMENTS Financing of this work at the University of Pitts-

burgh was provided by the U.S. National Science Foundation, through the U.S.-Japan Cooperative Science program. The author is indebted to the

VOL.

17, 1969

A. W. Mellon Educational and Charitable Trust for fellowship support, and to the Japan Society for the Promotion of Science for support during the present writing. It is a pleasure to acknowledge the assistance of Prof. M. D. Fuller for discussions during the work, and Prof. R. D. Wyckoff for use of lab facilities. REFERENCES

1. F. VICENA, Czech.J. Phy8. 4, 419 (1954).

2. M. KERSTEN, 2. angew. Phyz. 80,496 (1966). 3. H. DIETRICH and E. KNELL=, 2. MetaUk. 47, 716(1966). 4. A. SEEGER and H. KRONM~R, Physics. Chem. S&de 12, 298 (1960). 6. C. MATI!EUCI,C.R. h&d. St&c. Acad. Sci. Pa& 24,301 (1847);Ann8. Chem. Phye. (1968). 6. R. S. CARMIC~L~EL and M. D. FULLER, J. Cfeomagn. Geoelect.,Kyoto 19, 181(1967). 7. H. NAQAOKA, J. Coil. Sci. imp. Univ. To&o 2, 283, 304 (1888); Phil. Hag., Seties 6, 27, 117 (1889). 8. R. S. CAB~ICEAEL, PhiZ. Ma+ 17, 911 (1968). 9. J. BAUSCEINGER, Mitt mech. tech. Lab. Mtichen (1886). 10. J. D. LWAHN end R. P. FEMAR, Plasticity and Creep of

Metals. Wiley (1961). 11. F. VICENA, Czech. J. Phya. 5, 480 (1965).

12. 13.A. L~EY~ Phil. Msg. 4,792 (lgso)+

13. D. J. CRAIK and R. S. TEBBLE, Fewomugnetiam Ferromagnetic Domains. North-Holland ( 1966).

and