IEEE TRANSACTIONS ON MAGNETICS, VOL. 29, NO. 3, MAY 1993 2077

Direction of Change of Magnetization of a Ferromagnet Subjected to Stress

Ian M. Robertson

Abstract-The magnetomechanical effect for a quenched and tempered alloy steel has been studied. In most published work it has been found that stress causes the magnetization to move towards the anhysteretic magnetization. However in the pres- ent work it was found that under special conditions the mag- netization moves away from the anhysteretic when a cyclic stress is applied. This behavior is tentatively explained by ap- plying the Preisach model of ferromagnetic hysteresis.

INTRODUCTION T is usually found that the application of cyclic stress I to a ferromagnet causes an irreversible shift in its mag-

netization towards the anhysteretic magnetization. The anhysteretic can be regarded as the equilibrium magneti- zation in a given applied field: the magnetization which would exist if all hysteresis lag effects were eliminated. The anhysteretic curve lies midway between the ascend- ing and descending branches of the major hysteresis loop (to saturation) of the material.

This effect was noted in very early work by Ewing, who showed that vigorous tapping of soft iron wire drastically increased its initial permeability, almost eliminated re- manence, and reduced the area of the B-H hysteresis loop [ 13. Jiles and Atherton clearly demonstrated that both ten- sile and compressive stress cycles caused an irreversible change in magnetization towards the anhysteretic from points on the initial magnetization curve or on a major hysteresis loop for a steel specimen [2]. Further examples have been summarized in the review by Robertson [3].

However, the general validity of the principle has been challenged by the results of Atherton and Ton for the change in magnetization induced by cyclic stress initiated from points on minor hysteresis curves [4]. These authors suggested the existence of offset anhysteretic curves ap- plicable to minor hysteresis loops.

In the present work some further examples where the change in magnetization due to cyclic stress is away from the anhysteretic are reported. In most cases the change is toward the anhysteretic, but in special circumstances (even for starting points on a major hysteresis loop) the mag- netization moves in the opposite direction. The origin of this behavior is rationalized with reference to the Preisach model of Hysteresis [5]. The empirical nature of the

Manuscript received August 1, 1992; revised December 10, 1992. The author is with the Ship Structures and Materials Division, DSTO-

IEEE Log Number 9207497. MRL, P.O. Box 50, Ascot Vale 3032, Australia.

Preisach model should be kept in mind when following this approach.

EXPERIMENTAL PROCEDURE Measurements were carried out on a quenched and tem-

pered alloy steel with a hardness of 260 HV (correspond- ing to an ultimate tensile strength of 870 MPa). The major alloying elements in the steel are 0.15% C, 1.0% Mn, 1.3% Ni, and 0.5% Cr. It was water quenched from 900°C and tempered at 650°C.

The magnetic circuit consisted of two cylindrical rods of the steel (10.2 mm diameter by 210 mm) connected by two soft iron yokes as shown in Fig. 1. Coils for applying the H field and for measuring the induction, B , were wound on formers around the steel rods in an arrangement similar to that used by Lliboutry [6]. The loop arrow in Fig. 1 indicates that the two coils are connected in series. Compressive stress was applied along the axes of the rods, so that stress, applied field and measured induction all acted in the same direction. The purpose for which this work was originally carried out did not require accurate calibration of the applied field, H. Therefore the field is given here in terms of arbitrary linear units, one unit cor- responding to about 60 A/m.

The magnetic process which was camed out consisted of demagnetizing the specimens (D), applying a field H , , reducing the field by an amount H2 (bringing the field to HI-H2), and then applying and releasing a 200 MPa com- pressive stress n times. This process is designated DH1 H2 (a5) '. The magnetic induction was recorded throughout the process. The reversible and irreversible components of the change in induction during the stress cycling part of the process, A B r and A B i , were calcu- lated.

RESULTS Fig. 2 shows the normal induction curve for the steel

and a major hysteresis loop. Fig. 3 shows a typical result for the DHIH2 (a Z)4 process and indicates the compo- nents A B r and A B i due to stress cycling. For the case shown in Fig. 3, stress cycling reduces the magnetization of the specimens.

Results for the DH, H2 ( 0 5 ) ~ process with HI = 8 units and H2 taking on several values ranging from zero to 16 units are shown in Fig. 4. It can be seen that in most cases the irreversible change in induction is towards the anhys-

0018-9464/93$03.00 0 1993 IEEE

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Fig. 1. Schematic diagram showing the magnetic circuit consisting of two steel rods joined by soft iron yokes. The loop arrow indicates that the coils are connected in series.

IEEE TRANSACTIONS ON MAGNETICS, VOL. 29, NO. 3, MAY 1993

1 so0

-2odo -15 -10 -5 I: 6 10 1s ;

I

H /arbitrary mits

-1500k0 ; I I - -15 -10 -5 0 5 10 15 20 H /arbitrary mits

Fig. 2. Normal induction curve and major hysteresis loop (from H = 20 units) for the steel studied.

250

200

150 + \ E

m

100

50

a -, 3 -200 -150 -100 -50 Stress /MPa

-

f .Bi

- AB'

Fig. 3. Changes in induction during the magnetic pmess DHIa2(uo)4 with HI = 12, H2 = 11 units and u = -200 MPa.

teretic, and that the magnitude of AB' is very roughly proportional to the difference between the anhysteretic in- duction and the induction after the DH, n2 part of the pro-

Fig. 4. Changes in induction during the processes DH,p2(uZ)4 with HI = 8 units, five different values of H2 (H = HI - H 2 ) , and u = - 200

anhysteretic (- - -), reversible component of the induction change from stress cycling (-e-) and the irreversible component (+).

MPa. Normal induction curve (. . . . . .), descending branch (. . .*e . .),

cess (on the descending branch), as reported by Jiles and Atherton [2]. However, in the case H2 = 7 units (so that H is one unit after DH1 H2), ABi is negative even though the induction after DH, H2 lies below the anhysteretic. Clearly there is a range of H2 values close to 7 units for which stress cycling moves the magnetization away from the anhysteretic for this steel.

Similar results are shown in Figs. 5 and 6 for H I values of 12 and 14 units, respectively. Once again there is a narrow range of H2 values over which stress cycling causes the magnetization to move away from the anhys- teretic. It is also interesting to note that the magnitude of A B i is not simply related to the difference between the anhysteretic induction and the induction after DH, n2. For example, compare AB' in Fig. 6 for H = H I - H2 values of one and -4 units.

Comparing Figs. 4, 5 , and 6 it can also be seen that the reversible component of the change in induction due to stress cycling is determined almost entirely by H = H I - H2 and is only slightly influenced by the induction prior to the application of stress.

DISCUSSION The fact that AB' sometimes takes the induction further

away from the anhysteretic can be readily explained in terms of the Preisach model and the following argument:

1) As the applied field is initially increased to H I the induction lags behind the anhysteretic. Later application of stress tends to overcome the hysteresis lag, thus caus- ing an irreversible increase in induction (towards the an- hysteretic).

2) As the field is reduced to H = H1 - H2 the induction again lags, but this time in the opposite sense. Applica- tion of stress tends to overcome this lag also, causing an irreversible decrease in induction.

3) Over a narrow range of H2 values, the compromise

ROBERTSON: MAGNETIZATION OF A FERROMAGNET 2079

c E \ m

c E \ m

400 I

300 - I ....*

200.

100;

9

I I

-1 0 0 .

-200 ~

-300. m I "

-400

I I

-20 -16 -19 -5 0 5 10 15 20 H /arbitrary mite

Fig. 5 . As for Fig. 4 but with H I = 12 units.

aoo I

I r .. I *,,........ - . .

*.... 1"" 600 . _.'" , 1

I I

400.

. I

-600 1 Fig. 6. As for Fig. 4 but with H , = 14 units.

between these conflicting trends results in an irreversible change in induction which is away from the anhysteretic.

Fig. 7 shows Preisach diagrams for the DH1 n2 process in which H2 has different values relative to H1. The hatched region in Fig. 7(a) (H2 = 0) has reverse polarity but would have forward polarity in the equilibrium state (on the anhysteretic). Application of stress helps some do- mains in this region to change their polarity and thus in- creases the induction towards the anhysteretic.

Similarly the stippled regions in Fig. 7(c) and (d) (H2 > H , ) have forward polarization and would have reverse polarization at equilibrium. Stress helps some domains to overcome hysteresis lag and thus decrease the induction towards the anhysteretic.

The interesting case is that of Fig, 7(b) where H2 < H I and both types of region are present in the Preisach dia- gram. For the present steel, it appears from Figs. 4 to 6 that stress is more effective in reversing the polarization of domains in the stippled region of Fig. 7(b) than in the hatched region. This is physically acceptable for two rea- sons:

Fig. 7. Preisach diagrams for the process D H , & with a fixed value of H , and four values of Hz (a-d).

1) According to the Preisach model, the domains in the stippled region close to the line b = H I - H2 are on the brink of changing their polarity and would require only a small stimulus (e.g., stress) to switch over.

2) The difference between the upper and lower switch- ing fields of a domain is smaller the closer it is to the line a = b. The difference (a-b) can be regarded as an indi- cator of the strength of the pinning effect which is re- sponsible for hysteresis. Stress is therefore, potentially, more capable of reorienting domains close to the line a = b (i.e., in the stippled region) than those further away (Le., in the hatched region).

CONCLUSION This work confirms the principle that (in most cases)

cyclic stress applied to a ferromagnet causes its magne- tization to change towards the anhysteretic magnetization. However, under some circumstances the change may be away from the anhysteretic.

This anomaly apparently arises because stress is better able to reorient the direction of magnetization of some domains than that of others. Therefore, although stress may always reorient individual domains towards their own equilibrium orientation, the bulk magnetization does not always change towards the equilibrium magnetization.

REFERENCES

111 F. Brailsford, Magnetic Materials, London: Methuen, 1951. [2] D. C. Jiles and D. L. Atherton, "Theory of the magnetization process

2080 IEEE TRANSACTIONS ON MAGNETICS. VOL. 29, NO. 3, MAY 1993

in ferromagnets and its application to the magnetomechanical effect,”

[3] I. M. Robertson, “A review of investigations of the magnetization of steel due to the application of stress,” Muter. Forum, vol. 15, pp.

[4] D. L. Atherton and V. Ton, “The effects of stress on a ferromagnet on a minor hysteresis loop,” IEEE Trans. Mugn., vol. 26, pp. 1153- 1156, 1990.

[5] D. L. Atherton, B. Szpunar, and J . A. Szpunar, “A new approach to Preisach diagrams,” IEEE Trans. Magn., vol. 23, pp. 1856-1865, 1987.

[6] L. Lliboutry, “L’aimantation des aciers dans les champs magne- tiques,” Annales de Physique, vol. 6, p. 731, 1951.

J . P h y ~ . D: Appl. P h y ~ . , VOI. 17, pp. 1265-1281, 1984.

117-131, 1991.

Ian M. Robertson was born in Australia in 1955. He received the B. Met. degree from the University of Newcastle in 1979 and a Ph.D. in metal- lurgical engineering from the University of Illinois in 1983.

He has been employed in the steel and aluminum industries and has car- ried out research in a variety of fields including ferrous metallurgy, trans- mission electron microscopy of shape memory alloys, inelastic neutron dif- fraction, and formability and crystallographic texture control in aluminum alloys. Since 1988 he has been with the Defence Science and Technology Organisation where his interests include the magnetic properties of mate- rials and control of fatigue and fracture. Dr. Robertson is a member of the Institute of Metals and Materials Australasia and the American Society for Metals.