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Variation of magnetostrictive properties in grain-oriented and non-oriented electrical steel with texture under applied linear stress
Journal of Magnetism and Magnetic Materials 112 (1992) 222-224 North-Holland
/HI ,M 'I
Variation of magnetostrictive properties in grain-oriented and non-oriented electrical steel with texture under applied linear stress G.H. Shirkoohi and M. Boukhalfa Woifson Centre for Magnetics Technology, School of Electrical, Electronic and Systems Engineering, Unieersity of Wales Cardiff, Wales, UK
Variation of magnetostriction with texture, in HiB, spark abalated HiB, and two grades uf low silicon non-oriented materials are investigated under applied linear stress levels of around + 30 MPa. The anisotropic behaviour of magnetostriction is discussed using a simple theoretical model.
1. Introduction Stress sensitivity of magnetostriction in grainoriented electrical steel has been the subject of significant number of investigations, and the mechanism which cause this sensitivity, has also been explained by many authors [1-5]. The effect of stress on the magnetostriction at different angles to the rolling direction was previously investigated in grain-oriented steel [6,7]. Much of the work, however, has been directed at grain-oriented material. The aim of this investigation is to extend the studies in order to include non-oriented steels.
2. Experimental procedure Epstein size ( 3 0 x 30~ mm 2) strips of two grades of non-oriented, 0.2 and 1.3% silicon, and two batches of high permeabi!lty grain-oriented 3.25% silicon HiB, and spark abalated HiB electrical steels were magnetised under sinusoidal flux density of 1.3 T, 50 Flz, using a single strip
Correspondence to: Dr. G.H. Shirkoohi, Wolfson Centre For Magnetics Tec.~,onolo~;y, 3(1 The Parade, Roath, Cardiff CF2 3AD, UK.
tester of the form previously described [8]. Grain-oriented samples were cut at 0, 22.5, 45, 67.5 and 90 °, and non-oriented samples were cut at 0, 45, and 90° with respect to their rolling directions. Magnetostriction measurements were carried out under applied linear tensile and compressive stresses of around 30 MPa along the direction of magnetisation, using thermal compensated strain gauges placed in the centre and parallel to the longitudinal directions of each strip.
3. Results Fig. 1 shows typical variation of magnetostriction under applied linear stress, in spark abalated material, at different angles to the rolling direction, when magnetised at 1.3 T, 50 Hz. The stress free magnetostriction values are seen to be almost zero, and tensile stress results in negative magnetostriction, while compressive stresses causes positive magnetostriction. The magnitude of the magnetostriction under the influence of str=s~, seems to be dependent on the angle of magnetisation and the value of the applied stress. Magnitude of magnetostriction under applied compressive stress is seen to be the highest along
I13(14-8853/92/$05.()(1 ~ 1992 - Elsevier Science Publishers B.V. All rights reserved
G.H. Shirkoohi, M. Boukhalfa / Ma'gnetostriction in Si-Fe with texture and stress
the rolling direction, and in excess of 10 × 10 -6 As the angle of magnetisation is increased from the rolling direction towards 67.5 °, magnetostriction sharply reduces to around 2 × 10 -6, followed by a small increase at 90° to the rolling direction. Application of tensile stress results in the same, but less pronounced variation in the magnitude of magnetostriction. The effect of stress on magnetostriction, in HiB material, was very similar. Fig. 2 shows variation of magnetostriction under applied linear stress, in i.3% silicon non-oriented material, at different angles to the rolling direction, when magnetised at 1.3 T, 50 Hz. Under applied tensile stress, magnetostrictive variation is nearly independent o f texture, compressive stresses, however, results in small, but appreciable variation with texture, with the largest values of magnetostriction of around 7 × 10 -6 recorded along the rolling direction. Very similar variations were also observed in 0.2% silicon material.
223
10.
Key
e
8.~
I',
_,
Z
-
~:
- =
1~'-
t
45°to
R.D
9¢,.0 R.o
2
0
U N t ^ X I ^ I . S'111t~.~q ( M P ^ )
'['IINSION
( :ONPI~I(N.%II IN
i
-
"i
--~ ~
L
_ oo°,.o~.D
+ .-
~
.
.
.
~
Fig. 2. Variation of magnetostrictior~ under applied linear stress, in 0.2% silicon non-oriented material, at different angles to the rolling direction, whee magne':sed at 1.3 T, 50 Hz.
,
10.
Key - ~, -
00 °
t,o R.D
-,t--
Z2°5
¢"
-
~0
-30
-20
-10
-2
"1
45°
t,,, R . D
- o -
~°'S
~R.n
-
90°
t,o R.n
'
-
el -
'
~
-2.
I./NIAX]AJ. S T R e s s ( M P A ) -G.
-4
( : O M PI*JiNS tO N -4
•
4, D i s c u s s i o n
,
,
"['IINSION ,
-R.;
,
t ,,
of results
R.D
i
Fig. 1. Variation of magnetostriction under applied linear stress, in spark abalated material, at different angles to the rolling direction, when magnetised at 1.3 T, 50 Hz.
The results show that magnetostriction in the grain-oriented materials investigated is affected by texture under both tensile and compressive stress, the diversity of the variation of magnetostriction with texture is however, much larger under compression than under tension. Tensile stress results in an almost isotropic behaviour of magnetostriction in the two non-oriented steels, but the trend under compressive stress is similar to those observed in the grain-oriented steels, although their diversity with texture is seen to be much smaller. The anisotropic behaviour of magneto,~triction under applied stress could be explained in terms of the magnetoelastic energy in silicon iron material. In general, if an external uniform stress, ~r, is applied to a cubic ferromagnetic material, such as silicon-iron, a strain of magnetoela~dc energy
224
G.H. Shirkoohi, M. Boukhalfa / Magnetostriction in Si-Fe with texture and stress
will be stored in the domain, E A, which is given by [2,3],
ai'/31
EA
+ 0¢2fl5 + a.~/33
3)
- 3Alllo" ( @ l B 1 a 2 ~ 2 -F a2~ZO~3B3 "1-tff3~30~! ~ l ),
(1)
where ,~100 and Ai i~ are the values of the saturation magnetostriction constants, and (a~, c¢2, a 3) and (/31,/32 ,/33 ) are the directional cosines of the stress and the magnetisation with respect to the crystal axes. If both stress and magnetisation were applied to the domain pattern at an angle 0 to the rolling direction in the plane of the sheet, then a~ = 131 = cos O, a2 =/32 = c~3 =/33 = (sin 0 ) / V ~ , and hence eq. (1) becomes: Ea
=
-
In grain-oriented material, due to the high anisotropy, under both tensile and compressive stress the spread of magnetostriction with texture is more prominent. U n d e r compressive stress, free energy will be increased, which will cause the static domain pattern to change to a pattern which becomes more difficult to magnetise along the rolling direction, since the magnetisation vectors of the internal domains have to be rotated by 90 ° [1]. Free energy is reduced by the tension so that the domain structure of the material remains unaltered, but a spread of magnetostriction is observed which is a combination of some rotation of magnetisation vectors in grains which are not aligned in the direction of stress, and the directional strain energies.
Z cos 20 + 3 cos 40 + ~" ) '
X3,tll]cr(~i cos 20 + ~15 cos 4 0 - ~13) .
(2)
Now if we consider the angles at which the Epstein samples were cut, then the strain energy caused by stress in the samples is given by 0 = 0°; 0 = 22.5°; 0 = 45°;
E~ = +hloo o-+ 0.56hlllO" , Ex = +0.609Aloo o ' - 0.953AlllO- , E a = +0.062A,)0o-- 2.624Aill~r ,
0 = 67.5°;
E~ = +0.079Ai00o-- 1.483A]!lo- ,
0 = 90°;
E a = + 0.25,~00o-- 0.187alll~r.
In non-oriented materials, domains are distributed almost evenly amongst the six possible c~:,be edges directions. Application of tensile stress will cause some degree of alignment of the magnetisation vectors in the cube-edge directions near to that of applied stress. This results in an increase in the magnitude ot the magnetostriction which does not vary a great deal with texture. Compressive stress, on the other hand, will cause some of ~he magnetoe!astic vectors to take up directions near to right angles to the stress, and results in a larger increase in the magnetostriction, and enhances the small inherent anisotropy of the material. This corresponds to the energy terms for 0 °, 45 ° and 90 °.
5. Conclusions
Tensile stress results in an almost isotropic behaviour of magnetostriction in the two non-offented steels, which is due to the similarity in the n u m b e r of the domain vectors that are aligned towards the field direction, due to the tension. The trend under compressive stress is similar to those observed in the grain-oriented steels, and their small anisotropy is enhanced, as the population of the domain vectors affected by compression varies with texture.
References [1] W.D. Corner and J.J. Mason, Brit. J. Appl. Phys. 15 (1964) 709. [2] J.W. Shilling and G.L. Houze, Jr., IEEE Trans. Magn. MAG-10 (1974) 195. [3] A.J. Moses, J. Mat. Sci. 9 (1974) 217. [a] p I R ~ . t , ~ ~ . a I~ o .... !;. . . . D~,,. 1 ~ r : 11.4 (!967) 1~a'7 [5] G.H. Simmons and J.E. Thompson, Proc. lEE 17 (1971) 1302. [f)] A.J. Moses, IEEE Trans. Magn. MAG-17 (1981) 2872. [7] H.J. Stanbury, J. Magn. Magn. Mater. 26 (1982) 47. [8] A.J. Moses and D. Davies, IEEE Trans. Magn. MAG-16 (1980) 44.
/HI ,M 'I
Variation of magnetostrictive properties in grain-oriented and non-oriented electrical steel with texture under applied linear stress G.H. Shirkoohi and M. Boukhalfa Woifson Centre for Magnetics Technology, School of Electrical, Electronic and Systems Engineering, Unieersity of Wales Cardiff, Wales, UK
Variation of magnetostriction with texture, in HiB, spark abalated HiB, and two grades uf low silicon non-oriented materials are investigated under applied linear stress levels of around + 30 MPa. The anisotropic behaviour of magnetostriction is discussed using a simple theoretical model.
1. Introduction Stress sensitivity of magnetostriction in grainoriented electrical steel has been the subject of significant number of investigations, and the mechanism which cause this sensitivity, has also been explained by many authors [1-5]. The effect of stress on the magnetostriction at different angles to the rolling direction was previously investigated in grain-oriented steel [6,7]. Much of the work, however, has been directed at grain-oriented material. The aim of this investigation is to extend the studies in order to include non-oriented steels.
2. Experimental procedure Epstein size ( 3 0 x 30~ mm 2) strips of two grades of non-oriented, 0.2 and 1.3% silicon, and two batches of high permeabi!lty grain-oriented 3.25% silicon HiB, and spark abalated HiB electrical steels were magnetised under sinusoidal flux density of 1.3 T, 50 Flz, using a single strip
Correspondence to: Dr. G.H. Shirkoohi, Wolfson Centre For Magnetics Tec.~,onolo~;y, 3(1 The Parade, Roath, Cardiff CF2 3AD, UK.
tester of the form previously described [8]. Grain-oriented samples were cut at 0, 22.5, 45, 67.5 and 90 °, and non-oriented samples were cut at 0, 45, and 90° with respect to their rolling directions. Magnetostriction measurements were carried out under applied linear tensile and compressive stresses of around 30 MPa along the direction of magnetisation, using thermal compensated strain gauges placed in the centre and parallel to the longitudinal directions of each strip.
3. Results Fig. 1 shows typical variation of magnetostriction under applied linear stress, in spark abalated material, at different angles to the rolling direction, when magnetised at 1.3 T, 50 Hz. The stress free magnetostriction values are seen to be almost zero, and tensile stress results in negative magnetostriction, while compressive stresses causes positive magnetostriction. The magnitude of the magnetostriction under the influence of str=s~, seems to be dependent on the angle of magnetisation and the value of the applied stress. Magnitude of magnetostriction under applied compressive stress is seen to be the highest along
I13(14-8853/92/$05.()(1 ~ 1992 - Elsevier Science Publishers B.V. All rights reserved
G.H. Shirkoohi, M. Boukhalfa / Ma'gnetostriction in Si-Fe with texture and stress
the rolling direction, and in excess of 10 × 10 -6 As the angle of magnetisation is increased from the rolling direction towards 67.5 °, magnetostriction sharply reduces to around 2 × 10 -6, followed by a small increase at 90° to the rolling direction. Application of tensile stress results in the same, but less pronounced variation in the magnitude of magnetostriction. The effect of stress on magnetostriction, in HiB material, was very similar. Fig. 2 shows variation of magnetostriction under applied linear stress, in i.3% silicon non-oriented material, at different angles to the rolling direction, when magnetised at 1.3 T, 50 Hz. Under applied tensile stress, magnetostrictive variation is nearly independent o f texture, compressive stresses, however, results in small, but appreciable variation with texture, with the largest values of magnetostriction of around 7 × 10 -6 recorded along the rolling direction. Very similar variations were also observed in 0.2% silicon material.
223
10.
Key
e
8.~
I',
_,
Z
-
~:
- =
1~'-
t
45°to
R.D
9¢,.0 R.o
2
0
U N t ^ X I ^ I . S'111t~.~q ( M P ^ )
'['IINSION
( :ONPI~I(N.%II IN
i
-
"i
--~ ~
L
_ oo°,.o~.D
+ .-
~
.
.
.
~
Fig. 2. Variation of magnetostrictior~ under applied linear stress, in 0.2% silicon non-oriented material, at different angles to the rolling direction, whee magne':sed at 1.3 T, 50 Hz.
,
10.
Key - ~, -
00 °
t,o R.D
-,t--
Z2°5
¢"
-
~0
-30
-20
-10
-2
"1
45°
t,,, R . D
- o -
~°'S
~R.n
-
90°
t,o R.n
'
-
el -
'
~
-2.
I./NIAX]AJ. S T R e s s ( M P A ) -G.
-4
( : O M PI*JiNS tO N -4
•
4, D i s c u s s i o n
,
,
"['IINSION ,
-R.;
,
t ,,
of results
R.D
i
Fig. 1. Variation of magnetostriction under applied linear stress, in spark abalated material, at different angles to the rolling direction, when magnetised at 1.3 T, 50 Hz.
The results show that magnetostriction in the grain-oriented materials investigated is affected by texture under both tensile and compressive stress, the diversity of the variation of magnetostriction with texture is however, much larger under compression than under tension. Tensile stress results in an almost isotropic behaviour of magnetostriction in the two non-oriented steels, but the trend under compressive stress is similar to those observed in the grain-oriented steels, although their diversity with texture is seen to be much smaller. The anisotropic behaviour of magneto,~triction under applied stress could be explained in terms of the magnetoelastic energy in silicon iron material. In general, if an external uniform stress, ~r, is applied to a cubic ferromagnetic material, such as silicon-iron, a strain of magnetoela~dc energy
224
G.H. Shirkoohi, M. Boukhalfa / Magnetostriction in Si-Fe with texture and stress
will be stored in the domain, E A, which is given by [2,3],
ai'/31
EA
+ 0¢2fl5 + a.~/33
3)
- 3Alllo" ( @ l B 1 a 2 ~ 2 -F a2~ZO~3B3 "1-tff3~30~! ~ l ),
(1)
where ,~100 and Ai i~ are the values of the saturation magnetostriction constants, and (a~, c¢2, a 3) and (/31,/32 ,/33 ) are the directional cosines of the stress and the magnetisation with respect to the crystal axes. If both stress and magnetisation were applied to the domain pattern at an angle 0 to the rolling direction in the plane of the sheet, then a~ = 131 = cos O, a2 =/32 = c~3 =/33 = (sin 0 ) / V ~ , and hence eq. (1) becomes: Ea
=
-
In grain-oriented material, due to the high anisotropy, under both tensile and compressive stress the spread of magnetostriction with texture is more prominent. U n d e r compressive stress, free energy will be increased, which will cause the static domain pattern to change to a pattern which becomes more difficult to magnetise along the rolling direction, since the magnetisation vectors of the internal domains have to be rotated by 90 ° [1]. Free energy is reduced by the tension so that the domain structure of the material remains unaltered, but a spread of magnetostriction is observed which is a combination of some rotation of magnetisation vectors in grains which are not aligned in the direction of stress, and the directional strain energies.
Z cos 20 + 3 cos 40 + ~" ) '
X3,tll]cr(~i cos 20 + ~15 cos 4 0 - ~13) .
(2)
Now if we consider the angles at which the Epstein samples were cut, then the strain energy caused by stress in the samples is given by 0 = 0°; 0 = 22.5°; 0 = 45°;
E~ = +hloo o-+ 0.56hlllO" , Ex = +0.609Aloo o ' - 0.953AlllO- , E a = +0.062A,)0o-- 2.624Aill~r ,
0 = 67.5°;
E~ = +0.079Ai00o-- 1.483A]!lo- ,
0 = 90°;
E a = + 0.25,~00o-- 0.187alll~r.
In non-oriented materials, domains are distributed almost evenly amongst the six possible c~:,be edges directions. Application of tensile stress will cause some degree of alignment of the magnetisation vectors in the cube-edge directions near to that of applied stress. This results in an increase in the magnitude ot the magnetostriction which does not vary a great deal with texture. Compressive stress, on the other hand, will cause some of ~he magnetoe!astic vectors to take up directions near to right angles to the stress, and results in a larger increase in the magnetostriction, and enhances the small inherent anisotropy of the material. This corresponds to the energy terms for 0 °, 45 ° and 90 °.
5. Conclusions
Tensile stress results in an almost isotropic behaviour of magnetostriction in the two non-offented steels, which is due to the similarity in the n u m b e r of the domain vectors that are aligned towards the field direction, due to the tension. The trend under compressive stress is similar to those observed in the grain-oriented steels, and their small anisotropy is enhanced, as the population of the domain vectors affected by compression varies with texture.
References [1] W.D. Corner and J.J. Mason, Brit. J. Appl. Phys. 15 (1964) 709. [2] J.W. Shilling and G.L. Houze, Jr., IEEE Trans. Magn. MAG-10 (1974) 195. [3] A.J. Moses, J. Mat. Sci. 9 (1974) 217. [a] p I R ~ . t , ~ ~ . a I~ o .... !;. . . . D~,,. 1 ~ r : 11.4 (!967) 1~a'7 [5] G.H. Simmons and J.E. Thompson, Proc. lEE 17 (1971) 1302. [f)] A.J. Moses, IEEE Trans. Magn. MAG-17 (1981) 2872. [7] H.J. Stanbury, J. Magn. Magn. Mater. 26 (1982) 47. [8] A.J. Moses and D. Davies, IEEE Trans. Magn. MAG-16 (1980) 44.