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Consequences of magnetic aging for iron losses in electrical steels
ARTICLE IN PRESS
Journal of Magnetism and Magnetic Materials 304 (2006) e593–e595 www.elsevier.com/locate/jmmm
Consequences of magnetic aging for iron losses in electrical steels Marcos F. de Camposa,, Marı´ lia Emurab, Fernando J.G. Landgrafc a
Inmetro –Dimci/Dimat, Av. Nossa Senhora das Gracas 50 Xerem, Duque de Caxias, RJ 25250-020, Brazil b GlobalMag, Sa˜o Paulo, SP, Brazil c Instituto de Pesquisas Tecnolo´gicas—IPT, Av. Professor Almeida Prado 532, Sa˜o Paulo, SP 05508-901, Brazil Available online 20 March 2006
Abstract Electrical steels, when submitted to operation, present continuous decrease of their magnetic properties, depending on the carbon content. This effect is attributed to the increase of the size of carbides, a process also known as coarsening or Ostwald Ripening. Loss separation can offer a better understanding of this phenomenon. Experimental results show that all effect of aging is inside the hysteresis loss component, with the excess losses unaffected. The carbon content in electrical steels should be less than 25 ppm to avoid magnetic aging. r 2006 Elsevier B.V. All rights reserved. PACS: 75.50.bb Keywords: Silicon steel; Non-oriented electrical steels; Inclusions; Magnetic aging
1. Introduction During the life of electrical steels, a phenomenon named magnetic aging [1–5] may occur. This effect is due to microstructural changes: carbon and/or nitrogen in solid solution precipitate as iron carbides or nitrides, respectively, increasing the losses [2,3]. It has also been noted that the increase of coercivity or losses is a function of the particle size [2–5]. This process is analogous to the Ostwald Ripening of carbides resulting in increased hardness [6]. 2. Experimental Steel sheets 0.64 mm thick were used in aging experiments. The chemical composition of the steel is 0.031% C, 46 ppm N, 0.132% Mn, o0.005% Si, 0.035% Al, 0.031% P, 0.011% S. The six different decarburizing cycles produced samples with the six different amounts of carbon. Then, an accelerated aging was performed by means of a heat treatment at 225 1C during 24 h. The magnetic measureCorresponding author.
E-mail addresses: [email protected], [email protected] (M.F. de Campos). 0304-8853/$ - see front matter r 2006 Elsevier B.V. All rights reserved. doi:10.1016/j.jmmm.2006.02.185
ment was done in Epstein frame at 60 Hz and at quasistatic condition (0.005 Hz), for loss separation. 3. Results and discussion 3.1. Loss Separation and the aging effect In the loss separation procedure the total power losses Pt (W/m3 or W/kg) are separated into three components, the classical eddy or Foucault losses Pcl, the anomalous or excess losses Pan and hysteresis losses Ph (according the expression below). Pt ¼ Ph þ Pcl þ Pan :
(1)
With Pcl—due to eddy currents—is given by [7]: Pcl ¼
p2 f 2 B2max e2 , 6r
(2)
where Bmax is the maximum induction, e is the thickness of the sheet, f is frequency, r is resistivity. Ph is the area of the hysteresis curve—the BH loop -in the quasi-static mode times the frequency f: I Ph ¼ f BdH. (3)
ARTICLE IN PRESS M.F. de Campos et al. / Journal of Magnetism and Magnetic Materials 304 (2006) e593–e595
e594
discussion at the end of Ref. [11]: ‘‘there will be certainly irreversible energy losses due to the fracture of Neel spikes’’). Thus, Shockley, in 1951, was already indicating another dissipative mechanism, in addition, as above mentioned, to the heating by Joule effect according to the basic formula P¼ RI 2 where R is resistance, I is the current. Further, in the seventies, it has been recognized that formation and annihilation of domain walls give origin to irreversible losses [13–16]. A recently presented loss separation model [17] includes the above mentioned premises [13–16].
12 Pt
Losses (W/kg)
10 8
—— annealed - - - - aged
6
Pcl
4
Ph
2 Pan 0 0.000
0.005
0.010
3.3. Effect of aging on the coercivity 0.015
%C Fig. 1. Magnetic losses as function of carbon content. B ¼ 1:5 T, f ¼ 60 Hz. Data from Epstein frame.
90 80
annealed aged
Hc (A/m)
70
Louis Ne´el inclusion theory predicts H c V v [18], where Hc is the coercive field and Vv is the inclusion volume fraction. The present approach (see Ref. [2]) is based on the assumption that magnetostatic energy is stored around second phase particles (inclusions and carbides) and that magnetostatic energy can be decreased when domain walls intersect the particles, causing the walls to be ‘‘pinned’’ by the inclusions. The magnetostatic energy will be decreased when a wall intersects an inclusion. The energy dissipated in that process is the dipole magnetostatic energy decreased by a factor a.
60
DE ¼ 16m0 M 2s ðV inclusion Þ a.
50
There are three main situations [2] when a domain wall intersects inclusions:
40 30 0.000
0.005
0.010
0.015
%C Fig. 2. Coercive field as function of the carbon content, after the annealing and after the ‘‘accelerated’’ aging 24 h at 225 1C.
According to the data of Figs. 1 and 2 there is no aging if the carbon content is very low (o0.0025% C) confirming Ref. [1]. A very important result is obtained: all the aging effect is inside the Ph component. As it can be seen from Fig. 1, the Pan component, obtained by the difference Pan ¼ Pt Ph Pcl ., is not affected by aging. 3.2. Comments on the physical reasoning of loss separation Advancing ideas presented in the previous decade [8,9], Becker [10] made a suggestion that even the hysteresis loss component were caused by microeddy currents. However, Stewart [11,12] verified that even making the velocity of domain wall be almost zero, the hysteretic losses was not reduced to zero (as it would be expected if only microeddy currents were responsible for hysteretic component). The explanation was given by W. Shockley himself (see the
(4)
(i) Inclusions much larger than the domain wall thickness. In this case, it is supposed that the magnetic quadrupole formed when a wall bisects the inclusions reduces the magnetostatic energy to E/2 in each inclusion. Thus, the non-dimensional factor a is 12 in Eq. (4). (ii) Inclusions with diameter similar to the thickness of the domain wall. The magnetostatic energy stored in such a structure was estimated [2] to be 14 of the dipole energy resulting in reduction of 34 of the magnetostatic energy [2], i.e. a in Eq. (4) is a 34. (iii) Inclusions with diameter much smaller than the domain wall thickness. In this case the ‘‘pinning effect’’ is negligible. Taking into account that the increase of hysteresis area can be given by 4DH c Bmax , Eq. (4) can be rewritten as: DH c ¼
a m0 M 2s V Vinclusion , 12 Bmax
(5)
where VV is inclusion volume fraction. Using Bmax ¼ 1:5 T, and supposing all the C is in form of spherical Fe3C, and with also the supposition [2] that Fe3C can be considered a non-magnetic inclusion, we have the estimation, with Eq. (5) for %C 0.019 (see Refs. [3,4]): (i) inclusions much larger than the domain wall, a ¼ 12
ARTICLE IN PRESS M.F. de Campos et al. / Journal of Magnetism and Magnetic Materials 304 (2006) e593–e595
e595
DH c ¼ 141 A=m (1.77 Oe), (ii) inclusions near the size of wall, a ¼ 34, DH c ¼ 211 A=m (2.65 Oe), in excellent agreement with the experimental values for maximum DH c ¼ 2:522:8 Oe mentioned (for 190 ppm of Carbon) by Dykstra [3] and Leslie and Stevens [4].
component, with the excess losses unaffected. The increase of the hysteresis loss component can be attributed to the formation and annihilation of domain walls when interacting with large size inclusions (i.e., particles with diameter near or above the thickness of domain walls).
3.4. Comments on the application of the theory to the present results
Acknowledgment
In the case of the experiment described in this paper, the above theory (Eqs. (4) and (5)) gives (supposing, for example, Carbon content ¼ 0.006%), (i) larger inclusions (44 A/m), (ii) inclusions near the size of the wall (66 A/m). We conclude that in our case, the aging did not attained the peak of maximum, because the coercivity increase (from Fig. 2) was 10–15 A/m (thus, many of the inclusions should be of type (iii), i.e., smaller than the domain wall thickness). The chosen time for aging was not sufficient in this case, i.e., the magnetic aging is in the beginning. Refs. [3,4,19] show that the maximum DHc occurs for a giving time and temperature (it is an Ostwald Ripening process), while the presented theory—Eqs. (4) and (5)—is only able to predict the maximum DHc and does not take time into account. A model able to include the other variables—time and temperature—is in development, but this is subject to a forthcoming paper. 4. Conclusions Accelerated aging experiment (225 1C/24 h) showed that only for samples with less than 25 ppm of carbon the magnetic properties were not worsened. Loss separation shows that all effect of aging is inside the hysteresis loss
The support of CNPq-ProMetro, CAPES, FINEP is kindly acknowledged.
References [1] F.E. Werner, R.I. Jaffee, J. Mater. Eng. Perform. 1 (1992) 227. [2] L.J. Dijkstra, C. Wert, Phys. Rev. 79 (1950) 979. [3] L.J. Dijkstra, in: A.E. Berkowitz, E. Kneller (Eds.), Magnetism and Metallurgy, vol. 2, Academic Press, New York, 1969, pp. 513–522. [4] W.C. Leslie, D.W. Stevens, Trans. AIME 57 (1964) 261. [5] G.M. Michal, J.A. Slane, Met. Trans. A 17A (1986) 1287. [6] E. Davenport, E. Bain, Trans. Am. Soc. Met. 23 (1935) 1047. [7] J.J. Thomson, Electrician 28 (1892) 599. [8] H.J. Williams, W. Shockley, C. Kittel, Phys. Rev. 80 (1950) 1090. [9] R.H. Pry, C.P. Bean, J. Appl. Phys. 29 (1958) 532. [10] J.J. Becker, J. Appl. Phys. 34 (1963) 1327. [11] K.H. Stewart, J. Phys. Radium 12 (1951) 325. [12] K.H. Stewart, Ferromagnetic Domains, University of Cambridge, UK, 1954. [13] T.R. Haller, J.J. Kramer, J. Appl. Phys. 41 (1970) 1034. [14] T.R. Haller, J.J. Kramer, J. Appl. Phys. 41 (1970) 1036. [15] M. Guyot, A. Globus, Phys. Stat. Sol. (B) 59 (1973) 447. [16] M. Guyot, V. Cagan, J. Appl. Phys. 73 (1993) 5348. [17] M.F. de Campos, J.C. Teixeira, F.J.G. Landgraf, J. Magn. Magn. Mater. 301 (2006) 94. [18] L. Ne´el, Physica 15 (1–2) (1949) 225. [19] H. Hildebrand, ISIJ Int. 37 (1997) 65.
Journal of Magnetism and Magnetic Materials 304 (2006) e593–e595 www.elsevier.com/locate/jmmm
Consequences of magnetic aging for iron losses in electrical steels Marcos F. de Camposa,, Marı´ lia Emurab, Fernando J.G. Landgrafc a
Inmetro –Dimci/Dimat, Av. Nossa Senhora das Gracas 50 Xerem, Duque de Caxias, RJ 25250-020, Brazil b GlobalMag, Sa˜o Paulo, SP, Brazil c Instituto de Pesquisas Tecnolo´gicas—IPT, Av. Professor Almeida Prado 532, Sa˜o Paulo, SP 05508-901, Brazil Available online 20 March 2006
Abstract Electrical steels, when submitted to operation, present continuous decrease of their magnetic properties, depending on the carbon content. This effect is attributed to the increase of the size of carbides, a process also known as coarsening or Ostwald Ripening. Loss separation can offer a better understanding of this phenomenon. Experimental results show that all effect of aging is inside the hysteresis loss component, with the excess losses unaffected. The carbon content in electrical steels should be less than 25 ppm to avoid magnetic aging. r 2006 Elsevier B.V. All rights reserved. PACS: 75.50.bb Keywords: Silicon steel; Non-oriented electrical steels; Inclusions; Magnetic aging
1. Introduction During the life of electrical steels, a phenomenon named magnetic aging [1–5] may occur. This effect is due to microstructural changes: carbon and/or nitrogen in solid solution precipitate as iron carbides or nitrides, respectively, increasing the losses [2,3]. It has also been noted that the increase of coercivity or losses is a function of the particle size [2–5]. This process is analogous to the Ostwald Ripening of carbides resulting in increased hardness [6]. 2. Experimental Steel sheets 0.64 mm thick were used in aging experiments. The chemical composition of the steel is 0.031% C, 46 ppm N, 0.132% Mn, o0.005% Si, 0.035% Al, 0.031% P, 0.011% S. The six different decarburizing cycles produced samples with the six different amounts of carbon. Then, an accelerated aging was performed by means of a heat treatment at 225 1C during 24 h. The magnetic measureCorresponding author.
E-mail addresses: [email protected], [email protected] (M.F. de Campos). 0304-8853/$ - see front matter r 2006 Elsevier B.V. All rights reserved. doi:10.1016/j.jmmm.2006.02.185
ment was done in Epstein frame at 60 Hz and at quasistatic condition (0.005 Hz), for loss separation. 3. Results and discussion 3.1. Loss Separation and the aging effect In the loss separation procedure the total power losses Pt (W/m3 or W/kg) are separated into three components, the classical eddy or Foucault losses Pcl, the anomalous or excess losses Pan and hysteresis losses Ph (according the expression below). Pt ¼ Ph þ Pcl þ Pan :
(1)
With Pcl—due to eddy currents—is given by [7]: Pcl ¼
p2 f 2 B2max e2 , 6r
(2)
where Bmax is the maximum induction, e is the thickness of the sheet, f is frequency, r is resistivity. Ph is the area of the hysteresis curve—the BH loop -in the quasi-static mode times the frequency f: I Ph ¼ f BdH. (3)
ARTICLE IN PRESS M.F. de Campos et al. / Journal of Magnetism and Magnetic Materials 304 (2006) e593–e595
e594
discussion at the end of Ref. [11]: ‘‘there will be certainly irreversible energy losses due to the fracture of Neel spikes’’). Thus, Shockley, in 1951, was already indicating another dissipative mechanism, in addition, as above mentioned, to the heating by Joule effect according to the basic formula P¼ RI 2 where R is resistance, I is the current. Further, in the seventies, it has been recognized that formation and annihilation of domain walls give origin to irreversible losses [13–16]. A recently presented loss separation model [17] includes the above mentioned premises [13–16].
12 Pt
Losses (W/kg)
10 8
—— annealed - - - - aged
6
Pcl
4
Ph
2 Pan 0 0.000
0.005
0.010
3.3. Effect of aging on the coercivity 0.015
%C Fig. 1. Magnetic losses as function of carbon content. B ¼ 1:5 T, f ¼ 60 Hz. Data from Epstein frame.
90 80
annealed aged
Hc (A/m)
70
Louis Ne´el inclusion theory predicts H c V v [18], where Hc is the coercive field and Vv is the inclusion volume fraction. The present approach (see Ref. [2]) is based on the assumption that magnetostatic energy is stored around second phase particles (inclusions and carbides) and that magnetostatic energy can be decreased when domain walls intersect the particles, causing the walls to be ‘‘pinned’’ by the inclusions. The magnetostatic energy will be decreased when a wall intersects an inclusion. The energy dissipated in that process is the dipole magnetostatic energy decreased by a factor a.
60
DE ¼ 16m0 M 2s ðV inclusion Þ a.
50
There are three main situations [2] when a domain wall intersects inclusions:
40 30 0.000
0.005
0.010
0.015
%C Fig. 2. Coercive field as function of the carbon content, after the annealing and after the ‘‘accelerated’’ aging 24 h at 225 1C.
According to the data of Figs. 1 and 2 there is no aging if the carbon content is very low (o0.0025% C) confirming Ref. [1]. A very important result is obtained: all the aging effect is inside the Ph component. As it can be seen from Fig. 1, the Pan component, obtained by the difference Pan ¼ Pt Ph Pcl ., is not affected by aging. 3.2. Comments on the physical reasoning of loss separation Advancing ideas presented in the previous decade [8,9], Becker [10] made a suggestion that even the hysteresis loss component were caused by microeddy currents. However, Stewart [11,12] verified that even making the velocity of domain wall be almost zero, the hysteretic losses was not reduced to zero (as it would be expected if only microeddy currents were responsible for hysteretic component). The explanation was given by W. Shockley himself (see the
(4)
(i) Inclusions much larger than the domain wall thickness. In this case, it is supposed that the magnetic quadrupole formed when a wall bisects the inclusions reduces the magnetostatic energy to E/2 in each inclusion. Thus, the non-dimensional factor a is 12 in Eq. (4). (ii) Inclusions with diameter similar to the thickness of the domain wall. The magnetostatic energy stored in such a structure was estimated [2] to be 14 of the dipole energy resulting in reduction of 34 of the magnetostatic energy [2], i.e. a in Eq. (4) is a 34. (iii) Inclusions with diameter much smaller than the domain wall thickness. In this case the ‘‘pinning effect’’ is negligible. Taking into account that the increase of hysteresis area can be given by 4DH c Bmax , Eq. (4) can be rewritten as: DH c ¼
a m0 M 2s V Vinclusion , 12 Bmax
(5)
where VV is inclusion volume fraction. Using Bmax ¼ 1:5 T, and supposing all the C is in form of spherical Fe3C, and with also the supposition [2] that Fe3C can be considered a non-magnetic inclusion, we have the estimation, with Eq. (5) for %C 0.019 (see Refs. [3,4]): (i) inclusions much larger than the domain wall, a ¼ 12
ARTICLE IN PRESS M.F. de Campos et al. / Journal of Magnetism and Magnetic Materials 304 (2006) e593–e595
e595
DH c ¼ 141 A=m (1.77 Oe), (ii) inclusions near the size of wall, a ¼ 34, DH c ¼ 211 A=m (2.65 Oe), in excellent agreement with the experimental values for maximum DH c ¼ 2:522:8 Oe mentioned (for 190 ppm of Carbon) by Dykstra [3] and Leslie and Stevens [4].
component, with the excess losses unaffected. The increase of the hysteresis loss component can be attributed to the formation and annihilation of domain walls when interacting with large size inclusions (i.e., particles with diameter near or above the thickness of domain walls).
3.4. Comments on the application of the theory to the present results
Acknowledgment
In the case of the experiment described in this paper, the above theory (Eqs. (4) and (5)) gives (supposing, for example, Carbon content ¼ 0.006%), (i) larger inclusions (44 A/m), (ii) inclusions near the size of the wall (66 A/m). We conclude that in our case, the aging did not attained the peak of maximum, because the coercivity increase (from Fig. 2) was 10–15 A/m (thus, many of the inclusions should be of type (iii), i.e., smaller than the domain wall thickness). The chosen time for aging was not sufficient in this case, i.e., the magnetic aging is in the beginning. Refs. [3,4,19] show that the maximum DHc occurs for a giving time and temperature (it is an Ostwald Ripening process), while the presented theory—Eqs. (4) and (5)—is only able to predict the maximum DHc and does not take time into account. A model able to include the other variables—time and temperature—is in development, but this is subject to a forthcoming paper. 4. Conclusions Accelerated aging experiment (225 1C/24 h) showed that only for samples with less than 25 ppm of carbon the magnetic properties were not worsened. Loss separation shows that all effect of aging is inside the hysteresis loss
The support of CNPq-ProMetro, CAPES, FINEP is kindly acknowledged.
References [1] F.E. Werner, R.I. Jaffee, J. Mater. Eng. Perform. 1 (1992) 227. [2] L.J. Dijkstra, C. Wert, Phys. Rev. 79 (1950) 979. [3] L.J. Dijkstra, in: A.E. Berkowitz, E. Kneller (Eds.), Magnetism and Metallurgy, vol. 2, Academic Press, New York, 1969, pp. 513–522. [4] W.C. Leslie, D.W. Stevens, Trans. AIME 57 (1964) 261. [5] G.M. Michal, J.A. Slane, Met. Trans. A 17A (1986) 1287. [6] E. Davenport, E. Bain, Trans. Am. Soc. Met. 23 (1935) 1047. [7] J.J. Thomson, Electrician 28 (1892) 599. [8] H.J. Williams, W. Shockley, C. Kittel, Phys. Rev. 80 (1950) 1090. [9] R.H. Pry, C.P. Bean, J. Appl. Phys. 29 (1958) 532. [10] J.J. Becker, J. Appl. Phys. 34 (1963) 1327. [11] K.H. Stewart, J. Phys. Radium 12 (1951) 325. [12] K.H. Stewart, Ferromagnetic Domains, University of Cambridge, UK, 1954. [13] T.R. Haller, J.J. Kramer, J. Appl. Phys. 41 (1970) 1034. [14] T.R. Haller, J.J. Kramer, J. Appl. Phys. 41 (1970) 1036. [15] M. Guyot, A. Globus, Phys. Stat. Sol. (B) 59 (1973) 447. [16] M. Guyot, V. Cagan, J. Appl. Phys. 73 (1993) 5348. [17] M.F. de Campos, J.C. Teixeira, F.J.G. Landgraf, J. Magn. Magn. Mater. 301 (2006) 94. [18] L. Ne´el, Physica 15 (1–2) (1949) 225. [19] H. Hildebrand, ISIJ Int. 37 (1997) 65.