Magnetic Properties in Deformed Grain Oriented Electrical

© 2012 ISIJ 2100

ISIJ International, Vol. 52 (2012), No. 11, pp. 2100–2108

Magnetic Properties in Deformed Grain Oriented Electrical Steel: On the Role of Strain Hardening Exponent and Microstructural Developments

Satish Kumar SHEKHAWAT,1)* Basavaraj VADAVADAGI,1) Vijay Devidas HIWARKAR,2) Jayshri DUMBRE,2)

Asha INGLE,2) K. G. SURESH3) and Indradev SAMAJDAR1)

1) Department of Metallurgical Engineering and Material Science, IIT Bombay, Mumbai-400076 India. 2) Global R & Dcentre, Crompton Greaves Ltd. Mumbai-400042 India. 3) Department of Physics, IIT Bombay, Mumbai-400076 India.

(Received on April 12, 2012; accepted on July 4, 2012)

High permeability commercial CRGO, cold rolled grain oriented steel was subjected to uni-axial tensilestrain in three principal orientations: (110) <001>, (110) < 10> and (110)< 11>. The samples exhibitedremarkably different stress-strain behavior. The numerical values of the strain hardening exponent, n,largely determined the degradation in magnetic properties: namely increase in Hysteresis loss (H) anddrop in Permeability (μ). Changes in magnetic properties were also correlated with microstructural obser-vations: misorientation and dislocation density developments, relative recovery, residual strain and devia-tion from ideal <001>. The study established constitutive relationships between degradation in magneticproperties and various parameters of the deformed microstructures.

KEY WORDS: cold rolled grain oriented (CRGO); electrical steel; magnetic properties; misorientation; dislo-cation density; microtexture; stress.

1. Introduction

CRGO or cold rolled grain oriented electrical steel is theonly example of metallic material where complete texturecontrol has been achieved.1–9) The final product/laminationconsists of large grains, from millimeter to centimeter insize – depending on the exact processing route, of near Goss(110) <001> orientation.3,5,6,9) The CRGO sheets are typical-ly coated with forsterite (Mg2SiO4) and are scribed mechan-ically or by laser for domain refinement.4,5,7–13) Though thetransformer laminations use favourable <001> crystallo-graphic direction, ‘limited’ use of non <001> orientations incorners may also be required.14–16) The electrical lamina-tions, both oriented9,17) and non-oriented,9,18–24) can also besubjected to deformation (from handling, stacking, shearingand joining) for producing the actual equipment.

Any deformation is expected to cause elastic and plasticstrains resulting in changes of microstructure and residualstress state.9,19,21,25–32) These, in turn, may affect the magnet-ic properties.18,19,22,23,27,33–44) To a transformer manufacturerand end-user, hysteresis loss and permeability are the twoimportant properties. It has been reported4,33,37,39,40,43) thattensile residual stresses can even be beneficial: dependingon the specimen orientation and the magnitude of suchstresses;37,40,43) while compressive stresses are detrimentalfor hysteresis loss in a typical CRGO lamination. Such a

simple analogy is important if the strain state is simple andkept within yielding; beyond yielding the picture can bemore complicated. Cutting stresses, for example, areknown17–20,22,23,45,46) to have strong effects on the magneticproperties. Such cutting stresses or strains are, however,complex and simple correlation(s) between stress-strain,microstructural developments and degradation in magneticproperties does not exist in the domain of published litera-ture. For example, focussed studies41,42,47) have attempted torelate magnetic and mechanical hardening. Attempts werealso made to link plastic strain and increased dislocationdomain wall interactions.34,48–52) In a real-life deformedmicrostructures, however, there can be several aspects ofmicrostructure developments: dislocation substructures,residual stresses, misorientation and orientation develop-ments. Each of these aspects can be represented throughappropriate, and often multiple, characterization measures.Their collective effects on the magnetic properties of electri-cal steel, in general, and CRGO, in particular, need to becharted. This formed the motivation behind the present study.

Commercially available high permeability CRGO, Hi–BGrain Oriented Steel grade (HG–OS)3,6,53) was deformedthrough tensile testing. This allowed determination of typi-cal stress-strain behaviour of the CRGO sheets along 0°, 45°and 90° with rolling direction: respective orientations of(110) <001>, (110)< 11> and (110) < 10>. Samples wereobtained from different regions of the stress-strain curvesand their magnetic properties and microstructural featureswere then characterized. The objective of this study was to

1 1

* Corresponding author: E-mail: [email protected]: http://dx.doi.org/10.2355/isijinternational.52.2100

1 1

ISIJ International, Vol. 52 (2012), No. 11

2101 © 2012 ISIJ

obtain constitutive relationships between degradation inmagnetic properties and various aspects of microstructuraldevelopments.

2. Experimental Procedure

High permeability CRGO, Hi–B Grain Oriented Steelgrade with 3.2 wt% Si, was used for the present study. Ten-sile samples were prepared in three orientations (RD-0:(110) <001>, RD-45: (110) < 10>, RD-90: (110) < 11>)as per ASTM E8 standard.54) The CRGO samples, ~270 μmthick with ~3 μm Forsterite (Mg2SiO4) coating, were thendeformed in an InstronTM 3 345 tensile testing machine at 1mm/min cross-head speed. Depending on the sample orien-tations, a range of true strains (0.04–0.18) were achievedbefore the ultimate failure. The true stress-true strain (σ-ε)data was further analyzed to extract information on strainhardening exponent (n):

σ = k εn.................................... (1)

where k is a constant. Interrupted, at different true strains,tensile tests samples were also used for characterization ofmagnetic properties and microstructure.

2.1. Characterization of Magnetic PropertiesDeformed CRGO samples, with insulating coating, were

subjected to B-H (B and H represent respective strengths ofthe induced and imposed magnetic fields) loop measure-ments. The magnetic field (0–200 Oe) was applied along thetensile axis. The measurements were performed in anEpstein single sheet DC tester B-H Loop Tracer: ModelSMT-500/NOPS, make - KJSTM associates Inc. Manualwinding of copper wire (38 turns) was made on the middleof the samples and a search-coil Goss meter was used tomeasure the total magnetic field. Subsequently, sampleswere demagnetized twice to remove the effect of residualmagnetic moment. The B-H loops thus obtained were ana-lyzed for Hysteresis losses (at 1.7 Tesla) and permeability(at 1.5 and 1.7 Tesla).

2.2. Characterization of MicrostructureThe samples were prepared by standard metallographic

steps followed by electropolishing. The electro-polishinginvolved an electrolyte of glacial acetic acid and perchloricacid (92:8), ~25°C and 16 volts dc in a StruersTM Electropol-5 electropolisher. A final polishing was also done with sub-micron colloidal silica. All samples were extensively sub-jected to detailed EBSD (electron backscattered diffraction)and X-Ray Diffraction (XRD). EBSD measurements weremade on a FEI QuantaTM 200Hv scanning electron micro-scope using a TSL-OIMTM (Tex. SEM Ltd. – OrientationImaging Microscopy) package. Beam and video conditionswere kept identical between the scans and a minimum areaof 15 mm × 7 mm was covered (in 6–8 consecutive scans)at step sizes of 5 μm. For EBSD analysis, measurementpoints having confidence index (CI) more than 0.1 wereused: CI is a relative measure of statistical accuracy55,56) inautomated EBSD indexing. EBSD data were analyzed formisorientation developments (grain average misorientationor GAM) and deviation from <001> direction. GAM isdefined as the point to point misorientation within a grain,

where grain has been defined as the area enclosed by a con-tinuous boundary of more than 5° misorientation.

X-Ray Diffraction was done on a PanalyticalTM X’PertPRO MRD (Material Research Differactometer) systemwith: X-ray lens (poly-capillary) on the target side; PRS(Programmable receiving slit), PASS (Programmable antiscatter slit) and 0.02 rad Soller slits on and diffracted side.A point detector was used at 0.005° (3 s dwell) step size.The peak profiles were analyzed for d-spacing, dislocationdensity and X-Ray resolution function (XRD-RF). Disloca-tion densities were estimated by variance method using 4th

order moment: for further details the reader may refer else-where.57–60) Degree of peak resolution or XRD-RF60,61) ofKα1/Kα2 doublet for (220) peak was analyzed, quantitatively,by Eq. (2):

....................... (2)

where IMin is the minimum intensity of the Kα1/Kα2 doublet,Ikα1 is the maximum peak intensity of the Kα1 peak and IB

is the background intensity.

3. Results

Figure 1 offers possible correlations between tensilebehavior and magnetic properties. A closer look, at the fig-ure, indicates qualitative relationship between strain harden-ing exponent (n) and hysteresis loss (H). This aspect isbrought out more clearly in Fig. 2(a). As expressed numer-ically in Table 1, the trends in H and n showed a reasonablelinear fit: hardening led to increased losses. Figure 2(b) plotsthe trend between permeability and n – taken at both 1.5 and1.7 Tesla. Unlike the hysteresis loss, there appears to be‘limited’ linear correlation between μ and n as indicated inTable 1. The Figs. 1 and 2, and Table 1, compare the H andμ with n: the latter indicating hardening/softening behavior.

It was hence felt that such hardening/softening can

be better related to and . This has been attempted, as

shown in Fig. 3, and shows an improved linear fit: marginally

for and significantly for , see Table 2. In a word, the

estimated n, from tensile tests, appear to capture the trends inthe near linear degradation of the magnetic properties: namely

and .

Though the constitutive relations, Tables 1–2, appeareffective; actual industrial practices often involve complexstrain modes. In manufacturing operations (e.g. cutting, slit-ting, punching and handling) the prediction of strain hard-ening exponent ‘n’ is difficult. However, n is also expectedto reflect on the developments of deformed microstruc-tures.9,62) Hence, efforts were made to correlate differentquantifiable aspects of such deformed microstructures withmagnetic properties. Plastic deformation is expected tobring new lattice curvatures: often represented as grain aver-age misorientation or GAM values.26,63) In the past,62) GAMhas been related to strain hardening exponent quite effec-tively. Hence the reasonable linear fits, Fig. 4(a) and Table3, between H and GAM are not very surprising. However,

1 1

XRD RF − =−−

I I

I IMin B

K Bα1

⎛⎝⎜lnd

lnd

σε

⎞⎠⎟

dH

dεd

d

με

dH

dεd

d

με

dH

dεd

d

με

© 2012 ISIJ 2102


as in Fig. 4(b) and Table 3, even μ and GAM offered betterfits than μ and n (see Table 1). This was not apparent forthe so-called combined relationship; but was clearly notedfor the individual linear behaviors for RD-0, RD-45 andRD-90. An apparent rationale for this improvement wasavailability of more data points. EBSD’s measurementuncertainty for GAM, tested in a fully recrystallized mate-rial under identical beam and video conditions, is ~0.5°.This appears to be more sensitive than estimated (fromtensile testing) variations in n: thus ascertaining more datapoints for H and μ vs. GAM plots. Relationships between deg-

radation in magnetic properties and and changes

in GAM were also tried, as indicated in Fig. 5. These,

listed in Table 3, appear to offer excellent linear fits. Thedifferentiation, in general, improved the linear fit: especially

for the degradation in permeability for different ori-entations.

Similar exercises were done for other microstructural

parameters as well (see Table 4). These include: deviationfrom <001> (Fig. 6), estimated relative dislocation density(Fig. 7), changes in d-spacing (Fig. 8) and the X-ray reso-lution function or XRF (Fig. 9). All these values constituteimportant signatures of deformation. For example, plasticdeformation often has associated re-orientation of grains or

⎛⎝⎜dH

dεd

d

με

⎞⎠⎟⎛

⎝⎜dG

dε⎞⎠⎟

⎛⎝⎜d

d

με

⎞⎠⎟

Fig. 2. Relationship between (a) Hysteresis loss (H) and (b) Per-meability (μ) with strain hardening exponent (n). In (b),respective permeabilities are plotted for RD-0, RD-45 andRD-90; and values for both 1.5 and 1.7 Tesla are included.

Fig. 1. Measured values of true stress (σ), Hysteresis loss (H) and Permeability (μ) at different true strains (ε) for (a) (110)<001> (RD-0), (b) (110) < 10> (RD-45) and (c) (110) < 11>) (RD-90). RD represents rolling direction, while0/45/90 imply the respective angles with RD. In the σ-ε plots, after clear plastic yielding, different regimes ofstrain hardening exponents (n) are shown. Permeabilities at both 1.5 and 1.7 Tesla are included.

Fig. 3. Relationship between (a) and at (b) 1.5 and (c) 1.7 Tesla with strain hardening exponent (n).

Table 1. Hysteresis loss (H) vs. strain hardening exponent (n), Permeability (μ: for 1.5 and 1.7 Tesla) vs. strain hardeningexponent (n): linear relationships. The fit (least mean square) values are also included. Combined relationshipplus the relationships for RD-0, RD-45 and RD-90 are shown.

H, μ & n Linear RelationshipH vs. n Fit Linear Relationship

μ 1.5 vs. n Fit Linear Relationshipμ 1.7 vs. n Fit

combined H = 14.5n + 1.4 0.73 μ = –4 852n + 1 667 0.02 μ = –2 449n + 835.5 0.01

RD-0 H = 30.7n – 0.1 0.8 μ = –46 389n + 6 904 0.3 μ = –21 054n + 3 249 0.1

RD-45 Only one data set – Only one data set – Only one data set –

RD-90 H = 14.5n + 1.5 0.5 μ = –280.1n + 181.9 0.24 μ = –152.6n + 111.8 0.2

1 1

dH

dεd

d

με


2103 © 2012 ISIJ

crystals.9,27,29,30) Any such re-orientation or changes in therelative deviation from soft magnetic direction (<001>) isalso expected to affect the magnetic properties.36,64) Similar-ly, X-ray peak profiles can offer relative estimates for dis-location density, changes in d-spacing and the so-calledXRF. The dislocation densities can have significant effectson the domain wall movements and interactions,34,35,48–51)

while changes in the d-spacing represent the residual strain

or changes in the bcc unit cell itself. Both can thus affect themagnetic properties.49) Finally, the energy and distributionof the defects or dislocations is an important aspect for mag-netic properties.35,49,50) The former can be affected by theplastic deformation as well as dynamic recovery. XRF (orX-ray resolution function)61) can be a very accurate semi-quantitative index in bringing out the aspects of this dynam-ic recovery.60,61) As shown in the assorted figures (4 and 6–9) and tables (3 and 4), different aspects of deformed micro-structure developments appear to capture, albeit with differingdegree of scatter and possible differences in trend-lines, thevalues of H and μ. Though different trends or relationships canbe postulated; linear relationships appear to provide the mostcommon and generalized trend-lines. H was not very sensitiveto the nature of orientation (RD-0, RD-45 and RD-90) and thelinear trends were best captured by GAM and XRF. μ, on theother hand, was sensitive to the orientation and linear relation-ships appear to be best represented by deviation from <001>(at 1.5 Tesla) and XRF (at 1.7 Tesla).

Degradation in magnetic properties and with

strain were also plotted as a function of changes in micro-

Table 2. vs. strain hardening exponent (n), (μ: for 1.5 and 1.7 Tesla) vs. strain hardening exponent (n): linear

relationships. Other conventions are same as in Table 1.

, & nLinear Relationship

vs. nFit

Linear Relationship

vs. n; ( μ at 1.5)Fit

Linear Relationship

vs. n; (μ at 1.7)Fit

combined = –3.7n – 0.03 0.76 = –7.63n – 1.43 0.28 = –6.24n – 1.35 0.24

RD-0 = –7.3n + 0.285 0.8 = –2 870 161n – 0.54 0.72 = –22.28n – 0.73 0.30

RD-45 Only one data set – Only one data set – Only one data set –

RD-90 = –5.3n + 0.16 0.74 = –15.1n – 0.21 0.81 = –13.26n – 0.23 0.82

Table 3. Hysteresis loss (H) vs. grain average misorientation (GAM or G), Permeability (μ: for 1.5 and 1.7 Tesla) vs.

grain average misorientation (G), vs. , (μ: for 1.5 and 1.7 Tesla) vs. : linear relationships.

Other conventions are same as in Table 1.

H, μ & G Linear RelationshipH vs. G Fit Linear Relationship

μ vs. G; (μ at 1.5) Fit Linear Relationshipμ vs. G (μ at 1.7) Fit

combined H = 10.65G – 1.76 0.44 μ = –23 673G + 10 677 0.021 μ = –29 235G + 13 795 0.022

RD-0 H = 14.9G – 3.97 0.87 μ= –1 000 000G + 54 132 0.18 μ = –16 623G + 71 840 0.23

RD-45 H = 7.1G – 0.59 0.62 μ = –163G + 181.9 0.31 μ = 146.3G + 60.27 0.17

RD-90 H = 7.7G – 0.38 0.64 μ = –509.98G + 368.54 0.5 μ = –359.59G + 245.85 0.61

, & Linear Relationship

vs. Fit

Linear Relationship

vs. ; μ at 1.5Fit

Linear Relationship

vs. ; μ at 1.7Fit

combined = –2.13 + 0.38 0.67 = –4.24 – 0.64 0.23 = –4.2 – 0.43 0.3

RD-0 = –4.54 + 1.05 0.90 = –9.87 + 0.1 0.55 = –13.53 + 1.5 0.78

RD-45 = –5.99 + 0.51 0.85 = –5.99 + 0.51 0.85 = –5.84 + 0.53 0.83

RD-90 = –5.29 – 0.07 0.94 = –5.29 – 0.07 0.94 = –4.63 – 0.11 0.94

dH

dεd

d

με

dH

dεd

d

με dH

dεd

d

με

d

d

με

dH

dεd

d

με

d

d

με

dH

dεd

d

με

d

d

με

dH

dεd

d

με

d

d

με

dH

dεd G

d

( )

εd

d

με

d G

d

( )

ε

dH

dεd

d

με

d G

d

( )

ε dH

dεd G

d

( )

εd

d

με

d G

d

( )

εd

d

με

d G

d

( )

εdH

dεd G

d

( )

εd

d

με

d G

d

( )

εd

d

με

d G

d

( )

ε

dH

dεd G

d

( )

εd

d

με

d G

d

( )

εd

d

με

d G

d

( )

ε

dH

dεd G

d

( )

εd

d

με

d G

d

( )

εd

d

με

d G

d

( )

ε

dH

dεd G

d

( )

εd

d

με

d G

d

( )

εd

d

με

d G

d

( )

ε

Fig. 4. Effect of GAM on (a) Hysteresis loss (H) and (b) Perme-ability (μ). In (b), permeabilities at both 1.5 and 1.7 Teslaare included respectively for RD-0, RD-45 and RD-90.

⎛⎝⎜dH

dεd

d

με

⎞⎠⎟

© 2012 ISIJ 2104


Table 4. Hysteresis loss (H) vs. deviation from <001> (D), Permeability (μ) vs. deviation from <001> (D), Hysteresis loss(H) vs. relative dislocations density (DD), Permeability (μ) vs. relative dislocations density (DD), Hysteresis loss(H) vs. change in d-spacing (δd), Permeability (μ) vs. change in d-spacing (δd), Hysteresis loss (H) vs. X-ray res-olution function (X), Permeability (μ) vs. X-ray resolution function (X) , : linear relationships. μ: for 1.5 and 1.7Tesla are included. Other conventions are same as in Table 1.

H, μ & D Linear RelationshipH vs. D Fit Linear Relationship

μ vs. D; μ at 1.5 Fit Linear Relationshipμ vs. D; μ at 1.7 Fit

Combined H = 0.23D + 0.17 0.3 μ = –5 604D + 62 304 0.022 μ = –637.9D + 7 907 0.020

RD-0 H = 0.2D – 0.04 0.46 μ = –233.5D + 5 578 0.42 μ = –123.3D + 2 726 0.15

RD-45 H = 0.06D + 1.17 0.15 μ = –4.518D + 173.6 0.35 μ = –1.587D + 113.3 0.87

RD-90 H = 0.05D + 2.4 0.03 μ = 4.51D + 123.6 0.51 μ = 1.26D + 86.92 0.19

H, μ & DD Linear RelationshipH vs. DD Fit Linear Relationship

μ vs. DD; μ at 1.5 Fit Linear Relationshipμ vs. DD; μ at 1.7 Fit

Combined H = 0.29DD + 1.5 0.04 μ = –34 411DD + 71 752 0.037 μ = –3 695DD + 8 658 0.03

RD-0 H = 1.05DD – 0.42 0.60 μ = –19 195DD + 43 536 0.5 μ = –24 808DD + 57 555 0.63

RD-45 H = 1.58DD – 0.21 0.5 μ = –14.62DD + 154.2 0.02 μ = –6.741DD + 111.7 0.01

RD-90 H = 0.88DD + 1.29 0.4 μ = 97.86DD + 60 0.36 μ = 68.24DD + 26.97 0.38

H, μ & δd Linear RelationshipH vs. δd Fit Linear Relationship

μ vs. δd ; μ at 1.5 Fit Linear Relationshipμ vs. δd ; μ at 1.7 Fit

Combined H = –136.4 δd + 1.6 0.35 μ = 5e^6 δd + 41 485 0.05 μ = 67 427 δd + 5 839 0.058

RD-0 H = –163.4 δd – 0.95 0.33 μ = 2e^7 δd + 10 928 0.124 μ = 2e^6 δd + 15 005 0.135

RD-45 H = 43.41 δd + 1.56 0.173 μ = –1 366 δd + 137.4 0.088 μ = –1 393 δd + 103.5 0.119

RD-90 H = –146.3 δd + 1.8 0.318 μ = 568.7 δd + 175.3 0.002 μ = 729 δd + 111.8 0.01

H, μ & X Linear RelationshipH vs. X Fit Linear Relationship

μ vs. X; μ at 1.5 Fit Linear Relationshipμ vs. X; μ at 1.7 Fit

Combine H = 4.3X + 0.28 0.40 μ = –30 292X + 14 847 0.192 μ = –37 535X + 18 997 0.206

RD-0 H = 4.7X – 0.5 0.84 μ = –73 755X + 39 216 0.58 μ = –93 082X + 50 977 0.7

RD-45 H = 7.3X – 1.05 0.76 μ = 373X + 12.01 0.41 μ = 356.5X – 17.11 0.45

RD-90 H = 3.21X + 1.38 0.39 μ = –79.67X + 199.1 0.20 μ = –59.88X + 128.5 0.27

Fig. 5. Relationship between (a) and at (b) 1.5 and (c) 1.7 Tesla with .dH

dεd

d

με

d GAM

d

( )

ε

Fig. 6. Effect of deviation from <001> on (a) Hysteresis loss (H)and (b) Permeability (μ). In (b), permeabilities at both 1.5and 1.7 Tesla are included respectively for RD-0, RD-45and RD-90.

Fig. 7. Effect of relative dislocation density on (a) Hysteresis loss(H) and (b) Permeability (μ). In (b), permeabilities at both1.5 and 1.7 Tesla are included respectively for RD-0, RD-45 and RD-90. Relative dislocation densities were esti-mated by considering the value for the undeformed or asreceived CRGO as 1.


2105 © 2012 ISIJ

structural parameters: (Fig. 10),

(Fig. 11) and

(Fig. 12). Mathematical liner relations for the abovediscussed parameters are shown in Table 5. Changes in

Hysteresis loss was best captured, by linear trend-lines,

by changes in GAM ; while degradation in perme-

ability remained largely orientation sensitive and linear rela-tionships were best reflected in the changes in GAM (espe-

cially at 1.5 Tesla) and in

4. Discussion

The CRGO is often cited as a material with complete/ulti-mate texture control and hence the ideal material for trans-former core.1–9) The manufacturing practices, however, canimpose plastic deformation in the CRGO laminates.9,17–24)

Fig. 8. Effect of change in d-spacing (δd) on (a) Hysteresis loss(H) and (b) Permeability (μ). In (b), permeabilities at both1.5 and 1.7 Tesla are included respectively for RD-0, RD-45 and RD-90.

d deviation

d

( )< >001

εd Relativedislocationdensity

d

( )

εd XRF

d

( )

ε

⎛⎝⎜dH

dε⎞⎠⎟

⎛⎝⎜dGAM

dε⎞⎠⎟

d deviation

d

( ).

< >001

ε

Fig. 10. Relationship between (a) and at (b) 1.5 and (c) 1.7 Tesla with .

Fig. 11. Relationship between (a) and at (b) 1.5 and (c) 1.7 Tesla with .

Fig. 12. Relationship between (a) and at (b) 1.5 and (c) 1.7 tesla with .

dH

dεd

d

με

d Deviation

d

( )< >001

ε

dH

dεd

d

με

d RelativeD D

d

( . .)

ε

dH

dεd

d

με

d XRF

d

( )

ε

Fig. 9. Effect of XRF on (a) Hysteresis loss (H) and (b) Permeabil-ity (μ). In (a), intensity-2θ plots for two extreme XRF val-ues are shown. In (b), permeabilities at both 1.5 and 1.7 Teslaare included respectively for RD-0, RD-45 and RD-90.

© 2012 ISIJ 2106


For example, a large transformer core may weigh multipletons, with corresponding effects in elastic and plastic defor-mation and changes in magnetic properties.9,27,33,37,38,40,43)

This aspect is non-trivial: the core loss or iron loss, duringelectricity generation itself, was estimated,9) in 1990, at 400billion kWh. Degradation in the magnetic properties in atransformer core remains a real challenge to the technolog-ical society.

Deformation in the transformer core can be local, as in thecase of cutting stresses,17–22,45,46) or even bulk: example,stacking of laminates. Of course a range of exhaustive liter-ature exists: mainly correlating the strain aspect with mag-netic properties.34,36,38,40,41,43,47,50) There are two problems:rarely strain and magnetic properties have the same scal-ing,41,42,47) and the strains are often local and hence their effecton the bulk magnetic behavior can be diluted. This is wherethe present study becomes effective. The study brings outempirical or constitutive relationships between degradation

in magnetic properties and and strain hardening

exponent (n). In other words, more than the effective strainestimated patterns of hardening and softening, Fig. 3 and

Table 2, appear to have a direct correlation with CRGO per-formance.

This study also demonstrates approximately linear, thelinear nature was taken as a first approximation, relation-ships between different microstructural indices and hystere-sis loss (H) and permeability (μ). It extends such correla-tions to degradation in magnetic properties vs. changes inthe microstructural parameters. All such relationships arephenomenological and physical interpolations remain ‘lim-ited’. This is perhaps one of limitations, albeit unavoidable,of the present manuscript. It needs be noted that clear phys-ical relationships between different aspects of microstruc-ture and combined effects of all such aspects on the mag-netic properties do not exist. However, based on the presentfindings, it can be seen that while the strain dependence ofthe hysteresis loss is almost insensitive to the strainingdirection (which is the direction in which the magnetic fieldis also applied), the same is not true with the permeability.The most notable variation is seen in the decrease of the per-meability with strain for the RD-0 sample. It is well knownthat the magnetic permeability is the largest along the roll-ing direction and that it is very small in other directions. One

Table 5. vs. , vs. , vs. , vs. , vs. , vs. : linear relationships.

μ: for 1.5 and 1.7 Tesla are included. Where D represents deviation for <001>, DD represents relative dislocationdensity, X representing XRF value(s). Other conventions are same as in Table 1.


vs. Fit

Linear Relationship

vs. ; μ at 1.5Fit

Linear Relationship

vs. ; μ at 1.7Fit

combined = 0.63 + 0.13 0.62 = 1.7 – 0.85 0.39 = 1.66 – 0.67 0.5

RD-0 = 0.66 + 0.23 0.84 = 1.4 – 1.7 0.55 = 1.91 – 1 0.72

RD-45 = 0.20 – 0.01 0.31 = 1.47 – 0.49 0.9 = 1.44 – 0.44 0.9

RD-90 = 0.57 + 0.001 0.69 = 1.69 – 0.61 0.78 = 1.47 – 0.59 0.76


vs. Fit

Linear Relationship

vs. ; μ at 1.5Fit

Linear Relationship

vs. ; μ at 1.7Fit

combined = 0.087 – 0.23 0.01 = –1.28 – 1.97 0.18 = –1.08 – 1.75 0.17

RD-0 = –2.07 + 0.0 0.40 = 17.52 – 4.53 0.42 = 22.46 – 4.8 0.69

RD-45 = 3.88 – 0.15 0.46 = 3.5 – 1.30 0.15 = 3.36 – 1.23 0.15

RD-90 = –0.57 – 0.533 0.38 = –1.64 – 2.18 0.39 = –1.41 – 1.95 0.38


vs. Fit

Linear Relationship

vs. ; μ at 1.5Fit

Linear Relationship

vs. ; μ at 1.7Fit

combined = –1.04 + 0.004 0.12 = –0.86 – 1.671 0.01 = –1.04 – 1.411 0.013

RD-0 = 1.26 – 0.42 0.07 = –4.52 – 1.636 0.14 = –3.19 – 1.51 0.05

RD-45 = –0.16 – 0.072 0.03 = –3.25 – 0.38 0.74 = –3.16 – 0.34 0.72

RD-90 = –1.54 + 0.013 0.32 = –4.59 – 0.57 0.36 = –3.9 – 0.58 0.34

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2107 © 2012 ISIJ

of the most important contributions of applying a tensilestress to a magnetic material is the magnetostriction.64)

Materials with negative magnetostriction are known tocause a reduction in the permeability with increase in thetensile stress.64) Presence of stress results in stress anisotro-py, which causes a change in the magnetic behavior of thematerial because of its effect on the domain wall motion andthe domain rotation.4,33,35,42) Therefore, in such materials, themagnetic softness and hence the permeability decreasesconsiderably. In RD-45 and RD-90 samples, the variationwith stress is not systematic as the zero strain values them-selves are not as high as in the case of RD-0. Though thesearguments are consistent with the results, more detailed andfocused studies are required to throw more light on the mag-netization dynamics as a function of strain. In absence ofclear physics, empirical or constitutive relationships are thebest way of approaching a scientific or technological prob-lem. And that is exactly what has been attempted in thepresent study.

It would have been very interesting to ‘fit’ common andcombined relationship(s) between the different microstruc-tural aspects and the magnetic behavior. However, even thepresent data set, extensive they might be, appears inade-quate in building such a model: through regression and/orbrute numerical methods (such as artificial neural networkor ANN.65) Efforts of future research will indeed be focusedin such direction: success, as in any applied research, cannever be guaranteed. Hence the authors felt that the researchcommunity, in general, needs to be briefed about the inter-esting constitutive relationships between the degradation inmagnetic properties with strain hardening exponent and dif-ferent aspects of quantifiable microstructural changes. Thismanuscript can be considered successful if it can initiate fur-ther focused research on the role of deformation relatedmicrostructural developments in altering the magneticbehavior of electrical steels.

5. Conclusions

(1) Strain hardening exponent (n), as estimated fromtensile tests, offered reasonable linear correlations with deg-

radation in magnetic properties: and ; where H, μ

and ε represent hysteresis loss, permeability and strainrespectively.

(2) The magnetic properties and their degradations werealso related to different aspects of microstructural develop-ments: namely, in-grain misorientation developments (GAMor grain average misorientation), deviation from soft mag-netic direction or <001>, changes in d-spacing, estimateddislocation density and relative recovery of the dislocationsubstructure. The observed constitutive relationships wereapproximately linear, in the first approximation, with differ-ent fits noted for individual microstructural parameters.

(3) Though H or changes in H appeared insensi-

tive to sample orientation, orientation sensitivity was noted

for μ and .

(4) H was best fitted with n, GAM and XRF; while

offered the best linear relationship with n and . On

the other hand, fits of μ and did depend on the imposed

magnetic field (1.5 and 1.7 Tesla); and best linear correla-tions were estimated for deviation from <001> and XRF for

μ, and GAM and deviation from <001> for .

AcknowledgementsThe authors would like to acknowledge the use of the

National Facility of Texture & OIM (a DST-IRPHA facility)for this study. Financial support from IFCPAR/CEFIPRA(Indo-French Centre for the promotion of advance research)& DST (Department of Science & Technology) are alsoacknowledged. The authors would also like to acknowledgefinancial and material support from Crompton GreavesGlobal R & D centre.

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Magnetic Properties in Deformed Grain Oriented Electrical