Copyright ©JCPDS - International Centre for Diffraction Data 2004, Advances in X-ray Analysis, Volume 47.
RESIDUAL STRESS DISTRIBUTION IN GRAIN-ORIENTED
SILICON STEEL
Muneyuki Imafuku, Tamaki Suzuki
Advanced Technology Research Laboratories, Nippon Steel Corporation
Futtsu, Chiba 293-0011, Japan
Hiroshi Suzuki*
Department of Mechanical Engineering, Tokyo Metropolitan University
Hachioji, Tokyo 192-0397, Japan
Koichi Akita
Department of Mechanical Systems Engineering, Musashi Institute of Technology
Setagaya, Tokyo 158-8557, Japan
*Present Address: Neutron Science Research Center, Japan Atomic Energy Research
Institute, Nakagun, Ibaraki, 319-1195 Japan
ABSTRACT
We investigated the residual stress distribution in a grain of laser-irradiated and gearrolled grain-oriented Fe-3%Si silicon steels by X-ray stress measurement method in order
to clarify the effect of residual stresses on magnetic domain refining. Dotted cavity lines
were formed by Nd:YAG laser with a power density of 3.3 mJ/pulse for the laserirradiated sample. By using a newly developed X-ray stress measurement method for a
single crystal, the tensile residual stresses of 70-160 MPa were observed only in the
vicinity of the laser-irradiated lines. After annealing at 1027 K for 2 hours in hydrogen,
the residual tensile stresses were released and the domain-refining effect vanished. As for
the gear-rolled sample, grooves of 0.1 mm wide and 0.015 mm deep were induced at 5
mm intervals. After annealing under the same condition, the residual stresses around the
groove were released, whereas the refined magnetic domains were preserved. Therefore,
the residual stresses should have no relevance to the domain-refining, which explains the
tolerance to the thermal annealing for the gear-rolled ones.
INTRODUCTION
Grain-oriented Fe-3%Si steel, consisting of {110}<001> oriented large grains, is a soft
magnetic material mainly used for transformer cores. In order to reduce the energy
consumption in industries, the reduction in iron core loss has been strongly demanded.
This has been achieved mainly by improving {110}<001> alignment, making the thinnergauge material and refining the magnetic domain spacing[1]. Pulse laser irradiation [2]
and gear-rolling [3] techniques have been developed for the last purpose. It has been
recognized that the gear-rolled samples have a greater heat-resistance than the laser-
402
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Copyright ©JCPDS - International Centre for Diffraction Data 2004, Advances in X-ray Analysis, Volume 47.
irradiated ones and are suitable for the wound type iron cores [3]. In these processes, the
induced stresses or recrystallized micro grains might be effective for the magnetic
domain-refinement [4,5]. However, the actual survey of the stress distribution has not
been done and therefore, the difference of the domain-refining mechanism between the
two processes is not clear up to now.
The stress measurement of a large grain sample is impossible by the conventional X-ray
stress measurement method, sin2ψ method because the diffraction pattern from one grain
becomes spotty and cannot form a continuous cone. Recently, Suyama et al. have
proposed the x-ray stress measurement method based on the multiple regression analysis
from the diffraction spots from a single crystal and applied for the uniaxial loading test of
grain-oriented Fe-3%Si steel [6]. Very recently, Suzuki et al. have developed an
advanced high accurate system [7] and succeeded to measure the stress distribution in
laser-irradiated grain-oriented Fe-3%Si steel [8]. Furthermore, they proposed a new
analysis principle to determine the stress states [9].
In this study, we investigated the residual stress distribution in a grain of laser-irradiated
and gear-rolled grain-oriented Fe-3%Si silicon steels by the newly developed x-ray stress
measurement method for a single crystal in order to compare the mechanisms of the
magnetic domain refinement with special reference to the effect of residual stresses in
these two processes.
EXPERIMENTAL
Sample preparation
Figure 1 shows the sample preparation procedure in this study. Single crystal specimens,
15 mm X 15 mm X 0.23 mm, were cut out from the grain-oriented Fe-3%Si silicon steel
sheet without tensile film coating. These samples were annealed at 1027 K for 2 h in pure
hydrogen atmosphere in order to relief the induced stress by cutting.
After the stress relief annealing mentioned above, two types of magnetic domain refining
processes were applied. One is the laser-irradiation process. Dotted cavity lines were
formed by Nd:YAG laser with a power density of 3.3 mJ/pulse in air at room temperature
for the laser-irradiated sample. The pitch of the cavity line was 5 mm and the diameter of
the laser-focused cavity was about 0.18 mm. The other is groove forming process.
Grooves of 0.1 mm wide and 0.015 mm deep at 5 mm intervals were induced by gearrolling. Figure 2 shows the surface shapes of the specimens observed by the confocal
laser scanning microscope.
These samples were annealed again at the same condition (at 1027 K for 2 h in pure
hydrogen atmosphere) to investigate the thermal stabilities of the magnetic properties and
stress states.
X-ray stress measurement for a single crystal
Stress measurement in a single crystal is an important subject for material science and has
been studied for more than a decade [10-11]. Recently, a unique and practical X-ray
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Copyright ©JCPDS - International Centre for Diffraction Data 2004, Advances in X-ray Analysis, Volume 47.
stress measurement method for a single crystal has been developed by the present authors
and others [6-9]. Following is the essential point of this method applied in this study.
A lattice strain of ε L33 in the L3 direction on the laboratory coordinate system in the plane
stress condition is expressed with the stress components σ Suv on the specimen coordinate
system by the following equation [9]:
ε L33= -(θn-θ0)cot θ0 = γ3iγ3j πuk πvlSijkl σ Suv
= Anσ S11+Bnσ S12+Cnσ S22
(1)
Where, Sijkl is the elastic compliance of a single crystal, and π and γ are the
transformation matrices between the specimen and crystal coordinate systems, and crystal
and laboratory coordinate systems, respectively. In this equation, θ0 is the half of the
diffraction angle in the stress-free condition, and is usually unknown. An, Bn and Cn are
the variables which can be determined by the Miller indices of the measured diffraction
planes. θn is expressed as the following equation:
θn = -{(σ S11 An +σ S12 Bn+σ S22 Cn)/cot θ0} + θ0
(2)
By choosing the equivalent diffraction planes, α11, α12, α22, and θ0 can be calculated by
the multiple regression analysis method. In this analysis, at least four equivalent
diffraction planes should be measured.
Fe-3%Si Grain-oriented silicon steel
thickness：0.23mm
Grain
Cut out
Rolling Direction
Stress relief annealing（pure H2，1027K，2h）
Gear-rolling
Laser-irradiation
5mm
15mm
Nd:YAG laser
3.3ｍJ/Pulse
Grooves
15mm
15mm
θ＝70°
5mm
15mm
W:100μm
D: 15μm
Stress relief annealing（pure H2，1027K，2h）
Figure 1. Scheme of sample preparation procedure.
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Copyright ©JCPDS - International Centre for Diffraction Data 2004, Advances in X-ray Analysis, Volume 47.
100μm
100 µm
(a)
(b)
Figure 2. Microscopic images of the specimens around (a) the laser-irradiated cavity and
(b) the gear-rolled groove.
PSPC
Laser
displacement
meter
X-ray
In order to obtain the perfect
diffraction profile to determine the
accurate diffraction angle for each
plane with 1-dimentional position
sensitive proportional counter (PSPC)
type detector, χψ-oscillation method
[7] was utilized. The axes of the χ–
ψ-oscillation
oscillation
and
correspond to the direction of
collimated incident X-ray beam and
the vertical direction of the χ–rotation
axis. Figure 3 shows the X-ray stress
measurement apparatus used in this
study. The single crystal specimen
was mounted on the χψ-oscillation
stage. The measured position of the
specimen was adjusted at the rotation
center of the stage within ±20 µm
error by using the laser positioning
system.
Sample
ψ-oscillation
Oscillation stage
χ-oscillation
Figure 3. The stress measurement apparatus
for a single crystal.
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Copyright ©JCPDS - International Centre for Diffraction Data 2004, Advances in X-ray Analysis, Volume 47.
The orientations of the samples were measured by Laue method beforehand. The values
of the laser-irradiated and gear-rolled samples were (116 127 3)[-2 0 100] and (41 40 1)[5 2 100], respectively, which are closer to the so-called Goss orientation, {110}<001>. A
shield-tube X-ray source of Cr-Kα radiation with a power of 30 KV and 8 mA was used
in this study. The diameter of X-ray beam was 0.4 mm. Six equivalent 211 diffraction
planes of α-Fe, 211, 112, 121, 12-1, 11-2 and 21-1, satisfied reflection condition and
were chosen for the measurement. The stresses at 5 positions, 0 mm, 0.25 mm, 0.50 mm,
1.00 mm and 2.00 mm from the laser-irradiated cavity line and gear-rolled groove were
measured.
RESULTS AND DISCUSSION
Magnetic domain
The basic domain structures of the grain-oriented Fe-3%Si steel samples were measured
by a scanning electron microscope. Figure 4 shows the change in the width of the
magnetic domains by the two processes. Slab type 180-degree domains were observed
along the rolling direction of <001>, which is the easy magnetization axis of iron. The
width of the magnetic domains was approximately 0.7-1.0 mm before applying magnetic
domain refining processes. We can see from this figure that the 180-degree magnetic
domains were drastically refined to be less than 0.3 mm and were divided at the cavity
line and groove by the laser-irradiation and gear-rolling processes, respectively. After the
stress relief annealing mentioned above, the magnetic domains were returned to their
original state and the laser-induced cavities became ineffective in the case of laser
irradiation. On the other hand, the refined 180-degree magnetic domains were preserved
for the gear-rolling sample. These results suggest the origin of the magnetic domainrefining is different between these processes.
cavity Line
Laser-irradiation
Stress relief annealing（ pure H2，800℃，2h ）
Ｇｒｏｏｖｅ
Gear-rolling
Figure 4. Change in magnetic domains around the laser-irradiated cavity and the gearrolled groove.
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Copyright ©JCPDS - International Centre for Diffraction Data 2004, Advances in X-ray Analysis, Volume 47.
X-ray topography
Figure 5 shows the X-ray topographical images of the laser-irradiate and gear-rolled
grain-oriented Fe-3%Si silicon steel sheet. We can see from these photographs the highlighted lines corresponding to the laser cavities or grooves, suggesting that some kinds of
localized strains were induced near the lines in both processes. For the next step,
quantitative stress measurement is necessary in order to clarify the details of the stress
states of these samples.
5mm
(a) Laser-irradiated sample
(b) Gear-rolled sample
Figure 5. X-ray topographical images for (a) laser-irradiated and (b)gear-rolled samples.
Residual Stress Distributions
The residual stress distributions in laser-irradiated sample are shown in Fig. 6. σ11, σ22
and σ12 represent the plane stresses in rolling direction (1-direction), transverse direction
(2-direction) and the shear stress, respectively. It was found that the tensile stresses of
about up to 70 MPa in 1-direction and 160 MPa in 2-direction were induced just around
the laser-irradiated cavity line. The value of σ22 was almost two times larger than that of
σ11 since the neighboring cavities in 2-direction affected to increase the tensile stress. The
stress induced area was less than 0.5 mm, that is to say, the very limited area. σ11 and σ22
are considered to be the principle stresses in the surface plane because the shear stress,
σ12 is negligible as is seen in this figure. Considering the melting traces of the cavities as
is seen in Fig. 2, the thermal history effect (heating->cooling) was dominant rather than
the shock wave effect in the laser irradiation process. Consequently, the tensile stresses
were induced. Similar results had been reported for the laser peening of stainless steel in
air [12]. It was supposed that the local tensile stresses induced by the laser irradiation
destabilize the newly formed 90-degree magnetic domains so as to refine the 180-degree
domains. After the stress relief annealing, the residual tensile stresses were completely
released. At the same time, the domain-refining effect vanished as is shown in Fig. 4.
Therefore, we can say that the local tensile effect is essential for the laser irradiation
process.
Figure 7 shows the residual stress distributions in gear-rolled sample. We could not
measure the residual stress at X=0 mm (just at the groove position) since the diffraction
profiles were not good. Complex stress states, both compressive and tensile states, were
observed in the vicinity of groove. After annealing at 1027 K for 2 h in pure hydrogen
atmosphere, the residual stresses around the groove were released, whereas the refined
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Copyright ©JCPDS - International Centre for Diffraction Data 2004, Advances in X-ray Analysis, Volume 47.
408
magnetic domains were preserved as is shown in Fig. 4. Therefore, the residual stresses
were not the cause of the magnetic domain-refining.
The mechanism of magnetic domain refining can be explained with the analogy of the
previous scratching studies [13]. Once the groove is formed, new magnetic poles arise at
the new walls in the groove so as to refine the magnetic domains. This kind of shape
effect of grooves may be essential for the domain-refining instead of the induced residual
stress states in the gear rolling process. The better thermal stability of the refined
magnetic domains is suitable for the stress relief annealing processed on wound cores.
However, some further experimental studies, particularly the magnetic domain structures
near the cavity lines, should be required for the fully understand of the domain refining
mechanism.
200
Laser-irradiated/before annealing
σ22
σ11
σ12
150
100
50
0
-50
Laser-irradiated /after annealing
Residual stress, σ /MPa
Residual stress, σ /MPa
200
150
σ22
σ11
σ12
100
50
0
-50
0.0
0.5
1.0
1.5
Distance, X /mm
0.0
2.0
0.5
1.0
1.5
Distance, X /mm
2.0
Figure 6. The residual stress distributions in laser-irradiated sample before and after
annealing.
0
-100
-200
Gear-rolled / after annealing
200
Residual stress, σ /MPa
Residual stress, σ /MPa
σ22
σ11
σ12
100
-300
250
Gear-rolled / before annealing
200
100
50
0
-50
0.0
0.5
1.0
1.5
Distance, X / mm
2.0
σ22
σ11
σ12
150
0.0
0.5
1.0
1.5
Distance, X / mm
2.0
Figure 7. The residual stress distributions in gear-rolled sample before and after annealing.
Copyright ©JCPDS - International Centre for Diffraction Data 2004, Advances in X-ray Analysis, Volume 47.
CONCLUSION
The residual stress distributions in laser-irradiated and gear-rolled grain-oriented Fe-3%
silicon steels were measured by the newly developed X-ray stress measurement method
for a single crystal.
The tensile residual stresses of 70 to 160 MPa were observed only in the vicinity of the
laser-irradiated cavity line. After annealing at 1027 K for 2 h in pure hydrogen
atmosphere, the residual stresses were released, and the domain-refining effect vanished.
It was supposed that the local tensile stresses induced by the laser irradiation destabilize
the newly formed 90-degree magnetic domains so as to refine the 180-degree magnetic
domains. The local tensile stress caused by the thermal effect for domain-refining was
confirmed in the laser irradiation process.
In the case of groove forming process by gear rolling, complex states of compressive and
tensile stresses were observed in the vicinity of groove. After annealing at 1027 K for 2 h
in pure hydrogen atmosphere, the residual stresses around the groove were released,
whereas the refined magnetic domains were preserved. Therefore, the residual stresses
should have no relevance to the magnetic domain-refining. The shape effect so as to
induce the new magnetic poles at the grooves may cause the domain-refining in the gear
rolling process.
REFERENCES
[1] Y. Ushigami, H. Masui, Y. Okazaki, Y. Suga, N. Takahashi: J. Mater. Eng.
Performance, 5 (1996) 310.
[2] T. Iuchi, S. Yamaguchi, T. Ichiyama, M. Nakamura, T. Ishimoto and K. Kuroki: J.
Appl. Phys., 53 (1983) 2410.
[3] H. Kobayashi, K. Kuroki, E. Sasaki, M. Iwasaki and T. Takahashi: Physica Scripta:
T24 (1988) 36.
[4] M. Nakamura, K. Hirose, T. Nozawa and M. Matsuo: IEEE Trans. Mag., MAG-23
(1987) 3074.
[5] T. Nozawa, Y. Matsuo, H. Kobayashi, K. Iwayama and N. Takahashi: J. Appl. Phys.,
63 (1988) 2966.
[6] Y. Suyama, S. Ohya and Y. Yoshioka: J. Soc.Mat. Sci., Jpn, 48 (1999) 1437. (in
Japanese)
[7] H. Suzuki, K. Akita and H. Misawa: Mater. Sci. Res. Int., 6 (2000)255.
[8] H. Suzuki, K. Akita, H. Misawa and M. Imafuku: Mater. Sci. Res. Int., 8 (2002) 207.
[9] H. Suzuki, K. Akita and H. Misawa: Jpn J. Appl. Phys., 42 (2003) 2876.
[10] B. Ortner: J. Appl. Cryst., 22 (1989) 216.
[11] B. Ortner: Advances in X-ray Analysis, 29 (1986) 387.
[12] N. Mukai, N. Aoki, M. Obata, A. Ito, Y. Sano and C. Konagai: Proc. 3rd Int. Conf.
Nuclear Engineering (1995) 1489.
[13] M. F. Littmann: J. Appl. Phys., 38 (1967) 1104.
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