DEPENDENCE OF THE PERPENDICULAR RESIDUAL LEAKAGE
MAGNETIC FLUX DENSITY ON FATIGUE DAMAGE IN AN
AUSTENITIC STAINLESS STEEL
M. Oka1, T. Yakushiji2, Y. Tsuchida3 and M. Enokizono3
Department of Computer and Control Engineering, Oita National College of Technology,
1666 Maki, Oita, 870-0152, Japan
Department of Mechanical Engineering, Oita National College of Technology,
1666 Maki, Oita, 870-0152, Japan
3
Faculty of Engineering, Oita University, 700 Dannoharu, Oita, 870-1192, Japan
ABSTRACT. In order to estimate the amount of plane bending fatigue damage in an austenitic stainless
steel (SUS304), we were investigating the relationship between plane bending fatigue damage and the
perpendicular residual leakage magnetic flux density caused by martensitic structure induced by plane
bending fatigue. A specimen such as SUS304 had been excited in a constant external magnetic field
perpendicularly to measure dependence of the perpendicular residual leakage magnetic flux density on
plane bending fatigue damage accurately. The Z component of the magnetic flux density at 1 mm above a
specimen is measured by using a thin-film flux-gate (FG) magnetic sensor. Residual magnetization is
caused by partial martensitic structure in an austenitic stainless steel induced by cyclic bending stress.
From our experiments, we can evaluate dependence of the perpendicular residual leakage magnetic flux
density on plane bending fatigue damage and know the relationship between growth of a crack and the
perpendicular residual leakage magnetic flux density.
INTRODUCTION
Since an austenitic stainless steel such as SUS304 shows excellent mechanical strength
and corrosion resistance, it is widely used in not only parts of the food factory but also parts of
the nuclear power plant. It is necessary to prevent a big accident due to the deterioration of
these parts with use. We should accurately measure the remaining lifetime of these parts by
developing effective inspection technologies. Then, it is very important to know the remaining
lifetime of them used in structural components of the nuclear power plant made from an
austenitic stainless steel on the site. On the other hand, conventional electromagnetic
non-destructive evaluation (NDE) methods such as the eddy current testing are not effective
methods to measure the remaining lifetime or the amount of fatigue damage. Accordingly, the
perpendicular residual magnetization method was applied to evaluate the amount of fatigue
damage in an austenitic stainless steel [1]. We have already reported about the relationship
between the amount of plane bending fatigue damage and the leakage magnetic flux density at
1 mm above a specimen caused by residual magnetization [2], [3]. In our previous papers, the
direction of magnetic excitation is the X-axis (See Fig. 1). In this case, the magnetic flux
density in a specimen is not saturated. The measured magnetic flux density is very small. Then,
to get the bigger measured magnetic flux density than the previous method and to saturate the
magnetic flux density in a specimen, we excite a specimen in a constant external magnetic
field perpendicularly until the magnetic flux density in the specimen is saturated. So, we can
obtain about ten times the signal by this method using the thin-film flux-gate (FG) magnetic
CP657, Review of Quantitative Nondestructive Evaluation Vol. 22, ed. by D. O. Thompson and D. E. Chimenti
© 2003 American Institute of Physics 0-7354-0117-9/03/$20.00
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sensor [4], [5] which is also used in our previous papers. In this paper, we show the estimation
of the plane bending fatigue damage in an austenitic stainless steel, and the relationship
between growth of a crack and the perpendicular residual leakage magnetic flux density.
SPECIMENS AND THE FLUX-GATE MAGNETIC SENSOR
Fig. 1 shows the dimensions of a specimen, arrangement of the measuring range and
arrangement of the electrolytic polished range. All specimens are 1.0 mm thick austenitic
stainless steel plates (SUS304). They are cut out by the electrical discharge machining method
to be a plate like Fig. 1. They are not annealed. Some specimens have a blind hole with a
diameter of 0.3mm and a depth of 0.15 mm at the center of a specimen. In order to avoid the
influence of the surface state, the surface of the center part of a specimen is electrolytic
polished (Posphoric acid = 2000g, Gelatinous = 40g, Oxalic acid = 40g. Current = 5 A, Time
= 2 min.). This FG magnetic sensor can detect the Z component of the leakage magnetic flux
density (B2) at 1 mm above a specimen caused by perpendicular residual magnetization. The
Z-axis is taken in the direction of the thickness of the specimen. The sensitivity of this FG
magnetic sensor is about 30 mV/|iT. The FG magnetic sensor head and a specimen are placed
in perpendicular keeping 1 mm distance between them. Table 1 shows chemical composition
of SUS304 used in this experiments.
MEASUREMENT SYSTEM
Fig. 2 shows a setup of experimental equipment. The signal from the FG magnetic
sensor is digitized by an A/D converter and inputted to the computer. The measurement is
repeated twice. A smoothing algorithm such as the method of moving averages is used for
better processing of the FG magnetic sensor output and for reducing a noise. The FG magnetic
sensor is moved by a X-Y stage controlled with a computer.
Measuring range
Electrolytic polished range
FIGURE 1. The dimension of a specimen, arrangement of the measuring range and the arrangement of the
electrolytic polished range.
TABLE 1. The chemical composition of SUS3 04 in wt%.
c
0.04
Si
0.44
Mn
0.79
P
0.032
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S
0.006
Ni
8.21
Cr
18.20
FG sensor
heack
FG sensor/
drive circuit
FIGURE 2. The block diagram of experimental equipment.
EXPERIMENTAL METHOD
Measurement Method
To evaluation of plane bending fatigue damage in an austenitic stainless steel, the
experiments are carried out in the following procedure: At first, specimens are demagnetized
using an AC power supply and the exciting coil. The maximum magnetic flux density is
assumed to be 0.42 T. Secondly, specimens are magnetized in a static magnetic field (0.3 T)
by using a DC power supply and the exciting coil. All specimens are magnetized in the Z
direction as shown in Fig. 3. Thirdly, the distribution of the leakage magnetic flux density
caused by perpendicular residual magnetization at 1 mm above specimens is measured within
the range of 20 x 10 mm every 0.2 mm step. Partial transformation from austenite to
martensite is induced due to plane bending fatigue damage at the center. The area of
martensite is magnetized in the exciting magnetic field. Lastly, cyclic stress is added by a
plane bending fatigue testing machine (Uf 15, SHIMADZU CORPORATION) with a capacity
of 2.2 Nm operating at 30 Hz.
S-N Curve
To know the fatigue limit of our specimens (SUS304), we measured the relationship
between bending stress and the number of cycles (S-N curve). This relationship is shown in
Fig. 4. When the bending stress is 310 MPa, the specimen did not break up 1.0 x 107 cycles.
From this result, the fatigue limit of our specimens is estimated to be 310 MPa.
External exciting magnetic field
FIGURE 3. The direction of the external exciting magnetic field.
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The Distribution of Perpendicular Residual Magnetization
\
=> 0 0 0 0 C
>J
U)
U>
U)
U) O
D i—'
bO
U>
.£». 0
Bending stress (MPa)
To exclude the influence of the background magnetic field such as terrestrial
magnetism or another magnetic field caused by electrical machineries, we measured the
background magnetic field near the FG magnetic sensor as shown in Fig. 5. Then, all data,
which are shown in this paper, cancelled out from influence of background magnetic field
using the measured data shown in Fig. 5.
l.OE+04
^
l.OE+05
l.OE+06
l.OE+07
Number of stress cycles (N)
FIGURE 4. The relationship between bending stress and the number of cycles (S-N curve).
X-position (mm)
3
Y-position (mm)
FIGURE 5. The distribution of the background magnetic flux density near the FG magnetic sensor.
X-position (mm)
Y-position (mm)
FIGURE 6. The distribution of the Z-axis leakage magnetic flux density caused by perpendicular residual
magnetization (N=0, Undamaged specimen.).
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X-position (mm)
Y-position (mm)
FIGURE 7. The distribution of the Z-axis leakage magnetic flux density caused by perpendicular residual
magnetization (aa=340 MPa, N=l .0 x 105).
The distribution of the Z component of the leakage magnetic flux density (Bz) caused
by residual magnetization is shown in Fig. 6 (N=0). Since plane bending fatigue is not applied
at this time, transformation from austenite phase to martensite phase is not induced in an
undamaged specimen yet. In this case, the distribution of Bz is flatness. The value of Bz is not
zero on account of residual martensite. It is thought that the residual martensite was induced at
rolling. The distribution of Bz of the damaged specimen (0a=340 MPa, N=1.0 x 105) is shown
in Fig. 7. Partial transformation from austenite to martensite is induced due to plane bending
stress near the center of a specimen. So, the distribution of Bz near arched notches is large
originated in the shape of a specimen.
Fig. 8 shows the relationship between the change of the Z component maximum
leakage magnetic flux density (Bzmax, See in Fig. 7) and the bending stress. From this figure,
Bzmax clearly increases with the increase of the bending stress and the number of stress cycles.
The change of BZ^ obviously depends on the bending stress and the number of stress cycles.
Fig. 9 shows the relationship between the Z component leakage magnetic flux density
at the center (BzCmax> See Fig. 7) and length of a crack and number of stress cycles. The
specimen used in this figure has a small blind hole. And, bending stress is 320 MPa. When the
number of stress cycles was 1.3 x 105 times, the crack was found for the first time at the edge
of the hole. The crack grows slowly according to the number of stress cycles. But, the crack
grows rapidly before the specimen breaks. On the other hand, the value of BzCmax increases
almost in proportion to the number of stress cycles.
It is a comparison of BzCmax shown in Fig 10 when there is a small hole and when it is
not. One of specimens used in this experiment has a hole, and other one of specimens does not
have a hole. In the case of the specimen with a hole, the breaking point is 3.64 x 105. The
breaking point is 4.40 x 105 in the case of the specimen without a hole. Because the stress
concentrates near the hole compared with the specimen without the hole, the specimen with
the hole breaks early. The value of BzCmax obviously shows a similar tendency.
Number of cycles ( x l O 4 )
FIGURE 8. The relationship between B^a* caused by perpendicular residual magnetization and number of
stress cycles and amplitude of plane bending stress.
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0
5
10
15
20
25
Number of cycles ( x 104)
FIGURE 9. The relationship between BzCmax caused by perpendicular residual magnetization and length of a
crack and number of stress cycles (with a hole, aa=320 MPa).
i
-•-Without a hole
§ so
-0- With a hole
,x^
,
1 40
1 20
oc
AT
^HL^^
(»•""
m^^
s^
()
10
20
30
4(
Number of cycles (xld 4 )
FIGURE 10. The relationship between BzCmax caused by perpendicular residual magnetization and number of
stress cycles (with a hole, without a hole, 03=320 MPa).
CONCLUSIONS
In this paper, we have elucidated the following results for evaluation of plane bending
fatigue damage in an austenitic stainless steel using a FG magnetic sensor.
1. The signal obtained by our perpendicular residual magnetization method is about ten times
larger than obtained by our previous method.
2. The value of Bzmax obviously depends on the plane bending stress and number of stress
cycles.
3. We clarified the difference between the growth process of the crack and the increase
process of the perpendicular residual leakage magnetic flux density at 1 mm above a specimen.
4. We show the difference between the perpendicular residual leakage magnetic flux density
above a hole when there is a hole and it when there is not it.
REFERENCES
1. Nakasone, Y. Iwasaki, T. Shimizu and S. Kasumi; "Electromagnetic non-destructive
detection of damage in an austenitic stainless steel by the use of martensitic
transformation", Journal of the Japan society of Applied Electromagetics and Mechanics,
Vol. 9, No. 2, pp. 123-130, 2001.
2. M. Oka, T. Yakushiji and M. Enokizono, "Fatigue Dependence of Residual Magnetization
in Austenitic Stainless Steel Plates", IEEE TRANSACTIONS ON MAGNETICS, Vol. 37,
No. 5, pp. 3373-3375,2001.
3. M. Oka, T. Yakushiji, Y. Tsuchida and M. Enokizono, "Evaluation of Bending Fatigue of
Stainless Steels Using the Residual Magnetization Method", Journal of the Magnetics
Society of Japan, Vol. 25, No. 4-2, pp. 1075-1078, 2001.
4. Y. Yamda, K. Yoshimi, T. Munaka and R. Yosida, "Application of Thin-Film Fluxgate
Magnetic Sensor", New Ceramics, No. 2, pp. 15-20, 1998.
5. K. Yoshimi, Y. Fujiyama, T. Munaka, H. Nakanishi, T. Yoshida, and Y. Yamada,
"Microfabricated Thin-Film Flux-Gate Magnetic Sensor and its Applications",
SHIMADZU REVIEW, Vol. 56,No. l&2,pp.!9-28, 1999.
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