E-Journal of Advanced Maintenance Vol.1(2009) 77-82
Japan Society of Maintenology

Non-destructive Evaluation of Fatigue Damage in the Stainless Steel byUsing Electromagnetic Method
Mohachiro Oka1,* , Terutoshi Yakushiji1, Yuji Tsuchida2, and Masato Enokizono2
1
Oita National College of Technology, 1666 Maki, Oita, 870-0152, Japan
2
Oita University, 700 Dannoharu, Oita, 870-1192, Japan(Received; April 1st, 2009)
Abstract. The magnetic property of a semi-stable austenitic stainless steel (SUS304) is changed greatly bymartensitic transformation caused by fatigue. It is well known that there is a high correlation between theamount of fatigue damage and the residual leakage magnetic flux density caused by remanent magnetization ofit. On the other hand, because a micro structure of metallic materials such as austenitic stainless steels changes
by fatigue, it is thought that the resistivity of them changes as well as the change of remanent magnetization asmagnetic properties by fatigue. Therefore, we paid attention to the relationship between the amount of fatigue
damage and the resistivity of austenitic stainless steels, and did experiments that examined this relation. From
our experiments, the change of the resistivity clearly depends on the amount of fatigue damage in austenitic
stainless steels. This paper shows the relationship between electromagnetic properties and the amount of fatigue
damage of SUS304 and SUS316.
KEYWORDS: resistivity, 4-point probe, SUS304, SUS316, fatigue, non-destructive testing1.

Introduction

Many structural components used in chemical plants and power stations and etc. are made ofaustenitic stainless steels such as SUS304 (ANSI304) or SUS316 (ANSI316). They show excellent
corrosion resistance. From a viewpoint of economy and safety, it is necessary to prevent accidents
caused by the degradation of structural components made of them. To evaluate fatigue damage ofthem, the remanent magnetization method [1, 2] and the eddy current testing method [3] and etc. havebeen already proposed by some research gropes. These methods use the change of magnetism caused
by fatigue. In SUS304, transformation from the austenitic phase to the martensitic phase happens
easily by fatigue. On the other hand, fatigue increases the dislocation of metallic materials such as
austenitic stainless steels. It is thought that an increase of martensitic transformation and thedislocation changes not only magnetization bat also the resistivity (ρ) of metallic materials. Thismethod is called the resistivity method. Accordingly, to propose the new fatigue evaluation method
for austenitic stainless steels (SUS304 and SUS316) using the change of the resistivity, weinvestigated the relationship between fatigue damage and ρ using the 4-poit probe method. In thispaper, the result of this investigation is reported. And, the remanent magnetization method used forthe fatigue evaluation has already been shown in SUS304 and SUS316 [2, 4, 5]. Therefore, to show
the utility of the resistivity method, the results of the residual magnetization method are shown andcompared.
2.

The 4-point Probe Method

Figure 1 shows the schematic diagram of the 4-point probe method. A specimen used in ourexperiment is thin. Then, we calculated ρ by the thin film approximation method because the current
flows as shown in Fig. 2. Resistance R between x1 and x2 is shown by equation (1). Therefore, ρ iswritten as shown equation (2).
*Corresponding author, E-mail: oka@oita-ct.ac.jp
ISSN – 1883 – 9894/09 © 2009 – JSM and the authors. All rights reserved.

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M. Oka et al. / Non-destructive Evaluation of Fatigue Damage in the Stainless Steelby Using Electromagnetic Method

2d2 d ρ dxdxρ
V⎡ ρ⎤R=∫ ρln( x)⎥ =ln 2 =
=∫=⎢
x1
d2πxt
2πt x ⎣ 2πt
2πt2I
⎦dx2

ρ=πt ⎛V ⎞⎜ ⎟ln 2 ⎝ I ⎠(1)

(2)

Where, x, x1, x2, d, t, V, and I are defined as shown in Fig. 1. When ρ is calculated, the following
two approximations were done. The shape of the specimen was assumed to be an infinite plate. And,thickness (t) of a specimen and the probe spacing (d) were assumed to be t << d. These
approximations are not strictly correct. But, these assumptions are effective in case of this experimentbecause the shape of a specimen doesn't change while experimenting. From the results of ourexperiment, ρ of the specimen of this shape as shown in Fig. 3 is about 4 % larger than ρ of a plate of300 mm x 300 mm by 1 mm in thickness. The standard values of the resistivity of SUS304 andSUS316 are about 0.72 μΩm, and 0.74 μΩm respectively. These two our measurement values arecorresponding to these standard values well (See Fig. 10 and Fig.11.) .

Specimen

Fig. 1 The 4-point probe method.

3.

Fig. 2 The thin film approximation.

Experimental Method

Figure 3 shows the shape and dimensions of the specimen, the measurement area of the residual
leakage magnetic flux density (Bz), and the measurement point of ρ. All specimens are made ofSUS304 or SUS316. Thickness of a specimen is a 1.0 mm. Specimens are cut out by the electricaldischarge machining method as shown in Fig. 1. The applied stress was amended by using themeasured width and the measured thickness of the specimen of the stress concentration zone. In caseof SUS304, the experiment was done at about 30 ˚C to avoid the influence of temperature effect. We
experimented similarly for SUS316 in the vicinity of the room temperature of about 25 ˚C. Figure 4
shows a block diagram of a measurement system for the 4-point probe method used in ourexperiments. In this case, d which is each space of probes and t which is the thickness of a specimen
are 5 mm and 1 mm respectively. To make the good contact between a specimen and four probes,
special measurement apparatus was made. The probes have the spring internally, and they are plated
by gold. To know the influence of the resistivity of surface state on the measurement, the resistivity ofthe specimen that did electro-polish and the resistivity of the specimen that did not do electro-polishwere compared. As a result, there was no significant difference. Then, electro-polish of the specimen
was not done in this experiment.
To make clear the relationship between fatigue damage and ρ or the relationship between fatigue
damage and Bz, experiments were carefully carried out in the following procedure. This procedure isshown in Fig. 5. At first, specimens are demagnetized using a marketed demagnetizer. Secondly,specimens are magnetized by the static magnetic field (0.3 T) in the Z direction (See Fig. 3.). Thirdly,
the distribution of Bz caused by remanent magnetization is measured within the area of 30 x 40 mm

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M. Oka et al. / Non-destructive Evaluation of Fatigue Damage in the Stainless Steelby Using Electromagnetic Method

every 1 mm step as shown in Fig. 3 using the thin-film flux-gate magnetic sensor (the FG magneticsensor, SHIMADZU CORPORATION) [6]. Fourthly, ρ is measured by the 4-point probe method at
the center of a specimen as shown in Fig. 3. The applied current is 1 A. Lastly, cyclic bending stress isadded by a plane bending fatigue testing machine (UF15, SHIMADZU CORPORATION) with acapacity of 2.2 Nm operating at 30 Hz. This procedure is repeated until the specimen is destroyed.
Table 1 shows chemical composition of SUS304 and SUS316 used in our experiments. In the case ofSUS304, the applied bending stress (σa) were 290, 300, 300MPa in our experiment. Moreover, theapplied σa in SUS316 were 290, 300, 310, 320MPa.

Fig. 3 The shape of specimen.

Fig. 4 The measurement system.

Table 1 Chemical composition in wt%.
NiCrCSiPMnSMo

SUS304

8.21

18.20

0.04

0.44

0.03

0.79

0.01

-SUS31610.10

16.69

0.04

0.68

0.03

0.99

0.009

2.03

Fig. 5 Measurement procedure.

4.

Experimental Results and Discussions

4.1.

The distributions of Bz
The distributions of Bz are shown in Fig. 6, Fig. 7, Fig. 8, and Fig. 9. In Fig. 6 and Fig. 7, thespecimens were made of SUS304 and σa is 300 MPa. In Fig. 6, the number of stress cycles (N) is zero.
N is 1.4 x 105 in Fig. 7. In Fig. 8 and Fig. 9, specimens were made of SUS316 and σa is 300 MPa. In79

M. Oka et al. / Non-destructive Evaluation of Fatigue Damage in the Stainless Steelby Using Electromagnetic Method

Fig. 8, the number of stress cycles (N) is zero. N is 3 x 105 in Fig. 9. From these figures, Bz measured
by the FG magnetic sensor clearly catches the distribution of fatigue damage in SUS304 and SUS316.
In Fig. 8, Bz is large in the vicinity of both ends of Y-axis and in the center of X-axis as shown in twocircles. The value of Bz originates in the rust that remained at an electrical discharge machining. The
value of dBz as shown in Fig. 7 and Fig. 9 is a parameter to evaluate the amount of fatigue damage inaustenitic stainless steels.
The relationship among ρ and σa, and NFigure 10 shows the relationship among ρ and σa, and N when the specimen is SUS304. Figure
11 shows the same relationship as Fig. 10 for SUS316. From these figures, ρ increases clearlyaccording to an increase in N and σa. In Fig. 10 and Fig. 11, there are good correlations in N and σaand an increase in ρ in these figures though the measurement varies somewhat. Moreover, the goodcorrelation between σa and ρ exists as N similarly. The value of ρ immediately before the rupture
increases only by 1.5% in SUS304 and 1.7% in SUS316. It is thought that not only an increase in thedislocation and the micro-crack by fatigue damage but also the martensitic transformation by fatigue
damage is a cause in the change in ρ in SUS304. On the other hand, it is thought that only an increasein the dislocation by fatigue damage is a cause in the change in ρ in SUS316.

4.2.

5.

Conclusions

In this paper, we have elucidated the following the results for the evaluation of fatigue damage inSUS304 or SUS316 using ρ measured by the 4-point probe method. From our experiments, thetendency to the change of ρ by fatigue damage and the change of dBz by fatigue damage looks likewell. And, the change of ρ and dBz clearly depends on the amount of fatigue damage of both SUS304and SUS316. Therefore, there is a possibility that ρ can use to evaluate the amount of fatigue damage
in SUS304 and SUS316. However, the change of ρ and dBz is little different when N is small.
Therefore the cause of the change of ρ and dBz by fatigue damage might be different. It is thought thatthe resistivity method has detected the dislocation and an increase in the micro-crack. Therefore, thismethod has the possibility that steel and aluminum, etc. can be applied, too. In addition, it is necessary
to investigate the cause of an increase of dBz for SUS316 in detail.
Acknowledgments

30302020
B z (μT)B z (μT)

This work was supported in part by Grant-in-Aid for Scientific Research (C) No. 19560434.

10012-10-20 -15

3-10 -5-6Xposition(mm)10120-10-20 -150 5-15Y-position(mm) 10 1520dB z

Fig. 6 The distribution of Bz.

3-10 -5-6Xposition(mm)05 10-1515 20Y-position(mm)Fig. 7 The distribution of Bz.

(N = 1.4 x 105, σa = 300 MPa, SUS304)(N = 0, σa = 300 MPa, SUS304)

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M. Oka et al. / Non-destructive Evaluation of Fatigue Damage in the Stainless Steelby Using Electromagnetic Method

866420-220 14B z ( μ T)

108Bz (μ T)10-12420-220 14-3862-4-10 -16

X-position(mm)15Y-position (mm)8dB z

2-4 -10-16Y-position (mm)15

Fig. 9 The distribution of Bz.

(N = 0, σa = 300 MPa, SUS316)(N = 3 x 105, σa = 300 MPa, SUS316)
0.753

WNo.014(300MPa)
WNo.013(300MPa)
WNo.019(310MPa)
WNo.020(310MPa)
WNo.021(290MPa)
WNo.022(290MPa)

0.736

No15(320MPa)
No13(320MPa)
No9(310MPa)
No19(310MPa)
No20(300MPa)
No7(300MPa)
No21(290MPa)
No22(290MPa)

0.75
Resistivity ρ (μΩ・m)

0.738

0.734
0.732
0.73
0.728

0.747
0.744
0.741
0.738
0.735

0.726

0.732
0500001000001500002000002500000100000

Number of stress cycles (N )200000300000400000(SUS316)

No13(320MPa)
No15(320MPa)
No9(310MPa)
No19(310MPa)
No20(300MPa)
No7(300Mpa)
No21(290MPa)
No22(290MPa)

314
WNo.014(300MPa)
WNo.013(300MPa)
WNo.019(310MPa)
WNo.020(310MPa)
WNo.021(290MPa)
WNo.022(290MPa)

2.5
2dBz (μT)

10600000Fig. 11 The relationship among ρ and σa and N.

(SUS304)

12500000

Number of stress cycles (N)Fig. 10 The relationship among ρ and σa and N.

dBz (μT)

X-position(mm)5Fig. 8 The distribution of Bz.

0.74

Resistivity ρ (μΩ・m)

-15-5

86

1.5
140.5

20-0.500

50000

1000001500002000000250000

100000200000300000400000500000600000

Number of stress cycles (N )Number of stress cycles (N )Fig. 12 The relationship among dBz and σa and N.

Fig. 13 The relationship among dBz and σa and N.

(SUS304)(SUS316)81

M. Oka et al. / Non-destructive Evaluation of Fatigue Damage in the Stainless Steelby Using Electromagnetic Method

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