E-Journal of Advanced Maintenance Vol.7-2 (2015) 172-178
Japan Society of Maintenology

Non-Destructive Evaluation of Multiple-site Small Cracks in Low Cycle
Fatigue of Austenitic Stainless Steel by Four-point Probe DC Potential
Difference Method
Shio NAKANISHI1,*, Takayuki SUZUKI2 and Yuji NAKASONE1
1

Tokyo University of Science, 6-3-1 Niijuku, Katsushika-ku, Tokyo 125-8585, Japan
National Institute of Advanced Industrial Science and Technology, 1-2-1 Namiki, Tsukuba-shi,
Ibaraki 305-8564, Japan
2

ABSTRACTThis study has investigated multiple-site small cracks in the low cycle fatigue of SUS316L at 873K in air byusing the four-point probe DC potential difference method. Small probes with 1-mm spacing between theelectrodes were used in order to evaluate small cracks of some hundred micrometers. Morphology of the cracks
was evaluated by standard deviation of potential difference σV which detected by the probes and by the crack
density by laser microscopy. As a result, it was shown that σV monotonically increased with increasing numberof strain cycles and fatigue process was classified into four stages. Furthermore, statistical analysis showed thatthe cracks initiated at random sites in early stage. However, the randomness was diminished and σV increased
significantly with growth and coalescence of the cracks. These results revealed that standard deviation of
normalized potential difference could evaluate initiation, growth and coalescence of multiple-site small cracks
in each stage.
KEYWORDS

ARTICLE INFORMATION

Low cycle fatigue, Austenitic stainless steel, Multiple-site small cracks,
Crack growth and coalescence, Four-point probe DC potential difference
method, Statistical analysis

Article history:
Received 2 December 2014
Accepted 3 July 2015

1.

Introduction

Recently, in power plants, Condition-Based Maintenance (CBM) is required instead ofTime-Based Maintenance (TBM) in order to improve the safety and dependability of the plants.
Especially, on surfaces of structural components of the power plants, multiple-site small cracks
initiate, grow and coalesce due to high-temperature low cycle fatigue, and they finally form larger
cracks which cause fracture. In order to ensure the integrity of these power plants by CBM, it isnecessary to detect multiple-site small cracks growth and to predict fatigue life of structural parts
nondestructively.
DC/AC potential difference method can detect potential difference distribution around a single
crack/cracks and was applied to identify dimensions of a single large crack in previous studies [1, 2,
3]. A few researches [4, 5] reported variation in potential difference of multiple-site small cracks.
However, the relationship between changes in potential difference and behavior of multiple-site small
cracks has not yet been investigated. The present authors have applied the four-point probe DC
potential difference method to the non-destructive evaluation of multiple small cracks inhigh-temperature low cycle fatigue of an austenitic stainless steel JIS SUS316L. In each stage of thefatigue process, DC potential difference on specimen surfaces, and density and sizes of multiple-site
small cracks in specimens were measured and statistically analyzed [6, 7]. This paper describes thestatistical analysis of the growth behavior of multiple-site small cracks and the prediction of residuallife of the fatigue process by using four-point probe DC potential difference method.

2.

Experimental procedures*

Corresponding author, E-mail: 4513636@ed.tus.ac.jp

ISSN-1883-9894/10 © 2010 – JSM and the authors. All rights reserved.

172

S. Nakanishi, et al./ Non-Destructive Evaluation of Multiple-site Small Cracks

2.1. High-temperature low cycle fatigue tests
Figure 1 shows the geometry of specimens made of an austenitic stainless steel JIS SUS316L,
equivalent of AISI Type 316L. The chemical composition of the steel was shown in Table 1. Low
cycle fatigue tests were carried out at 873K in air under completely reversed tension and compression
strain control. A total strain range of t=1.5% was applied to specimens at a strain rate of 0.1%/sec.
An extensometer composed of two heat-resistant rods of a gage length of 12 mm were used tomeasure strain and to control the strain range to be applied to each specimen tested. Fatigue tests wereinterrupted and resumed repeatedly at adequate intervals until the fracture of specimens, or the time atwhich the maximum tensile stress decreased by 25% of the steady-state peak stress following thehigh-temperature low-cycle fatigue test method provided by JIS Z 2279-1992.
2.2. Four-point probe DC potential difference method
Potential difference was measured by DC potential difference measuring system which consistsof four-point microprobe, controller (Denshijiki Industry Co., Ltd. WT-4102), X-Y automatic stage
and data-collection PC. Figure 2 shows the schematic diagram of four-point microprobe with 1-mm
spacing between the electrodes. A pair of outermost electrodes supplies DC current, and the other pairof inner electrodes measures potential difference produced. Since the electrodes and their interval aresmall, this system can measure local potential difference which changes due to the initiation andgrowth of multiple small cracks. During the stop time of fatigue tests, specimen surfaces were buffedfirst with alumina suspension to remove oxide layer, then the four-point probe scanned specimen
surfaces at a step size of 0.5 mm in the longitudinal direction x and that of 1.4 mm in thecircumferential direction Figure 3 schematically illustrates the present measurement area of 10 mmin the longitudinal direction by 9.8 mm, or 140 degrees in the circumferential direction. The length ofthe measurement area in the radial direction was set to 140 degrees, because cement that prevented
extensometer slip during fatigue tests was applied to the remaining specimen surface. The

Fig. 1

Geometry of specimens (unit: mm).

Table 1 Chemical composition of the present austenitic stainless steel SUS316L (wt%).

C
0.019

Input
I

Si
0.39

Mn
0.81

Output

Input

V

P
0.028

S
0.001

Ni
12.00

Cr
17.59

Mo
2.1

I

1mm 1mm 1mm
Fig.2

Schematic illustration of four-point microprobe.

173

Fig. 3 Measurement area for potential difference, and crack density and sizes.

S. Nakanishi, et al./ Non-Destructive Evaluation of Multiple-site Small Cracks

400

N =1

N=1000～3000

200

Nf=3902

0
-200
-400

Peak/valley stress, MPa

Stress, σ, Mpa

400

Nf

200

0

-200

-400
-1

-0.5

0

0.5

1

1

100

1000

10000

Number of cycles, N

Strain, ε, %Fig. 4 Variations in stress-strain curves duringhigh-temperature low cycle fatigue of SUS316L.

10

Fig. 5 Time variation of peak/valley stresses duringhigh-temperature low cycle fatigue of SUS316L.

measurement area covers about 40 % of the specimen surface, and enough number of cracks wereobserved to determine statistical distributions of cracks and those of potential differences in thespecimen. The total number of measured points was 168 for each specimen inspected. The DC electric
current applied was 0.4 A or 0.8 A.
2.3. Crack density
The densities of multiple-site small cracks were measured by scanning laser microscopy during
the stop time of fatigue tests. Crack density ρ at a point (x, ) on a specimen surface was defined as
the number of cracks crossing a longitudinal line segment of 1 mm with the point (x, ) placed at thecenter of the line segment connecting points (x-0.5, ) and (x+0.5, ).

3.
3.1.

Results and discussion
High-temperature low cycle fatigue tests

Figure 4 shows an example of stress-strain curves observed in the present high-temperature low
cycle fatigue tests. Figure 5 shows a relationship between peak/valley stresses and number of strain
cycles N. Peak/valley stresses decreased gradually with increasing N and abruptly decreased justbefore final fracture. Figure 6 shows the photomicrographs of surface changes of the specimens tested.
Crack initiations were observed after N/Nf=0.26. At N/Nf=0.38~0.90, additional crack initiations were
scarcely observed, whereas crack growth accompanied by coalescence with other cracks were
frequently observed. Finally, a main crack was formed to cause fracture of specimens at N/Nf=1.
3.2.

Crack density

Figures 7 (a) through (c) show examples of histograms of crack density ρ. The solid lines in the
figures indicate theoretical Poisson distributions Po(ρa) calculated by using the mean crack density ρa.
The value of ρa increased with increasing number of strain cycles, and the values of ρa at N/Nf=0.38～
1 were larger than that at N/Nf=0.26. Figures 6 (b) and (c), however, reveal virtually no additional
crack initiation at N/Nf=0.38~1. These observations indicate that the increase of the mean crack
density ρa at N/Nf≧0.38 was mainly due to the growth and coalescence of the cracks.
The 2 goodness-of-fit tests reveal that crack density ρ was regarded to follow a Poisson
distribution at a significance level of α=10% at N/Nf=0.26. At N/Nf=0.38~0.9, however, thesignificance level at which the crack density was regarded to follow Poisson distributions decreased
down to α=0.1%, and increased a little to α=5% at N/Nf=1. These results imply that cracks initiatedindependently of one another at random sites at N/Nf=0.26, whereas that, at N/Nf≧0.38, additional
cracks scarcely initiated and the existing cracks grew and coalesced with one another so that the174

S. Nakanishi, et al./ Non-Destructive Evaluation of Multiple-site Small Cracks

0.1mm

θ

0.1mm

θ

0.1mm

θ

x
x
(a) N/Nf=0.26(b) N/Nf=0.64(c) N/Nf=1
Laser photomicrographs showing surface change during high-temperature fatigue of SUS 316L.

40

Significance level : α=10%Po(1.6)

30

20
10
0

0

2

4

6

8

10

50

40

Significance level : α=0.1%

Po(3.5)

30
20
10

0

0

Crack density, ρ, 1/mm

50
40
30
20
10
0

4

6

8

10

50

Significance level : α=5%40Po(4.0)

30
20
10

0
0
2
4
6
8 10
Crack density, ρ, 1/mm

Crack density, ρ, 1/mm(a) N/Nf=0.26(b) N/Nf=0.64(c) N/Nf=1
Variations in histograms of crack density during high-temperature fatigue of SUS 316L.

Significance level : α=10%N(1.00, 0.032)

0.6
1
1.4
Normalized potential diff., V/V0

Probability density, %Probability density, %Fig. 72

Probability density, %

50

50
40
30
20
10
0

Significance level : α=10%N(0.98, 0.072)

0.6

1

1.4

Normalized potential diff., V/V0

Probability density, %Probability density, %Fig. 6

Probability density, %

x

50
40
30
20
10
0

Significance level : α=1%N(0.96, 0.162)

0.6

1

1.4

Normalized potential diff., V/V0(a) N/Nf=0.26(b) N/Nf=0.64(c) N/Nf=1
Fig. 8 Variations in histograms of normalized potential difference during high-temperature fatigue of SUS
316L (I=0.8 A).

degree of the randomness in the crack sites was reduced.
The crack density  defined in the present paper depends not only on the number of cracks buton their surface lengths. Even if cracks grow without change in the number of the cracks, the crack
density can increase. The crack density defined in this paper can be affected by the initiation andgrowth of cracks.
3.3.

Potential difference

Figures 8 (a) through (c) show examples of histograms of normalized potential difference V/V0
obtained at I=0.8A, where V0 is average potential difference measured before the fatigue test of eachspecimen. The solid lines in the figures indicate theoretical normal distributions N(a, σV2) calculated
by using the mean a and the standard deviation σV of V/V0. In early stage of fatigue, the value of V/V0
varied very little, and varied widely with increasing N/Nf. At N/Nf=0～0.90, the normalized potential
difference V/V0 was regarded to follow normal distributions at a significance level of α=10%. At
fracture, i.e., N/Nf=1, V/V0 was regarded to follow a normal distribution at α=1%. Measurements ofthe potential difference were made at I=0.4A in some of the specimens tested, and almost the same
results for the statistical distributions of V/V0 were obtained.
The value of σV increased with increasing number of strain cycles, whereas the value of aremained almost a constant value of 1.0 throughout the entire life cycle. These results imply that the175

S. Nakanishi, et al./ Non-Destructive Evaluation of Multiple-site Small Cracks① 0 ≤ x ≤ 0.4② 0.8 ≤ x ≤ 1.2③ 1.6 ≤ x

V

V

V

x

Slit（Electrical discharge machining）
Length: 15mm
Wise: 0.3mm
Depth: d (0.1, 0.5, 1.0)0 1 x
ex. x=0 (mm)Potential
μV
difference VV,V
Potentialdifference,

0

0

1 2 x
ex. x=1 (mm)

1 2 3 x
ex. x=2 (mm)

0

300

②

200

100

0

③

①
d = 0.1
d = 0.5
d = 1.0
1

2

3

4

x mm
x,
mm
Fig. 9 Variation of potential difference across an artificial single surface crack with the relative positionof the four-point probe to the crack: the figure shows the right half of the variation profile, since thevariation is symmetric with respect to the origin of the local coordinate, i.e., x=0.

variation of σV characterizes the statistical distributions of V/V0 which reflect the growth behavior of
multiple-site small cracks.
Figure 9 shows the right half of the variation of potential difference across an artificial surface
crack, which is symmetric with respect to the origin of the local coordinate, i.e., x=0, with the relative
position of the four-point probe to the crack. In the cases where a pair of inner voltage measuring
needles of the probe stride over the crack, the potential difference V increases drastically as one of theneedles approaches to the crack flank (region ①). The potential difference V also increases
drastically as one of the outer current supplying needles approaches to the crack when the probemoves away from the crack (region ③). In the case where a current supplying needle and a voltage
measuring needle are placed on either side of the crack (region ②), the potential difference measured
here is lower than the remote potential difference value V0, which is equal to the average potential
difference measured before the fatigue test of the specimen. For a shallow crack, the variation in thepotential difference across the crack is so small that the potential difference value V remains almost its
remote value V0 across the crack. As a crack grows in surface length and in depth, the excess value of
V increases in regions ① and ③, whereas the reduced value of V decreases in region ②. The
regions of the excess potential difference becomes wider as the crack grows. In early stages of thepresent fatigue processes, when cracks were small both in surface length and in depth, the values ofthe potential difference measured by the multipoint microprobes did not vary so much around thevalue of the remote potential difference V0. In later stages of the fatigue processes, the sizes of thecracks differ greatly due to the power-law growth and the accelerated growth by coalescence withother cracks so that the values of V vary so much around V0 and the variance of V/V0 becomes larger.
Figures 10 (a) and (b) depict photomicrographs of multiple-site small cracks observed on thelongitudinal sections of specimens interrupted at N=2000 and fractured at Nf=5432, respectively.
Figures 11 (a) and (b) show crack depths measured at different longitudinal positions by using
photogrammetry procedures. Crack depth measured on the longitudinal sections in the interrupted
specimen ranged from 0.009 to 0.110 mm, whereas that in the fractured specimen from 0.012 to 1.910
mm. Figures 11 (a) and (b) demonstrate that most of the cracks measured were larger in the fractured
specimen than in the interrupted specimen.
3.4.

Prediction of residual fatigue life
Figure 12 shows the variations in standard deviation of the normalized potential difference V/V0,176

S. Nakanishi, et al./ Non-Destructive Evaluation of Multiple-site Small Cracks

σV, obtained at I=0.4 and 0.8A, and average crack density ρa with increasing N/Nf. The rate of increasein ρa was high in the initial stage of fatigue and gradually lowered in the latter stage, since crack
growth accompanied with coalescence was predominant in the latter stage of fatigue. The rate ofincrease in σV, however, became higher with increasing number of strain cycles and exhibited marked
increase at the last stage of fatigue, i.e., N/Nf≧0.9 due to the accelerated growth of the main crack.
Figure 12 implies that the present fatigue process in which multiple-site small cracks were involved
can be divided into four stages; i.e., Stage I (incubation stage), Stage II (initiation stage), Stage III(growth and coalescence stage) and Stage IV (accelerated growth stage). Stages I and II cannot beclearly distinguished by the V/V0 vs. N/Nf curve but by the 0 vs. N/Nf curve. The incubation time forcrack initiation during which no crack initiation was expected to occur was found as N/Nf≒0.12,
because the crack density remained zero until the N/Nf value reached approximately 0.12. Stages II
and III were divided according to the laser photo-micrographic observation that cracks started

0.1mm

0.1mm

22
1.2
1.8
1.8
1
1.6

0.8
0.8
1.4
0.6
0.6
1.2
0.4
0.4
1
0.2
0.2
0.8
000
00

2
2
2

4
4

6
6

8
8

10

12

14

Crack depth measured
on long. section, d, mm

Crack depth measured
on long. section, d, mm(a) N=2000 (interrupted)(b) Nf=5432 (fractured)Fig. 10 Laser photomicrographs of cracks observed on the longitudinal sections of two specimens; one
was interrupted at N=2000 and the other fractured at N=5432.

10 12 14Longitudinal position, x, mm

22
1.2
1.8
1.8
1
1.6

0.8
0.8
1.4
0.6
0.6
1.2
0.4
0.4
1
0.2
0.2
0.8
000
0
0

2
2
2

4
4
4

6
6
6

8

8
8

10

12

14

10 12
12 14
14
10

Longitudinal position, x, mm

0.35

5Applied Current
I=0.4A
I=0.8A

0.3
0.25

4
3

0.2

Ⅰ

0.15

Ⅱ

Ⅲ

2

0.1
0

1

Ⅳ

0.05
0

0.2

0.4

0.6

0.8

1

0

Mean crack density, ρa, 1/mm

Standard deviation of V/V0, σV(a) N=2000 (interrupted)(b) Nf=5432 (fractured)Fig. 11 Distributions of crack depths measured in the longitudinal sections of the two specimens shown in
Fig. 10.

N/Nf
Fig. 12 Variations in standard deviation of the normalized potential difference V/V0, σV, and the averagecrack density ρa indicating that the present fatigue process can be divided into four stages.

177

S. Nakanishi, et al./ Non-Destructive Evaluation of Multiple-site Small Cracks

coalescing with one another.
The detection of the onset of the final Stage IV by four-point probe DC potential difference
method can non-destructively predict the residual life of fatigue in which multiple-site small cracks
are involved. Fig.12 suggests that the residual life prediction can be made at N/Nf≒0.9 whichcorresponds to 390 to 810 cycles, or to the actual time duration of 3 to 6 hours. For actual structures
or machines, the time duration corresponding to 10 % of fatigue life is much longer so that there isenough time left to take countermeasures against fatigue fracture according to the prediction made by
the present method.

4.

Conclusion(1) Multiple-site small cracks initiated on the surfaces of specimens due to high-temperature low
cycle fatigue, and the sizes of the small cracks varied with the number of strain cycles according
to their growth and coalescence.
(2) Higher growth rate of larger cracks widened the size difference among multiple-site cracks tobring about much larger variation in local potential difference in the latter stage of the fatigue
process.
(3) The detection of the onset of the final Stage IV by four-point probe DC potential difference
method can non-destructively predict the residual life of fatigue in which multiple-site small
cracks are involved.

Acknowledgement
The authors would like to express their gratitude to Mr. M. Iwata at R&D Department, Denshijiki
Industry Co., Ltd. for his assistance for the four-point probe DC potential difference measurement.

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[2]
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[4]

[5]

[6]

[7]

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