E-Journal of Advanced Maintenance Vol. 6-4 (2015) 107-117
Japan Society of Maintenology

Main Factors for Fatigue Failure Probability of Pipes Subjected to Fluid
Thermal Fluctuation
Hideo MACHIDA1,*, Masaaki SUZUKI2 and Naoto KASAHARA2
1

TEPCO Systems Corporation, SHIBUSAWA CITY PLACE EITAI, 2-37-28 Eitai, Koto-ku, Tokyo
135-0034, Japan
2
The University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo 113-8656, Japan
ABSTRACT
It is very important to grasp failure probability and failure mode appropriately to carry out risk reduction
measures of nuclear power plants. To clarify the important factors for failure probability and failure mode ofpipes subjected to fluid thermal fluctuation, failure probability analyses were performed by changing the valuesof a stress range, stress ratio, stress components and threshold of stress intensity factor range. The importantfactors for the failure probability are range, stress ratio (mean stress condition) and threshold of stress intensity
factor range. The important factor for the failure mode is a circumferential angle range of fluid thermal
fluctuation. When a large fluid thermal fluctuation acts on the entire circumferential surface of the pipe, theprobability of pipe breakage increases, calling for measures to prevent such a failure and reduce the risk to theplant. When the circumferential angle subjected to fluid thermal fluctuation is small, the failure mode of piping
is leakage and the corrective maintenance might be applicable from the viewpoint of risk to the plant.
KEYWORDS

ARTICLE INFORMATION

Fracture Mechanics, Fatigue, Thermal Stress, Probabilistic Method, Crack
Growth, Piping, Nuclear Power Plant

Article history:
Received 30 July 2014
Accepted 26 January 2015

1.

Introduction

When fluid thermal fluctuation or thermal stratification of the coolant occurs in piping, cracks
due to thermal fatigue are initiated and a leak or a pipe breakage may be caused by their growth. The
influence of the piping failure on the risk to the nuclear power plants (NPPs) like core damage
frequency, etc., greatly depends on its failure modes (leak/break). Generally, the influence of a pipe
breakage on the risk to the NPPs is larger than that of leakage. The failure probability and the failuremodes (leak/break) of piping also greatly depend on loading conditions, material characteristics, etc.
Since the structural integrity evaluation to fluid thermal fluctuation is a fluid-structure coupling
problem, it is very complicated, its variation range of prediction is very wide, and there are many
influence factors. Although probabilistic evaluation is effective to quantify the influence of variationsof the factors, the random variable used in the evaluation should be selected for realistic/rational
evaluation. Therefore, it is necessary to clarify the main factors of a complicated fluid-structure
coupling problem. The probabilistic fracture mechanics (PFM) code is one of the tools which are able
to evaluate the failure modes and the failure probability of pipes subjected to thermal loadings.
Therefore, PFM analyses were carried out parameterizing the conditions related to thermal fatigue andcrack growth, and the influence of their conditions on the risk to the NPPs was evaluated. Based onthese parametric analysis results, the relationship between main factors and failure probability or
failure modes was examined and effective risk reduction measures were proposed.

2.

Clarification of Main Factors
To narrow down the factors to be evaluated, the influence of fluid thermal fluctuation on the*

Corresponding author, E-mail: machida-hideo@tepsys.co.jp

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

107

H. MACHIDA, et al./ Main Factors for Fatigue Failure Probability of
Pipes Subjected to Fluid Thermal Fluctuation

integrity of piping is clarified. Fluid thermal fluctuations downstream of mixing-tees and thermal
stratification interface by the cavity flow are representative causes of thermal fatigue. The
characteristics of loadings and the initiation/growth of cracks in these regions are shown in Table 1.
The temperature change caused by the thermal stratification is generally slow and the difference of
fluid temperature is relatively large. Therefore, the temperature range in the component is also wide
and its period is relatively long, and the whole pipe thickness responds to the temperature change ofthe fluid. On the other hand, in the case of the fast fluid thermal fluctuation downstream of themixing-tees, the structure's response to the temperature t is limited to the surface.
Table 1 Features of thermal load and crack growth
Items
Load type

TemperaturechangeThermal stressInitiated crack
Cracks develop on the

Crack growth

ThermalSlow and large

Large bending stress,

stratification

amplitude

small peak stress

ThermalRapid and small

Small bending stress,

Cracks develop partiallywith load cycles

fluctuation

amplitudelarge peak stresson the inner surface∆K < ∆Kth: crack is

entire circumferential
surface

Crack grows with load
cycles∆K ≥ ∆Kth: crack grows

arrested

Slow temperature change due to thermal stratification travels the entire thickness of pipes,
leading to an increased large bending stress, and a relatively small peak stress near the surface. Here,the peak stress is a stress generated according to the local temperature distribution near the internalsurface, and is the increment of the stress added to a bending stress. In the case of such stress
distribution, a crack might grow in depth. On the other hand, as for the stress due to small temperaturechange for a short period (fluid thermal fluctuation), temperature travel range is limited to the vicinityof the pipe surface. Therefore, the main stress component is peak stress, and bending stress isrelatively small. Crack growth due to this kind of peak stress is also limited to the vicinity of the pipe
surface, and the crack growth is arrested if the stress intensity factor range ( ∆K ) is less than thethreshold of stress intensity factor range ( ∆K th ) of the pipe material.
When a large stress is generated in the entire circumferential area of the pipe due to temperaturechange such as during thermal stratification, fatigue cracks are initiated all over the pipe surface,which coalesce into a crack running around the entire circumference of the pipe, causing pipe
breakage. When the circumferential angular range of pipe surface subjected to fluid thermal
fluctuation is limited to a certain angle, the cracks that are initiated are only partial and not
circumferential. Even in case of a large crack growth, the crack is likely to penetrate through thepipe wall only locally and the probability of a pipe breakage is very small.
Although the examination for both thermal stratification and thermal fluctuation has been carriedout in the series of thermal fatigue study as a part of the Japan Aging Management Program on
System Safety (JAMPSS) sponsored by Nuclear Regulation Authority (NRA), thermal fluctuation was
selected as the subject of this examination because the examination of loading conditions wascompleted. The influence of temperature difference of fluid, stress ratio, stress components(membrane, bending and peak), the threshold of stress intensity factor range, and peak stress
distribution and the influence the temperature fluctuation range in circumferential direction on failure
probability and failure mode (leak/break) was evaluated.

3.

Crack Initiation Probability Assessment

The failure probability of pipes due to thermal fatigue is evaluated according to the steps shownin Fig. 1. It is defined as the crack initiation, when the cumulative fatigue damage ( D f ) calculated by108

H. MACHIDA, et al./ Main Factors for Fatigue Failure Probability of
Pipes Subjected to Fluid Thermal Fluctuation

the following formulas exceeds 1.0.

Fig.1 Evaluation flowchart of failure probability due to thermal fatigue

Fi
i N fiD f = to ∑(1)

where F is the number of loading cycles per year [y-1], N f is the fatigue life given by the best fit
fatigue curve [-] and t o is operation year [y]. The variation in fatigue life is taken into consideration
as shown in Table 2 in this evaluation.

Items

Table 2 Crack initiation probability assessment conditions
ValuesRemarks

Material of pipe
Diameter of pipe, Do
Thickness of pipe, tTemperature
Temperature difference in hot/cold water,∆T

SUS30476.3 mm
7 mm
330 °C

Applied stress, ∆σ b , ∆σ p

Fig. 2 (for ∆T = 150 °C )Fatigue life, N f

Mean: calculated by thebest fit fatigue curve
defined by the designcodes [1].
Standard deviation: 0.47

150, 75, 35 °C―――
For fatigue life assessment.
Parametric analyses were carriedout for three cases.
Stress in ∆T = 75 or 35 °C case is
1/2 or 7/30 of stress shown in
Fig. 2 respectively.

Log-normal distribution.

The fatigue life N f is evaluated based on the design codes of fast breeder reactors [1]. The
probability of crack initiation, growth, penetration, and fracture are evaluated using PFM code
“PEPPER” [2]. PEPPER is the nonlinear PFM code aimed for application to the failure probability
evaluation of piping, and was developed by TEPCO Systems Corporation. First, the relationshipbetween crack initiation probability and operating years is calculated in this evaluation. Next, the109

H. MACHIDA, et al./ Main Factors for Fatigue Failure Probability of
Pipes Subjected to Fluid Thermal Fluctuation

growth of the crack is evaluated, and the relationship between conditional leak/break probability andoperation years is calculated. The failure probability is computed by multiplying conditional leak or
break probability with crack initiation probability.
The influence of some factors on the failure probability is examined in order to grasp theimportant factors. The factors which should pay attention to keep integrity of the NPPs are chosenfrom this result. Conditions of crack initiation probability assessment are summarized in Table 2.
Fluid temperature fluctuation at piping mixing area has almost the identical frequency characteristics
when their flow patterns are the same. Above characteristics can be described by the power spectrum
density function of fluid temperature normalized by temperature range before mixing and Strouhal
number. Furthermore, bending and peak thermal stress frequency response function to fluid
temperature was developed under constant Biot number [3]. By using these two functions, the power
spectrum density function of thermal stress can be obtained under the certain flow pattern,
temperature range (ex. 150°C) and Biot number. Inverse fast Fourier transform (FFT) can convert thepower spectrum density function of thermal stress to the time history, which is decomposed tohistogram of bending and peak stress considering their identical time by the rain flow counting
method. From above reason, the histogram for 150°C temperature range was obtained under thecertain flow pattern and Biot number. Biot number is a function of heat transfer coefficient, which isone of the influential parameters. Sensitivity analysis with treatment of heat transfer function asprobabilistic parameters was achieved separately. The relationship between stress ranges andfrequency them is shown in Fig. 2, and this histogram is used as an input of PFM analysis. The stressranges shown in Fig. 2 are for the case that temperature difference of hot/cold water is 150°C. Threecases of temperature difference between hot and cold fluid (150, 75 and 35°C) are assumed for crack
initiation and propagation analyses. Here, 35°C is the allowable limit temperature difference inGuideline for Evaluation of High-Cycle Thermal Fatigue of a Pipe [3], 150°C was set up from the
maximum temperature gradient when a residual heat removal system operates and 75°C is the half ofit. For the case that temperature difference is 75°C or 35°C, 1/2 (=75/150) and 7/30 (=35/150) of thestress ranges shown in Fig. 2 is assumed in the assessments.

Fig. 2 Histogram of thermal stresses due to thermal fluctuation

Material of piping is assumed as SUS304 in JIS Standard and the outside diameter and thicknessof pipe are 76.3 mm and 7 mm, respectively. Evaluation period is 40 years and operation ratio(operation stop period for periodic inspections, etc.) is not taken into consideration. The fatigue life
( N f ) is expressed by the following log-normal distribution [4]. The standard deviation of this fatigue
curve is 0.47 for the fatigue life [5].
1log10 N f

= A0 + A1 log10 ∆ε t + A2 (log10 ∆ε t ) 2 + A3 (log10 ∆ε t ) 4

110

(2)

H. MACHIDA, et al./ Main Factors for Fatigue Failure Probability of
Pipes Subjected to Fluid Thermal Fluctuation

A0 = 1.621827 − 4.567850 × 10 −8 T 2 R
A1 = 1.131346 − 8.665061 × 10 −9 T 2
A2 = 3.439663 × 10 −1
A3 = −1.374387 × 10 −2 + 4.910723 × 10 −5 R
R = log10 ε

where T is temperature [°C], ε is strain rate [mm/mm/sec], ∆ε t is total strain range [mm/mm].
In this evaluation, the evaluation temperature of the fatigue life was assumed to be 330 °C. Crack
initiation probabilities calculated from thermal stress conditions are shown in Fig. 3. Cumulative
crack initiation probability in all cases is extremely small, and especially those in 35°C and 75°C
temperature difference conditions, it is 0. Even if the temperature difference is 150°C, it is lower than
10-250, which is negligible from an engineering viewpoint. These results suggest that the possibility ofcrack initiation due to temperature fluctuation is very low and it is very important to prevent
generation of the defect during manufacturing.
-240

10

Probability of crack initiation [-]∆T=150 deg.C
Crack initiation probability in∆T=35 and 75 deg.C is 0.
-260

10

10

-280

10

-300

0

5

10 15 20 25 30
Operation time [year]

35

40

Fig. 3 Conditional probability of crack initiation

4.

Failure Probability Analysis

The failure probability is analyzed using the same pipe dimensions and loading conditions as
crack initiation probabilities assessment, as mentioned in Section 3. Since the initiation crack size dueto thermal fluctuation is not clear, the depth of initiation crack is set to 0.01, 0.5 and 1.0 mm, and an
aspect ratio (crack depth / crack length) is assumed to be 0.5 in this evaluation. The fatigue crack
growth rate shown below is used in this analysis. This formula is for austenite stainless steel in BWR
environment defined in the Fitness-For-Service (FFS) Codes in JSME [6].

(∆K )
da
= 2.9 × 10 −12 t r0.5
dN
(1 − R )2.12
3.0

(3)

∆K = K max − K min （if R ≥ 0 ）∆K = K max （if R < 0 ）111

H. MACHIDA, et al./ Main Factors for Fatigue Failure Probability of
Pipes Subjected to Fluid Thermal Fluctuation

R=

K min
K max

where da / dN is crack growth rate [m/cycle], K max is maximum stress intensity factor [MPa m ],K min is minimum stress intensity factor [ MPa m ], R is stress ratio and t r is loading rise time[sec] (it is assumed to be 1000 sec in this study). Probability density function for crack growth rate is
log-normal distribution with mean value of coefficient is 2.9 × 10 −12 and standard deviation is 0.54.
These distribution parameters were calculated from the statistical work of the data shown in the FFS
Codes. Conditions for crack stability assessment (limit load assessment method) are summarized inTable 3.
Table 3Crack stability assessment conditions

Items
Primary membrane stressPrimary bending stress
Secondary bending stressValues
14.4MPa
5.0 MPa
10.0 MPa

Remarks
Internal pressure (7.0 MPa)
Dead load
Thermal expansion stress

The relationship between cumulative failure probability and fluid thermal fluctuation range isshown in Fig. 4. In this case, the initial semielliptical crack depth was set as 0.01mm, and fully
reversed loading condition (stress ratio: R=-1) is assumed. When temperature difference is 150°C, thefailure probability for 40 years of operation is almost 1.0, although a very small crack is assumed. The
value of failure probability implies that the almost all cracks penetrate rapidly if a crack is initiated orexists, and hence, inservice inspection (ISI) is not effective in this case. For the case when thetemperature difference is 75°C, cumulative failure probability for 40 years of operation is about 0.4.
Although the examination interval defined in the FFS Codes is ten years, the cumulative failure
probability for the first ten years is about 2×10-2. This value is insufficient as reliability of boundary
components of nuclear power plants, and hence, ISI is not effective in this case too. In contract, forthe case when the temperature difference is 35°C, cumulative failure probability for 40 years ofoperation is 4.8×10-6, which is a sufficiently low value compared to the previous ones. In case of fluid
thermal fluctuation, failure of piping may be prevented if suitable inservice inspection or monitoringis carried out. These results suggest that more precise inspection and monitoring are important toprevent failure of boundary piping.

Conditional probability of failure [crack -1]

0

10
-2
10
-4
10
-6
10
-8
10
-10
10
-12
10
-14
10
-16
10
-18
10
-20
10
-22
10
-24
10
-26
10
-28
10
-30
10

a0 = 0.01 mm
c0 = 0.01 mm∆T = 35 deg.C∆T = 75 deg.C∆T = 150 deg.C
05

10 15 20 25 30
Operation time [year]

35

Fig. 4 Conditional probability of failure

112

40

H. MACHIDA, et al./ Main Factors for Fatigue Failure Probability of
Pipes Subjected to Fluid Thermal Fluctuation

5.

Influence of Typical Factors

In order to grasp the influence of high cycle thermal fatigue on risk to the plant, the importanceof some factors on the failure probability or failure mode (leak/break) of piping was examined.
Factors considered in this study are stress ratio, fluid thermal fluctuation patterns, lower threshold ofstress intensity factor range, peak stress distribution and angular range of fluid thermal fluctuation.
5.1.

Stress Ratio

The mean stress effect by thermal expansion, an internal pressure, etc. is taken into consideration
as a stress ratio. Examples of the failure probabilities for different stress ratios ( R ) are shown in Fig.
5. In this figure, the relationship between the stress ratio and a stress intensity factor is as follows.
R = 0 : K min = 0 , K max = ∆K

R = −1 : K min = −∆K∆K, K max =22

Conditional probability of failure [crack -1]

0

10
-2
10
-4
10
-6
10
-8
10
-10
10
-12
10
-14
10
-16
10
-18
10
-20
10
-22
10
-24
10
-26
10
-28
10
-30
10

∆T = 75 [deg. C]
a0 = 0.01 mm
c0 = 0.01 mm
R=0
R = -10

5

10 15 20 25 30
Operation time [year]

35

40

Fig. 5 Effect of stress ratio

The conditions of this analytical case are an initial crack depth of 0.01 mm , an initial crack
length of 0.02 mm and a fluid thermal fluctuation range of 75°C. The failure probability increases as
the stress ratio increases. Therefore, estimation of the mean stress results causes from internal pressure,dead weight, thermal expansion, etc. is very important for evaluating the failure probability
appropriately. Moreover, it is suggested that improvement of stress (heat treating, peening processing
etc. which provide compressive residual stress on the inner surface of pipes) by which the stress ratio
becomes small is an effective measure.
5.2.

Stress Component

In order to grasp the influence of stress components shown in Fig. 2 on the failure probability, ahistogram expressed by the stress range and its frequency was arranged as shown Fig. 6, and thefailure probability was analyzed for each load case as shown in Fig. 7.
Generally, the frequency decreases as the stress range increases, but the frequency is small insome peculiar cases (for example, load cases 3, 8 and 13). A peak stress component in these cases is113

H. MACHIDA, et al./ Main Factors for Fatigue Failure Probability of
Pipes Subjected to Fluid Thermal Fluctuation

Fig. 6 Histogram of stresses range and its frequency
0

10

-2

10

10

0

-3

10

Conditional probability of failure [crack -1]

Conditional probability of failure [crack -1]

Fig.7 Failure probability for each load case

-4

10

R=0
∆T = 75 deg. C
a0 = 1 mm

-6

10

-8

10

c0 = 1 mm

-10

10

-12

When ∆Kth is larger than 6 MPa-m1/2,-14

a crack does not grow.

10
10

-16

∆Kth = 0 MPa-m1/2

-18

1/2

∆Kth = 2 MPa-m-20∆Kth = 4 MPa-m1/2

10
10
10

-9

10

-12

10
-15
10

R = -1∆T = 75 deg. C
a0 = 1 mm

-18

10

-21

10
-24
10

c0 = 1 mm

10

When ∆Kth is larger than 4 MPa-m1/2,

-27

-30

a crack does not grow.

10

-33

10
-36
10

∆Kth = 0 MPa-m1/2∆Kth = 2 MPa-m1/2

-39

10

-22

10

-6

10

-42

0

5

10 15 20 25 30
Operation time [year]3540a) R = 0, a0 = 1.0 mm

10

0

5

10 15 20 25 30
Operation time [year]3540b) R = -1, a0 = 1.0 mm

Fig. 8 Effect of ∆Kth on failure probability

relatively large compared with other cases. The influence of both ends in Fig. 6 (a small stress range
and high frequency, and a large stress range and low frequency) on the failure probability is small, andmoderate stress load cases have a big influence on the failure probability in general. The reason of this
aspect is as follows.
1) When the stress range is small, crack growth rate is very small especially in small crack
condition.
2) When the stress range is large, the number of crack growth cycles is very small.
The failure probability depends greatly on the frequency of loading. As load cases 3, 8 and 13 of Fig.
6 have low frequency of loading, the failure probability becomes very low. These results suggest thatin thermal loading estimation, it is important to evaluate moderate stress range of temperaturefluctuation with accuracy compared with extremely small temperature fluctuation or extremely large
temperature fluctuation.
5.3.

Threshold of Stress Intensity Factor Range
When only the surface of piping responds to the temperature change of fluid as in a high cycle

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Pipes Subjected to Fluid Thermal Fluctuation

thermal fatigue, crack growth along pipe thickness stops if stress intensity factor is small comparedwith the threshold of stress intensity factor range ( ∆K th ), and failure of piping would be negligible.
Then, the influence of ∆K th on the failure probability was assessed, and the results are shown in Fig.
8. When the mean stress is large ( R = 0 ) and the initiated crack depth (depth from the inner surface
where a crack is initiated by fatigue damage) is more than 1 mm, the crack penetrates the pipe walland the failure probability reaches 1.0 when ∆K th is 2 [MPa m ] or less, and the crack does not
penetrate pipe wall when ∆K th is 6 [MPa m ] or more. When the mean stress is small ( R = −1 ),the crack does not penetrate the pipe wall when ∆K th is 4 [MPa m ] or more. These results
suggest that preventive maintenance for decreasing the stress ratio is effective in order to stop crack
growth. Since ∆K th in the common steel is 3 to 4 [MPa m ] , depending on the stress ratio, thecrack does not penetrate even if it is initiated due to thermal fatigue.
5.4.

Peak Stress Distribution Depth

Figure 9 shows the failure probability when the peak stress distribution depth (position where thepeak stress range is zero) is assumed (1/4)t, (1/2)t, and (3/4)t from the internal surface of a pipe. Here,applied stresses are as shown in Fig. 2, and the difference in the loading condition of each case is only
distribution of peak stress. As shown in this figure, the distribution depth of the peak stress is hardly
effective against the failure probability. The reason for this is that the bending stress which is acting
simultaneously with the peak stress has great influence on the failure probability. Stress component
generated by the temperature fluctuations is quite different by frequency of temperature fluctuations.
If temperature fluctuation is slow, the thermal bending stress is produced due to through wall
temperature distribution. If temperature fluctuation is rapid, the peak stress is produced due to peaktemperature distribution in the vicinity of the surface in contact with the fluid. In order to grasp theinfluence of stress components directly, the failure probabilities when only membrane stress ( ∆σ m ),bending-stress ( ∆σ b ), or peak stress ( ∆σ p ) acts are shown in Fig. 10. The analytical conditions inthese analyses are as follows;
1) Distribution depth of peak stress is parameterized from (1/4)t to (3/4)t,2) Stress amplitude is 100 MPa,
3) The number of loading cycle is 100 times/year.
The failure probabilities of piping subjected to membrane stress or bending stress are comparable.
On the other hand, the failure probability of piping subjected to peak stress is about six figures lower
than the case of membrane stress even when the distribution depth of peak stress is 3/4t, and when the
distribution depth is (1/4)t, the failure probability decreases drastically. Even if fluid thermal0-35

a0 = 0.01 mm-2

10

Conditional probability of failure [crack -1]

Conditional probability of failure [crack -1]

10c0 = 0.01 mm-4

10∆T = 75 deg.C
R=0

-6

10

-8

10

-10

10

Peak stress attenuation depth

-12

10

(1/4)t(1/2)t(3/4)t

-14

10

0

5

10 15 20 25 30
Operation time [year]

35

40

Fig. 9 Effects of peak stress distribution

10
-40
10
-45
10
-50
10
-55
10
-60
10
-65
10
-70
10
-75
10
-80
10
-85
10
-90
10
-95
10
-100
10
-105
10
-110
10
-115
10
-120
10
-125
10

a0 = 0.01 mm
c0 = 0.01 mm
R=0∆σp = 100 MPa, (1/4)t∆σp = 100 MPa, (1/2)t∆σp = 100 MPa, (3/4)t∆σm = 100 MPa∆σb = 100 MPa
05

10 15 20 25 30
Operation time [year]

Fig. 10 Effects of stress components

115

35

40

H. MACHIDA, et al./ Main Factors for Fatigue Failure Probability of
Pipes Subjected to Fluid Thermal Fluctuation

fluctuation range is comparable, the failure probability changes greatly with the stress components
and the failure probability is very low when only the surface of piping is influenced by fluid
temperature fluctuation (when the main stress component is peak stress).
5.5.

Circumferential Thermal Fluctuation Area

In NPPs, since installation of leak detection system and daily patrol are required in order toprevent coolant loss, if a rapid fracture of piping does not occur, the safety of a plant is kept at highlevel. For this reason, the consequence of breakage of piping is severe compared with leak. Assumingthat a crack occurred in fluid thermal fluctuation area in the circumferential direction, the relationshipbetween this area and failure mode was examined. The relationship between the initial crack length (itis equivalent to the circumferential thermal fluctuation area) and failure mode is shown in Fig. 11. As
shown in the figure, when the initial crack length is shorter than 180°, the failure mode is leakage.
Although the failure mode depends on the applied stress conditions used in crack stability evaluation,
the possibility of pipe breakage by fluid thermal fluctuation is very low downstream of mixing tees,
because the fluid thermal fluctuation area is generally limited to a small circumferential angle in thisportion. However, the break probability can become relatively high when the entire circumferential
direction of a pipe is subjected to temperature change like the cavity flow.

Fig. 116.

Effects of circumferential thermal fluctuation area

Conclusions

Case studies to clarify the relationship between the main factors and failure probability or failuremode for piping subjected to fluid thermal fluctuation were conducted. This examination result gives
useful information to clarify rational countermeasure for risk reduction and to evaluate the influenceof thermal fatigue on plant risk accurately. Fluid thermal fluctuation range, stress ratio (the meanstress effect), and lowest limit of stress intensity factor range are important for failure probability.
When the range which affects the fluid thermal fluctuation is below the semicircle of a pipe, the pipe
never breaks even if a crack penetrates, and the influence on the risk to the plant is expected to besmall. Since this examination is case studies on limited conditions, future subjects are expansion of
the evaluation conditions and the realistic evaluation based on the actual plant conditions.

Acknowledgement
This work has been carried out as a part of the Japan Aging Management Program on System
Safety (JAMPSS) sponsored by Nuclear Regulation Authority (NRA).

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H. MACHIDA, et al./ Main Factors for Fatigue Failure Probability of
Pipes Subjected to Fluid Thermal Fluctuation

References
[1]
[2]
[3]
[4]
[5]
[6]

Codes for Nuclear Power Generation Facilities —Rules on Design and Construction for Nuclear Power
Plants—, JSME S NC2-2012.
JWES, Probabilistic Fracture Mechanics for Risk-Informed Activities‐Fundamentals and Applications‐(Ver.1.01), JWES-AE-1204, (2012).
JSME, Guideline for Evaluation of High-Cycle Thermal Fatigue of a Pipe, JSME S 017-2003, (2003).
Explanation of Elevated Temperature Structural Design Standard for Monju Material Strength Standard (inJapanese), PNC TN241 85-08, (1985).
Material Test Data of SUS304 (in Japanese),, PNC TN9450, 2000-001, (1999)
Codes for Nuclear Power Generation Facilities —Rules on Fitness-for-Service for Nuclear Power Plants—,
JSME S NA1-2012, (2012).

117