E-Journal of Advanced Maintenance Vol.6 (2014) 14-23
Japan Society of Maintenology

Development of thermal fatigue evaluation methods of piping systems
Naoto KASAHARA1,*, Takamoto ITOH2, Masakazu OKAZAKI3, Yukihiko OKUDA4, Masayuki
KAMAYA5, Akira NAKAMURA5, Hitoshi NAKAMURA6 , Hideo MACHIDA7 and Masaaki
MATSUMOTO8
1

The University of Tokyo, School of Engineering, 7-3-1, Bunkyo-ku, Tokyo, 113-8656 Japan
Ritsumeikan University, 3 Nagaoka University of Technology, 4 TOSHIBA Corporation,
5
Institute of Nuclear Safety System, Incorporated, 6 ITOCHU Techno-Solutions Corporation,
7
TEPCO Systems Corporation, 8Mitsubishi Research Institute, Inc.
2

ABSTRACT
Nuclear piping has various kinds of thermal fatigue failure modes. Main causes of thermal loads are structural
responses to fluid temperature changes during plant operation. These phenomena have complex mechanisms
and many patterns, so that their problems still occur in spite of well-known issues. The guideline of the JSME
(Japan Society of Mechanical Engineering) for estimation of thermal fatigue failures in piping system is
employed as Japanese regulation. To improve this guideline, generation mechanisms of thermal load and fatigue
failure have been investigated and summarized into the knowledgebase. And numerical simulation methods toreplace experimental based methods were studied.
Furthermore, probabilistic failure analysis approach with main influence parameters was investigated to be
applied for the plant system safety. Thus, based on the knowledge, estimation methods revised from the JSME
guideline were proposed.
KEYWORDS

ARTICLE INFORMATION

Fatigue, Thermal Stress, Thermal Hydraulics, Numerical Simulation, Piping,
Nuclear Reactor Plant

Article history:
Received 23 December 2013
Accepted 7 May 2014

1.

Introduction

In spite of well-known issues from past time, thermal fatigue failures occur in nuclear power
plants [1]. One of the most major reasons is that the issue is caused by complex interactive
phenomena among thermal hydraulics, structural physics and material properties.
Kinds of thermal fatigue phenomena experienced in the world can be summarized as Fig. 1.
From view point of thermal loads, they are categorized into high and low temperature fluid mixing,
thermal stratification, system thermal transients and others[2]. Among them, “a. High cycle thermal
fatigue by temperature fluctuation at mixing zone between cold and hot fluid” and “b. Thermal fatigue
by temperature stratified layer at stagnant branch pipe” (Fig.2) are recognized as important modes inviewpoint of their frequency and difficulties of counter measurements, and their evaluation procedures weredeveloped as the JSME(Japan Society of Mechanical Engineering)'s Guideline for Evaluation ofHigh-Cycle Thermal Fatigue of a Pipe [2].
Japanese regulation for thermal fatigue issues mainly based on the JSME guideline．Recently,
this guideline is required to have reasonable safety margin and accountability. Clarification of
influence of fatigue issues on plant system safety is expected to the guideline due to the
Fukushima-daiichi nuclear plant accident．
From above background, the NRA (Nuclear Regulation Authority) project has launched. The
objectives of this project are the clarification of thermal loads by fluid temperature change and failure
mechanism, the proposals of rational evaluation methods for the JSME guideline, the development of
numerical simulation methods of thermal fatigue phenomena and the study of failure probability
evaluation methods for plant system safety.
*

Corresponding author, E-mail: kasahara@n.t.u-tokyo.ac.jp

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

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N. Kasahara, et al./ Development of thermal fatigue
evaluation methods of piping systems

Cyclic thermal
loadsHigh and low
temperature
fluid Mixing

Random temperaturefluctuation

Thermalstratification

Cavity flow into
stagnant space

Hot and cold spot
trembling

Inappropriate operation
Ground leak at valves

High cycle fatigue

High cycle fatigue
Low cycle fatigue

Sheet leak at valves
Low cycle fatigue
Ratchet deformation

System thermal transient
Etc.

Fig.1 Classification of thermal loads and induced failure modes in nuclear pipes

Mixing Zone
Hot fluid

Main Pipe

Cracksat elbow

Branch Pipe（stagnant)Cold fluid
A. High cycle thermal fatigue bytemperature fluctuation at mixing
zone between cold and hot fluid

B. Thermal fatigue by temperature
stratified layer at stagnant branch pipe

Fig. 2 Typical thermal fatigue failure modes dealt with JSME guideline

2.

Clarification of mechanism on loadings and failure

2.1. Loading mechanism“a. High cycle thermal fatigue by temperature fluctuation at mixing zone between cold and hot fluid”
Thermal load and failure mechanism at mixing zone of hot and cold fluids can be decomposed
into elemental processes as Fig.3. Dominant parameters during loading process from (A) to (D) areattenuation factors. Therefore clarification and consideration of their mechanism are main issues torationalize evaluation methods. Authors have studied frequency dependent attenuation mechanism([4] for example). At the stage (E), multi-axial loadings and valuable stress amplitudes become main
factors especially for thermal fatigue strength. Conditions at weldment, surface roughness anddeterioration due to aging have influence on fatigue strength. These are studied though international
cooperation especially with France who experienced thermal fatigue failure[1]．
“b. Thermal fatigue by temperature stratified layer at stagnant branch pipe”
Thermal load and failure mechanism at elbows of stagnant branch pipes due to temperature
stratification layer have not been clarified compared with above mixing pipes. When main pipes
connect to stagnant branch pipes, parts of main flow can invade into the branch pipe (so called cavityflow). In the case that main flow temperature is higher than branch pipes, temperature stratified layer
appear and their oscillations induce thermal fatigue on the branch pipes. Especially, it was known that15

N. Kasahara, et al./ Development of thermal fatigue
evaluation methods of piping systems

significant unstable oscillations and large fatigue damage can be induced when stratified layer exists
around elbows. Above mechanism was roughly understood as Fig.4. Current study focusses on
evaluation of stratified layer location [5].
Process(D)(A)

Hot Fluid TH

Cold Fluid TC

SurfaceTemperature
Ts(C)

Thermal Stress σ

(B)

Fluid
Temperature
Tf

Hot Fluid

Time

Time

ThermalFatigueTime

Cold Fluid

Influence
Factors(A) Temp.Fluctuation in
Main Flow(1) Turbulent
Diffusion in Fluid(B) Temp.Fluctuation in
Boundary Layer(2) Heat Transferfrom Fluid to
Structure(C) Temp.Fluctuation on
Structural Surface(D) Stress Fluctuation inside
Structure(E) Fatigue crack initiationand propagation(3) Heat
conduction andconstraint in
Structure(4) Multi-axial
random loads
and material
characteristics

Fig.3 Thermal load and failure mechanism at mixing zone of hot and cold fluids

Fig.4 Thermal load and failure mechanism at elbows of stagnant branch pipes due to temperature
stratification layer

2.2. Failure mechanism
Concerning failure mechanism, studies focus on particular issues of thermal fatigue induced by
fluid temperature change. One is strength of multiplication of high cycle and low cycle fatigue fromvarious kinds of thermal hydraulic phenomena during plant life. To clarify above mechanism, variable
amplitude fatigue tests were conducted. Their results clarified sensitivities of lower load limit of crack
propagation to loading histories. Details of fatigue strength study are introduced by the associatedpaper [6]. Another fatigue strength issue is multi-axial stress problems with proportional andnon-proportional loadings. Fig.5 shows history of principal stress components on the piping innersurface at mixing zone of hot and cold fluids. There are somewhat non-proportional characteristics.
Equi-bi-axial fatigue tests of circular plates under alternating air pressure were conducted as Fig.6 [7].
In the case of proportional loadings, bi-axial fatigue strength can adequately be evaluated by theequivalent stress [7]. On the other hand, non-proportional loadings reduce fatigue strength, the mostsignificant case of fatigue life is less than 10% of uniaxial loading one [8]. Therefore quantification
method of non-proportion degree and fatigue strength with this degree is under development for therealistic loadings as Fig.5.

16

N. Kasahara, et al./ Development of thermal fatigue
evaluation methods of piping systems

Fig.5 History of principal stress components at mixing zone of hot and cold fluids

Air

Window
Strain gageAir
chamber

Specimen
Air

Fig.6 Equi-biaxial fatigue tests of circular plates under alternating air pressure

3.

Proposals for the JSME guideline

A thermal stress prediction method of the JSME guideline for “a. High cycle thermal fatigue bytemperature fluctuation at mixing zone between cold and hot fluid” is basically the static equation
which calculates stress from temperature amplitude and material parameters as Eq.(1).

∆σ = FEα∆T
1 −ν∆T = TH − TL

(1)

Where E is Young’s modulus, α is thermal expansion factor, v is Poisson’s ratio and ΔT istemperature range between TH and TL. For consideration of attenuation factors in Fig.3, a constantdesign factor F is employed.
Actual thermal stress strongly depends on frequency of fluid temperature fluctuation as inFig.7[4]. In this figure, the horizontal axis is non-dimensional frequency and the vertical axis is thestress conversion ration from fluid temperature range. Thermal stress is attenuated due to temperaturehomogenization in low frequency range and heat transfer loss in high frequency area. These effects
were experimentally validated [2]. For considering frequency effect on thermal stress, the PowerSpectral Density (PSD) Method was developed [4,9 for example]. Furthermore, an equivalent stressamplitude method with constant frequency is proposed to simplify fatigue damage calculation processfrom the PSD of thermal stress. In Fig.9, an equivalent stress amplitude is the root mean square of thezero order moment of random signal µ 0 and frequency ν 0 can be derived from statistical theory[9]. Design margin was compared between the most precious evaluation method of the JSME
guideline (Step4) and the proposed equivalent stress amplitude method. The result shows that the
proposed method has almost homogeneous (around 10 times of fatigue damage factor) design margin

17

N. Kasahara, et al./ Development of thermal fatigue
evaluation methods of piping systems

than the JSME guideline (change from 10 to 20,000) as Fig.10[10], because the proposed method
considers frequency dependency of thermal stress as Fig.7.
Fluid
Temperature
Range

Heat Transfer

ΔTeffect for Thermal
StressΔT

Low Frequency

High Frequency
Δσ＝EαΔT／（１－ν）

Constant attenuation factor

Conventional method
100%Fluid amplitude isconverted to stress
JSME Guideline
Constant
attenuation factor
PSD Method
Frequency
dependent
attenuation factor

Fig.7 Frequency response of thermal stress①

Design Specification (Flow rate, Diameter,etc.)②
Flow Pattern Classification

PSD* of Fluid④
Frequency Transfer
Function

Frequency
PSD σHeat Transfer Coefficient

Gain G

PSD Tf③⑤
Frequency

PSD* of Stress

Frequency

Fatigue Curve of Material⑥
LCC Method⑦
Fatigue Damage Factor

StressFig.8 PSD Method for considering frequency effect

µ0
Tiµe

Frequency of occurrence ν 0

Fig.9 Proposal of Equivalent stress amplitude with constant frequency

18

N. Kasahara, et al./ Development of thermal fatigue
evaluation methods of piping systems
JSME guideline Step 4
Evaluation by equivalent stress amplitudeFig. 10 Comparison of Fatigue strength margins between JSME guideline and the proposed method(Impinging jet, ΔT=150deg)

Thermal stress mechanism of “b. Thermal fatigue by temperature stratified layer at stagnant
branch pipe” is different from “a. High cycle thermal fatigue by temperature fluctuation at mixing
zone between cold and hot fluid”. Temperature oscillation with the fixed layer model (Fig.11) issimilar to the later problem. Temperature oscillation with the moving layer model (Fig.12) can
approximate the former problem. Fig.13 compares thermal stress response between the fixed andmoving layer model. Thermal stress of the moving layer model is higher than the fixed model in both
low and high frequency area. The frequency response function of thermal stress for the proposed PSD
method can be applied for the fixed model, however underestimates for the moving model. To apply
the PSD method to “b. Thermal fatigue by temperature stratified layer at stagnant branch pipe”,
improved frequency response functions of thermal stress were studied.

Fig.11 Temperature oscillation with the fixed layer modelFig.12 Temperature oscillation with the moving layer model

19

N. Kasahara, et al./ Development of thermal fatigue
evaluation methods of piping systems

Fig.13 Comparison of thermal stress response between the fixed and moving layer mode

4.

Development of Numerical simulation method

The JSME guideline was basically developed from experimental data and static equations. To
replace experimental approach by simulation base one, fluid-structure numerical simulation methods
with the background data and knowledge base are under developing.
Fluid-structure numerical simulation has different approaches (Fig.14). Structural temperature
can be calculated by such two ways as thermal hydraulic (CFD) code and structural (FEM) code.
Through previous investigations, authors selected the CFD approach to avoid hypothesis of heattransfer coefficient. Therefore, a single fluid-structure thermal interaction CFD code is recommended
for considering local and temporal conjugate heat transfer between fluid and structure.
As for a turbulent model for the CFD analysis, the Dynamic LES (Large Eddy Simulation) modelis recommended through comparison of the CFD results with various models and experimental results
as shown in Table1[12, 13]. Heat transfer between fluid and structure is sensitive to mesh subdivisionsof boundary layer. Since long simulation time is required to evaluate low frequency temperaturefluctuation which is damageable on structures, computation time should be saved [13].

Fluid temperature
CFD

Structural temperature

CFD & FEM
FEM

Thermal StressFig.14 Fluid-structure numerical simulation for evaluation of thermal fatigue damage

20

N. Kasahara, et al./ Development of thermal fatigue
evaluation methods of piping systems

Table 1 Comparison of CFD models

5.

Turbulence
model

Mesh

Accuracy

Computati
Costonal time

Applicability

RANS

Coarse

Low

Short

Low

Low for non stationary
field

DES
(LES+RANS)

MediumMediumMediumMediumTo be confirmed for
spatial distribution

LES+Wallfunction

MediumMediumMediumMedium

LES

Fine

High

Long

Large

DNS

Very fine

High

Huge

Impractical

To be confirmed for heattransfer on the surface
To be confirmed forcomputational time andheat transfer on thesurface
Impractical

Probabilistic failure analysis approach for plant system safety

For considering fatigue failure in system safety and PSA approach, probabilistic failure analysis
methods are under development to consider the fatigue failure in system safety and PSA approach.
From view point of system safety, through wall cracks are important than clack initiation.
Therefore, probabilities of both crack initiation and propagation are required to evaluate possibilitiesof though wall cracks. Framework of probabilistic failure analysis approach for plant system safety
can be described as in Fig.15. When fatigue damage factor become 1.0, cracks with 1mm depth areassumed to be initiated. Crack shapes are hypothesized as semi elliptical ones and Paris law isassumed for propagation rate.
There are many influential parameters on loadings and strength in thermal fatigue phenomena.
Among them, dominant parameters are required to be extracted. By using the Monte Carlo method
and the framework of Fig.15, sensitivities of fatigue damage factors to influence parameters were
investigated. For example, lower threshold of crack propagation were successfully clarified as one ofthe dominant parameters (Fig.16). Details are explained in the associated paper [14].

Load sampling

Limit state function to predict failure life
from influence parameters

Crack initiation

G = f ( x1 , x2 ,  , xn )Crack propagation
Time

Response surface calculated
from limit state function

Failure probability surface considering scatterof influence parameters

SampleCycle number

Crack initiation Probability
Through wall probability

50%
failure5%
failureWallthickness

Amplitude

Fig.15 Probabilistic failure analysis approach for plant system safety

21

N. Kasahara, et al./ Development of thermal fatigue
evaluation methods of piping systems∆T=75˚C, R=0, a0=1mm∆T=75˚C, R=-1, a0=1mm

010Conditional probability of failure [crack-1]

Conditional probability of failure [crack-1]

10

a0=1 mmc0=1 mm∆T=75 deg.C-1

10∆Kth ≧10 MPa-m では
1/2

き裂伝播しない
Crack
dose not propagate∆Kth = 2 MPa-m 1/2

10-2∆Kth = 4 MPa-m 1/2∆Kth = 6 MPa-m 1/2∆Kth = 8 MPa-m

10

1/2

-3

0

5

10

15

20

25

30

35

40

0

a0=1 mm10-2

c0=1 mm∆T=75 deg.C

10-4

1/2
∆Kth ≧6 MPa-m では

10-6

Crackき裂伝播しない
dose not propagate
10-8∆Kth = 2 MPa-m 1/2∆Kth = 4 MPa-m 1/2

10-10

0

Operation time [year]

5

10

15

20

25

30

35

40

Operation time [year]

Fig.16 Examples of probabilistic crack initiation and propagation analysis results

Extracted dominant parameters will be utilized for developing the limit state function G. It can becalculated by the Monte Carlo method. However, this method requires huge computing and obtained
results will be not easy for comprehensive understanding.
For simplification and engineering use, applicability of the Advance First Order Second Moment(AFOSM) method is studied by normal distribution assumption of influence parameters. As similar
method to deterministic approach, there are the Load and Resistance Factor Design (LRFD) method,which utilizes partial safety factor for loads and strength corresponding to failure probability.
G(X) > 0: Safe

Limit state function G : G(X) < 0: Failure

Ln the case that load S and strength R, G = R-S
Various descriptions of G exist

Limit state function G
for reliable analysis
and various
evaluation methods

aonte Carlo simulation (aCS）



AFhSa

Approximation of failure probability tf by of normal distribution assumptionof influence parameters Lower cost than aCS

Simplified

Direct calculation of failure probability Pf from large sample calculation
Sampl numbr of G<0 / Total sample number = Pf

LRFD

Evaluation of partial safety factor (tSF) for loads and strength corresponding
to failure probability tf
 tSF for each influence factor in G can be obtained
 tSFs are non probabilistic factors and have good applicablity for conventional
design rules

Fig.17 Reliability analysis methods for realistic evaluation of failure probabilities considering many
influence parameters

6.

Conclusions(1) Clarification of mechanism on loadings and failure
Loading mechanisms were investigated on “a. High cycle thermal fatigue by temperaturefluctuation at mixing zone between cold and hot fluid” and “b. Thermal fatigue by temperature
stratified layer at stagnant branch pipe”. Concerning failure mechanism, studies focus on suchparticular issues as multiplication of high cycle and low cycle fatigue and multi-axial stress problems
with proportional and non-proportional loadings.

22

N. Kasahara, et al./ Development of thermal fatigue
evaluation methods of piping systems(2) Proposals for the JSME guideline
By considering frequency dependency of thermal stress, rational evaluation methods were
proposed, which has almost homogeneous design margin against various conditions than the JSME
guideline.
(3) Development of Numerical simulation method
To replace experimental approach of the JSME guideline by simulation base one, fluid-structure
numerical simulation methods were studied by using the two different codes for thethermal-hydraulics and the structure. For fluid-structure thermally coupled analysis, the Dynamic LES
model is recommend for the numerical simulation of the thermal-hydraulics.
(4) Probabilistic failure analysis approach for plant system safety
For considering fatigue failure in system safety and PSA approach, probabilities of both crack
initiation and propagation were studied. Framework of probabilistic failure analysis approach with thelimit state function was proposed. As candidates of probabilistic parameters of the limit state function,some dominant parameters of fatigue failure were extracted.

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

References[1] Faidy,C., Thermal fatigue in mixing areas: Status and justification of French assessment method,3rdInternational conference on fatigue of reactor components, EPRI-US NRC-OECD NEA, Seville, Spain,（2004）[2] Naoto KASAHARA, Thermal load and fatigue evaluation of nuclear piping, JSME-MMD, ATM'11,
OS18-1-1, (2011)[3] JSME, Guideline for Evaluation of High-Cycle Thermal Fatigue of a Pipe,S017-2003,(2003)[4] Kasahara,N.,Takasho,H. and Yacumpai,A., Structural response function approach for evaluation of thermal
striping phenomena, Nuc. Eng. Des., 212, pp281/292, (2002)[5] Yoshihiro ISHIKAWA, Yukihiko OKUDA and Naoto KASAHARA, Thermal fatigue of pipes induced by
fluid temperature change （CFD analysis of thermal stratification in a vertical branch pipe with a closedend）JSME, Annual Meeting(in Japanese), J032013,(2013)[6] M. Okazaki, , M. Muzvidziwa, R. Iwasaki, and N. KASAHARA, Effect of Thermo-Mechanical Loading
Histories on Fatigue Crack Growth, Behavior and The Threshold in SUS316 and SCM 440 Steels., -Forprevention of high cycle thermal fatigue failures-, EJAM, JSM, The same vol., (2014)[7] Takashi TSUJI and Masayuki KAMAYA, Thermal Fatigue of Pipes Induced by Fluid Temperature Change(Fatigue Strength of Stainless Steel under Bi-axial Load), JSME, Annual Meeting(in Japanese), J032024, (2013)[8] Takamoto Itoh, Masao Sakane, Kazuki Ohsuga, Multiaxial Low Cycle Fatigue Life under Non-proportional
Loading, International Journal of Pressure Vessels and Piping, No.7, (2013)[9] Shinsuke SAKAI, Satoshi OKAJIMA, Naoto KASAHARA and Satoshi IZUMI, Design Method for Random
Fatigue Based on Spectrum Characteristics, ASME, J. Pressure Vessel Technology, 134(3),031204.,(2012)[10] Takafumi Suzuki and Naoto Kasahara, Thermal Fatigue Evaluation Method of Pipes by Equivalent Stress
Amplitude, ASME, PVP2012-78347, (2012)[11] Akira NAKAMURA, Yoichi UTANOHARA, Koji MIYOSHI and Naoto KASAHARA, Simulation ofthermal striping at T-junction pipe using LES with parameters and temperature diffusion schemes,
OECD/NEA and IAEA, CFD4NRS-4, (2012)[12] Shaoxiang Qian, Shinichiro Kanamaru and Naoto Kasahara, High-Accuracy Analysis Methods of Fluid andStructure Temperature Fluctuations at T-Junction for Thermal Fatigue Evaluation, ASME, PVP2012-78159,(2012)[13] Hitoshi NAKAMURA, Hitoshi Kawahara, Bo Li and Naoto KASAHARA, Thermal fatigue of pipes
induced by fluid temperature change (Predictability of temperature fluctuations at T-junction pipes), JSME
2013 Annual meeting(in Japanese), J032012, (2013)[14] Hideo MACHIDA and Naoto KASAHARA, Thermal Fatigue of Pipes Induced by Fluid Temperature
Change(Study on Main Parameters for Failure Probability of Pipes) , JSME 2013 Annual meeting(inJapanese), J032032, (2013)23