E-Journal of Advanced Maintenance Vol.9-2 (2017) 118-125
Japan Society of Maintenology

Performance Based Maintenance Concept to Optimize Inspection Schedule
Masayuki KAMAYA1,
1

Institute of Nuclear Safety System, Inc., 64 Sata, Mihama-cho, Fukui 919-1205, Japan

ABSTRACTThis study is aimed at proposing a new maintenance concept; performance based maintenance (PBM). In a flaw
tolerance assessment, time duration until the next inspection is determined by crack growth prediction assuming
material degradation such as stress corrosion cracking and fatigue. In most cases, the crack growth prediction isexcessively conservative and no cracking is found by inspections. The fact of no indication by inspections
implies that cracks have not grown to more than a detectable size for the inspection technique applied. In the
PBM concept, this inspection result is considered in determining the next inspection schedule. In this study,
applicability of the PBM concept was shown for fatigue degradation of stainless steel components in apressurized water reactor primary water environment. The relationship between crack depth and number ofcycles obtained in the author’s previous study was used for the crack growth prediction. Then, crack growth fora postulated fatigue crack was predicted considering strain gradient in the depth direction caused by thermalloading. It was shown that the duration until the next inspection could be optimized based on the inspection
result together with the crack growth curve. A longer operation time before the inspection resulted in a longer
duration until the next inspection.
KEYWORDS

ARTICLE INFORMATION

Performance-based maintenance, fatigue, crack growth, maintenance,
inspection schedule

Article history:
Received 7 November 2016
Accepted 27 April 2017

1.

Introduction

Various in-service inspections are made at every fuel outage in nuclear power plants (NPPs).
Some inspections are intended to detect cracks due to stress corrosion cracking and fatigue. Althoughmany such inspections are made, only a few will detect cracks. The frequency and location of theinspections are determined according to rules determined by plant owners or fitness-for-service codessuch as the Japan Society of Mechanical Engineers (JSME) fitness-for-service code [1]. Suchinspections are carried out according to the rules regardless of past inspection results. Namely, once
the rules are determined, the inspections are continued even if no cracking has been found for a longtime. In order to maximize reliability of components and to minimize the risk of leakage due to crack
penetration or failure of components, frequency and location of the inspections should be optimized
for a given resource; e.g. frequency of the inspection can be reduced for locations at which cracks
have not been found for a long time without decreasing the reliability of the components. Moreover,by performing alternative inspections at more preferential locations for cracking, it is possible toincrease the reliability for the same number of inspections.
In order to optimize the frequency and location of inspections, in this study, a new concept of“performance based maintenance (PBM)” is proposed. The key idea behind the PBM is to reflect past
inspection results onto the future inspection schedule. It is reasonable to reduce the inspection
frequency or to omit the inspection if past inspections have shown no indication for a long time.
However, it is not easy to say an appropriate inspection frequency quantitatively. In the PBM concept,
the change in material degradation is represented by a curve, which is referred to as the postulated
crack growth curve, and inspection results of no indication are correlated to the degree of the material
degradation. The basic idea of the PBM and an example practical application are shown in this paper.
The PBM concept is applied to fatigue damage of stainless steel, though it is applicable to various
degradation phenomena, such as stress corrosion cracking, corrosion, wall thinning or wear. First, theinterpretation for inspection results of no indication is given. Then, in order to develop as assessment
procedure for the PBM, the postulated crack growth curve is developed for fatigue damage ofstainless steel pipes. Finally, a procedure for determining the inspection schedule is shown.
*

Corresponding author, E-mail: kamaya@inss.co.jp

ISSN-1883-9894/10 © 2017 – JSM and the authors. All rights reserved.

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Performance Based Maintenance Concept to Optimize Inspection Schedule

Fig.1 Schematic drawing representing the determination of crack growth curveby an inspection results of no indication.

2.

Interpretation of “No Indication” by Inspection

Although numerous results of “no indication” or “no crack” are accumulated during a long time
operation, these results are not utilized for other maintenance activities. In the PBM concept, theresults of no indication are utilized to determine the future inspection schedule. The general objectiveof inspections is to confirm that no cracking has been initiated. The objective is achieved if there is no
indication and then no special action is taken after the inspections. Namely, the current interpretationof no indication is that no damage has accumulated and there is no risk for cracking until the next
inspection if the inspection was made according to the rules. On the other hand, according to the flaw
tolerance concept [2], residual life is estimated from inspection results even if no crack is found by theinspection. It is possible to characterize the detectability of the inspection technique by the minimum
detectable size or the possibility of detection (POD). Then, the possible maximum crack size can be
identified from the results of no indication as schematically shown in Fig. 1. The degree of fatigue
damage can be quantified by the crack size [3]-[5] and the fatigue damage (crack size) is increased
during the plant operation even if the crack is not detected by the inspection. Although the actual
crack size is difficult to identify by the inspection, the possible largest size is determined from thedetectability of the inspection technique applied. According to the crack growth prediction, it ispossible to determine the residual life secured by the inspection. Duration until the next inspection
should be no longer than the residual life. The curve determined by the inspection is referred to as thepostulated crack growth curve (hereafter denoted as P-curve) [6][7]. The P-curve does not show theactual crack growth behavior, rather it shows the possible (most conservative) crack growth behavior
identified by the inspection.

3.
3.1.

Development of Postulated Crack Growth Curve (P-curve)
Crack growth prediction

In order to draw the P-curve for fatigue damage, reference was made to the fatigue tests forsolution heat-treated Type 316 stainless steel performed by the present author and Kawakubo [8][9].
The round-bar specimens of 10 mm diameter were subjected to strain-controlled tests in a room
temperature119

M. Kamaya/
Performance Based Maintenance Concept to Optimize Inspection Scheduleda2.76
 1.93  103  K ε 
dN

9
7
6

Crack growth rate da/dN, m/cycle

Surface length 2c, mm

1.E-04Δε =0.6%Δε = 1.2%
Δε = 2.0%
Prediction

8

5
4
3
2
1
0
0.0

0.2

0.4

0.6

0.8

1.0

N/Nf
Fig.2 Changes in crack surface length obtainedby strain-controlled fatigue tests andthat obtained by prediction using strain
intensify factor.

1.E-05
1.E-06
1.E-07Δε = 0.6%[22]Δε = 1.2%[21]Δε = 2.0%[5]σa = 250 MPa(1)[5]σa = 250 MPa(2)[5]σa = 270 MPa[5]CT specimen[21]1.E-08
1.E-09
1.E-101.E-11
0.01

0.1

1

10

Kε ,  103 m1/2

Fig.3 Crack growth rates obtained by low-cycle andhigh-cycle fatigue tests using round-bar
and compact tension (CT) specimens. Solidline shows the regression for the growth
rates obtained round-bar specimens.

laboratory environment. Strain range Δε was controlled to 0.6%, 1.2% or 2.0% for a constant strain
rate of 0.4%/s. The number of cycles to failure (fatigue life) Nf was 41,500, 5,937 and 1,495 cycles,
respectively. The crack initiation and growth behaviors during the tests were investigated by taking
replicas of the specimen surface using acetylcellulose films.
Figure 2 shows the changes in the surface length of the cracks which caused the specimen failure
with the number of cycles normalized by the fatigue life N/Nf. In the case of Δε = 1.2%, a crack of
41.2 μm length was observed at N/Nf = 0.09, then it grew continuously and caused the specimen
failure. Similar initiation and growth behaviors were observed for Δε = 0.6% and 2.0%. Namely, theincubation period before crack initiation was relatively short compared with Nf, and the initiated crackgrew without retardation. It should be noted that no crack coalescence was observed for the cracks
that caused the specimen failure. The results shown in Fig. 2 implied that the fatigue life almost
corresponded to the number of cycles for a small crack growing to a critical size for specimen failure.
The critical size was about 3 mm in depth. It was shown that the crack depth observed at fractured
surface of 10 mm diameter specimen was about 3 mm [10].
The crack growth rates were identified from the slope of each segment connecting adjacentpoints of the lines shown in Fig.2. Figure 3 shows the obtained crack growth rates together with thoseobtained for the high-cycle regime [8] and for the small scale yielding condition of compact tension
specimens [8]. The strain intensity factor range (ΔKε) [8][11][12], defined by Eq. (1), was used for
representing the crack growth driving force: K ε  f   a(1)where a is the crack depth and f is the geometrical constant for the stress intensity factor [8][13].
Since Fig. 2 included the growth rates obtained in the low-cycle fatigue regime, not the strain
intensify factor but the stress intensify factor was applied. In general, the J-integral value is used totake the effect of cyclic plastic strain into account [14]-[17]. In order to predict the crack growth for agiven strain range, the J-integral value was not applied because the J-integral value is calculated using
not only the strain range but also the stress range. It has been shown that the fatigue life of stainlesssteel correlated better with the strain range than with the stress range [18][19]. The fatigue lives ofwork hardened stainless steel were almost the same as those of annealed stainless steel for the samestrain range even if the stress amplitude was increased by the work hardening [20]. Actually, thefatigue life for component design is prescribed for the strain range [21]-[23]. Since the fatigue life
corresponded to the number of cycles for the small crack growing to the critical size and the fatigue
life correlated well with the strain range, it is reasonable for the crack growth driving force to be120

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Performance Based Maintenance Concept to Optimize Inspection Schedule

Thermal load

Strain concentration
Large strain amplitude
on surface

Crack

Initiation due tolocalized strain

Little strain amplitude

Tm

1.0

Time tK 1.8a  exp 

Ko
 w 

0.8

TmTfts
Fluid temperaturez

0.6

ΔKε /ΔKεo

Fluid temperature

Fig.4 Schematic drawing to explain strain gradient in the depth direction caused by thermal loading
and geometrical condition (strain concentration).

0.4
ts=1s
ts=10sts=20sts=100s
Eq. (4)0.2

w(20mm)

0.0
0.0

0.1

0.2

0.3

0.4

0.5

Crack depth a/w
Fig.5 Analyzed model for thermal loading causedby ramp change in fluid temperature.

Fig.6 Change in normalized strain intensity factor
with crack depth under various transient
times ts.

represented by the parameter using the strain range. The measured crack growth rates correlated wellwith ΔKε regardless of the loading amplitude and yielding condition [8][24]. Regression of the growth
rates obtained using round-bar specimens was derived as [12]:da2.76
 1.93  103   K ε  .
dN(2)The growth rate is given in m/cycle and ΔKε in m0.5.
By using Eq. (2), it is possible to predict the crack growth for the strain-controlled tests for agiven initial crack size. The predicted crack growth for an initial crack depth of 30 μm was shown in
Fig. 2, in which the surface length was assumed to be 2a. The change in the surface length with thenormalized number of cycles N/Nf did depend on the strain range and agreed well with the test results.
3.2.

P-curve for thermal loading

The main source of cyclic loads considered in design of NPP components is thermal load causedby change in operating modes such as plant startup and shutdown. The change in the fluid temperaturebrings about temperature fluctuation on the surfaces of components. The thermal strain and stress121

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Performance Based Maintenance Concept to Optimize Inspection Schedule
12

12
Thermal loading
Uniform loading

10

da
2.76
 1.93  103  K ε dN

8Crack depth, mm

Crack depth, mm

10Thermal loading
Uniform loading

6
4
2

da
2.20
 59.7  K ε 
dN

8
6
4
2

0.33Nf0.47Nf

0

0
0.0

0.2

0.4

0.6

0.8

1.0

0.0

0.2

0.4

0.6

0.8

N/Nf

N/Nf

(a) In air(b) In PWR water environment

1.0

Fig.7 P-curves for various loading and environmental conditions.

fluctuation is largest on the surface and it decreases in the depth direction. The strain gradient in the
direction is also caused by geometrical conditions. Fatigue cracking is initiated at the position of thelargest strain amplitude such as notch roots or edges of weld portions. The strain range at the stressconcentrated portion is largest on the surface and it decreases in the depth direction as schematicallyshown in Fig. 4. The strain gradient caused by thermal loading and geometrical condition affects theshape of the P-curve. Then, the effect of the strain gradient due to the thermal loading was consideredin the P-curve in this study.
Here, a ramp change of fluid temperature was assumed as shown in Fig. 5. The temperature waslinearly changed from Tm to Tm–ΔTf with a transient time of ts. By solving this thermal convection
problem assuming the plate thickness w = 20 mm and the constants for stainless steel [25], the thermal
strain distribution was obtained analytically as described in the Ref. [10]. Then, the geometricalconstant f for the strain intensity factor was derived using a weight function [26]. Figure 6 shows therelationship between the crack depth a/w and the strain intensity factor normalized by ΔKεo, which isdefined by: K εo  f  max(z=0)  a .

(3)Here, Δεmax(z=0) denotes the maximum strain on the surface during the temperature transient. The
normalized strain intensity factor was less than unity and decreased as the crack depth increased. Thismeans that the strain intensify factor became smaller compared with that obtained for a uniform
loading of Δεmax(z=0). Although smaller ts caused larger Δεmax(z=0), ΔKε/ΔKεo exhibited almost the samechange with a/w regardless of ts. It has been found that the change in ΔKε/ΔKεo was insensitive to theheat transfer coefficient between the fluid and the plate [10]. The change in ΔKε/ΔKεo with crack depth
was approximated by:Kε 1.8a  exp 
.
K εo
 w 

(4)

The change in the strain intensity factor in the depth direction represented by Eq. (4) was
considered in the crack growth prediction. Figure 7 shows the predicted crack growth (P-curve) for
the uniform and thermal loading conditions. The P-curves were also calculated for fatigue crack
growth in the pressurized water reactor (PWR) water environment, for which the growth rate equation
was obtained as [27]:da2.20
 59.7   Kε  .
dN

122

(5)

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Performance Based Maintenance Concept to Optimize Inspection Schedule

Fig.8 Maintenance concepts.

The initial crack depth was set to 30 μm for all cases. The initial depth of 30 μm gave good crack
growth prediction in Fig. 2. Stainless steel components do not fail in an instable crack propagationmanner even if the components have a crack because stainless steel exhibits good ductility even athigh temperature [28][29]. Therefore, leakage caused by crack penetration is the most possible failuremode. Although the critical depth was about 3 mm for 10 mm diameter specimen [10], it can be larger
in actual component. Then the final length of the P-curve was changed from 3 mm to 10 mm, whichcorresponded to half of the thickness. The inclination of the P-curve was more moderate (not so steep)for the thermal loading and for the PWR water environment. It is worth mentioning that the P-curve
did not depend on proportional constant of the crack growth rate equations. The power exponent of
2.20 for the PWR water environment resulted in more moderate crack growth although the predicted
fatigue life was shorter than that for the air environment.

4.

Performance Based Maintenance (PBM) Concept

From the P-curves shown in Fig. 7, the residual life secured by the inspection for which crack
depth detectability was 2 mm could be estimated as 0.33Nf and 0.47Nf for the air and PWR water
environments, respectively. For the PWR water environment, the residual life became 0.47/0.53  40
 35 years when the operation time before the inspection was 40 years. This means that no future
in-service inspections would be required, if the scheduled plant operation period is less than 60 years.
Longer operating time without any cracking warrants longer residual life after the inspection. Thus, in
the PBM, the inspection results of no indication can be utilized to determine the future inspection
schedule.
In general, in-service inspections have been carried out according to the rules, which were
determined prior to the plant operation. And for most of the rules, frequency and location were
determined empirically. Such a maintenance scheme is referred to as time based maintenance (TBM).
Inspections by the TBM concept are preformed regardless of the plant conditions. So-called condition
based maintenance (CBM) approach also has been applied for some components as an alternative to
the TBM approach. Conditions of the components can be monitored by various measurements forsuch items as vibration and local temperature. If the fatigue damage is monitored, duration until next
inspection can be determined based on the monitored fatigue damage. As shown in Fig. 8, the PBM
proposed in this study is one option for a maintenance strategy. The PBM is suited to relatively oldplants for which their long term operating experience can be utilized to optimize the inspection
schedule.

5.

Conclusion

In this study, a new concept of the performance based maintenance (PBM) was proposed for an
optimized inspection schedule. In the PBM concept, past operating experience of no indication is
utilized for determining the future inspection schedule. Longer operation time before the inspection
results in a longer duration until the next inspection when the inspection shows no indication. In order
to apply the PBM concept to fatigue damage, the P-curves for Type 316 stainless steel were developed123

M. Kamaya/
Performance Based Maintenance Concept to Optimize Inspection Scheduleusing fatigue test results. The thermal loading condition and the growth rate in the PWR water
environment were considered in the calculation of the P-curves. It was found that the residual life
secured by the inspection for which crack depth detectability was 2 mm was almost 0.47Nf. Thisimplied that the residual life after the inspection was about 35 years if the plant had already been
operated for 40 years.

References[1] Japan Society Mechanical Engineers, “Codes for Nuclear Power Generation Facilities: Rules on
Fitness-for-service for Nuclear Power Plants”, JSME S NA1-2012 (2012).
[2] S. R. Gosselin, F. A. Simonen, P. G. Heasler, S. R. Doctor. “Fatigue crack flaw tolerance in nuclear power
plant piping - A basis for improvements to ASME code section XI Appendix L”, NUREG/CR-6934 (2007).
[3] Y. Murakami, K. J. Miller, “What is fatigue damage? A view point from the observation of low cycle
fatigue process”, International Journal of Fatigue, Vol. 27, pp. 991-1005 (2005).
[4] M. Kawakubo, M. Kamaya, “Fatigue life prediction of stainless steel under variable loading (damage
factors determining fatigue life and damage evaluation for two-step test)”, Journal of the Society ofMaterials Science, Japan, Vol. 60, pp.871-878 (2011).
[5] M. Kamaya, M. Kawakubo, “Loading sequence effect on fatigue life of Type 316 stainless steel”,
International Journal of Fatigue, Vol. 81, pp. 10-20 (2015).
[6] M. Kamaya, T. Nakamura, “A flaw tolerance concept for plant maintenance using virtual fatigue crack
growth curve”, Proceedings of the ASME 2013 Pressure Vessels and Piping Conference, Paris, France, July,
paper no. 97851 (2013).
[7] M. Kamaya, T. Nakamura, “Fatigue damage management based on postulated crack growth curve”,
E-Journal of Advanced Maintenance, Vol. 7-1, pp. 43-49 (2015).
[8] M. Kamaya, M. Kawakubo, “Strain-based modeling of fatigue crack growth – An experimental approachfor stainless steel”, International Journal of Fatigue, Vol. 44 pp. 131-140 (2012).
[9] M. Kamaya, M. Kawakubo, “Damage assessment of low-cycle fatigue by crack growth prediction(development of growth prediction model and its application)”, Transactions of the Japan Society of
Mechanical Engineers Ser. A, Vol. 78 pp. 1518-1533 (2012).
[10] M. Kamaya, “Damage assessment of low-cycle fatigue by crack growth prediction (fatigue life undercyclic thermal stress)”, Transactions of the Japan Society of Mechanical Engineers Ser. A, Vol. 79,
pp.1530-1544 (2013).
[11] J. R. Haigh, R. P. Skelton, “A strain intensity approach to high temperature fatigue crack growth andfailure”, Materials Science and Engineering, Vol. 36, pp.133-137 (1978).
[12] M. Kamaya, “Low-cycle fatigue crack growth prediction by strain intensity factor”, International Journalof Fatigue, Vol. 72, pp. 80-89 (2015).
[13] Y. Murakami et al. (eds.), “Stress Intensity Factor Handbook, Volume 2”, Pergamon Press, pp.659-662(1987).
[14] N. E. Dowling, “Crack growth during low-cycle fatigue of smooth axial specimens”, ASTM STP 637, pp.
97-121 (1977).
[15] M. H. Elhaddad, N. E. Dowling, T. H. Topper, “J integral applications for short fatigue cracks at notches”,
International Journal of Fracture, Vol. 16, pp. 15-30 (1980).
[16] K. Tanaka, “Mechanics and micromechanics of fatigue crack propagation”, ASTM STP 1020, pp. 151-183(1989).
[17] A. J. McEvily, “The growth of short fatigue cracks: A review”, Material Science Research International,Vol. 4, pp. 3-11 (1998).
[18] C. E. Jaske, W. J. O'Donnell, “Fatigue design criteria for pressure vessel alloys”, ASME Journal ofPressure Vessel Technology, Vol. 99, pp.584-592 (1977).
[19] J. Colin, A. Fatemi, “Variable amplitude cyclic deformation and fatigue behavior of stainless steel 304L
including step, periodic, and random loading”, Fatigue & Fracture of Engineering Materials & Structures,Vol. 33, pp.205-220 (2010).
[20] M. Kamaya, M. Kawakubo, “Mean stress effect on fatigue strength of stainless steel”, International Journalof Fatigue, Vol. 74, pp. 20-29 (2015).
[21] ASME, “Rules for Construction of Nuclear Facility Components – ASME Boiler and Pressure Vessel Code
Section III”, ASME, New York (2013).
[22] Japan Society Mechanical Engineers, “Codes for Nuclear Power Generation Facilities: Rules on Design
and Construction for Nuclear Power Plants”, JSME S NC1-2012 (2012).
[23] O. K. Chopra, W. J. Shack, “Effect of LWR coolant environments on the fatigue life of reactor materials”,

124

M. Kamaya/
Performance Based Maintenance Concept to Optimize Inspection Schedule
NUREG/CR-6909, ANL-06/08 (2007).
[24] H. Kitagawa, S. Takahashi, C.M. Suh, S. Miyashita, “Quantitative analysis of fatigue process - microcracks
and slip lines under cyclic strains”, ASTM STP 675, pp.420-449 (1979).
[25] M. Kamaya, “Assessment of thermal fatigue damage caused by local fluid temperature fluctuation (Part I:
Characteristics of constraint and stress caused by thermal striation and stratification)”, Nuclear Engineering[26] M. Kamaya, “Assessment of thermal fatigue damage caused by local fluid temperature fluctuation (Part II:
Crack growth under thermal stress)”, Nuclear Engineering and Design, Vol. 268, pp.139-150 (2014).
[27] M. Kamaya, “Environmental effect on fatigue strength of stainless steel in PWR primary water – role ofcrack growth acceleration in fatigue life reduction”, International Journal of Fatigue, Vol. 55, pp. 102-111(2013).
[28] H. Machida, M. Itatani, M. Kamaya, “Revision of flaw evaluation methods of pipes having acircumferential flaw in JSME Fitness-for-service codes”, Proceedings of the ASME 2014 Pressure Vessels
and Piping Conference, Anaheim, CA, USA, July, paper no. 29053 (2014).
[29] M. Kamaya, “Elastic-plastic failure assessment of cold worked stainless steel pipes”, International Journalof Pressure Vessels and Piping, Vol. 131, pp. 45-51 (2015).

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