05_structural integrity evaluation of reactor pressure vessels during pts events using deterministic...

Structural integrity evaluation of reactor pressure vessels during PTS events using deterministic and probabilistic fracture mechanics analysis

Kazuya Osakabe, Hiroyuki Nishikawa Mizuho Information & Research Institute (MHIR)

2-3 Kanda-Nishikicho, Chiyoda-ku, Tokyo 101-8443, Japan [email protected] [email protected]

Koichi Masaki*, Jinya Katsuyama and Kunio Onizawa Japan Atomic Energy Agency (JAEA)

2-4 Shirane Shirakata, Tokai-mura, Naka-gun, Ibaraki 319-1195, Japan [email protected] [email protected] [email protected]

ABSTRACT

To assess the structural integrity of reactor vessels (RVs) during pressurized thermal shock (PTS) events, a deterministic fracture mechanics (DFM) approach has been widely used such as the procedure in JEAC4206-2007. On the other hand, the application of a probabilistic fracture mechanics (PFM) analysis method for the structural reliability assessment of RV has become attractive recently because uncertainties related to input parameters can be incorporated rationally. The probabilistic approach has already been adopted as the regulation on fracture toughness requirements against PTS events in the U.S. In this paper, in order to verify the applicability of a PFM method to JEAC4206-2007, deterministic and probabilistic analyses have been performed, and the effects of initial crack size defined in JEAC4206-2007 on the temperature margin obtained from DFM and the probability of crack initiation obtained from PFM have been evaluated. With regard to the PTS event variation, a stuck open valve scenario (SO) has been considered in addition to large- and small-break loss of coolant accident (LBLOCA, SBLOCA) and main steam line break (MSLB).

NOMENCLATURE CPI Conditional probability of crack initiation CPF Conditional probability of fracture DFM Deterministic fracture mechanics F Fast neutron fluence HTC Heat transfer coefficient KI Stress intensity factor KIc Fracture toughness LBLOCA Large break loss of coolant accident (LL) MSLB Main steam line break (MS) PFM Probabilistic fracture mechanics PRA Probabilistic risk assessment PTS Pressurized thermal shock PWR Pressurized water reactor RV Reactor vessel RTNDT Reference temperature for nil-ductile transition SBLOCA Small break loss of coolant accident (SL) SO Stuck open valve THA Thermal hydraulic analysis WPS Warm pre-stress ∆Tm Temperature margin INTRODUCTION

To maintain the integrity of the major components of nuclear power plants during the service life, it is important to

Proceedings of the ASME 2013 Pressure Vessels and Piping Conference PVP2013

July 14-18, 2013, Paris, France

PVP2013-97923

consider the aging degradation of the material and the initiation and growth of defects. As one of the most important components in aged light water reactors (LWRs), the structural integrity of

* Present address: Mizuho Information & Research Institute, Inc., 2-3 Nishiki-cho, Kanda, Chiyoda-ku, Tokyo 101-8443, Japan

1 Copyright © 2013 by ASME

reactor vessels (RVs) is assessed for a non-ductile fracture. Pressurized thermal shock (PTS) is one of the most severe

events to assess the structural integrity of the RVs. Japanese code prescribes rules based on deterministic fracture mechanics to prevent the RVs from non-ductile fracture under PTS events [1]. In the code, several factors such as neutron irradiation embrittlement of RV steel, the decrease of fracture toughness and a postulated crack are considered. Each of the condition of current deterministic procedure prescribed in Japanese code includes conservativeness. As a result, a considerable degree of conservativeness is included in the whole procedure. In addition, several conditions in the procedure are based on technical basis obtained over 20 years. It is necessary to reexamine the technical basis and confirm that the procedure is appropriate to the current regulation.

On the other hand, the U.S. NRC conducted 5-year study aiming to develop the technical basis for revision of the former PTS rule, 10CFR50.61 [2]. The motivation of the study called PTS reevaluation project is knowledge and data limitations in the early 1980s introduced to 10CFR50.61 that necessitate conservative treatments. Unnecessary conservativeness is reduced based on updated knowledge and data represented by new flaw model in a probabilistic fracture mechanics (PFM) analysis, which resulted in revisions of the PTS screening limit [3].

In this paper, in order to verify the applicability of a PFM method to the domestic code, deterministic and probabilistic analyses have been performed using the latest version of PASCAL (PFM Analysis of Structural Components in Aging LWRs) code [4-10] developed in JAEA. Effects of parameters such as initial crack size and margin of reference temperature for nil-ductile transition defined in JEAC4206-2007 on the temperature margin and the probability of crack initiation have been discussed.

COMPARISON OF ASSESSMENT PROCEDURES BETWEEN JAPAN AND THE U.S.

The main flowchart of the RV integrity assessment procedure for PTS events prescribed in JEAC4206-2007 is shown in Figure 1. The structural integrity is maintained if the stress integrity factor (KI) at the crack tip is less than fracture toughness (KIc) during PTS transients. Figure 2 shows flowchart of probabilistic estimation of through-wall cracking frequency of PTS reevaluation project in the U.S. PFM analysis was performed using FAVOR code [11] developed in Oak Ridge National Laboratory (ORNL). Input variables such as chemical composition and unirradiated RTNDT for PFM analysis, were determined as realistic values with variation, reducing unnecessary conservativeness as much as possible. Screening criteria of RTNDT is determined after through-wall cracking frequcency (TWCF) obtained from PFM following probabilistic risk assessment (PRA) and thermal hydraulic analysis (THA) is compared to acceptance criterion for TWCF.

Comparison of main parameters considered in this paper is listed in Table 1. Main differences are in the following: 1) Geometry and orientation of cracks

One of the most major parameters to affect to structural

integrity is crack geometry. A semi-elliptical inner-surface crack in the axial direction is postulated in JEAC4206-2007. The depth and the length of the postulated crack are 10mm and 60mm, respectively. Its size is based on inspection accuracy, fatigue crack growth during the service life and some conservativeness.

PTS reevaluation project in the U.S., a new flaw model is applied in PFM analysis. The model provides density and size for buried flaws in weld, buried flaws in plate, and surface flaws in weld and plate. The geometry and dimension depend on the location of flaw. The model is based on the experimental evidence gained from new inspection data, physical models and expert opinions. With regard to the surface-breaking flaws, the direction is assumed to be circumferential and the depth of the flaw is more than the thickness of cladding even though such flaws were not detected, because the data are not enough to extrude the possible existence completely.

2) PTS transients

If any type of PTS transients are not specified, large- and small-break loss of coolant accident (LBLOCA, SBLOCA) and main steam line break (MSLB) are used to calculate KI in the Japanese code. These three transients are selected with the objective of the severity to the structural integrity, i.e. the possibility to give larger KI. In the PTS reevaluation project, PRA has been conducted to determine sequence and its frequencies considered in the following THA and PFM analysis. PTS transients including stuck open valve (SO) could be selected in this procedure, the frequency of which is relatively higher than the three transients prescribed in JEAC4206-2007 even though these gives smaller KI. 3) Warm pre-stress

Warm pre-stress (WPS) is not considered in the procedure of structural integrity assessment in JEAC4206-2007, although various testing to clarify the effect of WPS have been conducted [12, 13]. This treatment may give conservativeness in the procedure.

Change in KI with timeKI value at Crack Tip

Fracture Mechanical Analysis

Axial semi-elliptical surface crack

Postulated CrackChange in Coolant TempratureChange in System Pressure

PTS Transient DataChemical Composition of Material (Cu, Ni)Fracture Toughness (RTNDT, Measured KIC)Fluence, Temperature

Embrittlement Prediction

Comparison of KIC and KI

Structural Integrity Assessment

Fracture Toughness(KIc) Curve at Evaluation

Lower bound curveCrack Tip Temperature

Temperature

KI

KIcKI

KIc

Figure 1 Flowchart of RV integrity assessment for PTS events


PRA (PTS)

THA

PFM

Sequence Definitions

Sequence Frequencies

P(t), T(t)HTC(t)

Conditional Probability of Thru-Wall Cracking

Yearly Frequency of Thru-Wall Cracking

Vessel damage, age, or operational metric

Year

ly F

requ

ency

of

Thru

-Wal

l Cra

ckin

g

Acceptance Criterion for TWC Frequency

Screening limit

Figure 2 Flowchart of probabilistic estimation of through-wall

cracking frequency

Table 1 Comparison of main conditions of assessment procedure between Japan and the U.S.

Item JEAC4206-2007 PTS reevaluation project in the U.S.

Crack geometry and orientation

Semi-ellipse axial surface crack Surface and embedded cracks

Crack dimension

Depth:10mm Length:60mm

Distributed crack size depending on crack geometry

PTS transients MS, SL, and LL All transients based on PRA(including MS, SL, LL, SO)

Warm pre-stress Not considered Considered SENSITIVITY ANALYSIS

Sensitivity analyses have been performed focusing on conditions which are mentioned in the previous section. Common analysis conditions are listed in Table 2. Assuming an RV of a typical 3-loop pressurized water reactor (PWR) plant in Japan, inner diameter, thickness of RV, thickness of cladding are set 2000mm, 200mm, and 5mm, respectively. Postulated crack is semi-elliptic surface axial crack based on JEAC4206-2007. Cladding of the RVs is not considered in JEAC4206-2007. To simulate actual RVs, the cladding is considered in the analysis. Therefore, the crack dimension in plate is to be 15mm deep (depth of crack: 10mm + thickness of cladding: 5mm) and 60mm long in this sensitivity analysis. This treatment leads to give larger KI. Embrittlement prediction formula used in this analysis is that of JEAC4201-2007 [14].

With regard to KIc, different curves shown in Figure 3 are used in each analysis. PASCAL Weibull type distribution using KIc data available in Japan [15] in the following equation is used in PFM analysis.

( ){ } ( ) ( ) ( TaTbTcppKIc ∆+∆∆−−= **2

**211ln)( )

]mMPa[ (1) where

( ) ( )( )TTa ∆−−=∆ 0004.0exp50.1030.131**2

( ) ( )( )TTb ∆−−=∆ 02084.0exp3632.757882.20**2 ( ) ( )( )TTc ∆−+=∆ 05219.0exp16973.006795.3

]C[oNDTRTTT −=∆

KIc curve for base metal in JEAC4206-2007 used in

deterministic fracture mechanics(DFM) analysis is as follows.

( )[ ]TKIc ∆+= 0343.0exp40.4391.32 ]mMPa[ (2) Time histories of inner pressure and fluid temperature

during SBLOCA are shown in Figure 4. This is also the results obtained in the same project that has been used as technical basis in JEAC4206-2007. Time histories of inner pressure and fluid temperature during SO are shown in Figure 5. This is one of the transients that are obtained from THA of Beaver Valley plant in PTS reevaluation project.

Crack growth point is the deepest point of crack. The comparison of KI and KIc is performed in DFM analysis and the conditional probability of crack initiation at the deepest point is evaluated in PFM analysis. Crack initiation at the surface points and crack arrest are not considered in this paper.

Table 2 Common analysis conditions Item Parameter

RV Geometry ID 2000 mm, Thickness 200 mm Cladding 5mm

Crack geometry, orientationand location Semi-elliptic axial surface crack

Average neutron fluence 2, 5, 10 [x1019 n/cm2, E>1MeV] Initial RTNDT and std. dev. 0oC and 10oC Embrittlement prediction JEAC4201-2007

Chemical composition Cu:0.16%, Ni:0.61%

Fracture toughness KIcPASCAL Weibull type (PFM)

KIc curve in JEAC4206-2007 (DFM)Crack growth point The deepest point of crack

0

50

100

150

200

250

-300 -250 -200 -150 -100 -50 0 50 100

T-RTNDT [oC]

KIc

[MP

a √m

]

PASCAL Weibull type p=1%PASCAL Weibull type p=50%PASCAL Weibull type p=99%JEAC4206 curve (for base metal)

Figure 3 KIc curves of PASCAL Weibull type and

JEAC4206-2007


0

5

10

15

0 10 20 30 40 50 60 70Time [min.]

Pre

ssur

e [M

Pa]

0

50

100

150

200

250

300

Tem

pera

ture

[o C]

Pressure

Temperature

Figure 4 Time histories of inner pressure and fluid temperature

during SBLOCA

0

2

4

6

8

10

12

14

16

18

0 50 100 150 200 250Time [min.]

Pre

ssur

e [M

Pa]

0

50

100

150

200

250

300

Tem

pera

ture

[o C]

PressureTemperature

Figure 5 Time histories of inner pressure and fluid temperature

during SO RESULTS AND DISCUSSION Effect of initial crack size

To evaluate the effect of initial crack size, analysis has been performed applying the conditions in Tables 2 and 3. PTS transient is domestic SBLOCA. The heat transfer coefficient (HTC) is assumed to be constant. The initial crack depths a0 vary from 2mm to 10mm and the initial crack aspect ratio, defined as the ratio of length to depth, is 6. In this paper, crack depth means that in the plate. The thickness of cladding is 5mm, therefore, the crack tip is located at 7mm from inner surface in the case of a0=2mm.

KI curves for 5 different initial crack sizes and KIc curve at fluence (f) =1x1020 n/cm2 are shown in Figure 6. The temperature margin values were calculated in DFM analysis. The schematic of the temperature margin is shown in Figure 7. In this figure, ∆Tm is the temperature margin when WPS is considered. It is defined as the difference between the temperature at the maximum value of KI and that at the KIc equal to the maximum value of KI. The temperature margin values ∆Tm at f=1x1020 n/cm2 are listed in Table 4. Although the KI value is relatively large because of large HTC, the structural integrity is maintained when WPS is considered. If the initial crack depth is larger, KI becomes larger, which leads to smaller

∆Tm. The conditional probabilities of crack initiation (CPIs)

obtained from PFM analysis are shown in Figure 8. The CPI in the case of a=10mm and is about 10 times higher than that in the case of a=2mm . It indicates that if the postulated initial crack size is decreased to 2mm with high inspection accuracy or smaller fatigue crack initiation during the service life, the effect corresponds to about 29 oC in temperature margin and one order in CPI.

It should be noted that the absolute values of temperature margins or CPIs can be varied depending on analysis conditions.

Table 3 Analysis conditions (effect of initial crack size) Item Parameter

PTS transient SBLOCA (HTC=21411Wm-2K-1)

Initial crack depth 2, 4, 6, 8, 10 [mm] Initial crack aspect ratio (ratio of length to depth) 6

WPS Considered

0

20

40

60

80

100

120

0 50 100 150 200 250 300

Temperature [oC]

K I o

r KIc [M

Pa

m1/

2 ]

a0=10mma0=8mma0=6mma0=4mma0=2mmKIc(f=10e19)

Figure 6 KI curves for 5 different initial crack sizes and KIc

curve at f=1x1020 n/cm2

0

10

20

30

40

50

60

70

80

0 50 100 150 200 250 300

Temperature [oC]

KI o

r KIc [M

Pa

m1/

2 ]

a0=2mm

KIc(f=10e19)

∆Tm

Figure 7 Schematic of temperature margin


Table 4 Temperature margins at f=1x1020 n/cm2

Initial crack depth a0 [mm] ∆Tm [oC] 2 53.5 4 32.9 6 26.9 8 25.0

10 24.6

1.E-07

1.E-06

1.E-05

1.E-04

1.E-03

1.E-02

1.E-01

1.E+00

0 2 4 6 8 10

Fluence [×1019 n/cm2, E>1MeV]

Con

ditio

nal p

roba

bilit

y of

initi

atio

n [-]

12

a0=10mma0=8mma0=6mma0=4mma0=2mm

Figure 8 Conditional probabilities of crack initiation in base

metal for different initial crack sizes Effect of PTS transients

PTS transient is one of the most major parameter in PFM analysis, because it affects not only to time history of temperature distribution used for calculating KIc but also to that of stress distribution used for calculating KI. Analysis conditions for PTS transients are listed in Tables 2 and 5. The SO transient is based on data of Beaver Valley shown in Figure 5.

KI curves for 4 different PTS transients and KIc curve at f=1x1020 n/cm2 are shown in Figure 9. KI values for SBLOCA, LBLOCA, and MSLB increase depending on rapid cooling of inner surface caused by the injection of emergency core cooling water. Then, they decrease with the decrease of difference between temperature at inner-surface and crack tip. On the other hand, KI value for SO is within a small scatter, giving a small peak caused by the increase of inner pressure shown in Figure 5. The KI value for SO is smaller than those of the other transients. Therefore, from the viewpoint of deterministic structural integrity assessment to prevent brittle fracture initiation against PTS, SO transient is not to be considered as important transient.

CPIs of all transient are shown in Figure 10. CPI of SO is almost the same as those of SBLOCA and MSLB, even though the KI value for SO is smaller. This is because the temperature in which KI gives the maximum value is different each other. In case of SO, it is about 100 oC. In case of SBLOCA and MSLB, they are around 120 oC to 130 oC. The scatter of KIc depends on temperature, which leads to smaller difference of CPI. In addition, the increase of CPI of SO accompanied with the increase of fluence is relatively smaller than those of other transients. This is the same trend shown in PTS reevaluation project in the U.S.

Table 5 Analysis conditions (effect of PTS transients)

Item Parameter

PTS transient SBLOCA, LBLOCA, MSLB, SO(HTC=21411Wm-2K-1)

Initial crack depth 10 [mm] Initial crack aspect

(ratio of length to depth) 6

WPS Considered

0

50

100

150

0 50 100 150 200 250 300

Temperature [oC]

KI,

KIc

[MP

a √m

]

SBLOCALBLOCAMSLBSOKIc

Figure 9 Time histories of KI during PTS transients

1.E-07

1.E-06

1.E-05

1.E-04

1.E-03

1.E-02

1.E-01

1.E+00

0 2 4 6 8 10

Fluence [×1019 n/cm2, E>1MeV]

Con

ditio

nal p

roba

bilit

y of

initi

atio

n [-]

12

SBLOCALBLOCAMSLBSO

Figure 10 Conditional probabilities of crack initiation in base

metal during PTS transients Effect of WPS

To verify the effect of warm pre-stress effects, analysis has been performed applying the conditions in Tables 2 and 6.

The CPIs obtained from PFM analysis are shown in Figure 11. In the case of SBLOCA, CPI in the case that WPS is not considered is about two orders higher than that in the case that WPS is considered. On the other hand, the CPIs of SO in the cases that WPS is and is not considered are almost the same. The difference of the effect of WPS on CPIs is due to the differences of KI curves. As shown in Figure 12, KI value of SBLOCA remains higher than KIc value while it decreases after showing the maximum value, that lead to crack initiation when WPS is not considered. In the case of SO, the difference of CPIs depending on WPS may not be seen because KI provides


maximum value at low temperature.

Table 6 Analysis conditions (effect of WPS) Item Parameter

PTS transient SBLOCA (HTC=21411Wm-2K-1)SO (Beaver Valley Plant in PTS

reevaluation project) Initial crack depth 10 [mm] Initial crack aspect

(ratio of length to depth) 6

WPS Considered Not considered

1.E-07

1.E-06

1.E-05

1.E-04

1.E-03

1.E-02

1.E-01

1.E+00

0 2 4 6 8 10

Fluene [×1019 n/cm2, E>1MeV]

Con

ditio

nal p

roba

bilit

y of

initi

atio

n [-]

12

SBLOCA WPS SBLOCA No WPSSO WPS SO No WPS

Figure 11 Conditional probabilities of crack initiation in base metal with or without consideration of WPS during SBLOCA

and SO

0

50

100

150

0 50 100 150 200 250 300

Temperature [oC]

KI,

KIc

[MP

a√m

]

SBLOCASOKIc

possibility of initiationboth when WPS is consideredand not considered

possibility of initiationonly when WPS is not considered

Figure 12 KI curves of SBLOCA and SO

SUMMARY AND CONCLUSIONS

As a study of applying PFM analysis for domestic RV integrity assessment, sensitivity analyses were performed. Conditions such as initial crack size, PTS transients and WPS were chosen in view of the conservative ness of domestic code or the difference from that of the U.S. The following conclusions are drawn:

From the sensitivity analyses, the effects of initial crack size, the transients and WPS to the structural integrity of the RVs have been assessed quantitatively. Specifically, in the case that crack depth is 2mm, the temperature margin increased about 29 oC and the CPI is one order lower than that in the case that crack depth is 10mm based on JEAC4206-2007. CPI by SO obtained from PTS reevaluation project in the U.S. is almost the same as those of SBLOCA and MSLB based on former study in Japan. The increase of CPI of SO accompanied with the increase of fluence is relatively smaller than those of other transients. This is the same trend shown in PTS reevaluation project. The effect of WPS on CPI may be considerable depending on PTS transients, especially for the PTS transients that KI value remains relatively higher after it provides maximum value.

It should be noted that the trend described above may be affected by input parameters. Some input conditions should be reexamined for “best estimate” values and models to reduce conservativeness in the future study. ACKNOWLEDGMENTS

This study was performed under the contract research entrusted from Nuclear Regulation Authority of Japan. REFERENCES 1. JEAC4206, 2007, “Nuclear Standards Committee of JEA,

Method of Verification Tests of the Fracture Toughness for Nuclear Power Plant Components,” Japan Electric Association.

2. EricksonKirk, M. et al, 2006, “Technical Basis for Revision of the Pressurized Thermal Shock (PTS) Screening Limit in the PTS rule (10CFR50.61),” NUREG-1806.

3. Title 10, Code of Federal Regulations, Part 50, Section 50.61a, 2010, “Alternate Fracture Toughness Requirements for Protection Against Pressurized Thermal Shock Events”, U.S. NRC.

4. Osakabe, K., Kato, D., Onizawa, K., and Shibata, K., 2006, “User’s Manual and Analysis Methodology of Probabilistic Fracture Mechanics Analysis Code PASCAL ver.2 for Reactor Pressure Vessel,” JAEA-Data/Code 2006-020, Japan Atomic Energy Agency. (in Japanese)

5. Masaki, K., Nishikawa, H., Osakabe, K. and Onizawa, K., 2011, “User’s Manual and Analysis Methodology of Probabilistic Fracture Mechanics Analysis Code PASCAL3 for Reactor Pressure Vessel (Contract Research),” JAEA-Data/ Code 2010-033. (in Japanese)

6. Shibata, K., Kato, D., and Li, Y., 2001, “Development of a PFM Code for Evaluating Reliability of Pressure Components Subject to Transient Loading,” Nucl. Eng. Des., 208, pp. 1-13.

7. Onizawa K, Shibata K, Osakabe K, Tanaka K., 2006, “Improvements to PFM Analysis Code PASCAL and Some Case Studies on RPV Integrity during Pressurized Thermal Shock,” Proceedings of ASME Pressure Vessels and Piping Division Conference, PVP2006-ICPVT11-93368.

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“Development of Probabilistic Fracture Mechanics Analysis Code PASCAL Ver.2 for Reactor Pressure Vessel,” Transaction of the Atomic Energy Society of Japan; 6(2): 161-171. (in Japanese)

9. Onizawa, K., Nishikawa, H. and Itoh, H., 2010, “Development of Probabilistic Fracture Mechanics Analysis Codes for Reactor Pressure Vessels and Piping Considering Welding Residual Stress,” Int. J. Pressure Vessels and Piping, 87, 2-10.

10. Onizawa, K., Masaki, K. and Katsuyama, J., 2012, "Probabilistic Structural Integrity Analysis of Reactor Pressure Vessels during PTS Events," Proceedings of ASME Pressure Vessels and Piping Division Conference, PVP2012-78836.

11. Williams, P.T., Dickson, T.L., and Yin, S., 2004, “Fracture Analysis of Vessels – Oak Ridge FAVOR, v04.1, Computer Code: Theory and Implementation of Algorithms, Methods, and Correlations,” NUREG/CR-6854.

12. D. Moinereau et al., 2012, "A EUROPEAN PROJECT FOR APPLICATION OF WPS IN RPV ASSESSMENT INCLUDING BIAXIAL LOADING: NESC VII" Proceedings of the 2012 ASME Pressure Vessels and Piping Division Conference, PVP2012-78044.

13. Guillaume Chas et al., 2011, “Fracture Toughness of a Highly Irradiated Pressure Vessel Steel in Warm Pre-Stress Loading Conditions (WPS)”, Proceedings of the 2011 ASME Pressure Vessels and Piping Division Conference, PVP2011-58029.

14. JEAC4201, 2004 and 2007, “Method of Surveillance Tests for Structural Materials of Nuclear Reactors,” The Japan Electric Association.

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05_structural integrity evaluation of reactor pressure vessels during pts events using deterministic...

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