Probabilistic Fracture Mechanics Probabilistic Fracture Mechanics Analysis of CRDM NozzlesAnalysis of CRDM Nozzles

Presented at:Presented at:NRC NRC –– MRP Alloy 600 MeetingMRP Alloy 600 Meeting

Rockville, MDRockville, MD

Presented by:Dr. Peter C. Riccardella

Structural Integrity AssociatesMay 22, 2002

EPRI

Outline of Presentation

• Overview of Methodology • Software Modifications

(to address comments from 2/21/02 NRC meeting)

• PFM Analyses in support of MRP RPV Head Penetration Inspection Plan♦ Susceptibility Categories♦ Inspection Types and Frequencies

EPRI

Key Elements of RPV Head NozzlePFM Analysis

• Probability of Leakage♦ Weibull Model based on Experience to Date ♦ Incorporated into Monte Carlo Model

• Fracture mechanics modeling for Stress Intensity Factors♦ Through-Wall Cracks♦ Part Through Wall Cracks

• Stress Corrosion Crack Growth Statistics• Effect of Inspections

♦ Inspection Interval♦ Inspection Reliability

EPRI

Weibull Models for Leakage

• Analysis by Dominion Engineering – B&W plants w/ Weibull slope of 3 ♦ Weibull Slope = 3.0♦ Weibull Theta* = 15.36 (avg.) ; 9.094 (worst case)

*Theta = Characteristic time to 63.3% probability of at least one leak in a head.

EPRI

Dominion Engineering Weibull Analysis (Beta = 3)

EPRI

Weibull Distributions used in PFMβ=3; θ=15 ± 6

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

0 5 10 15 20 25 30 35

EFPY

Cum

. Pro

babi

lity

of 1

st L

eak

High Weib (Th=9)Avg Weibul (Th=15)Low Weibull (Th=21)

EPRI

Fracture Mechanics ModelThrough-Wall Crack

1

3.9245"

0.563"

1.527 "

CRDM NOZZLE, 26.1 Deg. AZI MUTH , 18 0 Deg. UP HILL F LAW, w . INTE RF. FIT GA PS

ANSYS 5. 7OCT 30 200 1

10:21:0 5

ELEMENTS

TYPE NUM

U

Gap Elements represent vessel wall constraint opposite crack opening –Gaps could be adjusted to address effect of vessel wastage if applicable.

EPRI

Part-Through-Wall Flaw Model

No back wall constraint assumed in part-through-wall crack model, therefore vessel wastage not a factor

EPRI

Stress Intensity Factor ResultsB&W Type Plant

Degrees Inches Uphill Downhill30 0.9664 20.8 N/A70 2.2550 18.8 N/A160 5.1540 20.3 N/A180 5.3140 0.64 N/A220 6.4950 0.63 N/A260 7.6760 0.63 N/A300 8.8570 0.62 N/A30 1.0170 27.2 27.270 2.3730 24.0 24.0160 5.4240 24.5 24.5180 5.5920 23.4 1.0220 6.8350 23.8 2.4260 8.0770 26.9 6.0300 9.3200 26.5 11.530 1.0830 29.7 29.770 2.5260 26.1 26.1160 5.7750 26.5 26.5180 5.9530 28.4 0.4220 7.2760 23.2 1.7260 8.5990 23.6 7.5300 9.9220 24.9 16.630 1.2380 34.4 34.470 2.8830 27.1 27.1160 6.6020 29.2 29.2180 6.8060 37.7 4.5220 8.3190 31.2 6.7260 9.8310 26.6 12.7300 11.3440 29.9 25.9

26°

38°

Circumferential Crack Length

Stress Intensity Factor (ksi*(in)1/2)

Nozzle Angle

0°

18°

High Yield, Large Gap Case

EPRI

SCC Crack Growth Data for Nozzle Material in Reactor Environment

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

1E-13 1E-12 1E-11 1E-10

Power-Law Constant α at 325°C (617°F)

Cum

ulat

ive

Dis

trib

utio

n F

Heat Basis Data

MLE Log-Normal Distribution(Heat Basis)

Test Point Basis Data

Cubic Fit to Log-Residuals (PointBasis)

Assume CGR exponent β = 1.16

2.89×10-12

75th Percentile

5.00×10-12

EPRI

CGR Initiation vs. Growth Correlationrho = -0.8

-0.8

y = -0.7963x + 0.908R2 = 0.6329

0

0.2

0.4

0.6

0.8

1

1.2

0 0.2 0.4 0.6 0.8 1 1.2Random # for Leakage

Ran

dom

# fo

r Cra

ck G

row

th

EPRI

Software Modifications (to Address Comments from 2/21/02 NRC Meeting)

• Model Heats of Tubes rather than Individual Tubes♦ Head modeled by finite number of heats (1 to Ntubes)♦ Random variables for nozzle leakage and crack growth rate first

determined for each heat♦ Second set of random variables then determined for individual

tubes within a heat.♦ Correlation factor between leakage and crack growth rates applied

to both sets of random variables• Truncation of Tails of Distributions

♦ Crack Growth Rate Distributions (both heat-to-heat and within-heat) can be specified as either Log-Normal (un-truncated) or Log-Triangular (truncated)

• Degraded POD for Subsequent Inspections♦ Software now accepts “degradation factor” input for subsequent

inspections of leaking tubes which were previously inspected andmissed

EPRI

CGR Distributions Based on Heat Data

0.000

0.100

0.200

0.300

0.400

0.500

0.600

0.700

0.800

0.900

1.000

1.000E-09 1.000E-08 1.000E-07 1.000E-06 1.000E-05 1.000E-04

Power Law Constant at 617 F (in/hr)

Cum

ulat

ive

Dis

trib

utio

n F

Heat DataLog-NormalLog-Triangular

EPRI

Multiplier on CGR Distribution for Within-Heat Variability

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

0.01 0.1 1 10 100

Multiplier on Power Law Constant(for within-heat variability)

Cum

ulat

ive

Dis

trib

utio

n F

All Test DataLog-NormalLog-Triangular

EPRI

PFM Results w/ Modified Software(602°F Head Temp.; No Inspection)

0.20%

0.25% 0.27%0.28%

0.36% 0.37%

0.47%0.49%

0.50%

0.54%

0.61%0.64%

0.69%

0.74%

0.00%

0.10%

0.20%

0.30%

0.40%

0.50%

0.60%

0.70%

0.80%

20 20.8 21.6 22.4 23.2 24 24.8

EFPY

Prob

. (N

SC) Log-Triang; 3 Heats

Log-Triang; 69 HeatsLog-Norm; 3 HeatsLog-Norm; 69 Heats

EPRI

Benchmarking of PFM Resultswith respect to B&W Plants

0%

10%

20%

30%

40%

50%

60%

70%

80%

90%

100%

15 17 19 21 23 25 27

EFPYs

Cum

ulat

ive

Prob

abili

ty

LeaksLg.CircsNSCs

Oconee-3, Mar-0120.1 EFPY

EPRI

Technical Basis for Inspection Plan- Basic Concept -

• Start with “benchmarked” analysis parameters from B&W plant analysis

• Analyze plants at various head temperatures• Set risk categories based on probability of Net

Section Collapse (per year) and cumulative leakage probability

• Set inspection intervals based on effect of various inspections on probability of Net Section Collapse (per year)

EPRI

“Benchmarked” Analysis Parameters

• Head Temperature: Various from 560°F to 605°F • Weibull Parameters:

♦ Slope = 3♦ Beta = 15 ± 6 (Triangular)

• Crack Growth Rate Statistics♦ Heat-to-Heat - Log-Triangular: -15.25 ± 2.212♦ Within Heat – Log-Triangular: 0 ± 1.6

• Crack Growth vs. Leakage Correlation Factors♦ 0.8 – Heat-to-Heat♦ 0.8 – Within-Heat

• Acceptability Criteria: PDF of NSC < 1 x 10-3 per year

EPRI

Inspection Plan PFM Runs:Probability of NSC (per year)

0.00E+00

2.00E-04

4.00E-04

6.00E-04

8.00E-04

1.00E-03

1.20E-03

1.40E-03

1.60E-03

1.80E-03

2.00E-03

0 10 20 30 40 50 60 70

EFPYs

Prob

abili

ty. o

f NSC

(per

yea

r)

570 F575 F580 F586 F590 F594 F595 F597 F598 F602 F605 F

1 x 10-3

1 x 10-4

EPRI

Inspection Plan PFM Runs:Cum. Probability of Leakage

0%

10%

20%

30%

40%

50%

60%

70%

80%

90%

100%

0 10 20 30 40 50 60 70

EFPYs

Cum

. Pr

obab

ility

of 1

st L

eak

in H

ead

570 F575 F580 F586 F590 F594 F598 F602 F605 F

20%

75%

EPRI

PFM Convergence Study(@ 600°F)

0.00E+00

1.00E-03

2.00E-03

3.00E-03

4.00E-03

5.00E-03

6.00E-03

7.00E-03

8.00E-03

0 5 10 15 20 25 30 35

EFPYs

Prob

abili

ty o

f NSC

(per

yea

r)

0%

10%

20%

30%

40%

50%

60%

70%

80%

90%

100%

Cum

. Pro

babi

lity

of L

eak

NSC-10KNSC-100KNSC - 1000KLeaks-10K Leaks-100KLeaks - 1000K

EPRI

Definition of Susceptibility Categories Based on PFM Results

0

10

20

30

40

50

60

70

80

90

100

550 560 570 580 590 600 610

Current Temp.

Equi

vale

nt E

FPY

@ C

urre

nt T

emp.

NSC=1E-3NSC=1E-4Leaks = 75%Leak=20%LeaksCracks/No LeaksInsp/CleanSpring 02Later

3 pts

High RiskModerateRisk

Low Risk

EPRI

Correspondence of Susceptibility Categories to EDYs

0

10

20

30

40

50

60

70

80

90

100

550 560 570 580 590 600 610

Current Temp.

Equi

vale

nt E

FPY

@ C

urre

nt T

emp.

NSC=1E-3NSC=1E-4Leak-75%Leak=20%LeaksCracks/No LeaksInsp/CleanSpring 02Later5 EDYs10 EDYs15 EDYs18 EDYs5 EDYs

10 EDYs

15 EDYs

18 EDYs

3 pts.

EPRI

Inspection Frequency Runs:Probabilities of Detection

• Bare Metal Visual Inspections (BMV)♦ Initial POD = 0.6♦ POD for Subsequent Exams = 0.2 x Initial POD (when Leakage

missed)

• Non-Destructive Examinations (NDE)♦ POD = f(crack depth) per EPRI-TR-1020741

♦ 80% Coverage Assumed

1Dimitrijevic, V. and Ammirato, F., “Use of Nondestructive Evaluation Data to Improve Analysis of Reactor Pressure Vessel Integrity, “ EPRI Report TR-102074, Yankee Atomic Electric Co. March 1993

EPRI

Probability of Detection Curvesfor NDE

-0.2

0

0.2

0.4

0.6

0.8

1

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7

Crack Depth (in.)

Prob

. of D

etec

tion

(ND

E)

Full=V UT.8 x FullV

EPRI

0.00E+00

5.00E-04

1.00E-03

1.50E-03

2.00E-03

2.50E-03

3.00E-03

10 15 20 25 30 35

EFPYs

Prob

abili

ty o

f NSC

(per

yea

r)

No InspectionBMV ea. RFOBMV 2-EDYBMV 4-EDY

P(NSC) =.001 @ 18 EDY

Inspection Plan Technical Basis:Effect of Visual Inspection Runs

EPRI

0.00E+00

5.00E-04

1.00E-03

1.50E-03

2.00E-03

2.50E-03

3.00E-03

10 15 20 25 30 35

EFPYs

Prob

abili

ty o

f NSC

(per

yea

r)

No InspectionNDE 4-EDYNDE 8-EDY

P(NSC) =.001 @ 18 EDY

Inspection Plan Technical Basis:Effect of NDE Inspection

EPRI

Deterministic Crack Growth Analyses

• Uses Expert Panel recommended crack growth law♦ 2 x 75th Percentile of all data♦ da/dt = C(K-8.19)1.16

Temperature (ºF) C

580 3.604x10-7

590 4.665x10-7

600 6.008x10-7

602 6.316x10-7

605 6.806x10-7

EPRI

Deterministic Crack Growth Analyses

• Uses Stress Intensity Factors from plant specific analysis of Westinghouse plant♦ High Angle Nozzle (43.5° nozzle angle)♦ Higher Ks than B&W plant results

63.710.5730058.19.1626051.97.7522047.26.3418029.26.1616027.12.707034.41.1630

Ksi*in 1/2InchesDegreesK Circ. Crack Length

EPRI

Deterministic Crack GrowthAnalysis Results

Time for Initial Flaw Size of 30º Circumference to Grow to 165º

and 300º (EFPY) Westinghouse-Type Plant

Temperature (ºF)

165º 300º

580 23.7 31.7 590 18.3 24.6 600 14.2 19.1 602 13.5 18.2 605 12.5 16.8

EPRI

Deterministic Crack Growth ResultsAdded to Susceptibility Category Plot

0

10

20

30

40

50

60

70

80

90

100

550 560 570 580 590 600 610

Current Temp.

Equi

vale

nt E

FPY

@ C

urre

nt T

emp.

NSC=1E-3NSC=1E-4Leaks = 75%Leak=20%LeaksCracks/No LeaksInsp/CleanSpring 02LaterDetereministic

3 pts

High RiskModerateRisk

Low Risk

EPRI

Conclusions

• PFM Incorporates:♦ Weibull model of time to leakage♦ Finite Element Fracture Mechanics model for B&W type head♦ Crack growth rate statistics from Expert Panel♦ Effect of various inspection types, intervals and POD♦ Heat-basis analysis from NRC Comments♦ Log-Triangular and Log-Normal CGR Distributions

• Inspection Plan Technical Basis Runs:♦ Start with “benchmarked” analysis parameters from B&W plant

analysis♦ Analyze plants at various head temperatures♦ Set risk categories based on probability of Net Section Collapse

(per year) and cumulative leakage probability♦ Set inspection intervals based on effect of various inspection types

and frequency on probability of Net Section Collapse (per year)

EPRI

Conclusions (cont’d)

• Susceptibility Categories Based on PFM Results♦ Low –Risk:: 0 < EDYs < 10♦ Moderate Risk: 10 < EDYs < 18♦ High Risk: 18 < EDYs

• Inspection Type and Frequency Results♦ Inspection cases run with conservative POD assumptions♦ BMV each RFO upon entering High Risk Category reduces

probability of NSC to acceptable level indefinitely♦ NDE every 4 EDYs upon entering High Risk Category reduces

probability of NSC to essentially nil

• Deterministic Crack Growth Results♦ Conservatively bounds times from moderate to high risk

susceptibility regions