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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
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