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Probabilistic Fracture MechanicsProbabilistic Fracture MechanicsAnalysis of CRDM NozzlesAnalysis of CRDM Nozzles
Weibull Model for Time to FirstLeakage or Cracking
• Analysis method due to Dominion Engineering♦ Weibull Slope = 3.0 (assumed)♦ Determine best fit through field inspection results
• Analysis limited to just those plants that haveperformed non-visual NDE, plus those in whichvisual exams have found leakage or cracking♦ Population = 30 plants♦ 12 had leaks or significant cracking
• Plants w/ multiple affected nozzles extrapolatedback to predict time to first leak or crack♦ w/ assumed Weibull slope of 3
• Effects of different Weibull parameters addressedvia sensitivity studies♦ Slope b and characteristic failure time θ
EPRI
EPRI
EPRI
Material Crack Growth RateStatistics
• Stress corrosion crack growth data for Alloy 600taken from MRP-55
• Statistical distributions developed for heat-to-heatvariation as well as for variability of CGR within aspecific heat
• Statistical sampling of CGR for PFM analysisassumed to be correlated with Weibull statistics fortime to leakage (I.e. nozzles which leak early tendto be sampled from high end of CGR distribution)
• Crack growth statistics updated based on latestMRP-55 qualified data set♦ 26 heats♦ 158 data points
EPRI
CGR DistributionsBased on Heat Data
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
1E-08 1E-07 1E-06 1E-05
Power-Law Constant αααα at 617°F (in/hr & ksi-in^0.5)
Cum
ulat
ive
Dist
ribu
tion F
Log-mean α 's for 26 heats of Alloy 600material assuming β = 1.16 with fit log-normal & log-triang. distributions
α 25th Percentile = 1.07 ×10-7
α 75th Percentile = 4.21×10-7
25th Percentile
75th Percentile
α 50th Percentile = 2.12 ×10-7Median
Peak of log-triang. distribution = 1.8 ×10-6 ( 8.5 x median)
EPRI
Multiplier on CGR Distribution forWithin-Heat Variability
0.0000
0.1000
0.2000
0.3000
0.4000
0.5000
0.6000
0.7000
0.8000
0.9000
1.0000
0.100 1.000 10.000
Multiplier on Power Law Constant(for within-heat variability)
Cum
ulat
ive
Dis
trib
utio
n F
All Test DataLog-NormalLog-Triangular
Peak of log-triang. distribution = 4.2 x median
EPRI
New Base Case Results600°F No Inspection; New Weibull & CGR Fits
18.416.8
0.00E+00
2.50E-04
5.00E-04
7.50E-04
1.00E-03
1.25E-03
1.50E-03
1.75E-03
2.00E-03
2.25E-03
2.50E-03
2.75E-03
3.00E-03
0 5 10 15 20 25 30 35
EFPYs
PDF
of N
SC (p
er y
ear)
Max Stress Envelope
Stresses on 1500 Plane
Stresses on 1400 Plane11.5
Prior Analyses
Current Analysis
EPRI
Inspection Interval AnalysisParameters
• Head Temperature: Various from 580°F to 600°F• Weibull Parameters:
• Probability Targets:♦ Probability of NSC < 1 x 10-3 per plant per year♦ Low Probability of Leak (or significant cracking)
EPRI
Inspection Interval AnalysisProbability of Detection for NDE
• Non-Destructive Examinations (NDE)♦ POD = f(crack depth) per EPRI-TR-1020741
♦ 80% Coverage Assumed
• POD Curve Compared to Vendor InspectionDemonstrations
1Dimitrijevic, V. and Ammirato, F., “Use of Nondestructive Evaluation Datato Improve Analysis of Reactor Pressure Vessel Integrity, “ EPRI ReportTR-102074, Yankee Atomic Electric Co. March 1993
EPRI
POD Curve for NDE (IllustratingComparison to Vendor Demonstrations)
Probability of Detection Curve Used in MRPER Algorithm
0%
15%
30%
45%
60%
75%
90%
0.000 0.100 0.200 0.300 0.400 0.500 0.600 0.700
Flaw Size (in)
Prob
abili
ty o
f Det
ectio
n
FULLV Curve from Ref.1Vendor 1Vendor 2
Detected
Not Detected
EPRI
Effect of NDE on NSC(600 F Head, Various Inspection Intervals)
Comparison of Net Section Collapse Probabilities at 600oF
0.0E+00
2.5E-04
5.0E-04
7.5E-04
1.0E-03
1.3E-03
1.5E-03
1.8E-03
2.0E-03
2.3E-03
2.5E-03
0 5 10 15 20 25 30
EFPYs
PDF
of N
SC (p
er y
ear)
PDF of NSC (MAX ) w/oinspection [Base Case]
PDF of NSC (MAX) w/ 8-yrFULLV insp. (11.8)
PDF of NSC (MAX) w/ 4-yrFULLV insp. (11.8)
PDF of NSC (MAX) w/ 2-yrFULLV insp. (11.8)
EPRI
Deterministic Crack GrowthAnalyses
• MRP-55 CGR correlations used - 75th percentileαααα = 4.21 x 10-7, with factor of 2 applied forevaluation of OD connected circumferential flaws
• Stress Intensity Factors for envelope stress planeused to compute crack growth from 30° to ASMESection XI allowable crack length (~ 300°)
• Analyses performed for steepest angle nozzles intypical B&W and Westinghouse Plant
• Analyses run for various head temperaturesusing standard activation energy temperatureadjustment on crack growth law
• Results Indicate that probabilistic-basedinspection intervals are conservative
Growth time from 30 degree to 300 degree flaw, Westinghouse 49 degree nozzle TEMPERATURE DEGREES F
UPHILL (EFPH)
UPHILL (EFPY)
DOWNHILL (EFPH)
DOWNHILL (EFPY)
580 no growth no growth 125500 14.33 590 no growth no growth 97000 11.07 600 no growth no growth 76000 8.68 602 no growth no growth 72000 8.22 605 no growth no growth 67000 7.65
EPRI
Sensitivity Studies
• Effect of Worst Case θθθθ from Weibull• Effect of Weibull Slope b• Effect of Initiation-Growth Correlation Factor• Typical Plant-Specific Application
EPRI
Sensitivity to Weibull CharacteristicTime to Failure (θθθθ)
Comparison of Net Section Collapse Probabilities at 600oFBase Case vs Lower Bound Theta = 11.8 EDYs
0.0E+00
2.5E-04
5.0E-04
7.5E-04
1.0E-03
1.3E-03
1.5E-03
1.8E-03
2.0E-03
2.3E-03
2.5E-03
0 5 10 15 20 25 30
EFPYs
PDF
of N
SC (p
er y
ear)
PDF of NSC (MAX ) w/oinspection [Base Case]
PDF of NSC (MAX) w/ 4-yrFULLV insp. (11.8)
Lower Bound Theta - NoInsp.
Lower Bound Theta - 4 yrInsp.
EPRI
Sensitivity to Weibull Slope (b)Comparison of Net Section Collapse Probabilities at 600oF
Base case b=3 vs. b=3.46 and b=4.48
0.0E+00
2.5E-04
5.0E-04
7.5E-04
1.0E-03
1.3E-03
1.5E-03
1.8E-03
2.0E-03
2.3E-03
2.5E-03
0 5 10 15 20 25 30
EFPYs
PDF
of N
SC (p
er y
ear)
PDF of NSC (MAX ) w/oinspection [Base Case]
PDF of NSC (MAX) w/ 4-yrFULLV insp. (11.8)
No Inspect, b=3.46
No Inspect, b=4.48
EPRI
Effect of Inspections on Leakage
• Primary Goal of PFM is to ensure that inspectioninterval protects against nozzle ejection
• However, effect of inspections on leakageprobability (Weibull hazard rate) generated as by-product of analyses
• Results indicate that reasonable assuranceagainst leakage maintained, but this is dependenton inspection coverage (80% assumed)
EPRI
Leakage Probability (w/o NDE)
5%
10%
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 40
EDYs
Prob
. of L
eak
(or S
igni
fican
t Cra
ckin
g)
Cum F(t)Monte F(t)Leak Rate z(t)Monte z(t)PDF f(t)Monte f(t)
EPRI
Effect of NDEon Leakage Probability
5%
10%
0.00E+00
2.00E-02
4.00E-02
6.00E-02
8.00E-02
1.00E-01
1.20E-01
1.40E-01
1.60E-01
1.80E-01
2.00E-01
0 5 10 15 20 25 30 35 40
EDYs
Prob
. of L
eak
(or S
igni
fican
t Cra
ckin
g)
No Insp.FULLV@ 2-yr IntervalFULLV @ 4-yr IntervalFULLV @ 8-yr Interval
EPRI
Conclusions• Current PFM Incorporates:
♦ Updated Weibull model of time to leakage or cracking, including Spring-03results
♦ Finite Element Fracture Mechanics model updated addressing NRCcomments
♦ Crack growth rate statistics based on MRP-55 w/ correlation between timeto leakage and CGR
♦ Effect of inspection POD and intervals• Important Results
♦ 4 EDY inspection interval supports safety limit for nozzle ejection andreasonable goals for probability of leakage