Probabilistic Fracture Mechanics Analysis of CRDM Nozzles

Probabilistic Fracture MechanicsProbabilistic Fracture MechanicsAnalysis of CRDM NozzlesAnalysis of CRDM Nozzles

Presented at:Presented at:NRC MeetingNRC MeetingRockville, MDRockville, MD

Presented by:Dr. Peter C. Riccardella

Structural Integrity AssociatesJune 12, 2003

EPRI

Meeting Objectives

• Discuss new MRP analyses performed to addressNRC comments on prior analyses plus new data

• Establish agreement on major assumptions inPFM analysis

• Demonstrate use of probabilistic anddeterministic fracture mechanics analyses toestablish re-inspection intervals for non-visualNDE

EPRI

Major Presentation Topics

• Revised Stress Intensity Factor Calculations• New Weibull Analysis of Time to Leakage /

Significant Cracking• Material Crack Growth Rates• Effect of Inspections• Deterministic Analysis• Sensitivity Studies

EPRI

Fracture Mechanics Models

• Original analysis assumed part-through-wall (PTW)cracks (a/t = 0.5, length = 30º) when leakagepredicted from Weibull model

• PTW cracks were assumed to propagate from 30ºto 160º length, then transition to through-wallcracks for propagation from 180º to 300º

• NRC requested that we investigate effect ofassuming through-wall cracks over entirepropagation length (30º to 300º)

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Fracture MechanicsPart-Through-Wall Flaw Model

Part-through-wall axialcrack branches and turnscircumferential (parallel toJ-Groove Weld)

EPRI

Fracture MechanicsThrough-Wall Crack Model

1

3.9245"

0.563"

1.527 "

CRDM NOZZLE, 26.1 Deg. AZIMUTH, 180 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

Circumferential through-wallcrack of various lengths(Parallel to J-Groove Weld)

Back wall constraint modelseffect of interference atvessel wall

EPRI

Fracture Mechanics Models (cont’d)

• Original FM analyses modeled stresses onvarious planes parallel to J-groove weld root♦ (I.e. 1400, 1500 planes in next slide)

• Stresses transition from primarily residual toprimarily pressure loading as plane movesupward away from J-groove weld

• NRC requested that we investigate effect ofassuming crack follows plane of maximum stress

EPRI

Illustration of Stress Planes

1500 plane -

1400 plane -

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Stresses along Various Stress PlanesAVERAGE NORMAL STRESS DISTRIBUTION

38.5 Degree Nozzle, 50 ksi Yield Strength

-10000

-5000

0

5000

10000

15000

20000

0 20 40 60 80 100 120 140 160 180 200

AZIMUTH from Uphill Side (degree)

Stre

ss (p

si)

1400s

1500s

1600s

2100s

ENVELOP

1400s

1500's

1600s

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Stress Intensity FactorsUphill Cracking

Average Stress Intensity Factors vs. Crack AngleUphill Flaws; Envelop Stress

0

10000

20000

30000

40000

50000

60000

70000

0 20 40 60 80 100 120 140 160 180 200 220 240 260 280 300 320

Total Crack Angle (Degree)

Stre

ss In

tens

ity F

acto

r (ps

i-in0.

5 ), C

onst

rain

ed

BW-0 Deg.BW-18 Deg.BW-26 Deg.BW-38 Deg.

EPRI

Stress Intensity FactorsDownhill Cracking

Average Stress Intensity Factors vs. Crack AngleDownhill Flaws; Envelop Stress

0

20000

40000

60000

80000

100000

120000

140000

160000

0 20 40 60 80 100 120 140 160 180 200 220 240 260 280 300 320


Stre

ss In

tens

ity F

acto

r (ps

i-in0.

5 ), C

onst

rain

ed

BW-0 Deg.

BW-18 Deg.

BW-26 Deg.

BW-38 Deg.

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Stress Intensity Factor ComparisonStress Intensity Factor Comparison - B&W HeadUphill Flaws; SI w/Envelope Stresses vs. EMC^2

0

10000

20000

30000

40000

50000

60000

70000

0 20 40 60 80 100 120 140 160 180 200 220 240 260 280 300 320 340 360


Stre

ss In

tens

ity F

acto

r (ps

i-in0.

5 ), C

onst

rain

ed

BW-0 Deg.

BW-18 Deg.

BW-26 Deg.

BW-38 Deg.

EMC2-Sidehill

EMC2-Center

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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

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

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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)

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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

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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

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Max Stress Envelope

Stresses on 1500 Plane

Stresses on 1400 Plane11.5

Prior Analyses

Current Analysis

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Inspection Interval AnalysisParameters

• Head Temperature: Various from 580°F to 600°F• Weibull Parameters:

♦ Slope = 3♦ Theta = 16.45; +6.5, -4.65 (Triangular)

• Crack Growth Rate Statistics♦ Heat-to-Heat - Log-Triangular: -15.365 ± 2.14♦ Within Heat – Log-Triangular: 0 ± 1.4343

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

• Probability Targets:♦ Probability of NSC < 1 x 10-3 per plant per year♦ Low Probability of Leak (or significant cracking)

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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

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PDF of NSC (MAX ) w/oinspection [Base Case]

PDF of NSC (MAX) w/ 8-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

EPRI

Stress Intensity Factor SummaryB&W Type Plant

Crack Angle (degrees)

K - UPHILL SIDE FLAWS (psi-in^0.5)

K - DOWNHILL SIDE FLAWS (psi-in^0.5)

38 DEG. 26 DEG. 18 DEG. 0 DEG. 38 DEG. 26 DEG. 18 DEG. 0 DEG.

30 20141 17334 10711 6780 11227 10142 8985 6780

90 37722 34557 20565 15484 33760 26415 22528 15484

160 51559 47718 32124 26336 68230 53181 42552 26336

180 54337 49976 35163 29383 78168 60404 47890 29383

220 56867 53293 40401 34688 94384 75337 57878 34688

260 59702 56314 44839 38758 115569 90144 65578 38758

300 64773 63152 51868 44166 140471 104128 74058 44166

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Stress Intensity Factor SummaryWestinghouse Type Plant

Total Flaw Angle

(Degrees)

Average K on Crack Front

(psi-in^0.5) Downhill Uphill

30 28790 4942 90 59336 14302

160 84080 21782 180 86557 24115 220 89310 30100 260 92769 38017 300 93453 50009

EPRI

Deterministic Crack GrowthAnalysis Results

Growth time from 30 degree to 300 degree flaw, B&W 38 degree nozzle TEMPERATURE DEGREES F

UPHILL (EFPH)

UPHILL (EFPY)

DOWNHILL (EFPH)

DOWNHILL (EFPY)

580 218000 24.89 205000 23.40 590 168000 19.18 158000 18.04 600 131000 14.95 123000 14.04 602 125000 14.27 117000 13.36 605 116000 13.24 109000 12.44

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

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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

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Lower Bound Theta - NoInsp.

Lower Bound Theta - 4 yrInsp.

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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

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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

♦ Deterministic Fracture Mechanics analysis supports longer inspectionintervals

♦ Sensitivity studies indicate results not highly sensitive to reasonableranges of key variables

• Remaining Tasks♦ Complete analyses for CE and Westinghouse plant types♦ Documentation

Probabilistic Fracture Mechanics Analysis of CRDM Nozzles

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