status of recent practical applications of pfm to the

Status of Recent Practical Applications of PFM to the Assessment of Structural Systems in

Nuclear Plants in the United States

Mark Kirk* Senior Materials Engineer United States Nuclear Regulatory Commission Office of Nuclear Regulatory Research Division of Engineering, Component Integrity Branch [email protected]

International Symposium on Improvement of Nuclear Safety Using Probabilistic Fracture Mechanics Organized by the PFM Subcommittee, Atomic Energy Research Committee

of the Japan Welding Engineering Society

24th October 2014 – Tokyo, Japan

* The views expressed herein are those of the author. They do not constitute an official position of the USNRC.

mailto:[email protected]

Outline

• Comparison of deterministic & probabilistic approaches to structural integrity assessment

• Example Application 1: pressurized thermal shock (PTS) of the reactor pressure vessel (RPV)

• Example Application 2: leak before break (LBB) of primary system piping

• Concluding remarks

プレゼンター

プレゼンテーションのノート

Does this overall outline suit KINS?

• Easier … – than probabilistic analyses – to demonstrate their

conservatism than for a probabilistic analysis

• A simplified example – One variable (X1) controls

operating lifetime – A conservative upper

bound on X1 produces a safe (& reasonable) lower-bound estimate of operating life

Deterministic Analyses Why do we use them?

Ope

ratin

g Li

fetim

e

Single Controlling Variable, X1

Cons

erva

tive

uppe

r-bo

und

on X

1

Lower-bound estimate of operating life

Deterministic Analyses When do they break down?

Operating Lifetime

X1

X2

• A slightly less simplified example – Two variables (X1 & X2)

control operating lifetime – Conservative upper bounds

on X1 & X2 can produce a safe (but unreasonable) lower-bound estimate of operating life

• The unreasonableness becomes more extreme as the number of controlling variables increases (X1, X2, X3, … Xn)

Lower-bound estimate of operating life

Conservative upper-bound on X2

• To address deficiencies of the deterministic approach: – Conservatism quickly

multiplies • When every variable is

bounded • When inherently conservative

models are used – Does not scale well to multi-

variate problems • Quantifying the conservatism

of the answer becomes impossible

• Probabilistic approach – Conservatism & safety

ensured by controlling to the end result (failure probability)

Probabilistic Analyses Why might they be used?

An Incomplete List of Variables in a PTS Analysis

Deterministic vs. Probabilistic Reality

PFAILURE Distributions

Driving Force

Resistance Zero

DF R Small

DF R Large

Actual Situation (Reality)

The requirement imposed in a deterministic framework …

… is a comforting abstraction, but it obscures the fact that in the reality we seek to represent driving force and resistance are inherently distributed quantities.

Deterministic vs. Probabilistic Mathematical Models of Reality

PFAILURE Distributions Deterministic Models of Reality

Probabilistic

Driving Force

Resistance Zero

DF R DF R

DF R Small

DF R DF R

DF R Large

DF R DF R

Actual Situation (Reality)

Estimate: No “Failure” Estimate: PFAIL=0

Estimate: “Failure” Estimate: PFAIL= Very Small

Estimate: “Failure” Estimate: PFAIL= Large

Future events are correctly represented as probabilities, not absolutes.

Similarities • Both treat uncertainty

– Deterministic models bound uncertainty

– Probabilistic models quantify uncertainty

• Probabilistic models may contain deterministic aspects where full information is lacking, e.g.: – Conservative models – Bounding inputs – And so on …

Differences • How result is expressed

– Deterministic: “Failed” or “Not Failed”

– Probabilistic: A failure probability

• Who the decisionmaker is – Deterministic: Only the

engineering analyst (because “failure” is unacceptable)

– Probabilistic: Many people (because some failure probability can be accepted)

Deterministic vs. Probabilistic Similarities and Differences

Nothing changes by adopting a probabilistic analysis, other than acknowledging that which already exists.

PRESSURIZED THERMAL SHOCK First Example Application of PFM

TOPERATING = 290 oC

Secondary Break TMIN = 100 oC

Primary Break TMIN ~ 5 oC

Temperature

Frac

ture

Tou

ghne

ss

RTNDT@LIMIT

• 10 CFR 50.61 (PTS Rule) – Established 1985 – Conservatisms inherent to

basis for RTPTS can limit operable lifetime

• Considerations in development of 10 CFR 50.61a (Alternate Rule) – 10 CFR 50.61 conservatisms

will cause plant-specific submittals, all addressing the same issues

– Alternative approaches considered • Individual review of plant-

specific assessments • Comprehensive re-assessment

of PTS performed proactively & with thorough review by technical experts

Pressurized Thermal Shock

Initial RTNDT

Increasing Time in Operation

Key Aspects of 10 CFR 50.61a Development

• Policy Establishing a risk-informed limit consistent with Commission policy guidance

• Technical Translating this limit into screening tool expressed in terms of measurable variables (e.g., embrittlement, flaws)

• Communication and Education Obtaining input from and addressing the concerns of a diverse array of constituencies

プレゼンター


This is a more formal presentation of our analysis process.

10 CFR 50.61a Limits Follow from Policy Decisions

Mean ∆-Mean CDF 10-4/ry 10-5/ry LERF 10-5/ry 10-6/ry

Regulatory Guide 1.174

51 FR 28044, Safety Goal Policy Statement (1986)

SECY-00-0077, Modifications to Safety Goal Policy Statement CDF < 1x10-4/ry CDF & QHO limits for generic decisions

QHOs < 0.1% of the total public risk (prompt & latent)

10 CFR 50.61a Voluntary Alternative Pressurized Thermal Shock Rule

• Accident sequence progression study shows that through-wall cracking rarely leads to LERF

• Conservatively assumes equivalence of LERF and the yearly through-wall cracking frequency (TWCF) of the reactor pressure vessel

• Along with defense-in-depth considerations, a tolerable limit on TWCF established as 10-6/ry

Technical Approach

#1. Commission guidance drives performance metric, and limit value.

プレゼンター



#2. Staff develops & links models to estimate this performance metric.

Technical Approach

プレゼンター



#3. Metric estimated based on detailed analysis of 3 plants.

Beaver ValleyBeaver ValleyPalisadesPalisades

OconeeOconee

Technical Approach

プレゼンター



#4. These results + other insights motivate generalization to all plants.

Technical Approach

プレゼンター



Probabilistic Fracture Model

Flaw density, location,Length, & depth

FlawDistribution

Model

Pressure vs. time

Temperature vs. time

ThermalHydraulics

Model

EventSequence

EventFrequency

PRAModel

Fluence on Vessel IDNeutronics

Model

Material Property &Composition Data

CrackInitiation

Model

ConditionalProbability of

Crack Initiation

Through Wall Cracking

Model

ConditionalProbability of

Thru-Wall Cracking

MatrixMultiply

YearlyFrequency of

Thru-WallCracking

Fracture MechanicsModel

Next Slide

AppliedKI

Elastic Modulus

Vessel Diameter

Un-IrradiatedIndex

Temperature(RTNDT(u)*)

IrradiatedInitiation

ToughnessIndex

Temperature(RTTOUGH(I))

ResistanceKIc

ResistanceKIc

dKI/dt > 0AND

A-KI > R-KIc

InitiationToughnessTransition

Curve

CPI>0

StressIntensity

FactorModeldKI/dt

RTNDT(u)Method

RTNDT(u)(RVID)

YES

Generic?

YES

NOσ(u) = 0

σ(u) = S(µ,σ)+Conversion

to ToughnessTransition

TemperatureUn-Irradiated

Toughness IndexTemperature(RTTOUGH(U))

IrradiatedToughness Shift

(∆RTTOUGH)

1

+

CPI=0

NO

Vessel Thickness

Clad Thickness

CTEPLATE

Poisson’s Ratio

P&T vs. t

T vs. t

WeldFlaw?

NO

YES

RTTOUGH(I) =MAXIMUM OF RTTOUGH(I)

WELD, & RTTOUGH(I)

ADJACENT PLATE

Flaw Locationin Vessel Wall, x’

Flaw Depth, a

Flaw AspectRatio, 2c/a

Flaw Density, ρ

Weld σresidual

CTE Mismatchσresidual

CTEWELD

INDEX TEMPERATURE SHIFT MODEL

UNIRRADIATED INDEXTEMPERATURE MODEL

FRACTURE DRIVINGFORCE MODEL

SampledFluence At Flaw

CharpyIrradiation

ShiftModel

CharpyTemperatureShift (∆T30)

Oper.Temp.

Cu(RVID)

Thru-WallAttenuation

Model

Best-EstimateID Fluence

(Reg-Guide Calcs.)

Ni(RVID)

P(RVID)

Oper.Time

ProductForm

VesselMfg.

Conversionto Toughness

Shift

GlobalFluence

Uncertainty

SampledID Fluence

LocalFluence

Uncertainty

FluenceAt Flaw

CuUncertainty

SampledCu

NiUncertainty

SampledNi

PUncertainty

SampledP

Details of the Crack Initiation Model

Details of some models follow

KIc

Parameters of the Initiation Model

RTNDT 0

100

200

300

400

-150 -100 -50 0 50T-RT NDT [oC]

KJc

[M

Pa*m

0.5 ]

E1921 Valid E399 Valid

ASME KIC Curve

Parameters of Crack Initiation Model

0

100

200

300

400

-150 -100 -50 0 50T-RT NDT [oC]

KJc

[M

Pa*m

0.5 ]

E1921 Valid E399 Valid

ASME KIC Curve

Uncertainty Treatment in the Crack Initiation Model • Because of implicit conservative

bias, fracture toughness models based on the RTNDT index temperature contain a mix of

• Epistemic uncertainty in RTNDT, and

• Aleatory uncertainty in KIc

• Use of the best-estimate Master Curve index temperature (To) effectively removes epistemic uncertainty, leaving only the aleatory uncertainties produced by material variability

E1921 Valid

E399 Valid

1% LB

M edian

99% UB

T-To [oC]

PFM 21

Crack Initiation Toughness KJc

Crack Arrest Toughness

KIa

Upper Shelf Toughness

JIc

PFM 22

Crack Initiation Toughness KJc

Upper Shelf Toughness JIc

Upper Shelf Toughness: JIc Master Curve [EricksonKirk]

-200

0

200

400

600

800

1000

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

Temperature [oC]

∆J I

c = J

Ic -

J Ic(

288)

[kJ

/m2 ]

RPV Weld (U)RPV Weld (I)RPV Plate (U)RPV Plate (I)RPV Forging (U)HSLA PlateMild Steel PlateZA Fit to Data, alpha=1.75mm2.5% Bound97.5% Bound

Crack Arrest Toughness KIa

Crack Arrest Toughness: KIa Master Curve [Wallin, Kirk]

-150 -100 -50 0 500

50

100

150

200

250

95 % 5 %

KIa [

MP

a√m

]

T-TKIa [°C]

σ = 18 %

Crack Initiation Toughness: KJc Master Curve [Wallin]

0

100

200

300

400

500

600

700

800

-300 -200 -100 0 100 200 300

T - T o [oF]

1T E

quiv

alen

t KJc

[ks

i*in0.

5 ]

PC-CVN 1/2T 1T 2T 3 & 4T 6T 8T 9T 10T 11T 95% LB 1T MC 5% UB

PFM 23

Crack Arrest Toughness

KIa

Upper Shelf Toughness

JIc

Crack Arrest Toughness: KIa Master Curve [Wallin, Kirk]

-150 -100 -50 0 500

50

100

150

200

250

95 % 5 %

KIa [

MP

a√m

]

T-TKIa [°C]

σ = 18 %

Upper Shelf Toughness: JIc Master Curve [EricksonKirk]

-200

0

200

400

600

800

1000

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

Temperature [oC]

∆J I

c = J

Ic -

J Ic(

288)

[kJ

/m2 ]

RPV Weld (U)RPV Weld (I)RPV Plate (U)RPV Plate (I)RPV Forging (U)HSLA PlateMild Steel PlateZA Fit to Data, alpha=1.75mm2.5% Bound97.5% Bound

Crack Initiation Toughness: KJc Master Curve [Wallin]

0

100

200

300

400

500

600

700

800

-300 -200 -100 0 100 200 300

T - T o [oF]

1T E

quiv

alen

t KJc

[ks

i*in0.

5 ]


Lognormal ModelTKIa - To = 44.1e(-0.006To)

σ ln(∆RTARREST) = 0.39

-200

-100

0

100

200

-200 -100 0 100 200T o [oC]

T KIa

[o C

]

Wallin ORNL Mean 5% 95% 1:1

TUS = 0.7985To + 48.843R2 = 0.9812

-150

-50

50

150

-200 -100 0 100 200T o [oC]

T US [o C

]

AllWeldPlateForgingHSLAMild SteelLinear (All)

MC

: KJc

0

100

200

300

400

500

600

700

800

-300 -200 -100 0 100 200 300

T - T o [oF]

1T E

quiv

alen

t KJc

[ks

i*in0.

5 ]


Major Outcomes of PTS Re-Evaluation Analyses

• What operational transients most influence PTS

risk?

• What material features most influence PTS risk?

• Are these dominant material features / transients common across the fleet?

• New limits on embrittlement based on RI calculations

Important Transient Classes

1.E-14

1.E-13

1.E-12

1.E-11

1.E-10

1.E-09

1.E-08

1.E-07

1.E-06

1.E-05

1.E-04

550 650 750 850

Max RT [R]

August 2006FAVOR 06.1

Beaver

Oconee

Palisades

Fit4

3

2

0

9

8

7

6

5

4

550 650 750 850

Max RT [R]


Beaver

Oconee

Palisades

Fit4

3

2

1

0

9

8

7

6

5

4

550 650 750 850

Max RT [R]


Beaver

Oconee

Palisades

Fit

95th

Perc

entil

e TW

CF

Medium & Large ∅

Pipe Breaks

Main Steam

Line Breaks

Stuck-Open

Primary Valves

Important Transient Classes

0%

20%

40%

60%

80%

100%

200 250 300 350 400 450

Con

trib

utio

n to

Tot

al T

WC

F

Max RT [oF]

Medium and Large Diameter Pipe Breaks (LOCAs)Stuck Open Valves, Primary SystemMain Steam Line Breaks

Primary side faults dominate risk: lower temperature

Important Material Features 95

thPe

rcen

tile

TWC

F

1.E-14

1.E-13

1.E-12

1.E-11

1.E-10

1.E-09

1.E-08

1.E-07

1.E-06

1.E-05

1.E-04

1.E-03

550 650 750 850

Max. RTAW [R]


Beaver

Oconee

Palisades

Fit

2

0

8

7

6

5

550 650 750 850

Max. RTPL [R]


Beaver

Oconee

Palisades

Fit

2

0

8

7

6

5

550 650 750 850

Max RTCW [R]


Beaver

Oconee

Palisades

Fit

Axial Weld Flaws

Circumferential Weld Flaws

Plate Flaws

Important Material Features

0%

20%

40%

60%

80%

100%

200 250 300 350 400 450

Con

trib

utio

n to

Tot

al T

WC

F

Max RT [oF]

Axial Weld FlawsFlaws in Plates (remote from welds)Circumferential Weld Flaws

Axial weld flaws dominate risk: size & orientation

10 CFR 50.61 REQUIRED

10 CFR 50.61a VOLUNTARY

Reference Temperature Limits More restrictive Less restrictive

Plant-specific surveillance data check Required – 1 test Required – 3 tests

Plant specific inspection for flaws Not required Required

Less restrictive embrittlement limits are justified by new calculations, & enable longer operations, but

gating criteria must be satisfied to use 10 CFR 50.61a.

Outcome 50.61 vs. 50.61a Comparison

10 CFR 50.61a Limits for Plate Plants

1x10-6/ry TWCF limit

Simplified ImplementationRTMAX-AW ≤ 269°F, andRTMAX-PL ≤ 356°F, andRTMAX-AW + RTMAX-PL ≤ 538°F.

1x10-6/ry TWCF limit

Simplified ImplementationRTMAX-AW ≤ 222°F, andRTMAX-PL ≤ 293°F, andRTMAX-AW + RTMAX-PL ≤ 445°F.

tWALL < 9½-in.

tWALL = 10½- to 11½-in.

If plants can satisfy the gating criteria, most should be compliant with 10 CFR 50.61a.

• 50.61a opens the possibility for increased operational lifetime with no compromise to safety – New embrittlement limits

justified by more realistic analysis

• Making this change took considerable time & resources: – Complexity of the topic – “New” approach

(“probabilistic” instead of “deterministic”)

– Variety of stakeholders involved

• Unanticipated benefits – Comprehensive review of

all model components – Updated state of

knowledge influences regulations

10 CFR 50.61a Summary

1998

2000

2002

2010

2016

2014

2012

2008

2006

2004

Project Started

10 CFR 50.61a issued

1st consensus PFM code available

Technical reports approved by ACRS Rulemaking begins

DG-1299 released for public comment

Model Development

Building the technical

case

Deciding & Approving

Guidance

Com

mun

icat

ion

& co

nsen

sus b

uild

ing

Beaver Valley submits

Palisades submits

LEAK BEFORE BREAK Second Example Application of PFM

LBB Background Problem Being Addressed

• 10 CFR 50 Appendix A General Design Criteria 4: permits exclusion of local dynamic effects of pipe ruptures from design basis

• LBB-justified modifications to plant design (e.g. elimination of pipe whip restraints, jet impingement shields) have been approved … – Assuming that no active degradation mechanisms exist – But active degradation mechanisms (PWSCC) do exist

• Solutions – Short term: mitigations and inspections – Long term: probabilistic evaluation

LBB used in Oil and GasPraise first released

NUREG-1061SRP3.6.3 Rev 0

First LBB approval

First Alloy 600 cracking

LBB Reg Guide Draft

VC Summer crackPRO-LOCA first released

MPR-139

Wolf Creek

SRP3.6.3 Rev 1NUREG-1829RIS2008-25

xLPR initiatedxLPR pilot complete

xLPR V2 complete

LBB regulation-->

1975 1980 1985 1990 1995 2000 2005 2010 2015 2020

• Develop a probabilistic assessment tool that can be used to directly assess compliance with 10 CFR 50 App-A GDC-4

• Tool will be – Comprehensive with respect to

known challenges and loadings – Vetted with respect to scientific

adequacy of models and inputs – Flexible to permit analysis of a

variety of in service situations – Adaptable: able to accommodate

• evolving / improving knowledge • new damage mechanisms

xLPR Overview Goals & Timeline

2008

2010

2012

2018

2016

2014

Project Started

Pilot Study Complete

xLPR Version 2 Code Complete LBB Reg. Guide

2020

Criterion 4: Structures, systems, and components important to safety shall … shall be appropriately protected against dynamic effects. … However, dynamic effects associated with postulated pipe ruptures in nuclear power units may be excluded from the design basis when analyses … demonstrate that the probability of fluid system piping rupture is extremely low …

Technical Scope of xLPR Project xLPR = eXtremely Low Probability of Rupture

Prob

abili

ty D

ensi

ty (%

)

Failure Frequency / year

• Conduct analyses with baseline conditions (per SRP 3.6.3)

Change in risk acceptable?

• Conduct analyses with modified condition

Change in risk acceptable!

PWSCC

Weld Overlay

Baseline Results

Slide 35

Quantify effect of current mitigations & inspections to inform future decisions

xLPR Status & Team Members • Pilot study [Complete]

– To demonstrate feasibility – Determine appropriate

probabilistic framework – Develop plan for future

version

• V2.0 [Underway] – Develop tool for use in LBB

Reg. Guide development – Permit quantitative

assessment of compliance with GDC-4

– Prioritize future research efforts

• LBB Reg. Guide [Future] – Effort beginning in 2015 – Possible replacement or

augmentation to SRP 3.6.3

PEAI

xLPR Technical Flow

0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

0.45

Crack Mechanism

Loads

Initiation

Crack Coalescence

t=ti

Material Properties

t=t+∆t

yes

Inspection/ Mitigation

Crack Growth

Stability Leakage

Rupture, tf

Slide 37

OBJECTIVES • Develop and assess xLPR

management structure • Determine appropriate

probabilistic framework • Assess the feasibility of

developing a modular PFM code

FEATURES • Focused on pressurizer surge

nozzle DM weld with PWSCC

• Used comprehensive configuration management

• Developed detailed program plan for future activities

RESULTS • Demonstrated it is feasible to

develop a modular-based probabilistic fracture mechanics code within a cooperative agreement while properly accounting for the problem uncertainties

• Identified potential efficiency gains in the program management structure

• Selected commercial software as the computational framework

xLPR Pilot Study

xLPR Pilot Study Example Results

0

10

20

30

40

50

60

70

80

4.6E-08 6.7E-07 1.3E-06 1.9E-06 2.6E-06 3.2E-06

Prob

abili

ty D

istr

ibut

ion

Func

tion

Mean Probability of Rupture

Pressurizer surge nozzle dissimilar metal weld – PWSCC only

xLPR Version 2.0 Goals

• Version 2.0 is expanded to handle welds within piping systems approved for LBB – Appropriate materials, loads, degradation

mechanisms, mitigation, inspection, leak detection

• Rigorous quality assurance including verification and validation (V&V) process

• Capabilities of Version 2.0 will meet requirements for LBB lines, but must stay within available cost and schedule limitations

• Model inclusion in xLPR Version 2.0 does not guarantee regulatory approval.

xLPR Version 2.0 High Level Flow Chart

xLPR Version 2.0 Framework

GUI/Input database

Landing platform

Physical models

This strategy allows for multi-entities to share and work on the framework development in an efficient and parallel manner.

GoldSim software

Slide 42

Closing Remarks

• PFM in General A logical process for realistic assessment of structural reliability.

• RPV Integrity Successfully applied to PTS. Work is in-progress in other areas (normal heatup & cooldown).

• Primary Piping Integrity Work underway to apply PFM insights to LBB regulations and requirements.

プレゼンター



status of recent practical applications of pfm to the

Documents