Status of Recent Practical Applications of PFM to the Assessment of Structural Systems in Nuclear Plants in the United States

Transcription

1 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 * The views expressed herein are those of the author. They do not constitute an official position of the USNRC. 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 24 th October 2014 Tokyo, Japan

2 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 Slide 2

3 Deterministic Analyses Why do we use them? 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) lowerbound estimate of operating life Operating Lifetime Lower-bound estimate of operating life Conservative upperbound on X1 Single Controlling Variable, X1 Slide 3

4 Deterministic Analyses When do they break down? 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) Slide 4 X2 Operating Lifetime Conservative upperbound on X2 X1 Lower-bound estimate of operating life

5 Probabilistic Analyses Why might they be used? 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 multivariate problems Quantifying the conservatism of the answer becomes impossible An Incomplete List of Variables in a PTS Analysis Probabilistic approach Conservatism & safety ensured by controlling to the end result (failure probability) Slide 5

6 Deterministic vs. Probabilistic Reality The requirement imposed in a deterministic framework Actual Situation (Reality) Distributions P FAILURE Zero Driving Force Resistance 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. Small Large DF DF R R Slide 6

7 Deterministic vs. Probabilistic Mathematical Models of Reality Actual Situation (Reality) Models of Reality P FAILURE Distributions Deterministic Probabilistic Zero Driving Force Resistance DF R DF R Estimate: No Failure Estimate: P FAIL =0 Small DF R DF R DF R Estimate: Failure Estimate: P FAIL = Very Small Large DF R DF R Estimate: Failure DF R Estimate: P FAIL = Large Slide 7 Future events are correctly represented as probabilities, not absolutes.

8 Deterministic vs. Probabilistic Similarities and Differences Similarities Both treat uncertainty Deterministic models bound uncertainty Probabilistic models quantify uncertainty Differences How result is expressed Deterministic: Failed or Not Failed Probabilistic: A failure probability Slide 8 Probabilistic models may contain deterministic aspects where full information is lacking, e.g.: Conservative models Bounding inputs And so on Who the decisionmaker is Deterministic: Only the engineering analyst (because failure is unacceptable) Probabilistic: Many people (because some failure probability can be accepted) Nothing changes by adopting a probabilistic analysis, other than acknowledging that which already exists.

9 First Example Application of PFM PRESSURIZED THERMAL SHOCK Slide 9

10 Pressurized Thermal Shock 10 CFR (PTS Rule) Established 1985 Conservatisms inherent to basis for RT PTS can limit operable lifetime Considerations in development of 10 CFR 50.61a (Alternate Rule) 10 CFR conservatisms will cause plant-specific submittals, all addressing the same issues Alternative approaches considered Individual review of plantspecific assessments Comprehensive re-assessment of PTS performed proactively & with thorough review by Slide 10 technical experts Fracture Toughness Increasing Time in Operation Initial RT NDT Primary Break T MIN ~ 5 o C Temperature T OPERATING = 290 o C Secondary Break T MIN = 100 o C RT NDT@LIMIT

11 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 Slide 11

12 10 CFR 50.61a Limits Follow from Policy Decisions 51 FR 28044, Safety Goal Policy Statement (1986) SECY , Modifications to Safety Goal Policy Statement Regulatory Guide CFR 50.61a Voluntary Alternative Pressurized Thermal Shock Rule QHOs < 0.1% of the total public risk (prompt & latent) CDF < 1x10-4 /ry CDF & QHO limits for generic decisions Mean -Mean CDF 10-4 /ry 10-5 /ry LERF 10-5 /ry 10-6 /ry 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 Slide 12

13 Technical Approach Slide 13 #1. Commission guidance drives performance metric, and limit value.

14 Technical Approach Slide 14 #2. Staff develops & links models to estimate this performance metric.

15 Technical Approach Palisades Beaver Valley Slide 15 Oconee #3. Metric estimated based on detailed analysis of 3 plants.

16 Technical Approach Slide 16 #4. These results + other insights motivate generalization to all plants.

17 Probabilistic Fracture Model Fracture Mechanics Model Pressure vs. time Temperature vs. time Thermal Hydraulics Model Event Sequence Flaw density, location, Length, & depth Flaw Distribution Model Conditional Probability of Thru-Wall Cracking Through Wall Cracking Model Conditional Probability of Crack Initiation Crack Initiation Model PRA Model Fluence on Vessel ID Neutronics Model Yearly Frequency of Thru-Wall Cracking Matrix Multiply Material Property & Composition Data Event Frequency Next Slide Slide 17

18 Details of the Crack Initiation Model Details of some models follow Best-Estimate ID Fluence (Reg-Guide Calcs.) Global Fluence Uncertainty Flaw Location in Vessel Wall, x Sampled ID Fluence Flaw Density, ρ Flaw Depth, a Flaw Aspect Ratio, 2c/a Thru-Wall Attenuation Model Fluence At Flaw CPI=0 NO YES CPI>0 dk I /dt > 0 AND A-K I > R-K Ic Applied K I dk I /dt Stress Intensity Factor Model Vessel Diameter Vessel Thickness Elastic Modulus Poisson s Ratio P&T vs. t T vs. t CTE Mismatch σ residual Weld σ residual CTE PLATE CTE WELD Clad Thickness FRACTURE DRIVING FORCE MODEL Irradiated Toughness Shift ( RT TOUGH ) 1 Charpy Temperature Shift ( T 30 ) Conversion to Toughness Shift Charpy Irradiation Shift Model INDEX TEMPERATURE SHIFT MODEL Sampled Cu Sampled Ni Sampled P Cu Uncertainty Ni Uncertainty P Uncertainty Cu (RVID) Ni (RVID) P (RVID) Oper. Time Oper. Temp. Product Form Vessel Mfg. Sampled Fluence At Flaw Local Fluence Uncertainty Slide 18 Resistance K Ic Initiation Toughness Transition Curve NO Weld Flaw? YES RT TOUGH(I) = MAXIMUM OF RT TOUGH(I) WELD, & RT TOUGH(I) ADJACENT PLATE Irradiated Initiation Toughness Index Temperature (RT TOUGH(I) ) + Un-Irradiated Toughness Index Temperature (RT TOUGH(U) ) UNIRRADIATED INDEX TEMPERATURE MODEL Conversion to Toughness Transition Temperature Un-Irradiated Index Temperature (RT NDT(u) *) + σ (u) = 0 RTNDT(u) (RVID) NO Generic? YES σ (u) = S(µ,σ) RT NDT(u) Method

19 Parameters of Crack Initiation Model Parameters of the Initiation Model K Ic RT NDT 0 KJc [MPa*m 0.5 ] E1921 Valid E399 Valid ASME KIC Curve T-RT NDT [ o C] Slide 19

20 Uncertainty Treatment in the Crack Initiation Model Because of implicit conservative bias, fracture toughness models based on the RT NDT index temperature contain a mix of Epistemic uncertainty in RT NDT, and Aleatory uncertainty in K Ic Use of the best-estimate Master Curve index temperature (T o ) effectively removes epistemic uncertainty, leaving only the aleatory uncertainties produced by material variability KJc [MPa*m 0.5 ] E1921 Valid E1921 Valid E399 Valid E399 Valid ASME KIC Curve 1% LB M e dian 99% UB T-RT T-T NDT [ o C] o [ o C] Slide 20

21 Crack Initiation Toughness K Jc Crack Arrest Toughness K Ia Upper Shelf Toughness J Ic Slide PFM 21 21

22 Crack Initiation Toughness: K Jc 1T Equivalent K Jc [ksi*in 0.5 ] PC-CVN 1/2T 1T 2T 3 & 4T 6T 8T 9T 10T 11T 95% LB 1T MC 5% UB Crack Initiation K Jc Master Curve [Wallin] T - T o [ o F] K Ia [MPa m] PFM 22 Slide Crack Arrest Toughness K 95 % Ia 50 0 σ = 18 % 5 % T-T KIa [ C] Crack Arrest Toughness: K Ia Master Curve [Wallin, Kirk] JIc = JIc - JIc(288) [kj/m 2 ] Upper Shelf RPV Plate (I) Toughness 2.5% Bound J Ic RPV Weld (U) RPV Weld (I) RPV Plate (U) Temperature [ o C] RPV Forging (U) HSLA Plate Mild Steel Plate ZA Fit to Data, alpha=1.75mm 97.5% Bound Upper Shelf Toughness: J Ic Master Curve [EricksonKirk]

23 TKIa [ o C] Lognormal Model T KIa - T o = 44.1e (-0.006To) σ ln( RTARREST) = T Equivalent K Jc [ksi*in 0.5 ] Wallin ORNL 300 Mean 5% % 100 1: T o [ o C] 700 PC-CVN 600 1/2T 500 1T 400 2T & 4T 200 6T 100 8T 0 9T 10T 11T 95% LB 1T MC 5% UB 1T Equivalent K Jc [ksi*in 0.5 ] 800 PC-CVN 1/2T 1T 2T 3 & 4T 6T 8T 9T 10T 11T 95% LB 1T MC 5% UB T - T o [ o F] MC: K Jc T - T o [ o F] TUS [ o C] Crack Initiation All Toughness: Weld K Jc Master Plate Curve Forging [Wallin] HSLA Mild Steel Linear (All) T US = T o R 2 = T o [ o C] Crack 200 Arrest Toughness Upper Shelf Toughness 800 K Ia [MPa m] K Ia 100 Crack Arrest Toughness: K Ia Master Curve [Wallin, Kirk] PFM 23 Slide σ = 18 % 95 % 5 % T-T KIa [ C] JIc = JIc - JIc(288) [kj/m 2 ] J400 Ic RPV Weld (U) RPV Weld (I) RPV Plate (U) RPV Plate (I) Temperature [ o C] RPV Forging (U) HSLA Plate Mild Steel Plate ZA Fit to Data, alpha=1.75mm 2.5% Bound 97.5% Bound Upper Shelf Toughness: J Ic Master Curve [EricksonKirk]

24 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 Slide 24

25 Important Transient Classes Slide th Percentile TWCF 1.E-04 1.E-05 1.E-06 1.E-07 1.E-08 1.E-09 1.E-10 1.E-11 1.E-12 1.E-13 1.E-14 Medium & Large Pipe Breaks Max RT [R] August 2006 FAVOR 06.1 Beaver Oconee Palisades Fit Stuck- Open Primary Valves Max RT [R] August 2006 FAVOR 06.1 Beaver Oconee Palisades Fit Main Steam Line Breaks Max RT [R] August 2006 FAVOR 06.1 Beaver Oconee Palisades Fit

26 Important Transient Classes Contribution to Total TWCF 100% 80% 60% 40% 20% 0% Medium and Large Diameter Pipe Breaks (LOCAs) Stuck Open Valves, Primary System Main Steam Line Breaks Max RT [ o F] Primary side faults dominate risk: lower temperature Slide 26

27 Important Material Features 1.E-03 1.E-04 August 2006 FAVOR 06.1 August 2006 FAVOR 06.1 August 2006 FAVOR th Percentile TWCF 1.E-05 1.E-06 1.E-07 1.E-08 1.E-09 1.E-10 1.E-11 1.E-12 1.E-13 1.E-14 Axial Weld Flaws Max. RT AW [R] Beaver Oconee Palisades Fit Plate Flaws Max. RT PL [R] Beaver Oconee Palisades Fit Circumferential Weld Flaws Max RT CW [R] Beaver Oconee Palisades Fit Slide 27

28 Important Material Features Contribution to Total TWCF 100% 80% 60% 40% 20% 0% Axial Weld Flaws Flaws in Plates (remote from welds) Circumferential Weld Flaws Max RT [ o F] Axial weld flaws dominate risk: size & orientation Slide 28

29 Outcome vs a Comparison Less restrictive embrittlement limits are justified by new calculations, & enable longer operations, but gating criteria must be satisfied to use 10 CFR 50.61a. Reference Temperature Limits Plant-specific surveillance data check Plant specific inspection for flaws 10 CFR REQUIRED More restrictive Required 1 test Not required 10 CFR 50.61a VOLUNTARY Less restrictive Required 3 tests Required Slide 29

30 10 CFR 50.61a Limits for Plate Plants 1x10-6 /ry TWCF limit Simplified Implementation RT MAX-AW 269 F, and RT MAX-PL 356 F, and RT MAX-AW + RT MAX-PL 538 F. 1x10-6 /ry TWCF limit Simplified Implementation RT MAX-AW 222 F, and RT MAX-PL 293 F, and RT MAX-AW + RT MAX-PL 445 F. t WALL = 10½- to 11½-in. t WALL < 9½-in. Slide 30 If plants can satisfy the gating criteria, most should be compliant with 10 CFR 50.61a.

31 10 CFR 50.61a Summary 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 Project Started 1 st consensus PFM code available Technical reports approved by ACRS Rulemaking begins 10 CFR 50.61a issued Beaver Valley submits Palisades submits DG-1299 released for public comment Model Development Building the technical case Deciding & Approving Guidance Communication & consensus building Slide 31

32 Second Example Application of PFM LEAK BEFORE BREAK Slide 32

33 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 Gas Praise first released First LBB approval First Alloy 600 cracking VC Summer crack PRO-LOCA first released Wolf Creek xlpr initiated xlpr pilot complete xlpr V2 complete SRP3.6.3 Rev 0 RIS NUREG-1061 NUREG-1829 LBB regulation--> SRP3.6.3 Rev 1 MPR-139 Slide 33 LBB Reg Guide Draft

34 xlpr Overview Goals & Timeline 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 Slide 34 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 Project Started Pilot Study Complete xlpr Version 2 Code Complete LBB Reg. Guide

35 Technical Scope of xlpr Project xlpr = extremely Low Probability of Rupture Conduct analyses with baseline conditions (per SRP 3.6.3) Conduct analyses with modified condition Weld Overlay Probability Density (%) Change in risk acceptable! Baseline Results Change in risk acceptable? PWSCC Quantify effect of current mitigations & inspections to inform future decisions Slide Slide Failure Frequency / year

36 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 Slide 36 PEAI

37 xlpr Technical Flow Loads Material Properties Crack Growth Crack Coalescence t=t i Initiation t=t+ t Stability Leakage Inspection/ Mitigation yes Crack Mechanism Rupture, t f Slide Slide 37 37

38 xlpr Pilot Study 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 Slide 38

39 xlpr Pilot Study Example Results Pressurizer surge nozzle dissimilar metal weld PWSCC only Probability Distribution Function E E E E E E-06 Mean Probability of Rupture Slide 39

40 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. Slide 40

41 xlpr Version 2.0 High Level Flow Chart Slide 41

42 xlpr Version 2.0 Framework Landing platform GoldSim software GUI/Input database This strategy allows for multi-entities to share and work on the framework development in an efficient and parallel manner. Physical models Slide Slide 42 42

43 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. Slide 43