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NUREG-2228 Dfc, Weld Residual Stress Finite Element Analysis Validation - Part II - Proposed Validation Procedure.
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Issue date:	08/31/2018
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	Meyd, Donald
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NURE G-22 28Weld Residual S t ress Finite Element A nalysis V alidation Part II-P ropos ed Validati on ProcedureOffice of N uclear Regulator y Research AVAILABILITY OF REFERENCE MATERIALSIN NRC PUBLICATIONS NRC Reference Material As of November 1999, you may electronically access NUREG-series publications and other NRC records at

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NUREG-2 228 Weld R esidual S t ress Finite Element A nalysis V alidation Part II-Pr opos ed Validati on Procedure Manuscript Completed: Date Published: Prepared by

M.Benson P.Raynaud J.Wallace Michael B enson, N RC Project M anagerOf fi of N uclear Regulatory Research COMMENTS ON DRAFT REPORT Any interested party may submit comments on this report for consideration by the NRC staff. Comments may be accompanied by additional relevant information or supporting data. Please specify the report number NUREG-2228 in your comments, and send them by the end of the comment period specified in the Federal Register notice announcing the availability of this report. A ddr esses: You may submit comments by any one of the following methods. Please include Docket ID NRC-2018-0168 in the subject line of your comments. Comments submitted in writing or in electronic form will be posted on the NRC website and on the Federal rulemaking website http://www.regulations.gov. Federal Rulemaking Website

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ii i ABSTRACT Under a Memorandum of Understanding, the U.S. Nuclear Regulatory Commission and the Electric Power Research Institute conducted a research program aimed at gathering data on weld residual stress modeling. As described in NUREG

-2162, "Weld Residual Stress Finite Element Analysis Validation:

Part I-Data Development Effort," issued March 2014, this program consisted of round robin measurement and modeling studies on various mockups. At that time, the assessment of the data was qualitative. This report describes an additional residual stress round robin study and a methodology for capturing residual stress uncertainties.

This quantitative approach informed the development of guidelines and a validation methodology for finite element prediction of weld residual stress. For example, comparisons of modeling results to measurements provided a basis for establishing guidance on a material hardening approach for residual stress models. The proposed validation procedure involves an analyst modeling a known case (the Phase 2b round robin mockup) and comparing results to three proposed quality metrics. These recommendations provide a potential method by which analysts can bolster confidence in their modeling practices for regulatory applications.

v TABLE OF CONTENTS ABSTRACT ...............................................................................................................................iii LIST OF FIGURES

....................................................................................................................ix LIST OF TABLES

......................................................................................................................

xi EXECUTIVE

SUMMARY

.........................................................................................................

xiii ACKNOWLEDGMENTS

...........................................................................................................

xv ABBREVIATIONS AND ACRONYMS

....................................................................................

xvii 1 INTRODUCTION

................................................................................................................. 1-1 1.1 Phase 2b Effort .................................................................................................................. 1-1 1.2 Scope of This Report

......................................................................................................... 1-2 2 PHASE 2B ROUND ROBIN STUDY

.................................................................................... 2-1 2.1 Purpose

............................................................................................................................. 2-1 2.2 Mockup Fabrication ........................................................................................................... 2-1 2.3 Round Robin Participants

.................................................................................................. 2-3 2.4 Weld Residual Stress Measurements

................................................................................ 2-3 2.5 Modeling Guidance

............................................................................................................ 2-6 2.6 Results

............................................................................................................................... 2-7 2.6.1 Measurement Results

............................................................................................... 2-8 2.6.2 Modeling Results

...................................................................................................... 2-9 2.6.3 Discussion

............................................................................................................... 2-11 2.7 Conclusions ..................................................................................................................... 2-11 3 UNCERTAINTY QUANTIFICATION METHODOLOGY

....................................................... 3-1 3.1 Motivation

.......................................................................................................................... 3-1 3.2 Methodology ...................................................................................................................... 3-1 3.2.1 Functional Data

......................................................................................................... 3-1 3.2.2 Screening of Outlier Predictions

................................................................................ 3-2 3.2.3 Data Smoothing

........................................................................................................ 3-2 3.2.4 Amplitude and Phase Variability

............................................................................... 3-3 3.2.5 Modeling Amplitude and Phase Variability

................................................................ 3-4 3.2.6 Bootstrapping

............................................................................................................ 3-5 3.2.7 Uncertainty Characterization of the Measurement Data

........................................... 3-5 3.2.8 Tolerance Bounds versus Confidence Bounds

......................................................... 3-6 3.3 Results

............................................................................................................................... 3-6 3.3.1 Uncertainty Quantification for the Prediction Data

.................................................... 3-6 vi 3.3.2 Uncertainty Quantification for the Deep Hole Drilling Measurement Data

.............. 3-11 3.3.3 Uncertainty Quantification for the Contour Measurement Data

.............................. 3-15 3.4 Conclusions

..................................................................................................................... 3-16 4 WRS IMPACT ON FLAW GROWTH CALCULATIONS

....................................................... 4-1 4.1 Regulatory Application

....................................................................................................... 4-1 4.2 Inputs

................................................................................................

................................. 4-2 4.3 Superposition of Stresses

.................................................................................................. 4-3 4.4 Stress Intensity Factor and Crack Growth

......................................................................... 4-4 4.5 Flaw Growth Results

.......................................................................................................... 4-6 4.6 Discussion

......................................................................................................................... 4-8 4.7 Conclusion

....................................................................................................................... 4-11 5 VALIDATION PROCEDURE AND FINITE ELEMENT GUIDELINES

.................................. 5-1 5.1 Introduction

........................................................................................................................ 5-1 5.2 Material Hardening Law

..................................................................................................... 5-1 5.2.1 Difference in Means and Root Mean Square Error Functions

.................................. 5-1 5.2.2 Assessment of Prediction Trends

............................................................................. 5-2 5.2.3 Assessment of Root Mean Square Error

.................................................................. 5-8 5.2.4 Hardening Law Recommendation

........................................................................... 5-10 5.3 Modeling Guidelines

........................................................................................................ 5-10 5.4 Proposed Validation Scheme

.......................................................................................... 5-12 5.4.1 Overview of Approach

............................................................................................. 5-12 5.4.2 Benchmark

.............................................................................................................. 5-13 5.4.3 Circumferential Flaw Growth - Isotropic Hardening

................................................ 5-14 5.4.4 Circumferential Flaw Growth - Average Hardening

................................................ 5-15 5.4.5 Axial Flaw Growth - Isotropic Hardening

................................................................ 5-17 5.4.6 Axial Flaw Growth - Average Hardening

................................................................ 5-19 5.4.7 Overview of Quality Metrics

.................................................................................... 5-20 5.4.8 Quality Metrics for Axial Stress Predictions

............................................................ 5-21 5.4.9 Recommended Acceptance Measures - Axial Residual Stress

............................. 5-25 5.4.10 Quality Metrics for Hoop Stress Predictions

.......................................................... 5-25 5.4.11 Recommended Acceptance Measures - Hoop Residual Stress

.......................... 5-28 5.5 Summary of Validation Procedure

................................................................................... 5-29 5.6 Modeling a Nuclear Plant Application

.............................................................................. 5-30 5.6.1 Applicability of Validation Scheme and Acceptance Measures

.............................. 5-30 5.6.2 Welding Process

..................................................................................................... 5-32 vii 5.6.3 Hardening Law

........................................................................................................ 5-32 5.6.4 Best Practices for a Plant Application

..................................................................... 5-32 5.7 Conclusion

....................................................................................................................... 5-32 6 CONCLUSIONS

.................................................................................................................. 6-1 7 REFERENCES

.................................................................................................................... 7-1 APPENDIX A MOD EL-MEASUREMENT COMPARISONS

.................................................... A-1 APPENDIX B MATERIAL PROPERTIES

............................................................................... B-1 APPENDIX C TABLES FOR VALIDATION PROCESS

.......................................................... C-1 APPENDIX D ANALYSIS OF VALIDATION METRICS FOR AVERAGE HARDENING

......... D-1 APPENDIX E ANALYSIS OF VALIDATION METRICS FOR ISOTROPIC HARDENING

....... E-1 viii ix LIST OF FIGURES Figure 2-1: Phase 2b Mockup Geometry (Dimensions in inches [millimeters])

............................ 2-2 Figure 2-2: Participating Organizations

........................................................................................ 2-3 Figure 2-3: Deep Hole Drilling Measurement Setup

..................................................................... 2-4 Figure 2-4: Hole Drilling Measurements around Circumference

.................................................. 2-5 Figure 2-5: Contour Measurement Setup

..................................................................................... 2-5 Figure 2-6: Cuts to Extract Contour Specimen

............................................................................. 2-6 Figure 2-7: Hole Drilling Measurement: (a) Axial, (b) Hoop

.......................................................... 2-8 Figure 2-8: Hoop Stress

-Contour Measurement

........................................................................ 2-8 Figure 2-9: Axial Stress

-Contour Measurement

......................................................................... 2-9 Figure 2-10: Example Mesh

....................................................................................................... 2-10 Figure 2-11: Processed Isotropic Hardening Results: (a) Axial, (b) Hoop

.................................. 2-11 Figure 2-12: Processed Nonlinear Kinematic Hardening Results: (a) Axial, (b) Hoop

............... 2-11 Figure 3-1: Axial Isotropic Data after Smoothing

.......................................................................... 3-3 Figure 3-2: Amplitude and Phase Variability

................................................................................ 3-3 Figure 3-3: Axial Isotropic Data after Alignment

........................................................................... 3-4 Figure 3-4: 100 Sampled WRS Curves Based upon Round Robin Modeling Data

...................... 3-5 Figure 3-5: Contour Axial Stress Data

.......................................................................................... 3-6 Figure 3-6: Constructing Confidence Bounds on the Mean (Axial, Isotropic Case)

...................... 3-7 Figure 3-7: Constructing Tolerance Bounds (Axial, Isotropic Case)

............................................. 3-8 Figure 3-8: Bootstrap Tolerance Bounds on Isotropic Hoop Stress Predictions

........................ 3-10 Figure 3-9: Data Smoothing for Axial DHD Data

........................................................................ 3-12 Figure 3-10: Confidence Bounds on the Mean (Axial DHD Data)

.............................................. 3-13 Figure 3-11: Tolerance Bounds (Axial DHD Dat a) ..................................................................... 3-13 Figure 3-12: Confidence Bounds on Mean (Hoop DHD Data)

................................................... 3-14 Figure 3-13: Tolerance Bounds (Hoop DHD Data)

..................................................................... 3-14 Figure 3-14: 50 Extracted Stress Profiles

................................................................................... 3-15 Figure 3-15: Tolerance Bounds for Axial Contour Data.

............................................................. 3-16 Figure 4-1: ASME Code Flaw Disposition Procedure

................................................................... 4-1 Figure 4-2: Analytical Flaw Evaluation Procedure

........................................................................ 4-2 Figure 4-3: Loads from Various Sources

...................................................................................... 4-3 Figure 4-4: Superposition of Membrane, Crack

-Face Pressure, and Weld Residual Stresses

.... 4-4 Figure 4-5: SIF at Two Locations along Crack Front

.................................................................... 4-5 Figure 4-6: (a) K 90 and (b) Growth in Depth Direction

.................................................................. 4-7 Figure 4-7: (a) K 0 and (b) growth in length direction

..................................................................... 4-8 Figure 4-8: Flaw Growth after 20 Years ....................................................................................... 4-9 Figure 4-9: (a) Membrane Stresses, (b) Area under the Curve

.................................................. 4-10 Figure 5-1: Nonlinear Kinematic Hardening Predictions against the DHD Measurements

.......... 5-3 Figure 5-2: Isotropic Hardening Predictions against the DHD Measurements

............................. 5-5 Figure 5-3: Average Hardening Predictions against the DHD Measurements

............................. 5-6 Figure 5-4: Root Mean Square Error for Axial Stress Predictions

................................................ 5-9 Figure 5-5: Root Mean Square Error for Hoop Stress Predictions

............................................. 5-10 Figure 5-6: Comparison of DHD and Contour Axial Stress Predictions (a) Raw Data and (b) Difference in Means.

................................................................................................. 5-14 Figure 5-7: Smoothed Axial WRS Profiles and Mean, Isotropic Hardening

............................... 5-14 Figure 5-8: Circumferential Flaw Growth, Isotropic Hardening

................................

................... 5-15 Figure 5-9: Smoothed Axial WRS Profiles, Average Hardening

................................................. 5-16 x Figure 5-10: Circumferential Flaw Growth, Average Hardening

................................................. 5-16 Figure 5-11: Smoothed Hoop WRS Profiles, Isotropic Hardening

.............................................. 5-17 Figure 5-12: Axial Flaw Growth, Isotropic Hardening

................................................................. 5-18 Figure 5-13: Hoop WRS Profiles, Average Hardening

............................................................... 5-19 Figure 5-14: Axial Flaw Growth, Average Hardenin g ................................................................. 5-19 Figure 5-15: Stress Intensity Factor: (a) Isotropic Hardening and (b) Average Hardening

......... 5-20 Figure 5-16: Prediction C (Isotropic) against the Mean Prediction

............................................. 5-23 Figure 5-17: Prediction F (Isotropic) against the Mean Prediction

.............................................. 5-24 Figure 5-18: Comparison of First Derivatives

............................................................................. 5-24 Figure 5-19: Hoop Stress Prediction from Participant G

............................................................ 5-26 Figure 5-20: Hoop Stress Prediction from Participant C ............................................................. 5-27 Figure 5-21: Hoop Stress Prediction from Participant D

............................................................. 5-28 Figure 5-22: A Partial Arc Weld Repair

...................................................................................... 5-31 Figure 5-23: EWR Mockup

......................................................................................................... 5-31 xi LIST OF TABLES Table 2-1: Mockup Fabrication Steps

........................................................................................... 2-3 Table 2-2: Model Guidance

.......................................................................................................... 2-7 Table 4-1: Inputs for Flaw Growth Calculations

............................................................................ 4-3 Table 4-2: Symbol Definition for Equation 4-3 .............................................................................. 4-6 Table 5-1: Benchmark Cases and Their Location in Appendix A

................................................. 5-7 Table 5-2: Qualitative Assessment of Prediction Bias

.................................................................. 5-8 Table 5-3: RMSE for DHD Benchmark

......................................................................................... 5-9 Table 5-4: RMSE for Contour Benchmark

.................................................................................... 5-9 Table 5-5: Time to Through

-Wall ................................................................................................ 5-18 Table 5-6: Quality Metrics Applied to Phase 2b Axial Isotropic Predictions

............................... 5-22 Table 5-7: Quality Metrics Applied to the Phase 2b Axial Average Hardening Predictions

........ 5-25 Table 5-8: Quality Metrics Applied to Phase 2b Hoop Isotropic Predictions

.............................. 5-26 Table 5-9: Quality Metrics Applied to Phase 2b Hoop Average Hardening Predictions

............. 5-28 Table 5-10: Acceptance Measures for Axial Stresses

................................................................ 5-30 Table 5-11: Acceptance Measures for Hoop Stresses

............................................................... 5-30

xiii EXECUTIVE

SUMMARY

Weld residual stress (WRS) is known to be an important driver of primary water stress corrosion cracking in safety

-related nuclear piping. For this reason, it is desirable to formalize finite element modeling procedures for residual stress prediction. The U.S. Nuclear Regulatory Commission (NRC) and the Electric Power Research Institute have conducted joint research programs on residual stress prediction under a memorandum of understanding. These studies have involved modeling and measurement of WRS in various mockups. The latest of these studies, Phase 2b, is discussed in this document.

The Phase 2b mockup was prototypic of a pressurizer surge nozzle dissimilar metal weld, which forms part of the reactor coolant pressure boundary. Two sets of residual stress measurement data were obtained on the Phase 2b mockup: deep hole drilling and contour. Both these methods are strain

-relief techniques. In addition to the measurements, 10 independent analysts submitted finite element modeling results of the residual stresses in the mockup. Each participant was provided the same set of modeling guidelines, with the aim of reducing analyst

-to-analyst scatter as much as possible. These measurement and modeling data were then used to develop an uncertainty quantification methodology.

The residual stress uncertainty methodology consisted of constructing a statistical model of the data and using bootstrapping methods to calculate relevant 95/95 tolerance bounds and confidence bounds. This methodology improves on past work (e.g., NUREG-2162, "Weld Residual Stress Finite Element Analysis Validation: Part I-Data Development Effort," issued March 2014), which described uncertainty in WRS predictions only in qualitative terms. Furthermore, the results of the uncertainty quantification effort informed the development of a validation approach of residual stress finite element models.

The uncertainty quantification work provided methods to compare measurements to models, which in turn led to recommendations on hardening law (see Section 5.2). The validation method is a step-by-step procedure for comparing independent finite element modeling results of the Phase 2b mockup to the acceptance measures. If an analyst meets the criteria, then the modeling procedure may be applied with greater confidence to a real case. This procedure is intended as a recommendation rather than a regulatory requirement. It provides a means to demonstrate proficiency in finite element modeling of WRS. The validation methodology is aimed at WRS predictions for deterministic flaw growth evaluations.

The nuclear industry often performs flaw evaluations when seeking alternatives to established inspection and repair/replacement rules. These evaluations require a WRS assumption. If that assumption is based on finite element results, then following the validation procedure offers the industry one method to strengthen its case when seeking NRC approval. This document also investigated how differences in residual stress can affect these flaw evaluations. Important features of the stress profiles include the inner diameter stress, the stress magnitude at the initial flaw depth, and the depths at which the stress profile crosses zero. Decision

-makers can review these aspects of submitted stress profiles as another option for gaining confidence in residual stress predictions.

xv ACKNOWLEDGMENTS The authors would like to thank the following.

John Broussard of Dominion Engineering, Inc., Paul Crooker of the Electric PowerResearch Institute (EPRI), and Michael Hill of University of California, Davis for technicalcooperation in the joint NRC

-EPRI research program.Dusty Brooks, Remy Dingreville, and John Lewis of Sandia National Laboratory for theirexcellent work on developing an uncertainty quantification scheme for the round robi n dataset (see Chapter 3).The round robin modeling participants for contributing their work to this effort, as descri bed in Chapter

2.

xvi i ABBREVIATIONS AND ACRONYMS ASME Code American Society of Mechanical Engineers Boiler and Pressure Vessel Code DHD deep hole drilling EPRI Electric Power Research Institute EWR excavate and weld repair FE finite element fPCA functional principal components analysis ID inner diameter mm millimeter MPa megapascal NDE nondestructive examination NRC U.S. Nuclear Regulatory Commission OD outer diameter PWSCC primary water stress corrosion cracking RMSE root mean square error SIF stress intensity factor WRS weld residual stress i reference index k reference index k mean at the k th position through the wall thickness k standard deviation at the k th position through the wall thickness wi weighting factor for the i th WRS profile xi,kWRS stress magnitude of the ith profile at the kth position through the thickness f a function r radial position through the wall thickness t wall thickness of the weld or pipe d normalized distance through the wall thickness, d = r/t warping function T operating temperature P operating pressure time K I mode I stress intensity factor a half-depth of a flaw xviii c half-length of a flaw m membrane stress b bending stress cfp crack face pressure stress G b influence coefficient for global bending Q flaw shape parameter h(x,a) weight function for the Universal Weight Function Method s(x) stress variation along the crack face da/d flaw growth with respect to time KIth stress intensity factor threshold Q g activation energy R g ideal gas constant T abs absolute operating temperature Tref empirical reference temperature tabulated crack growth coefficient tabulated crack growth coefficient K 90 SIF at the deepest point along the crack front K 0 SIF at the surface point along the crack front g a function L number of locations through the wall thickness where a WRS magnitude is known n e number of sampled measurement WRS profiles n p number of sampled prediction WRS profiles s reference index h(d) difference in means function RMSEWRS quality metric on the root mean square error of stress magnitude WRSmean benchmark WRS (the mean of the isotropic predictions from the Phase 2b study)

D 1 first derivative of the WRS magnitude with respect to through

-wall position h interval between two positions through the wall thickness RMSE D1 quality metric on the root mean square error of D1 diffavg quality metric on the average difference between the prediction WRS and the benchmark value