Weld Residual Stress 

Finite Element Analysis 

Validation: Part 1 – Data 

Development Effort

Office of Nuclear Regulatory Research

NUREG-2162
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Weld Residual Stress 

Finite Element Analysis 

Validation: Part 1 – Data 

Development Effort

Manuscript Completed: February 2014

Date Published: March 2014

Prepared by: 

Michael Benson, David Rudland, and Aladar Csontos 

Michael Benson, NRC Project Manager

Office of Nuclear Regulatory Research

NUREG-2162

 

iii

ABSTRACT

This report is aimed at prediction of weld residual stress (WRS) in safety-related nuclear 

components. WRS is a significant driving force for primary water stress corrosion cracking. As 

such, it is an important input to deterministic and probabilistic flaw growth calculations.

The U.S. Nuclear Regulatory Commission’s objectives for this work include:

• Validate axisymmetric finite element modeling as a predictive tool for WRS, using robust 

experimental methods.

• Support the development of appropriate WRS/flaw evaluation review guidelines.

• Perform independent confirmatory research on industry guidance for executing WRS 

analysis.

• Assess and evaluate the adequacy of industry’s mitigation activities where WRS 

minimization is necessary.

• Improve WRS finite element analysis predictive methodologies.

• Determine estimates for WRS uncertainty distributions, which are needed in probabilistic 

analyses.

This report describes WRS measurement methods and finite element modeling techniques for 

predicting WRS. The measurement and modeling efforts were performed on both small-scale 

scientific specimens and on large-scale prototypic mockups of in-service nuclear plant 

components. For example, Chapter 4 describes results from a double-blind finite element round 

robin, where international participants completed finite element models of a prototype 

pressurizer surge nozzle without access to the measurement data. Validation criteria for WRS 

models will be developed in future research efforts.

v

TABLE OF CONTENTS

Section Page

ABSTRACT ............................................................................................................................... iii

TABLE OF CONTENTS..............................................................................................................v

LIST OF FIGURES ................................................................................................................... vii

LIST OF TABLES ......................................................................................................................xi

EXECUTIVE SUMMARY ......................................................................................................... xiii

ACKNOWLEDGMENTS ...........................................................................................................xv

ABBREVIATIONS....................................................................................................................xvii

UNIT CONVERSION ............................................................................................................... xix

NOTATIONS............................................................................................................................ xxi

1 Regulatory Purpose........................................................................................................... 1

1.1 Environmentally Assisted Cracking Operating Experience....................................... 1

1.2 Flaw Growth Evaluations ......................................................................................... 6

1.3 Uncertainties in WRS Input and Motivation of Research.......................................... 9

2 Weld Residual Stress Validation Techniques ...................................................................11

2.1 Validation Criteria ...................................................................................................11

2.2 Weld Residual Stress Measurement Techniques....................................................11

2.2.1. Diffraction-Based Methods..........................................................................12

2.2.2. Strain Relief-Based Methods ......................................................................13

2.3 Finite Element Modeling Techniques......................................................................15

2.3.1. Overview.....................................................................................................15

2.3.2. Thermal Model............................................................................................15

2.3.3. Mechanical Model.......................................................................................17

2.3.4. Additional FE Modeling Details ...................................................................17

2.4 WRS Validation Conclusions ..................................................................................18

3 Phase 1: Scientific Weld Specimens ...............................................................................19

3.1 Introduction.............................................................................................................19

3.2 Specimen Fabrication.............................................................................................19

3.2.1. Flat Plate Specimens..................................................................................19

3.2.2. Cylindrical Specimens.................................................................................22

3.3 Results and Discussion ..........................................................................................26

3.3.1. Surface Stress Measurements....................................................................26

3.3.2. Sources of Measurement Error...................................................................33

3.3.3. Sources of Modeling Uncertainty ................................................................34

3.4 Phase 1 Conclusions..............................................................................................35

4 Phase 2a: Fabricated Prototypic Nozzle..........................................................................37

4.1 Introduction.............................................................................................................37

4.2 Mockup Fabrication ................................................................................................37

4.3 Weld Residual Stress Measurement.......................................................................39

4.4 Double-Blind Finite Element Round Robin..............................................................40

4.4.1. Initial Approach to Assessing Modeling Uncertainty....................................40

4.4.2. Round Robin Participants ...........................................................................41

4.4.3. Modeling Package ......................................................................................41

4.4.4. Model Description.......................................................................................42

4.4.5. Post-Processing of Finite Element Results .................................................45

4.4.6. Data Analysis..............................................................................................46

4.5 Results and Discussion ..........................................................................................47

4.5.1. Measurement Results.................................................................................47
vi

4.5.2. Finite Element Modeling Results.................................................................50

4.5.3. Finite Element Dataset Trends....................................................................60

4.5.4. Summary of Round Robin Results..............................................................76

4.6 Sensitivity Studies ..................................................................................................77

4.6.1. Baseline Model ...........................................................................................77

4.6.2. Sensitivity Parameter Selection ..................................................................82

4.6.3. Coefficient of Thermal Expansion Sensitivity Study ....................................82

4.6.4. Heat Input Sensitivity Study ........................................................................85

4.6.5. Plastic Stress-Strain Response Sensitivity Study........................................90

4.6.6. Strain Hardening Law .................................................................................91

4.6.7. Anneal Temperature ...................................................................................93

4.6.8. Weld Pass Sequence..................................................................................94

4.7 Phase 2a Conclusions............................................................................................96

5 Phase 3: Pressurizer Nozzles from a Cancelled Plant......................................................99

5.1 Introduction.............................................................................................................99

5.2 Pressurizer Safety/Relief Nozzle Mockups .............................................................99

5.3 Weld Residual Stress Measurements...................................................................100

5.4 Finite Element Models ..........................................................................................101

5.5 Results and Discussion ........................................................................................101

5.6 Phase 3 Conclusions............................................................................................105

6 Phase 4: Optimized Weld Overlay on a Cold Leg Nozzle ..............................................107

6.1 Introduction...........................................................................................................107

6.2 Optimized Weld Overlay and Cold Leg Nozzle Mockup........................................107

6.2.1. Optimized Weld Overlay ...........................................................................107

6.2.2. Cold Leg Nozzle Mockup ..........................................................................108

6.3 Weld Residual Stress Measurements...................................................................111

6.4 Finite Element Models ..........................................................................................111

6.5 Optimized Weld Overlay Effectiveness .................................................................112

6.5.1. Axial Stresses, Room Temperature, Without Operating Loads .................112

6.5.2. Hoop Stresses, Room Temperature, Without Operating Loads.................115

6.5.3. Operating Condition Sensitivity Study .......................................................118

6.5.4. Weld Overlay Thickness Sensitivity Study ................................................119

6.5.5. Repair Weld Sensitivity Study...................................................................122

6.6 Double-Blind Finite Element Study .......................................................................127

6.6.1. Finite Element Predictions ........................................................................127

6.6.2. Predictions and Measurements Compared ...............................................129

6.6.3. Sensitivity Study in the Area without the Weld Repair...............................135

6.7 Phase 4 Conclusions............................................................................................140

7 WRS Uncertainty Scoping Study....................................................................................141

7.1 Background ..........................................................................................................141

7.2 Stress Intensity Factor Methods ...........................................................................141

7.3 Results and Discussion ........................................................................................143

7.3.1. Phase 2a Stress Intensity Factor Scoping Analysis ..................................143

7.3.2. Phase 4 Stress Intensity Factor Scoping Analysis ....................................144

7.3.3. Phase 2a Flaw Evaluation Scoping Analysis.............................................146

7.4 WRS Uncertainty Conclusions..............................................................................148

8 CONCLUSIONS.............................................................................................................149

9 KNOWLEDGE GAPS.....................................................................................................151

10 FUTURE WORK ............................................................................................................153

11 REFERENCES...............................................................................................................155
vii

LIST OF FIGURES

Figure Page

Figure 1-1 Representative Nozzle Cross Section.......................................................... 1

Figure 1-2 PWSCC Timeline......................................................................................... 3

Figure 1-3 Flowchart for ASME Code Flaw Disposition................................................. 7

Figure 1-4 Flowchart for IWB-3600 Evaluation (τ = time, a = crack depth, t = thickness)8

Figure 1-5 Schematic of Possible WRS Inputs in Flaw Growth Calculations ................. 9

Figure 2-1 Measurement of Interplanar Spacings through Diffraction...........................13

Figure 2-2 Incremental Slitting .....................................................................................13

Figure 2-3 Contour Method (Courtesy: Hill Engineering, LLC) .....................................14

Figure 2-4 Deep Hole Drilling (Courtesy: VEQTER, Ltd.)............................................15

Figure 3-1 Flat Plate Geometry (Courtesy: EPRI) .......................................................20

Figure 3-2 Welding Restraint for Plate Specimen (Courtesy: EPRI)............................21

Figure 3-3 Example Thermocouple Data (Courtesy: EPRI).........................................22

Figure 3-4 Example Laser Profilometry Data (Courtesy: EPRI)...................................22

Figure 3-5 Cylindrical Specimen Geometry (Courtesy: EPRI) .....................................23

Figure 3-6 Three Specimen Types (Courtesy: EPRI) ..................................................24

Figure 3-7 Cylinder C-5 Repair Weld Geometry (Courtesy: EPRI) ..............................25

Figure 3-8 Surface Stress Measurements for Plate P-3 (Courtesy: EPRI)...................27

Figure 3-9 Surface Stress Measurements for Plate P-4 (Courtesy: EPRI)...................27

Figure 3-10 X-ray Results Across the Weld (Courtesy: EPRI).......................................28

Figure 3-11 Deep Hole Drilling Results (Courtesy: EPRI) .............................................29

Figure 3-12 Deep Hole Drilling Results for along Repair Centerline (Courtesy: EPRI) ..29

Figure 3-13 Contour Method Results (Courtesy: EPRI).................................................30

Figure 3-14 Longitudinal Stress for Plate P-4 (Courtesy: EPRI)....................................31

Figure 3-15 Transverse Stress for Plate P-4 (Courtesy: EPRI) .....................................32

Figure 3-16 Hoop Stress for Cylinder C-3 (Courtesy: EPRI)..........................................32

Figure 3-17 Axial Stress for Cylinder C-3 (Courtesy: EPRI) ..........................................33

Figure 3-18 Stress Results from a Pulsed Neutron Source (open symbols: at weld/base 

metal interface)...........................................................................................34

Figure 4-1 Phase 2a Mockup.......................................................................................37

Figure 4-2 Weld Residual Stress Measurement Location.............................................40

Figure 4-3 Round Robin Participants ...........................................................................41

Figure 4-4 Example Model Features ............................................................................42

Figure 4-5 Butter Layer and Machining ........................................................................43

Figure 4-6 Weld Bead Geometry from Laser Data .......................................................43

Figure 4-7 Fill-In Weld..................................................................................................44

Figure 4-8 Machining Steps .........................................................................................44

Figure 4-9 Stainless Steel Closure Weld......................................................................45

Figure 4-10 Extraction of Results...................................................................................45

Figure 4-11 Axial Stress DHD/iDHD Measurements before Stainless Steel Weld..........47

Figure 4-12 Hoop Stress DHD/iDHD Measurements before Stainless Steel Weld .........48

Figure 4-13 Axial Stress Measurements after Stainless Steel Weld...............................49

Figure 4-14 Hoop Stress Measurements after Stainless Steel Weld ..............................49

Figure 4-15 Analysis 1a Axial Stress..............................................................................51

Figure 4-16 Analysis 1a Axial Stress, Late Results........................................................51

Figure 4-17 Analysis 1c Axial Stress..............................................................................52

Figure 4-18 Analysis 1c Axial Stress, US Participants....................................................52
viii

Figure 4-19 Analysis 1a Hoop Stress.............................................................................53

Figure 4-20 Analysis 1a Hoop Stress with Late Data .....................................................54

Figure 4-21 Analysis 1c Hoop Stress before Safe End Weld..........................................55

Figure 4-22 Analysis 1c Hoop Stress before Safe End Weld, US Participants ...............55

Figure 4-23 Analysis 2 Axial Stress................................................................................56

Figure 4-24 Effect of Safe End Weld on Axial Stresses..................................................57

Figure 4-25 Analysis 2 Axial Stress, with Late Results and Measurements....................57

Figure 4-26 Analysis 2 Hoop Stress...............................................................................58

Figure 4-27 Effect of Safe End Weld on Hoop Stress ....................................................59

Figure 4-28 Analysis 2 Hoop Stress, with Late Result after Safe End Weld ...................59

Figure 4-29 Analysis 1c Axial Stress - Isotropic Hardening ............................................60

Figure 4-30 Analysis 1c Axial Stress - Isotropic Hardening, US Participants..................61

Figure 4-31 Analysis 1c Axial Stress - Kinematic and Mixed Hardening.........................61

Figure 4-32 Analysis 1c Axial Stress - Isotropic and Kinematic, Model ‘C’ .....................62

Figure 4-33 Analysis 1c Axial Stress - Isotropic, Kinematic, and Mixed, Model ‘E’ .........63

Figure 4-34 Number of Times the Zero Stress is Crossed .............................................64

Figure 4-35 Analysis 1c Hoop Stress - Isotropic Hardening ...........................................65

Figure 4-36 Analysis 1c Hoop Stress - Isotropic Hardening, US Participants .................65

Figure 4-37 Analysis 1c Hoop Stress - Kinematic Hardening .........................................66

Figure 4-38 Analysis 1c Hoop Stress - Isotropic and Kinematic, Model ‘C.’....................67

Figure 4-39 Analysis 1c Hoop Stress - Isotropic and Kinematic, Model ‘E.’....................67

Figure 4-40 Analysis 1c Data with Averages Highlighted ...............................................68

Figure 4-41 Analysis 2 with Averages Highlighted .........................................................68

Figure 4-42 Analysis 1a Axial Stress Difference Plot .....................................................69

Figure 4-43 Measured and Predicted Temperature History – Analysis 1a, Model ‘I’.......70

Figure 4-44 Measured and Predicted Temperature History – Analysis 1b, Model ‘I’.......70

Figure 4-45 Analysis 1a Axial Stress Difference Plot – Excluding Model ‘I’ ....................71

Figure 4-46 Analysis 1a Hoop Stress Difference Plot – Excluding Model ‘I’ ...................72

Figure 4-47 Analysis 1c – 1b Axial Stress Difference Plot..............................................73

Figure 4-48 Analysis 1c – 1b Hoop Stress Difference Plot .............................................73

Figure 4-49 Axial Stress Through Wall Bending Caused by Safe End Weld ..................74

Figure 4-50 Hoop Stress Through-Wall Bending Caused by Safe End Weld .................75

Figure 4-51 Results ‘E’ As-Submitted and Corrected for Geometric Variation................76

Figure 4-52 Baseline Model Finite Element Mesh ..........................................................78

Figure 4-53 DM and Stainless Steel Weld Meshes ........................................................78

Figure 4-54 Peak temperature [K] Achieved in the Baseline Thermal Analysis ..............79

Figure 4-55 Axial Stress from Baseline Model before Stainless Steel Weld ...................80

Figure 4-56 Hoop Stress from Baseline Model before Stainless Steel Weld ..................80

Figure 4-57 Axial Stress from Baseline Model after Stainless Steel Weld ......................81

Figure 4-58 Hoop Stress from Baseline Model after Stainless Steel Weld .....................81

Figure 4-59 Coefficient of Thermal Expansion vs. Temperature for Three Materials ......84

Figure 4-60 Axial Stress for Coefficient of Thermal Expansion Sensitivity Study............85

Figure 4-61 Hoop Stress for Coefficient of Thermal Expansion Sensitivity Study...........85

Figure 4-62 Heat flux vs. Time for Magnitude Sensitivity Study......................................86

Figure 4-63 Axial Stress for Heat Flux Magnitude Sensitivity Study ...............................87

Figure 4-64 Hoop Stress for Heat Flux Magnitude Sensitivity Study ..............................87

Figure 4-65 Heat Flux vs. Time for Duration Sensitivity Study........................................88

Figure 4-66 Axial Stress for Heat Flux Duration Sensitivity Study ..................................89

Figure 4-67 Hoop Stress for Heat Flux Duration Sensitivity Study .................................89

Figure 4-68 Axial Stress for Plastic Stress-Strain Response Sensitivity Study ...............90

Figure 4-69 Hoop Stress for Plastic Stress-Strain Response Sensitivity Study ..............91
ix

Figure 4-70 Axial Stress for Hardening Law Sensitivity Study ........................................92

Figure 4-71 Hoop Stress for Hardening Law Sensitivity Study .......................................92

Figure 4-72 Axial Stress for Annealing Temperature Sensitivity Study...........................93

Figure 4-73 Hoop Stress results for Annealing Temperature Sensitivity Study...............94

Figure 4-74 Axial Stress for Weld Pass Order Sensitivity Study.....................................95

Figure 4-75 Hoop Stress for Weld Pass Order Sensitivity Study ....................................95

Figure 5-1 Schematic of the Safety and Relief Nozzle .................................................99

Figure 5-2 Actual Nozzle and FE Model before and after Pipe Weld..........................100

Figure 5-3 Axial Stress FE Predictions.......................................................................102

Figure 5-4 Hoop Stress FE Predictions......................................................................102

Figure 5-5 Axial Stress FE Predictions and Measurements........................................104

Figure 5-6 Hoop Stress FE Predictions and Measurement.........................................104

Figure 6-1 Phase 4 Model Geometry .........................................................................108

Figure 6-2 Cold Leg Nozzle Mock-Up after OWOL ....................................................109

Figure 6-3 Cold Leg Nozzle Geometry and Material Details.......................................110

Figure 6-4 Cold Leg Nozzle Axial Stresses [MPa]......................................................112

Figure 6-5 Cold Leg Nozzle Through-Thickness Axial Stresses.................................113

Figure 6-6 Cold Leg Nozzle Inner Diameter Axial Stresses [MPa]..............................114

Figure 6-7 ID Axial Stresses along Length of the Pipe ...............................................114

Figure 6-8 Cold Leg Nozzle Hoop Stresses [MPa] .....................................................115

Figure 6-9 Cold Leg Nozzle Through-Thickness Hoop Stresses ................................116

Figure 6-10 Cold Leg Nozzle Inner Diameter Hoop Stresses [MPa].............................117

Figure 6-11 Cold Leg Nozzle Inner Diameter Hoop Stresses.......................................117

Figure 6-12 ID Axial Stresses at Operating Pressure and Temperature.......................118

Figure 6-13 ID Hoop Stresses at Operating Pressure and Temperature ......................119

Figure 6-14 Axial Stresses through Weld Overlay Process ..........................................120

Figure 6-15 ID Axial Stresses for each OWOL Layer...................................................121

Figure 6-16 ID Hoop Stresses for Each OWOL Layer..................................................122

Figure 6-17 Cold Leg Nozzle with and without 25 Percent ID Repair ...........................123

Figure 6-18 Cold Leg Axial Stresses before OWOL with and without ID Repair [MPa].123

Figure 6-19 ID Axial Stresses before OWOL with and without ID Repair .....................124

Figure 6-20 Axial Stresses before OWOL with and without ID Repair..........................125

Figure 6-21 Axial Stresses after OWOL with and without 25 percent ID Repair [MPa] .125

Figure 6-22 ID Axial Stresses after OWOL with and without ID Repair ........................126

Figure 6-23 Axial Stresses after OWOL with and without ID Repair.............................127

Figure 6-24 Axial Stress with Weld Repair before the SS Weld ...................................128

Figure 6-25 Hoop Stress with Weld Repair before the SS Weld...................................128

Figure 6-26 Axial Stress in Repair Region before OWOL.............................................130

Figure 6-27 Hoop Stress in Repair Region before OWOL............................................131

Figure 6-28 Participant B Hoop Stress from Modified Analysis ....................................132

Figure 6-29 Axial Stress in Repair Region after OWOL................................................133

Figure 6-30 Hoop Stress in Repair Region after OWOL...............................................133

Figure 6-31 Axial Stress Averages...............................................................................134

Figure 6-32 Hoop Stress Averages..............................................................................135

Figure 6-33 Axial Stress Outside the Repair before OWOL .........................................136

Figure 6-34 Hoop Stress Outside the Repair before OWOL.........................................136

Figure 6-35 Axial Stress Outside the Repair before OWOL .........................................137

Figure 6-36 Hoop Stress Outside the Repair after OWOL............................................138

Figure 6-37 Axial Stress Averages before and after OWOL .........................................139

Figure 6-38 Hoop Stress Averages before and after OWOL ........................................139

Figure 7-1 Example Curve Fits ..................................................................................142
x

Figure 7-2 Flaw Geometry .........................................................................................143

Figure 7-3 Stress Intensity Factor for Axial WRS Profiles, Pre Safe End Weld...........144

Figure 7-4 Stress Intensity Factor for Axial WRS Profiles, Post Safe End Weld.........144

Figure 7-5 Example Fits of Phase 4 Data...................................................................145

Figure 7-6 Stress Intensity Factor, Before Closure Weld............................................145

Figure 7-7 Stress Intensity Factor for Phase 4 Axial WRS .........................................146

Figure 7-8 Extreme WRS Inputs ................................................................................147

Figure 7-9 Stress Intensity Factor and Flaw Depth against Time ...............................147
xi

LIST OF TABLES

Table Page

Table 1-1 Summary of Select PWSCC Events (page 1 of 3) ................................................... 4

Table 2-1 Summary of WRS Measurement Methods..............................................................12

Table 2-2 Material Properties for Thermal Model....................................................................16

Table 3-1 Chemical Composition of 304L Stainless Steel [46]................................................20

Table 3-2 Chemical Composition of Alloy 82 [47] ...................................................................20

Table 3-3 Welding Parameters for Plate Studies (Courtesy: EPRI)........................................21

Table 3-4 Cylinder Specimen Designations (Courtesy: EPRI) ...............................................24

Table 3-5 Cylindrical Specimen Weld Parameters (Courtesy: EPRI) .....................................26

Table 4-1 Phase 2a Mockup Material Specifications...............................................................38

Table 4-2 Typical Parameters for Main DM Weld ...................................................................39

Table 4-3 Typical Parameters for Fill-in Weld .........................................................................39

Table 4-4 Typical Parameters for Stainless Steel Weld ..........................................................39

Table 4-5 Analysis Stages......................................................................................................41

Table 7-1 Inputs for Flaw Evaluation Scoping Study.............................................................146

xiii

EXECUTIVE SUMMARY

The need to understand weld residual stress (WRS) in safety-related nuclear components 

began with the occurrence of intergranular stress corrosion cracking in boiling water reactors. 

Later, the discovery of primary water stress corrosion cracking (PWSCC) in pressurized water 

reactor dissimilar metal welds also demonstrated the need to understand the driving force for 

crack growth. Two prime examples of PWSCC in pressurized water reactors include:

(1) Cracking of Davis-Besse control rod drive mechanism nozzles in March 2002.

(2) Circumferential cracking in the Wolf Creek pressurizer nozzles in October 2006.

Advanced finite element analysis studies of PWSCC, which simulate natural crack growth by 

calculating the driving force along the entire crack front, showed that WRS was a significant 

input for flaw growth calculations. As part of the U.S. Nuclear Regulatory Commission’s 

(NRC’s) strategy for ensuring nuclear safety in PWSCC-susceptible components, a probabilistic

fracture mechanics code is under development. The Extremely Low Probability of Rupture 

(xLPR) code will analyze rupture probabilities in piping systems approved for Leak-BeforeBreak. An understanding of WRS and proper characterization of the associated uncertainty is 

vital for determination of rupture probabilities and appropriate confidence bounds for primary 

piping systems.

In addition, a nuclear plant owner may seek relief from required inspection programs or 

repair/replacement activities in PWSCC-susceptible components. A deterministic flaw growth 

evaluation in many cases provides the necessary technical basis to support the relief request. 

Such evaluation requires review and approval by the NRC staff before relief is granted. These 

calculations necessitate an assumption of the WRS present in the system. Safety evaluations 

require that the NRC staff make an informed judgment of whether the assumed WRS is 

accurate or conservative.

Finite element simulations of WRS involve a two-step process: (1) calculating the temperature 

distribution in space and time with an assumed heat input model and (2) calculating the stress 

field resulting from the temperature history. The models considered in this work were 

two-dimensional axisymmetric; i.e., a moving heat source was not explicitly modeled. Potential 

sources of modeling uncertainty include the choice of heat input model, choice of strain 

hardening law, bead geometry, process sequence, material property inputs, and 

post-processing of results.

WRS measurement, which is a specialized field requiring specific expertise, involves calculating 

stress from measured deformation or strain. Techniques include diffraction-based and strain 

relief-based methods. Diffraction methods rely on measurement of crystallographic lattice 

spacing, along with a specified reference lattice spacing, as a measurement of strain. Strain 

relief techniques involve mechanical perturbation of the component that releases the stress 

field. Strains measured when the stress field is released are used to back-calculate the stress. 

Each technique has its own limitations and uncertainties, and these must be taken into account 

for proper experimental execution and interpretation of results.

Validation of WRS finite element models with experiments is not a straight-forward topic. 

Approaches have been developed by organizations outside the NRC, such as the R6 code 

established in Europe. Rather than addressing specific validation criteria for use at NRC, this 
xiv

report discusses data collection efforts to support determining effective validation techniques 

and criteria. The development of validation criteria is left for future reports.

This work was performed under an addendum to the memorandum of understanding with the 

Electric Power Research Institute. It consisted of four research phases:

(1) Phase 1: Scientific Weld Specimens

(2) Phase 2a: Fabricated Prototypic Nozzle

(3) Phase 3: Pressurizer Nozzles from a Cancelled Plant

(4) Phase 4: Optimized Weld Overlay on a Cold Leg Nozzle

This research project found bulk WRS measurement techniques were significantly more reliable 

than surface techniques. Further, this project showed that across a wide range of groups, 

calculated WRS generally followed the profile shape of the measurements. However, the report 

identified significant analyst-to-analyst variability of calculated WRS values by up to ±200 MPa. 

In the future, establishing guidance on choice of strain hardening law (among other lessons 

learned) may reduce the observed scatter. This variability has a significant impact on 

calculations of the stress intensity factor, KI, and time-to-leakage in deterministic flaw analyses. 

Therefore, future work will focus on developing numerical procedures that reduce analyst-toanalyst scatter.
xv

ACKNOWLEDGMENTS

The authors would like to thank the following.

• Howard Rathbun and Matthew Kerr, both formerly at the U.S. Nuclear Regulatory 

Commission (NRC), for leading the Weld Residual Stress Validation Program. Much of 

the work presented in this document is a result of their technical and leadership efforts. 

Readers may refer to their publications on this topic [22], [23], [49].

• Paul Crooker of the Electric Power Research Institute (EPRI) and John Broussard of 

Dominion Engineering, Inc., for technical cooperation in the joint NRC-EPRI program.

• EPRI for the use of tables and figures from the Materials Reliability Program (MRP)-316 

report.

• Lee Fredette and Paul Scott at Battelle Memorial Institute for their work on weld overlay 

finite element simulations.

• Pacific Northwest National Laboratory, Edison Welding Institute, and Richard Olson at 

Battelle Memorial Institute for Mockup Design/Fabrication.

• Engineering Mechanics Corporation of Columbus for providing material properties for the 

round robin finite element analysis effort.

• VEQTER, Ltd. of Bristol, United Kingdom, for deep hole drilling and incremental deep 

hole drilling measurements and the use of Figure 2-4.

• Hill Engineering, LLC of Rancho Cordova, CA, for contour measurements and the use of 

Figure 2-3.

• Ed Kingston of VEQTER, Ltd.; Adrian DeWald of Hill Engineering, LLC; and EPRI for 

useful technical comments on this report.

• Gary Stevens, Raj Iyengar, and Joshua Kusnick of the NRC Office of Nuclear 

Regulatory Research for supplying the historical information on primary water stress 

corrosion cracking found in Chapter 1.

xvii

ABBREVIATIONS

2-D two-dimensional

AFEA Advanced Finite Element Analysis

ANO Arkansas Nuclear One

ASME Code American Society of Mechanical Engineers Boiler and 

Pressure Vessel Code

BMI bottom mounted instrument nozzle

BWR boiling water reactor

C-1, C-3, C-4, and C-5 cylindrical specimen designations for phase 1 work

CS carbon steel

DHD deep hole drilling

DM dissimilar metal

EPRI Electric Power Research Institute

FE finite element

FSWOL full structural weld overlay

GTAW gas tungsten arc welding

ID inner diameter

iDHD Incremental Deep Hole Drilling

IGSCC intergranular stress corrosion cracking

KWO mothballed Obrigheim Nuclear Power Plant

MOU memorandum of understanding

MRP Materials Reliability Program

NRC United States Nuclear Regulatory Commission

NDE nondestructive evaluation

OD outer diameter

OWOL optimized weld overlay

P-3, P-4, P-5, and P-6 plate specimen designations for Phase 1 Work

PWHT post weld heat treat

PWR pressurized water reactor

PWSCC primary water stress corrosion cracking

SIA Structural Integrity Associates

SONGS San Onofre Nuclear Generating Station

SS stainless steel
xviii

WE-3 Westinghouse three-loop plant

WRS weld residual stress
xix

UNIT CONVERSION

1 mm = 0.0394 in. = 3.281x10-3 ft

1 mm/s = 2.4 in./min

1 kg = 2.205 lbm

T[R] = T[K]*9/5

1 MPa = 20.9 kip/ft2

1 J/s = 3.414 BTU/hr

xxi

NOTATIONS

a crack depth

dhkl interplanar spacing for lattice planes with Miller indices hkl

dhkl,0 reference interplanar spacing

ε hkl lattice strain

Ehkl hkl-specific modulus

hkl Miller indices

θ Bragg angle

KI Mode I stress intensity factor

R outer radius

σii normal stress component

σ general stress magnitude

σ mean stress

t wall thickness

τ time

νhkl hkl-specific Poisson’s ratio

x through-thickness distance ID to OD

Q power density (weld thermal model)

a0 build-up time (weld thermal model)

C1 parameter affecting heat input time (weld thermal model)

C2 amplitude scaling parameter (weld thermal model)

S welding speed (weld thermal model)

E arc efficiency (weld thermal model)

V welding voltage (weld thermal model)

A welding current (weld thermal model)

K pre-exponential (weld thermal model)

σm axial membrane stress for operating loads

σb axial bending stress for operating loads

1

1 REGULATORY PURPOSE

1.1 Environmentally Assisted Cracking Operating Experience

Shack [1] initiated an early study of weld residual stress (WRS) due to the occurrence of 

intergranular stress corrosion cracking (IGSCC) in boiling water reactor (BWR) stainless steel 

components. This particular degradation mechanism often involved sensitization in the heat

affected zone of type-304 stainless steel welds. Later, primary water stress corrosion cracking 

(PWSCC) in pressurized water reactors (PWRs) raised the issue of WRS again. For both 

PWSCC and IGSCC, component susceptibility is thought to depend upon a combination of 

stress, material characteristics, and material environment.

In PWR coolant systems, nickel-based dissimilar metal (DM) welds are typically used to join low

alloy steel components—including the reactor pressure vessel, steam generators, reactor 

coolant pump casings, and the pressurizer—to stainless steel piping. Figure 1-1 shows a crosssection of a representative nozzle-to-pipe connection, including the DM weld [1]-[3]. In Figure 

1-1, the DM weld is indicated as “Alloy 82/182 Butt Weld.” The DM weld is fabricated by 

sequentially depositing weld passes as molten metal that cools, solidifies, and contracts, 

retaining stresses that approach or exceed the material’s yield strength.

Figure 1-1 Representative Nozzle Cross Section

These DM welds are susceptible to PWSCC as an active degradation mechanism that has led 

to reactor coolant system pressure boundary leakage. Operational issues associated with 

PWSCC events include expanded outage work scope, unplanned shutdowns, and 

repair/replacement activities. If a utility chooses to seek temporary relief from required repairs 

or inspections, then the licensee prepares a flaw evaluation for U.S. Nuclear Regulatory 

Commission (NRC) review. If approved by the NRC, the flaw evaluation is only valid for a 

specified time period.
2

One major PWSCC event in the U.S. fleet is the Davis-Besse Nuclear Station upper head 

wastage incident on March 5, 2002. PWSCC in the control rod drive mechanism nozzles led to 

boric acid contact with the vessel upper head. The acid reacted with the carbon steel head, 

resulting in a cavity approximately 130-194 cm2 in surface area and over 15 cm deep [4]-[6]. 

This event left the stainless steel cladding as the primary pressure boundary in that area. As a 

result of such cracking in vessel closure head penetration j-groove welds, WRS finite element 

simulations for that geometry have been performed and documented [7]. Furthermore, 

American Society of Mechanical Engineers Boiler and Pressure Vessel Code (ASME Code) 

Case N-729-1 provides volumetric inspection requirements for these j-groove welds. 

Independent confirmatory finite element analyses provided NRC staff with a technical basis for 

incorporating Code Case N-729-1 into NRC regulations [8]. Therefore, research on WRS has 

regulatory significance.

PWSCC has occurred in safety-related piping systems, as well. On October 13, 2006, the Wolf 

Creek Nuclear Operating Corporation performed inspections on pressurizer nozzle-to-safe end

DM and safe end-to-pipe stainless steel butt welds [9]. These inspections identified five 

circumferential indications in the surge, relief, and safety nozzle-to-safe end DM butt welds that

were attributed to PWSCC. These indications were the first occurrence of multiple and large 

circumferential indications in commercial PWRs. As a result of an NRC flaw evaluation scoping 

study that predicted little to no margin between leakage and potential rupture, the nuclear power 

industry conducted advanced finite element analysis (AFEA) [10]. This work took advantage of 

more realistic assumptions to address the NRC staff’s concerns regarding the potential for 

rupture without prior evidence of leakage. The industry’s and NRC staff confirmatory AFEA 

studies both demonstrated that through-wall axial weld residual stress profiles played a key role 

in whether the postulated PWSCC would grow through-wall to leakage or circumferentially to 

potential rupture characteristics.

Figure 1-2 and Table 1-1 through Table 1-3 provide a historical overview of select PWSCC 

events in domestic and international PWRs. Also in Table 1-1 through Table 1-3 are significant 

actions taken by the NRC and industry to deal with the PWSCC issue. One significant action is 

the issuance of Code Case N-770 by ASME in 2009. This Code Case spells out alternative 

inspection requirements to ASME Code Section XI for primary pressure boundary butt welds

subject to PWSCC [11]-[12].

PWSCC in safety-related nuclear components has led to significant actions from both the NRC 

and the U.S. nuclear industry. This degradation mechanism is driven by tensile WRS and other 

applied loads. Hence, proper assessment of these stresses is essential to predict PWSCC flaw 

growth.
3

Figure 1-2 PWSCC Timeline
4

Table 1-1 Summary of Select PWSCC Events (page 1 of 3)

Event Year Plant Description

1 1957 --- Susceptibility of Alloy 600 to IGSCC demonstrated in laboratory.

2 1972 KWO First steam generator tube (secondary side) leakage/cracking.

3 1978 Mihama-3, PWR, 

WE-3

Control Rod Cluster Guide Tube Support Pins. Alloy X750. 

Replaced (Heat Treatment, Shot Peening, Design Change, 

Torque change).

4 1979 Three Mile Island-1 First steam generator tube (primary side) leakage/cracking.

5 1982 Gravelines-1 Control rod guide tube support pins. Alloy X750. Multiple 

events.

6 1986 SONGS-3 Pressurizer Relief Valve Instrumentation nozzle cracking.

7 1987 Arkansas Nuclear 

One-2

Pressurizer Heater Sleeve. Alloy 600.

8 1989 Cattenom-2 1300 MWe Pressurizer Nozzles. Alloy 600. Multiple events.

Calvert Cliffs-2 Pressurizer heater penetration cracking.

9 1991 Bugey-3 CRDM nozzle. Alloy 600. First known case in 1991; multiple 

events.

10 1993 Palisades-1 Pressurizer power-operated relief nozzle. Alloy 600. First 

instance of PWSCC in a U.S. DM butt weld.

11 1994 Zorita Many cracks (boundary segregation).

12 1995 Saint Laurent-B1 Steam generator water box. Alloy 82. Only known case of Alloy

82 cracking in France.

13 1997 Chooz-B2 Electrical heaters. Type 316 SS. Multiple events.

--- U.S. NRC Generic Letter 97-01, “Degradation of Control Rod 

Drive Mechanism Nozzle and Other Vessel Closure Head 

Penetrations,” April 1, 1997.

14 2000 V.C. Summer “A”, “B”, and “C” hot leg pipe-to-RPV nozzle DM welds, “A” and 

“C” cold leg-RPV nozzle DM welds. Alloy 182/82. Spool piece 

replacement.

ANO-1 Cracks at 6 small nozzles in RCPB piping.

Ringhals-3, -4 RPV outlet/RCS hot leg nozzle safe end dissimilar metal butt 

weld cracking in Alloy 82/182.

Oconee-1 CRDM J-groove weld cracking.

15 2001 Oconee-3 First circumferential wall crack starting at OD.

16 2002 Davis Besse-1 CRDM Nozzle. Severe corrosion/wastage of RPV top head. 

Alloy 600. Replace head Alloy 690.

--- NRC issues letter to ASME Code Subcommittee on Nuclear 

Inservice Inspection requesting that it re-evaluate inspection and 

corrective action requirements.
5

Table 1-1 Summary of Select PWSCC Events (page 2 of 3)

Event Year Plant Description

17 2003 Takahama-1 Bottom Mounted Instrument (BMI) nozzle. Alloy 600. (ECT 

detected) Removed indication & WJP.

South Texas-1 Bottom Mounted Instrument (BMI) nozzle. Alloy 600. Half nozzle 

repair Alloy 690, 152, 52.

Tsuruga-2 Weld (Pressurizer relief valve nozzle). Weld Metal Alloy 132. 

(UT detected) Spool Piece Replacement (Alloy 690).

Tihange-2 Pressurizer surge line nozzle (weld).

Three Mile Island-1 Pressurizer Surge Nozzle (weld). Alloy 182/82.

18 2004 Chinon-B4 Partition plate of steam generator. Alloy 600. Multiple events.

--- Materials Reliability Project (MRP) issues a recommendation 

letter to the industry.

--- U.S. NRC issues Information Notice 2004-11, “Cracking in 

Pressurizer Safety and Relief Nozzles and in Surge Line Nozzle.”

--- U.S. NRC issues Information Notice 2004-01, “Inspection of Alloy 

82/182/600 Materials Used in the Fabrication of Pressurizer 

Penetrations and Steam Space Piping Connections at 

Pressurized Water Reactors.”

Ohi-3 CRDM Nozzle (RPV Penetration). Weld Metal Alloy 132. 

Claddings (Alloy 690 type) - Replacement of RVH.

19 2005 Calvert Cliffs-2 Hot Leg Drain nozzle.

--- ASME issues Code Case N-722, “Additional Examinations for 

PWR Pressure Retaining Welds in Class 1 Pressure Boundary 

Components Fabricated with Alloy

600/82/182 Materials, Section XI, Division 1”

--- MRP issues MRP-139, "Materials Reliability Program: Primary 

System Piping Butt Weld Inspection and Evaluation Guideline 

(MRP-139)."

ANO-2 Pressurizer Heater Sleeve.

--- U.S. NRC requests ASME Code Section XI Subcommittee on 

Nuclear Inservice Inspection to take actions to develop 

improvements in volumetric examinations.

D.C. Cook-1 Pressurizer Relief Valve Nozzle (weld). Alloy 182/82.

20 2006 Calvert Cliffs-1 Pressurizer Relief Nozzle, Hot Leg Drain Nozzle, and Surge 

Nozzle (weld). Alloy 182/82.

Wolf Creek-1 Pressurizer Relief Valve Nozzle (weld). Alloy 182/82. Full 

structural weld overlay.

Wolf Creek-1 Pressurizer Safety Injection Nozzle (weld). Alloy 182/82. Full 

structural weld overlay.

Wolf Creek-1 Pressurizer Surge Nozzle (weld). Alloy 182/82. Full structural 

weld overlay.

--- ASME issues Code Case N-740, “Dissimilar Metal Weld Overlay 

for Repair of Class 1, 2 and 3 Items.”

--- Industry and NEI developed an inspection plan for unmitigated 

pressurizer dissimilar metal butt welds that contain Alloy 82/182 

material.
6

Table 1-1 Summary of Select PWSCC Events (page 3 of 3)

Event Year Plant Description

21 2007 YongGwang-3

---

Steam Generator drain line nozzle. Alloy 600. Replace.

U.S. NRC issues Confirmatory Action Letters to 27 nuclear plants 

in response to the 2006 Wolf Creek PWSCC indications.

--- U.S. NRC acquires the St. Lucie-1 pressurizer that was removed 

from service in 2005.

Mihama-2 Weld (Steam Generator Inlet Nozzle). Type 316 SS (IGSCC). 

Spool Piece Replacement (Alloy 690), USP.

22 2008 Ohi-3 Weld (RPV Outlet Nozzle). Weld Metal Alloy 82. Remove, STP 

inlay, Cladding (Alloy 690 type).

--- EPRI issues MRP-2008-012, “Examination Results on Nozzles 

from removed St Lucie Pressurizer.”

YongGwang- 4 Steam Generator drain line nozzle. Alloy 600. Replace.

23 2009 --- ASME issues Code Case N-770, "Alternative Examination 

Requirements and Acceptance Standards for Class 1 PWR 

Piping and Vessel Nozzle Butt Welds Fabricated with UNS 

N06082 or UNS W86182 Weld Filler Material with or without 

Application of Listed Mitigation Activities”

24 2012 North Anna-1 Axially-oriented PWSCC cracking discovered in steam generator 

hot leg nozzle.

1.2 Flaw Growth Evaluations

ASME Code Section XI requires the application of nondestructive evaluation (NDE) techniques, 

such as ultrasonic testing, to assess the potential presence of flaws in safety-related 

components. If an indication is found in a nickel alloy DM weld, it is generally assumed to be a 

PWSCC crack. PWSCC cracks are not allowed in service, according to IWB-3430 of ASME 

Code Section XI (2008a) [13]. When nuclear plant owners decide to seek relief from required 

repair/replacement activities, they typically submit a fracture mechanics flaw evaluation to the 

NRC for review and approval. Flaw evaluations can also be used in cases where NDE 

inspection presents a hardship to the plant owner. A flaw is assumed to exist in the component 

in question, even without direct evidence of flaw, in these cases. In any event, flaw evaluations 

are good only for the length of time analyzed. Typically, PWSCC flaws are repaired during a 

subsequent refueling outage. Flaw evaluation procedures are described in IWB-3600 and 

Appendix C of ASME Code Section XI (also see Figure 1-3) [13].
7

Figure 1-3 Flowchart for ASME Code Flaw Disposition

An IWB-3600 evaluation typically involves analyzing the found flaw with the measured 

dimensions. Other steps include calculating the stress intensity factor (KI) at the surface point 

and deepest point of the crack front, estimating the PWSCC growth rate, advancing the crack in 

the length and depth dimensions, and performing a flaw stability calculation (see Figure 1-4).
8

Figure 1-4 Flowchart for IWB-3600 Evaluation (τ = time, a = crack depth, t =

thickness)

Methods for calculating KI can be found in [14]-[17]. They involve different representations of 

the through-wall stress distribution that creates mode I loading on the crack. This stress 

distribution should include both operating loads and WRS. WRS input into these calculations 

may take a range of forms, from conservative and simple to refined and complicated, as 

indicated schematically in Figure 1-5.
9

Figure 1-5 Schematic of Possible WRS Inputs in Flaw Growth Calculations

1.3 Uncertainties in WRS Input and Motivation of Research

Two documents, in particular, describe the NRC’s regulatory response to the Wolf Creek event 

described in Section 1.1 and the motivation for the present work. The first is a March 5, 2007 

letter from the NRC to the Nuclear Energy Institute [18]. This letter discussed eight points to be 

addressed in industry’s AFEA work described in Section 1.1. The second is a March 22, 2007 

letter from the NRC’s Advisory Committee on Reactor Safeguards [19]. Both of these letters 

discussed the potential for uncertainty in WRS assumptions.

To address NRC staff concerns, the Electric Power Research Institute (EPRI) performed 

sensitivity analyses for flaw growth calculations [10]. Studies such as these have demonstrated 

the significant impact WRS assumptions have on flaw growth analyses. There are uncertainties 

involved with determining the actual WRS distribution in a field component. Uncertainties may 

include material property variability and unknowns associated with fabrication procedure. 

Recent improvements in computational efficiency have facilitated advances in WRS predictions, 

but no universally accepted guidelines for these analyses have been established. Also, it is 

necessary to benchmark analytical results with experiments, as in [20],[21]. The assumptions Stress Magnitude

Position

Constant WRS through the wall thickness

Equal to the yield strength or some 

fraction of the yield strength

Polynomial representation of WRS 

through the wall thickness

Stress Magnitude

Position

Finite element model results

Stress Magnitude

Position
10

and estimation techniques employed in finite element modeling vary from analyst to analyst, 

causing variability in the predicted residual stress profiles for a given weld.

Therefore, the NRC initiated a WRS analysis validation program. This program consisted of 

four phases, with each phase intended to investigate progressively more realistic service 

conditions [22]-[24]. The NRC and EPRI completed this project under an addendum to the 

memorandum of understanding (MOU), which is a legal document allowing the NRC Office of 

Nuclear Regulatory Research and EPRI to perform cooperative research. The MOU is 

authorized under Section 31 of the Atomic Energy Act and/or Section 205 of the Energy 

Reorganization Act.

The NRC staff's objectives in completing this research program included:

• Validate axisymmetric FE modeling as a predictive tool for WRS, using robust 

experimental methods.

• Support the NRC's Office of Nuclear Reactor Regulation in development of appropriate 

WRS/flaw evaluation review guidelines.

• Perform independent confirmatory research on industry guidance for executing WRS 

analysis.

• Assess and evaluate the near-term adequacy of industry’s mitigation activities where 

WRS minimization is necessary.

• Improve WRS finite element (FE) analysis predictive methodologies.

• Determine estimates for WRS uncertainty distributions, which are needed in 

probabilistic analyses (e.g., xLPR Code – eXtremely Low Probability of Rupture 

[25],[26]).

This report is organized in the following manner. Chapter 2 describes WRS model validation 

techniques. Chapters 3-6 respectively cover the following four phases of the NRC/EPRI WRS 

Validation Program:

(1) Phase 1: Scientific Weld Specimens

(2) Phase 2a: Fabricated Prototypic Nozzles

(3) Phase 3: Pressurizer Nozzles from a Cancelled Plant

(4) Phase 4: Optimized Weld Overlay on a Cold Leg Nozzle

Each chapter describes fabrication of the mockups for WRS measurement, the measurement 

techniques employed, FE modeling efforts, and conclusions. Chapter 7 discusses implications 

of the findings in Chapters 3-6. Knowledge gaps and future work are also discussed at the end 

of the report.
11

2 WELD RESIDUAL STRESS VALIDATION TECHNIQUES

2.1 Validation Criteria

The three approaches to weld residual stress (WRS) estimation in flaw growth calculations 

shown in Figure 1-5 each represent various degrees of accuracy and conservatism. For 

instance, a constant WRS equal to the material yield strength is a highly conservative 

estimation. This approach does not require significant validation of the accuracy of the WRS 

input. Applying the more refined approach with finite element (FE) analysis may be more 

accurate, but it requires validation with experimental data. This line of reasoning is found, for 

instance, in the European R6 code for structural integrity assessments [21]. R6 specifies 

several criteria for a “High Standard of Validation,” such as:

• Use of two diverse measurement techniques (i.e., the techniques are based upon 

different physics)

• Predicted and measured transient temperatures should match within ±10 percent.

• Predicted and measured fusion zone area should match within ±20 percent.

• Predicted and measured distortions should be compared, if available.

• Stress intensity factors based upon the predicted WRS profile should be greater than 95

percent of that calculated with the measured profile.

Electric Power Research Institute’s (EPRI’s) Materials Reliability Program (MRP)-287 report 

suggests a criterion of ±10 MPa√m on stress intensity factor calculations. This report does not 

define or endorse any specific validation criteria. Rather, this report presents data that may be

used to develop such criteria. Determination of validation criteria is left for future work. 

Sections 2.2 and 2.3 describe measurement and modeling approaches that were employed to 

gather the data.

2.2 Weld Residual Stress Measurement Techniques

The experimental determination of residual stresses involves measurements on a specimen to 

quantify physical changes in the material due to residual stress (e.g., variations in lattice 

spacing, or strain and deformation from material removal). The residual stress is calculated 

from the experimental data. The mathematical procedures for calculating stresses range from 

simple application of Hooke’s Law in three dimensions to more sophisticated FE techniques.

The NRC and EPRI considered a wide variety of potential measurement techniques. Methods 

may vary based upon a number of factors. Table 2-1 provides an overview of the techniques 

considered and their characteristics. Certain techniques did not meet the needs of the project. 

For example, magnetic methods can only be used on ferromagnetic materials, and the Curie 

temperature of the nickel-chromium alloys of interest here is well below 0o

C. In the end, the 

residual stress measurement techniques applied in this work fell into two broad categories, 

according to the physics they are based upon: (1) diffraction-based methods and (2) strain 

relief-based methods.
12

Table 2-1 Summary of WRS Measurement Methods

2.2.1. Diffraction-Based Methods

Diffraction in general and diffraction for WRS measurement is introduced in engineering 

textbooks and elsewhere [27]-[31]. Fundamentally, diffraction measures crystal lattice 

interplanar spacings, dhkl, as illustrated in Figure 2-1. To calculate strain, the measured dhkl can 

be compared to a reference lattice spacing, dhkl,0, according to Equation 2-1.

 

,0

,0

hkl

hkl hkl hkl

ii d

d − d

ε = Equation 2-1

where, hkl

ii ε is the ii normal strain component. The exact method used to determine the 

reference lattice spacing varies from experiment to experiment. Typically in engineering 

components, the measurements are made in the assumed principal directions. After 

measurement of three (mutually-perpendicular) normal strain components, the calculation of 

normal stress is accomplished through application of Hooke’s Law in three dimensions 

(Equation 2-2).

 ( )



 





+ + − +

+ = hkl hkl hkl

hkl

hkl hkl

ii

hkl

hkl

ii

E

11 22 33 1 1 2

ε ε ε

ν

ν

ε

ν

σ Equation 2-2

where, σii is the ii normal stress component, Ehkl is the hkl-specific modulus, and νhkl is the hklspecific Poisson’s ratio. Successful application of diffraction to residual stress measurement 

relies on appropriate scattering statistics. This means that the scattering volume should contain 

a relatively large number of randomly oriented grains. Elements in solid solution have an effect 

on d-spacings, so any effect of chemical concentration gradients should be accounted for and 

may lead to increased measurement uncertainty. The strains measured with diffraction are 

averaged over the scattering volume.
13

Figure 2-1 Measurement of Interplanar Spacings through Diffraction

X-ray and neutron diffraction were both investigated as potential measurement techniques. Xray diffraction is considered to be a technique suitable for surface stress measurement, since 

the beam cannot penetrate into the bulk of the material. Neutron diffraction is considered 

suitable for bulk stress measurements in engineering materials. Neutron measurements can be 

made at two types of facilities: pulsed sources and reactor sources. Measurements at pulsed 

source facilities utilize a spectrum of wavelengths and time-of-flight techniques. A reactor 

source uses a single wavelength and scans through the Bragg angle, θ in Figure 2-1, to 

measure the diffraction pattern.

2.2.2. Strain Relief-Based Methods

Strain relief-based methods involve mechanically perturbing the specimen, thereby altering the 

existing stress field. Resulting strains or displacements are then measured. Calculation of 

stresses is often fairly sophisticated, involving finite element techniques [32]-[38]. These 

techniques are destructive or semi-destructive in nature.

Incremental slitting involves cutting the part along a linear path, as in Figure 2-2. At each 

increment of slitting, the strains are measured via strain gages. This technique can be 

appropriate for near-surface or through-thickness measurements. This technique provides the 

component of stress that is perpendicular to the cut along a linear path.

Figure 2-2 Incremental Slitting
14

The contour method (see Figure 2-3) involves complete sectioning of the component and 

measurement of surface deformation using a coordinate measuring machine. The original 

residual stress is determined through an inverse analysis using the measured surface 

deformation and a finite element model of the section. This technique provides spatial 

distribution of the stress over the entire cross-section of the cut. The component of the 

measured stress is perpendicular to the cutting plane. Due to the nature of the experiment, the 

contour method has difficulty resolving high stress gradients (e.g., surface stress variations due 

to machining) and may under-determine residual stress peaks in these situations. As with other 

mechanical techniques, the contour method assumes elastic material behavior and is 

susceptible to errors when stresses approach the material yield strength.

Figure 2-3 Contour Method (Courtesy: Hill Engineering, LLC)

Deep hole drilling (DHD) is illustrated in Figure 2-4. This technique for determining bulk 

stresses involves drilling a hole in the component and measuring the dimensions of the hole 

with an air probe. The drilled area is then trepanned using electro-discharge machining. The 

redistribution of residual stress due to trepanning affects the dimensions of the hole. A second 

air probe measurement of the hole provides the necessary information for residual stress 

determination. This measurement results in the spatial variation of three stress components 

(two normal and one shear) along the drilled path.
15

Figure 2-4 Deep Hole Drilling (Courtesy: VEQTER, Ltd.)

If residual stresses approach the material’s yield strength, plastic deformation of the material 

when the drilled area is cut out can potentially affect DHD measurement results. A modification 

of the DHD method (Incremental DHD or iDHD), which incrementally cuts out the drilled area, 

temporarily stopping the plastic flow of material and measuring its affect with an air probe, was 

developed to produce more reliable results in high stress regions. The DHD measurements 

presented here were supplemented with the iDHD method in regions with high anticipated 

residual stresses.

2.3 Finite Element Modeling Techniques

2.3.1. Overview

The two-dimensional (2-D) FE models employed in this work were sequentially-coupled thermalmechanical models. Using this approach, the transient heat transfer analysis (thermal model) 

was conducted to calculate the temporal and spatial distribution of temperature. This 

temperature distribution/history was then mapped to the structural analysis that calculated the 

stress field as a function of time (mechanical model). The 2-D models were either axisymmetric 

or generalized plane strain, depending on the geometry of the part being modeled.

2.3.2. Thermal Model

The thermal model calculates the temperature distribution in space and time, based upon the 

input material properties and the welding heat input model. Several methods exist to model the 

heat input during welding [39]. In a heat source model the total energy input as a function of 

time (J/s) accounts for the heat input from the welding torch. The 2-D nature of the models

applied in this work means that a moving heat source is not modeled. Rather, the weld bead, 

4 – A cylinder of material (5mm, 10mm or 15mm outside 

diameter) containing the reference hole along its axis is cut 

from the component.

5 – The diameter, ∅, of the reference hole is re-measured 

through the entire thickness of the cylinder and reference 

bushes.

Ø

2 – A reference hole (1.5mm, 3mm or 5mm diameter) is 

drilled through the component and reference bushes.

3 – The diameter, ∅0, of the reference hole is measured 

through the entire thickness of the component and 

reference bushes.

Ø0

1 – Reference bushes are attached onto the front and back 

surfaces of the component at the measurement location.

Cross-section 

through 

component

Weld

Bushes

 

 

 

 
16

with its associated spatially-distributed heat flux, is applied across the entire surface of the part 

simultaneously. However, one method is based on a moving heat source model originally 

developed by Goldak [40] and modified for 2-D axisymmetric geometry [41]-[43]. In this model, 

the power density, Q [W/mm2], is modeled as an exponential increase and decrease with time 

(Equation 2-3).

[ ( )]











 − + = − 2

0

2 1 0 exp

a

a Q K τ for τ > 1 + a0

Equation 2-3

[ ( )]











 − + = − 2

1

2 1 0 exp

a

a Q K τ for τ ≤ 1 + a0

where, ( ) ( ) ( )

0 1

2

a a

C E p V p A p K

+

× × × = , S(p)C

a 1

0 = , and S(p) a

2

1 = .

The user-specified weld parameters for this heat input model are defined as follows.

• S(p) = weld speed for pass p

• E(p) = arc efficiency for pass p

• V(p) = voltage for pass p

• A(p) = current for pass p

• τ = current time in seconds

Build up time and arrival time are given by:

• buildup time = a0

• arrival time = 1 + a0

C1 [mm] affects the duration over which the heat is applied, and C2 is a dimensionless amplitude 

scaling parameter. Table 2-2 lists the material property inputs used in the thermal model.

Table 2-2 Material Properties for Thermal Model

While Equation 2–3 approximates heating and cooling cycles that are experienced due to a 

moving heat source, the 2-D axisymmetric models employed in this work do not explicitly model 

a moving weld arc. Other commonly-used heat models may have similar, but not identical, 

exponential forms [39].

Description Dependencies

Density Constant

Latent Heat Constant

Solidus Temperature Constant

Liquidus Temperature Constant

Thermal Conductivity Function of Temperature

Specific Heat Function of Temperature
17

An alternative simplified approach to Equation 2-3 is to specify a constant heat flux with time 

over the weld bead elements. In either case, conduction to the adjacent elements and 

convection to the surroundings was modeled. The calculated transient temperatures can be 

compared to thermocouple data to calibrate thermal model parameters. While the chosen heat 

input model is often applied over a single weld bead, analysts may choose to “lump” a number 

of beads together and apply the heat over the entire lumped area. This approach requires 

careful calibration of the heat input model and may introduce uncertainties in the results [39].

2.3.3. Mechanical Model

The mechanical model calculates stress and strain based upon the temperature distribution 

determined by the thermal model. While exact methods vary from analyst to analyst, material 

property inputs for the structural model may include:

• coefficient of thermal expansion

• elastic modulus

• strain hardening law

• flow stress as a function of plastic strain

• creep law

• annealing temperature

Many of these parameters are a function of temperature.

During plastic deformation most metals harden, requiring increasing load to cause further plastic 

deformation. The chosen strain hardening law defines how hardening behavior is calculated in 

the FE model. Example hardening laws include: elastic-perfectly plastic, isotropic hardening, 

kinematic hardening, and mixed isotropic-kinematic hardening [39]. For isotropic hardening, the 

yield surface expands upon plastic deformation, such that the yield stress in tension is always 

equal to the yield stress in compression. The yield surface translates in the kinematic model, 

meaning that the yield stress is different in tension and compression. Real materials exhibit 

both isotropic and kinematic hardening behavior during deformation (mixed hardening). 

Development of hardening laws may require extensive material testing.

Creep properties may be used to simulate stress relaxation during post weld heat treating

(PWHT). Typically, the nozzle buttering on the carbon or low alloy steel nozzle is heat treated 

prior to service, so it is useful to simulate this step. For some FE software packages, the 

annealing temperature input causes all existing plastic strains to be analytically removed upon 

reaching that temperature.

2.3.4. Additional FE Modeling Details

For cylindrical geometry discussed in this report, the elements used in the thermal model were 

axisymmetric, diffusive heat transfer elements. Plane strain elements were used for the plate 

geometry. The mesh was fine at the weld passes and in the adjacent regions, where high 

stress and temperature gradients were expected. The mesh was allowed to coarsen away from 

those areas for computational efficiency. The boundary conditions varied, depending upon the 

geometry and type of constraint in the physical system. The thermal model allowed heat 

convection along the entire surface of the assembly. For the mechanical model in axisymmetric 

cases, one node in the nozzle region (see Figure 1-1) away from the welds was restrained from 
18

displacing parallel to the nozzle axis. Potentially, more than one node could be similarly 

restrained, without appreciably affecting the results [39].

The thermal model consisted of transient heat transfer steps for each weld pass. The 

mechanical model consisted of transient static response steps for each weld pass. Transient 

static response steps with time-dependent material behavior were required to simulate stress 

relaxation during heat treatment.

2.4 WRS Validation Conclusions

Chapter 2 provided a discussion of techniques for developing validation criteria for WRS FE 

simulations. Conclusions are as follows.

• While validation criteria have been proposed by other organizations, the NRC has not 

developed specific criteria for WRS model validation as of publication of this document.

• Validation criteria can potentially be based upon stress intensity factors, fusion zone 

area, root-mean-square differences between measurement and model results, and a 

combination of these and other quantities.

• Diffraction measurements are based upon changes in crystal lattice spacings relative to 

a chosen reference lattice spacing.

• Strain relief measurements are based upon measurements of strain and/or deformation 

when the dimensions of the material are physically altered.

• For WRS measurement, two independent measurements that are based upon different 

physics (e.g., a diffraction measurement and a strain relief measurement) have been

recommended to obtain confidence in measurement techniques.

• The FE techniques considered in this study include mostly 2-D models, so a moving 

heat source is not explicitly modeled.

• The thermal model can simulate heat input during welding based upon previouslydeveloped equations for moving arc analyses. A less sophisticated approach may 

involve holding weld bead elements at a certain temperature for a given time, while any 

temperature decrease is based solely upon conduction and convection.

• The mechanical model calculates strains (and stresses) based upon the temperature 

fields calculated in the thermal model.

• Several approaches are available to account for strain hardening material behavior, 

including: isotropic, kinematic, mixed, and elastic-perfectly plastic.
19

3 PHASE 1: SCIENTIFIC WELD SPECIMENS

3.1 Introduction

Phase 1 of the weld residual stress (WRS) Validation Program focused on small specimens that 

were not representative of nuclear plant components. Two geometries were considered: a 

grooved plate and a cylinder with a butt weld in the center. The purpose of Phase 1 was to 

efficiently develop knowledge of WRS measurement and modeling techniques. Discussion of 

the Phase 1 work can also be found in the Electric Power Research Institute’s (EPRI’s)

Materials Reliability Program (MRP)-316 report [45].

3.2 Specimen Fabrication

3.2.1. Flat Plate Specimens

Six flat plates were fabricated as shown in Figure 3-1. Two of those plates were used for 

material property characterization, while the other four were designated for WRS measurement. 

The plate material was 304L stainless steel (UNS S30403), and the deposited weld metal was 

Alloy 82 (UNS N06082). Nominal chemistry of these two materials is shown in Table 3-1 and 

Table 3-2 [46], [47].
20

Figure 3-1 Flat Plate Geometry (Courtesy: EPRI)

Table 3-1 Chemical Composition of 304L Stainless Steel [46]

Table 3-2 Chemical Composition of Alloy 82 [47]

The welding method for depositing filler metal in the groove was automated gas tungsten arc 

welding. The different plate specimens were designated P-3, P-4, P-5, and P-6, with welding 

parameters listed in Table 3-3. All weld passes were started on the same side of the plate. 

Restraint was applied during welding by an aluminum backing plate loaded by Belleville

washers with linear force/displacement behavior. The weld and restraint geometry is illustrated 

in Figure 3-2. The bolts in the restraint were preloaded to account for differential thermal 

expansion between the plate and fixture materials. Thermocouple data was collected during 

welding, and bead geometry was measured using laser profilometry between passes. Example 

data from thermocouples and laser profilometry are shown in Figure 3-3 and Figure 3-4, 

respectively.

C Mn P S Si Cr Ni N

0.03 2.00 0.045 0.030 0.75 18.0-20.0 8.0-12.0 0.10

C Mn Fe P S Si Cu Ni Ti Cr Nb + Ta

0.10 2.5-3.5 3.0 0.03 0.015 0.50 0.50 67.0 min 0.75 18.0-22.0 2.0-3.0
21

Table 3-3 Welding Parameters for Plate Studies (Courtesy: EPRI)

Figure 3-2 Welding Restraint for Plate Specimen (Courtesy: EPRI)

Root 

Passes

Remaining 

Passes

P-3 Plate Base Case 11 275/225 11.5 2.5 32 41

P-4 Decrease Travel Speed 7 275/225 11.5 1.5 32 41

P-5

Increase Current and 

Wire Feed Rate 7 375/325 11.8 2.5 58 58

P-6

Decrease Current and 

Wire Feed Rate 23 175/125 10.8 2.5 17 17

ID

Wire Feed Speed (mm/s)

Travel Speed 

Current (A) Voltage (V) (mm/s)

No. of 

Variable Tested Passes
22

Figure 3-3 Example Thermocouple Data (Courtesy: EPRI)

Figure 3-4 Example Laser Profilometry Data (Courtesy: EPRI)

3.2.2. Cylindrical Specimens

The fabrication materials for the cylindrical specimens included 304L stainless steel (SS), 308 

SS, and plain carbon steel (CS). Five cylindrical specimens were welded, according to the 

geometry in Figure 3-5. One of those specimens was used for material property 

characterization, while the others were used for WRS measurement. The specimens were 

fabricated with increasing weld complexity, as shown in Figure 3-6. Table 3-4 summarizes the 

specimen designations: C-1, C-3, C-4, and C-5. One specimen type consisted of two 304L SS 

cylinders welded with Alloy 82 (cylinder C-1). The second specimen type consisted of CS and 

304L SS ring for base material (cylinder C-3). The joint between the two materials included an 

Alloy 82 buttering weld. Finally, the most complex specimen consisted of a CS ring joined to a 

SS safe end with a buttering weld and an Alloy 82 dissimilar metal (DM) weld (cylinder C-5). 

The safe end was welded to a 304L SS ring with an E308L SS weld. Cylinder C-5 most closely 
23

approximated actual nuclear component welds, as illustrated in Figure 1-1. A repair weld was 

also applied to cylinder C-5. This repair involved machining a cavity into the weld, according to 

Figure 3-7, and filling the cavity with Alloy 82 weld metal.

The welding method for the circumferential butt weld was automated gas tungsten arc welding. 

Seven weld passes were deposited for each weld. The welding parameters for the three 

specimen types are shown in Table 3-5. The starts and stops were confined to a 90 degree 

sector, so that measurement could be taken on the opposite side of the weldment.

Figure 3-5 Cylindrical Specimen Geometry (Courtesy: EPRI)

141 165

30o

R 3.3

1.5

114

SECTION A-A

DETAIL B

Dimensions in mm

Weld-groove is axisymmetric
24

Figure 3-6 Three Specimen Types (Courtesy: EPRI)

Table 3-4 Cylinder Specimen Designations (Courtesy: EPRI)
25

Figure 3-7 Cylinder C-5 Repair Weld Geometry (Courtesy: EPRI)
26

Table 3-5 Cylindrical Specimen Weld Parameters (Courtesy: EPRI)

3.3 Results and Discussion

This section describes representative results from Phase 1 of the WRS Validation Program. 

Comprehensive results are found in the EPRI report MRP-316 [45].

3.3.1. Surface Stress Measurements

Figure 3-8 and Figure 3-9 show comparisons of several surface measurement techniques on 

the plate specimens. The results are plotted as the longitudinal and transverse components as 

a function of depth from the surface, where a position of 0 represents the original plate surface, 

a negative position represents the weld crown that extended above the plate surface, and a 

positive position represents distance through the thickness of the plate. In general, the surface 

techniques do not show good agreement. Figure 3-10 shows x-ray measurement results along 

a line perpendicular to the weld for a plate specimen. Since the same material exists on each 

side of the weld, more-or-less symmetric data is expected. This data showed rather highmagnitude values (i.e., ± 1,000 MPa) and unexpected asymmetry relative to the weld centerline.
27

Figure 3-8 Surface Stress Measurements for Plate P-3 (Courtesy: EPRI)

Figure 3-9 Surface Stress Measurements for Plate P-4 (Courtesy: EPRI)
28

Figure 3-10 X-ray Results Across the Weld (Courtesy: EPRI)

Figure 3-11 shows deep hole drilling results through the depth of a cylindrical specimen, as 

measured from a hole drilled through the weld centerline. Analogous results are shown for the 

repair weld centerline in Figure 3-12. These results showed reasonable magnitudes and 

smooth trends. They also demonstrated an increase in the hoop stress in the small cylinder 

resulting from the repair weld.
29

Figure 3-11 Deep Hole Drilling Results (Courtesy: EPRI)

Figure 3-12 Deep Hole Drilling Results for along Repair Centerline (Courtesy: EPRI)

Example results from the contour method are shown in Figure 3-13, which demonstrates that 

the contour method provides stress values distributed over a cross-section. The results from 

the contour measurements provided reasonable magnitudes and smooth trends.
30

Figure 3-13 Contour Method Results (Courtesy: EPRI)

Figure 3-14 and Figure 3-15 show a comparison of through-thickness modeling and 

measurement results for a plate specimen. Similar results for a cylindrical specimen are shown 

in Figure 3-16 and Figure 3-17. Model A in these figures implemented the elastic-perfectly 

plastic hardening law, while Models B and C implemented the isotropic hardening law. Model D 

used a bilinear kinematic hardening law. The best agreement between modeling and 

experiments was observed for the transverse stress in the plate specimen (Figure 3-15).

In some cases, most notably in Figure 3-16 and Figure 3-17, the neutron results exhibited a 

large degree of scatter. Nickel alloy welds can have large grains, preferred orientation, and 

chemical concentration gradients when joining dissimilar base materials. These effects can 

combine to affect results and greatly increase experimental difficulty. The large scatter in the 

data reported here is likely a result of these effects.
31

Figure 3-14 Longitudinal Stress for Plate P-4 (Courtesy: EPRI)
32

Figure 3-15 Transverse Stress for Plate P-4 (Courtesy: EPRI)

Figure 3-16 Hoop Stress for Cylinder C-3 (Courtesy: EPRI)
33

Figure 3-17 Axial Stress for Cylinder C-3 (Courtesy: EPRI)

3.3.2. Sources of Measurement Error

The diffraction-based results exhibited scatter. Chemical concentration gradients created during 

the welding process can affect the measured dhkl. This effect requires that the specimen be cut 

into small coupons to relieve the stress. A spatially-dependent dhkl,0 can then be measured. 

This process increases the experimental complexity and experimental error, as the scattering 

volume for the reference measurement may not be identical to that of the original measurement. 

Also, large grains and crystallographic texture, both of which may be present in weldments, can 

cause problems with scattering statistics. Performing the experiment at a pulsed neutron 

source, using techniques described by Brown et al. [48], may mitigate these problems. The 

stress measured at a pulsed neutron source can be based upon several diffraction peaks, rather 

than just a single peak. Results from a pulsed neutron source are shown in Figure 3-18 [48]. In 

this case, the neutron results showed reasonable trends and agreed well with modeling and an 

independent contour measurement. In general, however, diffraction techniques may not be 

optimal for the materials of interest in safety-related nuclear component welds. The data in 

Figure 3-18 is also shown in Figure 3-14 and Figure 3-15 as “Neutron Diff Facility C” and 

“Contour Facility C.”
34

Figure 3-18 Stress Results from a Pulsed Neutron Source (open symbols: at 

weld/base metal interface)

3.3.3. Sources of Modeling Uncertainty

It is evident in Figure 3-14 through Figure 3-18 that the various modeling results do not agree. 

The choice of hardening law, in particular, can be a large source of modeling uncertainty, since 

it has a direct effect on the calculation of stress. A lack of common procedures for post 

processing may have contributed to observed modeling uncertainty. Modeling variability 

increased when considering the cylinder specimens. This model geometry was likely more 

dependent on modeler assumptions taking weld cavity shrinkage into account for weld bead 

size and shape in the cylinder specimens, since the cylinder welds were less constrained than 

the plate specimens.
35

3.4 Phase 1 Conclusions

Phase I of the NRC/EPRI WRS Validation Program consisted of small scientific specimens for 

the purpose of developing modeling and measurement capabilities. Conclusions from this work 

include:

• Small plate and cylinder specimens allowed development of WRS measurement and 

modeling techniques.

• Results from near-surface stress measurements, using a variety of techniques, did not 

compare well with each other. Therefore, uncertainties are larger for near-surface 

residual stresses than for bulk residual stresses.

• Select results from diffraction-based techniques exhibited high scatter. The likely cause 

is the combined effects of large grains, crystallographic texture, and chemical 

concentration gradients associated with the nickel alloy DM weld. While certain 

experimental procedures can mitigate these effects, diffraction techniques may not be 

optimal for the materials present in safety-related nuclear component welds.

• Through-thickness strain relief measurements provided reliable results, in these studies.

• Potential sources of modeling uncertainty in the Phase 1 work included choice of 

hardening law, differences in post-processing procedures, and differences in weld bead 

geometry for the cylindrical specimens.

• Measurements and models showed some agreement.

• The Phase 1 results served to develop measurement and modeling techniques for 

application to prototypic mockups in later phases of the WRS Validation Program. While 

the hardening law assumption at this stage was known to be a source of modeling 

uncertainty, no attempt was made to restrict the choice of hardening law in studies that 

followed. The effect of hardening law can easily be separated when comparing various 

modelers’ results to each other and to experimental data. Through-thickness strain 

relief-based techniques were determined to be the primary source of WRS measurement 

information for the remaining phases of the WRS Program.

37

4 PHASE 2A: FABRICATED PROTOTYPIC NOZZLE

4.1 Introduction

The Phase 2a effort consisted of measurement and modeling on a prototypic pressurizer surge 

nozzle mockup. This phase of the research was intended to compare WRS model results with 

measurements and to assess modeling uncertainty. The modeling effort in this phase of the 

work included a double-blind finite element modeling round robin, where measurement data was 

hidden from the analysts. Discussion of the Phase 2a work can also be found in EPRI’s MRP316 report [45]. Phase 2b was an ongoing effort as of the publication of this document.

4.2 Mockup Fabrication

The geometry chosen for the WRS round robin was representative of a pressurizer surge 

nozzle, due to its safety significance and relevance to flaw evaluation [50]. The overall 

geometry is shown in Figure 4-1. The SA-105 carbon steel nozzle was attached to a hot-rolled 

steel plate to represent the stiffness of the nozzle in service. The stiffened nozzle was buttered 

with Alloy 82 (American Welding Society A5.14, ERNiCr-3, UNS N06082) weld material, post 

weld heat treated, and then welded to a forged F316L stainless steel safe-end. Finally, the safe

end was welded to a TP316 stainless steel, 14-inch diameter Schedule 160 pipe using a TP308 

weld.

Figure 4-1 Phase 2a Mockup

SA-105 Fabricated Nozzle

Buttering

DM weld 

with “fill-in” 

weld F316L Safe End

TP 308 Stainless 

Steel Weld

TP 316 Stainless Steel 

Pipe 14-in Sch 160
38

Mockup fabrication occurred in the following five steps.

• 137 butter passes of Alloy 82

• Heat treat (600-650o

C for 3 hours) and machining of the butter

• 40 passes of Alloy 82 (constituting the DM weld) to join the carbon steel nozzle to the 

stainless steel safe end.

• Machining of the DM weld root (i.e., at the inner diameter location.)

• 27 passes of Alloy 82 to make up the 360 degree fill-in weld.

At this point, residual stress measurements were made on the DM weld. The residual stress 

measurements were followed by the TP308 stainless steel safe end to pipe weld, with a second 

set of residual stress measurements made investigating the effect of the safe end to pipe 

closure weld. For the main DM weld and fill-in weld, laser profilometry measurements mapped 

the contour of each weld pass.

Temperature during mock-up welding was recorded as a function of time using thermocouples 

placed on the inner diameter (ID) and outer diameter (OD). Six thermocouples were placed on 

the top dead center location during the butter welding (three thermocouples each on the ID and 

OD). Thermocouple measurements were also made at both 45 and 90 degrees 

circumferentially from the top dead center (again, three thermocouples each on the ID and OD). 

For the repair and fill-in weld, the same thermocouple location could not be used on the ID, so

the locations of these thermocouples were shifted axially.

The materials for each component of the mock-up are shown in Table 4-1.

Table 4-1 Phase 2a Mockup Material Specifications

Component Material

Nozzle Carbon steel (SA-105)

DM Weld (including 

buttering, and fill-in)

Alloy 82: AWS A5.14 ERNiCr-2 

(UNS N06082)

Safe End F316L forged stainless steel

Stainless Pipe TP 316 stainless steel, 14-inch 

diameter Schedule 160

Stainless Steel Weld TP 308 stainless steel

The main DM weld was deposited using gas tungsten arc welding (GTAW) with 40 passes of 

1.1 mm (0.045 in.)-diameter Alloy 82 welding wire being fed externally (see Table 3-2). The

welding parameters for the main DM weld are given in Table 4-2. 
39

Table 4-2 Typical Parameters for Main DM Weld

Parameter Value

Current 220-285 A

Voltage 10.7-11.2 V

Travel Speed 2.54 mm/s

After the main DM weld was completed, the ID was machined to simulate the cavity for a 360

degree weld repair. The fill-in weld was deposited using automated GTAW with a total of 27 

passes. The typical welding parameters used to deposit each weld pass are listed in Table 4-3.

Table 4-3 Typical Parameters for Fill-in Weld

Parameter Value

Current 200 A

Voltage 15.5 V

Travel Speed 2.54 mm/s

The safe end to stainless steel pipe weld with material TP308 was completed in 28 passes with 

weld parameters given in Table 4-4.

Table 4-4 Typical Parameters for Stainless Steel Weld

Parameter Value

Current 90 - 147 A

Voltage 9.2 - 26 V

Travel Speed 1.27 mm/s

4.3 Weld Residual Stress Measurement

Various measurement techniques were discussed in Section 2.2. For this configuration, the 

through-wall axial and hoop stresses were of greatest interest since, in in-plant configurations, 

these stresses lead to mode I opening of circumferential and axial flaws, respectively. Based 

upon experience in Phase 1 (see Chapter 3), strain relief-based techniques were determined to 

be appropriate [32]-[38].

For the Phase 2a round robin mockup, a combination of deep hole drilling (DHD)/incremental 

deep hole drilling (iDHD) [32] was chosen for the through-thickness measurements. One goal 

of the round robin study was to assess the effect of the safe end to stainless steel pipe weld on 

stresses in the main DM weld. Hence, the above WRS measurements were taken before and 

after completion of the safe end to stainless steel pipe closure weld. Figure 4-2 shows the 

location of the WRS measurements: the DHD/iDHD measurements were taken through the 

centerline of the DM weld. The iDHD measurements were taken on the ID and OD of the DM 

weld. A total of six hole drilling measurements were performed at different locations around the 

circumference of the weld. Two sets of those measurements were performed without 

knowledge of the finite element data (i.e., double-blind), two prior to and two following the 

stainless steel pipe closure weld. The other four measurements were made after the finite 

element modeling data was made public.
40

Figure 4-2 Weld Residual Stress Measurement Location

Subsequent to the double-blind finite element (FE) round robin, the U.S. Nuclear Regulatory 

Commission (NRC) commissioned a set of contour measurements on the Phase 2a mockup. 

This data does not meet the double-blind criteria, but it does provide a useful independent 

check of the hole drilling data.

4.4 Double-Blind Finite Element Round Robin

This program consisted of an analytical international FE round-robin for the prototypical PWR 

pressurizer surge nozzle geometry. The results from the round robin FE modeling were 

compared to physical measurements performed on the mock-up. The study was double blind, 

i.e., the FE analysts and measurement practitioners were not allowed to compare their results 

before submission, permitting the NRC staff to develop unbiased measures of uncertainties in 

WRS predictions.

4.4.1. Initial Approach to Assessing Modeling Uncertainty

Before initiating the round robin, heat input and material properties were considered to be the 

most likely sources of modeling uncertainty. Therefore, the international round robin FE 

analyses were completed in two stages. In Analysis 1a, the geometry modeled included the 

nozzle and DM weld only (with no stainless steel weld). The analysts were not provided with 

either material properties or thermocouple data, but they were provided with laser profilometry 

data. For Analysis 1b, the NRC supplied each analyst with thermocouple data obtained during 

the fabrication process. For Analysis 1c, the NRC provided material properties extracted from 

test coupons matching the materials used in the actual nozzle mockup. It was thought that 

modeling uncertainty would decrease as the participants were provided more information from 

which to refine their models. In Analysis 2, the full mockup nozzle fabrication was modeled, 

including the stainless steel weld. Laser profilometry and thermocouple data for the stainless 

steel weld were provided to the analysts. These analysis stages are summarized in Table 4-5.

2 DHD/iDHD Before SS Weld

2 DHD/iDHD After SS Weld

 
41

Table 4-5 Analysis Stages

4.4.2. Round Robin Participants

Thirteen organizations representing the United States (eight), European Union (two), Japan 

(two), and Australia (one) submitted WRS FE results in support of the WRS FE round robin 

effort, summarized in Figure 4-3. Participation was not uniform for all analyses. Analysis 1a 

included ten independent results (and two late results), while Analysis 1c included nine 

independent results and Analysis 2 included eight independent results (and one late result). 

Three participants varied the hardening law assumed for a given analysis (typically isotropic and 

kinematic hardening), yielding multiple WRS profiles for a given model. Results marked as ‘late’ 

were received after the blind deadline and were not included in the data analysis, but were 

plotted against the dataset as a whole for comparisons.

Figure 4-3 Round Robin Participants

4.4.3. Modeling Package

NRC and EPRI prepared a modeling package in order to provide a formalized problem 

statement to each participant. Subject to the restrictions listed in Table 4-5, the modeling 

package included the following information:

Designation Stainless Steel Closure Weld Thermocouple Data Material Property Data

Analysis 1a Prior No No

Analysis 1b Prior Yes No

Analysis 1c Prior Yes Yes

Analysis 2 Post Yes Yes
42

• fabrication drawings that specified mockup dimensions

• thermocouple measurement locations and associated transient temperature data, such 

as shown in Figure 3-3

• laser profilometry data on the weld beads, such as shown in Figure 3-4

• punch mark locations and associated weld cavity shrinkage measurements

• WRS measurement locations, but not the associated data

• nominal material specifications

• welding details: bead sequence, current, voltage, wire feed speed, and travel speed

4.4.4. Model Description

FE modeling of WRS, in general, was introduced in Section 2.3. This section describes one 

participant’s model, as a demonstration of the approach one may take. The details in this 

section do not represent information that was provided to the participants. A 2-D schematic of 

the major geometric features modeled is provided in Figure 4-4 including the Alloy 82 butter, 

main DM and fill-in welds, and the stainless steel safe end weld. The mesh is fine around the 

weld locations.

Figure 4-4 Example Model Features

Round robin participants employed a wide range of weld bead refinement in modeling the butter 

layer. A high degree of weld bead refinement is shown in Figure 4-5, where 137 butter weld 

beads were deposited, closely approximating the mock-up weld bead geometry as measured by 

laser profilometry. Bead lumping, where the heat input of several weld passes was combined 

into a single larger weld bead, was also conducted by some analysts for the butter. Bead 

lumping ranged from four to eight beads to an entire row. After deposition of the butter, the 

weld was post-weld heat treated at 866-922 K for 3 hours. The butter was machined after heat 

treatment to the V-groove geometry required for the main DM weld. This machining process 

was implemented in the FE by material removal, followed by stress redistribution (equilibrium). 

Surface stresses imparted by the machining process were not captured by the FE, in any case.

Boundary Conditions:

•Fixed axially on left end and free on right end

•Equivalent convective cooling on both outer and inner 

diameter surfaces

SS Cladding

Alloy 82

Weld

Alloy 82

Butter

SS 

Weld

Fill-In 

Weld

SS Safe 

End

SS Pipe

SA-105
43

Figure 4-5 Butter Layer and Machining

Not all analysts used the laser profile data to generate bead geometry. In cases where the 

bead geometry was not used, individual weld beads were idealized as rectangles similar in area 

to the average bead size measured with the laser profilometry data. Unlike the buttering,

lumping of the main DM weld beads was not conducted, and all models were based on the DM 

Alloy 82 weld passes deposited during mock-up fabrication. Figure 4-6 is an example of how 

laser data was converted to DM weld bead geometry. Note that the final V-groove geometry 

was used to account for the shrinkage that occurs during initial weld passes when developing 

the model geometry.

Figure 4-6 Weld Bead Geometry from Laser Data

Alloy 82

Butter

(137 Passes)

Alloy 82

Weld

(40 Passes)
44

After completion of the main DM weld, the ID surface was machined to the geometry required 

for the 25 percent thickness fill-in weld. In the FE models, material was removed on the ID to 

generate a smooth surface, and stresses were allowed to redistribute, followed by the Alloy 82 

fill-in weld. This sequence is illustrated in Figure 4-7, modeling 27 weld passes and estimating 

the bead geometry from the laser data.

Figure 4-7 Fill-In Weld

The step pictured in Figure 4-8 removed the crown from the main DM weld and the fill-in weld, 

machined to the final geometry, and allowed stress redistribution (equilibrium).

Figure 4-8 Machining Steps

Fill-In Weld 

Groove 

Machined

Alloy 82 FillIn Weld

(27 Passes)
45

The final step in the FE models was the application of the stainless steel weld. For the model 

illustrated in Figure 4-9, 52 idealized weld passes were assumed for the stainless steel closure 

weld. Laser profilometry data for the safe end weld was distributed with the modeling package; 

the 52 beads in Figure 4-9 represent a specific analyst's assumption, while the actual mockup 

had 28 beads.

Figure 4-9 Stainless Steel Closure Weld

4.4.5. Post-Processing of Finite Element Results

Through thickness residual stress measurements were made at two locations 180 degrees 

apart, both before and after the application of the safe end weld. The DHD measurements 

provided experimental axial and hoop residual stress data. Round robin participants extracted 

model results along the centerline of the DM weld in order to allow direct comparison to 

experimental results, as illustrated in Figure 4-10. Since the DHD measurements were taken at 

room temperature, participant FE results were extracted at room temperature.

Figure 4-10 Extraction of Results

SS Safe End Weld

(52 Passes)

Axial Stress

Hoop Stress

Axial Stress

Hoop Stress

ISO KIN
46

As shown in Figure 4-10, the centerline of the DM weld was not the location of maximum stress, 

and further the stress distribution was asymmetric about the centerline of the DM weld. The 

development of an asymmetric residual stress profile across the can be attributed to the 

asymmetric geometry of the ID fill-in weld and the different material properties on each side of 

the weld centerline. While the DHD measurements represented a stress averaged over the 5 

mm core diameter used to make the DHD measurements, no effort was made to conduct similar 

averaging for the FE results.

4.4.6. Data Analysis

In the raw data, round robin participants provided stress results at different divisions through 

thickness (as a result of mesh geometry and extraction methodology), and the end state 

thickness of the component varied from model to model. To create uniform point spacing, the 

raw stress data was linearly interpolated to 50 uniform points through-thickness, producing an 

approximately 1-mm spatial resolution sufficient to capture the features present in the raw data.

The variation in end state thickness of the nozzle ranged from 46.5 to 51.6 mm in Analysis 1c. 

To account for this variation, raw data was normalized by thickness (x/t). DHD measurements 

were not able to measure surface stresses, and this data was normalized by the thickness of 

the nozzle at the measurement location. Variation in geometry modeled can have an effect on a 

given residual stress distribution, and geometry variability from participant to participant is 

discussed in detail below.
47

4.5 Results and Discussion

4.5.1. Measurement Results

Figure 4-11 and Figure 4-12 show the DHD/iDHD WRS measurement results for both axial and 

hoop stress components before application of the stainless steel weld as a function of throughthickness distance from the ID to the OD through the centerline of the DM weld. For each 

stress component, two measurements were taken in the nozzle 180 degrees apart from one 

another. As is typical of configurations in which the final weld passes are completed on the ID, 

the pre-stainless steel weld axial stress component was highly tensile at the ID and followed a 

commonly observed profile thereafter. Equilibrium considerations require that, on average, the 

integrated through-wall area under the axial stress distribution curve equate to zero, provided 

the stress is axisymmetric. This is reasonably observed in the axial DHD/iDHD results. The 

pre-stainless steel weld hoop stress distribution remains highly tensile between approximately 0

and 500 MPa.

Figure 4-11 Axial Stress DHD/iDHD Measurements before Stainless Steel Weld
48

Figure 4-12 Hoop Stress DHD/iDHD Measurements before Stainless Steel Weld

DHD/iDHD WRS measurements taken after the stainless steel weld are shown in Figure 4-13

and Figure 4-14. The axial and hoop stresses at the ID location reduced significantly as a result 

of the stainless steel weld. This reduction in ID stress after the stainless steel weld for certain 

geometries is significant for stress corrosion cracking susceptibility. After application of the 

stainless steel weld, the stresses still appear axisymmetric.

Also shown in Figure 4-13 and Figure 4-14 are contour measurements that were obtained after 

the round robin study results were made public. This independent measurement confirmed the 

stress magnitudes and concave down trend of the hole drilling data near the ID, although the 

hole drilling and contour hoop stress data did not agree for 0.3 ≤ x/t ≤ 0.45. The contour 

measurements show lower stress magnitudes near the OD than the hole drilling measurements.
49

Figure 4-13 Axial Stress Measurements after Stainless Steel Weld

Figure 4-14 Hoop Stress Measurements after Stainless Steel Weld
50

4.5.2. Finite Element Modeling Results

The figures in this section represent the round robin data set using the following conventions:

• Individual FE results are shown as squares, with individual models identified as A 

through J.

• Measurement results are shown as red circles.

• The blue lines in the figure represent the average of the FE dataset.

• The results are segregated by Analyses 1a, 1c, and 2, as described in Table 4-5. Note: 

Analysis 1b results are neglected in Section 4.5.2, since they do not provide additional 

insight.

Figure 4-15 plots axial stress results for Analysis 1a prior to the application of the stainless steel

weld, where participants were supplied neither mechanical properties nor thermocouple data. 

As is typical of the configuration in which the final weld passes were completed on the ID, the 

weld axial stress component is highly tensile at the ID. The FE results deviate from the average 

by a maximum of about ±200 MPa through thickness. At the OD the scatter is driven by result 

‘J’, which shows a trend between 0.8 to 1 x/t not observed in any other results. At mid-thickness 

from 0.3 to 0.6 x/t, the increase in variability is attributed to differences in where the zero stress 

is crossed. Late results are included in Figure 4-16 and are consistent with other results 

submitted for Analysis 1a.

The average of the modeling results and the axial stress measurement data did not always 

agree in magnitude, mainly for 0.1 ≤ x/t ≤ 0.4 and x/t ≥ 0.65. The FE results tended to 

underpredict the measurements in these areas. Both the measurements and the modeling 

showed a general trend of tension at the ID, decreasing to compressive stress at approximately 

x/t = 0.6, followed by an increase in stress to the OD.
51

Figure 4-15 Analysis 1a Axial Stress

Figure 4-16 Analysis 1a Axial Stress, Late Results.

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iDHD #1

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Average

residual stress measurements
52

Round robin participants were provided both thermocouple data and material property data for 

Analysis 1c. Analysis 1c axial stress results are plotted in Figure 4-17, showing very similar 

trends to Analysis 1a. Results from U.S. participants in the round robin, comprising results from 

NRC and industry contractors, are plotted in Figure 4-18 and show a similar variability in results 

to the entire dataset.

Figure 4-17 Analysis 1c Axial Stress

Figure 4-18 Analysis 1c Axial Stress, US Participants

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53

Figure 4-19 plots hoop stress results for Analysis 1a prior to the application of the safe end

weld, where participants supplied their own mechanical properties and were not provided 

thermocouple data. The pre safe end weld hoop stress distribution is highly tensile through 

thickness ranging between approximately 200 and 600 MPa through-thickness. The DHD 

results showed reasonable agreement with the average stress of the dataset. However, the 

scatter about the mean was as much as ±200 MPa, including the effect of hardening law. Late 

results not included in the calculated average are included in Figure 4-20 and are consistent 

with other results submitted for Analysis 1c.

Figure 4-19 Analysis 1a Hoop Stress

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54

Figure 4-20 Analysis 1a Hoop Stress with Late Data

Round robin participants were provided both thermocouple data and material property data for 

Analysis 1c, with hoop stress results plotted in Figure 4-21. The average stress of the dataset 

and the DHD measurements showed a similar trend: tension at the ID, followed by a decrease 

in stress to approximately x/t = 0.55, and ending with an increase in stress to the OD. The 

magnitudes of the average stress and the measurements did not always agree. The high 

scatter about the average observed in the previous results is also present. Results from U.S.

participants in the round robin, comprising results from NRC and industry contractors, are 

plotted in Figure 4-22 and show a similar variability in results to the entire dataset.
55

Figure 4-21 Analysis 1c Hoop Stress before Safe End Weld

Figure 4-22 Analysis 1c Hoop Stress before Safe End Weld, US Participants

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56

Application of the safe end weld produced a decrease on the ID axial stresses, clearly observed 

in the Analysis 2 axial stress dataset plotted in Figure 4-23 and Figure 4-24. The through 

thickness variability in predicted axial stresses observed in the data post safe end weld is very 

similar to that observed prior to the safe end weld. But, the agreement between the average 

stress of all data and the DHD measurements is somewhat less favorable than from the 

analyses with no safe end weld. Specifically, between 0.1 and 0.4 x/t the DHD data is 

consistently higher than the FE dataset average, and the FE results tended to underpredict the 

measurements as the OD surface is approached. There is also a difference in the concavity of 

the data in the ID region, with the measurements indicating concave down trends and the 

models indicating concave up trends. Late finite element results and measurements not 

included in the calculated average are included in Figure 4-25.

Figure 4-23 Analysis 2 Axial Stress

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Average
57

Figure 4-24 Effect of Safe End Weld on Axial Stresses

Figure 4-25 Analysis 2 Axial Stress, with Late Results and Measurements

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2 Average

1c Average

Stress reduction at ID observed

as a result of safe-end weld
58

Application of the safe end weld produced a decrease on the ID hoop stresses, clearly observed 

in the Analysis 2 hoop stress dataset plotted in Figure 4-26 and the Figure 4-27. The through 

thickness scatter in hoop stresses observed in the data post safe end weld is very similar to that 

observed prior to the safe end weld. But, the agreement between the average stress of all data 

and the DHD measurements is somewhat less favorable. The measurements exhibit lower 

stresses than the FE average from the ID to 0.65 x/t and showing reasonable agreement 

outside of this range. Late modeling and measurement results are included in Figure 4-28. 

Late modeling result ‘J’ is not consistent with FE results submitted for Analysis 2, but there is 

reasonable agreement between result ‘J’ and the DHD measurements, except at the OD. At the

OD, result ‘J’ shows a drop in stress that is persistent in Analyses 1 and 2 for both axial and 

hoop stresses.

Figure 4-26 Analysis 2 Hoop Stress

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Average
59

Figure 4-27 Effect of Safe End Weld on Hoop Stress

Figure 4-28 Analysis 2 Hoop Stress, with Late Result after Safe End Weld

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Stress reduction at ID observed

as a result of safe-end weld
60

4.5.3. Finite Element Dataset Trends

The intent of this section is to study trends in the round robin dataset and, to a more limited 

extent, identify why some individual results trend differently than the dataset as a whole. Global 

trends in the dataset are examined in the areas of material hardening law, thermocouple data, 

material properties, and the effect of safe end weld. The effect of material hardening law 

assumptions is investigated by plotting isotropic and kinematic results against the dataset as a 

whole. Difference plots are used to individually isolate the effect of providing thermocouple and 

material properties, as well as the application of safe end weld to the mock-up. For example, 

residual stress data from Analysis 1b are subtracted from the Analysis 1c for a given residual 

stress profile to isolate the effect of providing thermocouple data. This is referred to as a 

difference plot, showing the change in residual stress profile resulting from tuning the thermal 

model to thermocouple data or other single parameter change to the model. The effect of 

thermal model assumptions and part geometry are also assessed for select individual model 

results, though this is discussed in greater detail in the sensitivity studies described in Section

4.6.

As previously noted in this section, the choice of hardening law will have a large effect on the 

magnitudes of stresses evolved during a WRS simulation. This trend is evident in Analysis 1c 

when the data are grouped by hardening law. The grouping of results in Figure 4-29 represent 

round robin results that applied isotropic hardening; isotropic results develop greater maximum 

and minimum stresses when compared to the dataset as a whole. The grouping of results in 

Figure 4-30 is the subset of isotropic results from U.S. participants in the round robin.

Figure 4-29 Analysis 1c Axial Stress - Isotropic Hardening
61

Figure 4-30 Analysis 1c Axial Stress - Isotropic Hardening, US Participants

The grouping of results in Figure 4-31 represent round robin results that applied kinematic 

hardening (both linear and multi-linear); the shape of these curves is flatter as lower magnitude 

stresses are developed when compared to the dataset as a whole.

Figure 4-31 Analysis 1c Axial Stress - Kinematic and Mixed Hardening
62

Isotropic results tend to develop higher magnitude tensile axial stresses at the ID and OD than 

what is observed in the DHD data, while kinematic results tend to develop lower magnitude 

tensile axial stresses in this region. A similar trend is observed mid-thickness, with the isotropic 

results developing higher magnitude compressive stress and the kinematic lower than the DHD 

data. The magnitude of the stresses developed at the ID, OD, and mid thickness for the mixed 

hardening cases submitted show the best agreement with the stress magnitudes from the DHD 

measurements, though it is difficult to draw a conclusion from a single result given the scatter 

present in the dataset.

Highlighting isotropic and kinematic results for a given model provides additional insight to the 

global trends discussed above. Isotropic and kinematic results for a given model do not 

completely bound the dataset, as plotted in Figure 4-32 for model ‘C’ and in Figure 4-33 for 

model ‘E’. In the context of flaw evaluation (since initiation and growth depend strongly on 

residual stress), these results suggest variation in hardening law is an appropriate sensitivity 

study, but may not completely characterize model-to-model variability.

Figure 4-32 Analysis 1c Axial Stress - Isotropic and Kinematic, Model ‘C’
63

Figure 4-33 Analysis 1c Axial Stress - Isotropic, Kinematic, and Mixed, Model ‘E’

In addition to the discussion of magnitude, differences in the shapes of the WRS profiles must 

be considered. On this point there are subtle but significant differences between the results.

Figure 4-34 shows that DHD measurements cross zero stress at 0.4 and 0.75 x/t. The FE 

results show a broader distribution, crossing between 0.25 to 0.55 x/t, and again between 0.8 to 

1 x/t. These observations are consistent with sensitivity to thermal model tuning discussed later

in this section, where similar magnitude shifts in the zero-stress location for isotropic models 

were produced when the heat input model was adjusted to match thermocouple data.

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64

Figure 4-34 Number of Times the Zero Stress is Crossed

Grouping of hoop stress data by hardening law shows similar trends to those observed for the 

axial stresses. The grouping of results in Figure 4-35 represents round robin results that 

applied isotropic hardening; these isotropic results develop higher magnitude stresses than the 

dataset as a whole. The grouping of results in Figure 4-36 is the subset of isotropic results from 

U.S. participants in the round robin. The grouping of results in Figure 4-37 represents round 

robin results that applied kinematic hardening; the shape of these curves is flatter as lower 

magnitude stresses are developed when compared to the dataset as a whole. One set of mixed 

hardening results is plotted on Figure 4-37 in black. The mixed hardening results are similar to 

the kinematic results, but show better agreement with DHD data as higher stresses are 

developed from 0.1 to 0.3 x/t than are in the kinematic results. At 0.4 ≤ x/t ≤ 0.6, however, the 

mixed hardening results overpredicted the measurements.

0

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DHD

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65

Figure 4-35 Analysis 1c Hoop Stress - Isotropic Hardening

Figure 4-36 Analysis 1c Hoop Stress - Isotropic Hardening, US Participants
66

Figure 4-37 Analysis 1c Hoop Stress - Kinematic Hardening

Highlighting isotropic and kinematic results for a given model provides some additional insight to 

the global trends discussed above. As with the axial stresses, isotropic results for a given 

model do not completely bound the dataset. Results for model C plotted in Figure 4-38 bound a 

greater fraction of the dataset than results from model E plotted in Figure 4-39.
67

Figure 4-38 Analysis 1c Hoop Stress - Isotropic and Kinematic, Model ‘C.’

Figure 4-39 Analysis 1c Hoop Stress - Isotropic and Kinematic, Model ‘E.’

As previously discussed there is general agreement in terms of the WRS profile shape and the 

DHD data, visualized by the comparison of the FE averages to the DHD measurements. Two 

averages are plotted in Figure 4-40 and Figure 4-41, the average of FE results using (1) 

isotropic and (2) kinematic hardening as this affects the form of the WRS profile. Neither 

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g , y

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68

average captures the behavior of the measurement data. Furthermore, which average provides 

a better prediction of the measurements depends on the through-thickness location.

Figure 4-40 Analysis 1c Data with Averages Highlighted

Figure 4-41 Analysis 2 with Averages Highlighted

The effect of tuned thermal models on axial centerline WRS profiles is summarized in the 

difference plot (1b – 1a) in Figure 4-42. Not all participants chose to update their thermal 

model. For example, ‘B’ judged the 1a thermal model based on bead geometry was in 

reasonable agreement with the thermocouple data and did not update the thermal model for 

Analysis 1b. Results from ‘I’ highlighted in blue in Figure 4-42 represent the greatest sensitivity 

of WRS profiles to the thermal model tuning conducted in Analysis 1b. Comparison of the 

Analysis 1a thermal model results for ‘I’ to thermocouple data in Figure 4-43 show the heat input 

was originally significantly underestimated. In fact, the predicted temperatures were far below 

the melting temperature of the filler metal. The Analysis 1b updated thermal model results for ‘I’ 

(a) Axial Stress, Post Safe-End (b) Hoop Stress, Post SafeEnd

(a) Axial Stress, Pre Safe-End 

ISO KIN MIXED DHD

ISO Average

KIN Average

(b) Hoop Stress, Pre Safe-End
69

plotted in Figure 4-44 are in much better agreement with the thermocouple data. For Analysis 

1b, ‘I’ significantly increased the heat input to the weld producing changes to the ID and OD 

stresses, as well as to the mid-thickness stresses. Also illustrated in Figure 4-42 is that 

isotropic hardening shows a greater sensitivity to heat input changes than the kinematic results, 

a trend that is observed in all thermal model updates.

Figure 4-42 Analysis 1a Axial Stress Difference Plot

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Figure 4-43 Measured and Predicted Temperature History – Analysis 1a, Model ‘I’

Figure 4-44 Measured and Predicted Temperature History – Analysis 1b, Model ‘I’

Removing result ‘I’ from the dataset, as in Figure 4-45, shows that the thermal model tuning had 

a more modest effect on the centerline WRS profiles. Here kinematic results are largely 

unaffected by tuning of the thermal model in 1b. Isotropic results, however, exhibit a change in 

stress (increase or decrease) between 0.3 and 0.6 x/t indicating that zero stress has been 

crossed at a different location as a result of the thermocouple tuning. Further, the centerline 

WRS profile shape was largely insensitive to tuning of the thermal model, provided that the heat 

input was not significantly underestimated originally.

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Main DM Weld Bead 3 – Analysis 

1a

Main DM Weld Bead 3 – Analysis 

1b
71

Figure 4-45 Analysis 1a Axial Stress Difference Plot – Excluding Model ‘I’

Similar trends were observed for the hoop stress data, as illustrated in Figure 4-46. The above 

discussion suggests that the weld bead geometry and weld parameter data provided in Analysis 

1a was, in most cases, sufficient to constrain the heat input for the thermal modeling. The 

thermocouple data provided in Analysis 1b allowed verification of the heat input assumptions 

made in Analysis 1a. These observations are consistent with the sensitivity of WRS profiles to 

heat input described in Section 4.6, which notes that if the total amount of heat input is 

approximately correct the end state WRS profiles are stable. However, the time over which the 

heat is applied may have some effect.

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Figure 4-46 Analysis 1a Hoop Stress Difference Plot – Excluding Model ‘I’

The sensitivity to material properties was not as large as anticipated at the onset of this study, 

where it was assumed that use of a common material property dataset would produce a 

reduction in scatter for the end state centerline WRS profiles. While the use of the NRC 

material property had an effect on the axial WRS profiles, systematic variation is not observed 

for the (1c – 1b) difference plot in Figure 4-47. The hoop stresses appear more sensitive to 

material properties than the axial stresses, as shown in the (1c – 1b) hoop stress difference plot 

in Figure 4-48. Unlike the axial stresses, there are some hoop stress results that show 

systematic variation, specifically result ‘G’ is higher than the other results and result ‘J’ is lower 

in stress through-thickness than the average response. Aside from the two hoop results 

identified that show systematic variation, axial and hoop stress values change from 100 to 200 

MPa through thickness using the NRC material property dataset with no reduction in the scatter 

observed in the Analysis 1c results. The sensitivity of hoop stresses to material property input 

observed here is consistent with the findings of the FE sensitivity studies discussed in Section

4.6 of this report.

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Figure 4-47 Analysis 1c – 1b Axial Stress Difference Plot

Figure 4-48 Analysis 1c – 1b Hoop Stress Difference Plot

The driver for the axial and hoop ID stress reduction is the through-wall bending that occurs as 

a result of the safe end weld application. This stress reduction is important since SCC is likely 

to initiate in susceptible material on the pipe ID, therefore an appropriately sized safe end will 

lower the likelihood of SCC initiation through this reduction in ID stress. Figure 4-49 is the axial 

stress centerline difference plot (2 – 1c) showing the effect of the through-wall bending, while 

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-200

0

200

400

600

800

1000

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

Stress (MPa)

Distance from ID (x/t)

 

 

B - KIN

C - ISO

C - KIN

E - ISO

E - MIXED

E - KIN

F - ISO

G - ISO

I - ISO

I - KIN

J - ISO

Average
74

Figure 4-50 is the same for the hoop stress. The through-wall bending is predominantly elastic 

for both the FE and DHD results. A couple of the isotropic FE results show minor deviation from 

linearity, indicating that plasticity has occurred during the application of the safe end weld. DHD 

results show a drop off in stress as the OD approached. Scatter in the difference plot is similar 

in magnitude as for Analysis 1c and 2.

Figure 4-49 Axial Stress Through Wall Bending Caused by Safe End Weld

-800

-600

-400

-200

0

200

400

600

800

1000

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

Stress (MPa)

Distance from ID (x/t)

 

 

B - KIN

C - ISO

C - KIN

E - ISO

E - MIXED

E - KIN

F - ISO

G - ISO

H - ISO

I - ISO

I - KIN

J - ISO

iDHD #1

iDHD #2

Average
75

Figure 4-50 Hoop Stress Through-Wall Bending Caused by Safe End Weld

Though the round robin problem statement provided detailed geometric information, there were 

still variations in geometries modeled by some participants. All round robin participants 

informed the weld bead geometry by the laser profilometry data, whether by explicitly 

incorporating the laser profilometry data into the FE model or using the profilometry data to 

inform the idealized weld bead size.

Even with detailed geometric data provided, the thicknesses of the component modeled ranged

from 46.8 to 49 mm, representing a difference in component thickness of 5 percent that was 

accounted for by using a normalized thickness (x/t) and contributing to the model-to-model 

variability observed in the dataset. Result ‘E’ modeled a component thickness of 51.6 mm, but 

on closer examination this was a result of the weld cap and fill-in weld not being machined to 

the final component geometry specified. This will have an effect on the WRS profile, specifically 

the location of where the WRS profile will cross the zero stress axis. To estimate the magnitude 

of this effect, profile ‘E’ was normalized to the correct thickness by removing the part of the 

WRS profile associated with the fill-in weld (first 3 mm of the WRS profile) and weld cap (last 2

mm of the WRS profile). Stress redistribution was not accounted for, but the stress 

redistribution expected is not significant as it should be near an equilibrium condition. The plot 

in Figure 4-51 shows that the location of zero stress shifts by approximately 3 percent and the 

start of the fill-in weld by approximately 5 percent, contributing to the model-to-model variability 

observed in the dataset.

-800

-600

-400

-200

0

200

400

600

800

1000

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

Stress (MPa)

Distance from ID (x/t)

 

 

B - KIN

C - ISO

C - KIN

E - ISO

E - MIXED

E - KIN

F - ISO

G - ISO

H - ISO

I - ISO

I - KIN

J - ISO

iDHD #1

iDHD #2

Average
76

Figure 4-51 Results ‘E’ As-Submitted and Corrected for Geometric Variation

4.5.4. Summary of Round Robin Results

At the onset of the FE WRS round robin, it was assumed that providing thermocouple and 

material property data would reduce the variability associated with FE WRS models. This 

outcome was not observed in the dataset; rather similar variability was present in all phases of 

the study regardless of the amount of information provided to FE round robin participants. 

While there was significant scatter present in the international FE WRS round robin dataset,

there were consistent trends in the dataset, which are summarized below.

• Shape of the mean WRS profiles calculated by FE and experimentally measured by 

DHD were similar in Analysis 1 and 2. There is favorable agreement between the 

average of all results and the experimental DHD measurements for Analysis 1. For 

Analysis 2, the DHD measurement tended to be higher in magnitude than the average 

of all results until mid-thickness of the component.

• FE models using isotropic hardening evolved stresses higher in magnitude than those 

using kinematic hardening, with the annealed material properties provided by the NRC 

for Analysis 1c.

• In most cases the weld bead geometry and weld parameters provided were sufficient to 

constrain the FE thermal models; refining thermal models based on thermocouple data 

shifted the zero stress location.

• FE models using isotropic hardening showed a greater sensitivity to heat input, 

specifically the location of zero stress was sensitive to heat input. FE models using 

kinematic hardening showed less sensitivity to heat input. This observation can be 

attributed to annealing procedures in certain finite element packages. The yield surface 

expansion is reset when the temperature reaches the prescribed annealing 

temperature, leading to heat input sensitivity of the isotropic hardening models.

• The stainless steel safe end weld led to a pronounced reduction in stresses at the ID for 

both hoop and axial stresses, as a result of through-wall bending.
77

• Geometric variations (different component thicknesses, fill-in weld depths, and weld 

shrinkage) in models produced observable differences in WRS profiles, but these 

differences do not account for the entire model-to-model variation observed in the round 

robin dataset.

4.6 Sensitivity Studies

Given the presentation and analysis of the previous section, it is apparent that significant 

variation exists in the round robin FE data sets. In practice, this scatter inherently reduces 

confidence that FE calculation results are robust approximations to the true, physical state of 

stress of a structure. WRS FE simulations are complex in that there are many input variables 

and methods for approximating model details. Further, WRS fields are known to have a 

significant effect on flaw evaluation and probabilistic fracture mechanics calculation results. 

Therefore, it is important to gain an understanding of the significant sources of variability in 

WRS FE calculations. As a corollary, it is also useful to understand which FE input parameters 

have negligible effects on results, to avoid unnecessarily expending resources on model 

aspects that have little to no bearing on final results.

The standard procedure for assessing the impact of individual FE model inputs and features is 

to systematically vary individual parameters, run the analysis, and determine the effect on the 

results. This study employed the following procedure:

(1) Develop an FE model that produces reasonable results compared to other FE models

and measurements.

(2) Identify the full set of possible model inputs and features that are likely to have a 

significant impact on final results.

(3) Systematically vary the remaining model input parameters and features; observe and 

quantify the results.

4.6.1. Baseline Model

The baseline model geometry followed the specifications included in the original design 

package. Special mesh considerations were made to accurately model the mockup fabrication 

evolution, including ID back-chip and re-weld, and weld crown and ID machining. The main DM 

weld, ID re-weld, and stainless steel weld bead geometries followed laser profilometry data 

included in the modeling package. There was a high mesh density in the DM weld region and 

medium mesh density in the regions away from the welds (i.e., nozzle and pipe). The resulting 

mesh, as shown in Figure 4-52, had 7140 nodes and 6962 4-node linear axisymmetric 

quadrilateral elements. Figure 4-53 shows a close-up of the mesh in the vicinity of the DM and 

stainless steel welds.
78

Figure 4-52 Baseline Model Finite Element Mesh

Figure 4-53 DM and Stainless Steel Weld Meshes

Figure 4-54 shows a plot of the peak temperature in Kelvin achieved in the main DM weld and 

re-weld region. All weld beads were observed to have reached the annealing temperature of 

approximately 1500 K. In addition, the fusion zone surrounding the weld was a reasonable 

approximation to commonly observed sectioned and etched pipe welds. The baseline analysis 

assumed isotropic hardening. The material properties were identical to those used by other 

analysts in Analyses 1c and 2 in the round robin study.
79

Figure 4-54 Peak temperature [K] Achieved in the Baseline Thermal Analysis

Figure 4-55 through Figure 4-58 show the axial and hoop stresses from ID to OD along the 

centerline of the DM weld model before and after application of the stainless steel weld. As 

seen in Figure 4-55, the pre-stainless steel weld axial stress was highly tensile at the pipe ID, 

consistent with the fact that the final weld passes were in this region. Figure 4-57 shows a 

significant reduction in the ID axial stress due to the bending moment applied by the stainless 

steel weld. Figure 4-56 and Figure 4-58 show that the through thickness pre-stainless steel 

weld hoop stress was highly tensile and reduced in magnitude by the stainless steel weld. The 

baseline model results agreed well with the average of the round robin participants. This model 

should, therefore, provide a reasonable reference for the sensitivity studies in Sections 4.6.2

through 4.6.8.
80

Figure 4-55 Axial Stress from Baseline Model before Stainless Steel Weld

Figure 4-56 Hoop Stress from Baseline Model before Stainless Steel Weld
81

Figure 4-57 Axial Stress from Baseline Model after Stainless Steel Weld

Figure 4-58 Hoop Stress from Baseline Model after Stainless Steel Weld
82

4.6.2. Sensitivity Parameter Selection

The input categories considered in WRS FE analyses can be consolidated into the following 

groupings:

Thermal

• energy magnitude and duration (dictated by weld voltage, current, arc efficiency and 

deposition speed)

• density

• latent heat

• conductivity

• specific heat

• convective heat transfer coefficient

Mechanical

• coefficient of thermal expansion

• elastic properties (modulus and Poisson ratio)

• plastic properties (true stress vs. plastic strain)

• hardening law

• anneal temperature

Other

• weld bead shape

• weld pass order of deposition

The parameters chosen for this sensitivity study included energy magnitude and duration, 

coefficient of thermal expansion, plastic properties (true stress vs. plastic strain), hardening law 

(isotropic and kinematic), anneal temperature, and weld pass order of deposition. The following 

sections describe systematic variation of these model parameters and aspects, and their impact 

on centerline through-wall DM weld axial and hoop stresses. It was found that some of these 

model parameters had a significant effect on weld residual stresses, and some had a negligible 

effect.

In these studies, three representative sets of material properties are referred to:

• one employed a British Energy (BE)-led WRS validation effort [24], referred to as “BE 

properties,”

• one distributed to round robin participants referred to as “Phase 2 properties,” and

• the property set used in the baseline model, referred to as “Baseline properties.”

4.6.3. Coefficient of Thermal Expansion Sensitivity Study

Figure 4-59 shows the coefficient of thermal expansion as a function of temperature for the 

three sets of properties. The coefficient of thermal expansion values contained in the baseline 

model were replaced by those from the BE and Phase 2 properties, and the analysis was re-run 

to determine the sensitivity to these parameters.
83

(a)

(b)
84

(c)

Figure 4-59 Coefficient of Thermal Expansion vs. Temperature for Three Materials

Figure 4-60 and Figure 4-61 show the through-wall axial and hoop stress distributions along the 

centerline of the DM weld, before and after application of the stainless steel weld. Relatively 

small variation is seen in the results, indicating that variations in coefficient of thermal 

expansion, within the range of typical material property sets used by experienced modelers, has 

a negligible effect.
85

Figure 4-60 Axial Stress for Coefficient of Thermal Expansion Sensitivity Study

Figure 4-61 Hoop Stress for Coefficient of Thermal Expansion Sensitivity Study

4.6.4. Heat Input Sensitivity Study

Intuitively, the magnitude and duration of heat flux input during the welding simulation would 

have an effect on final through-wall stress distributions. To quantify these effects, independent 

sensitivity studies were performed in which the magnitude and duration of weld heat flux were 

varied relative to the baseline analysis. The thermal model described in Equation 2-3 provided

a convenient means of independently varying weld heat flux magnitude and duration; by varying 
86

input parameters in this model, a range of heat flux magnitudes and durations can be achieved. 

The magnitude of heat flux varies linearly with arc efficiency. In this study, the baseline arc 

efficiency values were scaled by factors of 0.25, 0.5 and 1.5 to provide a wide range of heat flux 

values. Note that only the arc efficiencies of the DM weld were scaled, whereas the arc 

efficiencies of the stainless steel weld remained unchanged. This range of heat inputs would 

significantly affect the peak temperatures calculated in the model. Figure 4-62 shows the 

resulting heat flux magnitudes as a function of time, including the baseline case. Figure 4-63

and Figure 4-64 show the final through-wall centerline DM weld axial and hoop stress 

distributions, after application of the stainless steel weld, for the various heat flux magnitude 

inputs. Clearly, for the magnitude of heat flux variation chosen, significant differences in final 

through-wall stresses were observed for these large changes in heat input. As the analysis in 

Figure 4-42 through Figure 4-45 indicates, however, these models are relatively insensitive to 

heat input given the modeling choices of most experienced analysts.

Figure 4-62 Heat flux vs. Time for Magnitude Sensitivity Study
87

Figure 4-63 Axial Stress for Heat Flux Magnitude Sensitivity Study

Figure 4-64 Hoop Stress for Heat Flux Magnitude Sensitivity Study
88

In the thermal heat flux model of Equation 2-3, S(p) is the weld speed for a given pass. By 

varying the weld speed, the duration of time over which the heat flux is applied changes. 

However, the total energy applied, calculated as the integral of the heat flux with respect to time, 

remains the same. In the baseline analysis, the travel speed was approximately 2.54 mm/s, 

with minor variations for specific passes. To provide a wide range of heat flux durations in the 

sensitivity studies, the travel speeds of 0.75, 1.75, and 5.0 mm/sec were analyzed. Figure 4-65

shows the resulting heat flux magnitudes as a function of time, including the baseline case. 

Figure 4-66 and Figure 4-67 show the final through-wall centerline DM weld axial and hoop 

stress distributions, after application of the stainless steel weld, for the various heat flux duration 

inputs. Relatively minor variations in the stress predictions based upon varying travel speeds 

are observed in these results.

Figure 4-65 Heat Flux vs. Time for Duration Sensitivity Study
89

Figure 4-66 Axial Stress for Heat Flux Duration Sensitivity Study

Figure 4-67 Hoop Stress for Heat Flux Duration Sensitivity Study
90

4.6.5. Plastic Stress-Strain Response Sensitivity Study

A sensitivity study was performed in which the plastic stress-strain response for the BE, Phase 

2, and baseline properties were employed. Note that each of these material property sets 

correspond to the annealed condition. Figure 4-68 and Figure 4-69 provide the axial and hoop 

stress results for these material properties. The models showed significant differences at the 

normalized through-wall distance of approximately 0.15. Other than the difference at x/t = 0.15, 

the remainder of the stress distributions are fairly consistent, with a moderate variation.

Figure 4-68 Axial Stress for Plastic Stress-Strain Response Sensitivity Study
91

Figure 4-69 Hoop Stress for Plastic Stress-Strain Response Sensitivity Study

4.6.6. Strain Hardening Law

A sensitivity study was performed in which the baseline material properties were used with 

linear kinematic and isotropic hardening laws. Note that only linear kinematic was studied; 

multi-linear kinematic and mixed isotropic/kinematic were not considered here. Figure 4-70 and 

Figure 4-71 respectively provide the axial and hoop stress results for the hardening law 

sensitivity studies. Clearly, changing the hardening assumption from isotropic to linear 

kinematic resulted in a large variation in stress distribution.
92

Figure 4-70 Axial Stress for Hardening Law Sensitivity Study

Figure 4-71 Hoop Stress for Hardening Law Sensitivity Study
93

4.6.7. Anneal Temperature

A sensitivity study was performed in which the anneal temperature for the Alloy 82/182 main DM 

weld was varied. For the baseline case, the anneal temperature was 1574 K, and for the 

sensitivity study, this temperature was varied to 1625 K and 1675 K. Figure 4-72 and Figure

4-73 provide the results for this sensitivity study. Little difference resulted from varying the 

anneal temperature.

Figure 4-72 Axial Stress for Annealing Temperature Sensitivity Study
94

Figure 4-73 Hoop Stress results for Annealing Temperature Sensitivity Study

4.6.8. Weld Pass Sequence

A sensitivity study was performed in which the order of deposition for the top two layers of the 

baseline model was reversed. Figure 4-74 and Figure 4-75 show the axial and hoop stress 

results, respectively, for this sensitivity study. The stress distributions were almost identical, 

except near the top of the main DM weld where the order of deposition was reversed, implying 

that order of deposition can play a significant role in stress distributions.
95

Figure 4-74 Axial Stress for Weld Pass Order Sensitivity Study

Figure 4-75 Hoop Stress for Weld Pass Order Sensitivity Study
96

4.7 Phase 2a Conclusions

Phase 2a of the NRC/EPRI WRS Validation Program consisted of measurements on a 

prototypic pressurizer surge nozzle mockup. A double-blind finite element round robin study 

was also completed, where measurement practitioners and modelers did not have access to 

each other’s results. Conclusions from this work are as follows:

• Deep hole drilling and incremental deep hole drilling measurements of the prototype 

mockup provided the following insights.

o Measurements at two locations along the circumference, but not at weld start/stop 

positions, showed similar magnitudes prior to the safe end to stainless steel pipe 

closure weld. After the stainless steel closure weld, axis symmetry was maintained.

o The measurements showed that, for the particular geometry studied here, the safe

end to stainless steel pipe weld had a beneficial effect on the stresses at the 

dissimilar metal weld location.

o Contour measurements, obtained after the Phase 2a results had been made public, 

confirmed certain trends noted in the hole drilling data. The contour results showed 

lower stress magnitudes near the OD than the hole drilling results.

• The double-blind finite element round robin study, which was conducted to gain an 

unbiased view of WRS modeling uncertainty, showed that:

o In some cases, the average of all modeling results compared well with the 

experimental results, both in magnitude and in trend. There were instances, 

however, where the measurements and models did not agree.

o The FE models captured the beneficial effect of the safe end to stainless steel pipe 

weld, which was also observed in the experimental work.

o Significant model-to-model variability exists.

o Providing information on thermocouple measurements and material property data did 

not reduce the model-to-model variability.

• Model uncertainty was assessed in this study, as described below.

o The aggregate modeling results deviated from the average by as much as ±200

MPa.

o The position at which the individual stress profiles passed through 0 varied from 

model to model, contributing to the model uncertainty.

o The choice of hardening law, while easily separable, contributed to the uncertainty 

observed in this study. Isotropic hardening tended to overpredict the measurements

at the ID and OD, while underpredicting the measurements at the mid-thickness 

location. The kinematic hardening models showed the exact opposite trends.

• Sensitivity studies performed by a single analyst provided the following insights:

o Coefficient of thermal expansion and annealing temperature were found not to have 

a significant impact on modeling results.

o Total heat input and the duration over which heat is applied were found to affect final 

modeling results. However, the changes in these model inputs studied here were 

quite large compared to what may be expected to occur among experienced 

analysts. The observations from the round robin study and the sensitivity studies 

indicate that the model results are only weakly sensitive to heat input.
97

o Plastic stress-strain properties were found to affect modeling results at specific 

through-wall locations.

o The choice of hardening law was shown to affect WRS modeling results.

o Weld bead application sequence was found to affect calculated stress profiles, 

especially near the OD when the bead sequencing changed in the final layer at the 

OD.

99

5 PHASE 3: PRESSURIZER NOZZLES FROM A CANCELLED 

PLANT

5.1 Introduction

The Phase 3 effort consisted of measurement and modeling on safety/relief pressurizer nozzles 

from a cancelled plant. This phase of the research was intended to compare weld residual 

stress (WRS) models with experiments and to assess modeling uncertainty. The modeling 

effort in this phase of the work included double-blind finite element (FE) modeling, where 

measurement data was hidden from the analysts. The modeling effort for Phase 3 was not as

extensive as Phase 2a. Discussion of the Phase 3 work can also be found in the Electric Power 

Research Institute’s (EPRI’s) Materials Reliability Program (MRP)-316 report [45].

5.2 Pressurizer Safety/Relief Nozzle Mockups

The Phase 3 mock-up components consisted of two safety/relief nozzles from the pressurizer of 

a canceled plant. Residual stress measurements were taken before and after the application of 

the stainless steel pipe weld. Two different nozzles were needed to accomplish this because of 

the destructive nature of the contour method (see Section 2.2.2). Figure 5-1 shows a schematic 

of the nozzle after the stainless steel (SS) weld was performed to join the nozzle to SS pipe. 

The dissimilar metal (DM) weld is indicated at the location of the Alloy 82 Butter and Weld 

material.

Figure 5-1 Schematic of the Safety and Relief Nozzle

Figure 5-2 shows one of the actual nozzles and finite element representations of it in the state 

both before and after the SS pipe weld. The nozzle without the SS pipe will be called Nozzle 

#2, and the nozzle with the SS pipe weld will be called Nozzle #3 throughout this Chapter. The 

two nozzles used for measurements were slightly different leading to variation in the 

measurements between the two nozzles. Each nozzle had its DM weld completed and was 
100

prepared for the subsequent SS weld to pipe section before it was removed from the canceled 

plant.

Figure 5-2 Actual Nozzle and FE Model before and after Pipe Weld

Nozzle #2 was 375 mm long with a 203 mm outer diameter (OD) and a 133-mm inner diameter 

(ID) at the DM weld location. Nozzle #3 was 711 mm long with a 201 mm OD and an ID of 113

mm at the SS pipe location.

5.3 Weld Residual Stress Measurements

Various WRS measurement techniques were discussed in Section 2.2. Two techniques were 

used by two independent providers in Phase 3. Deep hole drilling (DHD) and its variant, 

incremental deep hole drilling (iDHD), were performed on the nozzle mock-ups. The contour 

method was also used on the nozzle mock-ups. Both methods were used to find stresses in 

several locations in the mock-ups, but the measurements discussed here will be restricted to 

those measurements made along the through-thickness centerline of the DM weld areas of the 

mock-ups with no repair welds. Nozzle #2 was used in the pre-SS pipe weld state, and Nozzle

#3 was used only in the post-SS pipe weld state. Obviously, variations in the welding of the two 

different DM welds were introduced by this necessity and must be considered. The DHD/iDHD 

measurements were taken before the nozzles were sectioned for the contour method.

The DHD/iDHD measurements to be shown here were taken from drilled holes in the centerline 

of the DM weld producing both axial and hoop stress measurements for each hole drilled. The 

contour method produced an entire plane to measure with each cut. The nozzles were cut 

axially into arcs, producing two surfaces on which to measure hoop stresses through the DM 

weld thickness. Once these measurements were complete, the removed arc was then cut again 

on the transverse plane revealing an axial stress surface to measure. This surface passed 

through the center of the DM weld. The contour measurement report thus provided two hoop 

stress measurements for each nozzle, and a plane of axial stresses which was used to produce

four separate through-thickness axial measurements at different circumferential positions on the 
101

plane (see Figure 4-13 as an example). The multiple hoop and axial stress contour 

measurements were each averaged to simplify the presentation here.

5.4 Finite Element Models

Details of FE modeling of weld residual stress were discussed in Section 2.3. Four different 

analysts created FE models using geometry measurements reported and by scaling dimensions 

from micrographs taken at the planes where the contour method cuts were made. Each model 

was slightly different due to the differences in the nozzles themselves and the differences in the 

scaled dimensions used. Results are reported as through-thickness stresses with the distance 

through the thickness normalized to take out the variation in wall thickness in the models and 

the actual nozzles.

Other variations in the models were typical of those that would occur in industry when various 

modelers make FE predictions of the same geometry. The meshes were different. The butter 

and DM weld beads were visible in the micrographs provided and each modeler made 

assumptions as to the welding bead shape to use in their FE model. Two different software 

packages were used (ANSYS and ABAQUS). The nozzle component materials were known, 

but modelers used their own library of material properties representing behavior over the range 

of the welding process temperatures. Also, different hardening laws were used for the materials 

making a total of nine through-thickness stress predictions using isotropic hardening, kinematic 

hardening, or mixed hardening material behavior. In all cases, thermal models were calibrated 

against the provided weld micrographs, but the number and specific geometry of the weld 

passes modeled varied from analyst to analyst.

5.5 Results and Discussion

Figure 5-3 and Figure 5-4 show the results of the nine FE predictions for axial and hoop stress, 

respectively, through the thickness of the centerline of the DM weld. These results will later be 

compared to the measurements at the same location. The results were for the case after the 

SS pipe weld was performed (Nozzle #3 configuration). Each of the modelers found that, for 

this geometry, there was almost no difference at the DM weld mid-thickness stress before and 

after the SS weld was performed. However, stresses were different at other axial locations due 

to the application of the SS weld. This fact was attributed to the reduction in diameter and wall 

thickness at the SS pipe and the distance of the SS weld from the DM weld (126 mm). The SS

weld provided some reduction in the DM weld stresses in more uniform geometries as shown in 

Chapter 4 and other studies [58]-[61].
102

Figure 5-3 Axial Stress FE Predictions

Figure 5-4 Hoop Stress FE Predictions
103

Each modeler and each measurement technique reported a different number of data points 

through the thickness of the nozzle. The data provided from all models and measurements 

were linearly interpolated between provided data points to create 50 even steps through the 

thickness so that tabulated results could be compared directly. Averages were calculated at 

each step through the thickness.

Several observations can be made from these prediction comparisons. All of the results show 

similar trends. The average curve shows the ID axial stress is near neutral and then dips into 

the compressive region until it becomes tensile at 50 percent through the thickness and finally 

becomes neutral again at the OD. The hoop stress average curve shows the stresses to be 

compressive at the ID and tensile at the OD with the curves crossing into tension somewhat 

before 50 percent through the thickness from the ID.

The hardening law used for each prediction is indicated in the legend text as ISO, KIN, and 

Mixed. The annealed mid-range yield strength for the Alloy 82 DM weld was 265 MPa (38.4

ksi). The differences come about because of the strain cycles created in the welding process. 

The models following the isotropic hardening law allowed the material to strain harden to 

progressively higher yield strength upon cyclic loading and this produced higher stresses than 

did the kinematic hardening law. The results produced with kinematic hardening did not exceed 

the stress equivalent to the annealed yield strength of the material by nearly as much as the 

results from the models using the isotropic hardening law. The effect was most noticeable in 

the axial stress graph where the isotropic models produced high compression stresses at 20

percent through the thickness and high tension stresses at 80 percent through the thickness, 

while the kinematic models produced more damped stress swings.

Figure 5-5 and Figure 5-6, respectively, show the axial and hoop stress comparisons between 

the FE predictions and the measurements produced by the two different methods. The FE 

predictions were all performed on the same models representing both the Nozzle #2 and Nozzle

#3 configuration, and as mentioned previously, the through-thickness stresses in the DM weld 

were found to be almost identical for the cases before and after application of the stainless steel 

pipe weld. Only the Nozzle #3 configuration FE predictions are shown here because there is 

little or no difference from the Nozzle #2 results. The FE predictions are plotted as thin lines as 

in the previous figures. Both Nozzle #2 and #3 measurement results are included in the 

comparisons to allow an examination of the measured differences found in the cases before and 

after the SS pipe weld was completed. The contour method measurements are indicated by 

thick orange and green lines while the DHD/iDHD measurements are indicated by orange and 

green dots. The green colored measurements are for the Nozzle #2 (pre SS-Weld) 

configuration and the orange colored measurements are for the Nozzle #3 (post SS-Weld) 

configuration.
104

Figure 5-5 Axial Stress FE Predictions and Measurements

Figure 5-6 Hoop Stress FE Predictions and Measurement
105

Overall the FE predictions, contour method measurements, and Nozzle #3 DHD/iDHD 

measurements show similar trends. The DHD/iDHD measurements show a large difference in 

measured stress magnitude between the Nozzle #2 and #3 results that is not present in either 

the FE predictions or the contour method measurements. The hole drilling measurements may 

be showing some effect from the SS weld, as the trend is consistent with what may be expected 

(i.e., an increase at the OD and decrease at the ID after SS weld application). However, some 

of the variation in stress may be attributed to geometry differences in Nozzle #1 and Nozzle #2. 

The models and contour measurements did not register an effect of the SS weld.

As with the FE predictions, the measurements showed that the average ID axial stress was near 

neutral and dipping into the compressive region until it became tensile at or before 50 percent 

through the thickness. It became neutral again at the OD after rising to a peak at about 75

percent of the way through the thickness. The hoop stress graph shows the average of the 

stresses were compressive at the ID and neutral to tensile at the OD, with the curves crossing 

into tension before 50 percent through the thickness.

The four FE prediction curves from the models using isotropic hardening were distinguishable 

from those using kinematic hardening. The effect was most noticeable in the axial stress graph 

(Figure 5-5), where the isotropic models produced high axial compression stresses at 20

percent through the thickness, and high axial tension stresses at 80 percent through the 

thickness. The increase in tension stress toward the OD seems to match what was indicated by 

the DHD/iDHD measurements for Nozzle #3. The iDHD technique was applied in this area of 

residual stress at or above the material’s yield strength in order to minimize potential plasticityinduced measurement artifacts. FE predictions with kinematic hardening fell almost exactly on 

both contour measurement curves along the entire data range, for axial stresses. It should be 

noted that both DHD/iDHD and contour techniques were potentially susceptible to plasticity 

measurement artifacts at or near yield, making further comment on the accuracy of the 

measured residual stress profiles difficult.

5.6 Phase 3 Conclusions

Phase 3 of the WRS Validation Program consisted of measurement and modeling of WRS in 

components intended for nuclear power service. These components were of differing geometry 

than the mockup studied in the Phase 2a work (see Chapter 4), so differences in stress trends 

were expected. The following conclusions can be supported by this work.

• The modeling results in this work provided the following insights.

o Modeled stress trends were generally different in Phase 3, when compared to Phase 

2a. The stresses started near-neutral at the ID and became tensile at the OD. 

Phase 2a results indicated tensile stress at the ID with stress fluctuating from tensile 

to compressive and back to tensile at the OD. These dissimilarities were due to the 

significant differences in weld and component geometry. For instance, a large ID 

weld deposit was present in the Phase 2a mockup, whereas the Phase 3 nozzles 

were single-V groove welds more commonly found in plants.

o Unlike the observations of Phase 2a, application of the safe end to stainless steel 

pipe weld did not have an appreciable effect on modeling results. This observation 

can be attributed to different safe end geometries in the two mockups.

o Significant analyst-to-analyst scatter was observed in Phase 3.

o The choice of hardening law had a significant effect on the modeling results. 

Specifically, isotropic hardening models tended to predict higher stress magnitudes, 

with larger stress fluctuations, than kinematic hardening cases.
106

• The measurement results in this work provided the following insights.

o Hole drilling and contour measurements both confirmed the trend noted in the 

modeling: neutral stress at the ID and tensile stress at the OD. The two 

measurement techniques differed in the magnitude of the tensile stress at the OD, 

however.

O While the contour method showed no difference in measured stress before and after 

the safe end to stainless steel pipe weld, the hole drilling measurements indicated 

some differences between the two cases. At the very least, the effect of the 

stainless steel weld was not as dramatic in the Phase 3 studies as was observed in 

the Phase 2a studies, as expected considering the differences in safe end geometry.
107

6 PHASE 4: OPTIMIZED WELD OVERLAY ON A COLD LEG 

NOZZLE

6.1 Introduction

The Phase 4 effort consisted of measurement and modeling on a cold leg nozzle from a 

cancelled plant. This phase of the weld residual stress (WRS) Validation Program investigated 

the effectiveness of the Optimized Weld Overlay (OWOL), which is one method proposed by the 

U.S. nuclear industry for primary water stress corrosion cracking (PWSCC) mitigation. A 

significant portion of the work presented in this chapter consists of one analyst’s studies on the 

effectiveness of OWOL. Several additional analysts participated in a double-blind FE modeling

study, where measurement data was hidden from them. The double-blind modeling effort for 

Phase 4 was not as extensive as Phase 2a.

6.2 Optimized Weld Overlay and Cold Leg Nozzle Mockup

6.2.1. Optimized Weld Overlay

With the occurrence of PWSCC in U.S. pressurized water reactors (PWRs) (see Chapter 1), the 

commercial nuclear power industry has proposed a number of mitigation strategies for dealing 

with the problem. One of those strategies is the application of weld overlays that were 

successfully used in the past in mitigating intergranular stress corrosion cracking (IGSCC) in the 

BWR fleet. Since WRS provides the significant driving force for crack growth, weld overlays 

mitigate PWSCC by reducing the tensile residual stresses on the inside wetted surface of the 

dissimilar metal nozzle/pipe weld. A previous study investigated analytically the effectiveness of 

weld overlays, both full structural weld overlays (FSWOL) and OWOLs, as a mitigation strategy 

for PWSCC [51].

The minimum acceptable FSWOL thickness is equal to one-third the original pipe wall thickness 

as specified in Materials Reliability Program (MRP)-169 [53] and ASME Code Case N-504-4

[54]. The minimum length of the overlay is 0.75√(Rt) on either side of the dissimilar metal (DM)

weld to be treated, where R is the outer radius and t is the nominal thickness of the component. 

The total minimum length of the FSWOL is therefore 1.50√(Rt) plus the length of the DM weld to 

be treated.

The OWOL has been proposed for larger geometries (hot and cold leg nozzles) where FSWOL 

application becomes too time consuming for a typical nuclear plant refueling outage. The 

OWOL thickness is less than that of an FSWOL, leading to decreased application time. The 

required minimum axial length of the OWOL is defined in ASME Code Case N-754 [55] and is 

the same as that required for an FSWOL. The code case also says that the thickness must be 

sufficient to provide compressive residual stresses to preclude stress corrosion cracking growth.

Industry has proposed that an OWOL design is sufficient if it reduces tensile stresses in the 

dissimilar metal weld area to less than 69 MPa (10 ksi) with operating temperature and loads 

applied. Each OWOL must be designed for a specific geometry and application and must be 

evaluated on a case-by-case basis to demonstrate that the overlay is sufficient to mitigate the 

possibility of PWSCC.
108

6.2.2. Cold Leg Nozzle Mockup

Figure 6-1 shows a revolved version of the axisymmetric cold leg nozzle FE model with and 

without OWOL. Figure 6-2 shows a photograph of the Phase 4 mockup after application of the 

OWOL. Figure 6-3 shows the details of the cold leg nozzle geometry and materials. The nozzle 

was A508 class 2 carbon steel. The cladding, pipe, and safe end were stainless steel. The 

butter and dissimilar metal weld were made from alloy 82/182, and the secondary stainless steel

(SS) weld was made from Type 309 stainless steel filler metal. This model included a 25 

percent of the wall thickness deep inner diameter (ID), circumferential weld repair in the DM

weld. The results without the ID repair are included with the sensitivity study results and in 

measurements taken in the area outside the 30 degree partial arc repair region.

Figure 6-1 Phase 4 Model Geometry
109

Figure 6-2 Cold Leg Nozzle Mock-Up after OWOL
110

Figure 6-3 Cold Leg Nozzle Geometry and Material Details
111

Figure 6-3 also shows the dimensions of the cold leg nozzle model and mock-up. The pipe 

outer diameter (OD) was 889 mm (35 in.), and the pipe thickness was 87 mm (3.43 in.). The 

figure also shows the weld pass size that was used in the OWOL effectiveness studies. The 

butter, DM weld, and weld repair passes were roughly 2.5 mm by 5.0 mm (0.1 in. by 0.2 in.). 

The SS weld passes were roughly 2.5 mm by 6.3 mm (0.1 in. by 0.25 in.), and the buffer layer

and OWOL weld passes were 2.5 mm by 16 mm (0.1 in. by 0.625 in.).

The minimum thickness of the FSWOL for the mock-up shown in Figure 6-3 was one-third the 

DM weld thickness of 74.2 mm (2.92 in.), or 24.6 mm (0.97 in.). The OWOL thickness used was 

19.4 mm (0.765 in.), or approximately 25 percent of the DM weld thickness. The OWOL 

thickness was therefore approximately 75 percent of the minimum FSWOL thickness in this 

case. The total minimum length of the OWOL used for the cold leg nozzle geometry in this 

study was 1.50√(Rt) plus the length of the DM weld to be treated or 1.5√(444 mm x 74.2 mm) + 

61.5 mm = 356 mm (14 in.), and the actual length used on the mock-up was 541.3 mm (21.31 

in.) including the tapered ends. The length of the OWOL for the mockup is therefore 162% of 

the minimum FSWOL length.

The cold leg nozzle was similar to the Phase 2a surge nozzle (see Chapter 4) in materials and 

geometry. Both have a secondary SS weld in close proximity to the DM weld. The distance 

between centerlines of the DM weld and the SS closure weld was 95 mm (3.73 inches). A 

significant effect on the DM weld residual stresses would be expected from application of this 

weld.

6.3 Weld Residual Stress Measurements

Various WRS measurement techniques were discussed in Chapter 2. Two techniques were 

used by a single provider in the Phase 4 work: deep hole drilling (DHD) and its variant, 

incremental deep hole drilling (iDHD). To assess the effectiveness of the OWOL, the 

measurements were performed on the nozzle before and after application of the overlay.

6.4 Finite Element Models

Details of FE modeling of weld residual stress were discussed in Section 2.3. The modeling 

results presented in this study can be divided into two categories: (1) detailed analyses by one 

analyst on OWOL effectiveness and associated sensitivity studies and (2) double-blind analyses 

from different analysts (similar to, but not as extensive as, the round robin study presented in 

Chapter 4).

For the double-blind FE study, four different analysts created finite element models using 

geometric measurements reported for the mock-up features. Each model was slightly different 

because of the assumptions made about the weld pass layout and missing dimensions in the 

sketches provided. Results are reported as through-thickness stresses from the ID to the OD.

Other variations in the models were typical of those that would occur in industry when various 

modelers make FE predictions of the same geometry. The meshes were different. Each 

modeler made assumptions as to the welding bead shape to use in their FE model. Two 

different software packages were used (ANSYS and ABAQUS). The nozzle component 

materials were known, but modelers used their own library of material properties representing 

behavior over the range of the welding process temperatures. Also, different hardening laws 
112

were used for the materials making a total of six through-thickness stress predictions using 

either isotropic hardening, kinematic hardening, or mixed hardening.

6.5 Optimized Weld Overlay Effectiveness

6.5.1. Axial Stresses, Room Temperature, Without Operating Loads

Figure 6-4 shows an example axial stress contour plot before the SS safe end weld but after all 

DM welding was complete, including the 25 percent ID repair (top figure), after the SS closure 

weld was finished (middle figure), and after the OWOL had been completed (bottom figure). 

The arrows through the thickness indicate the path along which the data in Figure 6-5 were 

extracted.

Figure 6-4 Cold Leg Nozzle Axial Stresses [MPa]
113

Figure 6-5 Cold Leg Nozzle Through-Thickness Axial Stresses

Figure 6-4 and Figure 6-5 show that the DM weld was in tension at the ID, compression in the 

center, and tension at the OD after it was completed. The application of the SS weld had the 

effect of lessening the tension stress on the ID of the DM weld, and in fact, making it 

compressive. In this cross-section, the axial stress was slightly increased after applying the 

OWOL, with the final ID stress near zero.

The stresses along the specified path drop to compressive values at 25 percent of the original 

pipe thickness, which corresponds to the depth of the weld repair. This is typical of results 

found with ID weld repairs. The tensile stresses caused by the weld repair pushed a zone of 

compressive stress just beyond the depth of the repair.

Figure 6-6 and Figure 6-7 show the ID path and axial stress along that path. Figure 6-7

indicates the position of both the DM weld and the secondary SS weld with color coded vertical 

bars on the graph.
114

Figure 6-6 Cold Leg Nozzle Inner Diameter Axial Stresses [MPa]

Figure 6-7 ID Axial Stresses along Length of the Pipe
115

The stress was very high in tension in the butter and dissimilar metal weld before the SS weld 

was made. Once the SS weld was completed, the stresses along the ID were primarily 

compressive except in the area of the transition between the carbon steel nozzle and the butter. 

In this area the stresses remained tensile in the range of 69 MPa (10 ksi). After the OWOL was 

completed the maximum tension stress was slightly reduced to 35 MPa (5 ksi), but the area that 

was already compressive after the SS weld was complete had its compressive stresses reduced 

by the application of the OWOL. These results indicated little improvement for the application of 

the OWOL at room temperature and with no operating loads applied.

6.5.2. Hoop Stresses, Room Temperature, Without Operating Loads

Figure 6-8 and Figure 6-9 show the through-thickness hoop stresses before and after the 

application of the OWOL. The stress contour plot and the graph show that the secondary SS

weld had the effect of reducing the hoop stress in the DM weld, but not to the extent that it did 

for the axial stresses. The ID stress remained in tension in this cross-section. The OWOL 

reduced the through-thickness hoop stresses into compression for approximately the inner 50 

percent of the original wall thickness with the exception of one small spike into the tensile region 

at a quarter of the way through the original thickness at the peak of the 25 percent throughthickness ID weld repair.

Figure 6-8 Cold Leg Nozzle Hoop Stresses [MPa]
116

Figure 6-9 Cold Leg Nozzle Through-Thickness Hoop Stresses

Figure 6-10 and Figure 6-11 show the ID hoop stress along the length of the DM weld area of 

the cold leg nozzle. The graph shows that hoop stresses were very high on the ID of the DM

weld before the SS closure weld was made, and were reduced but remained tensile after the SS

weld was completed. The stresses were uniformly high at 414 MPa (60 ksi) in the DM weld

area before the SS weld and reduced to a uniform 138 MPa (20 ksi) after it was made. The 

OWOL reduced the hoop stresses in the area of concern to be compressive over the entire 

length of the DM weld area.
117

Figure 6-10 Cold Leg Nozzle Inner Diameter Hoop Stresses [MPa]

Figure 6-11 Cold Leg Nozzle Inner Diameter Hoop Stresses
118

6.5.3. Operating Condition Sensitivity Study

The previous cold leg nozzle stress plots were all made for analyses at room temperature and 

pressure. The following graphs show the effect of operating pressure and temperature on the 

cold leg nozzle axial and hoop stresses. An operating pressure of 15.5 MPa (2,250 psi) and an 

operating temperature of 300o

C (572oF) were used for the cold leg nozzle analyses.

Figure 6-12 shows the ID axial stress in the cold leg nozzle DM weld area after OWOL at room 

temperature and then at operating temperature and pressure. The application of operating 

conditions had a marked beneficial effect after the OWOL. It reduced the maximum stress 

magnitude to -69 MPa (-10 ksi) and maintained the remainder of the stresses in the DM weld

region compressive below the values achieved in the room temperature analyses.

Figure 6-12 ID Axial Stresses at Operating Pressure and Temperature

Similarly, Figure 6-13 shows the ID hoop stress in the cold leg nozzle DM weld area after 

OWOL at room temperature and then at operating temperature and pressure. Operating 

conditions raised the hoop stresses in the DM weld area, but they remained in compression for 

the whole area of concern after the OWOL.
119

Figure 6-13 ID Hoop Stresses at Operating Pressure and Temperature

6.5.4. Weld Overlay Thickness Sensitivity Study

A sensitivity study was conducted to examine the effect of weld overlay thickness on the 

residual stresses in the DM weld. The OWOL thickness was studied by observing the stresses 

as each overlay layer was applied. The stresses through the thickness and along the ID were 

examined as was done previously. The temperature of the nozzle was allowed to cool to 21o

C 

(70o

F) after the last weld bead in each layer of the overlay.

Figure 6-14 shows the axial stress results through the thickness at the interface between the 

butter and the DM weld for the layers, as defined in Figure 6-3. The graph shows an oscillating 

behavior of the stress profile. The application of one, two, and three layers made the ID stress 

progressively higher than the original stress with no weld overlay. The fourth layer brought the 

stress back down, but not down to the level that they were with no weld overlay. The remaining 

layers did not change the stress much in this cross-section. The axial stresses crossed from 

tensile to compressive at the ID in this cross-section, so no large change would be expected.
120

Figure 6-14 Axial Stresses through Weld Overlay Process

It is important to look at the stresses on the ID along the whole length of the PWSCC 

susceptible area to examine the effect on the most highly stressed region and the maximum 

effect of the OWOL. Figure 6-15 shows the axial stress along the ID of the cold leg nozzle. For 

this case, a smaller length of the nozzle is shown that includes only the butter and DM weld 

areas. The vertical bars in the graph indicate the location of the butter layer, as well as the DM 

weld, with the same color coding as used in the previous graphs. The maximum axial tension 

stress on the ID was found at the transition between the butter layer and the ferritic pressure 

vessel steel, as shown previously. The graph shows the same oscillation behavior as was 

displayed in the previous graph. The maximum stress with no weld overlay was 69 MPa (10 

ksi). The stress in this area increased to 186 MPa (27 ksi) after two layers were applied, and 

stresses remained higher than the original value until four layers were applied. The maximum 

stresses then remained lower than the original value with no weld overlay, with subsequent 

layers changing the stress little. The stress improvement for layers four through the completed 

OWOL at the maximum stress area became a detriment about halfway along the butter width. 

At this point, the weld overlay increased the stress from the value with no weld overlay at all. Of

course, it was shown earlier that the application of operating pressure and temperature reduced 

these stresses to values below what would be obtained with no weld overlay.
121

Figure 6-15 ID Axial Stresses for each OWOL Layer

Figure 6-16 shows the ID hoop stress. The graph shows that there was a progressive 

improvement in hoop stress with more layers of the weld overlay, but that this effect was not 

proportional to weld overlay thickness. The maximum value with no weld overlay was inboard 

of the transition between the butter and the pressure vessel steel. Application of layers one and 

two decreased the tension stress. The application of layer three made a large change in the 

hoop stress and reduced the maximum value, and the whole area encompassing the DM weld 

went into compression. Subsequent layers progressively improved on this by adding more 

compression with decreasing impact for each subsequent layer. This graph clearly shows that 

additional layer thickness did not improve the hoop stress substantially, and that the weld 

overlay could be considered “optimized” in terms of additional compressive stress being 

created.
122

Figure 6-16 ID Hoop Stresses for Each OWOL Layer

6.5.5. Repair Weld Sensitivity Study

A sensitivity study was performed examining the effect of ID repair depth on stresses before and 

after weld overlay. For the cold leg nozzle 0 and 25 percent ID repair depths were examined. 

Figure 6-17 shows the weld area of the cold leg nozzle model with the various materials and 

welds color-coded. The weld repair is shown in the lower figure and is colored yellow. Its peak 

was located at the interface between the butter layer and the DM weld. It was 25 percent 

through the original thickness of the weld area, and because the model was 2-D axisymmetric, 

the weld repair spanned the entire circumference of the ID. The comparison of the results with 

no weld repair and with the weld repair will show the differences in the stresses that would be 

found in a nozzle with a partial arc weld repair that only spanned 30 percent of the 

circumference. To a first approximation, the stresses in the model with the repair represent the 

stresses in the partial arc repair, and the stresses in the model with no weld repair represent the 

stresses everywhere else.
123

Figure 6-17 Cold Leg Nozzle with and without 25 Percent ID Repair

Figure 6-18 shows the axial stresses after welding was complete, but before any weld overlay 

was applied. The case with no repair is shown on the top, and the case with the 25 percent 

deep ID repair is shown at the bottom. There was a noticeable difference in the stress results in 

the area of the repair. In the case without the repair, the compressive stresses began closer to 

the ID, and there was a spike of tension stresses where the root pass grind out and re-weld took 

place. In the subsequent graphs the results for the case with no ID repair will be shown in a 

solid orange curve, while the 25 percent deep ID repair results will be indicated by a dashed 

orange curve.

Figure 6-18 Cold Leg Axial Stresses before OWOL with and without ID Repair [MPa]

Figure 6-19 shows the axial stresses along the ID of the nozzle with the location of the butter, 

DM weld, and SS safe end weld indicated by vertical color-coded bars. The graph shows that 
124

the highest tensile stress in the DM weld area was for the case without the 25 percent deep ID 

weld repair. The highest stress in the case with no ID repair was 138 MPa (20 ksi). The ID 

repair reduced this maximum to 69 MPa (10 ksi). The peak was also shifted toward the 

butter/steel interface at the left edge of the repair.

Figure 6-19 ID Axial Stresses before OWOL with and without ID Repair

Figure 6-20 shows the through-thickness axial stress at the butter/DM weld interface for this 

same case before any weld overlay was applied. The graph shows that, for this cross-section, 

the ID stresses were negative for both the case with no weld repair and for the 25 percent weld 

repair. Both stress distributions started out negative and proceeded slightly upward toward the 

tensile region before plunging back into compression, and then finally ended tensile toward the 

OD. The only marked difference between the two curves is that the plunge into compressive 

stresses took place at 25 percent through the thickness for the weld repair case, and the drop 

into the compressive regime for the case of no repair occurred at around 10 percent of the 

thickness where the ID root pass grind out and re-weld ends.
125

Figure 6-20 Axial Stresses before OWOL with and without ID Repair

Figure 6-21 shows the axial stress contour plot for the same two cases but after the OWOL was 

applied. The stress contours were similar, but with the same exception that was pointed out in

the previous stress contour plot. The 25 percent ID repair pushed the area of compressive 

stress slightly beyond the depth of the repair.

Figure 6-21 Axial Stresses after OWOL with and without 25 percent ID Repair [MPa]
126

Figure 6-22 shows the ID axial stresses for the two cases. The graph looks similar to that which 

was shown for the case before the OWOL was applied except that the axial tensile stresses 

have been somewhat diminished. The compressive stresses were also somewhat diminished. 

The peak tensile value in the DM weld area was reduced from 138 MPa (20 ksi) to 117 MPa (17 

ksi) for the case with no ID repair, and from 69 MPa (10 ksi) to 34 MPa (5 ksi) for the case with 

the ID weld repair. These results were at room temperature, and did not take into account the 

benefit in stress reduction caused by operating pressure and temperature.

Figure 6-22 ID Axial Stresses after OWOL with and without ID Repair

Figure 6-23 shows the through-thickness axial stress plot for the interface of the butter layer and 

DM weld. The graph has a similar profile as the one before the OWOL was applied for this 

cross-section. The curves started out slightly compressive and proceeded into the tensile 

region before plunging into the compressive area. Equivalent tensile values followed toward the 

OD. For this cross-section, the stresses were increased by the OWOL, but the location at which 

the curve representing the 25 percent ID repair turned compressive was 25 percent of the way 

through the original wall thickness.
127

Figure 6-23 Axial Stresses after OWOL with and without ID Repair

6.6 Double-Blind Finite Element Study

6.6.1. Finite Element Predictions

Figure 6-24 and Figure 6-25 show the results of the six FE predictions of the axial and hoop 

stresses, respectively, through the thickness of the centerline of the DM weld before the SS safe

end weld was completed. The results were from models with the 25 percent through-thickness 

weld repair. Not all modelers provided results for the area outside the weld repair region. The 

FE predictions and measurements in the area of the weld repair will be discussed first, as all of 

the modelers provided results for these cases.

Each modeler and each measurement technique reported a different number of data points 

through the thickness of the nozzle. These differences were due to the differences in models, 

meshes, and measurement techniques. The data provided from all models and measurements 

was linearly interpolated between provided data points to create 50 even steps through the 

thickness so that tabulated results could be compared directly. Averages were calculated at 

each step through the thickness. The graphs show the running average of the data presented 

as a thick blue line through the center of the data plots. The actual data is shown as thin colorcoded lines in these graphs.
128

Figure 6-24 Axial Stress with Weld Repair before the SS Weld

Figure 6-25 Hoop Stress with Weld Repair before the SS Weld
129

Several observations can be made from these comparisons of predictions. The average axial 

stress curve shows the ID axial stress was in tension at about 200 MPa (29 ksi) with a 

compressive minimum about 50 percent of the way through the thickness of the DM weld. The 

axial stresses then rose toward 200 MPa. The hoop stress average curve shows the stresses 

were tensile at the ID, while they remained tensile through the thickness of the DM weld. Two 

of the individual predictions dipped into the compressive region at about 60 percent of the way 

through the thickness. The average, and all but one individual prediction, shows that the OD

hoop stress was in tension and of a similar value as the ID tension stress.

Two predictions, in particular, showed unusual results for hoop stress as compared to the rest of 

the dataset. For the A results, the spike at the 20 mm location was not observed in the other 

results. This is likely attributed to the root pass grind out assumed by the modeler. The ID 

stress for this model was low compared to the dataset. The B results showed much larger 

stress fluctuations, from +600 MPa to -100 MPa, than the other models.

The hardening law used for each prediction is indicated in the legend text as ISO, KIN, or 

Mixed. The annealed yield strength for the Alloy 82 DM weld was 265 MPa (38.4 ksi). The 

differences in predicted values caused by the material hardening law came about because of 

the strain cycles created in the welding process. The models following the isotropic hardening 

law allowed the material to strain harden to progressively higher yield strength upon cyclic 

loading, and this produced higher stresses than did the kinematic hardening law. The results 

produced with kinematic hardening did not exceed the annealed yield strength of the material by 

nearly as much as the results from the models using the isotropic hardening law.

6.6.2. Predictions and Measurements Compared

A series of graphs will be used to show a comparison of the FE analysis predictions with the 

WRS measurements. Axial and hoop stress graphs will be examined for the state before the 

application of the OWOL and after the application of the OWOL. In both cases the stresses 

were measured in the center of the ID weld repair. As in Figure 6-24 and Figure 6-25, the FE

predictions are displayed as thin lines. The heavy blue line indicates the average of all 

predictions and measurements. The measurements are shown as red (DHD) and maroon 

(iDHD) dotted lines. The iDHD measurements were not taken for the whole depth of the 

measurements and are only shown where data was presented for this measurement technique.

Figure 6-26 and Figure 6-27 show the axial and hoop stress comparisons between the FE 

predictions and the measurements before the application of the OWOL. Overall the FE 

predictions and DHD/iDHD measurements showed very similar trends, although the A and B

predictions exhibited some unusual features. The axial stress predictions were relatively close 

to each other, and the DHD/iDHD measurements were within the scatter of the FE predictions 

and very near the average value. The axial stresses started out neutral at the ID, and then 

dipped to compressive at the depth of the 25 percent of the wall thickness ID weld repair. Two 

of the predictions using the isotropic material hardening laws dipped lower than the others in 

this area. The stresses then increased almost linearly from their low point to an OD tension 

value approximately equal to the weld material’s annealed yield strength.

The hoop stress predictions had a larger degree of scatter than the axial stress predictions. The 

predictions were relatively close to each other for the first half of the path, but diverged on the 

outer half. The measurements followed the predictions very well. Aside from the B prediction, 

all of the measurements and predictions showed the hoop stress to be in tension at the ID, to 
130

dip to neutral or negative in the center of the thickness, and then to return to tension at or above 

the level found at the ID. The A hoop stress prediction significantly overpredicted the stress for 

x greater than 25 mm.

Figure 6-26 Axial Stress in Repair Region before OWOL
131

Figure 6-27 Hoop Stress in Repair Region before OWOL

After the Phase 4 results had been made public, participant B made changes to the originallysubmitted model. The isotropic hardening law was modified to limit the maximum stress to be 

the flow stress, defined in this case as one-half the yield stress plus the ultimate tensile stress. 

Participant B also modified the bead sequence for the OWOL to match more closely what was 

done for the mockup. Figure 6-28 shows the new results compared against the original 

submission and participant D’s results for the case prior to the OWOL. This figure demonstrates 

that the new procedure eliminated the large compressive stresses that were not observed in the 

dataset as a whole. Other example revised results are found in [27]. Remaining results from 

this modified procedure are not shown in the ensuing discussion, since they were not doubleblind.
132

Figure 6-28 Participant B Hoop Stress from Modified Analysis

Figure 6-29 and Figure 6-30 show the axial and hoop stress comparisons between the FE 

predictions and the measurements after the application of the OWOL. In a general sense, there 

was reasonable agreement between the model results and the measurements. As before, the A

and B results exhibited some features that were not present in the rest of the dataset. Most 

notable is the large compressive hoop stress at the ID in the B results. The axial stress at the 

ID was hardly changed from the values found before the OWOL, but the curve through the 

thickness was flattened out by the application of the OWOL. The hoop stresses were reduced 

at the ID by the application of the OWOL but were relatively unchanged at the OD.
133

Figure 6-29 Axial Stress in Repair Region after OWOL

Figure 6-30 Hoop Stress in Repair Region after OWOL
134

A more convenient way to view the changes in stress state throughout the process is to look at 

the averages of all of the data in each of the states (after the DM weld but before the SS safeend weld, after the safe-end weld but before the OWOL, and finally after the OWOL). Figure 

6-31 and Figure 6-32 show the averages for the axial stress and hoop stresses, respectively, in 

the area of the weld repair. The axial stress plot shows a large reduction in stress due to the 

application of the stainless steel safe-end weld at the ID and very little change due to the 

application of the OWOL. The hoop stress plot shows that there was a reduction in ID stress 

due to the application of the stainless steel safe-end weld, and a further reduction in stress due 

to the application of the OWOL.

Figure 6-31 Axial Stress Averages
135

Figure 6-32 Hoop Stress Averages

6.6.3. Sensitivity Study in the Area without the Weld Repair

Only two of the providers of FE WRS predictions included results for the area without the weld 

repair, but measurements were taken in both the state before and after the application of the 

OWOL in this area of the mock-up. Figure 6-33 and Figure 6-34 show the FE predictions and 

DHD/iDHD measurements through the DM weld in the area 180 degrees circumferentially away 

from the partial arc weld repair. The FE predictions were done with two different software 

packages and two different material hardening laws. The A results were done in ABAQUS, and 

the D results were done using ANSYS. The A results used isotropic material hardening laws, 

and the D results used kinematic hardening. Also, the A results included an assumed root pass 

grind out and re-weld that was often done in larger nuclear piping welds as a last step in the DM 

weld process to remove inclusions in the first DM weld pass. This process was not performed 

on the mock-up or in the D analysis, and differences in the measurements and the A predictions 

indicate this fact.

The axial stress plot shows that the DHD and iDHD results were very close to each other, since 

plasticity effects were not present at these low stresses. Both the A predictions and 

measurements showed compressive stresses of nearly the same value at the ID, while the D

predictions showed slight tension at the ID. The A results showed the evidence of the root pass 

grind out and re-weld simulation indicated by a peak tensile stress and then dip to compressive 

stresses at about 10 percent through the thickness, which was the depth of the re-weld. 

Overall, the kinematic hardening predictions from D matched the measurement trend the best.
136

Figure 6-33 Axial Stress Outside the Repair before OWOL

Figure 6-34 Hoop Stress Outside the Repair before OWOL
137

The hoop stresses plotted in Figure 6-34 showed a very close match between the DHD and 

iDHD results, which were lower than both of the FE predictions at the ID. The A isotropic 

hardening predictions and the D kinematic hardening results showed a very close match at the 

ID of nearly 200 MPa (29 ksi) while the measurements exhibit slightly compressive stresses. 

While the D kinematic hardening predictions showed a nearly flat stress profile through the 

thickness with tension stresses hovering around 200 MPa (29 ksi), the A results showed the 

stress peak caused by the root pass re-weld and then stresses climbing to a tensile peak near 

the OD. The measurements and D kinematic hardening predictions showed a similar slope of

stress increase from the ID to the OD.

Figure 6-35 and Figure 6-36 show the post-OWOL results. Again, the DHD and iDHD 

measurements matched each other well. The predictions in both cases showed stresses at the 

ID higher than the measurements unlike in the post-OWOL plots for the weld repair region 

where the measurements matched the predictions well at the ID, see Figure 6-29 and Figure 

6-30.

Figure 6-35 Axial Stress Outside the Repair before OWOL
138

Figure 6-36 Hoop Stress Outside the Repair after OWOL

The FE axial stress predictions showed neutral values at the ID, while the measurements 

showed strongly compressive stresses greater than the weld material’s annealed yield strength. 

The A prediction again showed the evidence of the root pass re-weld in the inner 10 percent of 

the wall thickness, but aside from this difference, the two FE predictions matched well. They 

both showed neutral stresses at the ID and slightly compressive stresses through the thickness, 

until the stresses turned tensile in the OD area that corresponds with the OWOL thickness. The 

measurements matched the predictions well past the first 10 percent of the thickness in showing 

an almost linear increase in stress from the ID to the OD.

The hoop stresses plotted in Figure 6-36 showed agreement through the thickness, but 

variability was observed at the ID and OD. All of the results showed a neutral to compressive 

stress at the ID and tensile stress at the OD, and all showed a reduction in inner diameter stress 

produced by the OWOL.

Figure 6-37 and Figure 6-38 show the averages for the axial and hoop stresses, respectively, 

outside the weld repair. The curves show the same trends that were presented previously in 

Figure 6-31 and Figure 6-32 in the weld repair area. The axial stress plot shows very little 

change due to the application of the OWOL. The hoop stress plot shows that there is a 

reduction in ID stress due to the application of the OWOL.
139

Figure 6-37 Axial Stress Averages before and after OWOL

Figure 6-38 Hoop Stress Averages before and after OWOL
140

6.7 Phase 4 Conclusions

Phase 4 of the WRS Validation Program consisted of measurement and modeling of WRS in a

cold leg nozzle intended for nuclear power service, with an OWOL applied to the OD. The 

purpose of the study was to assess the effectiveness of the OWOL process. This section 

describes the conclusions from the Phase 4 work.

• The detailed FE studies on OWOL effectiveness provided the following insights.

o Absent operating temperature and pressure, the safe end to SS pipe closure weld 

was shown to have the largest beneficial effect on stress for the geometry studied 

here. Application of the OWOL showed a slight increase in axial stress and a slight 

decrease in hoop stress, relative to the SS closure weld state.

o Upon accounting for operating temperature and pressure in the FE model, the 

OWOL demonstrated a marked improvement in the stresses.

o Observing the calculated axial stresses after each OWOL layer showed that stresses 

tended to increase with the first two layers, decrease with the 3rd and 4th layers, and 

stabilized beginning with the 5th layer. The calculated hoop stresses showed 

continuous improvement with each layer, although the benefit of the first 3 layers 

was larger than that of the remaining layers.

o Modeling results with and without a repair, along with the OWOL, showed some 

differences. However, the differences were within 50 MPa.

• The modeling round robin, with measurements, supported the following conclusions.

o Two models in the dataset exhibited trends that were not observed in a majority of 

the models: specifically, a stress spike and large fluctuations in stress magnitude. 

Participant B modified the original modeling approach, after the double-blind results 

were made public, thereby correcting the unusual trends.

o This work confirmed observations from the OWOL effectiveness study, namely:

 At room temperature, the beneficial effect of the safe end to SS pipe weld 

outweighed the effect of the OWOL.

 The presence of a weld repair does not significantly impact the benefit of the 

OWOL.
141

7 WRS UNCERTAINTY SCOPING STUDY

7.1 Background

As discussed in Chapter 1, a nuclear plant licensee may seek temporary relief from required 

repair/replacement activities or seek to extend established inspection intervals. A fracture 

mechanics-based flaw growth calculation (e.g., Figure 1-4) is often reviewed by the U.S. 

Nuclear Regulatory Commission (NRC) before such a request is approved or disapproved. In 

these flaw evaluations, the Mode I stress intensity factor, KI, is calculated based upon various 

operating loads and the assumed through-wall weld residual stress (WRS) distribution. This 

Chapter uses analytical data from Phases 2a and 4 (Chapters 4 and 6, respectively) as inputs to

stress intensity factor and flaw growth calculations to perform a scoping analysis on the effects 

of uncertainty in WRS prediction.

7.2 Stress Intensity Factor Methods

Current methods for calculating KI for cracked pipes can be found in [14]-[17], which include the 

Universal Weight Function Method for surface cracks in cylinders. The American Petroleum 

Institute (API)-579/ASME Fitness-For-Service-1 standard [17] contains solutions developed 

under the principle of elastic superposition for a polynomial stress distribution [14]. This method 

requires fitting the actual stress profile with a 4th order polynomial, as in Equation 7-1.

 ( )

4

4

3

3

2

0 1 2 



 



  + 

 



  + 

 



  +



 



 = +

t

x

t

x

t

x

t

x

σ x σ σ σ σ σ Equation 7-1

where, σi are fitting coefficients and x is radial position along the pipe wall thickness. The stress 

intensity factor is then given by

 Q

a

t

a G

t

a G

t

a G

t

a K I G G π

σ σ σ σ σ















 



 



  + 

 



  +  



  +



 



 = +

4

4 4

3

3 3

2

0 0 1 1 2 2 Equation 7-2

where Gi are functions of pipe and flaw dimensions, a is the crack depth, and Q is the flaw 

shape parameter (Equation 7-3).

 

1.65

1 1.464 



 



 = +

c

a Q for a/c ≤ 1.0

 Equation 7-3

 

1.65

1 1.464 



 



 = +

a

c Q for a/c >1.0

where c is half the crack length.

As discussed in [15], the Universal Weight Function Method does not require a polynomial fit to 

the stress profile. Multiple inflections in WRS profiles can cause difficulties in curve fitting. 

Figure 7-1 shows curve fits for an example WRS profile.
142

Figure 7-1 Example Curve Fits

The fits in Figure 7-1 show partial curve fits, representing fits up to the crack tip (i.e., “moving 

fit”), and a complete curve fit (i.e., “static fit”). Researchers [62],[63] have investigated the effect 

of different curve fitting strategies, as well as the use of polynomial-based equations versus the 

Universal Weight Function Method. The standard of comparison for these studies was the finite 

element KI solution. This previous work has demonstrated that there are cases where the 

difficulties in polynomial fitting can affect the accuracy of the stress intensity factor calculation.

Figure 7-2 shows the flaw geometry considered in this study. The crack opened to the inside 

surface of the pipe wall thickness. The stress intensity factor was calculated for two locations 

along the crack front: the surface point, K0, and the deepest point, K90.
143

Figure 7-2 Flaw Geometry

The stress intensity factor was calculated assuming R/t = 3, c/a = 5, and a circumferential inner 

surface-breaking flaw. This work applies the API-579 method to calculate K0 and K90 given the 

WRS profiles in Chapters 4 and 6.

7.3 Results and Discussion

7.3.1. Phase 2a Stress Intensity Factor Scoping Analysis

Figure 7-3 shows K90 and K0 for the Phase 2a axial WRS distributions (see Chapter 4) for 

different values of a/t before completion of the safe end-to-pipe closure weld. The data points 

are characterized by whether the WRS input originated with an FE model and a specified 

hardening law or with measurement data. For K90, most of the data points fall below the KI’s 

for the measured profiles. The spread in the data is approximately 65 MPa√m for K90 and 45

MPa√m for K0.
144

Figure 7-3 Stress Intensity Factor for Axial WRS Profiles, Pre Safe End Weld

Figure 7-4 shows the same results for Phase 2a data after completion of the safe end-to-pipe 

closure weld. Again, K90 based upon the WRS measurements was greater than that based 

upon WRS predictions. The spread in the stress intensity factor values was as high as 70 

MPa√m for K90 and 50 MPa√m for K0.

Figure 7-4 Stress Intensity Factor for Axial WRS Profiles, Post Safe End Weld

7.3.2. Phase 4 Stress Intensity Factor Scoping Analysis

Figure 7-5 shows example curve fits for the axial WRS profiles from the Phase 4 results (see 

Chapter 6). The polynomial fits do not capture every feature of the finite element (FE) profiles.
145

Figure 7-5 Example Fits of Phase 4 Data

Figure 7-6 shows K90 for FE WRS profiles prior to completion of the SS closure weld. There 

were no measurement data on the Phase 4 mockup in this state. The spread in this data is 

approximately 40 MPa√m.

Figure 7-6 Stress Intensity Factor, Before Closure Weld

Figure 7-7 shows K90 calculated with a static fit and a moving fit of the WRS profile. The stress 

magnitudes were similar for the two cases, but the profile shapes were different. The red curve 

in Figure 7-7 was calculated from the measured profile, and it was generally higher than the 

other cases. The maximum spread in this data was approximately 85 MPa√m.
146

Figure 7-7 Stress Intensity Factor for Phase 4 Axial WRS

7.3.3. Phase 2a Flaw Evaluation Scoping Analysis

This Section extends the scoping analysis in Sections 7.3.1 and 7.3.2 to a flaw growth 

calculation to illustrate the effect of the variation in calculated weld residual stresses. Flaw 

growth calculations involve additional assumptions on operating loads, initial flaw geometry, and 

crack growth law. Table 7-1 shows the inputs used in this analysis.

Table 7-1 Inputs for Flaw Evaluation Scoping Study

σ m – axial membrane stress, σb – axial bending stress

The WRS curves in Table 7-1 (WRS1 and WRS2) are shown graphically in Figure 7-8. They 

represent an envelope of the entire pre-stainless steel closure weld Phase 2a data, rather than 

any single one calculated WRS curve. Flaw growth calculations were performed using the 

crack growth law described in MRP-115 [64]. The stress intensity factors and flaw depth are 

shown versus time in Figure 7-9 for three cases: WRS measurement from Phase 2a, the WRS1 
147

curve, and the WRS2 curve. The stress intensity factor curve based upon the measurements 

also shows ±10 MPa√m bars, which is a validation criterion suggested in MRP-287 [27]. These 

upper and lower bound WRS inputs lead to very different flaw growth results. While these 

results are not tied to a single calculation or specific for an operating weld at a plant, Figure 7-9

clearly shows the need to address the variability in calculated weld residual stresses as 

identified in this program.

Figure 7-8 Extreme WRS Inputs

Figure 7-9 Stress Intensity Factor and Flaw Depth against Time
148

The flaw evaluation scoping analysis presented in Section 7.3.3 is subject to the following 

limitations.

• The data in Figure 7-8 includes WRS predictions with different hardening law 

assumptions. Formulating guidance on hardening law choice is one option for reducing 

modeling uncertainty.

• The WRS inputs to this analysis do not represent any single analyst’s prediction.

• The data in Figure 7-8 is based upon WRS predictions made prior to the stainless steel 

closure weld, which is conservative for most welds of this type.

7.4 WRS Uncertainty Conclusions

The purpose of the work described in Chapter 7 was to make an initial assessment of the 

observed modeling uncertainty demonstrated in Chapters 4 and 6. These analyses do not 

evaluate the effectiveness of WRS modeling in the prediction of crack growth, but instead they 

illustrate the need to reduce the modeling uncertainty. This section describes the conclusions 

from this work.

• The WRS profiles from the FE studies can be difficult to fit with a polynomial. Literature 

studies have suggested that, despite the poor fit, reasonable stress intensity factors can 

be obtained from the polynomial-based equations. The Universal Weight Function 

Method [15],[16] offers an approach that does not rely on polynomial fitting and that 

improves the accuracy of the calculation for certain cases.

• When the stress intensity factor results in Figure 7-3 and Figure 7-4 are discriminated by 

the data source, the approximate spread in stress intensity factor calculations is as 

follows.

o 60 MPa√m for predictions based upon isotropic hardening

o 40 MPa√m for predictions based upon kinematic hardening, and

o 25 MPa√m for the deep hole drilling measurements

• The fitting procedure can be executed in two ways: a static fit, where the entire WRS 

profile is fit for each crack depth considered, and a moving fit, where the WRS profile is 

fit only up to the crack tip. This work showed that stress intensity factor magnitudes 

were similar for each case, but that the profile shape did change depending on the 

method chosen.

• Model validation criteria could potentially be based upon calculation of stress intensity 

factor with measured and modeled WRS distributions. The extremes of the observed 

data in the Phase 2a results did not meet a ±10 MPa√m criterion, which is a validation 

criterion suggested in MRP-287 [27]. However, filtering the data by hardening law type 

decreases the extremes, but does not allow the data to fall within the ±10 MPa√m 

criterion.

• The scoping analysis presented in Chapter 7, which focused on the conservative 

extremes of the WRS modeling results, demonstrated a large impact on primary water 

stress corrosion crack growth. Continued research is needed to develop finite element 

modeling guidelines that reduce modeling uncertainty to acceptable limits and to develop 

quantitative acceptance criteria for model validation.
149

8 CONCLUSIONS

The work in this report represents first-of-a-kind, double-blind weld residual stress WRS 

modeling and measurement campaigns on prototypic safety-related nuclear component 

mockups. While a variety of measurement techniques were initially considered for this work, 

strain-relief techniques proved to be the most reliable for the materials of interest. Application of 

diffraction techniques is possible, but the complicating effects of large grain size, 

crystallographic texture, and chemical concentration gradients present in these welds must be 

overcome to obtain reasonable results.

The finite element models considered in the modeling round robin studies were predominately 

2-D axisymmetric models. The model results did not always agree perfectly in trend and 

magnitude with the experimental data. However, there were cases where the average of the 

modeling results showed reasonable agreement with the experiments. A relatively large degree 

of analyst-to-analyst scatter was observed in this work. The effect of the observed scatter was 

evaluated in Chapter 7 by considering stress intensity factor calculations and flaw growth 

calculations. This work demonstrated the need to develop appropriate modeling guidelines to 

reduce uncertainty in WRS prediction.

Since plastic deformation is expected during the thermal cycles associated with welding, an 

appropriate strain hardening law must be chosen to predict the change in the yield surface due 

to plastic strain history. The choice of hardening law had a large effect on the modeling results. 

While the mixed hardening law provides the most accurate description of material behavior, the 

experimentation required to develop the material parameters is resource intensive. Developing 

guidelines for dealing with the hardening law issue will be important in future efforts. Post 

processing of FE results presents another potential source of uncertainty. For instance, no 

guidelines for extracting results were provided to the round robin participants in each research 

phase. This led to data massaging after the fact to promote reasonable comparisons among 

the various submissions. Other sources of uncertainty, such as process sequence, were 

identified through modeling sensitivity studies in this work.

The concept of quantitative validation of WRS models or modeling procedures is not straight 

forward. The European R6 code and the Electric Power Research Institute’s Materials 

Reliability Program-287 report have suggested criteria for model validation (see Chapter 2), but 

this report does not endorse those criteria. Nor does this report define alternative criteria for 

model validation. The data found in this report, along with data collected in future efforts, may 

help to define validation criteria going forward. The work in Chapter 7 demonstrated the 

difficulties of developing quantitative, objective acceptance criteria with such large uncertainties 

in WRS prediction. Therefore, development of modeling guidelines to minimize 

analyst-to-analyst uncertainty will also be important for establishing acceptance criteria.

151

9 KNOWLEDGE GAPS

The following lists the six U.S. Nuclear Regulatory Commission (NRC) objectives for the Weld 

Residual Stress Validation Program identified in Chapter 1.

• Validate axisymmetric finite element modeling as a predictive tool for WRS, using 

robust experimental methods.

• Support the NRC’s Office of Nuclear Reactor Regulation in development of 

appropriate WRS/flaw evaluation review guidelines.

• Perform independent confirmatory research on industry guidance for executing WRS 

analysis.

• Assess and evaluate the near-term adequacy of industry’s mitigation activities where 

WRS minimization is necessary.

• Improve WRS finite element analysis predictive methodologies.

• Determine estimates for WRS uncertainty distributions, which are needed in 

probabilistic analyses (e.g., xLPR Code–eXtremely Low Probability of Rupture 

[25],[26]).

Development of flaw evaluation guidelines for NRC reviewers is linked to an informed judgment 

of expected modeling uncertainty. Knowledge gaps to address this objective include a lack of 

validation criteria, a large degree of modeling uncertainty, and a lack of guidance for FE 

modeling of WRS. Future efforts should focus on resolving these open issues. One avenue for 

addressing these concerns is producing ASME Code guidance for WRS input development, 

which NRC staff has been actively engaged in.

An accurate description of WRS uncertainty distributions for probabilistic assessments has not 

been formulated. Preliminary work in the xLPR project has applied more rigorous statistical 

tools than considered in this report to quantify uncertainty of WRS profiles. Lessons learned in 

modeling practices from this work, including choice of hardening law and post processing, were 

applied to the xLPR project. Additional modeling efforts specific to the xLPR project were an 

ongoing effort as of publication of this document.

153

10 FUTURE WORK

The U.S. Nuclear Regulatory Commission should focus future weld residual stress research on 

addressing the knowledge gaps developed in the previous section. Suggestions for future work 

are as follows.

• Develop specific validation criteria for comparing WRS measurement and modeling 

results.

• Establish guidelines for WRS input development for deterministic flaw evaluations, 

including finite element best practices, should be established.

• Develop additional guidance for accounting for uncertainty in WRS inputs for flaw 

evaluations.

• Focus future finite element round robin studies on reducing model-to-model variability, 

given lessons learned in FE modeling best practices.

• Apply more robust methods to quantify modeling uncertainty in future round robin efforts.

155

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