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Uncertainty Characterization of the EPRI/NRC

Weld Residual Stress Round Robin Data

Michael L. Benson and Matthew J. HomiackU.S. Nuclear Regulatory Commission

2016 International LWR Materials Reliability Conference and Exhibition

August 1-4, 2016

Chicago, IL

The view expressed herein are those of the authors and do not reflect

the views of the U.S. Nuclear Commission

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Background and Introduction

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WRS Research at NRC

• 4-year program under MOU with EPRI, ended in

December 2015

• Number of measurement and modeling studies– Small, scientific specimens

– Full-scale mockups and components from cancelled

plants

• NUREG-2162 and MRP-316

•Scientific Weld Specimens•Phase 1A: Restrained Plates (QTY 4)

•Phase 1B: Small Cylinders (QTY 4)

•Purpose: Develop FE models.

Ph

ase

1 -

EP

RI

•Fabricated Prototypic Nozzles

•Type 8 Surge Nozzles (QTY 2)

•Purpose: Prototypic scale under controlled conditions. Validate FE models.

Ph

ase

2 -

NR

C

•Plant Components•WNP-3 S&R PZR Nozzles (QTY 3)

•Purpose: Validate FE models.

Ph

ase

3 -

EP

RI

•Plant Components•WNP-3 CL Nozzle (QTY 1)

•RS Measurements funded by NRC

•Purpose: Effect of overlay on ID.

Ph

ase

4 -

EP

RI

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Phase 2a Study

• Reasonable agreement on average between

measurements and models

• Significant scatter about the average

• Incrementally providing participants more information

(e.g., material properties, thermocouple

measurements) did not improve the scatter

• Gained confidence in the hole drilling and contour

measurement techniques

• Future work: improving, characterizing,

understanding the prediction uncertainty

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Phase 2b Study

• Second pressurizer surge line mockup, similar to Phase 2a

• Hole drilling and contour measurements

• Crafted a set of modeling guidelines

• Participant questionnaire

• Initiated a second international round robin

• Obtained another dataset of measurements and models

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Sandia National Laboratory Uncertainty Project

• NRC recognized a need for more sophisticated

treatment of the round robin dataset

– Quantify uncertainty

– Discuss measurement-model comparisons

• Sandia has worked on NRC/EPRI’s Extremely Low

Probability of Rupture (xLPR) project, with expertise in

statistics and probability

• Sandia recently finished a project to describe

uncertainty in the Phase 2b dataset

• Objective: overview and introduction of Sandia’s work

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Overview of Phase 2b Results

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Hole Drilling Measurements

• Four 1.5-mm diameter holes drilled through the

centerline of the dissimilar metal weld, 90° apart

• One-dimensional representation of the stress variation

through the wall thickness

• Both axial and hoop stresses determined from a single

measurement

• Natural representation is from OD to ID, given that

drilling procedure starts on OD

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Contour Measurements

• Contour measurement requires completely destroying

the part

• Two-dimensional representation of the stress state on

the relevant cut planes

• Axial stresses measured at centerline of the dissimilar

metal weld between the nozzle/butter and the safe end

• Hoop stresses measured along the axial position of the

part

• One-dimensional stress profiles can be extracted from

this data

mid-weld path

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Modeling Results

• Results from two hardening laws: isotropic and

kinematic

• Two-dimensional contour plots provided by participants,

but no raw data

• Raw data supplied as one-dimensional profile along the

dissimilar metal weld centerline, reported ID to OD

Isotropic Hardening

Kinematic Hardening

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Need for Data Processing

• Ultimate objective is to benchmark finite element results against the measurements; not straight-forward

• Various datasets require processing the raw forms before making meaningful comparisons

– Sort

– Interpolate

– Normalize

– Convert 2-D data to 1-D data

• Various measurements

– What’s the correct benchmark?

– Simple average?

– Use of multiple benchmarks?

– What’s the uncertainty of benchmark(s)?

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Overview of Sandia’s Methodology

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Describing Functional Data

• WRS is functional data

• Two aspects of functional data

– Amplitude variability

– Phase variability

• In the xLPR project, a method to describe uncertainty and statistically sample WRS was developed

– Kurth and Sallaberry, et. al: PVP2016-63962 and PVP2016-63963

– Accounts for expected features of a WRS curve: point-to-point correlation, force balance requirements

– Harmonize the two methods in the future?

dfWRS

phase

amplitude

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Step 1: Smooth Data

• WRS modeling data is discrete by nature, but WRS is a

continuous function of depth in reality

• Smoothing with spline functions allows for representation of

the WRS as a continuous function

• Smoothing can introduce additional uncertainty, which must

be assessed

Raw Data

Smoothed Data

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Step 2: Register the Data

• Aligns the data

• Warping functions

• Characterizes and removes phase variability

Smoothed Data

Registered Data

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Step 3: Construct Probabilistic Model

• The probabilistic model is based upon Functional Principle

Components Analysis

• Modeling amplitude variability requires registered (aligned) data

• Modeling phase variability requires the warping functions used to

register the data

• Combine the two models, allowing sampling

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Step 4: Bootstrapping

• A statistical sampling method used to estimate uncertainty on a distribution parameter

– mean

– quantiles

• Iteratively sample from the probability model, estimating the parameter (e.g., the mean) each time

• Construct confidence bounds based upon the results, without a priori assigning a distribution type to the data

• Now, we can estimate how well we know the mean and confidence bounds

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Closing

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Summary

• Provided broad overview of a method to characterize uncertainty in the Phase 2b round robin dataset

• Discussed only the method for characterizing modeling uncertainty

• Characterizing measurement uncertainty also challenging

– WRS not measured directly, so the “measurement” is actually a combination of measurement and models

– Limited data

– Diverse data: axial stress vs. hoop stress, contour method vs. hole drilling techniques

• Comparing measurements to models

– What constitutes a “reasonable” prediction?

– What hardening law provides the best prediction?