Astm stp 1598 2017

Title: Fatigue and fracture test planning, test data acquisitions and analysis / editors, Zhigang Wei, Kamran Nikbin, Peter C.. Establishing a Multi-Laboratory Test Plan for Environmen

STP 1598 Editors:

Zhigang Wei Kamran Nikbin Peter C McKeighan Gary D Harlow

Selected technical PaPerS

StP1598

Editors: Zhigang Wei, Kamran Nikbin, Peter C McKeighan, and D Gary Harlow

Fatigue and Fracture Test

Planning, Test Data Acquisitions and Analysis

ASTM STOCK #STP1598

DOI: 10.1520/STP1598-EB

ASTM International, 100 Barr Harbor Drive, PO Box C700, West Conshohocken, PA 19428-2959 Printed in the U.S.A.

Library of Congress Cataloging-in-Publication Data

Names: Wei, Zhigang, 1970- editor | Nikbin, Kamran M., editor | McKeighan,

P C (Peter C.), editor | Harlow, D Gary, editor.

Title: Fatigue and fracture test planning, test data acquisitions and

analysis / editors, Zhigang Wei, Kamran Nikbin, Peter C McKeighan, D

Gary Harlow.

Description: West Conshohocken, PA : ASTM International, [2017] | Series:

Selected technical papers ; STP1598 | “ASTM Stock #STP1598.” | Includes

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April, 2017

THIS COMPILATION OF Selected Technical Papers, STP1598, Fatigue and ture Test Planning, Test Data Acquisitions and Analysis, contains peer-reviewed

Frac-papers that were presented at a symposium held May 4–5, 2016, in San Antonio, Texas, USA The symposium was sponsored by ASTM International Committee E08 on Fatigue and Fracture and Subcommittee E08.03 on Advanced Apparatus and Techniques

Symposium Chairpersons and STP Editors:

Zhigang Wei

Tenneco Inc Grass Lake, MI, USA

Kamran Nikbin

Imperial College London

London, UK

Peter C McKeighan

Symmetry Engineering and Forensic Consulting LLC

Shingle Springs, CA, USA

D Gary Harlow

Lehigh University Bethlehem, PA, USA

Foreword

Establishing a Multi-Laboratory Test Plan for Environmentally Assisted Fatigue 1 Matthias Bruchhausen, Kevin Mottershead, Caitlin Hurley, Thomas Métais,

Román Cicero, Marc Vankeerberghen, and Jean-Christophe Le Roux

Experimental Study on Surrogate Nuclear Fuel Rods Under Reversed

Hong Wang and Jy-An John Wang

Xijia Wu, Guangchun Quan, and Clayton Sloss

Fracture Mechanical Testing of In-Service Thermally Aged Cast Stainless Steel 58 Martin Bjurman, Björn Forssgren, and Pål Efsing

Calorimetric Studies and Self-Heating Measurements for a Dual-Phase

Noushin Torabian, Véronique Favier, Saeed Ziaei-Rad, Justin Dirrenberger,

Frédéric Adamski, and Nicolas Ranc

Fatigue Studies on Impacted and Unimpacted CFRP Laminates 94 Raghu V Prakash, Mathew John, Deepika Sudevan, Andrea Gianneo,

and Michele Carboni

Application of Kresidual Measurements to Fracture Toughness Evaluations 119 Gongyao Wang, Kimberly Maciejewski, and Mark James

Sensitivity Study on Parameters that Influence Automated Slope Determination 133 Stephen M Graham

Contribution to the Evaluation of Stress-Strain and Strain-Life Curves 151 Michael Wächter and Alfons Esderts

Contents

Methods Development for Nonlinear Analysis of Fatigue Data 186 Bruce A Young, Richard C Rice, Steven R Thompson, and Doug Hall

Data Processing Procedure for Fatigue Life Prediction of

Hong-Tae Kang, Xiao Wu, Abolhassan K Khosrovaneh, and Zhen Li

More Accurate Elastic Compliance Equation and Its Inverse Solution

Xian-Kui Zhu

A Novel Nonlinear Kinematic Hardening Model for Uniaxial/

Hao Wu and Zheng Zhong

Fatigue Damage Indicators Based on Plastic Deformation 246 Grzegorz Socha

A Fatigue Failure Mode Transition Criterion for Sizing Load-Carrying

Shizhu Xing and Pingsha Dong

Analysis of Nonproportional Multiaxial Fatigue Test Data of Various

Jifa Mei and Pingsha Dong

A Theory for Mathematical Framework and Fatigue Damage Function

Hoda Eskandari and Ho Sung Kim

Verification and Validation of Accelerated Testing Methods for

Limin Luo, Jason Hamilton, Zhigang Wei, and Robert Rebandt

Load Spectrum Test and Fatigue Failure Study of High-Speed

Wenjing Wang, Jinyi Bai, Sichun Li, Hongwei Zhao, and Weiguang Sun

Practical and Technical Challenges of the Exhaust System Fatigue

Mark T Seitz, Jason D Hamilton, Richard K Voltenburg,

Limin Luo, Zhigang Wei, and Robert G Rebandt

ASTM STP1598 contains a collection of 20 peer-reviewed papers from the sium on Fatigue and Fracture Test Planning, Test Data Acquisitions and Analysis held May 4–5, 2016, in San Antonio, Texas, USA The symposium was sponsored

Sympo-by ASTM Committee E08 on Fatigue and Fracture in conjunction with the 2016 May standards development meetings of the Committee The symposium was attended by a number of professionals representing several countries, including the United States, Canada, United Kingdom, Germany, Australia, Netherlands, Sweden, China, and India The driving force behind this symposium is the revision

of several relevant ASTM standards, especially ASTM E739-10 (2015), Standard Practice for Statistical Analysis of Linear or Linearized Stress-Life (S-N) and Strain- Life (ε-N) Fatigue Data.

Understanding and preventing fatigue failure and fracture of engineering rials and structures are critical in several industries Material testing is fundamen-tal to gaining a better understanding of fatigue and fracture phenomena, as well as

mate-to guide materials selection, product design, and quality control In fact, ing design, development, and validation heavily relies on accurate test data and the proper interpretation of test data Although a significant amount of knowledge and understanding has been gained over the last several decades via material testing, there still remains a substantial amount of improvement needed due to procedural deficiencies and limitations The need for testing improvement is becoming more critical as materials are increasingly stretched to their limits by extreme conditions

engineer-of temperature, stress, corrosive environments, and longer service life cycles With new applications, some of the previously tested materials and procedures prove inadequate and inconsistent, demanding a collective and interdisciplinary effort

to generate reliable and high-quality data To embrace the new developments, the following areas of particular interest were selected as the main themes for the sym-posium: 1) test planning, 2) data acquisition and processing, and 3) data analysis and interpretation Although many of the papers and presentations include content focused on these three topics, the symposium co-chairs were pleased to welcome other closely related topics and emerging issues in fatigue and fracture

The major objective of the symposium was to provide a forum for engineers, agers, researchers and scholars worldwide to exchange ideas, share best practices,

man-Overview

discuss challenges, and identify opportunities and directions for future ments and applications Specific objectives include:

develop-1) Showcase the most current research and advances in these areas;

2) Promote a systematic, unified materials test plan for improved data acquisition and analysis; and

3) Collect information and supporting documents for updating existing fatigue, creep, and fracture test standards and identify the needs for new standards.Two keynote lectures at the symposium were presented by Krishnaswamy Ravi-Chandar (The University of Texas at Austin) and Youshi Hong (Institute of Mechanics, Chinese Academy of Sciences), respectively, at the beginning of each day of the two-day symposium A panel discussion on “The Challenges and Opportunities in Fatigue and Fracture Test Planning, Test Data Acquisitions, and Analysis” was held at the end of the first day of the symposium The panel consisted of the following experts in their respec-tive areas: Michael Shepard (MTS Systems Corporation), Steven Thompson (AFRL/RXSA), Dan Lingenfelser (HBM nCode Federal LLC), Peter McKeighan (Symmetry Engineering and Forensic Consulting LLC ), and Charlotte Belsick (Lockheed Martin) Bruce Young (Battelle) served as a substitute chair in the last day of the symposium.The papers presented in the symposium were arranged into four sessions: Session 1: Testing Planning and Performance Characterization

Session 2: Data Acquisition, Quality Assurance, and Analysis

Session 3: Modeling/Simulation, Interpretation, and Correlation

Session 4: Verification, Validation, and Applications

The papers collected in this STP are arranged in the same order These papers provide a diverse source of new information regarding test planning, data acquisition and analysis that can help accelerate the revision of the existing standards and the development of new standards These papers also represent a significant contribution

to ASTM E08’s commitment to expanding the knowledge base that supports design and testing as related to fatigue and fracture

The symposium co-chairs express our sincere gratitude to ASTM staff for all their contributions to planning throughout the many months preceding the symposium and the STP1598 publication Additionally, Dr Markus Heinimann (Arconic) and Charlotte Belsick (Lockheed Martin) are also highly appreciated for their help and support Furthermore, this STP would not have been possible without the atten-tiveness and countless hours volunteered by our peer reviewers to ensure that all of the manuscripts were suitable for publication Finally, special thanks are given to the authors and reviewers of the papers for their outstanding efforts in writing and reviewing efforts that make the symposium and the STP possible It is our sincere hope that these selected technical papers contribute significantly to the further advancement of the relevant topics

Matthias Bruchhausen,1Kevin Mottershead,2

Caitlin Hurley,3Thomas Me´tais,4Roma´n Cicero,5

Marc Vankeerberghen,6and Jean-Christophe Le Roux7

K Nikbin, P C McKeighan, and D G Harlow, Eds., ASTM International, West Conshohocken,

PA, 2017, pp 1–18, http://dx.doi.org/10.1520/STP159820160047 8

ABSTRACT

The European project INCEFA-PLUS will characterize environmental fatigue

in pressurized water reactor (PWR) conditions The aim is to develop newguidelines for assessing environmental fatigue damage susceptibility of nuclearpower plant (NPP) components The consortium consists of 16 public and privateorganizations from across Europe The project is structured in two phases: Thefirst phase is an extensive fatigue testing program; in the second phase, aprocedure for estimating the environmental fatigue degradation of the materialswill be formulated During the test phase, a selection of austenitic stainless steels

Manuscript received February 29, 2016; accepted for publication September 15, 2016.

1 European Commission, Joint Research Centre, Westerduinweg 3, 1755 LE Petten, The Netherlands

2 Amec Foster Wheeler, Clean Energy, Europe, Walton House, Birchwood Park, Birchwood, Warrington,

Cheshire WA3 6GA, United Kingdom

3 VTT Technical Research Centre of Finland Ltd., Espoo, 02044 Finland http://orcid.org/

0000-0003-4810-1997

4 EDF-DIPNN SEPTEN, 12-14 Avenue Antoine Dutrie `voz, 69628 Villeurbanne, France

5 Inesco Ingenieros, 39005 Santander, Spain

6 SCK  CEN, Nuclear Materials Science Institute, Boeretang 200, B-2400 Mol, Belgium

7 EDF-R & D, Materials and Mechanics of Components Dept., Avenue des Renardie `res-Ecuelles, 77818 Moret Sur Loing Cedex, France

8 ASTM Symposium on Fatigue and Fracture Test Planning, Test Data Acquisitions and Analysis on May 4–5,

2016 in Grand Hyatt, San Antonio, TX.

STP 1598, 2017 / available online at www.astm.org / doi: 10.1520/STP159820160047

used in NPPs will be characterized with regard to fatigue The test matrix willfocus on the effects of mean strain, strain amplitude, hold time periods, andsurface roughness on fatigue life Sensitivities to these parameters will be tested

in PWR environments with additional tests in air for reference purposes Thestudy of hold time effects will lead to very long testing times, limiting thetotal number of tests It is therefore crucial to establish a test matrix that allowsthe study of the principal effects of interest while taking into account thenuisance effects, such as different specimen geometries, particular materialmicrostructures, and other laboratory-dependent factors that may not be well-controlled Methods and considerations for establishing a single test matrix arepresented in this work

f ;airto the fatiguelife in LWR environment at operating temperature (300C) Nf ;LWR300 , as shown inEq 1:

Thus, different damaging effects are taken into account by determining factorsfor individual effects and multiplying these factors to calculate the cumulative impact

of all effects There is, however, experimental evidence that this method can lead tooverly penalizing estimates for the fatigue life under plant conditions [2 5]

To address some of these issues, the project, Increasing Safety in NPPs by ering Gaps in Environmental Fatigue Assessment (INCEFA-PLUS), has recentlybeen launched within the European Horizon 2020 framework [6 8] The projectaims at developing new guidelines for the assessment of environmental fatiguedamage susceptibility of NPP components It is carried out by a consortium consist-ing of 16 private and public organizations from across Europe

Cov-The focus is on studying the influence of the mean strain, strain amplitude,hold time, and surface roughness parameters on fatigue life To acquire data forestimating the impact of these parameters and their possible interactions on fatiguelife, a consistent test matrix has been established The test matrix is based on adesign of experiments (DoE) approach and takes into account a number of nui-sance factors in addition to the parameters directly targeted within the project

DoE is a method for establishing optimized test plans that was pioneered inthe first half of the twentieth century [9] The widespread use of computers has led

to its application in many areas of science and engineering, including materials ence and fatigue in particular [10–13] However, examples of using DoE for coor-dinating round-robin studies including a larger number of laboratories seem to beless common

sci-The INCFEA-PLUS project started in July 2015 and is expected to last for fiveyears The testing will be carried out in three phases, each of which is scheduled tolast one year The current work pertains to the establishment of a test matrix for thefirst testing phase

Description of the Methodology

The DoE approach establishes a test plan by systematically varying all relevantindependent variables (“factors”) to study their impact on the dependent variables(“responses”) [9,14,15] This is a fundamental difference for another frequentlyused approach sometimes referred to as one-factor-at-a-time (OFAT) The OFATmethod implicitly assumes that the impacts of the different factors on the responseare independent from each other In reality, however, the impact of one factor oftendepends on the value of another factor This dependence of the impact of one factor

on the value of another factor is called “interaction.”

The difference between the OFAT and DoE approaches is shown cally in Fig 1 for an example with two factors, X1 and X2 In both cases, fiveexperiments (“runs”) are carried out with both factors in an upper, a lower, and

schemati-a centrschemati-al level In the OFAT schemati-approschemati-ach, the fschemati-actors schemati-are chschemati-anged sepschemati-arschemati-ately fromthe center point, whereas they are modified simultaneously in the DoE ap-proach From the distribution of the test conditions in the x –x plane, it is

clear that the case shown in Fig 1adoes not contain any information about theinteractions.

The advantage of the DoE approach is that it allows taking interactions into count An example for interaction are the impacts a rough, plant-relevant surfacefinish (as compared to a polished laboratory surface) and the PWR environment(as compared to air) have on the fatigue life of stainless steels There is experimentalevidence that the combined effect of both, the rough surface and the PWR environ-ment, is less detrimental on the fatigue life than an estimate based on the individualimpacts of both factors would lead us to expect [4,12]

ac-During a test campaign, a number of runs (tests) i are carried out where thesettings of the factors X1 and X2 are varied between runs (with possibly someduplications)

When a problem with a single response Y and two factors X1and X2is ered, the corresponding model equation for run i is:

consid-Yi¼ b0þ b1X1iþ b2X2iþ b12X1iX2iþ ei: (3)

In this equation, X1iand X2iare the values of the factors for this specific run, b0,

b1, and so on are the unknown model parameters, and eiis the error term b12is themodel parameter characterizing the interaction between the factors X1and X2.For more factors and interactions, the model inEq 3can be extended:

For a model with k factors including all main effects and two-factor interactionsand n experimental runs, the model matrix X has the entries (Eq 6):

377

If not all possible interactions or effects are taken into account in the model,the corresponding terms are omitted in the model matrix and the matrix becomessmaller

The unknown model parameters (which are to be determined from the testdata) are the components of the vector b, as shown inEq 7:

b¼

b0

b1

bk

b12

b1k

b23

bk1;k

2666666666

3777777777

In most cases, interactions of more than two factors are not relevant; therefore,they are currently not considered for INCEFA-PLUS Initially, only two levels foreach factor are considered, so no quadratic terms are included in the model

It is helpful to use the normalized values 61 for the upper and lower levels ofthe factors Xiinstead of their physical values This allows direct assessment of therelative impacts of the different effects by comparing the values of the correspond-ing model parameters b Also, the impact of numerical and categorical factors inthe investigated factor range can be compared

Depending on the aim of a test campaign (e.g., screening, prediction), differentoptimization criteria and algorithms can be used for optimizing the test matrix.Two frequently used optimization approaches are the D-optimal and the I-optimaldesign In D-optimal designs, the variance of the model regression coefficients(parameters b inEq 4) is minimized Mathematically, this corresponds to maximiz-ing the determinant Xj 0Xj where X0is the transposed X D-optimal designs are usedfor studies focusing on the identification of those effects that have the most signifi-cant impact on the response They are best suited for screening studies In I-optimaldesigns, the smallest average variance of the prediction is sought These designs are

best suited for studies aiming at an accurate prediction of the response Y Becausethe focus of the first phase of the experimental campaign is identifying the most rel-evant effects, a D-optimal design will be used.

Application to the Project

FACTORS OF INTEREST

In relation to the project, mean strain, strain amplitude, surface roughness, holdtime, and the environment (air or PWR conditions) are the factors under consider-ation Initially, two levels will be used for every factor These are:

TABLE 1 Specifications of the air environment.

TABLE 2 Specifications of the PWR water chemistry.

Lithium content ppm Li 2 ppm 6 0.2 ppm as LiOH Boron content ppm B 1000 ppm 6 100 ppm as boric acid Dissolved hydrogen cc(STP)H 2 /kg H 2 25 6 5 cc(STP)H 2 /kg H 2 O

package There are, however, additional “nuisance” factors and constraints to beconsidered.

NUISANCE FACTORS AND CONSTRAINTS

The number of tests that can be carried out is of course limited However, thanks tothe relatively large number of partners committed to the project, 74 tests are alreadyforeseen in the first test phase For the entire project, approximately 300 tests areexpected to be carried out

Another aspect is the duration of the individual tests; tests under real plant ditions would simply take too long, especially when hold times are included in thetests The test conditions therefore need to be chosen with regard to achieving real-istic test durations

con-These considerations are valid for any fatigue-related test program For the lar project discussed in this work, there are additional factors that need to be considered:

particu-• Laboratory: The tests will be distributed over ten different project partners It

is expected that “laboratory” will not be a determining factor in the tests; thishowever has to be verified, so an additional categorical factor “laboratory” isintroduced In cases where the same organization carries out tests in air and inPWR environment, two completely different test installations will be used.The factor “laboratory” refers to the actual test rig in which the tests are car-ried out—not to the organization For the purpose of this study, these test rigsare considered as different laboratories Finally, seven laboratories will be test-ing in air and nine will be testing in a PWR environment

• Specimen Type: For the tests in PWR conditions, two types of specimens will beused Although most of the tests in PWR conditions will be carried out usingstandard fatigue specimens in an autoclave, some laboratories will use hollowspecimens with the simulated PWR water flowing inside the specimen This dif-ference of specimen geometry has consequences for the stress state While thefull specimens have a purely axial stress in the gage length, the hollow specimensare exposed to an additional circumferential stress introduced by the pressurizedwater A previous study on thermomechanical fatigue has found differences be-tween full and hollow specimens, but these were smaller than the differencesamong laboratories [16] Because these tests were performed without internalpressurization of the hollow specimen, the impact of the specimen type (“full” or

“hollow”) still needs to be investigated for PWR testing A recent study showedsystematic differences between hollow and smooth specimens [17]

• Material: Although most of the tests will be carried out on a common heat of 304Lstainless steel, some partners will also bring data from national programs into theproject These tests will be performed on materials of interest for the respective na-tional programs In order to align the testing on these different materials as far aspossible with the project’s test plan, for the common material, suggestions for testconditions for those materials will be included in the common test program Thisrequires adding “material” as an additional categorical variable

“Outlier specimens” will be microstructurally analyzed to establish whetherthere are any flaws that might explain their premature failure Such microstructural

anomalies can be considered as an additional nuisance factor However, the structural analysis can only be performed post-test and is therefore not incorporat-

micro-ed in the planning of the test campaign

The constraints that need to be incorporated in the test program are rized in Table 3 These constraints lead to a large number of factor settings beingpredefined in the test matrix that is reproduced in Table A1in the appendix Theentries in the blue fields of the table are fixed by the five constraints inTable 3andcannot be modified for optimizing the test plan

summa-IMPLEMENTATION OF CONSTRAINTS IN THE TEST MATRIX

The commercial software package JMP 12 [18] has been used for determining anoptimized test program As mentioned in the earlier section, “Description of theMethodology,” establishing the D-optimal design means finding the settings ofthe test parameters in each run leading to the maximum of the determinant

X0X

j j The program uses the coordinate exchange algorithm [19] for that pose Initially, a random value (61) is attributed to each factor in every run.Then the program replaces the value for each factor successively by the oppositevalue (e.g., 1 is replaced by þ 1) The effect of the exchange of the factor setting

pur-on the determinant Xj 0Xj is calculated, and the value resulting in the largerdeterminant is kept The algorithm cycles through all factors until no furthermodification leading to a larger determinant can be found At that point, a localmaximum has been found

In order to find a global maximum, the next step is to start the same processwith a new random seed of þ1 and 1 for all entries in the matrix and to restartthe same procedure with different initial values The best of all locally optimizeddesigns is considered to be the globally optimized design Typically, around 1,000random seeds are used

The program allows enforcing combinations of factor values by means of acovariates table This table has a row for every individual test run in the test cam-paign Each row has several fields that define the laboratory, the specimen type, theenvironment, and the material for each test Therefore, these test parameters arefixed in advance and cannot be changed anymore during the optimization of thetest matrix This allows implementing Constraints 1–4 listed inTable 3

TABLE 3 Constraints predefining some factor settings in the test matrix.

1 Each laboratory carries out a predefined number of tests The number of tests varies among

laboratories.

2 Each laboratory will test either in air or in PWR conditions, not in both.

3 Each laboratory will use only a single type of specimen: either full or hollow.

4 Some laboratories will carry out (a part of) their test program on their own material.

5 Although full specimens can have either surface finish (smooth or rough), hollow specimens

The program also allows explicit interdicting of certain combinations of factorvalues By disallowing the combination of “hollow specimens” with a “rough surfacefinish,” Constraint 5 can be implemented.

As can be seen from Eqs3through6, the test matrix X and therefore the minant Xj 0Xj do not depend only on the number of factors and runs in the testprogram but also on the effects included in the model Before the D-optimal testmatrix can be determined, the terms to be included in the model have to beselected

deter-EFFECTS TO BE CONSIDERED

Only main effects and second-order interactions will be taken into account duringthe first phase of the project The number of parameters NPin a model with k fac-tors at two levels including all main effects, all second order interactions, and theintercept (b0inEq 3) is:

NP¼ k þ 1 þk  k  1ð Þ

It is clear fromEq 8that the number of parameters NPincreases quadraticallywith k, which can lead to very complex models

In the present case, however, not all of the possible effects are considered

equal-ly important by the project partners Some of the possible interactions will be carded, which reduces the complexity of the model

dis-If an interaction between the factor “laboratory” and one of the other factorswas active, that would mean that, for example, the effect of “hold time” or “strainamplitude” would vary among laboratories This is considered unlikely, and interac-tions between the factor “laboratory” and any of the other factors will be discarded.The main effect “laboratory” will be maintained throughout This reduces the num-ber of model parameters by seven (the factor “laboratory” has seven possibleinteractions)

Most of the tests will be carried out on the same heat of 304L The specimensfrom this material are all being manufactured in the same workshop to minimizevariations during the production process itself Also, some of the tests in the frame-work of national programs will be performed on 304L (albeit on a different heat).For details, refer to the test matrix in the table in the appendix Due to the limitednumber of tests being performed on “national program” materials, the “material”factor interactions cannot be studied and have therefore been discarded from thetest matrix In contrast, the main effect “material” is maintained This furtherreduces the number of model parameters by six (the factor “material” has sixremaining potential interactions since the factor “laboratory” was already removed

in the previous step)

Some of the remaining interactions cannot be studied because the factors volved in these interactions cannot be varied For example, the “hollow specimens”

in-will all have a smooth surface finish; therefore, the data collected during the projectwill not allow studying the interaction between the type of specimen and the surfacefinish These interactions are marked “assessment not possible” inTable 4 Becausetwo out of the four interactions in that category were already discarded during one

of the previous steps, the total number of model parameters is reduced by two,which leads to 22 remaining parameters

Some of the remaining main effects and interactions cannot be separated cause they are changed simultaneously between runs These problems are due tothe constraints that the factors “laboratory,” “specimen type,” and “environment”are predefined for every test and cannot be varied The factors “laboratory” and to alesser degree of certainty “specimen type” are not expected to have a major impact

be-on the fatigue life To cbe-onfirm (or invalidate) these expectatibe-ons, the impact of thesefactors and the corresponding interactions (labeled with “screening” inTable 4) onthe test outcome will nevertheless be checked during the evaluation To that end, ascreening evaluation will be carried out first

For this screening evaluation, the runs will be divided into three groups: thefirst group contains all tests in air, the second group contains all tests in PWR water

on full specimens, and the third group contains the tests in PWR water on hollowspecimens In each of these groups, the effect of the factor “laboratory” can be in-vestigated If the corresponding model parameters b are small, the laboratories have

no major effect and can be removed from the analysis The same procedure willthen be applied to all the tests in PWR water (Groups 2 and 3) where the impact ofthe “specimen type” will be assessed If the factor “specimen type” does not have amajor impact either, it can be removed from the analysis, and the complete data setcan be analyzed, taking into account only the effects in the green fields in Table 4.This is also the model on which the optimization of the test matrix is based

Analysis of the Test Matrix

The full test matrix is reproduced in the table in the appendix In this section, some

of its characteristics will be discussed

A useful property for the design is to allow the model effects to be determinedindependently from one another The degree to which a given design allows thiscan be analyzed using the covariance among the different effects The covariance oftwo random variables x and y is defined inEq 9:

cov X; Yð Þ ¼ E X  E X½ð ð ÞÞ Y  E Yð ð ÞÞ (9)where E Xð Þ refers to the expected value (i.e., mean) of X

The correlation of two variables is the covariance normalized by the product ofthe standard deviations (Eq 10):

corr X; Yð Þ ¼cov X; Yð Þ

TABLE 4 List of all possible parameters (intercept, main effects, and second-order interactions).

The effects in the gray cells (“assessment not possible,” “discarded”) will not be assessed; those in the orange cells (“screening”) will be analyzed in a first screening analysis (see text for details) The remaining effects (green) are targeted by the project.

Material

Hold time * Mean strain

Hold time * Strain amplitude

Hold time * Surface roughness

Hold time * Environment

Hold time * Specimen type screening evaluation

Mean strain * Strain amplitude

Mean strain * Surface roughness

Mean strain * Environment

Mean strain * Specimen type screening evaluation

Strain amplitude * Surface roughness

Strain amplitude * Environment

Strain amplitude * Specimen type screening evaluation

Surface roughness * Environment

Surface roughness * Specimen type assessment not possible

Environment * Specimen type assessment not possible

Environment * Lab assessment not possible

Specimen type * Lab assessment not possible

Material * Surface roughness discarded

The correlation is a measure of the linear dependence between two bles If the correlation is 0, the variables are independent For the test matrixthat means that if the correlation of two effects is 0, their respective impacts onthe test outcome (i.e., the fatigue life) can be determined independently fromeach other.

varia-The color map on correlations in Fig 2shows the correlations among all theeffects included in the model

The factor “material” is different from the other factors in that it is a cal (i.e., non-numerical) variable with four levels To be able to carry out calcula-tions, this type of variable is transferred into a set of four variables (e.g., m1, m2,

categori-m3, and m4) Each of these can take the two values 0 and 1 For example, m1¼ 1means “Material 1” one was selected for that test, whereas m1¼ 0 means “Material 1”was not selected Because exactly one material is used in every test, the factors

m1to m4are coupled This coupling can be expressed asEq 11:

FIG 2

X4 j¼1

It follows that there are only three independent variables mi Consequently,only three are listed inFig 2

The red diagonal in the plot (corr ¼ 1) indicates the trivial fact that each effect

is correlated with itself The important point to notice is that most of the other relations are close to 0 The current design will allow separating the physical effectsbased on the data and estimating the targeted effects independently from oneanother

cor-The standard deviation for the different model parameters depends on thecharacteristics of the measurements (hardware, procedures) as well as on the testmatrix and can therefore not be determined before the actual tests have been car-ried out However, different test matrices can be compared with regard to theircontributions to the overall standard deviation One of the measures that can beused for that purpose is the “fractional increase of confidence interval length” (FI)[20] The FI measures by which fraction a design increases the confidence interval

of the parameter estimates compared to an ideal, orthogonal design in which the

TABLE 5 Comparison of the “fractional increase of confidence interval length” for the INCEFA-PLUS

and the design with reduced constraints.

Term

INCEFA-PLUS Design

Design with Reduced Constraints

Ratio (INCEFA-PLUS/ Red Constraints)

Mean strain*strain amplitude 0.0151 0.0156 0.9679

Mean strain*surface roughness 0.0153 0.0163 0.9387

Strain amplitude*hold time 0.0161 0.0265 0.6075

Strain amplitude*surface roughness 0.0161 0.0150 1.0733

correlations between any two different effects are 0 The FI should be as close aspossible to zero The FI for the ithparameter and n experimental runs is given by

The results are listed in Table 5 The performance for most parameters is verysimilar for both designs The largest differences show for the effects “Environment”and “Environment*mean strain.” The worst performance of both designs occurs forthe material effects This is related to the strong imbalance between the number oftests for the different materials with very limited number of tests on the materialsfrom national programs This is also reflected in the higher correlation of the mate-rial effects visible in the correlation map (Fig 2)

Hence, the biggest disadvantage the constraints have on the INCEFA-PLUSproject is not a loss of certainty of the parameter estimates but the fact that some ofthe main effects and interactions cannot be estimated simultaneously

Conclusions

The DoE methodology is used to establish a common test matrix for a Europeanproject on environmentally assisted fatigue A number of constraints has to betaken into account in the formulation of the matrix These constraints prevent asimultaneous evaluation of all effects targeted in the study and the nuisanceeffects A stepwise evaluation is proposed to eliminate nuisance effects from theevaluation and to allow the remaining effects to be addressed with a singlemodel

The resulting design is almost orthogonal The constraints do not lead to astrong increase of the parameter estimates compared to a less constricted, hypothet-ical design The main consequence of the constraints is that not all relevant effectscan be analyzed simultaneously

ACKNOWLEDGMENTS

This project has received funding from the Euratom Research and Training gramme 2014–2018 under Grant Agreement No 662320

TABLE A1 Final test matrix.

Lab Env.

Specimen Type Material

Mean Strain

Strain Amplitude

Hold Time Surface Roughness

TABLE A1 (Continued)

Lab Env.

Specimen Type Material

Mean Strain

Strain Amplitude

Hold Time Surface Roughness

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[5] Me ´tais, T., Karabaki, E., De Baglion, L., Solin, J., Le Roux, J.-C., Reese, S., and Courtin, S.,

“European Contributions to Environmental Fatigue Issues Experimental Research in

Conference , Anaheim, CA, July 20–24, 2014, http://dx.doi.org/10.1115/PVP2014-28207

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“INCEFA-PLUS (Increasing Safety in Nuclear Power Plants by Covering Gaps in

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[12] Le Duff, J A., Lefranc ¸ois, A., Vernot, J P., and Bossu, D., “Effect of Loading Signal Shape and

of Surface Finish on the Low Cycle Fatigue Behavior of 304L Stainless Steel in PWR

Conference , Bellevue, WA, July 18–22, 2010, http://dx.doi.org/10.1115/PVP2010-26027

[13] Brandl, E., Heckenberger, U., Holzinger, V., and Buchbinder, D., “Additive Manufactured AlSi10Mg Samples Using Selective Laser Melting (SLM): Microstructure, High Cycle

[14] Goos, P and Jones, B., Optimal Design of Experiments: A Case Study Approach, Wiley, Hoboken, NJ, 2012.

[15] NIST/SEMATECH e-Handbook of Statistical Methods , National Institute of Standards

section1/pri11.htm (accessed November 16, 2015).

[16] Loveday, M S., Bicego, V., Ha ¨hner, P., Klingelho ¨ffer, H., Ku ¨hn, H.-J., and Roebuck, B.,

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2008, pp 382–390.

[17] Twite, M., Platts, N., Mclennan, A., Meldrum, J., and McMinn, A., “Variations in Measured Fatigue Life in LWR Coolant Environments Due to Different Small Specimen Geo-

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Hong Wang1and Jy-An John Wang2

Experimental Study on Surrogate

Nuclear Fuel Rods Under

Citation

Wang, H and Wang, J.-A J., “Experimental Study on Surrogate Nuclear Fuel Rods Under Reversed Cyclic Bending,” Fatigue and Fracture Test Planning, Test Data Acquisitions and Analysis, ASTM STP1598, Z Wei, K Nikbin, P C McKeighan, and D G Harlow, Eds., ASTM International, West Conshohocken, PA, 2017, pp 19–36, http://dx.doi.org/10.1520/STP159820160051 4

ABSTRACT

The mechanical behavior of spent nuclear fuel (SNF) rods under reversed cyclicbending or bending fatigue must be understood to evaluate their vibrationintegrity in a transportation environment This is especially important for high-burnup fuels (>45 GWd/MTU), which have the potential for increased structuraldamage It has been demonstrated that the bending fatigue of SNF rods can beeffectively studied using surrogate rods In this investigation, surrogate rodsmade of stainless steel 304 cladding and aluminum oxide pellets were testedunder load or moment control at a variety of amplitude levels at 5 Hz using theCyclic Integrated Reversible-Bending Fatigue Tester developed at Oak RidgeNational Laboratory The behavior of the rods was further characterized usingflexural rigidity and hysteresis data, and fractography was performed on the

Manuscript received February 29, 2016; accepted for publication October 5, 2016.

1 Oak Ridge National Laboratory, Materials Science and Technology Division, PO Box 2008, MS-6069, Oak Ridge,

public-access-plan ).

4 ASTM Symposium on Fatigue and Fracture Test Planning, Test Data Acquisitions and Analysis on May 4–5,

2016 in Grand Hyatt, San Antonio, TX.

STP 1598, 2017 / available online at www.astm.org / doi: 10.1520/STP159820160051

failed rods The proposed surrogate rods captured many of the characteristics ofdeformation and failure mode observed in SNF, including the linear-to-nonlineardeformation transition and large residual curvature in static tests, pellet-pelletinterface and pellet cladding mechanical interaction, failure mechanisms, and largevariations in the initial structural condition Rod degradation was measured andcharacterized by measuring the flexural rigidity; the degradation of the rigiditydepended on both the moment amplitude applied and the initial structuralcondition of the rods It was also shown that a cracking initiation site can belocated on the internal surface or the external surface of cladding Finally, fatiguedamage to the bending rods can be described in terms of flexural rigidity, and thefatigue life of rods can be predicted once damage model parameters are properlyevaluated The developed experimental approach, test protocol, and analysismethod can be used to study the vibration integrity of SNF rods in the future.

a through-wall crack is not formed, the extent of cracking needs to be evaluated

to determine if the cladding will fail as a result of stresses caused by normal dling or transportation [1]

han-Testing a spent nuclear fuel (SNF) rod is not trivial First, SNF rods are highlyradioactive SNF testing must be conducted in a hot-cell environment and the rodscan be accessed only by manipulators Thus, the test setup, specimen loading, andtest operations must be as simple as possible Second, a fuel rod has a compositestructure that originally consists of fuel pellets and cladding, which has been modi-fied significantly by the high-burnup process Various failure modes could be trig-gered during transportation, including fracture and splitting Bending-induced

failure can be captured only by an effective testing approach Finally, rod vibrationduring transportation is not well-characterized.

An innovative hot-cell testing system, the Cyclic Integrated Bending Fatigue Tester (CIRFT), was developed recently by Oak Ridge NationalLaboratory (ORNL) [2 6] Although the use of the CIRFT to test SNF rods gen-erated many interesting data [7], a number of important issues that arise fromthe testing system and the rod itself—including fatigue and failure mechanisms

Reversible-of SNF rods—remain to be addressed It has been shown that a direct tion of these issues in a hot cell is prohibitive because of high cost and limitedaccess

examina-The mechanical behavior of SNF rods can be effectively studied using surrogaterods by exploiting similar methods of controlling fatigue and failure mechanismsbetween the surrogate rods and the actual rods In this investigation, surrogate nu-clear fuel rods made of stainless steel (SS) 304 cladding and aluminum oxide or alu-mina pellets are used to study the related fatigue and failure behaviors andmechanisms After a brief introduction to the experimental technique, test resultsand discussion will be provided

Experimental Technique

TESTING SETUP

The bending test system is composed of a U-frame testing setup for applyingbending loads on the spent fuel rod test specimen and a unit for measuring thecurvature of the rod during bending Dual linear motors (Bose ElectroForce Sys-tem Dual LM2 TB, MN) [8] are used to apply the forces symmetrically, and line-

ar variable displacement transformers (LVDTs) and load cells are installed tomeasure/control displacements (disp1 and disp2) and loads (load1 and load2) atthe respective loading points The U-frame setup is mounted to a breadboard orreaction base along with the dual linear motors The use of the U-frame setupconverts the forces at two loading points into a moment applied to the rod speci-men The rod is coupled to the U-frame using two rigid sleeves or grips A com-pliant layer made of cast epoxy is used between the grips and the rod to protectthe rod specimen from any contact damage The deformation of the rod is mea-sured by three LVDTs; using three LVDTs eliminates the effect of the epoxy layer

on the deformation measurement, which would be significant if a single LVDTwere used The main components of the testing system are shown inFig 1alongwith the installed rod specimen that is located ahead of three LVDT probes, asindicated by the arrow The sign designation of the curvature used in this study

is shown inFig 2

SPECIMEN PREPARATION

The model material for claddings is SS 304 tubes with an inner diameter (ID) of9.708 mm, outer diameter (OD) of 11.07 mm, and length of 152.40 mm SS claddings

FIG 1 (a) U-frame setup integrated to Bose dual LM2 TB and (b) the enlarged view of the specimen section with three LVDTs mounted to measure the deflections of the rod at three points.

(a)

(b)

with two LVDTs for disp1, disp2 (inside covers)

Three LVDTs to measure deflections of rod

are prepared from commercial SS 304 tubes purchased from McMaster-Carr.5Theoriginal OD and ID are modified using turning and reaming Model fuel pellets areshort alumina cylinders 9.53 mm in diameter and 15.24 mm in length, preparedfrom high-temperature nonporous alumina rods also purchased from McMaster-Carr The model materials for SNF rod components and the geometrical sizes ofcladdings and pellets are selected to simulate the SNF rod specimens in hot-celltests [4].

The pellet–cladding interface (PCI) and pellet-pellet interface (PPI) are filledwith cast epoxy (3M DP420, MN) The same epoxy is used in mounting the gripsonto the rod A 24-h curing period generally is needed to allow the epoxy used inthis study to reach full strength A schematic showing the structure of the surrogaterod is given inFig 3

TESTING PROCEDURE

Both monotonic testing and reversed cyclic testing are performed The monotonictesting is conducted under displacement control The displacement of each motor isset at a rate of 0.2 mm/s to 10.00 mm and back to 0 mm at the same rate

The fully reversed cyclic testing consists of measurements and cycling Themeasurements are conducted at various numbers of cycles using three cycles of0.05-Hz sine waves at predetermined amplitudes The cycling is conducted underload control using a 5-Hz sine wave The selection of load amplitudes for cycling is

FIG 3 Schematic showing model rod when (a) uncapped and (b) capped (Drawing is

not to scale.) PCI ¼ pellet-to-cladding interface; PPI ¼ pellet-to-pellet interface;

based on the results of the monotonic test Finally, the cyclic test stops wheneverthe following events occur: (1) the disp1 or disp2 is out of predetermined limits(64 to 66 mm) or (2) the cycle number exceeds one or two million.

After the fatigue tests, all specimens are examined using an optical microscope(Nikon Nomarski Measure Scope MM-11, Tokyo, Japan), and then fractography isconducted on the selected specimens

where h is the sensor spacing, 12 mm The curvature generated by compressive loads

is designated as negative, and the curvature generated by tensile loads is designated

as positive (Fig 2) As a result, the tension is on the y side (below the neutral axis)for a negative curvature and on the þy side (above the neutral axis) for a positivecurvature

The moment-curvature loop or M-j loop (Fig 5) can be characterized by momentrange DM and curvature range Dj, flexural rigidity R, and flexural hysteresis UM Thelatter two are defined byEqs 3and4:

FIG 5 Quantities used in the characterization of the moment-curvature (M-j) loop.

DM

U M = ∫ Mdk

Dk

being mainly associated with the energy dissipation attributed to the damages to therod induced by cyclic loading.

Experimental Results

STATIC TESTS

Two surrogate rods (#19 and #20) are monotonically loaded according to theprocedure suggested in the previous section, and both survive loading to themaximum displacement without failure The load and deflection data are proc-essed using Eqs 1and2; the M-j plots obtained for the two rods are similar toeach other, as shown inFig 6 The plots usually begin with a linear response andthen exhibit a nonlinear response starting from approximately 25 Nm (C) A de-tailed examination indicates a slight slope change around 10 Nm (B) Apparently,neither rod attains the ultimate strength of the materials at the maximum curva-ture (D) The subsequent unloading reveals a slope similar to that of the secondlinear stage of the plots and a significant amount of residual curvature (E) Thetransient point from the linear to the nonlinear stage is significant because it sig-nifies that an important damage mechanism has been activated These resultsprovide original input to the selection of load amplitude in the cyclic bendingtests The M-j responses reveal that the surrogate rods, including the variouscharacteristic points and large residual curvature tested, in fact resemble those

FIG 6 Moment-curvature (M-j) curves based on monotonic loading where the characteristic points are labeled.

A C

D

B

E

observed in the testing of SNF [7]; thus they partially justify the use of the posed surrogate rods to investigate SNF fatigue in the equivalent loading condition.

pro-CYCLIC TESTS

Three moment amplitudes are selected for the reversed cyclic bending tests: 20.32,25.40, and 30.48 Nm Three or five rods are tested at each of these amplitudes.Three rods (#13, #21, and #26) tested at 20.32 Nm survive more than 2.6  106cycles without failure All other rods are tested to failure and, as expected, the num-ber of cycles to failure depends on the moment amplitudes, as shown inFig 7

Online monitoring is enabled to capture the variation in curvature during ing Measurement data sets are acquired when a test reaches a designated number

test-of cycles and is interrupted However, the following discussion will focus more onthe data obtained from online monitoring The fatigue responses for flexural rigidi-

ty and hysteresis based onEqs 3and4are given inFig 8

The fatigue life of the rods depends on their initial condition and the level ofmoment amplitude applied As can be seen, there is a large variation in the condi-tion of the rods, as measured by the pre-fatigue rigidity For example, the initial ri-gidity level for the rods tested at 20.32 Nm vary widely between 80 and 95 Nm2 Asimilar degree of variation is found for other amplitudes The curvature at cyclezero generally cannot be captured during a test, so the initial rigidity is evaluated

FIG 7 Moment amplitude as a function of cycles or cycles to failure Tests stopped

with no failure (#13, #21, and #26) are indicated by arrows The prediction line is based on the damage model, as will be discussed in the later section on fatigue

at the low cycle numbers, such as cycle number one The variations in the initialcondition of the rods are associated with the materials and the preparation of therod specimens Nevertheless, the range of initial flexural rigidity obtained is similar

to the effective rigidity estimated based on the contributions of the components of

FIG 8 Variations in (a) flexural rigidity and (b) flexural hysteresis as a function of cycle number Moment amplitudes are shown.

25.40 Nm

the rods (cladding and pellets) [4] It is observed that the degradation rate of therigidity depends on the level of moment amplitude A higher moment means amore significant degradation, as expected At a lower level, such as 20.32 Nm, thedecreasing trend is quite appreciable, even though large local fluctuations areinvolved.

It is interesting to see that the flexural hysteresis usually is quite noticeable inthe pre-fatigue stage, even at a moment as low as 20.32 Nm This should be under-standable because such a level of moment is nonetheless higher than at the criticalpoint (B) where the slope of the M-j curve changes The subsequent cycling isshown to have enhanced the level of flexural hysteresis A larger moment corre-sponds to a more significant enhancement of the hysteresis A correlation is clearlyseen between the decrease in flexural rigidity and the increase in flexural hysteresis,

as illustrated inFig 9

For the rods tested to failure, the failure usually occurs near a PPI It is apparentthat there is a substantial stress concentration within the SS cladding arising fromthe pellet cladding mechanical interaction (PCMI) near the PPI It is the stress con-centration that induces cracking of the SS cladding The crack initiation sites areseen near the maximum stress points over the cross-sections of the bending rodsand can be located at either the internal surface (#11) or the external surface of thecladding (#23), as shown inFig 10 Obviously, a detailed microstructure of initiationsite cannot be obtained using the optical microscope at such magnification but

FIG 9 Relationship between flexural rigidity and flexural hysteresis obtained by

reversed cyclic bending tests.

30.48 Nm

25.40 Nm 20.32 Nm

needs an advanced analysis such as scanning electron microscopy On the externalsurface of rod #23, the cracking initiation site is found to align with the machiningmarks quite well, indicating a machining flaw is the origin of failure However, notethat the internal surface initiation of cracking is not necessarily related to low-moment cycling, nor is the external surface initiation related to intermediate orhigh-moment cycling In fact, if the stress intensity factor amplitude of a flawexceeds a threshold value of the cladding material [10], that flaw will be activated topropagate; the location of the potential flaws are mostly a result of material fabrica-tion processes Cracking can also be seen near the two maximum-stress areas onthe end face of the alumina pellet The debris resulting from the locally crushed alu-mina can be observed near the cracking initiation site on the SS cladding.

Note that the PPI-dominated failure and the role of PCMI in the failure of ding revealed in this study are very similar to those observed in SNF rods in hot-cell tests [7] The similarity of the failure modes between surrogate rods and realSNF rods is another important proof of the feasibility of using surrogate rods tostudy the fatigue failure mechanism and fatigue life prediction in SNF rods

clad-Discussion

FATIGUE DAMAGE CHARACTERIZATION

Fatigue damage in composites can be modeled using the reduction in stiffness Thestiffness is characterized in different ways: a modulus term based on a stress/strain

FIG 10 (a) Crack initiation site, as indicated by the arrow near the internal surface of the cladding for rod #11 tested under 620.32 Nm N f ¼ 6.78  105cycles;

magnification 40 (b) Crack initiation site as indicated by the arrow on the external surface of the cladding for rod #23 tested under 625.40 Nm,

graph [11] or a fatigue modulus based on the resultant strain at the applied stresslevel [12] For the surrogate rods—in which the structural heterogeneities such asPPIs, PCIs, and the pellets themselves are at the same scale as the rods—the charac-terization of the fatigue-damaged rod, D, can be described in terms of flexural rigid-ity R as follows:

Several damage models have been proposed for the composite structures[13–16] Our experimental observation shows that, for the surrogate rods, D can beexpressed effectively as a power law function of cycle number N,

where aij(i,j ¼ 1,2) are the secondary curve-fitting parameters, and the subscripts i, jrepresent the fitting for the primary parameters in Eq 9 The relation of the initialdamage value, as measured by a2, to the moment inEq 10bexists because the rigiditydepends upon the moment once loading enters into the nonlinear stage (Fig 6) In thelatter case, a higher moment means a lower rigidity R0and a lower level of initial fa-tigue damage, according toEq 7