Wei | Nikbin | McKeighan | Harlow Fatigue and Fracture Test Planning, Test Data Acquisitions and Analysis ASTM INTERNATIONAL Helping our world work better www.astm.org ASTM International ISBN: 978-0-8031-7639-3 Stock #: STP1598 ASTM INTERNATIONAL Selected Technical Papers Fatigue and Fracture Test Planning, Test Data Acquisitions and Analysis 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 bibliographical references Identifiers: LCCN 2017000407 | ISBN 9780803176393 (pbk.) Subjects: LCSH: Materials Fatigue Classification: LCC TA418.38 F364 2017 | DDC 620.1/1260724 dc23 LC record available at https://lccn.loc.gov/2017000407 ISBN: 978-0-8031-7639-3 Copyright © 2017 ASTM INTERNATIONAL, West Conshohocken, PA All rights reserved This material may not be reproduced or copied, in whole or in part, in any printed, mechanical, electronic, film, or other distribution and storage media, without the written consent of the publisher Photocopy Rights Authorization to photocopy items for internal, personal, or educational classroom use, or the internal, personal, or educational classroom use of specific clients, is granted by ASTM International provided that the appropriate fee is paid to the Copyright Clearance Center, 222 Rosewood Drive, Danvers, MA 01923, Tel: (978) 646-2600; http://www.copyright.com/ The Society is not responsible, as a body, for the statements and opinions expressed in this publication ASTM International does not endorse any products represented in this publication Peer Review Policy Each paper published in this volume was evaluated by two peer reviewers and at least one editor The authors addressed all of the reviewers’ comments to the satisfaction of both the technical editor(s) and the ASTM International Committee on Publications The quality of the papers in this publication reflects not only the obvious efforts of the authors and the technical editor(s), but also the work of the peer reviewers In keeping with long-standing publication practices, ASTM International maintains the anonymity of the peer reviewers The ASTM International Committee on Publications acknowledges with appreciation their dedication and contribution of time and effort on behalf of ASTM International Citation of Papers When citing papers from this publication, the appropriate citation includes the paper authors, “paper title,” STP title, STP number, book editor(s), ASTM International, West Conshohocken, PA, year, page range, paper doi, listed in the footnote of the paper A citation is provided on page one of each paper Printed in Mayfield, PA April, 2017 Foreword THIS COMPILATION OF Selected Technical Papers, STP1598, Fatigue and Fracture Test Planning, Test Data Acquisitions and Analysis, contains peer-reviewed 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 Contents vii Overview Establishing a Multi-Laboratory Test Plan for Environmentally Assisted Fatigue 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 Cyclic Bending Hong Wang and Jy-An John Wang 19 Low Cycle Fatigue of Cast Austenitic Steel Xijia Wu, Guangchun Quan, and Clayton Sloss 37 Fracture Mechanical Testing of In-Service Thermally Aged Cast Stainless Steel Martin Bjurman, Björn Forssgren, and Pål Efsing 58 Calorimetric Studies and Self-Heating Measurements for a Dual-Phase Steel Under Ultrasonic Fatigue Loading Noushin Torabian, Véronique Favier, Saeed Ziaei-Rad, Justin Dirrenberger, Frédéric Adamski, and Nicolas Ranc 81 Fatigue Studies on Impacted and Unimpacted CFRP Laminates Raghu V Prakash, Mathew John, Deepika Sudevan, Andrea Gianneo, and Michele Carboni 94 Application of Kresidual Measurements to Fracture Toughness Evaluations Gongyao Wang, Kimberly Maciejewski, and Mark James 119 Sensitivity Study on Parameters that Influence Automated Slope Determination Stephen M Graham 133 Contribution to the Evaluation of Stress-Strain and Strain-Life Curves Michael Wächter and Alfons Esderts 151 v Methods Development for Nonlinear Analysis of Fatigue Data Bruce A Young, Richard C Rice, Steven R Thompson, and Doug Hall 186 Data Processing Procedure for Fatigue Life Prediction of Spot-Welded Joints Using a Structural Stress Method Hong-Tae Kang, Xiao Wu, Abolhassan K Khosrovaneh, and Zhen Li 198 More Accurate Elastic Compliance Equation and Its Inverse Solution for Compact Specimens Xian-Kui Zhu 212 A Novel Nonlinear Kinematic Hardening Model for Uniaxial/ Multiaxial Ratcheting and Mean Stress Relaxation Hao Wu and Zheng Zhong 227 Fatigue Damage Indicators Based on Plastic Deformation Grzegorz Socha 246 A Fatigue Failure Mode Transition Criterion for Sizing Load-Carrying Fillet-Welded Connections Shizhu Xing and Pingsha Dong 258 Analysis of Nonproportional Multiaxial Fatigue Test Data of Various Aluminum Alloys Using a New Damage Parameter Jifa Mei and Pingsha Dong 278 A Theory for Mathematical Framework and Fatigue Damage Function for the S-N Plane Hoda Eskandari and Ho Sung Kim 299 Verification and Validation of Accelerated Testing Methods for Fatigue Life Assessment Limin Luo, Jason Hamilton, Zhigang Wei, and Robert Rebandt 337 Load Spectrum Test and Fatigue Failure Study of High-Speed Train Carbody Anti-Yawing Seat Wenjing Wang, Jinyi Bai, Sichun Li, Hongwei Zhao, and Weiguang Sun 359 Practical and Technical Challenges of the Exhaust System Fatigue Life Assessment Process at Elevated Temperature Mark T Seitz, Jason D Hamilton, Richard K Voltenburg, Limin Luo, Zhigang Wei, and Robert G Rebandt vi 371 Overview ASTM STP1598 contains a collection of 20 peer-reviewed papers from the Symposium 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 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 StrainLife (ε-N) Fatigue Data Understanding and preventing fatigue failure and fracture of engineering materials and structures are critical in several industries Material testing is fundamental to gaining a better understanding of fatigue and fracture phenomena, as well as to guide materials selection, product design, and quality control In fact, engineering 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 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 symposium: 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, managers, researchers and scholars worldwide to exchange ideas, share best practices, vii discuss challenges, and identify opportunities and directions for future developments and applications Specific objectives include: 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 RaviChandar (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 respective 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 attentiveness 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 viii FATIGUE AND FRACTURE TEST PLANNING, TEST DATA ACQUISITIONS AND ANALYSIS STP 1598, 2017 / available online at www.astm.org / doi: 10.1520/STP159820160047 Matthias Bruchhausen,1 Kevin Mottershead,2 Caitlin Hurley,3 Thomas Me ´tais,4 Roma´n Cicero,5 Marc Vankeerberghen,6 and Jean-Christophe Le Roux7 Establishing a Multi-Laboratory Test Plan for Environmentally Assisted Fatigue Citation Bruchhausen, M., Mottershead, K., Hurley, C., Me ´tais, T., Cicero, R., Vankeerberghen, M., and Le Roux, J.-C., “Establishing a Multi-Laboratory Test Plan for Environmentally Assisted Fatigue,” 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 1–18, http://dx.doi.org/10.1520/STP1598201600478 ABSTRACT The European project INCEFA-PLUS will characterize environmental fatigue in pressurized water reactor (PWR) conditions The aim is to develop new guidelines for assessing environmental fatigue damage susceptibility of nuclear power plant (NPP) components The consortium consists of 16 public and private organizations from across Europe The project is structured in two phases: The first phase is an extensive fatigue testing program; in the second phase, a procedure for estimating the environmental fatigue degradation of the materials will be formulated During the test phase, a selection of austenitic stainless steels Manuscript received February 29, 2016; accepted for publication September 15, 2016 European Commission, Joint Research Centre, Westerduinweg 3, 1755 LE Petten, The Netherlands Amec Foster Wheeler, Clean Energy, Europe, Walton House, Birchwood Park, Birchwood, Warrington, Cheshire WA3 6GA, United Kingdom VTT Technical Research Centre of Finland Ltd., Espoo, 02044 Finland http://orcid.org/ 0000-0003-4810-1997 EDF-DIPNN SEPTEN, 12-14 Avenue Antoine Dutrie`voz, 69628 Villeurbanne, France Inesco Ingenieros, 39005 Santander, Spain SCK CEN, Nuclear Materials Science Institute, Boeretang 200, B-2400 Mol, Belgium EDF-R & D, Materials and Mechanics of Components Dept., Avenue des Renardie`res-Ecuelles, 77818 Moret Sur Loing Cedex, France ASTM Symposium on Fatigue and Fracture Test Planning, Test Data Acquisitions and Analysis on May 4–5, 2016 in Grand Hyatt, San Antonio, TX C 2017 by ASTM International, 100 Barr Harbor Drive, PO Box C700, West Conshohocken, PA 19428-2959 Copyright V 382 STP 1598 On Fatigue and Fracture Test Planning, Test Data Acquisitions and Analysis should be considered in addition to the other factors mentioned earlier Once all of these factors are identified, quantified, and applied to the RLDA load or strain data, the rainflow cycle counting can be performed with the help of the linear Miner’s damage rule Miner’s rule predicts that failure occurs when damage is greater than or equal to one Two safety factors can be used to evaluate the margin of safety: the load safety factor and the cycle safety factor Fig schematically shows the safety factors as obtained by comparing the design curve (R90C90) as obtained from the bench test and the damage curve as obtained from the RLDA analysis Consideration of Temperature Effects in Product Validation The following four fundamental technical issues are investigated in this section: (1) development of a thermal modification factor for both load-based and strainbased cold testing, (2) a load transformation technique to convert the variable loading data under variable temperature environment into an equivalent series of loading data at a reference temperature, (3) an interpretation of the damage mechanism under the combined variable loading and temperature, and (4) the development of “equivalent” temperatures for hot testing These four issues are the fundamental technical barriers to the development of cold testing and hot testing for vehicle exhaust products as well as for other products with similar loading and temperature conditions THERMAL MODIFICATION FACTOR FOR COLD TESTING The purpose of introducing a thermal modification factor is to allow engineers to evaluate fatigue damage using material properties at room temperature, with RLDA FIG Safety factors as obtained by comparing the design curve (R90C90) as obtained from the bench test and the damage curve as obtained from the RLDA analysis SEITZ ET AL., DOI 10.1520/STP159820160084 and DWC being conducted at room temperature, while the system experiences simultaneously the vibratory and thermal loads in the field [1] Hence, compensation for temperature’s effect on the exhaust components is needed In damage calculations, the measured load or strain history are multiplied by the thermal modification factor KC for further rainflow counting and damage assessment Because fatigue life is very sensitive to the load or strain level, the accuracy in KC estimation is critically important Procedures for determining the thermal modification factors are developed and reported here for both load-based and strain-based cold-testing methods In these procedures, the component bench tests under the same load are conducted and the geometrical mean of the fatigue cycles to failure at the room temperature and the operating temperature or the equivalent temperature are compared and used to calculate the thermal modification factor The load-based method is straightforward, whereas the strain-based method is more convoluted because of the involvement of the strain amplification effects, which reflects the relationship between the measured strain in the location and the equivalent strain in terms of the unnotched base material at the failed notch location Load-Based Thermal Modification Factor The development of the thermal modification factor KCP for the load-based method can be best reflected in Fig 9, which basically shows the linear relationship between the applied load range DP and the cycles to failure Nf at different temperature levels in a log-log plot The curves at different temperature levels are parallel to each other for simplicity purposes and that is usually a good approximation for most engineering materials Additionally, the fatigue life is usually a decreasing function of FIG Thermal modification factor for the load-based cold testing 383 384 STP 1598 On Fatigue and Fracture Test Planning, Test Data Acquisitions and Analysis temperature at the same applied loads, so that the curves go downward as temperature increases The procedure for estimating the thermal modification factor for the loadbased method can be stated as follows: Conduct cold (at room temperature TR ) component bench test at a load level and record the geometrical mean of the cycles to failure, NfR , which is the cycle vertically projected onto the logðNÞ axis from Point A shown in Fig Conduct hot (at an equivalent constant temperature TE or with a hightemperature profile) component bench test at the same load level and record the geometrical mean of the cycles to failure, NfE , which is the cycle vertically projected onto the logðNÞ axis from Point B shown in Fig Calculate the distance between the two geometrical means of the cycles to failure: jABj ¼ log NfR log NfE Project Point B onto the load-life line at the room temperature TR and Point C is formed; calculate the distance between the two geometrical means of the loads: kP ¼ jBCj ẳ logDPE ị logDPR ị, which can be calculated from the existing mean load-cycle curve generated from a two-load level test or estimated when the slope b of the curve is known in advance, and the formula kP ¼ jBCj ¼ bjABj b ¼ 1=3 is often assumed for steels The load-based thermal modification factor is finally calculated as KCP ¼ 10kP The following two aspects should be noted First, Step-1 through Step-5 is the basic procedure for obtaining a load-based thermal modification factor In practice, a thermal modification factor from two different load levels can be estimated based on the same procedure Then compare the two factors obtained, and the factor with a larger value can be used for conservative purposes Second, the procedure drawn from Step-1 through Step-5 and the geometrical relationship shown in Fig indicates that DPE ¼ KCP DPR , but it does not explicitly indicate how to modify the loading data PðtÞ based on the obtained thermal modification factor KCP However, it should be noted that the definitions of the load range at room temperature and the equivalent temperature are DPR ¼ PRP PRV and DPE ¼ PEP PEV , respectively Clearly, DPE ¼ KCP DPR can be directly obtained from PEP ¼ KCP PRP and PEV ¼ KCP PRV The subscripts P and V represent the peak and the valley in a cycle Strain-Based Thermal Modification Factor A similar thermal modification factor procedure can be developed for the strainbased method This method requires both the measured strain at the location near the notch (5–10 mm away) and the fatigue strain-cycle (E-N) of the un-notched material However, there are two important differences between the load-based method and the strain-based method First, the fatigue E-N curves are usually not linear because both low-cycle and high-cycle fatigue data are collected The total strain approach is often used to unify the low-cycle and the high-cycle data, which can be described using elastic SEITZ ET AL., DOI 10.1520/STP159820160084 strain-life and the plastic strain-life, respectively The elastic strain and plastic strain are measured or estimated from a stable cyclic stress-strain hysteresis loop [8] Traditionally, the elastic strain-cycle and the plastic strain-cycle are usually described using the Woăhler curve for high-cycle fatigue and the Manson-Coffin curve for low-cycle fatigue The nonlinear behavior of the total strain range cycles to failure in a log-log plot is schematically shown in Fig 10 Even though the curves are nonlinear, the strain-based thermal modification factor can still be easily calculated as KCe ¼ 10ke , which is similar to the formulae used in the load-based method The only difference is that Point C is obtained by nonlinear extrapolation rather than linear extrapolation as is the case with the load-life curve Second, a significant difference of the strain-based approach from the loadbased method is that a strain amplification effect has to be introduced to link the measured strain and the strain at the weld notch, which is supposed to be approximately represented by the strain-cycle data of the material in terms of fatigue life It should be noted that the failure often occurs in either the welds or the heat-affected zones, which cannot be directly measured Instead, the strain is often measured at a location that is about mm to 10 mm away from the welded notch Fig 11 schematically shows the failure location and the location where the nominal strain is measured In order to quantify the strain amplification effect, the strain amplification factor (SAF) is defined in this paper, and the analysis of elastic-plastic stress-strain relationship is required to find the solution Fig 12 schematically shows the relationship between the cyclic stress and strain It is assumed that the same stress-strain FIG 10 Thermal modification factor for strain-based cold testing 385 386 STP 1598 On Fatigue and Fracture Test Planning, Test Data Acquisitions and Analysis FIG 11 Schematic of the locations where the nominal strain is measured and where failure occurs due to the equivalent local strain relationship is applicable to the base material and the welds It should be noted that welds and their heat-affected zones have different properties than the parent or base material, but in practice, the latter is often used as far as the linear elastic FIG 12 The representation of the SAF Ke in the cyclic stress-strain curve SEITZ ET AL., DOI 10.1520/STP159820160084 mechanical behavior is concerned The simplest definition of the SAF can be expressed in Eq 2: Kf ¼ e=e: (2) Again, e is the strain measured using a strain gage, and e is the local strain, from which the associated strain range De can be estimated by the total strainbased strain-cycle as expressed in Eq [8]: De ¼ ef d c 2Nf ỵ 2ef 2Nf E (3) where rf and ef are the fatigue strength coefficient and fatigue ductility coefficient, and d and c are the fatigue strength component and fatigue ductility exponent Nf is the number of cycles to failure, which is obtained from the fatigue bench test The factor Kf is often determined from a specific SAF determination test with a certain load and a certain temperature but applied to the RLDA with various loads and temperatures It should be noted that Kf is generally a function of both loading amplitude and operating temperature The amplitude effects on the value of the amplification factor are schematically illustrated in Fig 12, which shows a cyclic elastic-plastic stress-strain curve The cyclic stress-strain curve shows a linear elastic part and a nonlinear plastic part Without losing generality, it is assumed here that the measured strain is elastic in the analysis Based on the relative strain severity during real RLDA loading and the SAF test, the following four scenarios can be created: • Scenario-I: The equivalent strain at the notch under SAF loading and RLDA loading are all located in the elastic domain, say Kf ¼ e1 =e1 ¼ Kf 1 , as shown in Fig 12 • Scenario-II: The equivalent strain at the notch under SAF loading is elastic but that under RLDA loading is plastic, Kf ¼ e2 =e2 ẳ Kf 2 ã Scenario-III: The equivalent strain at the notch under SAF loading is plastic but that under RLDA loading is elastic • Scenario-IV: The equivalent strains at the notch under both SAF loading and RLDA loading are plastic For Scenario-I, as long as the equivalent strain at the notch is in the elastic range, the SAF will be a constant Therefore, to estimate the equivalent strain experienced at the weld notch, the RLDA load can simply be modified by multiplying the measured strain history with the single SAF In this case, Kf ¼ e1 =e1 can also be called the strain proportionality factor Clearly, Scenario-I is preferred in terms of testing and analysis because of its linearity In Scenario-II, the strain at the notch under the RLDA is underestimated because Kf is calibrated in the elastic domain In the plastic part, the plastic strain increases more drastically than the stress or load Clearly, the damage estimated from Scenario-II is non-conservative ScenarioIII is just the opposite of Scenario-II, and the predicted damage from RLDA would be over-conservative Scenario-IV is more complex, and the conservativeness depends on the details of the RLDA loading and the SAF calibration 387 388 STP 1598 On Fatigue and Fracture Test Planning, Test Data Acquisitions and Analysis It should be noted that the conversion between stress range and amplitude should be performed correctly Finally, it is noted that the SAF is different from the notch factor as defined in Neuber’s rule and other similar definitions, which deals with the relationship between the notched specimen and the separate un-notched specimen [17,18] Overall, for the strain-based method, the stain amplification factor and the thermal modification factor can be combined to form a new factor, K ¼ KCe Kf , which can be used for RLDA data modification and eventual damage and life assessment LOADING TRANSFORMATION USING DAMAGE EQUIVALENCY PRINCIPLE If the temperature variation is not significant and the material fatigue behavior is not very sensitive to temperature, a specific temperature level can be approximately used for both temperature response characterization and rainflow counting The hanger rods at bends and the brackets on body sides in a vehicle exhaust system are such examples However, for some of the exhaust applications with variable temperatures, the use of the isothermal assumption can lead to significant errors—in particular for the pipes that have direct contact with the gas flow For anisothermal fatigue, the preferred approach in the automotive industry is to use the fatigue curves obtained from isothermal tests at several different temperature levels Then, the temperature in question is interpolated from the tested fatigue curves However, a critical issue in life assessment of anisothermal applications is how to count the cycles for the loads with a superimposed variable temperature profile In order to take the temperature effect into account, several methods have been proposed to handle the temperature variation [19,20] In these methods, the maximum temperature over the duration of the fatigue cycle is determined for a given cycle to make the life assessment conservative; hence, the worst-case scenario is actually considered An effective cycle-counting procedure has been recently proposed [21] for loading data under variable amplitude temperature and mechanical loadings The procedure first converts the loading data to an equivalent form at a reference temperature using the damage equivalency principle This can be done by simply multiplying a temperature-dependent factor to account for the temperature effect Subsequently, the standard rainflow counting method can be used to count the cycles The key to the procedure is briefly described as follows For a fatigue event under constant stress range Dri and constant temperature Ti , fatigue damage D accumulated in a cycle can be expressed as Eq 4: DẵDrTi ị ẳ Nf ẳ Dri ịm f ðTi Þ (4) where Ti is a temperature-dependent constant and f Ti ị is a temperature-related function; m ẳ 1=b and b is defined in Eq The subscript i represents the temperature level i; f ðT Þ function in power law and Arrhenius forms are often [21] The used 1=m S-N curve corresponding to this is Nf ¼ Drịm f T ị1 or Dr ẳ Nf f T Þ1=m SEITZ ET AL., DOI 10.1520/STP159820160084 By applying the damage equivalency principle and under the isothermal assumption, constant stress range Dri at temperature Ti can be transformed into the temperature level i associated stress range DrRi at the reference (R) temperature TR Then, the damage equivalency DẵDrTi ị ẳ DẵDrTRi ị can be expressed in Eq 5: Dri Þm f ðTi Þ ¼ ðDrRi Þm f ðTR Þ (5) DrRi ẳ Dri ẵf Ti ị=f TR ị1=m : (6) or Eq 6: With the help of DrRi ¼ rRiP rRiV and Dri ¼ riP riV , Eq can be derived: rRi ẳ ri ẵf Ti Þ=f ðTR Þ1=m : (7) Subscripts P and V represent the peak and valley in a cycle, respectively Therefore, a loading profile including the peaks, valleys, and any data points in between can be converted to an equivalent form with Eq based on the temperature profile and the reference temperature Similarly, for another fatigue event under constant stress range Drj and constant temperature Tj , based on the equivalency damage principle, the stress range time history can be transformed into an equivalent form at the reference tempera 1=m From, rRi in Eq and rRj , it is clear that the ture TR : rRj ¼ rj f Tj =f ðTR Þ framework of stress transformation at different temperature T are the same Therefore, for a general stress loading profile with variable temperature, the general form of the transformation can be expressed in Eq 8: rR t ị ẳ rt ịg ẵT t ị; TR ẳ rt ịff ẵT t ị=f TR ịg1=m (8) where g ẵT t ị; TR ẳ ff ẵT t Þ=f ðTR Þg1=m With the transformation technique, the original stress history rðt Þ with variable temperature history T ðt Þ can be transformed to stress history rR ðt Þ at a constant reference temperature TR In damage assessment, the rainflow counting can be directly conducted on the transformed loading profile, and the damage can then be calculated from the fatigue S-N curve at the reference temperature Fig 13a schematically shows that transformation of a cyclic loading time history rðt Þ with a constant loading amplitude and stress range Dr ¼ riP riV at a constant temperature Ti into a damage equivalent cyclic loading time with a constant amplitude loading amplitude stress range DrRi ¼ rRiP rRiV at a constant temperature TR This simple and specific example is the one from which Eqs 5–7 are derived The application of the procedure for variable loading profile and a constant temperature is schematically shown in Fig 13b The procedure for both variable loading and temperature profiles is shown in Fig 13c It should be noted that for the r t data at temperature TR , there are infinite sets of DrR that generate the same 389 390 STP 1598 On Fatigue and Fracture Test Planning, Test Data Acquisitions and Analysis FIG 13 Transformation of stress histories into their equivalent form at a reference temperature TR : (a) constant amplitude stress at a constant temperature Ti , (b) variable amplitude stress at a constant temperature Ti , (c) variable stress and temperature histories, and (d) the linear relationship between the original stress input and the resulting equivalent stress output (a) (c) (b) (d) equivalent damage, such as the loading waves as highlighted on the insert shown on the right middle of Fig 13a However, there is only one set of loading waves satisfying the transformation, Eq 7, with the proportional factor g ẵT t ị; TR The unique linear relationship among the original input stress and the output stress at two temperatures Ti and Tj is schematically shown in Fig 13d DAMAGE MECHANISMS UNDER COMBINED VARIABLE LOADING AND TEMPERATURE The damage accumulation under variable load (stress) and temperature can be understood by studying the stress-temperature diagram shown in Fig 14a, in which SEITZ ET AL., DOI 10.1520/STP159820160084 FIG 14 (a) The loading path represented in a stress-temperature diagram, (b) stress variation caused by temperature change, and (c) the equivalent stress due to the temperature variation (b) (a) (c) a half-cycle is presented with several possible loading paths Without losing generality, we assume that r2 > r1 and Tj > Ti In practice, the loading-path dependency of the damage is essentially unknown Theoretically, as well as being shown as follows, the path dependency seems to have intrinsic characteristics of the variable load and temperature Among infinite loading paths, the following three typical loading paths are the most significant in both mechanisms’ description and mathematical operation: (1) Path-I: the loading path ABD, (2) Path-II: the loading path ACD, and (3) Path-III: the straight path AD Path-I undergoes a temperature increase (i.e., the path AB) at a constant stress before it undergoes a stress increase Dr ¼ r2 r1 at the temperature Tj (i.e., the path BD) The Path-II has a similar loading path but in an opposite order: stress increase Dr ¼ r2 r1 (path AC) at the temperature Ti , followed by a temperature increase DT ¼ Tj Ti (path AB) For both Path-I and Path-II, the stress change part at a constant temperature can be well-described by the isothermal fatigue theory, in which a fatigue S-N curve is sufficient to describe the fatigue behavior However, the fatigue damage caused by temperature change at a given stress is different from the deformationbased mechanism and requires further data collection to build up a new database 391 392 STP 1598 On Fatigue and Fracture Test Planning, Test Data Acquisitions and Analysis Fig 14b illustrates the transformed stress profile as obtained from the transforma- tion technique and the variable temperature profile Path-III shows a combined and simultaneous temperature and stress increase, and it is more representative of the cases as experienced in real applications Scenario-III will be used here to demonstrate the effects of the combined variable stress and temperature on the damage accumulation Based on Eq and Eq 6, the damage per cycle at temperature Ti and Tj is DðTi Þ ¼ ðDrÞm f ðTi Þ and D Tj ¼ ðDrÞm f Tj , respectively The accumulated damage per cycle D ¼ ðDrÞm f ðT Þ can be considered as a result of the integration of a damage growth rate over the domain [0, Dr] Similar treatment has been studied for fatigue crack growth [22,23] The differential form of the damage growth rate at a constant temperature T can be written as: dD ẳ mDr ịm1 f T ị: dr (9) Integrating Eq 9, with D ¼ at r ¼ 0, leads to D ẳ Drịm f T ị at r ¼ Dr To investigate the loading path effect, the power law f T ị ẳ T c and c ¼ is assumed in this study From f ðT Þ ¼ T c , it can be seen that c > indicates an increased damage rate with temperature and that is usually the case for fatigue at elevated temperature From Fig 14a, it is found that the temperature and the stress increment are not independent, rather there is a linear relationship that can be expressed as in Eq 10: Tj Ti T¼ (10) r þ Ti Dr Clearly, T ¼ Ti when r ¼ and T ¼ Tj when r ¼ Dr; therefore, the new crack growth equation under the combined stress and temperature loading can be expressed in Eq 11: dD m Tj Ti Dr ịm ỵ mT1 Dr Þm ¼ (11) Dr dr Integrating Eq 11 with D ¼ at r ¼ leads to: mTj ỵ Ti D ẳ Drịm mỵ1 (12) at r ẳ Dr When Ti ¼ Tj , Eq 12 is reduced to the damage per cycle at a constant m m temperature; when mTi < Tj , D DT ẳ Ti ị ẳ mỵ1 Drị Tj Ti > and D D T ¼ Tj ¼ ðDrÞ Ti Tj < Therefore, the damage caused by the linear path is between that caused by the same stress range at the highest temperature and that caused by the same stress range at the lowest temperature The damage mechanism under the combined variable load and temperature can be schematically shown in Fig 14c According to Miner’s.linear damage rule, the damj age caused by a stress range Dr at Ti and Tj are Di ¼ Nfi and Dj ¼ Nf , respecj tively; Dj > Di because Nf < Nfi , as shown in the logðDrÞ logðNÞ curve; see Point A SEITZ ET AL., DOI 10.1520/STP159820160084 and Point B in Fig 14c According to Eq 12 and Fig 14c, the variation in temperature at ij ij the same stress range results in a new cycles to failure Nf , damage Dij ¼ Nf , and Dj > Dij > Di Based on the loading transformation technique shown earlier, the equivalent stress ranges will be DrRi and DrRj , at the reference temperatures Ti and Tj , respectively Both transformed stress ranges result in the same damage at their respective reference temperatures because they are equivalent according to the load transformation technique as described in the earlier section on the thermal modification factor for cold testing DEVIATION OF “EQUIVALENT” TEMPERATURE FOR HOT TESTING In hot testing, the ideal scenario would be that the tests are conducted at a wide range of temperature levels to accurately interpret the temperature effects However, hot RLDA, hot calibration, and hot bench testing are expensive and time consuming In order to reduce the cost, the amount of tests needs to be reduced The temperature profile from RLDA is predetermined, and it is unique for a run for a given vehicle, operating condition, and road condition Definitely, different runs will result in different loading profiles, which are random and can be described in a statistical manner Hot calibration at different temperatures is relatively easy Hot component bench testing is the area where the testing cost could increase It would be costly and time consuming to test at two and more than two temperature levels because 13 component tests need to be conducted at each temperature level Therefore, testing at a single temperature level is preferred Then, which temperature should be used? Room temperature definitely would not be considered because it does not reflect the hot RLDA characteristics The peak temperature can reflect the hot RLDA behavior but it would be over-conservative Therefore, an “equivalent” temperature concept would be helpful Clearly, the equivalent temperature should be derived from the damage equivalency principle An equivalent temperature can be described by equalizing the damage values made by the load data at variable temperatures for a given period of time and the damage by the same loading at a constant “equivalent” temperature for the same given period of time Because the damage accumulation for a load with variable temperature has been determined from the equivalent damage principle, as shown earlier, the damage can be calculated using the Miner’s linear damage rule for the calculated cycles for different ranges using the rainflow counting and the fatigue S-N database at various temperatures Generally speaking, the equivalent temperature is not necessarily a constant It could be a variable temperature as long as the accumulated damage is the same However, a constant temperature is preferred in component bench testing The high-level mathematical formula to determine the equivalent temperature using the damage principle can be expressed as: Dẵrt ị; T t ị ẳ DẵrR t ị; TR t ị ẳ Dẵrt ị; Te (13) The principle is simple and the numerical calculation is trivial and straightforward, but in some simplified cases, some analytical solutions can be obtained 393 394 STP 1598 On Fatigue and Fracture Test Planning, Test Data Acquisitions and Analysis Generally, the temperature and the loading are coupled, and the procedure to find an equivalent temperature has to be determined numerically using Eq 13 A muchsimplified formula can be derived for the special case: the temperature effects are symmetrical with respect to the statistical mean of the load, so that the overall contribution from the load variation at variable temperature conditions can be cancelled out Usually, this assumption can be reinforced with the independent and random load, which means the occurrence of one does not affect the other This is reasonable for some applications—for example, the vehicle vibration is caused by the road condition and the temperature is caused by the engine condition Listed next is a procedure to demonstrate how to derive the equivalent temperature approach for these simplified cases Without losing generality, a constant load is assumed here to simplify the analysis and the load-temperature independency assumption From Eq 4, the damage made during a unit time can be written as dD ẳ DPịm f ẵT t ịndt, with n ẳ N=t0 representing the cycles N per unit time t0 Therefore, the total damage during the Ð Ðt time period of t0 can be integrated as D ¼ dD ¼ 00 DPịm f ẵT t ịndt It should be noted that DP is also a function of temperature T An alternative equivalent temperature profile Te ðt Þ that can make the same amount of damage is expressed in Eq 14: ð De ẳ dD ẳ t0 DPịm f ẵTe t Þndt (14) Assuming that the load and the temperature are weakly dependent on each other and the load range variation is not significant over time, then Eq 14 can be further simplified and it becomes Eq 15: ð t0 f ẵT t ịdt ẳ t0 f ẵTe ðt Þdt (15) Further assuming that the equivalent temperature Te is a constant, the formula can be expressed as: t0 Te ẳ f 1 f ẵT t Þdt (16) t0 where f 1 is the inverse function of f ẵT t ị It should be noted that load-dependent temperature is often used in some applications For example, in low-cycle thermal-mechanical fatigue analysis, Taira [24] recommends the peak temperature as an equivalent temperature if the operating temperature is high enough to cause creep while the mean temperature as an equivalent temperature when the operating temperature is relatively low Examples and Results The following three case studies are used to demonstrate the procedures developed in the previous text section on consideration of temperature effects in SEITZ ET AL., DOI 10.1520/STP159820160084 product validation, with the emphasis on handling of the temperature effects: (1) the estimation of the value of the thermal modification factor for a welded exhaust component at a constant temperature environment, (2) the estimation of the value of a non-welded exhaust component at a variable temperature environment, and (3) the damage calculations from the transformed “equivalent” loading profile at two different reference temperatures and the calculation of load-temperature independent equivalent temperature and load-temperature-dependent equivalent temperature CASE-1: CONSTANT SKIN TEMPERATURE FOR A WELDED GASOLINE EMISSION CONTROL DEVICE Fig 15a shows the test setup of a component bench test for gasoline emission control The component design is the cone-to-pipe structure with a 360 weld connection Test samples are made of 409 stainless steel welded with 409 weld wire The nominal material thicknesses at the crack area are 1.6 mm (cone) and 1.75mm (pipe) The room-temperature component bench test uses a nominal strain of 501 l in/in magnitude Multiple samples are tested and their bench lives result in a mean of 175,035 cycles Fig 15b shows the fatigue failure location at the 360 weld A second batch of samples of the same design are bench tested with the same oscillating load but with a constant skin temperature of 450 C The bench lives in the second test result in a mean of 31,463 cycles Based on the procedure described earlier on the thermal modification factor for cold testing and b ¼ 1=3, the estimated SAF KCP is 1.772 It indicates that, to compensate for the temperature effects, the cold RLDA load data should be multiplied by 1.772 to calculate the damage as would be experienced by the vehicle exhaust during hot operation FIG 15 (a) Component bench test setup of a gasoline emission control device and (b) fatigue crack in the component during the bench test (a) (b) 395