STP 1439 Fatigue Testing and Analysis Under Variable Amplitude Loading Conditions Peter C McKeighan and Narayanaswami Ranganathan, editors ASTM Stock Number: STP1439 ASTM 100 Barr Harbor Drive PO Box C700 West Conshohocken, PA 19428-2959 INTERNATIONAL Printed in the U.S.A Library of Congress Cataloging-in-Publication Data Fatigue testing and analysis under variable amplitude loading conditions/Peter C McKeighan and Narayanaswami Ranganathan, editors p cm. (STP; 1439) "ASTM Stock Number: STP 1439." Includes bibliographical references and index ISBN 0-8031-3479-7 (alk paper) Materials Fatigue Testing Congresses I McKeighan, R C (Peter C.) II Ranganathan, Narayanaswami II1 Series: ASTM special technical publication; 1439 TA418.38.F378 2005 620.1'126'0287 dc22 2005004747 Copyright © 2005 AMERICAN SOCIETY FOR TESTING AND MATERIALS 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 the American Society for Testing and Materials International (ASTM) provided that the appropriate fee is paid to the Copyright Clearance Center, 222 Rosewood Drive, Danvers, MA 01923; Tel: 978-750-8400; online: http://www.copyright.com/ 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 To make technical information available as quickly as possible, the peer-reviewed papers in this publication were prepared "camera-ready" as submitted by the authors 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 Printed in Mayfield, PA May 2005 Foreword The Symposium on Fatigue Testing and Analysis Under Variable Amplitude Loading Conditions was a joint international event conducted by ASTM International Committee E08 on Fatigue and Fracture and the Fatigue Commision of French Metallurgical and Materials society (SF2M) The symposium was chaired by Dr Peter C McKeighan, Southwest Research Institute, San Antonio, Texas, USA and Professor Narayanaswami Ranganathan, Laboratoire de Mrcanique et Rhrologie, University Franqois Rabelais de Tours, Tours, France The symposium was held from 29-31 May 2002 in the prestigeons town hall of the city of Tours (Hotel de Ville) The following two pages show the highlights of the three day symposium The Symposium would not have been as successful as it was without the assistance from the city of Tours, the Ecole Polytechnique (Drpartement Productique), the University of Tours and all of the other kind sponsors There are a number of groups that had a significant impact on the organization of the meeting These groups functioned at a variety of different levels and are described further below INTERNATIONAL SCIENTIFIC C O M M I T E E A Bignonnet (France), A Braun (USA), A Davy (France), A de Koning (Holland), K Donald (USA), G Glinka (Canada), R L Hewitt (Canada), G Marquis (Finland), E Macha (Poland), J C Newman (USA), I Sinclair (UK), C M Sonsino (Germany) and M Thomsen (USA) ORGANIZING COMMITEE Chairmen: P C McKeighan (SwRI, USA), N Ranganathan (LMR, EIT) Members: C Amzallag (EDF), C Bathias (CNAM), G Baudry (Ascometal Creas), A Bignonnet (PSA), J F Flavenot (CETIM), Y Franchot (SF2M), A Galtier (Usinor R&D), G Henaff (ENSMA), M Huther (Bureau Veritas), H P Lieurade (CETIM), J Petit (ENSMA), P Rabbe (CEM), L Remy (ENSM Paris), J Renard (ENSM Paris) LOCAL O R G A N I Z I N G COMMITTEE D Sigli, L Vet, N Ranganathan, D Ouahabi, A Tougui, R Leroy, O Girard, E Meichel, E Lacroix FIG Welcome ~peech by the Mayor of Tours, M Jean Germain, M Ranganathan helps with the translation FIG, Concert by the children's choir FIG Attentive audience FIG Distinguished audience listening to the mayor's ~7~eech m FIG One of the speakers FIG The students of the Polytechnique school who helped with organizing the meeting FIG - - A view of the ceiling of the Historic Town Hall FIG Discussion in the corrido~Dn Pete McKeighan of Tours < Contents Overview xi F A T I G U E T E S T I N G AND L A B O R A T O R Y E X P E R I E N C E Principles of Variable Amplitude Fatigue Design and Testing CETIN MORRIS SONSINO Role of Variable Amplitude Fatigue Standards in Improving Structural Integrity STEPHEN W HOPKINS,MICHAELR MITCHELL,AND J MI~NIGAULT 24 A Framework for a Standardization Effort for Fatigue Crack Growth Testing Under Variable Amplitude Spectrum Loading PETER C MCKEIGHAN 36 AND FRASER J M c M A S T E R Variable Amplitude Fatigue Crack Growth Using Digital Signal Processing Technology J KEITH D O N A L D AND KEN G E O R G E 53 Variable Amplitude Loading on a Resonance Test Facility STEFAN POTING, M A R K U S TRAUPE, J O A C H I M HUG, A N D H A R A L D Z E N N E R 67 Development of a DCPD Calibration for Evaluation of Crack Growth in Corner-Notched, Open-Hole SpecimenS KENNETH GEORGE, HAROLDS REEMSNYDER, J KEITH D O N A L D , A N D R O B E R T J B U C C I 81 AEROSPACE APPLICATIONS The F/A-18E/F Full-Scale Static and Fatigue Test P r o g r a m s - - A n Overview-99 M I C H A E L G S U L L E N T R U P Spectrum Editing for a Full-Scale Fatigue Test of a Fighter Aircraft Wing with Buffet Loading ROY L HEWITT,JAN P WEISS, AND PETER K NOR 113 Large Commercial Aircraft Loading Spectra: Overview and State of the Art LAURENCE LE DIVENAH A N D J E A N - Y V E S BEAUFILS Spectrum Fatigue Testing and Small-Crack Life Prediction Analysis on a Coupon Similar to a Critical Design Detail of a CF188 Hornet Component MARKO YANISHEVSKYAND RICHARDA EVERETT,JR vii 127 140 viii CONTENTS Effect of Transient Loads on Fatigue Crack Growth in Solution Treated and Aged Ti-62222 at -54, 25, and 175~ R STEPHENS,RALPHI STEPHENS, SHANNON C BERGE, DAVID E LEMM, AND CHRISTOPHER D 154 GLANCEY Spectrum Coupon Testing of Fatigue-Resistant Fasteners for an Aging Military A i r c r a f t - - F R A S E R J McMASTER AND PETER C, M c K E I G H A N 171 Crack Initiation at a Notch under Constant and Selected Variable Amplitude Loading Conditions NICOLAS GI~RARD, RENI~ LEROY, OLIVIER GIRARD, AND N A R A Y A N A S W A M I R A N G A N A T H A N Fatigue Resistance Evaluation and Crack Kinetics Study for Aero Engine Fan Blades under Random Vibration NIKOLAV V TUMANOV 186 200 D E S I G N A P P R O A C H E S AND M O D E L L I N G High Cycle Variable Amplitude Fatigue of a Nodular Cast Iron GARY B MARQUIS, B ROGER RABB, AND PAIVI K A R J A L A I N E N - R O I K O N E N 215 Prediction of Crack Growth Under Variable-Amplitude and Spectrum Loading in a Titanium Alloy JAMES C NEWMAN,JR AND EDWARDe PHILLIPS A Model for the Inclusion of Notch Plasticity Effects in Fatigue Crack Growth AnalysiS DALE L BALL 232 251 Comparisons of Analytical Crack Closure Models and Experimental Results under Flight Spectrum Loading R CRAIGMcCLUNG,FRASERJ McMASTER, AND JAMES H FEIGER 278 Multi-Mechanism Synergy in Variable-Amplitude Fatigue n SUNDER,NOELE A S H B A U G H , W J PORTER s AND A H ROSENBERGER Crack Growth and Closure Behavior of Short and Long Fatigue Cracks under Random Loading Ji-HO SONG, CHUNG-YOUBKIM, AND SHIN-YOUNGLEE 299 320 Calculation of Stress Intensity Factors for Cracks in Structural and Mechanical Components Subjected to Complex Stress Fields ZHIHUAN WU, GRZEGORZ GLINKA, H1ERONIM JAKUBCZAK~ AND LENA NILSSON 335 Fatigue Life Modelling and Accelerated Tests for Components under Variable Amplitude Loads w E L - R A T A L , M BENNEBACH, XIAOBIN LIN, AND R PLASKITT 349 CONTENTS ix OTHER APPLICATIONS On the Causes of Deviation from the Palmgren-Miner Rule ARTHUR J 369 MCEVILY, S ISHIHARA~ AND M ENDO Fatigue Design and Experimentations with Variable Amplitude Loadings in the Automotive I n d u s t r y - - J E A N - J A C Q U E S THOMAS, ANDRI~ BIGNONNET, 381 AND GEORGES PERROUD High Cycle Fatigue Testing and Analysis Using Car Standard Sequence-FRANCK MOREL AND NARAYANASWAMI RANGANATHAN 395 Degradation Parameters and Two-Stress Block Fatigue of Angle-Ply C a r b o r Fiber Reinforced Epoxy JORG PETERMANN, S HINZ, AND KARL SCHULTE 408 Study on Fatigue Design Loads for Ships Based on Crack Growth A n a l y s i s - YASUMITSU TOMITA, KIYOSHI HASHIMOTO, NAOKI OSAWA, KOJI TERAI, AND 420 YEHONG WANG Life Prediction by Observation and Simulation of Short Crack Behavior in a Low Carbon S t e e l - - J O A C H I M HUNECKE AND DIETER SCHONE 435 LOAD INTERACTION Effect of Overloads and Underloads on Fatigue Crack Growth and Interaction E f f e c t S - - F E R N A N D O ROMEIRO, MANUEL DE FREITAS, AND S POMMIER 453 Overload Effects in Aluminum Alloys: Influence of Plasticity and E n v i r o n m e n t - - N A R A Y A N A S W A M I RANGANATHAN, ABDELLAH TOUGUI, 468 FLORIAN LACROIX, AND JEAN PETIT Periodic Overloads in the Near Threshold Regime BERNHARDTABERNIG, RE1NHARD PIPPAN, JI~R6ME FOULQU1ER, ALAIN RAPAPORT, AND SANDRINE 482 SERENI Fatigue Reliability Analysis of an Overload Effect in Welded Joints Including Crack Initiation and Plastic Zone as Random Variables pHiLippE DARCIS AND NAMANRECHO 492 Load History in Fatigue: Effect of Strain Amplitude and Loading Path-VI~RONIQUEAUBIN, PHILIPPE QUAEGEBEUR~ AND SUZANNE DEGALLAIX 505 PROBABILISTIC AND MULTIAXIAL EFFECTS Fuzzy Probabilistie Assessment of Aging Aireraft Structures Subjected to Multiple Site Fatigue Damage uNYiME o AKPAN,PHILIP A RUSHTON, TIMOTHY E DUNBAR, AND TAMUNOIYALA S KOKO 521 X CONTENTS Probabilistic and Semi-Probabilistic Format in Fatigue Ship Classification R u l e s - - M I C H E L HUTHER, ST~PHANIE MAHI~RAULT, GUY PARMENTIER, AND GUY Cl~SARINE 535 Comparison of the Rain Flow Algorithm and the Spectral Method for Fatigue Life Determination under Uniaxial and Multiaxial Random L o a d i n g - TADEUSZ ,LAGODA, EWALD MACHA, AND ADAM NIES~LONY Validation of Complex Wheel/Hub Subassemblies by Multiaxial Laboratory Tests Using Standardized Load Files OERHARD FISCHER 544 557 Fatigue Life of a SG Cast Iron under Real Loading Spectra: Effect of the Correlation Factor Between Bending and Torsion ~mE• BANVmLET, THIERRY PALIN-LUC, AND JEAN-FRAN(~OIS VITTORI Index 567 581 570 FATIGUETESTING AND ANALYSIS FIG Load sequence of the signal applied to the specimens, in plane bending, in torsion, and in combined plane bending and torsion 20 r v 10 20 10 o -10 -20 -3( 30 Frequency (Hz) 40 B 50 60 FIG, Power Spectral Density (PSD) of the signal applied to the specimens, in plane bending, in torsion, and in combined plane bending and torsion FIG Probability density (on the left - dark line is a theoretical gaussian distribution) and probability repartition of the normalized load sequence (on the righO BANVILLET ET AL ON CORRELATION OF BENDING/TORSION FIG 571 Rainflow cycle number versus mean and amplitude moment values (torsion case) Two types of fatigue tests under combined loadings were done First, the same loading sequence (Fig 2) was applied simultaneously in bending and in torsion with different ranges The bending and torsion moments were synchronous Second, the bending and torsion moments follow the same loading sequence but out of synchronism Two different de-synchronisms between each loading were tested For each case the maximum nominal stresses (elastic stresses) are the same because tests were load controlled The local maximum and minimum stresses on all the sequence are given in Table with the root mean square value of the normal and shear stresses Maximum and minimum stresses were computed with an elastic-plastic finite element analysis [ 12] TABLE Loading conditions (stresses in MPa) Loading CMt,Mb Torsion Plane bending Pl bend + To 0.04 Pl bend + To 0.62 Pl bend+ To 0.94 O'max 17max O'min 1;min (YRMS '~RMS 363 240 240 225 254 186 186 167 -313 -248 -248 -233 -231 -172 -172 -147 130 90 90 90 82 56 56 56 To characterize the load desynchronism between Mt and Mb, the correlation factor, CMt,Mb, w a s computed for the complete sequence (1) CM,,Mb= cov(Mt, Mb) (1) where cov(Mt, MJ) is the covariance of the torsion moment Mt and the bending moment Mb SMb and SMt are, respectively, the standard deviation of Mb and Mt When CMt.gb is equal to 1, the two loads are synchronous, there is a perfect correlation between them, and the load path is 572 FATIGUE TESTING AND ANALYSIS proportional; when CMt, Mb iS equal to 0, there is no correlation between ACt and Mb Figure shows the different load paths corresponding to the multiaxial loadings applied to the specimens G=0.94 C=0.04 C=0.62 60 60 60 40 40 40 2O 20 20 g o 0 -20 -20 -20 -40 -40 -40 -60 -50 M b (N.rn) 50 -60 -50 M b (N.rn) 50 -60 -50 M b (N.m) 50 FIG Load paths applied on the specimens in combined bending and torsion with different correlation factors CMt,Mb (noted C) Fatigue Test Results The fatigue test results are given in Table N3~5 is the median fatigue life, NJ0.16 and NJ~84 are, respectively, the fatigue lives for a failure probability of 0.16 and 0.84 The number of specimens is different because test time was very long TABLE Loading Torsion Plane bending Plane bend + To Plane bend + To Plane bend + To Results of the fatigue tests (Nf in number of sequences) C_M~tMb 0.04 0.62 0.94 Nf05 Nf0.16 Nf084 Nb specimen 19 020 11 268 12 688 989 28 513 21 270 10 10 49 760 587 16 496 21 782 630 269 113 677 25 322 43 406 Life Calculation Method Analysis and Discussion Brief Literature Review At present, the main fatigue models presented in literature are based on critical plane approaches Nevertheless, regarding all the different proposals, the choice of a particular method is not always evident Models have to be chosen depending on both the material and the observed failure mode Socie's works on different steels [7] also underlines that the cracking mode may be dependent on the fatigue regime Nowadays it is usually accepted that for ductile steels, fatigue cracks initiate along the persistent slip bands (local plasticity phenomenon) generated by local shear stress On the other hand, for brittle materials, crack initiation phase is very short, and the more adapted criteria are based on the maximum tensile stress [13,14] To BANVILLET ET AL ON CORRELATION OF BENDING/TORSION 573 take into account all the material behavior, many authors usually propose using a combination of shear and tensile stresses or strains calculated on a critical plane Different criteria are tested hereafter: 9 a strain based one developed for low cycle fatigue (LCF) regime stress based approaches proposed for high cycle fatigue (HCF) regime a stress-strain one to predict life whatever the regime is In the following models, except for the Morel's one, the damage parameter used has been proposed originally for cyclic loading, then used by some authors for variable amplitude multiaxial loading [4] Fatemi and Socie's Model [2 4] When fatigue crack initiation is dominated by plastic shear strains, these authors recommend the use of the FS model (2) For each material plane oriented by the unit normal vector fi, the cycle counting method is applied on two variables: the shear strains gx,n(t) and gy,n(t) (see Fig A.1 in the Appendix: coordinate system definition) l" i The right-hand side of Eq is the description of the strain-life Manson-Coffin curve in torsion The term on the left-hand side represents the damage parameter on the plane experiencing the largest range of the shear strain (critical plane) Finally, life is computed on the critical plane where the total damage is maximum In this term, kl is a material parameter identified by fitting uniaxial against pure torsion fatigue data This parameter is varying with finite life N• When the strain-life Manson-Coffin curve is not known in torsion, FS propose to approximate this curve from the tensile strain-life curve [2] Smith, Watson, and Topper's Model (SWT) [1] This model was proposed for the first time in 1974 to take into account the mean stress effect on the tensile fatigue strength Recently, Socie observed [7] that short fatigue cracks grow on the plane perpendicular to the maximum principal stress and strain (Mode I) He recommends using the SWT damage parameter, ~,,aO',,max(3) calculated on the maximum normal strain plane For each material plane, the cycle counting method is applied on the normal strain En(t) (see Fig A in the Appendix) The critical plane is the plane where the damage is maximum (total Miner sum is maximum) )2 En'aO'n'max # /E (2Ni)2b + cr', g', (2Nf)b+" (3) This criterion, which does not express any influence of the shear stress on life, is more adapted to brittle materials For a finite life Nf, the ratio between the tensile and torsional fatigue limits is constant whatever the material is and equal to (1 + v) ~ which corresponds quite well to the GGG40 and GGG60 cast irons [13,14] and the studied one Socie's Proposal for HCF Region [7] According to the previous author for HCF and a ductile material, most of the fatigue life is consumed by crack initiation on planes where the shear stress amplitude is maximum In this case, Socie proposes the stress based approach (4) The cycle counting algorithm is applied for each material plane on both the shear stresses Xx,n(t) 574 FATIGUETESTING AND ANALYSIS and Xy,n(t) For each one of these variables, the critical plane is that experiencing the largest range of the corresponding shear stress Life is finally computed on the critical plane where the total damage is maximum ra+k/r =r:'(2N:~ ~ (4) The right-hand side of Eq is the elastic part of the strain-life The terms of the left-hand side represent the damage parameters defined on the plane experiencing the largest range of the cyclic shear stress, k2 is a material parameter identified by fitting Eq with tension and torsion fatigue data Wang and Brown's Model [5,6] Wang and Brown developed a model restricted first to LCF and MCF according to the hypothesis that fatigue crack growth is controlled by the maximum shear strain with an important additional role of the normal strain excursion over one reversal of the shear strain acting on the plane where the shear strain is maximum This proposal was extended to HCF (5) by taking into account the mean stress effect on fatigue lifetime by using the Morrow correction The cycle counting algorithm is applied for each material plane on both the shear stresses ex,n(t) and ~y,n(t) For each one of these variables, the critical plane is this experiencing the largest range of the corresponding shear strain Life is finally computed on the critical plane where the total damage is maximum Ya-]-S.8~n=O+Oeq-g(1-Oe))O''f-2G (2Nf~ q-O+l.)pq-gO-l.)p)~lf(2Nf~ E (5) 6c, is the normal strain excursion between two turning points (consecutive extrema) of the shear strain versus time acting on the maximum shear strain plane S is a material parameter identified by fitting tension against torsion fatigue data Morel Approach [8,9] Morel developed a model for polycrystalline metals in HCF based on the accumulation of mesoscopic plastic strain He assumes that crack initiation occurs by failure of the most stressed grains along the plane experiencing the maximum value of the parameter Ta,Ra~sdefined by (6) This author shows that this quantity is proportional to an upper bound value of the cumulated mesoscopic plastic strain T~:Ms(O,qk)= I?fT2e~s(O,(k,~/)d ~ (6) T~,RMsis the root mean square of the macroscopic resolved shear stress amplitude acting on a line determined by the angle W from fixed axis in the plane defined by its angles t9 and [7] According to the author, the number of cycles to crack initiation Nffollows the analytical Eq N:=plnl ]+ql r"~m ) r t r -film) r, (7) \ra-riim) In this equation p, q, and r are functions of the hardening and softening material parameters, assuming that the behavior of each grain of the material can be described by a three phases law (hardening, saturation, and softening) They can be identified by fitting an S-N curve or BANVILLET ET AL ON CORRELATION OF BENDING/TORSION 575 following the procedure described in [9] is the amplitude of the macroscopic resolved shear stress on the critical plane, rt~mis the generalized fatigue limit depending on the loading and two endurance limits [9] Note that for the Morel method, the damage accumulation is done step by step, so calculated life is sensitive to the order of the stress levels Life Calculation Procedure Used in This Study [12] In the present paper, the material parameters kl and k2 are the mean values of these parameters for life varying between l0 s and 106 cycles Kim and Park [15] observed for different materials that these values are varying with the lifetime and may influence the predictions Thus, the method to identify them also could have a non-negligible role Strain and stress histories are computed from the loading history (bending and torsion moments versus time) by using an elastic-plastic finite element analysis, with the hypothesis that the material (EN GJS 800-2) follows an isotropic hardening rule Then, on the cycle counting variable of each model, the rainflow cycle counting method was used to extract the cycles from the stress or strain time history For each extracted cycle i, the elementary damage d~ (according to each author) is calculated and accumulated by using the Palmgren-Miner rule This damage parameter also is computed on each material plane Pfi, oriented by the unit normal vector fi, in order to look for the critical plane Pfic' which depends on the method Damage is accumulated by using the same law, with the hypothesis D = 2~di = when the fatigue crack initiates The Morel calculation method was applied using the step by step damage accumulation according to its author Compar&on Between Predictions and Experiments As illustrated in Fig 7, prediction methods (Table 3) seem to be very sensitive to the loading path, especially for the very low correlation factor: C = 0.04 The ratios between simulated and experimental life reach the value of 34 Indeed, the predictions are inside the following intervals: SWT: WB: So: FS: M: Npred Npred Npred Npred Npred e e ~ e e [Nexp/1.1; 7.7Nexp], [-Nexp/34.6; 4.3 Nexp], [Nexp/5.3; 16.2 Nexp] [Nexp/4.5; 7.1 Nexp] [Nexp/1.7; 5.5 Nexp] For any non-proportional loading tests, the errors are higher than a factor of two, either in the safety area or in the unsafe one This may be explained by the fact that all the tested methods were mainly developed for ductile materials, while the spheroidal graphite cast iron EN GJS 800-2 is not ductile Wang-Brown and Fatemi-Socie give correct predictions, but they are much more scattered than Morel's proposal, whose predictions for the tested material with our non-proportional fatigue test conditions are less scattered compared with the experiments Its predictions are inside the smallest interval [Nexp/l.7; 5.5 Nexp] For a general point of view, the main predicted lives are longer than experimental lifetimes This fact is often observed in the literature [13] To correct this, Sonsino et al [16] propose to use a damage parameter to crack initiation D (total Miner sum), smaller than 576 FATIGUE TESTING AND ANALYSIS C=0.62 Tors ~, C=0.04 105 v 103 1r l O3 FIG Experimental life (seq) 10s Comparison between median experimental lives and simulated lives Table Simulation results (Nf in number of sequences, S WT = Smith-Watson-Topper, FS = Fatemi-Socie, WB = Wang-Brown, So = Socie HCF, M = Morel) Loading CMt,Mb Torsion Plane bending Plane b e n d + T o Plane b e n d + T o Plane b e n d + T o 0.04 0.62 0.94 SWT 23 965 10 297 380 891 64 710 27 693 FS 14 066 14 050 11 019 67 650 24 333 WB 18 830 11 180 438 41 016 53 309 M 73 408 22 797 29 946 53 070 18 492 So 96 308 40 403 397 155 177 137 216 Nf0s 19 020 11 268 49 760 587 16 496 Effect o f the Correlation Factor on Life Figure shows the experimental lives and the standard deviation of the experimental life (with lognormal distribution hypothesis) for our different fatigue tests under combined loadings The number of tested specimens is indicated in brackets According to this figure and due to the scatter of experimental lives (see standard deviation), the influence of the correlation factor on life is low for this material and our tests Nevertheless, a synchronism shift seems to improve fatigue strength (around a median life factor of five between tests where C = 0.04, and C = 0.94) This observation also has been done on cast iron by Grubrisic [14] and Palin-Luc [10] under sinusoidal loading conditions For the studied material, under constant amplitude multiaxial fatigue tests (bending and torsion), the phase shift effect on the fatigue limit improves the fatigue strength, but only % at 106 cycles [17] Shift of phase influence is often discussed in literature For Sonsino, it is dependent on both the type of test (load or strain controlled) [18] and the material [19]: for ductile materials (structural steels), the shift of phase reduces the fatigue strength; semi-ductile materials (forged aluminium, cast steels) are not sensitive to the shift of phase, and the phase shift improves the fatigue strength of brittle materials (cast aluminium, cast iron, sintered steel) BANVILLET ET AL ON CORRELATION OF BENDING/TORSION 1~ ['::i::: :!i::~::!:i:i :" '::iii:! :::i::2 i i i :':ii :7:::" :::::::::::: ~104 :.!4::~C.).: : : " - : :!::!:::i 577 ":::: : (7.spec.) 103 0.2 0.4 0.6 Gorrelalion factor 0,8 FIG Experimental life On sequences) versus the correlation factor for fatigue tests in combined bending and torsion," 68 % of the possible lives are in the interval illustrated by the vertical straight lines (standard deviation) One reason for this low influence is proposed The material used for machining the specimens is not completely brittle Furthermore, fatigue tests were carried out under load control: that means that nominal stresses were controlled for each test, but local stresses were different Elastic-plastic finite element analysis shows that local small plastic strains occurred in the specimens loaded under synchronous loadings For synchronous combined bending and torsion tests (C = 0.94), the maximum Von Mises equivalent stress was equal to 391 MPa This is higher than the corresponding value for uncorrelated tests (C = 0.04), for which the maximum Von Mises equivalent stress was 333 MPa In this last case, total strains were smaller than under proportional fatigue tests (C = 0.94); thus, life may be a little bit longer than under synchronous tests Conclusion and Prospects Random multiaxial fatigue tests (with stress controlled conditions) carried out on smooth specimens made of the EN GJS 800-2 spheroidal graphite cast iron show a low influence on the median life of the correlation factor between the bending and torsion loadings This effect is not significant in middle high cycle fatigue if the scatter of experiments is considered Local small plastic strains are pointed out to explain this Comparison between fatigue data and simulations made with five fatigue life calculation methods shows that their predictions are good for proportional loadings, but there are large errors for non-proportional loadings, probably because most of the methods were proposed for ductile materials Morers proposal gives the best predictions for this SG cast iron and these tests According to the fact that most of the predictions are unsafe, it seems prudent to use a damage parameter lower than to predict crack initiation in design department This point is in agreement with Sonsino's [16] conclusions The knowledge of the material behavior under non-proportional load paths always remains an open question, and research must progress in this way Future work also must be done to develop a life prediction method adapted to non-proportional loading case 578 FATIGUETESTING AND ANALYSIS References [1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11] [12] [13] [14] [15] [16] Smith, J., Watson, P., and Topper, T., "A Stress Strain Function for Fatigue of Metals," Journal of Materials (JMLSA), 4, No 5, 1970, pp 293 298 Fatemi, A and Socie, D., "A Critical Plane Approach to Multiaxial Fatigue Damage Including Out-of-Phase Loading," Fatigue and Fracture of Engineering Materials and Structures, 11, No 3, 1988, pp 149 165 Bannantine, J., "A Variable Amplitude Life Prediction Method," Ph.D thesis, University of Illinois, Urbana-Champaign, 1989, p 270 Bannantine, J and Socie, D., "A Variable Amplitude Multiaxial Life Prediction Method," Fatigue under Biaxial and Multiaxial Loading, ESIS 10, K Kussmaul, D L McDiarrnid, and D.F Socie, Eds., Mechanical Engineering Publication, London, 1991, pp 35 51 Wang, C and Brown, M., "Multiaxial Random Load Fatigue: Life Predictions Techniques and Experiments," Multiaxial Fatigue and Design, ESIS 21, A Pineau and G Cailletaud, Eds., Mechanical Engineering Publications, London, 1996, pp 513 527 Wang, C and Brown, M., "Life Prediction Techniques for Variable Amplitude Multiaxial Fatigue Part I: Theories," Journal of Engineering Materials and Technology, 118, 1996, pp 367 370 Socie, D., "Critical Plane Approaches for Multiaxial Fatigue Damage Assesment," Advances in Multiaxial Fatigue, ASTM STP 1191, D L McDowell and R Ellis, Eds., ASTM International, West Conshohocken, PA, 1993, pp 36 Morel, F., "A Critical Plane Approach for Life Prediction of High Cycle Fatigue under Multiaxial Variable Amplitude Loading," International Journal of Fatigue, 22, 2000, pp 101 119 Morel, F., "Fatigue Multiaxiale Sous Chargement d'Amplitude Variable," Ph.D thesis, ENSMA, Poitiers, France, 1996, p 210 Palin-Luc, T., Lasserre, S., and B6rard, J-Y., "Experimental Investigation on the Significance of the Conventional Endurance Limit of a Spheroidal Graphite Cast Iron," Fatigue and Fracture of Engineering Materials and Structures, 21, 1998, pp 191 200 Palin-Luc, T and Lasserre, S., "Multiaxial Fatigue Testing Machine Under Variable Amplitude Loading of Bending and Torsion," Recent Advances in Experimental Mechanics, J F Silva Gomes et al., Eds., A A Balkema, Rotterdam, 1994, pp 965 970 Banvillet, A., "Pr6vision de Dur6e de Vie en Fatigue Multiaxiale Sous Chargements R6els: Vers des Essais Accfl6r6s," Ph.D Thesis, ENSAM, Bordeaux, France, 2001, p 204 Lagoda, T., Macha, E., Nieslony, A., and Mtiller, A., "Fatigue Life of Cast Irons GGG40, GGG60 and GTS45 Under Combined Random Tension with Torsion," Fracture Mechanics: Application and challenges, M E M Fuentes and A Martin-Meizoso, Eds., ECF13, San Sebastian, Spain, 2000, on CD-Rom Grubisic, V., "Festigkeitsverhalten yon Sph~irogub bei Kombinierter Statischer und Dynamischer Mehrachsiger Beanspruchung," Tech Rep., LBF-Fraunhof~r Institute, Darmstadt, Bericht Nr FB-149, 1979 Kim, K S and Park, J C., "Shear Strain Based Multiaxial Fatigue Parameters Applied to Variable Amplitude Loading," International Journal of Fatigue, 21, 1999, pp 475 483 Sonsino, C M., Kaufman H., and Grubisic, V., "Transferability of Material Data for the Example of a Randomly Loaded Truck Stub Axle," SAE Teeh paper series, 970708, 1997, pp 22 BANVILLET ET AL ON CORRELATION OF BENDING/TORSION 579 [17] Palin-Luc, T and Lasserre, S., "An Energy Based Criterion for High Cycle Multiaxial Fatigue," European Journal of Mechanics, A/Solids, 17, No 2, 1998, pp 237 251 [18] Sonsino, C M., "Influence of Load and Deformation-Controlled Multiaxial Tests on Fatigue Life to Crack Initiation," International Journal of Fatigue, 23, 2001, pp 159 167 [19] Sonsino, C M and Kueppers, M., "Fatigue Behavior of Welded Aluminium Under Multiaxial Loading," In: Proceedings of the 6th International Conference on Biaxial/Multiaxial Fatigue & Fracture, M M de Freitas, Ed., ESIS, Lisboa, Portugal, 2001, pp 57 64 Appendix M , i ""t' i ~'"',, ~ "" (2,)3,s cartesian coordinates system linked with the specimen surface (2',~',ff) cartesian coordinates system linked with de plane Pfi orientated by ft FIG A Coordinate systems used to define the unit normal vector fi orientating each material plane Pfi at the point M on the surface of the specimen STP1439-EB/May 2005 Author Index A Akpan, Unyime O., 521 Ashbaugh, N E., 299 Aubin, V6ronique, 505 Hinz, S., 408 Hopkins, S W., 24 Hug, Joachim, 67 Htinecke, Joachim, 435 Huther, Michel, 535 B Ball, Dale L., 251 Banviellet, Alexis, 567 Beaufils, Jean-Yves, 127 Bennebach, M., 349 Berge, Shannon C., 154 Bignonnet, Andr6, 381 Bucci, Robert J., 81 Ishihara, S., 369 Jakubczak, Hieronim, 335 K C C6sarine, Guy, 535 I) Karjalainen-Roikonen, P~iivi, 215 Kim, Chung-Youb, 320 Koko, Tamunoiyala S., 521 L Darcis, Philippe, 492 de Freitas, M., 453 Degallaix, Suzanne, 505 Donald, J Keith, 53, 81 Dunbar, Timothy E., 521 Lacroix, FIorian, 468 Lagoda, Tadeusz, 544 Le Divenah, Laurence, 127 Lee, Shin-Young, 320 Lemm, David E., 154 Leroy, Ren6, 186 Lin, X., 349 E El-Ratal, W., 349 Endo, M., 369 Everett, Richard A., Jr., 140 M F Macha, Ewald, 544 Mah&ault, St6phanie, 535 Marquis, Gary B., 215 McClung, R Craig, 278 McEvily, A J., 369 McKeighan, Peter C., 36, 17 I McMaster, Fraser J., 36, 171,278 M6igault, J., 24 Mitchell, M R., 24 Morel, Franck, 395 Feiger, James H., 278 Fischer, Gerhard, 557 Foulquier, J6r6me, 482 G George, Kenneth, 53, 81 G6rard, Nicolas, 186 Girard, Olivier, 186 Glancey, Christopher D., 154 Glinka, Grzegorz, 335 H Hashimoto, Kiyoshi, 420 Hewitt, Roy L., 113 Copyright9 by ASTM lntcrnational N Newman, J C., Jr., 232 Nieslony, Adam, 544 Nilsson, Lena, 335 Nor, Peter K., 113 581 www.astm.org 582 FATIGUETESTING AND ANALYSIS O Osawa, Naoki, 420 P Palin-Luc, Thierry, 567 Parmentier, Guy, 535 Perroud, Georges, 381 Petermann, J., 408 Petit, Jean, 468 Phillips, E P., 232 Pippan, Reinhard, 482 Plaskitt, R., 349 Pommier, S., 453 Porter, W J., 299 P6ting, Stefan, 67 Q Schulte, K., 408 Sereni, Sandrine, 482 Song, Ji-Ho, 320 Sonsino, Cetin Morris, Stephens, Ralph I., 154 Stephens, Robert R., 154 Sullentrup, Michael G., 99 Sunder, R., 299 T Tabernig, Bekrnhard, 482 Terai, Koji, 420 Thomas, Jean-Jacques, 381 Tomnita, Yasumitsu, 420 Tougui, Abdellah, 468 Traupe, Markus, 67 Tumanov, Nikolay V., 200 V Quaegebeur, Philippe, 505 R Rabb, B Roger, 215 Ranganathan, Narayanaswami, 186, 395, 468 Rapaport, Alain, 482 Recho, Naman, 492 Reemsndyer, Harold S., 81 Romeiro, E, 453 Rosenberger, A H., 299 Rushton, Philip A., 521 Vittori, Jean-Franqois, 567 W Wang, Yehong, 420 Weiss, Jan P., 113 Wu, Zhihuan, 335 Y Yanishevsky, Marko, 140 Z Sch6ne, Dieter, 435 Zenner, Harald, 67 STP1439-EB/May 2005 Subject Index A AFGROW, 154 AFNOR, 24 Airbus, 127 Aircraft, 53, 99, 113, 127, 140, 171,232, 251,521 Aluminum alloy, 81, 186, 278, 299, 320, 468, 482 Angle-ply laminates, 408 ANSI, 24 ASTM, 24 ASTM E 647, 36 Automation, 53 Automobiles, 349, 395, 381,557 B Bauschinger effect, 453 "Beat like" load, 67 Bending, 567 Biaxial loading, 505 Biaxial stress, 544 Biaxial Test Facility, 557 Block fatigue, 408 Buffet, 113 C Carbon fiber reinforced epoxy, 408 CARLOS, 395 Cast iron, 567 nodular, 215 CFRP, 408 Classification rules, 535 Cold expansion, 171 Complex stress fields, 335 Compounding method, 521 Compression, 278 Compressive underloads, 154 Constant amplitude, 24 Constraint, 232, 278 Comer notch, 81 Correlation factor, 567 Coupons, 171 Crack closure, 154, 215, 232, 278, 299, 320, 482 plasticity-induced, 453 Crack front incompatibility, 299 Crack initiation, 186, 492 Crack propagation rate, 482 Crack simulation, 435 Cycle counting, 381 Damage accumulation, 3, 395 summation, 369, 381 tolerance, 127 Degradation, 408 Delay, induced by overload, 468 Digital signal processing, 53 Direct current potential crop calibration, 81 E ECISS, 24 Elastic-plastic stress-strain response algorithm, 251 Electromagnetic test facility, 67 Endurance limit, 24 Engine fan blades, 200 Environment, 468 Epoxy, carbon fiber reinforced, 408 Equivalent amplitude, 200 ESIS, 24 Eurocycle load program, 557 Experimental proof, Experimental spectrum tests, Extra-hardening, 505 F FALSTAFF, 53 Fasteners, fatigue-resistant, 171 FASTRAN, 140, 154, 232, 278 Fatigue, 171 Fatigue crack growth, 53, 81, 154, 232, 251,278, 299, 320, 369, 420, 453, 468, 492 testing, 36 Fatigue crack nucleation, 395 Fatigue design, 420 Fatigue life, 186 assessment, Fatigue testing, 36, 300 full-scale, 99 FEM analysis, 453 First order reliability method, 521 Flight spectrum loading, 278 Fractography, 154 583 584 FATIGUETESTING AND ANALYSIS Fracture mechanics, 186, 232, 278 Full-scale testing, 113 Fuzzy modeling, 521 G Gassner-lines, Green's function, 251 H High cycle fatigue, 215, 395, 544 ISO, 24 L Life improvement, 17 I Life prediction, 140, 154, 186, 215, 395, 420, 435, 492, 544, 567 Load interaction, 278 Load spectrum, 127 Load time history, 67 Local strain, 186 Long cracks, 320, 482 Low carbon steel, 435 Low-cycle fatigue, 505 M Mean value effect, 381 Microstructural defect, 186 Mini-TWIST flight spectrum, 53, 232 Multiaxial fatigue, 349 Multiaxial loading, 395, 557, 567 Multiple site damage, 521 Multiple two-step loading, 369 N Nickel-base super-alloy, 299 Nodular cast iron, 215 Nonlinear stress field, 335 Non-proportional loading, 544, 567 Notch, 186 plasticity, 251 Optical microscopy, 435 Overloads, 154, 232, 369, 453, 468, 492 periodic, 482 P Palmgren-Miner rule, 369 Periodic overloads, 482 Plasticity, 232, 468 cyclic, 505 notch, 25 I Plasticity-induced crack closure, 453 Plastic zone, 492 Poisson's ratio, 408 Probabilistic analysis, 521,535 R Rainflow algorithm, 381,544 Rainflow counting, Random fatigue resistance, 200 Random loading, 67, 320, 544 Random vibration, 200 Reconstitution, Reliability analysis, 492 Residual stress effect, 299 Resonance control, 67 Resonance test facility, 67 Response surface, 521 Safety factors, 535 Semi-probabilistic, 535 Servo-hydraulic closed-loop control, 53 Ships, 420, 535 Short cracks, 81, 186, 320, 435, 482 Small-crack life prediction, 140 Spectrum editing, 113, 278 Spectrum fatigue, 140 Spectrum loading, 3, 36, 67, 232 Spectrum testing, 171,544 Stainless steel, duplex, 505 Standardization, 36 Standards, international, 24 Static testing, full-scale, 99 Steel, 395 low carbon, 435 Stiffness, 408 Stochastic resonance, 200 Storm model, 420 Strain amplitude, 505 Strain energy density parameter, 544 Strain measurement, 99 Stress envelope, 200 Stress intensity factors, 232, 251,335 Stress intensity range, threshold, 482 Stress-strength interference analysis, 381 Structural analysis, 127 INDEX Structural certification, 99 Structural integrity, 24 Suspension modules testing, 349 T Temperature, 154 Tensile overloads, 154 Test acceleration, 349 Threshold of stress intensity range, 482 Thresholds, 299 Titanium alloy, 154, 232 Torsion, 567 Transient loads, 154 Truncation methodology, 113 TWIST spectrum, 186 Two-step loading, 369 585 U Underloads, 154, 369, 453 V Variable amplitude fatigue, 3, 24, 215 Variable amplitudeloading, 36, 53, 67, 81, 140, 186, 232, 299, 349, 369, 381, 395,420, 453, 535, 557, 567 W Weight function, 335 Welded joints, 492, 535 Welding irregularities, 420 Wheel/hub subassembly, 557