Astm stp 1280 1997

STP 1280 Multiaxial Fatigue and Deformation Testing Techniques Sreeramesh Kalluri and Peter J Bonacuse, editors ASTM Publication Code Number (PCN): 04-012800-30 ASTM 100 Barr Harbor Drive West Conshohocken, PA 19428-2959 Printed in the U.S.A Copyright by ASTM Int'l (all rights reserved); Wed Dec 23 19:33:23 EST 2015 Downloaded/printed by University of Washington (University of Washington) pursuant to License Agreement No further reproductions authorized Library of Congress Cataloging-in-Publication Data Multiaxial fatigue and deformation testing techniques / Sreeramesh Kalluri and Peter J Bonacuse, editors (STP ; 1280) "ASTM STP publication code number (PCN): 04-012800-30." Includes bibliographical references and index ISBN 0-8031-2045-1 Materials Dynamictesting Materials Fatigue Deformations (Mechanics) I Kalluri, Sreeramesh I1 Bonacuse, Peter J., 1960ill Series: ASTM special technical publication ; 1280 TA418.32.M85 1996 620.1' 126 DC21 96-37368 CIP Copyright 1997 AMERICAN SOCIETY FOR TESTING AND MATERIALS, 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 MateriEls (ASTM) provided that the appropriate fee is paid to the Copyright Clearance Center, 222 Rosewood Drive, Danvers, MA 01923; Tel: 508-750-8400; online: http:// www.copyright.com/ Peer Review Policy Each paper published in this volume was evaluated by three peer reviewers The authors addressed all of the reviewers' comments to the satisfaction of both the technical editor(s) and the ASTM 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 these peer reviewers The ASTM Committee on Publications acknowledges with appreciation their dedication and contribution to time and effort on behalf of ASTM Printed in Philadelphia, PA February 1997 Copyright by ASTM Int'l (all rights reserved); Wed Dec 23 19:33:23 EST 2015 Downloaded/printed by University of Washington (University of Washington) pursuant to License Agreement No further reproductions authorized Foreword This publication, Multiaxial Fatigue and Deformation Testing Techniques, contains papers presented at the Symposium on Multiaxial Fatigue and Deformation Testing Techniques, which was held in Denver, Colorado, on 15 May 1995 The Symposium was sponsored by the ASTM Committee E8 on Fatigue and Fracture Sreeramesh Kalluri, NYMA, Inc., NASA Lewis Research Center, and Peter J Bonacuse, U.S Army Research Laboratory, NASA Lewis Research Center, presided as symposium chairman and cochairman, respectively, and both were editors of this publication Copyright by ASTM Int'l (all rights reserved); Wed Dec 23 19:33:23 EST 2015 Downloaded/printed by University of Washington (University of Washington) pursuant to License Agreement No further reproductions authorized Contents Overview MULTIAXIAL TESTING FACILITIES Testing Facilities for Multiaxial L o a d i n g of T u b u l a r Specimens F ELLYIN AND J WOLODKO A S t r u c t u r a l Test Facility for I n - P l a n e Biaxial Testing of A d v a n c e d M a t e r i a l s - P A BARTOLOq~A, J R ELLIS, AND A ABDUL-AZIZ 25 A d j u s t a b l e W o r k Coil Fixture Facilitating the Use of I n d u c t i o n H e a t i n g in Mechanical Testing J R ELLIS AND P A BARTOLOTTA 43 MULTIAXIAL DEFORMATION Biaxial D e f o r m a t i o n E x p e r i m e n t s O v e r Multiple S t r a i n Regimes M p MILLER AND D L McDOWELL 65 E x p e r i m e n t a l D e t e r m i n a t i o n of Yield a n d Flow Surfaces U n d e r Axial-Torsional Loading -c J LISSENDEN, B A LERCH, J R ELLIS, AND D N ROBINSON 92 Additional H a r d e n i n g Due to T e n s i o n - T o r s i o n N o n p r o p o r t i o n a l Loadings: Influence of the L o a d i n g P a t h Shape -s CALLOCH AND D MARQUIS 113 Notch-Tip Stresses a n d S t r a i n s U n d e r N o n p r o p o r t i o n a l L o a d i n g - - M N K SINGH, G GLINgA, AND R N DUBEV 131 MULTIAXIAL FATIGUE C r a c k Initiation Life B e h a v i o r U n d e r Biaxial L o a d i n g Conditions: E x p e r i m e n t a l B e h a v i o r a n d Prediction H NOWACK, D HANSCHMANN, W OTT, K.-H TRAUTMANN, AND E MALDFELD 159 A n Axial-Torsional, T h e r m o m e c h a n i e a l Fatigue Testing Techalque -s KALLUR1 AND P J BONACUSE 184 F r e t t i n g Fatigue S t r e n g t h of Specimens Subjected to C o m b i n e d Axial a n d T r a n s v e r s a l L o a d i n g - - w SW1TEK 208 Copyright by ASTM Int'l (all rights reserved); Wed Dec 23 19:33:23 EST 2015 Downloaded/printed by University of Washington (University of Washington) pursuant to License Agreement No further reproductions authorize Characterization of Ceramic Matrix Composite Tubes Under Uniaxial/Biaxial Monotonic and Cyclic Loading K LIAO, E R GEORGE,AND K L REIFSNIDER 224 STRUCTURAL FAILURE AND C R A C K PROPAGATION UNDER MULTIAXIAL LOADING Plane Stress Crack Resistance Curves of an Inclined Crack Under Biaxial Loading-C DALLE DONNE AND H DOKER 243 Instability and Failure of Corrugated Core Sandwich Cylinders Under Combined Stress P PATEL, T NORDSTRAND, AND L A CARLSSON 264 Crack Propagation in Cruciform IMI 834 Specimens Under Variable Biaxial Loading K.-H TRAUTMANN, E MALDFELD, AND n NOWACK 290 Copyright by ASTM Int'l (all rights reserved); Wed Dec 23 19:33:23 EST 2015 Downloaded/printed by University of Washington (University of Washington) pursuant to License Agreement No further reproductions authorized STP 1280-E B/Feb 1997 Overview The importance of fatigue and deformation of materials under multiaxial loads has gained significant recognition over the last quarter century The advances in sophisticated materials testing equipment and digital computer systems have enabled many researchers to explore a multitude of testing techniques to assess the behavior of materials and structural components The result has been the evolution of several testing procedures and generation of indispensable multiaxial fatigue and deformation data on different types of materials Theoretical models have been developed to estimate the deformation behavior and fatigue lives of materials under multiaxial loading conditions Numerous conferences and symposia have been sponsored by various societies to document the technical achievements in the field Two such ASTM sponsored symposia have resulted in the following valuable special technical publications: (1) Multiaxial Fatigue (ASTM STP 853) and (2) Advances in Multiaxial Fatigue (ASTM STP 1191) This special technical publication is the result of a third ASTM sponsored symposium on Multiaxial Fatigue and Deformation Testing Techniques, which was held on 15 May 1995 in Denver, Colorado The symposium on Multiaxial Fatigue and Deformation Testing Techniques was sponsored by the ASTM Committee E8 on Fatigue and Fracture and its Subcommittee E08.05 on Cyclic Deformation and Fatigue Crack Formation The symposium's focus was on state-of-the-art testing techniques for characterizing the multiaxial fatigue and deformation behaviors of monolithic and composite materials The main purpose of the symposium was to facilitate the development of standardized procedures for testing structural materials under multiaxial loading conditions This volume contains a set of fourteen papers, which were presented at the Symposium on Multiaxial Fatigue and Deformation Testing Techniques These papers deal with both experimental and theoretical aspects of the multiaxial fatigue and deformation behaviors of structural materials The papers are separated into the following categories: (l) Multiaxial Testing Facilities, (2) Multiaxial Deformation, (3) Multiaxial Fatigue, and (4) Structural Failure and Crack Propagation Under Multiaxial Loading These four broad categories are intended to provide an orderly grouping of the presented papers Multiaxial Testing Facilities Multiaxial testing is performed typically on tubular or cruciform specimens The tubular specimens are employed for axial, torsional, internal pressure, external pressure, or combinations of these types of loads, whereas the cruciform specimens are used for biaxial tensile or compressive loads The first paper in this category deals with the development of a multiaxial testing facility that is suitable for tubular specimens The capability of this facility is demonstrated by testing composite specimens manufactured from glass-fiber reinforced epoxy tubes The second paper describes a test facility that is designed to perform in-plane biaxial tests on cruciform specimens and on structural elements of advanced materials Different features of the test facility include a digital controller and associated software to control four hydraulic actuators, a quartz lamp radiant furnace, an environmental chamber, and an in situ crack monitoring system The third paper in this category illustrates the design and performance of a coil fixture for inductively heating cylindrical specimens during mechanical testing This novel approach subdivides the induction coil into three individually adjustable segments It is shown that temperature variation in the gage section of a large tubular specimen can be controlled to within 1% of the nominal test temperature with the adjustable induction coil fixture Copyright by ASTM Int'l (all rights reserved); Wed Dec 23 19:33:231 EST 2015 Downloaded/printed by Copyright9 by (University ASTM International www.astm.org University of Washington of Washington) pursuant to License Agreement No further reproductions authorized MULTIAXIAL FATIGUE AND DEFORMATION TESTING Multiaxial Deformation Deformation of materials under monotonic and cyclic multiaxial loads has been the subject of many investigations in the last two to three decades In particular, the shapes of the multiaxial load paths (proportional versus nonproportional) have been shown to have a significant influence on the hardening behavior of materials Each of the four papers in this category addresses a different aspect of the multiaxial deformation behavior of materials In the first paper, a succinct review of the research under large strain conditions is presented and the effects of large compressive and torsional prestrains on the subsequent large strain deformation behavior of 304L stainless steel are experimentally evaluated In addition, experimental results depicting the influence of a large'torsional prestrain on the subsequent small strain biaxial deformation behavior of the 304L stainless steel are illustrated, and issues for modeling the small strain deformation data are discussed The second paper describes procedures for experimentally determining the room temperature yield and high temperature flow surfaces of 316 stainless steel under axial-torsional loading with a commercially available high temperature extensometer An inelastic strain offset criterion is used to determine the yield surfaces, whereas a constant inelastic strain rate criterion is employed to establish the flow surfaces The third paper addresses the influence of the loading path shape on the cyclic axial-torsional hardening behavior of 316 stainless steel In this experimental investigation authors identify nonproportional loading paths that lead to higher levels of hardening than the conventional 90 ~ out-of-phase axial-torsional loading The final paper proposes two analytical models based on strain energy density to estimate the stresses and strains at the root of a notch under multiaxial nonproportional loading In order to validate the models, results generated from the models are compared with stress-strain data obtained from finite element analyses Multiaxial Fatigue Fatigue under multiaxial loads has been the topic of many investigations with emphasis both on experimental and theoretical aspects Predicting the multiaxial fatigue crack initiation life requires complete knowledge of the cyclic stresses and strains and life prediction models that are appropriate for the damage mechanisms exhibited by the particular material under consideration In this category, the first paper reports experimental results from a biaxial fatigue crack initiation study on cruciform specimens manufactured from an aluminum alloy Fatigue lives under proportional and nonproportional loading histories are estimated with two incremental plastic work based fatigue life prediction approaches, which account for the influence of mean stresses The second paper describes, in detail, a testing technique for performing strain-controlled, thermomechanical fatigue tests on thin-walled tubular specimens under combined axialtorsional loading conditions Four types of axial-torsional, thermomechanical fatigue tests are described, and experimental results generated on a cobalt-base superalloy, Haynes 188, are discussed The third paper deals with fretting fatigue of machine elements subjected to combined axial and transverse loading Experimental results from fretting fatigue tests on normalized steel specimens are presented, and fracture mechanics is used to estimate fretting fatigue limits The final paper in this category describes a technique for conducting monotonic and cyclic tests under uniaxial and biaxial loads on ceramic matrix composite tubes Uniaxial and biaxial fatigue behaviors of a ceramic matrix composite and damage and failure modes exhibited by the composite under the investigated loading conditions are discussed Structural Failure and Crack Propagation Under Multiaxial Loading The final category in this book contains three papers on the topics of structural failure and crack growth under multiaxial loading conditions The first paper deals with crack growth under Copyright by ASTM Int'l (all rights reserved); Wed Dec 23 19:33:23 EST 2015 Downloaded/printed by University of Washington (University of Washington) pursuant to License Agreement No further reproductions authoriz OVERVIEW mixed Mode I and Mode II conditions in cruciform specimens made from an aluminum alloy and a structural steel Crack resistance curves under mixed mode conditions, presented in terms of the magnitude of a crack tip displacement vector, are compared to the conventional R-curves obtained with compact-tension and center-cracked specimens The second paper presents results from an experimental and analytical study on the structural failure of corrugated board cylinders Failure data generated in experiments under compressive and torsional loads are compared to the failure envelope obtained with finite element analysis and Tsai-Wu criterion In the third paper, experimental results obtained in a crack growth study on cruciform specimens made from a titanium alloy are reported Block loading histories consisting of major and minor cycles are imposed on the cruciform specimens containing crack initiator sites prepared with electric spark discharge The crack growth rates observed under different block loading histories are compared The experimental techniques presented in this book show some of the significant improvements that have occurred in the field of multiaxial testing during the past five to ten years It is our sincere hope that the papers contained in this book will shed some light on multiaxial testing techniques and that this book will serve as a valuable technical resource We would like to thank the authors and reviewers without whose contributions and metic, ulous efforts this book would not have been possible We are grateful to the ASTM staff (Ms Dorothy Savini, Hannah Sparks, Shannon Wainwright, Monica Siperko, Kathy Dernoga, and Helen Hoersch) for their professional assistance, cooperation, and patience Sreeramesh Kalluri NYMA, Inc., NASA Lewis Research Center, Cleveland, Ohio; symposium chairman and editor Peter J Bonacuse U.S Army Research Laboratory, NASA Lewis Research Center, Cleveland, Ohio; symposium cochairman and editor Copyright by ASTM Int'l (all rights reserved); Wed Dec 23 19:33:23 EST 2015 Downloaded/printed by University of Washington (University of Washington) pursuant to License Agreement No further reproductions authorized Multiaxial Testing Facilities Copyright by ASTM Int'l (all rights reserved); Wed Dec 23 19:33:23 EST 2015 Downloaded/printed by University of Washington (University of Washington) pursuant to License Agreement No further reproductions auth 296 MULTIAXIAL FATIGUE AND DEFORMATION TESTING 1(400/0) + 5(40010) 400 1(400/0) + 100(400/0) 400 AAAAAAAA VVVVVV z 200 EL" 1+5 (40010) + S(400/120) t +-100 (400/0) + 100(400/120) 400 400 z z u." 120 ~o i ,o` I 1(40010) + 5(400/200) 400 1(40010) + 100(4001200) 400 200~J~ , z u." 200 NN ol 1(40010) + 5(400/280) 40O 28O z M 1(40010) + 100(400/280) ,ooj/ ~z / YOO / 280 FIG 6a Block histories with the same maximum load Copyright by ASTM Int'l (all rights reserved); Wed Dec 23 19:33:23 EST 2015 Downloaded/printed by University of Washington (University of Washington) pursuant to License Agreement No further reproductions authorized TRAUTMANN ET AL ON VARIABLE BIAXIAL TESTING 1(40010) + 100(40010) 1(400/0) + 5(40010) 400 z -~ 200 O AAAAAA fVVVVVl - - - 1+5 '~176 z-~ (40010) + 100(340160) 4o0 1(40010) + 5(340160) 340 340 Z Z u." 60 60 0 I Noo N 400 l _ Z 1(400/0) + 100(3001100) (40010) + 5(300/100) 4oo u_" 297 300 Z u_" 100 100 FIG 6b Block histories with the same mean load orientation of the crack branches and of the loading axes was not found As long as the crack branches did not reach the opposite side of the specimens, their shape was quarter circular or elliptical Bifurcation and branching of the crack branches was also often observed If the crack phenomena are considered, two aspects are of importance First, is fracture mechanics able to explain the observed behavior? Second, certain characteristics of the material as, for example, anisotropy influence the crack propagation behavior? Fracture mechanics solutions for a crack in a plane specimen with an infinite width from the literature show that, if equal biaxial stresses are applied, the Mode I stress intensity factor always remains the same independently of the angle the crack forms with the loading axes [3] This correlates with the observations in the tests showing that the orientations of the crack branches varied arbitrarily In a previous investigation [1], it was found that the cracks propagated preferably transverse to the rolling direction A behavior as found in the present investigation was different from that Copyright by ASTM Int'l (all rights reserved); Wed Dec 23 19:33:23 EST 2015 Downloaded/printed by University of Washington (University of Washington) pursuant to License Agreement No further reproductions authorized 298 MULTIAXIAL FATIGUE AND DEFORMATION TESTING c) (400/0) + 100(400/120) 1(400/0) + 5(400/120) 4O0 400 z , iNN u." 120 20 - 100 (40010) + 100(340/60) 1(400/0) + 5(340/60) 4OO 340 z 340 ~ ~ z u." u_" 60 60 t, 100 II I d) 1(400/0) + 100(400/200) 400/0) + 5(400/200) 400 z ~ z 200 200 " of 100-,'1 1(400/0) + 100(3001100) 1(400/0) § 5(3001100) 400 400 1 ~ 300 z z u_" u." 100 100 o 100 FIG 6c and d minor cycles Block histories with the same amplitude but with different mean stresses in the Copyright by ASTM Int'l (all rights reserved); Wed Dec 23 19:33:23 EST 2015 Downloaded/printed by University of Washington (University of Washington) pursuant to License Agreement No further reproductions authorized 299 TRAUTMANN ET AL ON VARIABLE BIAXIAL TESTING 1(400/0) + 100(400/280) CAL (400/0) CAL (400/200) @@ @ F1 t F ~ - 11~ F2 F1 FIG Typical orientations of cracks as observed in the biaxial tests Quantitative Crack Propagation Behavior In the biaxial tests, the extension of the C ] C crack branches was recorded as a function of number of blocks The data points for all crack branches being present on one specimen were then plotted into one diagram as shown in Fig 8a for a block loading history of Type 1(4~176+ 5(400/200)(see Fig 6), as an example In the biaxial tests as considered here, two crack branches became dominant For these two branches, a new diagram was generated with the crack propagation rate, log dc/dN, on the ordinate and the crack length, c, on the abscissa (see Fig 8b) The dc/dN values were calculated from the crack advances, Ac, during the number of cycles, AN, between two measurements in the tests These data were then plotted versus the mean value of the crack lengths between the two measurements A comparison of the dc/dN versus c curves from all tests showed that the curves did not show any significant irregularities or deviations from a smooth curve as the cracks changed from part-through crack to through crack These dc/dN versus c curves stem from data as measured on the upper surface of the specimen It has to be assumed that the crack front 1(4oom)§ s(4oor~) ]0 ,_,7 E E6 il|ilJ Z IO VVVVV ) o O ,'-5 tT~ J t'- ~4 ~2 e3 ~4 500 1000 1500 2000 2500 3000 3500 4000 Number of blocks, N FIG 8a Crack length versus N-behavior for the individual crack branches Copyright by ASTM Int'l (all rights reserved); Wed Dec 23 19:33:23 EST 2015 Downloaded/printed by University of Washington (University of Washington) pursuant to License Agreement No further reproductions authorized 300 MULTIAXIAL FATIGUE AND DEFORMATION TESTING 1E+00 1E-01 O c3 1E-02 ~ ~ "~ E c3 A Z 1E-03 -o : ~r o4 - "o c4 1E-04 1E,05 C r a c k l e n g t h c [mm] 10 FIG 8b dc/dN versus c-behavior for the block history as specified in Fig 8e, propagation became much more complicated through the specimen At the beginning, its shape is almost semicircular After it has penetrated the opposite side, crack propagation has to accelerate rapidly Later on, it reaches its new stable position where the visible crack lengths on the upper and the opposite side are about the same In Fig 8b, the shape of the (log) dc/dN versus c curve appears different from the expected shape because the scale of the x-axis is linear If a log-scale had been chosen, the resulting curves would appear approximately as straight lines The observed dc/dN versus c-behavior could be described by a simple exponential equation like the well-known Paris equation It has to be noticed, however, that block loading was applied in the tests The derived coefficients, C, and exponents, n, of the equation for the individual tests have been listed in Table From the individual dc/dN versus c curves of the dominant crack branches, a mean value was determined and plotted versus the crack length These mean values were then plotted onto one curve This curve was used for all further considerations Block Histories Where the Major Cycle and the Minor Cycles Exhibit the Same Maximum Stress In Fig 9a, the dc/dN versus c behavior from the tests where the maximum stress of the major and minor cycles was kept the same and with 100 minor cycles is shown Figure 9b shows the corresponding behavior for block histories with minor cycles The following tendencies become visible As the amplitudes of the minor cycles became higher, the crack propagation rates increased significantly in the tests with block histories with 100 minor cycles The dc/dN versus c curve for the history with 1(4~176+ 100(4~176 (see Fig 6) was very close to the dcldN versus c curve for constant amplitude loading Copyright by ASTM Int'l (all rights reserved); Wed Dec 23 19:33:23 EST 2015 Downloaded/printed by University of Washington (University of Washington) pursuant to License Agreement No further reproductions aut TRAUTMANN ET AL ON VARIABLE BIAXIAL TESTING 301 TABLE Coefficients and exponents of crack propagation equation, dc/dN = C - c", for load types investigated Loading Type 1(4OO/o)+ 5(4o0/~o) 1(4o%) + 5(40~ 1(4OO/o)+ 100(4~176 1(4OO/o)+ 100(4~176 1(4o%) + 5(3o0Ao0) 1(4OO/o)+ 4(ao0Ao0) 1(4~ + 100(300/100) 1(4~176 + 5(40%8o) 1(4~176+ 100(4~176 1(4~176+ 5(44o0A2o) 1(4~176+ 100(4~176 l(4~176 + 5(~~ 1C~~ + 100(3a~ CAL(4O0/o) CAL(4O0/o) CAL(4O0/2O0) Crack No Coefficient, C Exponent of c, n cl c22 c3 c4 cl c2 cl c2 c3 c4 cl c2 cl c2 cl c2 c3 c4 c3 c42 cl c2 cl c2 cl c3 c4 c1 c2 c1 c2 c1 c32 c4 0.0010939 0.0014900 0.0011826 0.0012646 0.0084634 0.0089509 0.0113675 0.0127529 0.0009210 0.0007670 0.0008562 0.0008562 0.0055276 0.0042281 0.0005722 0.0007282 0.0046170 0.0028370 0.0015338 0.0019363 0.0291588 0.0250220 0.0006989 0.0014959 0.0108023 0.0110868 0.0106734 0.0003843 0.0003020 0.0003809 0.0004723 0.0000945 0.0000778 0.0000831 2.019 2.216 2.132 2.173 2.069 1.996 2.198 2.064 1.709 2.266 2.523 2.401 1.795 1.883 2.494 2.418 2.076 2.310 2.623 2.621 2.164 2.335 2.520 2.132 3.044 3.048 2.382 1.497 2.366 2.226 2.299 2.076 2.259 2.132 For the block histories with minor cycles, the tendency was roughly the same and the dc/dN versus c curve for the block history with the second largest amplitude of the minor cycles intersected the curve with the largest amplitude of the minor cycles (constant amplitude loading) The fact that the dc/dN versus c curves for the block histories with and with 100 minor cycles and with force ranges between 120 and 400 kN and between and 400 kN were closest together and that this tendency was more pronounced for the histories with minor cycles indicates that crack closure influences may be present and that the crack opening level is somewhat more controlled by the major cycles under the histories with minor cycles Block Histories Where the Minor Cycles Exhibit the Same Mean Stress The crack propagation behaviors under block histories with 100 and with minor cycles with the same mean stress but different amplitudes of the minor cycles in all tests are shown Copyright by ASTM Int'l (all rights reserved); Wed Dec 23 19:33:23 EST 2015 Downloaded/printed by University of Washington (University of Washington) pursuant to License Agreement No further reproductions auth 302 MULTIAXlALFATIGUE AND DEFORMATIONTESTING 1E+01 t 0t CAL 4Q~O IIIIIIIIIh1/1111/ 1E+O0 o 1E-01 400 ~1400/01 + 100(40012001 t3 E E Z "0 ~ 11::-02 "0 E-03 / 1E-04 I I I I J I d / I I I I Crack length c [mm] I I P I 10 FIG 9a -dc/dN versus c-behavior for block histories with 100 minor cycles that exhibited the same maximum stress of the major and of the minor cycles in Figs 10a and 10b, respectively The mean stress was half the maximum stress of the major cycles As expected, increasing the amplitude of the minor cycles led to an increase in the crack propagation rates Block Histories Where the Minor Cycles Exhibit the Same Amplitude but Different Mean Stresses Figures 1l a and 1l b show the results from two sets of bl( ,ck histories where the mean stress of the minor cycles was varied but where the amplitude wz s kept constant Figure la shows Copyright by ASTM Int'l (all rights reserved); Wed Dec 23 19:33:23 EST 2015 Downloaded/printed by University of Washington (University of Washington) pursuant to License Agreement No further reproductions autho TRAUTMANN ET AL ON VARIABLE BIAXIAL TESTING 303 1E+00 so cAI.~ ,:AAAAAA - orVVtVV E-01 1(40e/0) + ~ , ~ t l ) 120 ~, _o E-02 1(4~t0) + ,, ,_,q ff E S{4OOnO0) 40O r~F~r-r7 _ 9"u 1E-03 _ o ,,.o ,-~r ~ " : i / E-04 15-05 i I i I !' 1! I I , I i I , i C r a c k length c [ m m ] ~ I i I 10 FIG b ~ c / d N versus c-behavior for block histories with minor cycles that exhibited the same maximum stress of the major and of the minor cycles the crack propagation behavior for block histories with 100 minor cycles, and Fig l b shows the behavior for block histories with minor cycles Increasing the mean stress of the minor cycles led to an increase in the crack propagation rates Although the test results were again largely varied and despite the fact that one block test with 100 minor cycles already ended at a crack length of about nun, there was again some indication of a crack closure influence In the tests with minor cycles, the increase in crack propagation rates was higher for the block history with the larger amplitude as the mean stress was increased From the experimental results, some trends became visible One is that crack closure may Copyright by ASTM Int'l (all rights reserved); Wed Dec 23 19:33:23 EST 2015 Downloaded/printed by University of Washington (University of Washington) pursuant to License Agreement No further reproductions a 304 MULTIAXIAL FATIGUE AND DEFORMATION TESTING 1E+01 - - o t " C A L 400/(I E+00 j = o 1E-01 114~#0} + 100(34~#60) Q E E ~ ~1_ ~ II 1(40(IR) + t 0 ( 0 / 0 ) z -~ E-02 z E-03 1E-04 i I I ~l i I I L I I I I Crack i I I I I 10 length c [mm] FIG lOa