Astm stp 338 1963

SYMPOSIUM ON FATIGUE TESTS OF AIRCRAFT STRUCTURES: LOW-CYCLE, FULL-SCALE, AND HELICOPTERS Presented at the FOURTH PACIFIC AREA NATIONAL MEETING AMERICAN SOCIETY FOR TESTING AND MATERIALS Los Angeles, Calif., Oct 1-3, 1962 Reg U S Pat Off ASTM Special Technical Publication No jj8 Price $10.50; to Member.s $7,35 Published by the AMERICAN SOCIETY FOR TESTING AND MATERIALS 1916 Race St., Philadelphia 3, Pa BY AMERICAN SOCIETY FOR TESTING AND MATERIALS 1963 Library of Congress Catalog Card Number: 63-15793 Printed in Baltimore, Md September, 1963 FOREWORD The papers in this Symposium on Fatigue of Aircraft Structures were presented during four sessions held on October 1-3, 1962, at the Fourth Pacific Area National Meeting of the Society, Los Angeles, Calif The symposium, sponsored by Committee E-9 on Fatigue, was organized into three broad categories The first section on Low-Cycle Fatigue was organized by Ivan Rattinger of Aerospace Corp The second group of papers dealing with Helicopter Fatigue Problems was organized by M J McGuigan, Jr., of Bell Helicopter Corp The final section of this symposium, on Problems in Design and Evaluations of Full-Scale Structures, was presented under the leadership of M S Rosenfeld of the Navy Air Material Center The over-all chairman of the symposium program was H F Hardrath, National Aeronautics and Space Administration A transcript of the panel discussion on low-cycle fatigue held during this symposium was supplied by Ivan Rattinger Presiding oflScers of the sessions were R E Peterson, Westinghouse Electric Corp.; F B Stulen, Curtiss-Wright Corp.; H J (rover, Battelle Memorial Inst.; and T J Dolan, L^niversity of Illinois Acting as session chairmen were Messrs McGuigan, Hardrath, Rattinger, and Rosenfeld NOTE.—The Society is not responsible, as a body, for the statements and opinions advanced in this publication CONTENTS Introduction—H F Hardrath Low-Cycle Fatigue Low-Cycle Axial Fatigue Behavior of Mild Steel—J T P Yao and W H Munse The Effect of Mean Stress on Fatigue Strength of Plain and Notched Stainless Steel Sheet in the Range from 10 to 10' Cjxles—W J Bell and P P Benham Low-Cycle Fatigue of Characteristics of Ultrahigh-Strength Steels—C, M Carman, D F Armiento, and H Markus Low-Cycle Fatigue of Ti-6A1-4V at - F—R R Hilsen, C S Yen, and B V Whiteson Low-Cycle Fatigue Properties of Complex V\'elded Joints of High Strength 301, 304L, 310, and AM-355 Stainless Steel Sheet Materials at Cyrogenic Temperatures—J L Christian, A Hurlich, and J F Watson Effect of Stress State on High-Temperature Low-Cycle Fatigue—C R Kennedy Panel Discussion of Low-Cycle Fatigue 25 47 62 76 92 107 Helicopter Fatigue Empirical x^nalysis of Fatigue Strength of Pin-Loaded Lug Joints—A A Mittenbergs Statistical Evaluation of a Limited Number of Fatigue Test Specimens Including a Factor of Safety Approach—Carl Albrecht Helicopter Fatigue Substantiation Procedures for Civil Aircraft—J E Dougherty and H C Spicer, Jr 131 150 167 Design and Evaluations of Full-Scale Structures An Aluminum Sandwich Panel Test Under Mach-2.4 Cruise Conditions—W D Buntin and T S Love 179 Estimation of the Fatigue Performance of -Aircraft Structures—J Schijve 192 Discussion 214 Aircraft Structural Fatigue Research in the Navy—M S Rosenfeld 216 Discussion 238 Small Specimen Data for Predicting Life of Full-Scale Structures—C R Smith 241 Programmed Maneuver-Spectrum Fatigue Tests of Aircraft Beams Specimens— Leonard Mordfin and Nixon Halsey 251 Discussion 274 STP338-EB/Sep 1963 SYMPOSIUM ON FATIGUE TESTS OF AIRCRAFT STRUCTURES: LOW-CYCLE, FULL-SCALE, AND HELICOPTERS INTRODUCTION BY H F HARDRATH1 Following a precedent set at previous West Coast National Meetings of the Society, ASTM Committee E-9 on Fatigue again sponsored a Symposium on Fatigue of Aircraft Structures at the West Coast Meeting held in Los Angeles, Calif., Oct 1-5, 1962 As indicated by the presiding officer of one of the sessions, fatigue research may concern itself with any of several levels of complication: (1) the basic mechanism may be studied from the physical and metallurgical points of view; (2) simple specimens may be tested to study the mechanical behavior of the material under carefully controlled loading conditions; (3) notches or other discontinuities may be used to introduce partially the effect of shape of practical parts; (4) subassemblies may be studied to introduce the effects of somewhat more complicated joints; (5) complete structures may be subjected to necessarily simplified representations of expected loading conditions; and (6) service failures may be analyzed The symposium includes papers treating each of these phases of fatigue study and Fatigue Branch, NASA-Langley Research Center, Hampton, Va Copyright 1963 by ASTM International introduces effects of high and low temperature As with other symposia on fatigue, this one does not conclude that the problem is now solved It does, on the other hand, attempt to assemble representative current thinking on the problem with particular emphasis on aeronautical and missile applications Several papers present procedures for correlating observations that should be particularly helpful to designers One paper incorporating studies of the combined influence of loads and temperatures is almost certain to be the forerunner of a variety of such studies that will be carried out in connection with future vehicles The papers are organized into three broad categories: (1) low-cycle fatigue problems; (2) helicopter fatigue problems; and (3) problems encountered in design and evaluation of full-scale structures Grateful acknowledgment is made of the contributions of the authors, the session chairmen, presiding officers, those who reviewed papers prior to the meeting, the West Coast Coordinator, and the participants in the discussions www.astm.org Low-Cycle Fatigue STP338-EB/Sep 1963 LOW-CYCLE AXIAL F A T I G U E BEHAVIOR OF M I L D STEEL B Y J T P Y A O AND W H MUNSE2 SYNOPSIS A general hypothesis that describes the cumulative effect of plastic deformations on the low-cycle fatigue behavior of metals is presented and verified with results of a variety of tests on steel specimens Limited correlations with existing test data from other low-cycle fatigue tests on aluminum-alloy specimens indicate that it may be possible also to extend this hypothesis to metals other than steel NOTATIONS Ac, Af , A0, Ar, C, Dc, df , d0 , dr, i, m, «, N, q, Cross-sectional area at the test section of the specimen after precompression, sq in Cross-sectional area at the test section of the specimen at fracture, sq in Original cross-sectional area at the test section of the specimen, sq in Cross-sectional area at the test section of the specimen, re-machined after precompression, sq in A constant Diameter at the test section of the specimen after precompression, in Diameter at the test section of the specimen at fracture, in Original diameter at the test section of the specimen, in Diameter at the test section of the specimen, re-machined after precompression, in Number of applications of tensile load Empirical parameter obtained from slope of log Aet versus log N diagram Number of applications of tensile load prior to fracture Number of cycles to failure Plastic true strain, per cent Assistant Professor of Civil Engineering University of N e w Mexico, Albuquerque, N Mex Professor of Civil Engineering, U n i v e r s i t y of Illinois, TJrbana, 111 Copyright^ 1963 by ASTM International qc\, Plastic true precompressive strain, per cent qf , Plastic true strain at fracture in simple tension, per cent 022 099 218 219 Geometric m e a n -28.6 -28.6 -28.6 7580 7580 7580 42 770 37 561 40 100 Test Series B-1 0-2 0-5 ] \ \ fact that the fatigue properties of the beam specimens are similar to those of full-scale aircraft structures (Fig 1), it appears that this specimen design has merit for studying the fatigue behavior of aircraft structures EFFECTS OF PRELOAD Bennett and Baker (5) showed that the application of a prestress prior to fatigue testing produces an increase in fatigue life providing the prestress is considerably greater than the maximum stress of the fatigue cycle However, if the prestress is only slightly larger than the maximum fatigue stress, a slight Cycles to Deviation from Interval, cycles Fatigue Failure Mean, per cent -6 Tests were conducted in the present investigation to evaluate the effect of preloading on the basic fatigue properties of the beam specimens Each specimen was subjected to one cycle of 100 per cent of limit load immediately prior to the start of a constant-load-amplitude fatigue test In the fatigue test the load was cycled between a preselected load level and 14.3 per cent of limit load The results of these tests are given in Table III together with the results for test series B-1 (from Table II), in which the first load cycle applied to each specimen is considered a preload The effects of preloading may be eval- 261 MORDFIN AND H A L S E Y ON F A T I G U E T E S T S OF BEAM SPECIMENS uated by comparing Tables II and III These effects are in agreement with those found by the other investigators Furthermore, the comparison shows that when the preload is applied in a direction opposite to the maximum fatigue load, a significant reduction of the fatigue life takes place Bennett and Baker (s) and Templin (6) obtained similar results load was applied immediately prior to the start of the fatigue test, and additional single overloads were applied at periodic intervals throughout the fatigue test The interval was approximately equal to 10 per cent of the basic fatigue life of the specimen at the fatigue load level under consideration The fatigue loads were cycled between the preselected load levels and 14.3 per cent of limit load Table IV lists the fatigue load levels, the intervals between overloads, the number of fatigue cycles to failure, the EFFECTS OF PERIODIC OVERLOADS Heywood (8) attributed the effects of prestressing to the introduction of com- TABLE v.—RESULTS OF CONSTANT-LOAD-AMPLITUDE FATIGUE TESTS WITH PRELOADING TO 100 PER CENT OF LIMIT LOAD AND PERIODIC UNDERLOADING TO 25 P E R CENT OF LIMIT LOAD Loads cycled between 14.3 per cent of limit load and indicated load levels Test Series Specimen Load Level, per cent of limit load Cycles Interval, cycles Fatigue to Failure Deviation from Mean, per cent U-1 • 126 127 Geometric m e a n 100 100 100 238 238 238 125 099 110 1 U-2 ] 124 125 Geometric mean 80 80 80 573 573 573 049 063 980 -12 14 120 121 Geometric m e a n 60 60 60 601 601 601 27 671 22 650 25 000 11 122 123 Geometric m e a n 40 40 40 34 637 34 637 34 637 164 156 248 638 202 000 -19 23 I U-3 U-4 \ • pressive residual stresses He conjectured that these residual stresses diminish gradually during fatigue cycling and that by applying overstresses at periodic intervals during the fatigue process, the residual stresses could be restored Heywood showed that this technique led to substantially greater effects than prestressing A series of fatigue tests was conducted to investigate the effect of periodic overloads on the constant-load-amplitude fatigue lives of the beam specimens The overload level employed was 100 per cent of limit load One cycle of over- deviations from the geometric mean at each load level, and the results for test series B-1 (Table III) with every 221st load cycle considered as an overload Specimens 206 and 207 failed under the application of an overload; all other specimens failed at the fatigue load level except specimen 209, which did not fail A comparison of Tables II, III, and IV confirms Heywood's contention since, in general, it shows that when preloading is beneficial periodic overloading is more beneficial, and when preloading is detrimental, so is periodic overloading 262 SYMPOSIUM ON FATIGUE OF AIRCRAFT STRUCTURES cycling between 25 and 14.3 per cent of limit load The intervals were approximately equal to 10 per cent of the fatigue life of the preloaded specimens Table V lists the fatigue load levels, the intervals between underloading, the number of fatigue load cycles to failure, and the deviations from the mean at each fatigue load level EFFECTS OF PERIODIC UNDERLOADING Some tests were conducted to explore the possibility of obtaining increased fatigue lives through a combination of periodic underloading and preloading Beam specimens were subjected to a preload of 100 per cent of limit load and then fatigue tested with loads cycling between designated load levels and 14.3 100 90 80 a o ^ 70 " 60 v^ '^^^ \ x^^ \ Overlooded > C u N^v ^ fc \\ o x \ Bosic \ uncertointy in load v-Moximum un /'^-Moximum Prelooded fPrelooded ~\ond underlooded »cott»r in li(« 30 10' 10* Cycles to failure FIG 8.—Comparison of S-N Curves for Beam Specimens Subjected to Various Treatments Minimum Load: 14.3 Per Cent of Limit Load TABLE VI.—COMPREHENSIVE SPECTRUM, 20-HR BLOCK Load Range, per cent of limit load XT u t r- \ N""'''" °f Cycles 14.3 14.3 14.3 14.3 14.3 14.3 14.3 14.3 14.3 14.3 per per 17 per 65 per 172 per 283 per 1000 per 1000 per 280 per per to to to to to to to to to to 115 100 85 70 55 40 25 -14.3 -28.6 lifetime block block block block block block block block block per cent of limit load At equal intervals during each fatigue test the specimen was subjected to 100 applications of load The effect of the underloading may be evaluated by comparing Tables III and V This comparison reveals no consistent effect of periodic underloading in that no significant changes in fatigue life occur as a result of cycling at 25 per cent of limit load The number of underload cycles involved in these tests was far too small to qualify properly as coaxing, which can improve the fatigue strengths of some materials (9); however, 7075-T6 aluminum alloy is relatively unaffected by coaxing (10) The relative effects of preloading, overloading, and underloading on the MORDFIN AND H A L S E Y ON F A T I G U E T E S T S OF B E A M fatigue properties of the beam specimens under positive loads are shown in Fig 8, in which smooth curves are faired through the mean lives given in Tables TABLE VII.—TEST SPECTRUMS, 20-HR BLOCKS Loads cycled between 14.3 per cent of limit load and indicated load levels Load Level, per cent of limit load Spectrum f i i f j J 1I f ' 1 I , i Cycles per Block 100 85 70 55 17 65 172 100 85 70 55 40 17 65 172 283 100 85 70 55 40 25 17 65 172 283 1000 100 85 70 55 -14.3 17 65 172 1000 280 100 85 70 55 -14.3 -28.6 17 65 172 280 115 100 85 70 55 1» 17 65 172 " Prior to start of test II to V Also shown in the figure are the maximum scatter observed in life (test series P-4, Table III) and the maximum uncertainty in load (6 per cent) For most of the test data the scatter and the uncertainty were considerably smaller than these maximum values 263 SPECIMENS SPECTRUM FATIGUE TESTS Six test spectrums were used, all being variations of the comprehensive aircraft spectrum given in Table VI This tabulation represents an early spectrum prepared by the Bureau of Naval Weapons Each block was intended to simulate the loads experienced by a military airTABLE VIII.—RESULTS OF SPECTRUM FATIGUE TESTS Spectrum [ i f J i ( \ I r i f i r J i Specimen Blocks to Failure Deviation from Mean, per cent 128 129 130 Geometric m e a n 361 220 242 268 35 -18 -10 134 135 136 Geometric m e a n 141 155 196 162 -13 -4 21 203 204 Geometric m e a n 126 138 132 -5 139 220 Geometric m e a n 170 86 121 40 -29 138 304 305 Geometric m e a n 129 68 102 96 34 -29 131 132 133 Geometric m e a n 193 282 202 222 -13 27 -9 craft during a typical 20-hr interval of its service life This spectrum is now considered obsolete The spectrum fatigue tests were used to study the effects of the various steps in the spectrum in order to determine which of them must be included in spectrum fatigue tests that are intended to provide estimates of aircraft service life The load levels and the cycles per block at each load level for the six spectrums used are given in Table VII Load 264 SYMPOSIUM ON FATIGUE OF AIRCRAFT STRUCTURES was cycled between the designated load levels and 14.3 per cent of limit load Within each block the load levels were applied in descending order from the highest to the lowest (or most negative) level Some effects of this sequence of load application are discussed in Appendix I.' The results of the spectrum tests are given in Table VIII Each specimen failed at 100 per cent of limit load within the first three cycles of the block following the completed number of blocks to failure shown in the table EFFECTS OF VARIOUS SPECTRUM LOAD LEVELS The desire to eliminate unnecessary load levels from a test spectrum is based upon the need to minimize the time required for testing The apparatus required to conduct programmed tests involving, say, eight load levels is not significantly more complex nor more costly than that needed for four load levels The basic test spectrum (spectrum 1, Table VII) consists of four load levels ranging from 100 to 55 per cent of limit load; the mean fatigue life of the beam specimens under this spectrum was 268 blocks The 40 and 25 Per Cent of Limit Load Levels: Spectrum is identical with spectrum except that it includes one more load level, 40 per cent of limit load The mean fatigue life under spectrum was found to be 162 blocks, 60 per cent of the life under spectrum This indicates that the 40 per cent of limit load step is rather damaging and that its omission from the test spectrum results in unrealistically high estimates of service life Spectrum is identical with spectrum ' See p 270 except that it includes still another load level, 25 per cent of limit load Table VIII shows that the mean life under spectrum is further reduced to only 49 per cent of the mean life under spectrum When this result is viewed in terms of the scatter in the test data, however, it appears that the additional decrement in life may be a manifestation of the scatter rather than a real attribute of the 25 per cent of limit load step Additional test data would be required to make this determination with certainty Even if the 25 per cent of limit load step does reduce the spectrum fatigue life, the degree of reduction may not be sufficiently serious to warrant the additional testing time required by its inclusion in the test spectrum Zero and Negative Load Levels: Table VII shows that spectrums and are the same as spectrum except that they include load cycles to zero and negative load levels Table VIII shows that the inclusion of these steps reduced the life of the beam specimens to 45 and 36 per cent of the mean life under spectrum If these results are considered together with the results of the periodic overloading tests, it is seen that when high positive load levels and low negative load levels are both present in a test spectrum, each acts to reduce the fatigue life under the other In test series 0-5 (Table IV) occasional loadings to 100 per cent of limit load reduced the fatigue life at —28.6 per cent of limit load by introducing detrimental residual tensile stresses into the subsequent failure surface Under spectrums and the regular application of load cycles to small negative load levels reduced the fatigue life under high positive loads, presumably by causing the beneficial residual compressive stresses, which were introduced into the subsequent failure MoRDriN AND HALSEY ON FATIGUE TESTS surface by the high positive loads, to decay more rapidly The latter result is similar to that which is obtained with gust-load spectrums and with ground-to-air-to-ground cycles, which include zero and negative load levels Wallgren (11), for example, showed that when positive and negative gust loads below the nominal fatigue or BEAM SPECIMENS 265 The relative closeness of the lifetime reductions obtained with spectrums and suggests that the major portion of the damage done by the zero and negative load levels is due to the —14.3 per cent of limit load level, which is common to both spectrums However, the test results are inadequate to confirm this premise FIG 9.—Typical Failures of Beam Specimens Tested at (o) Higher Load Levels and (6) Lower Load Levels limit are added to an otherwise complete maneuver and gust loads spectrum, the fatigue life is reduced by about 20 per cent Schijve and Jacobs (12) believe that this effect is, on the average, closer to 50 per cent Payne (7) showed that the addition of periodic negative loads reduced spectrum fatigue life significantly These results support the recommendation made by Lundberg and Eggwirtz (13) that, although maneuver loads are the most important for fighter aircraft, gust loads should be included in the test spectrum The 115 Per Cent of Limit Load Preload: The effect of a preload of 115 per cent of limit load on the fatigue life under the basic 4-level spectrum may be evaluated by comparing the results for spectrums and It is seen that the preload reduced the mean fatigue life from 268 to 222 blocks (17 per cent); this reduction loses meaning, however, when compared with the variations in fatigue life obtained from specimen to specimen Swartz and Rosenfeld (14) tested fullscale 7075-T6 aircraft structures under 266 SYMPOSIUM ON FATIGUE OF AIRCRAFT STRUCTURES a similar 4-level spectrum with and without a preload to 115 per cent of limit load Their results show a 16.5 per cent increase in fatigue life with the preload, but here, too, the variations in lifetime from specimen to specimen make this conclusion questionable These findings are in agreement with the effects of preloading discussed earlier The 4-level spectrum is essentially a maneuver-loads spectrum which consists of load levels that are relatively high compared with the preload Under these TABLE IX.—COMPARISON OF TEST RESULTS WITH P R E D I C T E D FATIGUE LIVES UNDER SPECTRUMS AND Blocks to Failure Reference Spec- Spectrum trum Test results Linear rule Tangent M u n s e et al Gatts Valluri Liu-Corten Henry Smith Modified LiuCorten Table VIII 268 162 (2) (17) (18) (19) (20) (21) (22) 43 60 23 39 48 66 64 76 37 60 21 37 44 60 62 71 Appendix I I 181 178 conditions preloading has a relatively small effect; however, if the spectrum contained lower load levels, of the order of gust loads, or if a higher preload had been employed, a distinct improvement in life probably would have been observed as a result of preloading Nicole (15) has expressed the conviction that the demonstration of sufficient fatigue resistance should be made without the benefits of preloading Shanley (16) recommended that any beneficial loading which is expected to occur but once in the life of an aircraft should be ignored because of the possibility that certain aircraft will not experience this loading, (joing a step further, Schijve and Jacobs (12) feel that high loads occurring with a frequency of less than about ten in the anticipated life should not be included in the test spectrum DESCRIPTION OF FAILURES Typical failed specimens are shown in Fig Failures at the higher load levels (150, 100, and 80 per cent of limit load) were similar to that of Fig 9(a), while those at the lower load levels were similar to that of Fig 9(6) Nearly all failures occurred at the center of the specimen or at one rivet spacing away from the center Frequent inspections usually did not reveal the presence of fatigue cracks prior to failure In the few cases where cracks were detected, at least 93 per cent of the ultimate life had elapsed COMPARISON OF TEST RESULTS WITH PREDICTED FATIGUE LIVES Numerous theories of cumulative fatigue damage have been proposed Several of these were used to predict the fatigue lives of the beam specimens under spectrums and Some details of the calculations involved in making the predictions are discussed in Appendix 11.^ Comparisons of the predicted lives with the test results are given in Table IX Insufficient data were available for predictions based on the theories of Richart and Newmark (23), Marco and Starkey (24), and Freudenthal and Heller (25) The method proposed by Manson, Nachtigall, and Freche (26) is inapplicable With the exception of the modified Liu-Corten method, all of the theories are highly conservative with respect to spectrums and Even more significant is the fact that none of the theories, in' See p 270 MORDFIN AND H A L S E Y ON F A T I G U E T E S T S OF B E A M eluding the modified Liu-Corten, properly accounts for the damage of the 40 per cent of limit load step, which is the difference between spectrums and The test results show a reduction in life of 40 per cent as a result of this step, while the best prediction of this reduction (linear rule) is only 14 per cent These findings should not be surprising Most damage theories not properly account for the beneficial effects of the residual compressive stresses that are introduced by high positive load levels Therefore, the theories are conservative when applied to spectrums and 2, which consist solely of high positive load levels As suggested earlier, the addition of negative load levels to a spectrum causes the residual stresses to decay and thereby reduces their beneficial effects Hence, the theories might be expected to provide more accurate life predictions when applied to spectrums consisting of both positive and negative load levels The drawback is that most theories, including the Liu-Corten, not contain provision for handling both positive and negative load levels These considerations suggest that, although a theory may give a safe prediction for fatigue life under spectrum loading, it is not necessarily capable of evaluating the relative effects of the individual load levels in the spectrum CONCLUSIONS The bending fatigue properties of a 7075-T6 built-up beam specimen were found to bear similarities to the fatigue properties of certain typical full-scale aircraft structures Also, the fatigue behavior of the beam specimen is notably insensitive to minor variations in testing technique and material The test results warrant the following conclusions regarding the constant-load- SPECIMENS 267 amplitude fatigue properties of the beam specimens: Preloading at 100 per cent of limit load improved the fatigue life of the specimens at fatigue load levels of 60 per cent of limit load or less, provided the preload was applied in the same direction as the subsequent fatigue loads The effect of this preloading was negligible or slightly detrimental to fatigue life under load levels of 80 per cent of limit load or higher When the preload and the fatigue loads were applied in opposite directions a reduction in life resulted Periodic overloading at 100 per cent of limit load affected the fatigue properties in the same way as preloading did, only more so Specifically, under conditions in which preloading was beneficial, periodic overloading was more beneficial, and where preloading was ineffective or detrimental, so was periodic overloading Periodic underloading at 25 per cent of limit load with a relatively small number of cycles produced no significant changes in the fatigue life under fatigue loads applied in the same direction as the underloading Spectrum fatigue tests were carried out on the beam specimens using several variations of the comprehensive spectrum in Table VI The test results justify the following conclusions regarding the necessity of including all of the load levels in spectrum fatigue tests which are intended to provide estimates of service life The 40 per cent of limit load step caused significant damage, and its inclusion in the test spectrum is necessary The 25 per cent of limit load step was less damaging, and under certain conditions its omission from the test spectrum may be justified The zero and negative load levels 268 SYMPOSIUM ON FATIGUE OF AIRCRAFT STRUCTURES were severely damaging, but there is reason to suspect that most of this damage may be attributed primarily to the — 14.3 per cent of limit load level Preloading at 115 per cent of limit load did not significantly affect fatigue life under a truncated spectrum consisting solely of high positive load levels (55 to 100 per cent of limit load) None of the currently available theories of cumulative fatigue damage was adequate for the dual purpose of predicting fatigue life under spectrum loading and evaluating the effects of individual load levels in a spectrum A cknowledgments: The research program described in this paper was carried out at the National Bureau of Standards under the sponsorship and with the financial assistance of the Bureau of Naval Weapons The authors acknowledge the contributions of Silas Katz, who prepared the basic design of the pneumatic system for the fatigue testing machine; Richard H Harwell, Jr., who patiently fabricated and refabricated parts for the machine; and Thomas A Robusto, Jr., Howard W Stone, Jr., Philip Granum, and Thomas D Field, Jr., who assisted in the performance of some of the tests APPENDIX I EFFECTS OF LOADING SEQUENCE IN PROGRAMMED SPECTRUM FATIGUE TESTS In what sequence should the load levels in each block of a test spectrum be applied in order to simulate service fatigue most closely? Probably a random sequence is best However, limitations of testing equipment frequently require that a programmed sequence be used In this case, the problem is reduced to selecting a programmed sequence that produces fatigue damage at a rate approximately equal to the rate at which a random sequence produces damage Selecting a programmed sequence that meets this requirment is extremely complex, if not impossible, with the present state of knowledge Approaching this problem on an analytical basis, Rosenthal (27) examined the residual stresses that are introduced by the high load levels of the spectrum and the decay of these stresses at the other load levels His findings indicate that the desired sequence depends on the exact spectrum and test specimen under consideration This unhappy conclusion has inadvertently been confirmed experimentally Consider, for example, the extreme types of programmed sequences, namely, those in which the loads in each block are applied in ascending order of magnitude and those in which they are applied in descending order Schijve and Jacobs (12) found the descending sequence to be more damaging than the ascending sequence Freudenthal and Heller (28) reached the same conclusion and also showed that both of these sequences were more damaging than their random sequences On the other hand, Naumann, Hardrath, and Guthrie (29) found the ascending sequence more damaging than the descending one, with their random sequences being intermediately damaging All of these investigators worked with gust-load spectrums and specimens fabricated from 7075T6 aluminum alloy The most likely conclusion is that the disparity in their results stemmed from differences in their spectrums and specimen designs Payne (7), Kuhn (30), and others have expressed the viewpoint that whatever the effect of sequence may be, it would become smaller as the block size is reduced Unfortunately the available facts not support this The test results reported by Schijve and Jacobs (12), Naumann, Hardrath, and Guthrie (29), and Gassner (31) show no systematic variation of the sequence effect with block size A sizeable effort, both analytical and experimental, would be required to establish a practical understanding of the sequence MORDFIN AND H A L S E Y ON F A T I G U E 40 TESTS OF B E A M SPECIMENS 269 60 Blocks to failure FIG 10.—Effect of Assumed Value of Fatigue Limit on Predicted Life Under Spectrum According to Valluri (19) 100 F50 200 Blocks to foiture FIG 11.—Effect of Assumed Value of d on Predicted Fatigue Life Under Spectrum According to Liu and Corten (20) 270 SYMPOSIUM ON FATIGUE OF AIRCRAFT effect A better approach would be to concentrate on the development of apparatus STRUCTURES capable of applying loads of preselected spectrums in random sequences APPENDIX II CALCULATION OF PREDICTED FATIGUE LIVES These comments refer to the predictions of fatigue life given in Table IX The following interpolations of Fig were used in applying the linear damage rule Load Level, per cent of limit load Fatigue Life, cycles 200 300 15 600 85 70 55 The following interpolations of the preloaded curve in Fig were used in applying Smith's method (22) Load Level, per cent of limit load 85 70 55 Fatigue Life, cycles 350 17 000 43 000 where: S'l Sg K = = = = load level, the highest load level in spectrum, the endurance limit, and a constant In the calculations this term was set equal to unity, resulting in predicated fatigue lives which are closer to the actual ones The Liu-Corten method (20) contains a constant, d, which, according to its developers, " may be obtained most simply from a two-stress-level repeated block fatigue experiment of the component or full-size structure." Accordingly, the constant, d, was computed from the results of test series 0-2, 0-3, and U-1, and produced the following values: Test Series 0-2 0-3 U-1 Average 4.17 8.25 The constant fi for Munse's method (17) 1.58 was calculated to be 0.51 for spectrum and 4.67 0.56 for spectrum The methods of Gatts (18), Valluri (19), A value of 4.7 was used to predict the faand Henry (21) require use of a fatigue limit tigue lives shown in Table IX for the LiuThe effect of fatigue limit on the fatigue life Corten method The feeling has been expressed, however, under spectrum as predicted by one of these methods (19) is shown in Fig 10 It is that a two-stress-level experiment may not seen that the prediction improves as the provide the best value of d for spectrum fatigue limit increases While it is doubtful fatigue life predictions In fact, Swartz and that a true fatigue limit exists for the beam Rosenfeld (32) showed that a value of 8.25 specimens, a value of 35 per cent of limit gave reasonable predictions for a variety of full-scale aircraft structures under spectrum load was used on the basis of Fig The damage function in Valluri's method loadings The predictions shown in Table I X (19) contains the following term among for the modified Liu-Corten method were calculated by using a value of 8.25 instead of others: 4.7 for d The variation of the predicted fatigue 5, - S, In life with d is given in Fig 11 for spectrum K For a predicted life of 268 blocks under - Se spectrum \, d = 10.3; with this value the In K predicted life under spectrum is 266 blocks MORDFIN AND H A L S E Y ON F A T I G U E T E S T S OF BEAM SPECIMENS 271 REFERENCES (1) D M Howard and S Katz, "Repeated Load Tests of Aircraft Wing Beam Specimens Under Bending and Bending-Torsion Loads," Nat Bureau of Standards, unpublished report (2) ARTC/W-76 Aircraft Structural Fatigue Panel, "Aircraft Fatigue Handbook, Vol II—Design and Analysis," Aircraft Industries Assn., Washington, D C (1957) (3) L Mordfin and R, L Bloss, "Simple Strain Gauge-Based Load Controller," Review oj Scientific Instruments, Vol 33, No 7, p 772 (1962) (4) M S Rosenfeld, private communication (5) J A Bennett and J L Baker, "Effects of Prior Static and Dynamic Stresses on the Fatigue Strength of Aluminum Alloys," Journal of Research, Nat Bureau of Standards, Vol 45, No 6, p 449 (1950) (6) R L Templin, "Fatigue of Aluminum," Proceedings, Am Soc Testing Mats., Vol 54, p 641 (1954) (7) A O Payne, "Determination of the Fatigue Resistance of Aircraft Wings by Full-Scale Testing," in Full-Scale Fatigue Testing of Aircraft Structures, edited by Plantema and Schijve, Pergamon Press, New York, N Y., p 76 (1961) (8) R B Heywood, "The Influence of PreLoading on the Fatigue Life of Aircraft Components and Structures," Current Paper No 232, Aeronautical Research Council (London) (1956) (9) T J Dolan, "Concepts of Fatigue Damage in Metals," in Fatigue, Am Soc Metals, p (1953) (10) G M Sinclair, "An Investigation of the Coaxing Efifect in Fatigue of Metals," Proceedings, Am Soc Testing Mats., Vol 52, p 743 (1952) (11) G Wallgren, "Fatigue Tests with Stress Cycles of Varying Amplitude," Aeronautical Research Institute of Sweden, Report No 28 (1949) (12) J Schijve and F A Jacobs, "ProgramFatigue Tests on Notched Light Alloy Specimens of 2024 and 7075 Material," Reports and Transactions, Nat Aeronautical Research Inst (Amsterdam), Vol XXIV (1960) (13) B Lundberg and S Eggwirtz, "The Relationship Between Load Spectra and Fatigue Life," in Fatigue in Aircraft Structures, edited by A M Freudenthal, Academic Press, New York, N Y., p 255 (1956) (14) R P Swartz and M S Rosenfeld, "The Effect of Preloading on the Variable Amplitude Fatigue Characteristics of a Slab Horizontal Tail for a Typical Fighter Airplane," Naval Air Material Center, Report No NAMATCEN-ASL-W23, Part III, Jan 18, 1961 (15) W Nicole, "Some Results of Fatigue Tests with Parts of Vital Importance of the Ground Attacker P-16," in Full-Scale Fatigue Testing of Aircraft Structures, edited by Plantema and Schijve, Pergamon Press, New York, N Y., p 364 (1961) (16) V R Shanley, "Discussion of Methods of Fatigue Analysis," Proceedings, Symposium on Fatigue of Aircraft Structures, WADC TR 59-507, p 182, Aug., 1959 (17) W H Munse, J R Fuller, and K S Petersen, "Cumulative Damage in Structural Joints," Bulletin 544, Am Railway Engineering Assn., June-July, 1958, p 67 (18) R R Gatts, "Application of a Cumulative Damage Concept to Fati~ue," Transactions, Am Soc Mechanic-1 Engrs., Vol 83, Series D, p 527 (1961) (19) S R Valluri, "A U.^ified Engineering Theory of Hi h Stress Level Fatigue," Aerospace Engineering, Vol 20, No 10, pp 18, 19, 68-69, Oct., 1961 (20) H W Liu and H T Corten, "Fatigue Damage Under Varying Stress Amplitudes," NASA TN D-647, Nov., 1960 (21) D L Henry, "A Theory of FatigueDamage Accumulation in Steel," Transactions, Am Soc Mechanical Engrs., Vol 77, p 913 (1955) (22) C R Smith, "Fatigue-Service Life Prediction Based on Tests at Constant Stress Levels," Proceedings, Soc Experimental Stress Analysis, Vol XVI, No 1, p (1958) (23) F E Richart, Jr and N M Newmark, "An Hypothesis for the Determination of Cumulative Damage in Fatigue," Proceedings, Am Soc Testing Mats., Vol 48 p 766 (1948) (24) S M Marco and W L Starkey, "A Concept of Fatigue Damage," Transactions, Am Soc Mechanical Engrs., Vol 76, p 627 (1954) (25) A M Freudenthal and R A Heller, "On Stress Interaction in Fatigue and a Cumulative Damage Rule," Journal of the Aero/Space Sciences, Vol 26, No 7, p 431 (1959) 272 DISCUSSION ON FATIGUE T E S T S OF BEAM SPECIMENS (26) S S Manson, A J Nachtigall, and J C Freche, "A Proposed New Relation for Cumulative Fatigue Damage in Bending," Proceedings, Am Soc Testing Mats., Vol 61, p 679 (1961) (27) D Rosenthal, "Influence ot Residual Stress on Fatigue," in Metal Fatigue, edited by Sines and Waisman, McGraw-Hill Book Co., New York, N Y., p 170 (1959) (28) A M Freudenthal and R A Heller, "Accumulation of Fatigue Damage," in Fatigue in Aircraft Structures, edited by A M Freudenthal, Academic Press, New York, N Y., p 146 (1956) (29) E C Naumann, H F Hardrath, and D C Guthrie, "Axial Load Fatigue Tests of 2024-T3 and 7075-T6 Aluminum-Alloy Sheet Specimens Under Constant- and Variable-Amplitude Loads," NASA TN D-212, D e c , 1959 (30) P Kuhn, "Fatigue Engineering in Aircraft Structures," in Fatigue in Aircraft Structures, edited by A M Freudenthal, Academic Press, New York, N Y., p 295 (1956) (31) E Gassner, "Performance Fatigue Testing with Respect to Aircraft Design," in Fatigue in Aircraft Structures, edited by \ M Freudenthal, Academic Press, New York, N Y p 178 (1956) (32) R P Swartz and M S Rosenfeld, "Variable Amplitude Fatigue Characteristics of a Slab Horizontal Tail for a Typical Fighter Plane," Naval Air Material Center, Report No NAMATCEN-ASL-1023, Part II, Sept 18, 1961 DISCUSSION The answer to the apparent discrepancy in the effect of spectrums and in the two papers is that although the spectrums are defined the same in terms of limit load, limit load is defined differently in the two papers Mr Rosenfeld called limit load the manufacturer's de- sign limit load, which was approximately 57 per cent of ultimate static strength; we have defined limit load as 67 per cent of ultimate static strength Therefore, the load levels applied in the two series of tests are not the same The conclusion derived from the two series of tests is that adding cycles of 22.8 per cent of ultimate static strength did not affect the fatigue life of the horizontal tail, while adding cycles of 26.8 per cent of ultimate static strength caused a significant reduction in the life of the beam specimens M R C R SMITH.^—Regarding loss in life due to negative loading, I have data showing high negative loads improve life ' Senior Structures Engineer, Republic -\viation Corp., Farmingdale, L I., N Y See p 216 ' Fatigue Laboratory, General Convair, San Diego, Calif M R R L BENEDICTO.I—Table V I I I of the paper shows a large decrease in life from spectrum to These are the same spectra as used in the Rosenfeld paper on "Aircraft Structural Fatigue Research in the Navy."^ In Rosenfeld's paper, however, an increase in life from spectrum to is shown Could the authors comment on the reasons for the difference? Ms LEONARD MORDFIN (author).— Dynamics/ i H I S PUBLICATION is one of many issued by the American Society for Testing and Materials in connection with its work of promoting knowledge of the properties of materials and developing standard specifications and tests for materials Much of the data result from the voluntary contributions of many of the country's leading technical authorities from industry, scientific agencies, and government Over the years the Society has published many technical symposiums, reports, and special books These may consist of a series of technical papers, reports by the ASTM technical committees, or compilations of data developed in special Society groups with many organizations cooperating A list of ASTM publications and information on the work of the Society will be furnished on request