Astm stp 519 1973

CYCLIC STRESS-STRAIN M BEHAVIOR ANALYSIS, EXPERIMENTATION, A N D FAILURE PREDICTION A symposium sponsored by ASTM Committee E-9 on Fatigue AMERICAN SOCIETY FOR TESTING AND MATERIALS Bal Harbour, Fla 7-8 Dec 1971 ASTM SPECIAL TECHNICAL PUBLICATION 519 L F Coffin and Erhard Krempl, symposium co-chairmen List price $28.00 04-519000-30 AMERICAN SOCIETY FOR TESTING A N D MATERIALS 1916 Race Street, Philadelphia, Pa 19103 Copyright by ASTM Int'l (all rights reserved); Mon Dec 21 11:10:56 EST 2015 Downloaded/printed by University of Washington (University of Washington) pursuant to License Agreement No further reproductions authorized BY A M E R I C A N S O C I E T Y F O R T E S T I N G A N D M A T E R I A L S 1973 Library of Congress Catalog Card Number: 72-86244 NOTE The Society is not responsible, as a body, for the statements and opinions advanced in this publication Printed in Philadelphia, Pa May 1973 Copyright by ASTM Int'l (all rights reserved); Mon Dec 21 11:10:56 EST 2015 Downloaded/printed by University of Washington (University of Washington) pursuant to License Agreement No further reproductions authorized Foreword The Symposium on Cyclic Stress-Strain Behavior Analysis, Experimentation, and Failure Prediction was sponsored by Subcommittee E09.08 on Fatigue Under Cyclic Strain of Committee E-9 on Fatigue and held in Bal Harbour, Fla., 7-8 Dec 1971 L F Coffin, General Electric Co., and Erhard Krempl, Rensselaer Polytechnic Institute, presided as co-chairmen Copyright by ASTM Int'l (all rights reserved); Mon Dec 21 11:10:56 EST 2015 Downloaded/printed by University of Washington (University of Washington) pursuant to License Agreement No further reproductions auth Related ASTM Publications Damage Tolerance in Aircraft Structures, STP 486 (1971), $19.50 Effects of Notches on Low-Cycle Fatigue, STP 490 (1972), $3.00 Stress Analysis and Growth of Cracks, STP 513 (1972), $27.50 Testing for Prediction of Material Performance in Structures and Components, STP 515 (1972), $28.50 Copyright by ASTM Int'l (all rights reserved); Mon Dec 21 11:10:56 EST 2015 Downloaded/printed by University of Washington (University of Washington) pursuant to License Agreement No further reproductions authorized Contents Introduction Time-Dependent Effects A Study of Thermal Ratchetting Using Closed-Loop, Servo-Controiled Test Machines R H STENTZ Cyclic Stress-Strain Behavior of Two Alloys at High Temperature C E JASKE, H MINDLIN, AND J S PERRIN Effects of Temperature and Deformation Rate on Cyclic Strength and Fracture of Low-Carbon Steel-H ABDEL-RAOUF, A PLUMTREE, AND T H TOPPER Intergranular Fatigue Fracture of Chemical Lead at Room Temperature MASAKl KITAGAWA Cyclic Deformation and Failure of Polymers 13 28 58 70 T A JOHNSON Notch Effects An Automatic Flash Photomicrographic System for Fatigue Crack Initiation S t u d i e s - - R A L P H PAPIRNOAND 98 B S PARKER The Effect of Load Interaction and Sequence on the Fatigue Behavior of Notched Coupons J M POTTER Cyclic Inelastic Deformation and the Fatigue Notch Factor-B N LEIS, C V B GOWDA, AND T H TOPPER Applications of Finite Element Stress Analysis and Stress-Strain Properties in Determining Notch Fatigue Specimen Deformation and Life D F MOWBRAY AND J E MCCONNELEE Crack Propagation in Notched Mild Steel Plates Subjected to Cyclic Inelastic Strains -c v B GOWDAAND T H TOPPER 109 133 151 170 Cumulative Effects The Physical Justification of the Term "State of Fatigue of Materials Under Cyclic Loading" J BURBACH 185 Copyright by ASTM Int'l (all rights reserved); Mon Dec 21 11:10:56 EST 2015 Downloaded/printed by University of Washington (University of Washington) pursuant to License Agreement No further reproductions authorized Cumulative Fatigue Damage Under Complex Strain Historiesd R W LANDGRAF 213 The Role of Cyclic Strain Behavior on Fatigue Damage Under Varying Load K KOIBUCHI AND S KOTANI 229 Engineering Analysis of the Inelastic Stress Response of a Structural Metal Under Variable Cyclic Strains H R JHANSALEAND W.H TOPPER 246 Periodic Overloads and Random Fatigue Behavior P WATSON, D S HODDINOTT, AND J P NORMAN 271 Copyright by ASTM Int'l (all rights reserved); Mon Dec 21 11:10:56 EST 2015 Downloaded/printed by University of Washington (University of Washington) pursuant to License Agreement No further reproductions authorized STP519-EB/May 1973 Introduction Modern machinery is required to perform reliably under a variety of operating conditions Power generation equipment such as nuclear reactors and steam and gas turbines have to respond quickly to the changing power demands of our technological society; aircraft structures and jet engines are to perform reliably under frequent take off, cruise, and landing operations These are only two examples of the cyclic operating pattern imposed on modern machinery The cyclic operating pattern, the increasing demands on reliability imposed by the consumer-oriented society, and the drive for an economic design require sophisticated design methods for critical components subjected to severe cyclic loadings An essentially static, time-independent viewpoint is no longer feasible in these cases It will be necessary to calculate the stresses and strains and assess the accumulated damage by following through the operating history of these critical components Central to this new design approach is the recognition that each severe cycle can cause a permanent damage in the material During the projected lifetime of the machine the total accumulated damage in highly-stressed components will have to be less than the damage which will lead to mechanical failure The objective in the development of a modern design approach for criticallystressed components is therefore the accurate assessment of the damage caused by the elements of the operating history The Symposium on Cyclic Stress-Strain Behavior Analysis, Experimentation and Failure Prediction focuses on three vital aspects of the damage assessment in engineering materials Experimental techniques to determine the cyclic stress-strain behavior and the initiation of cracks in materials are discussed The importance of time (rate) dependent processes as they affect deformation and crack initiation is delineated in various papers Notches and their life-reducing effect are examined from an experimental and analytical point of view In the latter, elasto-plastic computer programs are employed The crack initiation and crack propagation phase are separated Copyright by ASTM Int'l (all rights reserved); Mon Dec 21 11:10:56 EST 2015 Copyright9 by by ASTM International www.astm.org Downloaded/printed University of Washington (University of Washington) pursuant to License Agreement No further reproductions authorized CYCLIC STRESS-STRAIN BEHAVIOR and treated individually The problems of damage definition, damage accumulation, and life prediction under variable amplitude loading receive attention in several papers The reader of these papers will realize the interdisciplinary nature of the subject, and he will certainly recognize the contributions made by the metallurgical, materials testing, and analytical disciplines For the development of reliable damage assessment and life prediction methods to be used in the design of modern machinery, an interdisciplinary approach is absolutely essential We want to thank the authors for their contributions and their willingness to discuss the subject across the boundaries of classical disciplines We sincerely hope that this Special Technical Publication will be used by designers and will stimulate further interdisciplinary work towards the development of rational and reliable life prediction methods for realistic operating conditions L F Coffin, Jr Corporate Research & Development Center, General Electric Company, Schenectady, N.Y Erhard Krempl Mechanics Division, Rensselaer Polytechnic Institute, Troy, N.Y Copyright by ASTM Int'l (all rights reserved); Mon Dec 21 11:10:56 EST 2015 Downloaded/printed by University of Washington (University of Washington) pursuant to License Agreement No further reproductions a R H Stentz ~ A Study of Thermal Ratchetting Using Closed-Loop, Servo-Controlled Test Machines REFERENCE: Stentz, R.H., "A Study of Thermal Ratehetting Using Closed-Loop, Servo-Controlled Test Machines," Cyclic Stress-Strain Behavior Analysis, Experimentation, and Failure Prediction, A S T M STP 519, American Society for Testing and Materials, 1973, pp 3-12 ABSTRACT: A new testing technique has been devised for studying thermal ratchetting behavior It employs low-cycle fatigue-type specimens (hourglass shape) in conjunction with two closed-loop, servo-controlled testing machines operating in unison to provide an exact simulation of the familiar three-bar assembly Diametral extensometers are employed in conjunction with an analog strain computer to provide instantaneous values for the total axial strain and to isolate the mechanical and thermal strain components Stress-strain measurements are recorded continuously throughout each cycle to provide an extensive evaluation of the response to initial load level, maximum and minimum cycle temperatures, hold-time effects, different specimen diameters, and rate of temperature cycling Demonstration tests are described which employ 304 and 316 stainless steel specimens subjected to an initial stress level of 10 000 psi and a temperature cycle from 1100 to 800 F KEY WORDS: fatigue (materials), testing equipment, servomechanisms, cyclic temperature, stresses, strains Thermal ratchetting involves a unidirectional accumulation of plastic deformation resulting from a successive application of a thermal stress This phenomenon has been studied extensively [1-6] 2, and particular attention has been focused on the use of the three-bar assembly as an analytical model This approach permits an analysis to be made of thermal ratchetting behavior in response to the primary variables of external load and the cyclic temperature profile Conditions which are pertinent to thermal stress ratchetting and have an important effect in determining the extent of this phenomenon are the following: the amplitude and the rate involved in the temperature cycle, tVice president, Mar-Test Inc., Cincinnati, Ohio 45215 2The italic numbers in brackets refer to the last of references appended to this paper Copyright by ASTM Int'l (all rights reserved); Mon Dec 21 11:10:56 EST 2015 Copyright9 by by ASTM International www.astm.org Downloaded/printed University of Washington (University of Washington) pursuant to License Agreement No further reproductions authorized P Watson ~, D S, Hoddinott ~, and J P Norman ~ Periodic Overloads and Random Fatigue Behavior REFERENCE: Watson, P., Hoddinott, D S., and Norman, J P.,"Periodic Overloads and Random Fatigue Behavior," Cyclic Stress-Strain Behavior Analysis, Experimentation, and Prediction, A S T M STP 519, American Society for Testing and Materials, 1973, pp 271-284 ABSTRACT: The occurrence of occasional high amplitude strain cycles in an otherwise stationary random strain time history considerably reduces the fatigue life of mild steel specimens The acceleration of damage is shown to occur throughout the cyclic damage process The significance of this effect in terms of fatigue in railway vehicles is emphasized The results of overload studies are often confusing because of the influence of induced residual stresses In this work, care was given to ensure that no such effects occurred KEY WORDS: fatigue (materials), railroad cars, loads (forces), strains, cycles, cyclic loads, damage, crack initiation, crack propagation, scanning electron microscopy In the past there has been considerable research effort aimed at understanding the effects of overloads on fatigue behavior; the results, however, have indicated both detrimental and beneficial effects and not unnaturally have therefore led to some confusion The changes in life have usually been far in excess of those predicted by linear damage hypotheses This paper reports experiments in which occasional high strain cycles are applied to specimens during random strain fatigue tests The results indicate a reduction in life due to the overstrains The shorter lives are explained in terms of accelerations in both stages of crack growth The strain-time histories used in the tests were taken from strain gages attached to railway components in service Previous investigations of the effect of overloads in fatigue can be broadly grouped into constant amplitude and variable amplitude categories tScientific officer, scientific officer, and project engineer, respectively, Fatigue Research Group~ Materials Engineering Section, British Railways Research Dept., London Road, Derby, England 271 Copyright by ASTM Int'l (all rights reserved); Mon Dec 21 11:10:56 EST 2015 Downloaded/printed Copyright9 by by ASTM International www.astm.org University of Washington (University of Washington) pursuant to License Agreement No further reproductions authorized 272 CYCLIC STRESS-STRAIN BEHAVIOR Constant Amplitude Much of the early work was aimed at establishing the effect of overstressing on the fatigue limit; Moore and Kommers [1] demonstrated a detrimental effect At about the same time French [2] and Langer [3] derived methods of predicting this effect More recently Manson [4], Topper et al [5, 6], and Plumtree at al [7], in their attempts to understand such effects in terms of basic fatigue processes, have shown that the application of an overstrain in the form of a short initial block of high strain cycles reduces fatigue life at a subsequent lower strain level for a wide range of metals In addition, many results of work concerned with the effect of loading sequence in fatigue [8-12] have shown a similar detrimental effect of high stresses The reductions have been attributed to the removal of beneficial residual stresses, to more rapid initiation of cracks, and to acceleration of crack growth rates On the other hand, there is considerable reported work which shows an improvement in fatigue life when high amplitude pre-loads or pre-strains are applied [13-15] In most cases the pre-strain causes initial hardening of the material which tends to reduce the subsequent deformation under stress controlled testing conditions This is most noticeable at the lowest stresses when the lives are increased due to the slower crack growth rates Residual stresses can be important in high-low fatigue tests, since the method of application and removal of the pre-strain controls the magnitude and sign of the induced mean stress This effect, demonstrated by Topper at al [16], may well account for much of the confusion that exists in the interpretation of block program tests in fatigue Variable Amplitude Several investigations have shown that pre-loading and periodic overloading can increase fatigue resistance under variable amplitude conditions Schijve [17], in a report of random flight simulation tests on aluminum 2024-T3, produced results which show that as the maximum stress in the program is increased, the subsequent life-to-failure increases His explanation of these unexpected results is based on stress interaction effects and, in particular, on the induction of compressive residual stresses near the crack tip Other investigators [18-22] who report life improvements due to overloads have used similar explanations If the overload is compressive, then a decrease in life would be expected Jacoby [23] reports a life reduction of about 45 percent due to the inclusion of ground-air-ground cycles with gust loadings Almost without exception the results published have used load-controlled tests on specimens containing a stress raiser The resulting anomalies may be 2The italic numbers in brackets refer to the list of references appended to this paper Copyright by ASTM Int'l (all rights reserved); Mon Dec 21 11:10:56 EST 2015 Downloaded/printed by University of Washington (University of Washington) pursuant to License Agreement No further reproductions authorized WATSON ET AL ON OVERLOADS AND RANDOM FATIGUE 273 related to the use of nominal stress values as opposed to the more critical local stress-strain measurements The local stress-strain approach [24, 25] attempts to relate fatigue failures to the values of the stress and strain in the small element of the material where failure originates Hence, any residual stresses induced by overloads will be included in a damage evaluation which can then be carried out on a cycle by cycle basis [26, 27] The present work is an investigation of the effect of periodic overstrains in random fatigue Strain histories from a vehicle in service were used to isolate and study this effect in a mild steel Care was taken during the experiment to ensure that no residual stresses resulted from the applied overstrains Stage I and Stage II of the cyclic damage process [28] are considered separately Experimental Procedure Strain-Time History A strain record from the strain-gaged bogie of a 100-ton tank wagon travelling at 96 kph (60 mph) over continuous welded track of good quality was used as the basic input signal for these tests The periodic overstrains occurred when the vehicle passed over points and crossings in the track The statistics of the basic strain record were weakly stationary, and it was possible to select a 7-min sample including the overstrains This, and a second sample with the high amplitude cycles eliminated, were re-recorded on magnetic tape The high strains occupied 0.6 percent of the time in the first sample Figure shows small samples of both signals The normalized FIG Strain-time histories Copyright by ASTM Int'l (all rights reserved); Mon Dec 21 11:10:56 EST 2015 Downloaded/printed by University of Washington (University of Washington) pursuant to License Agreement No further reproductions authorized 274 C Y C L I C STRESS-STRAIN B E H A V I O R power spectral densities of the two signals are shown in Fig The average frequency in each case was Hz ~) Z - (b) 0 i I 20 FREQUENCY (,HZ) L I 4O FIG Psd's of testing signals" (a) track strains only, (b) track strains with points and crossings strains Material and Specimens The material used was a specially prepared vacuum melted mild steel supplied in the form of 20-mm-diameter hot-rolled bar; this was normalized at 890 C for 20 giving the fine grained microstructure shown in Fig The chemical composition is given in Table 1, and Table lists the mechanical properties The monotonic and cyclic stress-strain curves are shown in Fig The cyclic stress-strain curve was generated using the incremental step test technique described by Landgraf et al [29] Copyright by ASTM Int'l (all rights reserved); Mon Dec 21 11:10:56 EST 2015 Downloaded/printed by University of Washington (University of Washington) pursuant to License Agreement No further reproductions authorized WATSON ET AL ON OVERLOADS AND RANDOM FATIGUE 275 FIG Microstructure of normalized vacuum melted mild steel, • 150 TABLE l Chemical composition, % c si Mn Ni S P Cr < Mo < Fe = 0.10 0.50 0.40 0.07 0.016 0.003 0.01 0.01 balance The smooth axial specimens used has a 10-mm-long, 10-mm-diameter gage length G r e a t care was taken during preparation to ensure that the material was free from residual stresses at the start of the test, particularly in view of the suggestion that overstressing reduces life by removing beneficial residual stresses from the surface After machining, the specimens were mechanically polished and then stress-relieved by heating at 650 C in vacuo for l h and furnace cooling Finally, the surface was electrochemically polished using a chrome-acetic acid solution Copyright by ASTM Int'l (all rights reserved); Mon Dec 21 11:10:56 EST 2015 Downloaded/printed by University of Washington (University of Washington) pursuant to License Agreement No further reproductions authorize CYCLIC STRESS-STRAIN BEHAVIOR 276 TABLE Mechanical properties 210 • 109 N / m 292 • 106 N / m 414 • 106 N / m z 76% Modulus of elasticity 0.1% offset yield strength Ulth~ate streagth Reduction of area True fracture ductility 1.43 4XIO Z w I I I 005 O.OI O'OIS STRAIN AMPLITUDE FIG Monotonic and cyclic stress-strain curves Test Equipment The specimens were tested under strain control in a servo-hydraulic machine using the two strain records as the command signals The records were played back on the FM tape equipment with automatic rewind facilities During rewind, which lasted less than 50 s and occurred every 4000 s, muting circ.uits reduced the command signal to zero The longitudinal strain in the specimens was measured continually over a gage length of 10 mm using a specially developed clip-on extensometer, and the signal was used as feedback to the servo-loop The extensometer output and the axial load in the specimen were monitored on a high speed chart recorder Regular calibrations of both transducers were carried out throughout the test program The true rms of the specimen strain-time history was regularly monitored using a digital time domain analyzer The same instrument was Copyright by ASTM Int'l (all rights reserved); Mon Dec 21 11:10:56 EST 2015 Downloaded/printed by University of Washington (University of Washington) pursuant to License Agreement No further reproductions autho WATSON ET AL ON OVERLOADS rAND RANDOM FATIGUE 277 also used to check periodically that the mean stress remained at zero throughout each test This indicated that no residual stresses were induced during the transitions from the overstrains to the basic track strains Testing Series The tests were carried out in two parts In the first part a series of tests to failure was performed to establish the overall contribution of the high strain cycles to fatigue life The failure criterion was separation of the specimen In the second part an attempt was made to identify the contribution of the high strain cycles to the various stages of the fatigue process In these tests, specimens were cycled for various fractions of the anticipated lives at rms strain levels for each version of the signal A section from the surface of each of the specimens was then removed and examined in a scanning electron microscope Results and Discussion Fatigue Life The results of the fatigue tests are shown in Fig The ordinate is the rms of the track strains only, that is, excluding the strains due to points and crossings ~J T R A C K STRAINS WITHOUT POINTS & CROSSINGS O T R A C K STRAINS WITH POINTS AND CROSSINGS 1'5 IG3 S g LJ ~ I J I IO S 10 I IO6 TIME TO FAILURE (SECONDS) FIG Effect of points and crossings on fatigue life These results clearly indicate the damaging influence of a few high strain cycles At the higher rms levels, where there is plasticity in many of the cycles, the effect is small However, as the rms levels decrease there is a Copyright by ASTM Int'l (all rights reserved); Mon Dec 21 11:10:56 EST 2015 Downloaded/printed by University of Washington (University of Washington) pursuant to License Agreement No further reproductions authorized 278 CYCLIC STRESS-STRAIN BEHAVIOR significant reduction in life for those tests which included the high points and crossings strains The ratio of the magnitudes of the high strain cycles and the basic track signal was constant As the rms strain decreased, an increasing number of the track cycles were completely within the elastic range, and the relative influence of the higher strains increased In this work, the detrimental effect of high strains was established in the absence of induced residual stresses Practical situations, however, may well include such stresses, but it is felt that they should be dealt with in a separate procedure In railway practice most structures are designed for long lives; it is clear, therefore, that the strains caused by points and crossings in welded railway track make a major contribution to fatigue damage in railway vehicles If the graphs were extended on the life axis, then a state would be reached in which virtually all of the damage would be due to the high strain cycles Thus, an improvement in general track conditions may have little beneficial effect as far as fatigue damage in vehicles is concerned Any reduction in the number and severity of points and crossings, however, could be of considerable value The results raise other points of interest If it is assumed that most of the damage is a result of a few high cycles, then a serious problem exists for any conventional damage evaluation Linear damage summations frequently underestimate the effect of occasional high strains in long life fatigue The problem is greatest when the track strains are just large enough to contribute to the damage We suggest that the use of the same damage law with basic fatigue data obtained from previously overstrained specimens would be generally more successful Fatigue life has been related to the rms of the applied signal In Fig the lives have been plotted against the rms of the entire signal in each case The differences in life at similar rms levels demonstrate the limitations of this widely used relationship It has also been suggested [30,31] that for stationary, Gaussian signals the fatigue life is related to power spectral density (psd) The psd's of the signals in these tests are very similar, as seen in Fig 2, but the lives at the same rms level are different These results show that when only a small proportion of the signal, 0.6 percent of time in this case, deviates from being stationary and Gaussian, the relationship is invalid Cyclic Damage In order to explain the reported effects it is necessary to examine the entire cyclic damage process Forsyth [28] divides fatigue life into two stages The first stage encompasses the initial cycles during which cyclic hardening or softening takes place, the development of extrusions and intrusions on the surface, and the subsequent growth of a crack through a few grains under the influence of the alternating shear stress A second stage, culminating in failure, consists of the growth of the crack after it changes Copyright by ASTM Int'l (all rights reserved); Mon Dec 21 11:10:56 EST 2015 Downloaded/printed by University of Washington (University of Washington) pursuant to License Agreement No further reproductions autho WATSON ET AL ON OVERLOADS AND R A N D O M FATIGUE r-] TRACK STRAINS TRACK STRAINS WITH POINTS 279 wt~rHOUT POINTS & CROSSING AND CROSSINGS 14 i" si O ,o4 I I I S tO rlu~ TO r~-t~t I I to' (sEe.t~as) F I G Rms (strain) versus time to failure direction from being governed by slip systems to lying at approximately 90 deg to the maximum tensile axis It is generally agreed that in constant amplitude fatigue Stage I crack growth dominates at low strains associated with long lives, but Stage II occupies most of the life in the high strain, short life region [32] In this work, Stage I and Stage II were considered separately Initially, surface observations were used to study the damaging influence of the high strain cycles These observations indicate the progress of cyclic damage from the first appearance of slip bands until the development of significant microcracks The specimens examined were cycled at two levels of rms strain, one at 0.06 percent and the other at 0.049 percent Figures and show the surfaces of two specimens which were subjected to identical strain-time histories except for the inclusion of high strain cycles Figure shows the surfaces of specimens with similar amounts of surface damage The first had experienced 200 000 s of the basic track strains; the second had experienced 80 000 s of the signal which included the points and crossings, at the same rms level A typical acceleration of the surface damage is demonstrated in these photographs Careful study of the specimen surfaces at different stages of life leads to the conclusions that occasional high amplitude strains in a random strain time history accelerate surface damage, lead to earlier microcracks and to their more rapid growth These effects not seem to account entirely for the difference in life found in the tests It is reasonable to assume therefore that differences may Copyright by ASTM Int'l (all rights reserved); Mon Dec 21 11:10:56 EST 2015 Downloaded/printed by University of Washington (University of Washington) pursuant to License Agreement No further reproduction 280 CYCLIC STRESS-STRAIN BEHAVIOR FIG Surface damage o f two specimens tested at same rms level f o r 10 000 s using track strains (a,c) and track and points and crossings strains (b,d) (Original fig reduced ~ IA th.) also occur in Stage II growth plus, of course, the possibility of earlier final fracture occurring as the high strains are applied Visual examination of the fracture surfaces of specimens subjected to the high points and crossing strains revealed a characteristic banding as shown in Fig 10 These bands not occur on specimens tested with the basic track strains only The Copyright by ASTM Int'l (all rights reserved); Mon Dec 21 11:10:56 EST 2015 Downloaded/printed by University of Washington (University of Washington) pursuant to License Agreement No further reproductions authorized WATSON ET AL ON OVERLOADS AND RANDOM FATIGUE C~ "s~s (,),,,so 281 0') ~ 600 @)x ,200 FIG Surface damage o f two specimens tested at same rms level f o r 40 000 s using track strains (a,c) and track and points and crossings strains (b,d) (Original fig reduced ~ V4 th.) narrow, lighter colored bands were presumed to be associated with high strains and, in view of their color, were taken to indicate a temporary acceleration of Stage II crack growth rate [33] This interpretation is reinforced by the absnece of such bands on the specimen tested with points and crossings at high rms level where there was no reduction in life Copyright by ASTM Int'l (all rights reserved); Mon Dec 21 11:10:56 EST 2015 Downloaded/printed by University of Washington (University of Washington) pursuant to License Agreement No further reproductions authorized 282 CYCLIC STRESS-STRAIN BEHAVIOR FIG Surface damage o f specimens tested at the same rms level (a) after 200 000 s using track strains (b) after 80 000 s using track and points and crossings strains, (Original fig reduced V4th.) FIG lO Fracture surfaces o f specimens tested using (a) track strains (b) track and points and crossings strains (Original fig reduced ~ 2/3 rd.) It is concluded, therefore, that the presence of the high occasional overstrains at low and medium overall strain levels influence all stages of the cyclic damage process In particular, there are major accelerations in the early damage and microcrack propagation stages Copyright by ASTM Int'l (all rights reserved); Mon Dec 21 11:10:56 EST 2015 Downloaded/printed by University of Washington (University of Washington) pursuant to License Agreement No further reproductions authorized WATSON ET AL ON OVERLOADS AND RANDOM FATIGUE 283 Conclusions In the absence of residual stresses periodic high overstrains make a major contribution to fatigue damage The decrease in life due to these occasional overstrains is a result of an acceleration in Stage I crack growth, and to a lesser extent, in Stage II growth It is probable that all fatigue damage in vehicles designed for long lives is a result of the high strains arising from major track irregularities The commonly used relationships between fatigue life and the rms and psd of the applied signal are not valid under these realistic service conditions A cknowledgments This work was undertaken in the Fatigue Research Group of British Railways Research Department, Derby, England We acknowledge the permission of British Railways Board to publish this paper Thanks are due to R G Rebbbeck and R McLester for their critical and helpful review of the manuscript, and to J Chelu and Mrs J Hick for experimental assistance We would also like to thank C V B Gowda of the University of Waterloo, Canada, for his presentation of this work at the ASTM symposium References [11 Moore, H E and Kommers, J B., Engineering Experimental Station Bulletin 124, University of Illinois, 1921 [2] French, H J in Transactions, American Chemical Society of Steel Treatment, Vol 21, 1933, p, 899 [3] Langer, B F., Journal of Applied Mechanics, Vol 4, 1937, p 160 [4] Manson, S S., Freche, J C., and Ensign, C R., in Fatigue Crack Propagation, ASTM STP 415, American Society for Testing and Materials, 1967, pp 384-412 [5] Topper, T H and Sandor, B I., in Effects of Environmental and Complex Load History on Fatigue Life, ASTM STP 462, American Society for Testing and Materials, 1970, pp 93104 [6] Watson, P and Topper, T H., "The Effect of Overstrains on the Fatigue Behavior of Five Steels," presented at 1970 Fall Meeting The Metallurgical Society of AIME, Cleveland, Ohio, Oct 1970 [7] Owens, J P., Watson, P., and Plumtree, A., "The Effect of Prestrain on the Cyclic Behavior of a-Titanium," presented at International Conference on Mechanical Behavior of Materials, Kyoto, Japan, Aug 1971 [8] Erickson, W H and Work, C E., "A Study of the Accumulation of Fatigue Damage in Steel," Proceedings, American Society for Testing and Materials, Vol 61, 1961, p 704 [9] Henry, D k in Transactions, American Society of Mechanical Engineers, Vol 77, 1955, pp 913-918 [10] Manson, S S., Nachtigall, A J., and Freche, J C in Proceedings, American Society for Testing and Materials, Vol 61, 1961, pp 679-703 [11] Grover, H J., Gordon, S A., and Jackson, L R., "Fatigue of Metals and Structures," Bureau of Aeronautics, Department of the Navy, 1954 [12] Yokabori, J., The Strength, Fracture and Fatigue of Materials, Noordhoff, Groningen, The Netherlands, 1965 Copyright by ASTM Int'l (all rights reserved); Mon Dec 21 11:10:56 EST 2015 Downloaded/printed by University of Washington (University of Washington) pursuant to License Agreement No further reproductions authorized 284 CYCLIC STRESS-STRAIN BEHAVIOR [13] [14] [15] [16] [17] [18] [19] [20] [21] [22] [23] [24] [25] [26] [27] [28] [29] [30] [31] [32] [33] Thompson, N and Wadsworth, N J., Advances in Physics, Vol, 7, 1958, pp 72-166 Frost, N E., Metallurgia, Vol 62, 1960, pp 85-90 Laird, C., Ph.D thesis, University of Cambridge, 1962 Topper, T H., Sandor, B I., and Morrow, J., Journal of Materials, Vol 4, No 1, March 1969, pp 189-199 Schijve, J., "Cumulative Damage Problems in Aircraft Structures and Materials," 1lth Conference of the International Committee on Aeronautic Fatigue, Stockholm, May 1969 Edwards, P R., "An Experimental Study of the Stress Histories at Stress Concentrations in Aluminum Alloy Specimens Under Variable Amplitude Loading Sequences," Royal Aircraft Establishment Technical Report 70004, Jan 1970 Kessler, A F and Hillberry, B M., "The Effect of Periodic Overstress on the Fatigue Life of Notched Aluminum Specimens," Society of Automotive Engineers, Paper 710599, June 1971 Boissonant, J., in Fatigue of Aircraft Structures, Pergamon Press, New York, 1963 Hudson, M C and Raju, K N., "Investigation of Fatigue Crack Growth Under Simple Variable Amplitude Loading," NASA TN-D-5702 Gerber, T L and Fuchs, H O in Achievement of High Fatigue Resistance in Metals and Alloys, ASTM STP 467, American Society for Testing and Materials, 1970 Jacoby, G H., "Fatigue Life Estimation Processes under Conditions of Irregularly Varying Loads," Technical Report AFML-TR-67-215, Air Force Materials Laboratory, Aug 1967 Endo, T., and Morrow, J., JournalofMaterials, Vol 4, No 1, March 1969, pp 159-175 Topper, T H and Gowda, C V B., "Local Stress-Strain Approach to Fatigue Analysis and Design," presented at the Design Engineering Conference and Show, American Society of Mechanical Engineers, Chicago, May 1970 Wetzel, R M., Ph.D thesis, University of Waterloo, Waterloo, Ontario, Canada, 1971 DoMing, N E., "Fatigue Failure Predictions for Complicated Stress-Strain Histories," Department of Theoretical and Applied Mechanics, Report 337, University of Illinois, Jan 1971.Forsyth, P J E., "A Two Stage Process of Fatigue Crack Growth," Proceedings, Crack Propagation Symposium, Cranfield, 1961 Landgraf, R W., Morrow, J., and Endo, T., Journal of Materials, Vol., No 1, March 1969, pp ! 76-188 Smith, S H in Accoustical Fatigue in Aerospace Structures, W J Trapp and D M Forney, Jr., Eds., Syracuse University Press, New York, 1965 Paris, P C., "Crack Propagation Caused by Fluctuating Loads," ASME Paper 62-Met-3, presented at the AWS-ASME Joint Conference, Cleveland, Ohio, April 1962 Laird, C and Smith, G C., Philosophical Magazine, Vol 8, 1963, pp 1945-1963 Jacoby, G., "Application of Microfractograpy to the Study of Crack Propagation Under Fatigue Stresses," NATO AGARD, Report 541 Copyright by ASTM Int'l (all rights reserved); Mon Dec 21 11:10:56 EST 2015 Downloaded/printed by University of Washington (University of Washington) pursuant to License Agreement No further reproductions authorized