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Some studies into the fatigue properties of 2024-T3 sheet aluminum White, Robin Tristram 1965

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SOME STUDIES INTO THE FATIGUE PROPERTIES OF 2024-T3 SHEET ALUMINUM by ROBIN TRISTRAM WHITE BASo, University of British Columbia, 1963. A THESIS SUBMITTED IN PARTIAL FULFILMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF APPLIED SCIENCE in the Department of Mechanical Engineering We accept this thesis as conforming to the required standard THE UNIVERSITY OF BRITISH COLUMBIA JANUARY, 1965 i i In presenting this thesis in partial fulfilment of the requirements for an advanced degree at the University of British Columbia, I agree that the Library shall make i t freely available for reference and study. I further agree that permission for extensive copying of this thesis for scholarly purposes may be granted by the Head of my Department or by his representatives. It is understood that copying or publication of this thesis for financial gain shall not be allowed without my written permission. Department The University of British Columbia, Vancouver 8 , Canada. i i i ABSTRACT A large number of axially loaded specimens of 2024-T3 aluminum sheet alloy were fatigued to failure in alternating tension. The stress ratio was kept constant at .05 and maximum stresses were chosen to cause failure in the upper part of the S-logN curve where failure is by progressive hardening. The specimens were prepared in three ways, unpolished in which the rough edges were rounded, chemically polished in which the central section was polished chemi-cally, and mechanically and chemically polished in which the central section was rubbed with emery paper then polished chemically. Macroscopic and microscopic examinations of chemically polished speci-mens tested at a maximum stress of 47.5 ksi were also made. Statistical analysis was used to f i t experimental frequency distribu-tions to the l i f e values at each stress level, to determine the effect of the different polishing methods and to determine the effect of a light o i l coating. Of the two tried, the Lognormal and the Weibull, the Weibull distribution provided a better f i t and was easier to use than the Lognormal. For the three different polishing groups, the mechanically and chemically polished specimens gave the longest lives at a l l stress levels followed by the chemically polished then the unpolished speci-mens. Also both groups whioh received a final chemical polish showed S-logN curves with a much rounder knee than did the unpolished group. Coating the specimens with a light non-corroding o i l resulted in a l l cases in an increase in l i f e and in more scatter in the l i f e values. The increases ranged from 20$ to 62%, At the knee of the S-logN curve, a l l groups showed a bimodal. distribution in the l i f e values. This was f e l t to be the result of a change in the failure mechanism such as the one postulated by Wood. Examination of the fracture surface and of small cracks which formed near the edges indicated that the failure occurred in two stages; nucleation and growth of a small non-distorting fatigue crack followed by transition to a rapidly propagating ductile crack. Obaervations of the failures showed that i t took approximately 1000 cycles from the appearance of the f i r s t small crack to when the ductile crack had propagated through the section. Microscopic examination showed that the fatigue cracks were intercrystalline and grew on the surface along slip marking which formed ahead of the tip of the crack. The only effect the crystal structure had was in the direction of the slip band formation. There was no indication that the mechanism b y which the cracks initiated was different than the one by which they propagated. The cracks initiated at the sur-face and grew through to the other side. Once they reached the other side a ductile crack formed and final failure soon followed* X ACKNOWLEDGEMENTS The author is grateful to Professor W.O. Richmond who, as research supervisor, contributed time, effort and ideas to this investigation. Thanks are also due to Dr. E. Teghtsoonian and Mrs. W. Armstrong for their advice and for making available the f a c i l i t i e s of the Department of Metallurgy. Special thanks must also go to the graduate students and technicians of the Mechanical Engineering and Metallurgy Departments for their invaluable assistance. Funds for the project were provided by the National Research Council through Grant-In-Aid of Research NRC A1687 to W.O. Richmond. Funds for the purchase of the Sonntag fatigue testing machine were provided in a Major Equipment Grant from the National Research Council. V TABLE OP CONTENTS page no, I Introduction 1 II Review of Previous Work o © © . . . , 0 0 , 0 , 0 , 0 0 0 0 o o . o . o . . o . » o o » . o 6 1* Mechanism of Fatigue O , o , o o , , , o o o , , o « . , , , , , , , o o o o o o , « o o 6 H Mechanism o o . » o o o , 0 , 0 0 0 0 0 * 0 0 . o o o o o , o , , o , o o « o o o o o , o o , o 8 F Mechanism . o o « . . o o . . , . . o . . . o o . o . . o o o o o . . . . . . . . . . . . . . 10 S MeChanlSOl o o o o o o o « o o , . . o o o o « o o o o o o o , o . o o e o o « o . e o o , , o 11 Surface Effects . • • . . 0 . . a . o . . . . , o . o o , o . o « « 9 . o o o . o 0 . . . . 13 2. Statistical Aspects 0 0 o o o o o . o o . . . . . . . o o . . , , , o o o o o . o . o o 20 Lognormal Distribution 0 0 0 , 0 0 0 0 . 0 0 . . 0 . 0 0 . 0 . 0 , 0 , 0 0 0 0 0 , 0 2\ Weibull Puncti on 0 0 0 0 0 . . 0 . © . 0 . 0 . 0 0 0 0 0 , 0 0 0 0 0 0 , . 0 0 , o o . , o 23 III Test Procedure O o o o o o . . 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 . 0 0 . 0 0 0 . . o o . o o . o o 29 1, Testing Machine 0 0 0 . © . . . o o o , , , , , , , , , . , , © 0 0 0 0 , 0 0 0 0 , , , 0 0 29 2, Load Monitoring System o o o o o o o o o o © o , , , . o o , , . 0 0 0 0 0 0 . 0 0 0 32 3, Fatigue Specimens o o o . . , 0 0 0 . , o o o © . . . 0 0 , 0 . 0 0 . 0 0 0 0 0 0 34 4* Machining of Specimens 0 0 . . . . . . 0 . 0 . 0 . 0 0 0 0 0 . , , 0 . 0 . 0 0 0 0 0 37 5. Polishing and Edge Preparation . . 0 . 0 , 0 0 . 0 . . . 0 0 0 , 0 0 . . . . 42 6 0 Measurement of Minimum Section . 0 0 0 0 0 0 0 0 0 0 . 0 0 . 0 0 0 0 0 . 0 0 45 7. Loading Precauti ons o o , . 0 0 0 0 0 0 0 0 0 . o o . o . o o o o o o . o o o o o o o o 45 IV Test Program o ^ o o o o o o o o o o o o o o o o o o o o o o o o o o o e o o o o o o o o o o o o o o 46 V Statistical Analysis of Results . 0 0 0 , 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 51 1. Comparison of Distributions . o o o o a o 0 o o o o o o « 0 o 0 » o o © o » « 0 51 2. Distribution Curves 0 . 0 0 0 0 0 . 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 . . 54 3. Effect of Oil Coating 0 0 , 0 . 0 , 0 0 0 0 0 0 0 0 0 0 0 0 0 , 0 0 0 0 0 0 0 0 0 0 0 56 4© Effect of Polish Method , „ . . . , 0 . 0 0 0 0 . 0 . . 0 0 0 0 . 0 0 0 0 0 0 0 0 , 57 VI Observations of Fracture Mechanism . . 0 0 0 0 . 0 . 0 0 0 . 0 0 . 0 0 0 0 0 0 58 1. Macroscopic Observations 0 0 . 0 0 . 0 0 0 0 0 0 0 0 . 0 0 0 0 . 0 . 0 0 , 0 0 0 0 58 2, Microscopic Observations 0 0 0 0 0 0 0 0 0 0 0 0 . 0 0 0 0 0 0 0 0 0 0 0 0 0 . 0 0 65 vi Table of Contents e o n t . page no. VX X 1 D i S CT1S S i On 0 o » O O 0 O O O O © O « 0 » » e O O O O » . O O O O 0 O O O « O O » » O O O O O O O 0 O O O 74 10 EffeCt Of Oi1 C O a t i n g O 0 o « o o o o o o o o o o o o o » o o o o o o o o 0 o o 0 o o o 74 2« Effect of Polishing Method 0 0 0 0 0 0 . . 0 0 0 0 . 0 0 0 0 0 . 0 0 . 0 0 0 76 3. The Bimodal Distribution in Transition Region .......77 4. Fatigue Crack Initiation and Propagation „<,<,<,<,..,<,<..<.«.<..> 79 VXXI C O n C l U S i O n S 0 0 0 0 0 . o o o o o o o o 0 o . o o o o o o » o o o 0 0 0 0 0 0 O 0 0 » * * 0 0 0 0 0 < > 0 81 Appendices . . 0 0 . . 0 0 0 0 0 0 0 0 0 0 0 0 0 . 0 0 . 0 0 . 0 0 . 0 . 0 0 0 0 0 0 0 . . 0 0 . . 0 . 0 0 0 0 . 0 83 l a Tabulation of Results 0 0 . 0 . 0 0 0 0 0 0 0 0 0 0 0 0 0 . . o . o o . o . o o . o . . . . . 83 2. G*rapbs Figs. 34. to 55* 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 85 3o Calibration of Sonntag Machine 0 0 0 0 0 0 0 0 0 0 0 . 0 0 0 0 0 0 0 0 0 0 0 0 0 0 107 B i b l i O g r a p h y . o . . » # » # 0 . . o . o . . O O . O O O O . O « O . O O O « O O O 0 . O O O O . O O « « 0 0 O 111 v i i LIST OP FIGURES F i g u r e page no. 1. I d e a l i z e d S—logN curve .................................... 7 2. Hardening Range of S-logN curve ........................... 9 3. Fat i g u e Range of S-logN curve ............................ 10 4. Pseudo—safe Range of S—logN curve . . . . . . . . . . . . . . . . . . . . . . a . 12 5. Notch-Peak topography generated by t o and f r o f i n e s l i p ...... . . « • © • . . . . • . • . . . . . . © . • . • . . . o . o . e . . . . . 14 6. Mott mechanism of e x t r u s i o n f o r m a t i o n .................... 15 7 . C o t t r e 1 1 — H u l l mechanism . . . . . o . . o . ........................ 16 8. F u j i t a o x i d a t i o n mechanism ............................... 18 9. T y p i c a l shape of Lognormal frequency d i s t r i b u t i o n CUPV6 O 0 O O O O O O O O O O O O O O O O O O O O * * O O O O O O O O O O * O * * * * * O * O O O O 0 » O O 0 2 X 10. V a r i a t i o n of We i b u l l d i s t r i b u t i o n with b ................. 25 11. L o c a t i o n of W e i b u l l mean ................................. 28 12. I n t e r n a l mechanism of Sonntag machine .................... 30 X 3 o Grr i p ass6ml)Xy 000000000*000000000*0000000000000*00*00*0000 3X 14. Block diagram of s t r a i n gage load monitoring system ...... 34 X 5 a F a t i g u e specimen 0 0 0 0 0 0 0 0 0 0 0 0 0 00 o o o o o o o o o o o o o o o o o o o * * o o o * o 3 3 I60 S t r e s s e i o n g a t i o n curve f o r 2 0 2 4 - T 3 aXuminum 00000000*0000 3 6 X7o Specimen numbering system 000000000*00000000*0000000000000 3 8 13« Punching J i g 9 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 * 0 0 0 0 0 0 0 * 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 3 9 X 9 » Ij&tli f i x t u r e 000000000000000000000*00000000*0000*000000*00 4 0 20. Sequence of specimen's machining operations .............. 41 21. Flow chart of chemical p o l i s h o p e r a t i o n .................. 44 2 2 o TypicaX s t r e s s cycXe 000000000000000***000**0*000*0000*000 4 6 2 3 a Test program 000000000000*0***000000000000*000000000000* 00 4-7 v i i i List of Figures cont. Figure page no. 24. Cyclic stress elongation for Smax of 54 ksi ............... 49 25. Typical fracture surface ................................... 60 26. Specimen in which two cracks have propagated simultaneously ........................................... 62 27. (a) Crack formed in region of fracture .................... 64 (b) End of crack similar to one in (a) .................... 64 28. (a) Crack which has not grown through to other side ........ 66 (b) Same crack after deep etch ............................ 66 29. Portions of crack in Fig. 28(a) at high Hl£l_jXl_ f i C8.iji OH o e o o o o o o o o o o o o o o o c a o o o o o o o o v o e o o o o o o o o o o o o o o 6 T 30. Examples of slip lines forming ahead of large 31. (a) Slip markings forming ahead of large crack ............. 69 (b) Effect of precipitate particle .......................« 69 32. (a) Effect of multiple s l i p o o o o o o o o o o o * » o e > c o o 0 o o o o o o o o o o o o 70 (b) Slip markings at edge of specimen 0 0 o ° o o o o Q o o * a * c o o o Q o o 70 33o (a) Crack forming at fracture o o o o o o o o o o o o o e o o + o o o o o o o o o o e * 71 (b ) After l i g h t 0tO_l C O O O O O O Q * O O * O O O O O O O O » O + O O O Q O O O O O O O O O < > O 71 34. 39/ 40. 52/ Tests for Lognormal distribution .......................... 85 Tests for W@ibU.ll diS t r ibUt i On o e o o o o * o o a o o o o o o o o » o o o o o o o o o 91 53. Comparison of polishing methods not~olled specimens ...... 104 54. Comparison of: polishing methods, oiled specimens ......... 105 55. Effect of o i l coating on S-logN curves ................... 106 56. Lever calibration fixture . o o o o o o o o . o o o o o o c . o . o o o o . o . o . o . e 109 57. Loading spring calibration curve . „ o . o . 0 . o o o . . . . . . . . . . . . . . 110 ix LIST OP SYMBOLS Smax Maximum stress Smin Minimum stress N Number of cycles to failure N Mean l i f e of population CT Standard deviation of population N Mean l i f e of logarithms of population lives — Og (Jj Standard deviation of logarithms of population lives log f(N) Normal probability function f^(N) Logn.ormal probability function f (N) Weibull probability function EJ(N) Lognormal distribution function P^(N) Weibull distribution function No Minimum l i f e parameter of Weibull function Na Characteristic l i f e parameter of Weibull function b Weibull slope parameter A Number of specimens in a population J Order number of specimens for calculating plotting position N50$ Median l i f e P Gamma function P (N) Probability of failure at mean li f e I INTRODUCTION 1. Fatigue, is an exceedingly complex type of failure which occurs when metals are subjected to varying stresses. It appears in one form or another in practically every machine or vehicle which moves, and is without doubt the cause of most material failures. It is also the least understood of a l l material fractures and the most di f f i c u l t to allow for in design. That i t is s t i l l poorly understood certainly cannot be blamed on lack of investigation, for i t has been under intensive study by mechanical engineers, metallurgists, and solid state physi-cists for well over one hundred years. In fact, i t is not unusual to find bibliographies on fatigue which contain hundreds of publica-tions, and this l i s t is growing by at least f i f t y papers a year. There are three factors associated with fatigue failures which have limited rational explanations to rather simplified cases. First of a l l , the atomistic mechanism leading to the fi n a l failure i s complicated and di f f i c u l t to observe. Secondly, the fatigue pro-perties of any particular metal are greatly affected by a large number of external conditions such as$ testing atmosphere, humidity, temperature, coatings, surface roughness, and specimen size, to mention a few. Thirdly, the fatigue conditions must be defined by at least three variables, two values of applied stress and the number of cycles to failure. This means that without a basic under-standing of the problem every possible combination of applied stress must be tested before the fatigue properties of a metal are known. Nevertheless, many advances have been made, and i t is 2 . worthwhile to note some of the results. Due to early work by Ewing and Humfrey ( l ) * , Eosenhain and Ewen ( 2 ) , Moore ( 3 ) and others, the events leading up to failure were known by 1930 to consist of an initiation period in which small fatigue cracks formed, a propagation period in which one or more of the fatigue cracks propagated slowly under the repeated stresses, and finally a rapid fracture which resulted from the remaining undamaged material being stressed beyond i t s ultimate strength. Gough and his associates ( 4 ) , extended the basic understanding of the process by specifying that deformation in fatigue was by classical slip, and that i t was similar in many ways to the slip found in unidirectional deformation. Following Gough, most work was done to consolidate and extend these ideas with the help of the newly developed dislocation theory of metal deformation (the concept of dislocations was f i r s t proposed in 1934 by Taylor ( 5 ) ) , and i t was the late 1950's before Wood (6) recognized that the fatigue mechanism was substantially different for high and low values of applied stress. With the advent of light alloys and their use by the air-craft industry, work was done to determine the effects of external conditions such as temperature, humidity, cold work, hardness, etc. Once i t was recognized that the free surface of the metal was intimately connected to the fatigue properties, attention was turned to the effects of surface preparation. Wadsworth and Hutching ( 7 ) found a linear relation between the logarithm of fatigue l i f e of •Numbers in brackets refer to references listed in the Bibliography. copper and the logarithm of air pressure. Haigh and Jones (8) showed that the fatigue l i f e of lead specimens could be increased by a factor of ten when their surfaces were covered with oi l or water. Electropolished specimens of steel were found to have sub-stantially different fatigue lives than did specimens which were mechanically polished (9). In view of the large number of complicating conditions, i t is not d i f f i c u l t to see that results obtained in different labora-tories under supposedly similar conditions could be expected to vary considerably. George and Mantle (lO) found the fatigue l i f e of sheet specimens were much greater i f the edges were rounded and smoothed before testing. Other investigators had warned of the dangers of scratches and sharp notches which could induce premature crack initiation. Recently Dunsbie (l l ) found, in a comparison of results obtained by ten laboratories across Canada, that in only three of the laboratories were the results comparable. In a l l cases he attributed the discrepancies to poor testing machine calibration, different testing conditions and different specimen preparation. One further point which needs to be made concerns the statistical behaviour of metals under cyclic stress. Any group of fatigue specimens, supposedly identical in every way, and fatigued to failure under identical test programs, do not a l l f a i l at anything near a unique number of stress cycles. At f i r s t the reason seems obvious in that for any experiment there is always some scatter in the results, simply due to random variations in the test conditions 4. and that there is no reason to assume that fatigue testing should be different. However, there are two peculiarities in the scatter in fatigue results which indicate a more basic reason. One is that the actual amount of scatter is larger than can be explained by random variations in testing. In fact, i t is not unusual to get results varying by factors of ten or more for many stress levels. Two, i f the scatter was due to random errors, then the distribution of the test results would be normal, whereas in practice the l i f e distributions are found to be skewed to the right with a long t a i l asymptotically approaching the l i f e axis at infinity. The study of this experimental l i f e distribution is the subject of continuing research, both in trying to explain i t s existence, and in developing appropriate mathematical relations which can be used to predict results. There is every reason to believe that these two problems wil l soon be solved. Keeping in mind the experiments which had been done and the problems s t i l l remaining to be solved, a program was initiated using 2024-T3 sheet aluminum' alloy specimens which were cycled in fluctuating tension. The object of the work was to try and evaluate the suitability of different fatigue l i f e distributions, and to deter-mine the effect which polishing methods, and o i l coatings had upon the fatigue properties. In particular, the changes in the l i f e distributions and the S-logN curves received olose attention. 5. In addition microscopic studies of small fatigue cracks which formed in the metal surface were made. It was hoped, that these observations combined with those made by other investigators, would contribute to a better understanding of the fatigue process in alloyed structures cycled in fluctuating tension. Also i t was felt that an understanding of the method of crack initiation and propagation would be a definite advantage when i t came to explaining the results of the previous experiments on polishing methods and o i l coatings. REVIEW OF PREVIOUS WORK 6, 1. MECHANISM OF FATIGUE A comprehensive review of the various fatigue mechanisms that have been proposed has been published by Gohn (12) and i t will serve no purpose to repeat i t here. Instead, this section will deal with a few of the recent investigations, with particular refer-ence to the work of Wood on the initiation of fatigue .cracks., Most of the early conclusions on the fatigue mechanism originated from the work of Gough and his co-workers (4) the most important of which are summarized below, a) The mechanism of deformation by fatigue is slip on ordinary slip systems. b) The deformation appears to be controlled by the resolved shear stress acting on these systems. c) Strain hardening occurs at a l l stress amplitudes for most materials, and this strain hardening is not only affected by the f i r s t application of stress, but is also dependent upon the range of the applied stress and the number of stress repetitions. d) Slip bands represent traces of slip planes on the surface of the specimen and eracks are always associated with these bands. The concept that the mechanism, by which a crack forms and propagates, is substantially different for high and low applied stresses, was f i r s t presented by Wood in a paper in 1957 (6) and then 7. extended in 1963 (13). He succeeded in isolating the different mechanisms according to the applied stress amplitude and he used these mechanisms to explain the peculiar shape of the common S-logN curve.-cycles to failure log scale Pig. 1. Idealized S-logN curve showing where different mechanisms operate Pig. 1. is an idealized S-logN curve for a face centered cubic metal, such as aluminum. It has been divided according to Wood into the H, P and S regions. These regions denote the approximate locations of the three different fatigue meohanisms and are named in accordance with the type of deformation observed. The H region is so named because of the large amounts of lattice distortion and strain hardening which occur. The failure is similar to a static failure. On the other hand, the P or pure fatigue 8. region corresponds to a deformation mechanism which is peculiar to fatigue. This is the so-called fine slip which causes l i t t l e or no strain hardening and produces unusual surface disturbances. Finally, the S or pseudo-safe mechanism, which occurs for very long lives, is characterized by dispersal of isolated fatigue damage that has formed early in the l i f e . Due to some as yet unknown lattice property, the P and S mechanisms are found only in face centered cubic metals. Body centered cubic metals, such as steel, go directly from an H type mechanism to a mechanism similar to the later stages of the S mechanism. It is this property which accounts for the well defined endurance limit of body centered cubic metals. Before describing the three mechanisms in more detail, i t is important to remember that they have only been observed for fully reversed stress cycles and i t is possible that there are even different mechanisms for other types of stress applications* Never-theless, the concept of different mechanisms acting at high and low stress levels is important and is necessary to a complete under-standing of the fatigue process. H Meohanism The events leading to failure in the H region of the S-logN curve are shown schematically in Pig. 2. They begin by a breaking down of each grain into regions of different lattice orientation, separated by irregular boundaries of distortion and internal strain. The regions are known as subgrains and their disorder i s readily proved by X-ray analysis (6). Very soon after the subgrains form, pores start to appear in the subgrain boundaries and as the cycling continues, the pores multiply and spread into oavities, elongated along the subgrain boundaries* New oavlties form continually throughout the l i f e of the specimen and gradually coalesce into microoracks much smaller than a grain. Eventually a macrocrack forms by the linking together of microoracks. Once this happens complete failure soon follows. The important point as far as crack nucleation is concerned, is that the i n i t i a l micro-cracks are essentially non-propagating. They form, not by propagation of a single cavity but by continued formation of new ones cycles to failure log scale Fig, 2, Hardening range from Wood et al , (13) (a) Formation of subgrains (b) Formation of pores (c) Formation of microcracks 10. F Mechanism X-ray studies ( 6 ) show that at stress amplitudes corresponding to the F range of the S-logN curve, slip movements occur with very l i t t l e accompanying distortion. Furthermore, microscopic studies show that the slip movements occur on closely spaced planes only one or two microns apart,. To distinguish i t from the coarse ductile slip movements usually associated with deformation processes i t i s designated fine slip and i t is this fine, non-hardening slip which characterizes the F mechanism. F range cycles to failure log scale Fig. 3 f Fatigue range from Wood et a l . (l3)< See text for description of insets 11. Pig. 3. illustrates the events leading to fracture. With the f i r s t few stress applications the to and fro fine slip movements form zones of distortion within which pores soon form. Further cycling causes the pores to multiply and disintegrate the zones along their lengths. Accompanying the pore formation, the slip zones broaden by cross slip until they cover whole grains. Associated with the above changes ln the body of the material are a number of surface phenomena which form in the areas where the slip zones cut the surface. One type of formation is shown in Pig. 3. and a l l are discussed in more detail later. Nucleation of a fatigue crack is thought to be initiated by the surface distur-bances. Once i t forms, i t propagates along the already damaged slip zone and failure soon follows. In summary then, in the P region, the mechanism is entirely different from the progressive hardening of the H range. The major damage is s t i l l internal pore formation which develops without any associated work-hardening, and does not, in i t s e l f , nucleate the i n i t i a l macrocrack. S Mechanism paoe centered cubic metals subjected to low stress levels which results in very long lives, exhibit structural changes different from those common to either the H or the P range. Pig. 4. illustrates these changes. 12. \ \ \ \ \ \ S range cycles to failure log scale Fig. 4 , Pseudo-safe range from Wood et a l . (13) (a) Fatigue zone after prolonged cycling (b) Islands of fatigue damage (c) Damaged zone disappear (d) Surface markings As in the F range, fine slip zones form early in the fatigue l i f e of the material, and after some time, islands of damage, different from the pore of the F range, appear. As the cycling continues the islands of damage are dispersed leaving the undamaged zones of fine slip, which then spread by cross slip and cover whole grains. In effect, though the material goes through a period of weakness, where the islands of damage form, once this damage is dispersed the material is strengthened and the chance of failure is reduced. It is this damage dispersal which characterizes the S mechanism. Body centered cubic metals display an endurance limit 13. because they go directly from the H mechanism to a mechanism much like the later stages of the S mechanism (14). A l l that forms are wide zones of fine, non-distorting, non-hardening slip, and there is never any damage which can lead to failure. These then are the events leading to initiation of a crack in the different regions of the S-logN curve. Whether the major portion of the fatigue l i f e i s taken in nucleating a crack, or in propagating the crack, is s t i l l a matter of controversy. Also, how a fatigue crack propagates, is not known with certainty, though some theories have been developed on the basis of strain hardening in a region of plastic deformation at the tip of the crack. What is known with certainty is that fatigue cracks usually start at a free surface and that the surface condition plays a dominant role in the fatigue properties of the material. This wil l be discussed in the next section. Surface Effects The effect of the free surface on fatigue failures has been extensively investigated. Alden and Backofen (15) found that surface cracks in aluminum single crystals could be prevented by forming a thick coherent oxide film on the surface. They demonstrated that i t was only necessary to keep the oxide film free from cracks in order to extend the fatigue l i f e indefinitely. Thompson et a l . (l6) and Coffin (17) have shown that the fatigue lives for face centered cubic metals cycled in both the H and P range, can be extended indefinitely by periodic removal of a small surface layer (20 to 30 microns for 14. small amplitudes). These experiments and others demonstrate conclusively that cracks usually start at the surface. Very likely part of the reason for this lies with the previously mentioned surface phenomenon. Perhaps the most important of these are the so called extrusions and intrusions observed on fatigued metals. Forsyth ( l 8 ) was the f i r s t to notice that where the zones of fine slip (F mechanism) contacted the metal surface, thin ribbons of metal were extruded from the zones. Wood ( 7 ) in his observations on copper and brass observed surface disturbances which could be considered to be extru-sions. He also found that there were notches or intrusions associated with the extrusions. Other investigators have confirmed these results ( 1 9 , 2 0 ) . Theoretical arguments to account for these phenomena have been developed by Wood ( 7 ) , Cottrell and Hull ( 1 9 ) , and Mott ( 2 1 ) , and others have extended them. Pig. 5 . Notch-peak topography generated by to and fro fine slip, from Avery and Baokofen ( 2 2 ) 15. Wood considers the formation of the peaks and notches to be the result of the to and fro fine slip within the fatigue zones, such that blocks of metal w i l l move with respect to each other. The process is shown pictorially in Fig. 5. The other two processes are somewhat more complicated and depend upon dislocation motions. Mott considers that a dislocation lying in the surface, with a component of i t s Burgers Vector perpendicular to-the surface, can by cross slipping, be made to travel in a loop by stress reversals and that this motion w i l l result in an intrusion or an extrusion depending upon the direction of the motion. He also reasons that this situation will likely be associated with a cavity and that the conditions for formation of a cavity by a Fujita type mechanism (23) are present due to the fine slip on closely spaced planes. It is this cavity which precititates the i n i t i a l crack. A diagram of this type of extrusion model is shown in Fig. 6. Fig. 6. Mott model of extrusion formation from Avery and Backofen (22) . 16. Pig. 7. shows the Cottrell-Hull mechanism of intrusion -extrusion formation. Here A and B represent two Prank-Read sources lying on intersecting slip planes. A is considered to lie on a more favourably oriented plane so that i t wi l l be the f i r s t to move upon application of an increasing stress. Where the slip plane cuts the surface a small step w i l l appear by the action of the A source. As the stress is increased further, B w i l l become activated and cause a seeond surface step. Upon reversal of the stress, A w i l l again be activated f i r s t . However, by the motion of B, i t has moved slightly upwards so that the reverse slip results in an intrusion. The same is true for B except that in this case an extrusion forms. No cross-slip has been necessary. Further cycling increases the size of the extrusions and intrusions. Pig. 7. Cottrell-Hull mechanism for intrusion -extrusion formation 17. Of the three models just discussed, none can account for the observed rapid formation of extrusions. In addition the Cottrell-Hull model is not compatible with those experiments which have found cross slip to be important, i f not necessary for fatigue failure. There are also some cases where extrusion formation has been suppressed while failure has s t i l l occurred. On the strength of these findings, though they may have a large effect, there can be no justification in proposing a mechanism for fatigue based solely upon intrusion -extrusion models. While i t must be pointed out that there is no justification for basing a failure mechanism solely on oxidation effects since fatigue can occur at temperatures near absolute zero, there is s t i l l a large body of evidence which indicates that oxidation plays an important role in determining fatigue behaviour at room temperature. The two best known experiments are those of Haigh and Jones ( 8 ) who found that the fatigue l i f e of lead specimens could be increased by a factor of ten when the faces were covered with o i l or water, and by Wadsworth and Hutchings ( 7 ) who have shown a linear relationship between the logarithm of fatigue l i f e of copper and logarithm of air pressure. 18, oxide oxide layer adsorbed oxygen s l i p plane Pig. 8. Oxidation mechanism as proposed by Fujita from Fujlta ( 24 ) Fujita ( 2 4 ) has proposed a mechanism which makes use of the idea that oxidation can play an important role, Pig. 8„ Briefly, he considers that a "elean" ledge of metal w i l l be exposed to the atmosphere, by the slip movements during the f i r s t half cycle. As soon as this ledge forms, a monolayer of oxide w i l l form on i t , and shortly after this there wil l be an aisorbed oxygen layer within the surface. On the next half cycle the oxide layer w i l l be stripped away leaving the adsorbed oxygen to be transported into the interior. If this oxygen can diffuse across the slip plane i t wil l form oxide particles and since oxide particles represent strong obstacles to 1 9 . dislocation motion, pile ups of dislocations wi l l form behind them. Once this happens the chance of a crack nucleating is greatly enhanced. In a l l likelihood, any oxidation mechanism is more com-plicated than this, and in fact there are a number of other mechanisms which could be imagined. Nevertheless, Fujita's mechanism s t i l l serves to indicate the probable effect oxidation plays in the fatigue process. 20. 2. STATISTICAL ASPECTS The occurrence of scatter in the results of experimental investigations has long been recognized as an inherent property of the investigation. In most instances the scatter is merely the result of small errors in the instruments or in the reading of values. In these cases the scatter follows the Gaussian or error distribution curve and because this curve is symmetric and well understood theoreti-cally and because the amount of the variation is not large, there is not usually much of a problem. Unfortunately, fatigue experiments are not blessed by any of these mitigating properties. Not only is the size of the variations in lives abnormally large, but the distribution of lives, as found experimentally, is also badly skewed and in fact, the degree of skewedness is dependent upOn the size of the applied stress. Since the experimental l i f e distribution is not symmetric and has not been obtained theoretically, the search for distribution functions which can be used has gained considerable importance in the past ten or fifteen years. Three that have received attention are the Lognormal, the Weibull and the Gumbel distributions. Of these, the one proposed by Gumbel has proved to be so unwieldy to apply that i t is seldom used. The rest of this section w i l l therefore only attempt to discuss the important parts of the Lognormal and Weibull distribu-tions and their application to fatigue data. 21. Lognormal Distribution The Lognormal distribution is a widely used modification of the Gaussian or Normal distribution, in which the arithmetic fatigue l i f e is replaced by the logarithm of the fatigue l i f e . Making this substitution has the effect of skewing the distribution to the right and shifting the mean point to the left. A typical curve shape is shown in Pig. 9. a) o a o< a> U cycles to failure log scale Pig. 9. Typical shape of lognormal. Frequency distribution curve The most common form of the Normal distribution is (25)? f(N) = T Z T f c r exp 2CT' 22. where: f(N) is the computed height of the ordinate at a distance N from the origin N is the mean of the sample Cfis the standard deviation of the sample The Lognormal distribution follows from the Normal by substituting the logarithm of N for N. Thus; Where N, is the mean, and CT, is the standard log ' log deviation of the logarithms of N. They may be simply calculated from the formulas: A rr - V l o g NL CJTog -A where A is the number of specimens in the sample. For purposes of computation the distribution is used in i t s cumulative form, usually designated F^N) to distinguish i t from the probability distribution. F 1 (N) is defined as: F(N)=/f(t)di - C D which physically is the area under the distribution curve f^(N). 23. To test the f i t of a set of data, i t is f i r s t divided up into group ranges of N, and the cumulative percent failed is then plotted against the logarithm of N on special logarithmic probability paper. This paper is prepared with an ordinate scale so designed that a true Lognormal distribution w i l l plot as a straight line, with it s mean value falling at the 50%> ordinate. In other words i f the data plots as a straight line with the calculated mean fal l i n g at the 50% ordinate, the data is Lognormally distributed, i f i t is not, then a new distribution must be found. More details on the use of probability paper w i l l be found in reference (26). Weibull Function (27, 28, 29) The Weibull distribution function is an application of the weakest link, or extreme value theory f i r s t developed by Fisher and Tipper (30). This theory leads to a family of three distribution functions, one of which can be selected to represent the fatigue l i f e distribution of a group of specimens. It is named in honour of W. Weibull who f i r s t applied i t to fatigue data. The general form of the distribution function i s : fp(N) = (NaT No) N-No b-l exp N-Nc No-Nc 2 4 . where: N is the specimen l i f e as before No is the minimum l i f e parameter Na is the characteristic l i f e , occurring at the 63.2 percent failure point for the population b is the Weibull slope parameter Fig. 10. shows some typical distribution curves of f (N) N-No plotted against ^ & N q . The function gives a simple exponential curve for b equal to one and i t is a good approximation of the Normal distribution for b equal to 3.57. When f^N) is plotted against N, curves for b values greater than 1, intersect the l i f e axis to the left of the point of maximum frequency of failures. The point of intersection of the curve with the l i f e axis is No and is known as the minimum l i f e of the distribution. The cumulative function for the fraction of population failed at l i f e N i s : This can be easily transformed to: I- FZ(N) ^ b log ( M a - No) - b log (Na-No) 2.5 2.0 0 0.4 0.8 1.2 1.6 2.0 2.4 2.8 3-2 N-No/Na-No Fig, 10. Typical Weibull distribution curves showing variation of slope parameter b 2 6 . This equation plots as a straight line on Weibull probability paper, which may be purchased or constructed from square log-log paper. Construction details are found in reference (27). The linear relationship allows for a simple graphical method of estimating the parameters Na, No, b. To do this, the data is f i r s t ordered from one to A in order of increasing fatigue l i f e . Then the ordered N values are plotted along the the abscissa of the Weibull paper against an estimate of the percentage of popula-tion failed. The estimate of percentage of population failed is a function of the size of the sample A, and may be obtained from tables, or calculated from the relation? Estimate of plotting position - J-(HN2)-(21NEH)(£I) A where J is the order number of the specimens. For the cases where No is zero, the data w i l l plot as a straight line, and the distribution parameters may be estimated in the following way. Na is the value of N at the intersection of the fitted line and F (N ) » 6 3 . 2 $ , and b is the slope of the fitted line. When No is not zero, the plotted line w i l l curve downwards. In this case No oan be estimated by t r i a l and error, by guessing at the l i f e value which the curve seems to be asymptotically approaching (No*) and then replotting the data. When Ho* equals No the data w i l l plot as a straight line. 27. Since the degree of skewednesa of the Weibull curve varies with b, the mean l i f e (if) will In general be different from the median l i f e ( N^Q^) a^d w i l l also be a function of b. It can be determined from the relation which is derived in reference (29). For computational purposes, F,£]ff) is shown plotted as a function of b in Fig, 11. Once b is known for a set of data, the value of F^N) corresponding to b can be determined from Fig. 11. and N can then be determined from the Weibull plot. 28. Weibull slope b Fig. 11. Location of mean l i f e (u) from Johnston (27) I l l TEST PROCEDURE 29. 1. TESTING MACHINE Axially loaded sheet specimens of 2024-T3 aluminum alloy were fatigued in fluctuating tension in a Sonntag, model SF-l-U, fatigue machine. The main components of the machine are shown in Pigs. 12. and 13. It i s of the spring and rotating mass type in which static and dynamic loads are applied independently of each other. Static loads are applied by extending a pair of loading springs fixed between the lower specimen grip and the machine, base. Since the SF-l-U model is not equipped with a static load maintainer, any deformation in the specimen results in a decrease in the static load which can only be corrected by stopping the machine and re-extending the springs. Sinusoidal dynamic loads are provided by a rotating counterweight mounted between the springs and the lower specimen grips. The dynamic load is independent of the specimen stiffness when the natural frequency of the lower grip structure and the static load springs is the same as the dynamio load frequency. P i g . 12. I n t e r n a l mechanism of A. Frame E. B. Load springs F. C. D i a l i n d i c a t o r G. D. O s c i l l a t i n g p l a t e n H. Sonntag machine E c c e n t r i c s h a f t E c c e n t r i c load s c a l e Frame suspension s p r i n g s Counter 31. Fig„ 13. G r i p assembly A. O s c i l l a t i n g p l a t e n D. Upper specimen g r i p B. Lower specimen g r i p w i t h s t r a i n gages C. Specimen E, Frame 32. 2. LOAD MONITORING SYSTEM Although the machine is factory equipped with meohanical means to set the static and dynamic loads, metal film strain gages were mounted on the shank of the upper specimen grip in order to have a second means of checking the specimen load, and also to pro-vide continuous load monitoring throughout the test. The strain gage system consisted of the grip, an E l l i s BA-13 bridge amplifier and a Tektronix 502A oscilloscope. The block diagram of the system is shown in Pig. 14. and i t is explained below. The BA-13 unit consists of a Wheatstone bridge, of which two arms are formed by the strain gages on the grip, an AC amplifier, and a chopper which alternately shorts and opens the output of the bridge before i t goes to the amplifier. Thus when the output is shorted a zero signal is fed to the amplifier. When i t is opened the f u l l static and dynamic signal is passed and eventually displayed on the oscilloscope screen. Since the bridge is i n i t i a l l y balanced before a load is placed on the grips, when the chopper shorts the output, a signal corresponding to the balanced condition of the bridge is fed to the amplifier. On the other hand, when there is a load on the grip the bridge w i l l be unbalanced due to the strain gage properties. Hence, when the chopper opens, a signal corresponding to the unbalanced condition is passed to the amplifier. For static loads then, the output displayed on the osoilloscppe screen is a square wave with 33. the top line corresponding to the unbalanced condition and the bottom line the balanced condition. A precise calibrated potentiometer is used to balance the bridge and balance is indicated when the square wave degenerates into a line. The setting of the potentiometer is then a measure of the load applied to the strain gages and i t is a simple matter to convert the potentiometer readings to corresponding grip loads. The strain gage system also provides a means!of measuring dynamic loads. For the sinusoidal dynamic forces produced by the Sonntag machine, the peak to peak amplitudes are of interest. They are found by adjusting the calibrated potentiometer until the null or balanced line coincides f i r s t with the lower then the upper peak. The amount that the potentiometer has to be adjusted is a measure of the peak to peak amplitude of the load. An accurate calibration of the loading springs and the strain gaged grip were done at the beginning of the testing and the c a l i -bration was checked periodically during the testing program. Further details of the calibration are in Appendix III. 34 Pig. 14. Block diagram of strain gage load monitoring system (a) wheatstone bridge (b) amplifier (c) oscilloscope 3. FATIGUE SPECIMENS The specimens used were identical to those designed by the National Research Council for its co-operative fatigue research pro-gram ( l l ) . Their shape and dimensions are shown in Fig. 15. A l l specimens were cut from a 4 f t . by 12 f t . sheet of 2024-T3 aluminum alloy of nominal thickness 0.050 in. Tensile tests done on an Instron tensile testing machine showed the 2024-T3 alloy to have a yield strength of 51 ksi and an ultimate strength of 70 ksi, both values being based upon the i n i t i a l cross-sectional area of the speci-mens. Fig. 16. shows the stress elongation diagram obtained. Fig. 15. Fatigue specimen cut from 2024-T3 aluminum sheet showing c r i t i c a l dimensions 37. 4. MACHINING- OP SPECIMENS Three operations were required to manufacture the specimens. The large sheets were f i r s t sheared into 4 f t . by 8 in. strips, the strips were then sheared into 1.5 in. by 8 in. blanks, with their long axis parallel to the rolling direction. As each blank was cut, i t was numbered according to its position on the large sheet. Pig. 17. indicates the numbering sequence. v Next two 1/2 in. diameter holes were simultaneously punched In eaoh blank by a special j i g , mounted on a Pamco 50 A punch press. The j i g and press are shown in Pig. 18. Finally, the two 7 in. radii were cut on a lathe,: with the aid of a fixture (Fig. 19.) built especially for the turning operation. Approximately 20 specimens could be machined- at one time. The accurately positioned mounting posts eliminated any appreciable dimensional variation in the specimens and careful work by the machinist resulted in a smooth edge surface and reduced variations which could arise from the machining operation. After machining, eaoh specimen was cleaned in a bath of trichlorethane, coated with light non-corroding aviation o i l , and then wrapped in oiled paper. A l l the specimens were stored this way until removed for polishing, measuring, and f i n a l testing. Al B 1 A2 B2 A3 B3 Ql R l Q2 R2 Q3 R3 A 3 2 B32 Q31 R31 Q32 R32 1 Jj' Fig„ 17. Numbering sequence of specimens 39 = 40, Pig. 19o Lathe fixture 42. 5. POLISHING AND EDGE PREPARATION After maohining, the specimens usually had rough edges produced by the cutting tool, and light scratches on their flat surfaces. The three polishing methods used were largely determined by these imperfections. Unpolished This group of test specimens were left in the same con-dition as they were after machining, except that the rough edges were rounded by rubbing with 0 grit emery polishing paper. Past exper-ience had shown that this was necessary as the rough edges tended to initiate cracks prematurely. Chemically Polished The edges of the specimens in this group were rounded the same way as the unpolished specimens and the central section was chemically polished. The polishing solution used was made to a commercial formula, supplied by the Aluminum Co. of Canada (.31). The polishing action produced a bright olean surface and reduced roughness by dissolving metal from high spots at a faster rate than from low spots. Approximately .005 in. was removed from the surface. Deep scratches were not removed, but were brightened along with the rest of the surfaces. The flow chart of the polish operations is shown in Pig. 21. 43 Chemical and Mechanical Polish Since the chemical polishing did not in general remove enough metal to erase the scratch marks, one group of specimens was mechanically polished on the edges and flats, with 0 grit emery polishing paper before chemical polishing* This procedure resulted in a surface free from scratches but with the same surface roughness obtained by chemical polishing. For referenoe purposes, the approximate surface roughness for each type of polishing, was measured with a Brush Surface Indicator. The values found were essentially the same for a l l and averaged 5 micro inches rms in both the longitudinal and lateral directions. DEGREASING IN TRI-CHLORETRANE WATER RINSE Room Temp. NITRIC ACID DIP APP. 50$ WATER RINSE Room Temp. CHEMICAL BRIGHTENING 105-H5°C Vigorous A g i t a t i o n WARM WATER RINSE 45-50°C NITRIC ACID DIP APP. 50$ WATER RINSE DRYING P i g , 21. Plow Chart of chemical p o l i s h o peration from Aluminum Co, of Canada Report (31) 45. 6. MEASUREMENT OF MINIMUM SECTION In order to calculate the cross sectional area of the minimum section the width and thickness had to be measured. The thickness was measured with a standard ten thousandths micrometer. The width was measured on a Wild optical projector fitted with a ji g to locate the center of the specimen. 7. LOADING PRECAUTIONS In order to minimize eccentricities of loading, the grips were aligned with respect to each other by means of a f l a t ground l / 4 in. steel plate which held the grips in line while they were tightened into their seats. This operation was assisted by balancing the strain gage bridge before the grip was seated so that any un-desirable distortion caused by the tightening action produced an output on the oscilloseoplc screen. When placing the specimens in the grips the strain gaged grip again proved useful in detecting unwanted mis-alignment caused by tightening the securing bolts In the grips. Fretting of the specimens in the grips proved to be a problem at low stresses. It was largely prevented by applying a coat of grease to the part of the specimen which fitted in the grip. When applying the dynamic load the motor was always started slowly. If this was not done unwanted resonant loads were applied during the f i r s t few loading cycles. TEST PROGRAM 46. Tests were conducted at maximum stresses of 64 ksi, 54 ksi, 47.5 ksi, 42 ksi and 38 ksi. In a l l oases the minimum stress was ,05 Smax. This particular ratio was chosen to eliminate buckling and vibration in the specimen. Fig. 22. Typical stress cycle for fluctuating tension Approximately 20 specimens of each polishing group except the chemically polished ones were tested at each stress level. No chemical polished specimens were tested at 38 ksi because of an error made in the polishing operation. What the error was was not deter<= mined, however i t resulted in very much longer lives for one batch of specimens. Half of the specimens in each polishing group were coated with o i l before testing and the remaining half were left in a clean condition. 47 o In order to reduce bias in the selection of the specimens, tables of random-sampling numbers (32) were used to determine test-ing order, and to divide each group into oiled and not-oiled. The procedure for using the tables is given in reference (33). In a l l but two cases, the specimens were tested in groups corresponding to their letter designation, i.e. A group, B group, e t c The test program is tabulated in Pig. 23. The results of a l l the tests are also tabulated and will be found in Appendix I. NO. OP SPECIMENS TESTED Maximum Stress Not-pollshed "— — I — Chemical Polish Emery & Chemical Polish 64 ksi 54 ksi 47.5 ksi 42 ksi 38 ksi Oiled Not-Oiled Oiled Not-Oiled Oiled Not-Oiled 1 3 11 11. 11 12 10 11 3 2 2 3 7 8 11 9 4 5 3 2 5 5 5 10 9 8 13 11 Pig. 23. Test Program Failure at a l l the stress levels, except the one at Smax of 38 ksi was by an H type mechanism. In the tests at 64 ksi and 54 ksi there was yielding and elongation in the. specimens during the f i r s t few loading cycles. For these loads the f i r s t three or four cycles were applied in an Instron testing machine before loading in the 48„ Sonntag fatigue testing machine. A l l yielding was completed after these i n i t i a l cycles. Pig. 24. shows stress elongation curve for the precycling. The effects of temperature and humidity are not known with oertainty, however large changes in either of them probably has some effect. Because i t was not practical to control temperature or humidity near the testing machine, a continuous record of both variables was kept to check that changes were not too great. In this way, i t was found that in any one test the maximum temperature change was about 20°P and the maximum relative humidity change about 15$. Over the entire testing program which lasted approximately a year, the maximum and minimum values of temperature and humidity recorded were about 90°P and^O 0? and 85$ and 45$ respectively. 80 .150 Elongation in. Pig. 24. Cyclic stress elongation curve for specimen tested at Smax of 54 ksi from Instron testing machine chart 50. Photomicrographs of small cracks which formed in the epeoimen surfaoe were made on a Reichert micrograph. Because of the brighter surfaoe finish, a l l the observations were made on speoi= mens whieh were chemically polished before they were fatigued. No further polishing was done before the photomicrographs were taken. A l l the observations of small cracks were taken from specimens tested at an Smax of 47.5 ksi. This was because the scatter in the lif e values was small at this stress level and i t was easy to predict when any specimen would f a i l . A small incipient fatigue crack was always accompanied by a small surface depression Which made detection f a i r l y simple. V STATISTICAL ANALYSIS OP RESULTS 51. / 1. COMPARISON OP DISTRIBUTIONS* One of the objectives of the present investigation is to determine which distribution function, the Lognormal or the Weibull, is the most suitable for use in fatigue experiments, In order to avoid repeating a l l the results for both distributions, this section wil l be used to discuss the application ,of the distributions to some of the more representative data, and to decide which distribution is to be used in the remainder of the report. The most complete set of results are for the tests at a maximum stress of 47.5 ksi and 42 ksi, and these w i l l be used as a basis for comparison between the two distributions. -These data are shown plotted in its cumulative form on logarith-mic probability paper in Pigs 0 34. to 39. and on Weibull probability paper in Pigs. 41. t o 46. A few of the most scattered points have been ignored when drawing the curves, however i t should be remembered that the ordinate plotting positions are only estimates, subject to error, and that the number of points plotted Is relatively small. A least squares approximation for drawing the curves was not f e l t to be justified,, Comparison of the graphs in each of the cases indicates that, except for Pig, 34., the data plots are curved on logarithmic proba-b i l i t y paper and except for Pigs, 45. and 46. are straight lines on *A11 the graphs referred to in this section w i l l be found in Appendix II page 85. 52. the Weibull probability paper., This is, of course, a point in favour of the Weibull distribution. However, ten or even twenty points are relatively few for statistical analysis and the fi n a l choice must be delayed until other comparisons are made. One disadvantage of the Lognormal distribution is that i t is a single distribution which a population of data either f i t s or does not f i t . There is no way to account for data that is slightly differently distributed and, in fact ? there is no way to estimate meaningfully how much difference there i s . On the other hand, the Weibull function is a family of distribution functions, and goodness of f i t is never really a problem. Rather i t is a case of finding the particular distribution which best f i t s the data. This is done very simply by a graphical determination. In addition, the Weibull distributions makes possible the estimation of a minimum l i f e , the determination of confidence limits and enables comparisons to be made between different data populations. The above points indicate that the Weibull distribution offer a number of advantages over the Lognormal distribution for analysing fatigue data, hence i t w i l l be used exclusively throughout the rest of the analysis. Before presenting more results i t is relevant to point out one of the limitations of any statistical analysis. Whenever a small set of data is used there is always a chance that the data wil l not follow the exact distribution. In other words, though the experimental data wil l approximate the exact distribution most of the 53c time, there are always going to be cases where an abnormal number of specimens will f a i l at the high and the low end, and s t i l l others where the specimens w i l l a l l f a l l towards the center of the distribu-tion. The only way that this type of error can be eliminated is to have very large amounts of data. For the rather small amount of data that is available from this investigation, there is a good chance that at least one of the sets wil l contain an erroneous grouping. 54, 2. DISTRIBUTION CURVES* A l l the data have been plotted on Weibull probability paper and are found in Pigs, 40, to 52, They are grouped according to stress level and polishing method, and each figure oontains a curve of the o i l coated and not=oil coated specimens. Since there is very l i t t l e scatter in the.test results for Smax of 64 ksi and 54 ksi, no attempt was made to find the l i f e distribution except for the mechanically and chemically polished group which is shown in Pig, 40, The other groups were assumed to have similar distributions. Pig. 46, illustrates results for the mechanically and chemically polished set for an Smax of 42 ksi. The oiled group contains points near the short l i f e end which at f i r s t seem to be erroneous. These results have been deliberately retained because i t was f e l t that they were necessary for drawing of the correct straight line. No attempt was made to pass the curve through them. Both Pigs. 45. and 46, show evidence of a minimum l i f e (lo). Since none of the other graphs show this, and since? there is no apparent reason for only these groups to have minimum lives, i t is probable that there is an error in the data grouping. The curves for Smax of 38 ksi, Pigs, 47, to 50, show a bt=> modal distribution between short and long lives, which is indicative of a transition in the failure mechanism. That the distribution is *A11 graphs referred to in this section w i l l be found in Appendix II page 85, 55. indeed bimodal is shown rather conclusively in Figs. 51. and 52. Because of the very long lives involved for the specimens failing by the F mechanism, there is not much data for this group and the curves ,Figs, 48. and 50., are subject to a good deal of revision. Nevertheless they do seem to plot as straight lines and are useful in indicating trends. Figs, 49. and 50. are examples of groups in which an abnormal number of specimens have failed at the ends of the distributions and not many near the center. As a partial correction the data was plotted assuming a larger data group with the mid-value data missing. This has the effect of straightening the curve again. Possibly more data would justify this decision. On the whole the curves show a consistent trend towards wider distributions i.e. smaller slope parameters b, as the stress i s decreased. Also of interest is that at higher stress levels the distributions become skewed to the left rather than to the right as would be expected i f the data was Lognormally distributed. 56. 3. EFFECT OF OIL COATING The effect of the o i l coating on the fatigue l i f e is evident from the curves of Figs, 40. to 50., both in the change in slope and the increase in mean l i f e (if). Quantitatively the increase in mean l i f e of the oiled specimens over the not-oiled ones goes from 20% for the unpolished group at Smax of 42 ksi and 47.5 ksi, up to 62$ for the mechanically and ohemically polished group tested at Smax of 42 ksi. The slope of the curves for the not-oiled specimens i s , in a l l but one case, higher than the oiled specimens. This regularity suggests that the o i l coating has a definite effect upon the failure mechanism. Fig. 55. is an S-logN curve of a l l the groups tested and shows the difference between the oiled and not-oiled specimens. Note that while the largest apparent difference occurs at high stress levels the largest numerical difference is at the low. stress levels, where the curves become parallel to the l i f e axis. For instance at an Smax of 38 ksi the l i f e of not~oiled, not-polished group is 290,000 cycles while for the oiled mechanically and chemically polished group i t is 2,200,000 cycles, almost on order of magnitude larger. 57. 4. EFFECT OF POLISHING- METHOD Though the tests at 38 ksi are not complete, especially for the chemically polished group, a few interesting trends are apparent from the S-logN curves Figs. 53. and 54. Both for the oiled and not-oiled groups the results are the same in that the unpolished specimens display lower lives than do either the chemically polished or the mechanically and chemically polished specimens. It is also apparent that the unpolished specimens display a much sharper knee, indicating a more abrupt transition from the F to the H mechanism. For both oiled and not-oiled specimens both the groups that have had a chemical polish .are ;numerically close together and exhibit the same curve shapes. This trend indicates that the chemical polishing has a more dominant effect than does any mechanical polishing. More tests need to be done at low stress levels in order to verify the present results and to see what limiting stress the curves approach. More tests are also needed in the transition region, especially between Smax of 38 ksi and 42 ksi. Otherwise the curves coincide well with previous published results for sheet specimens of 24S-T3 (34), which i s the previous designation for 2024-T3 alloy. In view of the fact that the published curves are based upon rela-tively few tests no detailed comparisons are justified. OBSERVATIONS OF FRACTURE MECHANISM 58. i One of the most pressing problems, especially for smooth surface specimens, is to resolve whether the majority of the fatigue l i f e is taken up in initiating a crack, or in propagating i t across the section. Wood's view is that while small cracks form early in the l i f e , they are essentially non-propagating, and most of the l i f e is spent nucleating the cracks. When enough are formed that they coalesce to form a macrocrack, finajl failure follows soon after. The present observations tend to confirm this view, 1, MACROSCOPIC OBSERVATIONS One of the f i r s t observations made was that the fi n a l failure was always quite violent, almost like an explosion. The mere violence of the fracture seemed to indicate a rapid phenomena, and when no success was obtained in finding surface cracks at later stages in the fatigue l i f e , i t was assumed that the specimens were fracturing immediately, or soon after, the f i r s t large fatigue crack was formed. The f i r s t visual observations of a crack forming and propagating across the structure were made on mechanical and chemical polished specimens tested at Smax of 47.5 ksi. These f i r s t observations resulted in an important discovery. It was that while the sequence of crack formation and fin a l failure occupied a very small percent of the specimen l i f e (less than 1000 cycles), there was nevertheless a definite period between the formation of the f i r s t small crack and its transition into a typical unstable ductile crack. The stable period of the fatigue crack was, in fact, long enough so as to allow 59. the machine to be stopped, before the fin a l fracture occurred. The sequence of events leading to the fin a l failure con=» sisted of the formation of a small crack, in nearly a l l cases near the edge of the specimen, followed after some time by an unstable ductile crack whloh rapidly propagated across the remaining section. The only large scale deformation associated with the i n i t i a l crack was a slight crater like depression which formed at the surface and which provided the f i r s t visible means of detection. The two types of crack are readily identified on a frac-tured specimen, Fig. 25. is a sketch of a fractured section. Most of the fracture (Section A) is extremely rough at a 45 degree angle to the applied stress direction and is typical of a ductile fracture. This section corresponds to the unstable f i n a l crack. What has been designated as the fatigue crack corresponds to the shorter portion (Section B). This part of the fracture surface is not, in general, at 45 degrees to the applied stress direction but instead is very nearly perpendicular to the specimens face. Later observations showed that the dependence of the mieleation mechanism upon the resolved shear stress was not violated. Aa i t turned out, the crystal orientations play a major part In determining the direction of the In i t i a l fatigue crack. 60 Front view Back view Fig, 25. Sketch of typical fracture surfaces., (A) Ductile crack portion ( B ) Fatigue crack portion On the whole the fracture surface left by the fatigue crack portion was quite smooth and shiny compared to that left by the ductile crack. It also resulted, as mentioned, in very few associated surface markings. This indicated that there was no appreciable plastic deformation due to the fatigue crack, for i f there had been, coarse slip markings would be evident. On the other hand the ductile part of the crack caused a profusion of coarse slip markings starting from the end of the fatigue crack and growing in a wave in the direction of crack growth. Comparison with tensile specimens showed these slip markings to be identical to those formed by unidirectional deformation. There are possibly two reasons why the slip markings should appear in this way. First of a l l , as the crack propagates across the section, the area of unfailed material is continually reduced, and the stress is increased proportionally. Secondly, as the crack becomes larger and longer, the stress concentration at its tip, increases. Very likely, the combination of these two relatively high stresses is sufficient to load the metal at the tip of the crack above its macroscopic yield strength, and cause large amounts of ductile s l i p . As the crack becomes longer the volume of plastically deformed metal grows, thereby giving rise to the wave of deformation markings. Fortunately, the fact that this wave of slip markings did exist, made i t a simple matter to pinpoint the place where the f i r s t small crack appeared, and to trace the failure sequence in specimens that were not visually observed to fracture. Doing this showed, with= out a doubt, that the sequence of events was the same for a l l the stress levels, and that, as expected, the length of the i n i t i a l fatigue crack became longer at lower stress levels. Though most of the cracks started at one of the edges a very small percentage started in the middle and grew simultaneously towards the edges. Other specimens showed how, occasionally, more than one crack could form and grow. Fig. 26. is a good example where two cracks have propagated simultaneously. In most cases, i f more than one crack nucleated, they did so almost simultaneously. 62, M i c r o s c o p i c examination hardly ever showed any very small independent cracks forming a f t e r i n i t i a t i o n of the dominant crack. P i g , 26, Specimen i n which two cracks have propagated simultaneously In a number of specimens which f a i l e d a t Smax of 47,5 k s i , the high s t r e s s c o n c e n t r a t i o n which produced the p r e v i o u s l y d e s c r i b e d coarse s l i p markings a l s o caused short c a v i t i e s and cracks t o open w i t h i n the d i s t o r t e d area. P i g . 27a„ i s an example of one such crack. They were g e n e r a l l y very r e g u l a r i n shape, q u i t e short and with branched ends as shown i n P i g . 27b, There i s no evidence to determine whether they were small microcracks which had formed independently of the main crack, or whether they were formed e n t i r e l y by the r a p i d high s t r e s s a p p l i c a t i o n r e s u l t i n g from f a i l u r e . I t i s I n t e r e s t i n g though, that Wood noticed s m a l l non-propagating c r a c k s forming throughout the 63. stressed dross section. I f this type of formation is characteristic of fatigue then i t would be easy to explain the above mentioned crack formation. (b) Fig. 27. (a) Crack formed in region of coarse slip close; to fracture surfaoe (b) End of crack similar to one in (a). 120x 65. 2. MICROSCOPIC OBSERVATIONS Pigs. 28ao and 29= are photomicrographs of a fatigue crack which has not yet reached an unstable length and has not grown through to the opposite side of the specimen. Observations of similar cracks show that this is the typical form of such a crack. The crack is a great deal more jagged and rough than Is expected from a macro-scopic examination, especially in the amounts of dense fine slip. The slip markings are the fine black markings which at f i r s t appear to be fine cracks. Closer observation, however, shows them to be mostly surface markings and further confirmation that they are indeed slip markings is given in Pig. 28b. This is the same crack as in Pig. 28a. and 29« after a deep etch. Here two things are apparent. Pirst the fact that there are no longer any radial markings apparent, and secondly the correspondence between the orientation of the markings as seen in Pigo 29» and the grain structure. Near the edge, the markings are at about 45 degrees to the specimen axis (A), a bit further in, they abruptly ohange to about 30 degrees (B) and ( c ) , then they change back to 45 degrees again (D). These observa-tions leave no doubt that the markings are indeed slip lines that have appeared on the surface. The effect these slip lines have upon the direction of the crack growth is quite apparent. In Pig. 2 9 . where the slip markings are inclined at a small angle to the normal to the stress direction, the craok follows them as much as possible. When, however, the slip Fig, 28* (a) Crack which has not yet grown thorugh to th* other side of the specimen (b) Same oraok a f t e r deep etoh.app. 5 min* Ful l e r s etoh. 140x Pig. 29. Portions of crack shown in Pig. 28. (a), (b), & (c) are marked in Pig. 28(a). not etched. 700x reduced l/2 for reproduction 68. Fig. 30. Examples of slip lines forming ahead of large fatigue crack. 700x 69. (b) Pig. 31. (a) Slip markings forming ahead of fatigue crack, Also shows what appear to be pores forming along slip markings, (b) Effect of precipitate particle on direction of crack propagation, 700x 70. (b) Fig. 3 2 . (a) Part of crack in Fig. 28(a) showing how large fatigue crack follows intersection of multiple slip lines. (b) Region where crack intersects edge. Notice how crack jumps perpendicular to slip markings. 700x 71. ( b ) P i g . 33. (a) Crack that was forming just at time final fracture occurred. (b) After light etch approximately 30 sec. Fullers etch. Notice back of slip markings near tip. 120x 72. direction is steeply inclined, the orach: compromises between following the slip line and following the direotion of maximum normal stress. For instance, where the slip markings are at 45 degrees, the crack follows the slip direction for a while then i t jumps perpendicularly to the next slip band and follows i t for a while. Where there is multiple slip in a single grain, the oraok follows the intersection of the two slip systems. That the slip markings form before the crack is shown in Fig. 29a. 30, and 31a, In Fig, 29a, slip markings are forming on two different systems ahead of the main crack tip, and the crack is attempting to follow both branches. The lower slip markings are in a different grain and i t is possible that the crack finds i t easier to change direotion rather than cross a grain boundary. The precipitate particles which are in evidence everywhere on the surface seem to have a large effeot upon the growth of the crack. Fig. 31b„ is a good illustration of how one such particle has altered the growth. Note the slip markings which are not apparent anywhere but at the particle. These would indicate that the crack has been held up and has had to wait for slip bands to form ahead. It also seems to indicate that the slip bands are associated with the cyclic stress rather than unidirectional stress and need time to form. The precipitate particles near the forked crack tip in Fig. 29a, have Obviously influenced the progress of the lower branch and could be a partial reason for the crack changing direction. 73. In a few of the specimens which had completely fractured secondary cracks were observed away from the fracture surface. Pig. 33a, shows one such crack and Pig, 33b. the same crack after a light etch. In neither of these pictures is there much indication of associated slip, despite the fact that the shape of the crack is quite similar to the ones previously discussed. It could be that a small crack was just forming when the main crack became unstable and that the resulting rapid release of energy, caused this crack to propagate. This could also account for the relatively straight portion near the tip of the crack as well as the absence of slip markings, providing that the slip markings in the other photographs were caused by the cyclic stress and not exclusively by stress con-centration around the crack. VII DISCUSSION 7 4 o 1 . EFFECT OF OIL COATING The observations that the o i l coating increases the mean fatigue l i f e , that i t results in increased scatter in the distribution curves and that the difference in mean l i f e between oiled and not-oiled specimens Increases with decreased stress level, a l l add to the evidence of an oxidation mechanism,. The reasons for this con-clusion are as follows. First of a l l i t must be assumed that regardless of any other effect, the o i l w i l l allow less surface oxidation than i f the surface was exposed. Secondly, i t is f a i r l y obvious that i f an oxidation mechanism is operating due to the fluctuating stresses, then the effect upon the metal will be time dependent and w i l l be more evident for long lives than for short lives,, Under these circumstances we would expect that, at any particular stress level, the longest lived specimens would show the greatest difference^ Short lived specimens where more basic flaws are causing failure, would not exhibit much change. It would also be expected that the effect of the o i l would become more pronounced as the stress is decreased and the lives increase^ The fact that the present results follow the expected pattern confirms the existence of an oxidation mechanism* Though no microscopic observations have been made, i t is worthwhile to mention a fact concerning the oxidation mechanism. Aluminum, as is well known, when exposed to air rapidly forms a coherent non-reactive oxide film which in most cases prevents any 75, corrosion of the base metal. Somehow then, the stress cycling must be exposing unoxidized metal to the air and this action must in turn cause a speed up in the nucleation and growth of the fatigue crack. While the mechanics of this mechanism is unknown, the fact that oxidation has an effect for fluctuating tension rules out the oxidation mechanism proposed by Fujita or in fact any mechanism which requires a period of compressive stress. It is apparent that a more basic mechanism, which can operate during every type of stress cycle is needed. 7 6 , 2. EFFECT OF POLISHING METHOD Regardless of the previous treatment, both the groups which received a f i n a l chemical p o l i s h show very s i m i l a r S-logN curves, i n d i c a t i n g that the chemical p o l i s h i n g a c t i o n overrides the e f f e c t of the other p o l i s h i n g methods. The most probable reason f o r t h i s i s that the chemical p o l i s h i n g smooths and blunts deep scratches which a mechanical p o l i s h cannot reach. This a c t i o n combined with a better p o l i s h i n g of the edges i s enough ..to eliminate p o t e n t i a l s t r e s s r a i s e r s and cause an appreciable increase i n fatigue l i f e . In so f a r as the increase i n l i f e r e s u l t i n g from the mechanical p o l i s h i s concerned, i t i s suggested that, i n a d d i t i o n to the smoothing e f f e c t , the abrading a c t i o n work hardens a t h i n layer of metal on the surface which i s not removed by the chemical p o l i s h i n g . This work hardened layer then acts as a d i s l o c a t i o n b a r r i e r , much l i k e a t h i c k oxide f i l m , and i n h i b i t s the"formation of la t e n t f a t i g u e cracks. 7 7 , 3. THE BIMODAL DISTRIBUTION IN TRANSITION REGION It has been observed that the S-logN curves do not show a sharp knee, but rather go through a period in which both H and F mechanisms operate While this behaviour confirms the existence of the different mechanisms, since there would not be a bimodal distribu-tion i f there were not two mechanisms, more careful consideration indicates that Wood's theory is no-f; entirely compatible with the results of the present work. At this polnt 9 i t is Important to recall that Wood's original conclusions were based upon the results of unworked, poly-crystalline materials, strain cycled in fully reversed torsion. Under these conditions he found that the change from the H to the F region corresponded to a change in the mode of deformation from rather coarse distorting slip to fine slip which left the crystal structure unchanged. More important and relative to the present work, he also found that repeated applications of small unidirectional strains, (essentially this is the same as fluctuating tension), had a cumulative effect and in time produced coarse slip and crystal distortion identical to that observed in the H region. In other words for a fluctuating tension stress there should be no region characterized by fine slip like Wood's P region, yet this investigation has shown without doubt that a different mechanism is operative for long lives. Once again, we can only speculate upon this phenomena, and wait until more metall©graphic observations are made before any 78. definite conclusions are reached. The f i r s t idea that comes to mind is that the rapid change of slope of the S-logN curve may correspond to a change in the failure mechanism from a nucleation and propagation of flaws by plastic strains to one in which failure occurs by propagation of existing flaws by fluctuating elastic strains. Furthermore, the stress at which the S-logN curve changes from the F to the H region, would now correspond to the lowest stress at which dislocation motion could occur. The fact that this stress, for the present results at least, is so far below the observed macroscopic yield point, would be due to the distorted crystal structure of the 2024-T3 alloy which permits isolated disloca-tions to move under a relatively low applied stress. The occurrence of both types of failures in the transition region would now be a result of the imperfect nature of the material such that the crystal structures of some specimens will be unfavourably oriented for dis-location motion, whereas for others the converse would be true. 79. 4. FATIGUE GRACK INITIATION AND PROPAGATION It has been observed, that for the relatively high applied stresses, a small stable crack forms quite late in the fatigue l i f e of the material, that this crack forms, most of the time, at the edge of the specimen and near the surf ace and that; this formation is accompanied by a slight depression in the surface. It was also noticed that the crack propagates under the action of repeated stresses and along surface slip markings, which form ahead of the tip of the crack. A l l these observations point to a nucleation and a growth mechanism (for they could very well be the same) which requires easy dislocation motion and i t is apparent that the easier the motion the more rapid will be the fi n a l failure. The Beeming dependence upon a free surface is simply beeause at the surface there is less constraint than there is in the interior of the metal, and dislocation motion is easier. At the edges where there are surfaces on three sides, the surface area per unit volume is largest and i t is natural for cracks to initiate there. It could be that the crack once i t has formed, grows simultaneously perpendicular to the surface and across the specimen and that soon after i t has grown across the entire thickness i t changes into a ductile tensile crack. It is clear that for the cracks photographed there is an appreciable degree of stress concentration, as evidenced by the slip markings forming at the t i p . It is also possible that the process of initiation and propagation is the same, 80. and that once a very small crack forms the stress concentration causes rapid growth. Wood's assertion that the f i n a l fracture occurred by a tear-ing through sufficiently perforated material is not confirmed* Certainly, the ductile portion has no characteristics, sufficiently unusual as to indioate a separate meohantsm. Similarly, there was no indication at least on the surface, of non-propagating cracks or oavities forming far ahead of the main crack. Future observations in the body of the material may prove this to be false, however the observations discussed here show no definite confirmation. The role of oxidation is not clear and had i t not been for the tests with oiled specimens, i t would not have been suspected. Certainly, theories that postulate transport into the body of the material by reversal of dislocation motions are not suitable for fluctuating tension type tests. In general i t may be concluded that a more general mechanism is needed. VIII CONCLUSIONS 81. Axially loaded specimens of 2024-T3 sheet aluminum have been fatigued in fluctuating tension at a stress ratio of „05i» Tests were done for specimens prepared by rounding the edges, chemically polishing the minimum section, and mechanically and chemically polishing the minimum section. The effect of the different polishing methods and of an o i l coating was determined by s t a t i s t i c a l methods. Studies of the fracture surface and of small surface cracks revealed some-thing of the mechanism by which fatigue cracks form and propagate. The specific conclusions which have arisen from the research ares 1. The Weibull distribution function offers more scope than the lognormal distribution function for analysing fatigue data. 2. The polishing method has an appreciable effect upon the fatigue l i f e of the 2024-T3 alloy at a l l stress levels. Specimens which were mechanically polished with fine emery polishing paper, then chemically polished gave the I longest lives. 3. The distribution of fatigue lives is not changed by the polishing method, 4. Coating the metal with a light non-corroding o i l , increases the mean l i f e from 20$ to 62$ and increases the width of the l i f e distribution. These effects are attributed to the fact that the o i l inhibits the effectiveness of any oxidation mechanism by reducing the amount of free oxygen in contact with the surface. 5. The operation of different fatigue mechanisms is confirmed by the occurrence of a bimodal distribution near the endurance limit stress. 6. The fi n a l fracture occurs in three parts? nucleation and growth of a fatigue crack by the fluctuating stresses, followed by rapid propagation of a ductile crack. Most of the fatigue l i f e of the material is spent in nucleating the i n i t i a l fatigue crack. 7. In most cases, the fatigue crack nucleates at the material surface, near one of the edges. 8. The fatigue crack is intercrystalllne. In propagates along the surface and is influenced by slip markings which form ahead of the tip. The only effect which the crystal structure has, is in determining the direction of the slip markings. The only deformation associated with the fatigue crack is the formation of a slight hollow at the metal surface. There are never any coarse slip bands resulting from the fatigue crack. 9. It appears that at the stress levels investigated, the cracks propagate in much the same way as they form. Since nearly a l l failures were in the H region Wood's observations for this region are confirmed for fluctuating tension. APPENDICES 83, APPENDIX I TABULATION OF RESULTS Maximum CYCLES TO FAILURE x 10 Stress Not Chemically Mechanically & Polished Polished Chemically Polished Oiled Not Oiled Oiled Not Oiled Oiled Not Oiled 64 ksi 26 19 28 21 31 19 33 21 31 35 54 ksi 70 46 64 57 52 51 47 92 60 57 51 53 64 87 59 94 61 91 68 47.5 51 57 92 68 112 89 ksi 83 72 95 97 140 92 83 73 107 100 165 102 89 74 159 114 173 107 92 75 162 115 185 110 99 86 187 129 113 117 92 225 135 121 119 92 136 122 124 101 129 136 106 130 139 115 84. Appendix I Tabulation of Results cont. 42 ksi 74 78 70 94 238 144 86 79 150 147 257 165 89 84 152 170 280 173 107 94 157 172 286 191 109 99 247 182 316 247 114 100 288 194 480 249 135 106 298 233 493 316 144 108 394 273 503 373 149 110 413 277 802 163 121 674 187 131 134 1037 38 ksi 126 84 154 209 233 310 374 229 187 210 324 345 500 242 204 266 333 468 526 269 428 308 339 513 613 251 374 377 805 4965 314 1059 1517 12920 339 1473 4555 13871 394 3180 12567 17845 I960 5880 14582 \ 2380+ 4035 13932 11248 21167 2237+ 9985+ 12709+ .15370+ APPENDIX 2 GRAPHS Pigs. 34. to 55. 85. 9 9 . 9 99 95 90 80 m 70 3 60 M « 50 <r< ^ 40 30 2 20 "rl as o 10 5 2 1 0.5 0.1 / / / / / AA Q AA col F ( IA K 1 1 i i A oiled not-oiled / O 10 4 5 6 7 8 9 105 2 3 4 5 6 7 89 ^ cycles to failure - 1ST Pig. 34. Test for Lognormal distribution not-polished Smax = 42ksi 86, 99.99 99.9 99 1± . 5 -4 2 3 4 5 6 7 8 9 10"^  2 3 4 5 6 7 8 9 1 0 cycles to failure-N Pig. 35« Test for Lognormal distribution chemically polished Smax = 42 ksi 87. 99.99 99.9 99 95 <D 90 U rH •H 80 OS <H 70 «H o 60 >» 4* *H 50 rH •H 40 , 0 XI 30 o 20 10 5 2 1 .5 10 / s / / / A / / /> / t i / / A , r f > / \ / \. 1 ' c. / / h A. i 1 A o i l ed O not -oiled 4 5 6 7 8 9 KT 2 cycles to failure"-» N 5 6 7 8 910 Pig. 36. Test for Lognormal distribution mechanically and chemically polished Smax = 42 ksi 88. / / 0 / // j A / / • ( / i u 1 J 1 1 ( T i A oil Led O no1 ;-oiled 10 4 5 6 7 8 910 2 cycles to failure - N 3 4 5 6 7 8 9 10 Pig. 37. Test for Lognormal distribution not-polished Smax = 47.5 ksi 89. 99.99 99.9 99 95 90 80 70 60 50 40 30 20 10 5 2 1 .5 3 a) o -p X> a) o u - -/ / A / o ol ( / r i 1 y /\ oiled O not-oiled / •10 4 5 6 7 8 910 2 cycles to failure = 1 5 6 7 89 10 Pig. 38. Test for Lognormal distribution chemically polished Smax = 47.5 ksi 99.99 99.9 99 2 1 *5 . .11 ; I - I I I I I I I I | 1 I I I I I 1 IO4 2 3 4 5 6 7 8 9 IO5 2 3 4 5 6 7 8 9 10 cycles to failure-K" P i g . 39. Test f o r Lognormal d i s t r i b u t i o n mechanically and chemically polished Smax = 47.5 k s i 91. 98 95 90 80 70 60 o> 50 u n r - l •rt 40 as S 30 25 2 20 § 16 u 14 12 10 8 / { ) / / / ) ) / 1 / / i 1 q / 1 / / / c / / A oi: Led 7 W 8 x 103 b 4,00 . : i • i 3 1 O not-oiled 59x10^ 11.50 1 I i i I i (• 10 4 5 6 7 8 910 2 cycles to failure - N 3 4 5 6 7 89 10 Pig. 40. WeibuIL distribution for fatigue l i f e mechanically and chemically polished Smax s 54 ksi 92 % iH • H a) o jo a) x> o 98 95 90 80 70 60 50 40 30 25 20 18 16 14 12 10 8 / / 0 d 1 1 //•• < / J A - ( / / r c f ) r C u 1 I 1 6 1, 1. 1 / 1 / / f // 1 y 1 / ) J U b ^ oiled 103 xlO5 4.02 O not-oiled 86 x 103 5.15 1 — i 1——1—1—i—u_ 10 4 5 6 7 8 9 1 0 2 oyoles to failure - 1 3 4 5 6 7 8 91 s Pig. 41., Weibull distribution for fatigue l i f e not-polished Smax » 47«5 ksi 93. u t—i •H OS VI «M O X» a! •§ u PM 98 95 90 80 70 60 50 40 30 25 20 18 16 14 12 10 8 10 HT b A oiled 143 x10 3 3.28 O mot-oiled 109 x10 3 5.15 4 5 6 7 8 9 10 cycles to failure 4 5 6 7 8 910 Pig. 42, Weibull distribution for fatigue l i f e chemioally polished Smax = 47.5 ksi 94. "ZT N A oiled 153 x10 4.35 O no-fr-oiled 111 x 103 8.15 J I L 10^  4 5 6 7 8 9 10 2 cycles to failure - B 4 5 6 7 8 910 Pig. 43. Weibull distribution for fatigue l i f e mechanically and chemically polished Smax » 47.5 ksi 95. J, J 1 I •fl V A n 1 / A •6.1 J Ai 9 k u t 1 r L/ 1 i / / // A I . / / U b A oiled 123 xlO 3 3.98 O not-oiled 103 x10 3 5.40 10 4 5 6 7 8 9 KT 2 cycles to failure - N 3 4 5 6 7 8 910 Pig. 44. Weibull distribution for fatigue l i f e not-polished Smax » 42 ksi 96. Fig. 45° Weibull distribution for fatigue l i f e chemically polished Smax =» 42 ksi 97. 10 4 5 6 7 8 9 10 2 cycles to failure-N (AV<0 4 5 6 7 8 910 Pig. 46, Weibull distribution for fatiguelife mechanically and chemically polished Smax = 42 ksi 98. Pig. 47. Weibull distribution for fatigue l i f e not-polished Smax » 38 ksi failure by H mechanism 99. Pig. 48. Weibull distribution for fatigue l i f e not-polished Smax = 38 ksi failure by F mechanism 1 0 0 , 93 95 9 0 8 0 7 0 6 0 5 0 4 0 u 3 0 0 rH -rH aj 2 5 SH <H 2 0 o 1 8 16 +» •H 14 rH -H JQ 1 2 Ql X> 1 0 O rH PH 8 1 0 ' b A oiled 7 0 0 xlO 3 l a 7 3 Based on A s l O 6 , 7 , 8 omittet 3 O not-oiled 6 7 0 x 1 0 ' 1 , 4 8 Based on A = 8 1 , 7 omitted l l 3 4 5 6 7 8 9 1 0 2 cyoles to fail u r e - ! 4 5 6 7 8 9 1 0 Pig. 49= Weibull distribution for fatigue l i f e mechanically and chemically polished Smax = 3 8 ksi Failure by H mechanism 101. Pig. 50. Weibull distribution for fatigue l i f e mechanically and chemically polished Smax = 38 ksi failure by P mechanism 98 95 90 80 70 60 50 40 30 25 20 18 16 14 12 10 8 6 A " A L A ^ A y A A A/ A I 3ased on A a 14 I i. mechanicall y & chemically ! iled, si 1 1 1 — L J E /A polished, o Smax » 38 k — t - i — ^ 1 4 5 6 7 8 9 10 cycles to failure-F Pig, 51° Weibull plot of a l l data 103. 2 3 4 5 6 7 8 9 10 cycles to failure - N Comparison of polishing methods not-oiled specimens o \ I \ >-v • u O — -rt \ J ) <0> mechanically & chemically polished Q chemically polished • not-polished '. I l 1 l l i 1 l 1 I 1 1 __ 2 3 4 5 6 7 89 10 2 3 4 5 6 7 8 9 10 2 3 4 5 6 7 8 9 10 2 3 45 cycles to failure - N Fig. 54. Comparison of polishing methods oiled specimens 1 2 3 4 5 6 7 8 9 10 2 3 4 5 6 7 8 9 10 2 3 4 5 6 cycles to failure - N Fig. 55^  Comparison of oiled & not-oiled specimens 107. APPENDIX 3 STATIC AND DYNAMIC CALIBRATION OF SONNTAG MACHINE Static Calibration The load springs and grip were calibrated simultaneously by means of a lever and scale pan arrangement designed especially for this purpose,, The assembled device is shown in Fig; 56„ For this calibration the grip with strain gages was attached to the lower platen and accurately calibrated ten pound weights were used to load the bar. By virtue of the system geometry, 10 pounds on the scale pan resulted in a load of 100 pounds at the springs and grip 0 The measuring potentiometer on the BA-13 bridge amplifier had 1000 divisions and i t was adjusted by means of a multiplying potentiometer so that one division corresponded to an increment change of one pound at the grip. Once the potentiometer was adjusted, the grip c a l i -bration was complete. The entire strain gage system was found to be linear within the range 0 to 1000 pounds. The spring constant of the load springs was determined by loading the springs up to 1000 pounds and then down t@ 0 again in increments of 100 pounds. After each increment of load, the spring deflection was measured with the attached dial indicator, Fig. 12. A curve of load vs spring deflection was then plotted, Fig. 57. It was found in this way that the springs were entirely linear and that their spring constant was 4.15 pounds/inch, 108, + The load could be measured to ~ 2 pounds with the + strain gages and to about <*> 3 pounds by the dial indicator which measured the spring deflection. The strain gage system, since i t was connected directly to the specimen, could sense extraneous loads resulting from the gripping action and grip misalignment. This proved to be a definite advantage when placing the specimen ln the grips. Dynamic Calibration The threaded eccentric which provided the dynamic load was factory calibrated so that dynamic loads of = 2 pounds could easily be set. There was no way to adjust this calibration. The only thing which could be done was to compare the dynamic load indi-cated by the eccentric with the peak to peak amplitude measured by the strain gage system. This was accomplished by applying a static + load of 500 pounds and then measuring the dynamic load from - 100 pounds up to i 500 pounds in increments of 100 pounds. Unfortunately, the eccentric was so much more accurate than the strain gage system, that l i t t l e was accomplished by this calibration except to confirm approximately, that the eccentric calibration was correct and that the dynamic load was in fact sinusoidal and undistorted. 109. 1000 900 Pig. 57. Load deflection curve from loading spring calibration 111c BIBLIOGRAPHY 1. J.A. Ewing and J.CW, Humfrey, "The Fracture of Metals under Repeated Alternations of Stress", Philosophical Transactions, Royal Society (London), Series A, Volume 200, 1903, pp. 241-250. 2. W. Rosenhain and 0. Ewen, "Intercrystalline Cohesion in Metals", Journal, Institute of Metals, Number 2, 1912, p. 149. 3. H.P. Moore, "Manual of the Endurance of Metals under Repeated Stress", Publication Number 13, Engineering Foundation, New York, N.Y. 1927. 4. H.J. Gough, "Crystalline Structure Relation to Failure of Metals - Especially by Fatigue", Proceedings American Society of Testing Materials, Volume 33, Part III, 1933, pp. 3-114. 5. G.I. Taylor, "Plastic Deformation of Crystals", Proceedings of the Royal Society (London), Series A, Volume 145, 1934, pp. 362-404. 6. W.A. Wood, "Some Basic Studies of Fatigue in Metals", Conference on Fracture, Swampscott, Mass. 1959, p. 142. 7. N.J. Wadsworth and J. Hutchings, "The Effect of Atmospheric Corrosion on Metal Fatigue", Philosophical Magazine 3, 1958, p. 1154. 8. B.P. Haigh and B. Jones "Atmospheric Action in Relation 1to Fatigue in Lead", Journal, Institute of Metals, Volume 43, Number 1, 1930, pp. 271-281. 9. P.G. Forrest, "Fatigue of Metals", Pergamon Press, 1962, p. 178. 10. R.E. George and J.B, Mantle, "The Effeot of Edge Preparation on the Fatigue Life of Flat Plate Specimens", Materials Research and Standards, Volume 2, Number 12, 1962, 11. J.A. Dunsble, "A Preliminary Analysis of the Results of some Comparative Fatigue Tests conducted by Eight Canadian Laboratories", National Aeronautical Establishment, Structures Laboratory, Memorandum, 1963. 12. G,R, Gohn, "Fatigue of Metals, Part 1, The'Mechanism of Fatigue", Materials Research & Standards, 1963, pp. 106-115. 1 1 2 , 1 3 . W.A. Wood, S.McK. Cousland and K,R, Sargent, "Systematic Micr©structural Changes Peculiar to Fatigue Deformation", Acta Metallurgica, 1 9 6 3 , p. 6 4 3 , 1 4 . W.A, Wood, W.H. Reimann and K.R, Sargent, "Comparison of Fatigue Mechanisms in BCC Iron and FCC Metals", American Institute of Metallurgical Engineers, Metallurgical Society Transactions, Volume 2 3 0 , Number 3 , ' 1 9 6 4 , pp« 5 1 1 - 5 1 8 . 1 5 . T.H. Alden and W.A. Backofen, "The Formation of Fatigue Cracks in Aluminum Single Crystals", Acta Metallurgica, Volume 9 , 1 9 6 1 , p. 3 5 2 . 1 6 . No Thompson, N.J. Wadsworth and N 0 Louat, "The Origin of Fatigue Fractures in Copper", Philosophical Magazine 1 , 1 9 5 6 , p. 1 1 3 . 1 7 . L,F, Coffin, "Cyclic Straining - Fatigue", Symposium on Internal Stresses and Fatigue in Metals", General Motors, U.S.A. 1 9 5 8 . 1 8 . P.J.E. Forsyth, "Slip-Band Damage and Extrusion", Proceedings of the Royal Society (London), Series A, Volume 2 4 2 , 1 9 5 7 , p . 1 9 8 . 1 9 . - -A.H. Cottrell and D. Hull, "Extrusion and Intrusion by Cyclic Slip in Copper", Proceedings of the Royal Society (London), Series A, 1 9 5 7 . 2 0 . D. Hull, "Surface Structure of Slip Bands on Copper Fatigued at 2 9 3 ° , 9 0 ° , and 4.2°K", Journal Institute of Metals, 8 6 , 1 9 5 8 , p 0 4 2 5 , 2 1 . N„F. Mott, "A Theory of the Origin of Fatigue Cracks'!, Acta Metallurgica, Volume 6 , 1 9 5 8 , p. 1 9 5 , 2 2 . D,H, Avery and W,A. Backofen, "Nucleation and Growth of Fatigue Cracks", Fracture of Solids, Drucker and Gilman editors, Interscienoe Publishers, 1 9 6 2 , p. 3 3 9 . 2 3 . F.E. Fujita, "Dislocation Theory of the Fatigue Fracture of Ductile Metals", Science Reports, Research Institute of Tohoku University, Series A, Volume 6 9 1 9 5 4 , pp, 5 6 4 = 5 7 2 . 2 4 . F.E, Fujita, "Oxidation and Dislocation Mechanisms in Fatigue Craek Formation", Fracture of Solids, Drucker and Gilman editors,, Interscienoe Publishers 1 9 6 2 , p. 6 5 7 , 2 5 . D.R, Whitney, "Elements of Mathematical Statistics", Henry Holt and Co., 1 9 5 9 , 113. 26. F.E, Croxton and D.J. Cowden, "Applied General Statistics", Prentice Hall, 1952. 27. ASTM Committee E-9, "The Weibull Distribution Function for Fatigue Life", Materials Research and Standards, Volume 2, 1962, p. 405. 28. L.G. Johnson, "What the Test Engineer needs in the Way of Statistics", Industrial Mathematics, Volume 9, 1958. 29. L.G. Johnson, "The Statistical Treatment of Fatigue Experiments", General Motors Research Laboratories, GMR-202, 1959. 30. R.N. Fisher and L.H.C. Tippet, "Limiting Forms of the Frequency Distribution of the Largest or Smallest Member of a Sample", Proceedings Cambridge Philosophical Society, Volume 24, Part 2, 1928, p. 180. 31. "Description and Operating Instructions for Chemical Brightening of Aluminum and its Alloys", Aluminum Co. of Canada Ltd. Report, February 1951. 32. M.G. Kendall and B.B. Smith, "Tables of Random Sampling Numbers", Tracts for Computers, Number xxiv, Cambridge University Press, 1951. 33. w . Weibull, "Fatigue Testing and Analysis of Results", Pergamon Press, 1961. 34. H.J0 Grover, S.M. Bishop,,:and L.R. Johnson, "Axial-Load Fatigue Tests on Sheet Specimens of 24S-T3 and 75S-T6 Aluminum Alloys and of SAE 4130 Steel", NACA TN-2324, 1951. 35. P.J.E. Forsyth, "Fatigue Damage and Crack Growth in Aluminum Alloys", Acta Metallurgica, 1963, p. 703. 36. T.H. Alden, "Fatigue Fracture In Pure Metals", Journal of Metals, Volume 14, Number 11, November 1962, pp. 828-835. 37. P.Ho Armitage, "Statistical Aspects of Fatigue", Metallurgical Reviews, Volume 6, Number 23, 1961, pp.. 353-385. 38. Averbach, Felbeck, Hohn, Thomas, "Fracture", The Proceedings of an International Conference on the Atomic Mechanisms of Fracture held in Swampscott, Mass. MIT Technology Press, 1959, 20 papers. 39. "Mechanisms of Fatigue in Crystalline Solids", Proceedings of an International Conference, Acta Metallurgica, 1962, pp0 643-817o 20 paperso 114. 40. T. Broom and R.K. Ham, "Hardening by Fatigue", Proceedings of the Royal Society (London), Series A, 1959, pp. 186-199. 41. L.J. Demer, "Fatigue Crack Detection Methods", WADC TR 55-86 1 & 2, 1955. 42. L.J. Demer, "A Review of Observations on the Cracking Characteristics and Fractures of Laboratory Fatigue Specimens", WADC TR-55-527, 1955. 43. W.S. Fricke, "Fatigue Gauges of Aluminum Foil", Materials Research and Standards, Volume 2, 1962, pp. 268-269. 44. R.R. Gatts, "Applications of a Cumulative Damage Concept to Fatigue", Transactions of American Society of Mechanical Engineers, 83-D, 1961, pp. 529-540. 45. H.J. Grover, S.A. Gordon and L.R. Jackson, "The Fatigue of Metals and Structures", NAUWEPS 00-25-534, I960. 46. M.R. Hempel, "Slip Bands, Twins and Precipitation in Fatigue", Fracture, Swampscott, Mass. Paper Number 19, 1959, p. 386. 47. A.J. Kennedy, "Processes of Creep and Fatigue in Metals", John Wiley and Sons, New York, N.Y. 1962. 48. A.H. King, "Investigation of Small Cyclic Strains by Etch Pits at Dislocation Sites", Nature, Volume 197, 1963. 49. H.W. Liu, "Fatigue Crack Propagation and Applied Stress Range - An Energy Approach", American Society of Mechanical Engineers, Journal of Basic Engineering, Volume 85, Series D, Number 1, 1963, p. 116. 50. J.R. Low, "Mior©structural Aspects of Fracture", Fracture of Solids, Interscience Publishers, 1963, p. 197. 51. F.A. McClintock, "A Criterion for Minimum Scatter in Fatigue Testing", American Society of Mechanical Engineers, Journal of Applied Mechanics, Volume 22, 1956, pp. 427-429. 52. W.M, Murray, "Fatigue and Fracture of Metals", MIT Technology Press, 1950. 53. "A Discussion on Work Hardening and Fatigue in Metals", N.F, Mott Chairman, Proceedings of the Royal Society (London) 1957, pp. 145-227. 54. P. Paris and F. Erdogan, "A Cri t i c a l Analysis of Crack Propagation Laws", American Society of Mechanical Engineers, Journal of Basic Engineering Volume 85, Series D, Number 4, 1963, pp. 528-534. 55, S.R, Swanson, "An Investigation of the Fatigue of Aluminum Alloy Due to Random Loading", University of Toronto, Institute of Aerophysics, Number 84, 1963. 56. S.R. Valluri, "A Unified Engineering Theory of High Stress Level Fatigue", Journal of Aerospace Science, Volume 20, Number 20, 1961. 57. N.J. Wadsworth, "Work Hardening of Copper Crystals Under Cyclic Straining", Acta Metallurgica, Volume 11, 1963, p. 663. 58. T. Yakobori, "Unified Engineering Theory of Metal Fatigue", The Technology Reports of Tohoku University, Volume xxvii, Number 2, 1962, 

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