High Cycle Fatigue: A Mechanics of Materials Perspective part 50 potx

476 Appendix A 3 failures of ropes used in working inclines, 4 failures of bridges, 262 broken rails, 12 cases of flooding of permanent way, 10 slips in cuttings or embankments, and 8 fires in trains. These results indicate that 15.1% of the accidents were due to axle failures. This is consistent with the results quoted by Lardner [5], who indicated that 18% of the accidents were due to axle failures at a much earlier date. Stretton [9] compiled the total number of axles of all descriptions which broke when running during 1878 through 1885. These results are given in Table A.2. He also summarized data for 1883 on the total number of axles in use, the number of axles broken when running, and the number taken out in shops as flawed. These results are reproduced in Table A.3. Wilson [10] compiled the causes of accidents on British railroads for the period of 1872 through 1875. He indicated that there were 162, 133, 229 and 478 axles failures during 1872, 1873, 1874 and 1875, respectively. FATIGUE OF RAILROAD AXLES Apparently, the earliest documented research on fatigue of materials was conducted by Albert [21], who performed repetitive tension tests on hoist chains in the mines in the Harz mountains as early as 1828. Poncelet [22] first used the term fatigue in his book Table A.2. Axles broken in eight years, 1878–1885 [9] Year Engine axles Tender axles Carriage axles Wagon axles Salt van axles Total Crank or driving Leading or trailing 1878 266 21 19 3 221 10 540 1879 248 24 23 3 190 8 496 1880 251 27 25 1 192 18 514 1881 262 21 37 3 200 17 540 1882 242 22 32 2 140 13 451 1883 247 28 21 2 141 11 450 1884 200 23 24 6 113 19 385 1885 190 31 17 4 130 5 377 Table A.3. Engine axles broken or defective, 1883 [9] Number in use Broken in running with passenger trains Broken in running with goods trains Taken out in shops flawed Crank axles 12 943 70 108 680 Straight axles 1 905 10 19 24 14 848 80 127 704 Appendix A 477 in 1839. According to Smith [23], “The spectacular growth of the railroads in the 1830s was accompanied by an equally spectacular growth in the number of failures of wrought- iron axles, and the failure of some of the iron bridges that were being built in large numbers.” As a result, considerable research and discussion took place in the engineering communities on axle failures. According to Haigh [24], Mechanical fatigue was first recognized as a mode of fracture differing from that produced by loads acting steadily, in the course of an investigation from 1840 to 1842, carried out by the engineers of the London and Birmingham Railway. Crankshafts, of tough irons that showed high ductility in bending tests, were found to fail in service by the gradual development of a crack in a brittle manner, without any considerable preliminary local distortion. The immediate difficulty was overcome by limitation of piston speed; and, as a precaution, axles were periodically examined for cracks in the early stages of development. Observations of axle failure processes Apparently, the first published observations of axle failure processes were due to Arnoux in France [25]. Edwards [25] described Arnoux’s observations as follows: The fracture commences at the lower angle of the axle on the side of the traction, which is evidently in fixed axles the point of greatest fatigue, and in those axles which have given way under the weight of the load, the fissure has in some instances nearly traversed the axle before it broke entirely, and it is then easy to trace the accident from its engine. I will endeavour to describe its usual appearance by the following diagram (Figure A.1a); the arrow shows the direction in which the carriage moves. The fracture invariably originates at the angle a, and appears to progress at intervals by zones as shown by the lines in the diagrams, the first, at the point a becoming perfectly black, the colour of each being lighter as they (b) (a) a b Figure A.1. Arnoux observations of axle failures; (a) Edwards; (b) Morin. 478 Appendix A gradually extend form this point, and as the contact of the two sides of the fracture becomes more intimate, the grain of the iron towards the angle a is coarse, and has a large crystalline texture, which diminishes in size as the fracture approaches the angle b, at which point the metal remains slightly fibrous, having evidently undergone a more rapid deterioration at its point of greatest strain. A similar description of Arnoux’s observations was given by Morin [26], as can been seen by comparing Figures A.1a and 1b. At about the same time, Rankine [27] ∗ showed that a gradual deterioration takes place in axles. He presented drawing of five specimens, representing the exact appearance of the metal at the point of fracture, which in each case occurred at the re-entering angle, where the journal joined the body. The fractures appear to have commenced with a smooth, regularly-formed, minute fissure, extending all round the neck of the journal, and penetrating on an average to a depth of half an inch. They would appear to have gradually penetrated from the surface towards the centre, in such a manner that the broken end of the journal was convex, and necessarily the body of the axle was concave, until the thickness of sound iron in the centre became insufficient to support the shocks to which it was exposed. In all the specimens the iron remained fibrous; proving that no material change had taken place in its structure.” Rankine published the figures in a discussion of a paper by Kirkaldy [28]. Glynn [29], who personally experienced two axle failure incidents in 1843, presented similar observations on the fracture of tender axles. He stated that Both the fractures presented the same appearance (Figure A.2); for about 1/2 inch in depth all round, there was a perfectly smooth cleft of a blue and purple colour; this annular cleaving appeared to have been produced by a constant process; the central crystallized part being gradually reduces in diameter, until it was barely able to sustain the weight, and it broke on being exposed to a sudden strain.  It is observed, that the fracture commences at the end of the key groove, which is about 1/4 inch from the shoulder, against which the wheel is fixed. The author is of opinion, that the breaking action commences with the first journey of the tender, and that the axles continually receive such injury as they would, if they were laid over the edge of an anvil at A, and received a constant succession of smart blows from a hammer upon the point B, the axle being constantly turned round. McConnell [30] made similar observations in 1849 and stated that “a gradual breaking up of the fibre at the back of the wheel goes on, which is shown by an annular space, varying from 3/8 to 3/4 inch in breadth; the strength is completely destroyed of this ∗ During the early 19 th century, engineers did not publish their research results, but presented them at various society meetings. Reporters that were present at the meetings documented the presentations and discussions in various publications. As a result, the research work was described in many publications. Appendix A 479 A B Figure A.2. Fracture of railway carriage axle. portion, and a sudden shock of the wheel upon some point of the road competes the fracture of the axle.” Stopfl [31] made a significant, but little noticed, contribution to the understanding of the fatigue of railroad axles. He indicated that 18 locomotive axles failed in one year on the north Austrian railroad and, as a result, the Austrian government initiated a test program to investigate and find ways to prevent such failures. These tests were performed to explore factors influencing the axle failure process. He did not accept the prevalent explanation of the failure process based on the then prevalent crystallization theory of fatigue. He tested specimens with different geometries and showed that the appearance of the fracture surface is a function of the way the axles are loaded, disproving the crystallization theory of fatigue. He stated that abrupt shape changes affected the failure process. Moreover, he observed that failed axles had developed either circumferential or part through cracks, which showed evidence of a color change (rusting) on the fracture surfaces. Based on these observations, he concluded that the cracks developed gradually during service, prior to the final failure. Marcoux [26] noticed that axles, made with good quality iron, broke because small cracks that are difficult to recognize are formed at the axle shoulders. If these cracks (which are shallow when first formed) remain unobserved, the axles break at that location when they penetrate 10–15 mm in the axle. He thought that these cracks are caused by vibration of the axles, and that effect is produced in an analogous manner to what happens when one breaks a wire while bending it several times in different directions. Figure A.3 Figure A.3. Marcoux observations on crack growth in axles. 480 Appendix A reproduces his sketch indicating the gradual growth of cracks observed on axles on mail coaches. Finally, in a continuation of a discussion on axles, McConnell [32] indicated that The axle  broke in ordinary working close at the back of the wheel as is usually found, and the fractured ends afford the most distinct proof of the annular space, which was  observable all round the surface of the fracture; and this is not only short grained and crystalline, but there is also  evident distinct separation to the extent of the annular space which it would appear takes place some time before the final fracture, as if each successive blow, heavy or light, lateral or vertical, received or transmitted through the wheels, had each tended to destroy its proportion of cohesion of the previously crystallized substance of the axle at that particular place where the fracture occurs. McConnell tested the center section of the axle and found that it was not damaged. Consequences of axle failure observations The aforementioned observations on axle failures during service had a number of impor- tant consequences. First of all, they led to an engineering solution to the axle failure problem. This was done by Rankine [27] and, independently, by Stopfl [31]. Rankine [27] “proposed, in manufacturing axles, to form the journals with a large curve in the shoulder, before going to the lathe, so that the fibres shall be continuous throughout,  Several axles having one end manufactured in this manner, and the other by the ordinary method, were broken; the former resisted from five to eight blows of a hammer, while the latter were invariably broken by one blow.” This extract from the paper indicates that Rankine correctly realized the importance of the stress concentration at a re-entrant corner and presented an engineering solution for improving the performance of railroad axles. Simi- larly, Stopfl [31] recommended the use of gradual thickness transitions and made specific recommendations for the manufacturing of railroad axles. Another engineering consequence of the observed failures of railroad axles was the practice to limit the service life of axles on passenger carriages. Arnoux [25, 26] indicated that it was the practice not to touch axles before they saw 60,000 to 70,000 kilometers of service. Marcoux [26] recommended the axles be “renewed” after having provided 60,000 kilometers of service. In a sense, the endurance limit for the service loading on the axles was 60,000 kilometers. At the end of this service life, the axles were either replaced or repaired. If repaired, their service life was further limited. Moreover, the French government appointed a commission to investigate means of avoiding railroad accidents [33] as a result of the Versailles to Paris railroad accident. The report of the commission [34, 35] recommended monitoring the usage of axles to establish their useful life, before being reworked and/or replaced. Appendix A 481 Finally, Haigh [36] stated in 1925 And it is interesting to note that several of the conclusions reached before 1842 are still of practical value in comparable circumstances. It was found that the safe mileage decreased rapidly with speed; and that piston speed afforded a serviceable basis of comparison for different designs and different metals. A piston speed of 1,000 feet per minute soon came to have a recognized significance as a standard for the purpose. Periodic inspection was instituted at this same period, with the result that fatigue cracks were often detected before they extended far enough to cause breakdown. Beginning of systematic fatigue testing of axles The French commission report [8, 34, 35] described an apparatus for submitting axles of locomotives and cars to all the movements and resis- tances, to which they may be exposed in use. By this method, we shall evidently arrive at the same results as by observations of axles which have seen much service. This apparatus being kept in constant operation, enables us to arrive more speedily at an estimate of the course of crystallization, taking into account, at the same time, the changes occasioned in the nature of iron by variations of temperature. According to With [8], “The Austrian government has had the same idea, and it has the merit of having put in operation some time since, in consequence of the almost daily breaking of axles, upon the State railroad, after having been kept in perfectly good order for five years.” With [8] presented results of experiments that were published in Journal des Chemins de Fer. The experimental apparatus consisted of a bent axle, which was firmly fixed up to the elbow in timber, and which was subjected to torsion by means of a cog-wheel connected with the end of the horizontal part. At each turn the angle of torsion was 24  . A shock was produced each time that the bar left one tooth to be raised by the next. An index adapted to the apparatus indicated the number of revolutions and shocks. The test results and observations are summarized in Table A.4. These results are also presented by Wood [37], who indicated that the experiments were performed in France. Engerth [38], von Burg [39] and Schrötter [40] indicated that Kohn performed the first controlled tests to find the effect of alternating torsion on wrought iron, the crank-shaped samples being subsequently broken in a hydraulic press, after as many as 128,309,000 reversed torsion cycles. Schrötter, analyzing Kohn’s results, concluded that repeated torsion can change the fracture of a bar from fibrous to crystalline and then lamel- lae. It should be noted that the Kohn data is identical with the results presented by With [8]. Hence, the question remains whether the results given by With are actually those of Kohn. 482 Appendix A Table A.4. Experiments and observations on axles (With [8]) No. of Torsions Observations 32400 No failure and no change in texture upon being fractured in hydraulic press 129000 Broken after the test. “No alteration of the iron could be discovered, by the naked eye, on the surface of rupture; but tried with a microscope, the fibres appeared without adhesion, like a bundle of needles.” 388000 Broken in two. “A change in its texture, and an increased size in the grain of the iron, was observed by the naked eye. 3888000 “ the axle was broken in many places; a considerable change in its texture was apparent, which was more striking towards the centre; the size of the grains diminished towards the extremities.” 23328000 “ completely changed in its texture; the fracture in the middle was crystalline, but not very scaly.” 78732000 “ fracture, produced by an hydraulic press, showed clearly an absolute transformation of the structure of the iron: the surface of rupture was scaly like pewter.” 128304000 “ presented a surface of rupture like that in the preceding experiment. The crystals were perfectly well defined, the iron lost every appearance of wrought iron.” Discussions of the causes of fatigue failures The fatigue failures were characterized by an apparent change from fibrous to crystalline structure of the wrought iron. This failure mode classification seems to have been intro- duced in 1724 by Réaumur [23] and in the early 1820’s by Tredgold [41]. We now know that the crystalline appearance of the failure surfaces was actually evidence of brittle fracture, but this was contrary to the knowledge available to the then practicing engineers. The prevalent explanation of the failures was that the wrought iron crystallized as a result of the repetitive loading and various explanations were sought for the phenomenon [42, 43]. Vignoles [43] stated that François and Aubert attributed fractures of broken axles to the magnetic or electric changes in the molecular structure of iron, caused by friction on the bearings and great velocities. Moreover, Vignoles believed that it was probable that the continual strains and percussions to which the cranked axle is subjected will account for the changes in the molecular constitution of the iron. Nasmyth [44] was of the opinion that the alternate strains in opposite directions, which the axles were exposed to, rendered the iron brittle, from the sliding of the particles over each other. York [45] attributed fracture in railway axles to the sudden strains and injury produced by concussions and vibration. In a discussion on the strength of railway axles, McConnell [30] expressed the opinion that the iron in the axles crystallized during usage. R. Stephenson [Ref. [30], p. 22] disagreed with McConnell and mentioned cases of “vibration going on from year to year without any sensible change occurring in wrought or cast-iron.” Finally, Slate [Ref. [30], p. 26] stated that he “did not think that any change from a fibrous to a crystalline texture was produced in iron unless it were strained beyond the limit of its elasticity.” He further stated that Appendix A 483 he had made a machine in which he put an inch square bar subjected to a constant strain of 5 tons, and an additional varying strain of 2 1/2 tons, alternately raised and lowered by an eccentric 80 or 90 times per minute, and this motion was continued for so long a time that he considered it equal to the effect of 90 years’ railway working, but no change whatever was perceptible; and therefor he was one of those who did not believe in a change from a fibrous to a crystalline structure in iron. McConnell [32] also presented some instances of tough fibrous wrought-iron being rendered brittle and breaking off quite square with a close-grained fracture from the effect of the concussion of very small blows rapidly repeated for a long period; the blows being very small in force compared to the strength of the iron. These specimens are from the machines for making shanks  The hammer in these machines is about 2 1/2 lb. weight, and is lifted by a rod 3/8 inch square, which has a pull upon it of about 12 lbs. from the difference of leverage; the hammer strikes 120 blows per minute, The lifting rods always break with a close-grained short fracture, although made of the toughest and most fibrous iron that can be obtained, and they sometimes last only a few months; the rods break near to the end, which is fixed with a coupling, and the deterioration of the iron appears to be confined within a small portion, the iron remaining quite tough and fibrous within an inch of the fracture,  Another specimen from the same machines is the lever for pushing off the work from the machine when stamped; the lever is about 1/2 inch square, made of the toughest wrought- iron, it is 9 inches long, and falls back against a stop at one-third of its length from the centre of motion at the bottom, being thrown back sharply by a spring, the total strain upon the lever varying from about 1 lb. to about 12 lbs., according to the accidental circumstances in the working of the machine. These levers all break off quite short and close-grained within an inch of the part that strikes against the stop, but the iron continues quite fibrous and unchanged to within an inch of the point of fracture, as shown in the specimen. They were driven at the same speed ; but they broke so frequently, lasting sometimes only a few weeks, that it was determined at last to reduce the speed of the machines from 120 to about 100 blows per minute, and in consequence of this reduction in speed the levers are much less frequently broken, and last on the average about four times as long as before. In a subsequent discussion, R. Stephenson [46] indicated that since their last meeting he had turned his attention to ascertain, if possible, whether any real difference exists in the molecular arrangement of the material or structure of a piece of iron called crystalline, and a piece of iron called fibrous; and for this purpose he had examined them under a powerful microscope, and it would, probably, surprise the members to know that no real difference could be perceived, and that if he had not previously seen with the naked eye the specimens called fibrous and crystalline, he should not have been able to distinguish the one from the other in the microscope. The best specimen he could select of the kind called fibrous, exhibited to the naked eye an arrangement of dark and light lines, but the light lines composing the apparent fibre were, in point of fact, as crystalline as the other kind of iron, and, therefore, however fibrous it might appear, it was essentially a crystalline 484 Appendix A mass. Even in a piece of iron, with large facets, which appeared extremely crystalline, when one of the crystals was examined, it gave much the same appearance under the microscopy as a fibrous surface gives to the naked eye; in fact, it would appear to consist of bundles of fibres broken through at certain angles, just as slate was observed in the quarries to break in particular rhomboidal forms. Now, in the instance of slate, there was nothing fibrous or crystalline, but owing to the large scale something resembling the appearances to the observed in iron-like fibres being broken through in particular planes. Mr. Adams “Opined that the appearance called crystalline was caused by nothing more or less than a bundle of fibres, consisting of many small crystals being sheared off square, forming one facet.” G. B. Thorneycroft [47, 48] discussed the quality of iron, manufactured in different ways, and stated “that the compression of iron, when cold, is certain to change fibrous, into granular iron, and that vibration or bending, even to a slight extent, if continued for any length of time, has the effect of compressing all the particles consecutively.” He also presented some experimental results to justify the use of straight axles. He [48] further stated that “If a shoulder was left on an axle, it should be curved, for if it was left square, it would induce fracture at that part. It would appear that there was a constant progressive tendency to fracture whenever opportunity was afforded for commencing.” In a discussion of the form of shafts and axles, T. Thorneycroft [49] stated To determine what these elements of self-destruction are, and to what extent they are in operation, has lately occupied the highest mathematical and practical talent of this kingdom; and they have recorded as the result of their experiments and investigation, that to resist the effects of reiterated flexure, iron should scarcely be allowed to suffer a deflection equal to one-third of its ultimate deflection, for should the deflection reach one half of its ultimate deflection, fracture will sooner or later take place. Braithwaite [50], in 1854, was apparently the first to use the term fatigue in the title of a paper. He stated “that the term ‘fatigue’ as applied to  deterioration of metal, was suggested by Mr. Field; ” He gave numerous examples of the occurrence of fatigue failures in practice and stated that There have been many instances of the sudden, and unexpected fracture of axles, cranks, crank-pins, levers, cranes, crane-chains, hooks, &c., and almost of all parts of various kinds of machinery, when subjected to continuous, and repeated strains, jerks, or concussions, and it is very remarkable, that in all cases, the destructive effect of this fatigue, was evident, in the metal at the fractures being altered in its structure.  the Author has arrived at the conclusion, that many of the railway accidents, to bridges, ash-pans, parts of locomotive engine, carriages, or the chains connecting them, hitherto deemed unaccountable, are to be attributed to the fatigue of the metal, and he is of opinion, that a rigid examination, and sub- sequent strengthening, or changing of the parts, where necessary, of all bridges, machinery, and engines, will greatly tend to the prevention of such accidents, which, unhappily, must, on railways, always be of a very serious kind. Appendix A 485 During the discussion of this paper, Fairbairn said that his experience led him to believe, that fractures in iron and other metals, subjected to severe strain, were, in many cases, due to some original imperfection in the manufacture; it was then only a question of time, how soon fracture would occur. In all cases of bodies subjected to intermittent strain, a progressive deterioration appeared to take place in the resisting powers of the material, in consequence of which, they would ultimately give way, under a load which they were at first fully equal to sustain, and this deterioration of strength appeared to proceed rapidly, or slowly, as the strains bore a greater, or less ratio to the ultimate resistance. Thus crank-axles were frequently subjected to a succession of jerks which could not be resisted for any length of time, even by iron of the best quality. He believed that wrought iron exposed to constant variations of strain, frequently underwent a complete change in molecular structure, assuming a crystalline, instead of a fibrous arrangement. In concluding the discussion, Braithwaite stated that most of the  remarks confirmed his views on the subject. When shafts had not been unduly loaded, they lasted well; but when called upon to perform increased duty, they incurred fatigue, and consequently, broke. The vibrating action upon a wheel, however, was not exactly analogues to that upon a shaft; still, increased duty would produce the same effect upon the former as upon the latter. So also with bridge girders; if they were originally constructed of proper dimensions, and of good metal, they would last; but that strength would no longer suffice, if the weight of the engines was increased, and they were impelled at a greater velocity. It was the excess of duty to which rails and bridge girders were now exposed, that was the main cause of their deterioration. McConnell [51, 52] described a process for manufacturing sound hollow axles and experimentally showed that the hollow axles were superior to solid ones. In the discussion of the paper [52], Mr. Slate remarked, that in reference to the crystallization produced in iron by concussion, he thought the effect did not take place unless the strain was beyond the elastic limit more than five or six tons per inch, so as to cause a permanent change in the arrangement of the particles of the iron. He had tried an experiment in connexion with Mr. Wild, in which a weight was suspended by a bar an inch square, and was lifted up and down eighty times per minute by an eccentric worked by a steam engine constantly, night and day. This was continued for a length of time that was supposed equivalent to the effect of twenty-five years’ work, but no change or crystallization in the iron was perceived. FATIGUE OF RAILROAD STRUCTURES On 27 August 1847, a commission was appointed by the British government to inquire into the conditions to be observed by Engineers in the application of Iron in Structures exposed to violent concussions and vibration;  to ascertain such principles and form such . geometries and showed that the appearance of the fracture surface is a function of the way the axles are loaded, disproving the crystallization theory of fatigue. He stated that abrupt shape changes affected. of its elasticity.” He further stated that Appendix A 483 he had made a machine in which he put an inch square bar subjected to a constant strain of 5 tons, and an additional varying strain of. in particular planes. Mr. Adams “Opined that the appearance called crystalline was caused by nothing more or less than a bundle of fibres, consisting of many small crystals being sheared off