466 Applications It is clear, then, that if the pressure is sufficient to cause yielding of the cylinder due to hoop stresses beyond the elastic limit, this yielding will take place first at the inner diameter. The residual stress state that results from plastic straining will depend on the cylinder geometry, material strain-hardening characteristics, unloading behavior of the material, and the level of strain hardening imposed. A typical circumferential stress state near the inner diameter (see [70] for example) is depicted schematically in Figure 8.78 where the tensile stresses due to loading are added to the residual stresses, the latter being compressive. The net stresses can then be used to calculate the resultant value of K, the stress intensity, using methods such as weight functions as done in [70]. In that article, the authors point out that the computed stress intensity is the sum of the contributions due to the internal pressure loading, the residual stresses, and the internal pressure acting on the crack faces. The resulting values of K can be as depicted schematically in Figure 8.79 where the value of K decreases with increase in crack length near the inner diameter. Thus, it is possible for a crack to initiate but arrest due to the decrease in K with crack length as depicted. As long as the stress intensity is below threshold, there should be no further crack extension. In determining the threshold for crack propagation, two issues should be considered. First, it should be established whether the applied cyclic loading is in the LCF or HCF regimes. If it is in HCF, involving very large cycle counts, then the use of K th is warranted. On the other hand, if the loading is LCF involving a low number of cycles such as start up and shut down of a mechanical system, then the use of K th can be conservative because K th typically corresponds to a growth rate of 10 −10 m/cycles (see Section 8.4). A value of K corresponding to a higher growth rate would suffice, provided that the total crack extension during LCF was within acceptable limits. The second issue, Applied stress Superposition Residual stress ID OD Stress Figure 8.78. Schematic diagram of stresses near inner diameter of pressurized cylinder. HCF Design Considerations 467 ID OD Stress intensity Crack location Figure 8.79. Schematic diagram of stress intensity in pre-stressed pressurized cylinder. one that is normally neglected in design, is to use a value of K th that represents the threshold of the material that has been subjected to strain hardening. Since such data are rarely available, this procedure is normally not followed and the values of K th for the unstrained material are sufficient, if not conservative. From a technical point of view, the local strain hardening near the crack tip during crack growth far exceeds the strain hardening applied to the bulk material during the autofrettage process. Thus, the use of K th of the unstrained material is acceptable. REFERENCES 1. Nicholas, T. and Maxwell, D.C., “Mean Stress Effects on the High Cycle Fatigue Limit Stress in Ti-6Al-4V”, Fatigue and Fracture Mechanics: 33rd Volume, ASTM STP 1417, W.G. Reuter and R.S. Piascik, eds, American Society for Testing and Materials, West Conshohocken, PA, 2002, pp. 476–492. 2. Tabernig, B., Powell, P., and Pippan, R., “Resistance Curves for the Threshold of Fatigue Crack Propagation in Particle Reinforced Aluminium Alloys”, Fatigue Crack Growth Thresholds, Endurance Limits, and Design, ASTM STP 1372, J.C. Newman, Jr., and R.S. 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Drechsler, A., Kiese, J., and Wagner, L., “Effects of Shot Peening and Roller-Burnishing on Fatigue Performance of Various Titanium Alloys”, Proceedings of the ICSP7, 7th International Conference on Shot Peening, Warsaw, 1999, pp. 145–152. 59. Guagliano, M. and Vergani, L., “An Approach for Prediction of Fatigue Strength of Shot Peened Components”, Engineering Fracture Mechanics, 71, 2004, pp. 5015–5512. 60. Rodopoulos, C.A., Curtis, S.A., de los Rios, E.R., and SolisRomero, J., “Optimisation of the Fatigue Resistance of 2024-T351 Aluminium Alloys by Controlled Shot Peening – Methodol- ogy, Results and Analysis”, Int. J. Fatigue, 26, 2004, pp. 849–856. 61. Curtis, S., de los Rios, E.R., Rodopoulos, C.A., and Levers, A., “Analysis of the Effects of Controlled Shot Peening on Fatigue Damage of High Strength Aluminium Alloys”, Int. J. Fatigue, 25, 2003, pp. 59–66. HCF Design Considerations 471 62. Nalla, R.K., Altenberger, I., Noster, U., Liu, G.Y., Scholtes, B., and Ritchie, R.O., “On the Influence of Mechanical Surface Treatments – Deep Rolling and Laser Shock Peening – on the Fatigue Behavior of Ti-6Al-4V at Ambient and Elevated Temperatures”, Mat. Sci. Eng., A355, 2003, pp. 216–230. 63. Clauer, A.H. and Fairand, B.P., Interactions of Laser-Induced Stress Waves with Metals, ASM International, Materials Park, OH, 1979. 64. Ruschau, J.J., John, R., Thompson, S.R., and Nicholas, T., “Fatigue Crack Growth Rate Char- acteristics of Laser Shock Peened Titanium”, Jour. Eng. Mat. Tech., 121, 1999, pp. 321–329. 65. Ruschau, J.J., John, R., Thompson, S.R., and Nicholas, T., “Fatigue Crack Nucleation and Growth Rate Behavior of Laser Shock Peened Titanium”, Int. J. Fatigue, 21, Supp. 1, 1999, pp. S199–S209. 66. Clauer, A.H. and Holbrook, J.H., “Effects of Laser Induced Shock Waves on Metals”, Shock Waves and High-Strain-Rate Phenomena in Metals, M.A. Meyers, and L.E. Murr, eds, Plenum Press, New York, 1981, pp. 675–702. 67. Lykins, C. and John, R., “Prediction of Crack Growth in a Laser Shock Peened Zone”, Proceedings of International Symposium on Inelastic Deformation, Damage and Life Analysis, V.K. Arya, ed., Springer-Verlag, May 1997. 68. Kang, K.J., Song, J.H., and Earmme, Y.Y., “Fatigue Crack Growth and Closure Behaviour Through a Compressive Residual Stress Field,” Fatigue Fract. Engng. Mater. Struct., 13, 1990, pp. 1–13. 69. Timoshenko, S.P. and Goodier, J.N., Theory of Elasticity, 3rd edn, McGraw-Hill, New York, 1970, p. 71. 70. Thumser, R., Bergmann, J.W., and Vormwald, M., “Residual Stress Fields and Fatigue Analysis of Autofrettaged Parts”, Int. J. Pressure Vessels and Piping, 79, 2002, pp. 113–117. Appendix A ∗ Early Railroad Accidents and the Origins of Research on Fatigue of Metals George P. Sendeckyj ABSTRACT The origins of research on fatigue of metals are reviewed. It is shown that early railroad axle failures and railroad bridge collapses were the driving forces behind the development of the field of fatigue of metals. The early work on failure of railroad axles led to the correct description of the fatigue crack growth process and engineering solutions of the axle fatigue failure problem. The work on developing design criteria for iron bridge structures led to the first fatigue design criterion. All of this occurred before Wöhler’s systematic fatigue experiments. INTRODUCTION The beginning of systematic research in fatigue of metals is linked to the numerous axle failures on the early railroads and especially to the deadly accident on the Paris- Versailles railroad on 11 May 1842 [1]. The extent of the early axle failures is poorly documented in the literature [2–11], since axle failures were seldom involved in deadly railroad accidents. Moreover, proof testing of axles and daily inspections were instituted by the Belgian government in 1843 [8] as a means of preventing accidents due to axle failures. As is shown in the next section, limits on the service life of axles were also instituted. Nevertheless, axle failures were common affecting the economics of railroad operations. As the trains became faster and larger, railroad bridge failures became rather common. This led to the investigation of iron structures subjected to impact and vibratory loading. As is show herein, many research efforts were performed before Wöhler’s systematic fatigue experiments during the 1856–1870 time period [12–18]. The initial experiments were on railroad axles and consisted of low cycle fatigue (actually repetitive impact) tests, ∗ This document is an unpublished manuscript contributed by Dr. George Sendeckyj. This research was per- formed in the Materials and Manufacturing Directorate, Air Force Research Laboratory, Wright-Patterson Air Force Base, Ohio. The author would like to thank Ms. Jeannie Stewart, the inter-library loan librarian, for obtaining copies of most of the references. 472 Appendix A 473 which led to engineering solutions to the fatigue failure problem. These early experiments cannot be considered to be true fatigue experiments. True fatigue research activities started with the systematic testing performed as part of the work to develop design criteria for railroad bridge structures. This work included design of the first fatigue test machines and systematic fatigue testing of iron beams manufactured by various suppliers. The tests were of relatively short duration (less than 100,000 cycles). Longer duration tests (some lasting over 10 8 cycles) were also performed before Wöhler’s systematic experiments. EARLY RAILROAD ACCIDENTS The first documented railroad passenger fatality occurred on 15 September 1830, the day upon which the Manchester and Liverpool railroad was formally opened [2]. The first American railroad accident to kill a passenger happened on 11 November 1833 and was caused by a broken axle on one of the cars [11]. Besides these historical firsts, there were many accidents during the development of the early railroads that led to various engineering and safety innovations. These included numerous locomotive and carriage axle failures that caused derailments [11], with serious economic consequences but not many passenger fatalities. This is apparent from the following railroad safety statistics. Gillespie [4] stated that On the English railroads, according to the parliamentary returns, between 1840 and 1845, both inclusive, more than 120,000,000 of passengers were carried, and of these only 66 were killed, or one in nearly two millions; and only 324 others were in any way injured, or one in nearly four hundred thousand. On the Belgian railroads, 6,609,215 persons travelled between 1835 and 1839, and of these 15 were killed and 16 wounded. But of these, 26 were persons employed on the railroads, and only 3 passengers were killed and 2 wounded. In 1842, of 2,716,755 passengers, only three were killed, and of these one was a suicide, and the other two met their deaths by crossing the line. On French railroads, 212 miles in length, of 1,889,718 passengers who travelled over 316,945 miles, in the first half of 1843, not one was either killed or wounded, and only three servants of the railroad suffered. Comparing with this the travelling by horse-coaches in the same region, we find that in seven years, from 1834 to 1840, 74 persons were killed, and 2073 wounded! Lardner [5] provided the actual statistics for horse-coach travel in Paris and its environs for the years 1834 through 1840, which are reproduced in Table A.1. Moreover, he analyzed 100 randomly selected railroad accidents and found that 18 were due to broken wheels or axles and 14 were due to defective rails. The Versailles to Paris railroad accident of 11 May 1842 is considered by some as the crucial event in the development of fatigue of materials [1] because it was caused by an axle failure and there were many fatalities. According to Adams [2], the train that went from Versailles to Paris 474 Appendix A Table A.1. Ordinary horse-drawn coach accidents in Paris and its environs Year Killed Wounded 1834 4 134 1835 12 214 1836 5 220 1837 11 361 1838 19 366 1839 9 384 1840 14 394 was densely crowded, and so long that two locomotives were required to draw it. As it was moving at a high rate of speed between Bellevue and Meudon, the axle of the foremost of these two locomotives broke, letting the body of the engine drop to the ground. It instantly stopped, and the second locomotive was then driven by its impetus on top of the first, crushing its engineer and fireman, while the contents of both the fire-boxes were scattered over the roadway and among débris. Three carriages crowded with passengers were then piled on top of this burning mass and there crushed together into each other. The doors of these carriages were locked, as was then and indeed is still the custom in Europe, and it so chanced that they had all been newly painted. They blazed up like pine kindlings. Some of the carriages were so shattered that a portion of those in them were enabled to extricate themselves, but the very much larger number were held fast; and of these such as were not so fortunate as to be crushed to death in the first shock perished hopelessly in the flames before the eyes of a throng of lookers-on impotent to aid. Fifty-two or fifty-three persons were supposed to have lost their lives in this disaster, and more than forty others were injured; the exact number of the killed, however, could never be ascertained, as the pile-up of the cars on top of the two locomotives had made of the destroyed portion of the train a veritable holocaust of the most hideous description. The apparent inconsistency between the early railroad fatality statistics and the large num- ber of accidents due to axle failures can be readily reconciled. Huish [19] indicated that The carriage stock of railway Companies is generally of so superior a kind, both as to design and construction, that accidents arising from their failure are very rare. The wheels and axle-boxes are the most severely tested parts of the vehicle, but if originally of a proper construction, give very little trouble in their maintenance and repair. During the last four years, only six wheels have failed, in the very large stock of the London and North Western Company. If, however, there is no part of the railway machinery which so little danger may be apprehended as the passenger carriage, the same cannot be claimed on the part of the merchandise wagon. Whether the absence of direct danger to human life, or an injudicious economy, has been the cause, the fact is, that in no portion of the system has so little improvement been exhibited, and in which, as the present moment, there is so great a necessity for a complete modification. In this respect England is far behind the Appendix A 475 Continent. The axles of wagon stock have, in many instances, been of the most faulty model and material. The accidents to the trains, from the fracture of these parts, have been very numerous, while the destruction of property has been sufficient to have paid for the very superior vehicle. In one recent instance, several hundred axles, of a peculiar form, were removed from a leading railway, after a short experience of their working. The New York State Senate report [6] indicated that To guard more effectually against the accidents arising from the alleged deterioration of the iron , it has been the practice, on some roads, to run the wheels and axles one year only under passenger cars, and then transfer them to freight cars. The safety beams have been introduced on the cars of many of our roads, by means of which the axle is upheld when broken. This has undoubtedly been the means of safety, by keeping the fractured ends of the axle suspended until the motion of the train could be arrested; but, in many cases, it is not calculated to hold them with sufficient steadiness to prevent the wheels from leaving the rail. This is an early example of fail-safe design practice. Twenty accidents occurred during the first year of operation of the Great Western Railway in Canada [7]. Of these accidents, only one was due to an axle failure. According to the report, Mr. William Scott, formerly one the Engineers to the Company, in his evidence, states “that on examination the iron of the axle appeared to be very bad – the worst that he had ever seen, and that he believes, but is not positive, that there must have been a visible flaw before the occurrence.” If such had really been the case, it ought to have been detected in the daily and close examination of all the rolling stock in use enjoined by the regulations of the Company; but on the other hand, the usual examination is declared to have taken place, and no flaw to have been discovered, and as to the pre-existence of the flaw, Mr. Scott is himself doubtful. As this quotation indicates, by 1854 it was common practice to daily inspect the rolling stock as a safety measure. Simon [20] summarized results from an official paper issued by the Association of German Railways on broken axles in 1865. He indicated that 153 axles broke and 40 were discovered before complete breakage occurred. The probable cause of breakage was: 17 cases of bad workmanship of axle, 32 cases of bad material, 21 cases of bad design, 6 cases of overloading, 10 cases of want of grease or oil, 46 cases of too long use, and 3 cases due to breakage of another axle. Thus, 30% of the failures were due to fatigue. Stretton [9] summarized railroad accidents during 1889 as reported to the Board of Trade. There were 106 collisions, 44 cases of passenger train derailments 13 cases of trade goods train derailments, 8 cases of trains travelling in the wrong direction through facing points, 30 cases of trains running into stations at too high a speed, 135 cases of trains running over cattle, 44 instances of trains running through gates at level crossings, 239 failures of axles, 9 failures of couplings, 668 failures of tires, 2 failures of wheels, . breakage occurred. The probable cause of breakage was: 17 cases of bad workmanship of axle, 32 cases of bad material, 21 cases of bad design, 6 cases of overloading, 10 cases of want of grease. Testing, ASTM STP 536, American Society for Testing and Materials, Philadelphia, 1973, pp. 79–94. 40. Vasudevan, A. K. and Sadananda, K., A Review of Crack Closure, Fatigue Crack Threshold and Related. by some as the crucial event in the development of fatigue of materials [1] because it was caused by an axle failure and there were many fatalities. According to Adams [2], the train that went from