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The history of fatigue in structures, components and metals dates back to early 19th century when failures of chains in mines were reported due to dynamic loading, and fatigue testing of these chains was performed for mitigation (Shütz 1996). In consideration to this, the first wires to avoid fatigue failure were invented. Since then, more than 100,000 papers related to fatigue were published and it would be a challenging task to provide a detailed historical overview. Thus, this report includes the historical overview that is most relevant as background for its objectives.par
The term “fatigue” was first mentioned by an English engineer, Braithwaite, in the literature in 1854. In his paper, he described fatigue failure in brewery equipment, water pumps, crankshafts, railway axles, levers, cranes and so on. Back then, many disastrous railway accidents occurred, including Versailles rail accident on 5 October 1842 when a train returning to Paris derailed at Meudon after the leading locomotive broke an axle due to fatigue, causing between 52 to 200 deaths. Fatigue failures of axles, couplings and rails became a serious problem and a cause of numerous railway accidents by the end of 19th century. par
From 1860 to 1870, a German railway engineer August Wöhler, presented “Wöhler curves” in terms of S-N curves, to determine the fatigue strength of railway axles based on fatigue testing. Before that, Wöhler measured the service loads on railway axles using self-developed deflection gauges. Wöhler also introduced the concept of safety factors, where two sets were required: a set for maximum stress in service for static strength, and the second set for allowable stress amplitude under dynamic loading. These safety factors were provided for ensuring design for infinite life. However, these factors were valid only for un-notched specimens and fatigue testing was recommended for other geometries. Wöhler presented this test data in tables. Spangenberg, successor to Wöhler, plotted this data into curves, in the form of linear abscissa and ordinate. In 1910, an American scientist, O. H. Basquin proposed a log-log format to plot this data, the same way as S-N curves are presented in fatigue design standards today.par
Based on an assessment of Wöhler’s test data, the first constant fatigue life diagram was published by Gerber in 1974, in which the effect of static loading was included in addition to stress range, a parameter necessary for inclusion in bridge design. After 1920s, the fatigue failures in aircrafts resulted in research to investigate representative long-term loading and fatigue capacity of aircraft components. The structural components testing became a part of qualification procedure for new elements, and later it became a common practice to perform testing of large components of aircrafts in fatigue as opposed to small-scale test data. However, failures continued to occur, like in Comet crashes in 1954, which upon investigation were found out to be due to unsatisfactory detailing of the corners of the windows in combination with incorrect test procedure that provided residual stresses at the hot spot areas, which resulted in the difference between the actual capacity and that of laboratory test component. This fact demonstrated the importance of a good detailed design to achieve a sufficient fatigue capacity and the need for performing realistic component testing in laboratory. It is important that the structural geometry of the component and the fabrication are representative for the actual structure in terms of boundary condition and loading. It was also concluded that the failure of Comet airplanes that these structures were not fail-safe (Edwards 1988). Due to these accidents, the requirements for component testing in the aircraft industry were improved. In addition to that, it was concluded that the fatigue strength of a material does not necessarily correspond with the strength of the material because high-strength aluminum alloy was used in the Comet airplanes. Hence, the fatigue crack initiation in the base material is considered to be improved, also the crack growth parameters are considered to be rather constant with increasing tensile strength of material. The crack growth is considered to be a function the Young’s modulus of the material used rather than the strength of the material. Furthermore, aircraft accidents in the late 1960s led to the development of advanced research programs on fatigue strength based on fracture mechanics.par
In 1881, Johann Bauschinger analyzed that the elastic limit of materials changes under repeated stress cycles. The hypothesis by Mason and Coffin in 1950s were based on these analysis, which are still applicable in assessment of low cycle fatigue (Manson 1954; Coffin 1954,1984).Low cycle fatigue is defined as stress ranges leading to repeated plastic strain during loading and unloading, such that material does not possess elastic behaviour during a load cycle, after yielding during large load amplitude. They also described the behavior of materials under cyclic inelastic strain amplitudes by a four-parameter equation that originated the field of Low-Cycle fatigue. par
In 1960s, the finite element method was developed, which became a common practice to study stress concentrations, and is still used to analyze the stress concentrations. Before that, Gustav Kirsch calculated the elastic stress concentration factor for a hole in infinite body equal to 3. The combination of linear elastic theory of solids and advanced mathematics helped in derivation of stress concentration factors at notches and it was presented by Johnson (1961).par
in 1937, Neuber published a book with detailed theoretical calculations of the stress concentration factor $K_t$ and fatigue notch concentration factor $K_f$, which is still recommended for the study of these factors. In 1950s, the National Advisory Committee for Aeronautics (NACA) tried to transform these factors into engineering practice, but it proved to be an insufficient in accuracy and required huge experimental effort. However, it is still useful for a more qualitative understanding of the fatigue behavior of notched specimen. par
Radaj (1996) and Radaj et al. (2006) developed a notched stress method based linear elastic finite element analysis, which is linked to a notch stress S-N curve and is commonly used for research and in industry for special cases.
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