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lec20_notes - MASSACHUSETTS INSTITUTE OF TECHNOLOGY...

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MASSACHUSETTS INSTITUTE OF TECHNOLOGY DEPARTMENT OF MECHANICAL ENGINEERING CAMBRIDGE, MASSACHUSETTS 02139 2.002 MECHANICS and MATERIALS II SPRING 2004 SUPPLEMENTARY NOTES c L. Anand and D. M. Parks FATIGUE CRACK PROPAGATION 1
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We have emphasized that most engineering materials contain small crack-like defects, or they can readily develop them during service. If a crack exists in a structure, then the stress field in the vicinity of the crack tip is given by K I σ ij ( r, θ ) f ij ( θ ) as r 0 , 2 πr where the stress intensity factor is K I = Q σ πa , with σ the far-field applied Mode I tensile stress, a the crack length, and Q the configu- ration correction factor. Under small–scale yielding, and when monotonically increasing far-field load is applied to the body, then a necessary condition for crack extension is K I = K Ic , where K Ic is a material property called the plane strain fracture toughness. The above criterion for fracture is deceptively simple. In practice there are problems associated with identifying the shape and size of a crack, with carrying out a proper stress analysis, and in obtaining accurate and/or valid data for K Ic . Also, cracks can extend in a sub-critical manner, which means that a component initially thought to be safe against fracture may become dangerous after a period of service. Subcritical crack nucleation and growth can occur under constant or fluctuating loads. In the former case, crack extension is usually controlled by an aggressive environment which causes stress corrosion cracking ; we shall return to a study of this phenomenon later. Subcritical crack nucleation and growth under fluctuating loads is called “fatigue.” It is this phenomenon to which we now turn our attention. Failure occurring from repeated fluctuating stresses or strains is called fatigue. The word “fatigue” was introduced in the 1840’s and 1850’s in connection with such failures which occurred in the then rapidly developing railway industry. It was found that railroad axles failed regularly at shoulders, and that these failures appeared to be quite different from failures associated with monotonic testing. Even then, elimination of sharp corners was recommended. The process of fatigue failure may be defined as a process in which there is progressive, localized, permanent microstructural change occurring in a structure when it is subjected to boundary conditions which produce fluctuating stresses and strains at some material point or points. These microstructural changes may culminate in the formation of cracks 2
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Axle Bearing Fatigue Fracture Location Wheel Figure 1: Schematic of rotating bending fatigue failure in railway axles. and their subsequent growth to a size which causes final fracture after a sufficient number of stress or strain fluctuations.
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