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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 DEFECT-FREE FATIGUE 11. INTRODUCTION Fatigue Failure is the failure of components under the action of repeated fluctu-ating stresses or strains. 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. 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 bound-ary conditions which produce fluctuating stresses and strains at some material point or points. These microstructural changes may culminate in the formation of cracks and their subsequent growth to a size which causes final fracture after a sufficient number of stress or strain fluctuations. The adjective “progressive” implies that the fatigue process occurs over a period of time or usage. The occurrence of a fatigue failure is often very sudden, with no external warning; however, the mechanisms involved may have been operating since the beginning of the time when the component or structure was put to use. The adjective “localized” implies that the fatigue process operates preferentially at specific local areas, rather than homogeneously throughout the body. These vulnerable areas can have high local strains and stresses due to stress and strain concentrations caused abrupt changes in geometry and/or material imperfections. The phrase “permanent microstructural changes” emphasizes the central role of cyclic plastic deformations in causing irreversible changes in the substructure. Countless investigations have established that fatigue results from cyclic plastic deformation in every instance, even though the structure as a whole is practically elastic. A small plastic strain excursion applied only once does not cause any substantial changes in the substructure of materials, but multiple repetitions of very small plastic strains lead to cumulative damage ending in fatigue failure. We note that although fatigue is popularly associated with metallic materials, it can occur in all engineering materials capable of undergoing plastic deformation. This includes polymers, and composite materials with plastically deformable phases. Plastically non-deformable materials such as glasses and ceramics, in which deformations at ambient temperatures are truly elastic everywhere, do not fail by fatigue due to repeated stresses. However, recent data has shown that polycrystalline ceramics can exhibit fatigue crack growth under certain circumstances. Such a process is still consistent with our definition in the sense that local irreversible deformation at the crack tip associated with processes such as microcracking, frictional sliding, particle detachment and crack face wedging are involved in the fatigue process. Furthermore, these local mechanisms in brittle materials can give rise to macroscopic 2behavior which is phenomenologically similar to plasticity. There are currently two principal methodologies for design and maintenance to resist fatigue failure of components, defect-free and defect-tolerant. These two approaches are based on the how the crack size a in a component increases with the number of stress or strain cycles N imposed on the component. 1. DEFECT-FREE DESIGN AND MAINTENANCE APPROACH: The defect-free approach is mostly used to design small components which are not safety critical. In this approach, it is assumed that no crack-like defects pre-exist. That is, the initial crack size a is taken to be zero. Figure 1 shows a schematic of the behavior of crack size, a, versus the number of applied cycles of loading, N , for an initially uncracked component. The number of cycles to fatigue failure of the com-ponent is denoted by Nf (the subscript “f ” here refers to “failure”) . The total number of loading cycles to failure may be conceptually decomposed as Nf = Ni + Np, (1) where Ni is the number of cycles required to initiate a fatigue crack, and Np is the number of cycles required to propagate a crack to final fracture after it has initiated. Of course, the precise boundary between these two regions depends on the value chosen for the “initiation” crack size, ai. Although the total fatigue life, within the defect-free approach, consists of an “ini-tiation” life and a “propagation” life, fatigue “failure” is often said to have occurred when a crack has initiated. This simplification is adopted since usually Np � Ni; in such case, the “propagation” life, Np, can be neglected in comparison to the “initiation” life, Ni, and total fatigue life, Nf , is approximated as Nf ≈ Ni. Further, a fatigue crack in a typical engineering component is often said to have “initiated” when it is readily visible to the naked eye, that is ai ≈ 1 mm. Of course, specific circumstances (e.g., “small” components) may require adoption of other, more appropriate, definitions of fatigue “initiation” and initiation crack size. 30Crack Size, aNumber of cycles, NxNiNpNfaiacFigure 1: Schematic of crack length, a, versus number of loading cycles, N , in an initially uncracked component. The defect-free methodology is usually sub-divided into two sub-categories. (a) High-cycle fatigue: High-cycle fatigue is associated with local cyclic stresses which are of


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