Abstract
Combining the application of the shakedown theory and a multiscale approach to analysis of fatigue allows interpreting all types of fatigue problems in an efficient manner. The description of the stabilized mechanical state after shakedown at the engineering macroscopic scale and at the mesoscopic scale of grains gives access to the engineering values which will drive the fatigue damage of the structure. The evolution of stress and strain tensors thus obtained for a cycle of fatigue allows predicting the fatigue strength of structures. At high cycle fatigue (HCF), when elastic shakedown takes place, the fatigue strength can be described by a simple combination of mesoscopic shear amplitude and hydrostatic tension at any point of the calculated structure, irrespective of the complexity of the structure and the loading. Two new developments incorporating spectral or modal approaches allow analyzing the fatigue resistance of structures undergoing vibrations in a very efficient manner. At low cycle fatigue (LCF), from the stabilized state of stress and strain, the fatigue strength is derived from a combination of the inelastic strain energy and the hydrostatic pressure. Numerous examples of fatigue analysis are presented.
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