Introduction to Fatigue Analysis in Mechanical Design by the Multiscale Approach

Abstract

Crack initiation under high cycle fatigue is a localized phenomenon that occurs in some highly stressed grains of the metallic material. Therefore, the study of high cycle fatigue problems in a rational way is best performed by the introduction of the mesoscopic scale of material description (i.e. the scale of the metal grains of a metallic aggregate) in addition to the usual macroscopic scale of continuum mechanics. The principles of such a multiscale approach in high-cycle fatigue of metallic structures are presented in this work. The multiscale approach is settled on the assumption that under high-cycle fatigue loading a structure will not be fractured by fatigue if an elastic shakedown state is reached at the macroscopic as well as at the mesoscopic scale. The concept of the fatigue limit criterion coincides thus with the possibility of a cyclically loaded structure to tend to an elastic shakedown state at all scales. Extensions of Melan’s elastic shakedown theorem to realistic material behaviour are discussed in this article. These theorems allow an easy estimation of the mechanical parameters at the elastic shakedown state at both the macroscopic and mesoscopic scales. Some examples of application of the extended Melan’s theorem are provided. The relationships between mesoscopic and macroscopic quantities are studied within the framework of undamaged as well as damaged materials. In the case of undamaged materials, some additional assumptions allow to link the mesoscopic quantities to the usual (macroscopic) stresses and strains through closed form relationships.