Local vs. Global Ratcheting in Cracked Structures

Abstract

The classical approaches in shakedown analysis are based on the assumption that the stresses are eventually within the elastic range of the material everywhere in a component (elastic shakedown). Therefore, these approaches are not very useful to predict the ratcheting limit (ratchet limit) of a cracked component/structure in which the magnitude of stress locally exceeds the elastic range at any load, although in reality the configuration will certainly permit plastic shakedown. The Non-Cyclic Method (NCM) has been proposed recently to determine both the elastic and the plastic ratchet boundary of a component or structure under cyclic loading by generalizing the static shakedown theorem (Melan’s theorem). The proposed method is based on decomposing the loading into mean (time invariant) and fully reversed components. When a cracked structure is subjected to cyclic loading, the crack and its vicinity behave differently (local) than the rest of the structure (global). The crack may propagate during the application of cyclic loading. This will affect both local and global behavior of the cracked structure. This paper investigates global and local ratcheting of the cracked structures using the NCM and fracture mechanic parameters.