Ratcheting/Shakedown Analysis of Cracked Structures

Abstract

The classical approaches in shakedown analysis are based 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. In recent years, the “Non-Cyclic Method” (NCM) was proposed by the present authors to predict the entire ratchet boundary (both elastic and plastic) of a component/structure 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. The applicability of the NCM has been demonstrated for several uncracked components and structures using both analytical and numerical schemes. The present paper extends the NCM further to analyze plastic shakedown for two simple cracked components.