Shakedown Analysis of Thick Cylinder with a Radial Opening with Primary Load Cycling In-Phase with Secondary Load

Abstract

Shakedown and ratcheting behaviour of thick cylinder with and without radial crosshole is investigated in this paper by inelastic finite element analysis. Bree diagram was developed for the case of constant primary and cyclic secondary loading where the thermal gradient is varying linearly through the thickness for a thin cylindrical vessel. In the presented analysis the primary load is considered to be cycling strictly in-phase with the secondary loading and elastic-perfectly plastic material model is used. The results of FE analysis carried over thin cylinder was used to validate the methodology incorporated for distinguishing between cyclic behaviours (i.e. elastic shakedown, plastic shakedown and ratcheting). The thick cylinders considered have thickness ratio (Ri/t) = 2 and opening radius ratio (ri/Ri) = 0.2. The results indicate that the modified Bree diagram (i.e. considering both the loadings to be in-phase) derived for thin cylinder is sufficiently conservative and can be used to predict the shakedown behaviour of thick cylinders. However for thick cylinders with crosshole the ratcheting/shakedown boundary is significantly different and using the results of thin cylinder would be unsafe. The importance of selecting the most appropriate loading condition for analysis is also highlighted.