Elastic Core Concept in Shakedown Analysis

Use of an Elastic Core concept in finite element inelastic analysis of shakedown for components subjected to cyclic loading is described. The Elastic Core is defined as the portion of the wall which remains elastic during the entire history of cyclic loading. If it can be shown that the Elastic Core continues to exist in the wall of a component during consecutive cycles, there is no ratchet. It is shown how elastic-plastic cyclic analysis conducted only for a limited number of cycles can be used to confirm the presence of the Elastic Core. The Elastic Core concept was introduced to bound the accumulated strain for structures in elevated temperature service including plasticity and creep (1974, 1979). The resulting evaluation method is included in the ASME Code. The ASME Boiler and Pressure Vessel Code, Section III and Section VIII, Division 2 provide rules for the evaluation of plastic ratcheting in components subjected to cyclic loading. These evaluations use results of elastic analysis for components subjected to mechanical and thermal loading below the creep regime. Equations defining the onset of plastic ratchet in the Code are based on a simplified one-dimensional model including sustained membrane stress and cyclic thermal bending stress. Therefore, they only provide approximate results. The proposed use of finite element analysis extends the application of the Elastic Core for redundant structures of complex geometry and loading conditions. The results obtained herein also show the usefulness of the Code method in predicting the behavior of these structures.