Ensuring sufficient safety against ratchet is a fundamental requirement of pressure vessel design. Determining the ratchet boundary can however prove difficult when using a full elastic plastic finite element analysis and a number of direct methods have been proposed that overcome the difficulties associated with ratchet boundary evaluation. Here, a new approach based on fully implicit methods, similar to conventional elastic-plastic methods, is presented. The method utilizes a two-stage procedure. The first stage determines the cyclic stress state, which can include a varying residual stress component, by repeatedly converging on the solution for the different loads by superposition of elastic stress solutions using a modified elastic-plastic solution. The second stage calculates the constant loads which can be added to the steady cycle whilst ensuring the equivalent stresses remain below a modified yield strength. During stage 2 the modified yield strength used is updated throughout the analysis thus satisfying Melans Lower bound ratchet theorem. This is achieved through the same elastic plastic model as the first stage, using a modified radial return method. The methods that have been proposed here are shown to provide better agreement with upper bound ratchet method than the Hybrid method, however some limitations in this type of method have been identified and are discussed.

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