A fully implicit, lower bound, multi-axial solution strategy for direct ratchet boundary evaluation: theoretical development

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Abstract

Ensuring sufficient safety against ratchet is a fundamental requirement in pressure vessel design. Determining the ratchet boundary can prove difficult and computationally expensive 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 Finite Element 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 is updated throughout the analysis, thus satisfying Melan’s Lower bound ratchet theorem. This is achieved utilizing the same elastic plastic model as the first stage, and a modified radial return method. The proposed methods are shown to provide better agreement with upper bound ratchet methods than other lower bound ratchet methods, however limitations in these are identified and discussed.
Original languageEnglish
Article number051202
Number of pages11
JournalJournal of Pressure Vessel Technology
Volume135
Issue number5
Early online date9 Apr 2013
DOIs
Publication statusPublished - 26 Aug 2013
EventASME Pressure Vessels and Piping Conference 2012 - Toronto, Canada
Duration: 15 Jul 201220 Jul 2012

Keywords

  • lower bound strategy
  • multi-axial solution
  • ratchet boundary

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