Finite Element Based Automated Analysis for Determining Ratchet, Shakedown and Elastic Limits

Abstract

In order to determine the ratchet and shakedown limit curves for even a simple component, such as a tube under a constant pressure load and cyclic thermal load, can be a daunting task when using conventional analysis methods (elasto-plastic cyclic finite element analysis) that require repeated iterative simulations to determine the state of the structure, elastic, shakedown, plastic or ratchet. In some cases, the process is further complicated by the difficulty in interpreting results of the cyclic loading to determine in which regime the structure is. Earlier work by Abou-Hanna and McGreevy was able to demonstrate limit load analysis of a structure whose yield strength is modified based on cyclic load, provided the ratchet limit [1]. The method, called Anisotropic Load Dependent Yield Modification (LDYM), was implemented by using a user subroutine with ABAQUS, a general commercial finite element code. The approach adopted provided ratchet limits for only one individual cyclic load value. The work presented here describes a process for analyzing the structure and determining the elastic, shakedown and ratchet boundaries all in one finite element simulation using only one analysis step. The approach manipulates the structure material behavior that enables the resetting of the material characteristics to their original values in order to be able to analyze the structure for different sets of cyclic and primary load combinations. The process was verified using problems available in the literature, such as the Bree tube and Ponter’s Holed Plate. Additionally, a tubular T-joint was used as an example of the effectiveness of the process for a three dimensional complex geometry. The tubular T-joint results are verified against baseline data from the iterative elastic-plastic simulations used to determine the elastic, shakedown, and ratchet limits. The work presented highlights the advantages and limitations of this numerical approach which requires little interaction with the analyst.