Finite element three-dimensional elastic-plastic creep analysis

Abstract

This paper presents a continued development of computationally efficient finite element methods for accurately predicting the isothermal three-dimensional elastic-plastic creep responses of thick and thin shell structures subjected to mechanical and thermal loads. This work is applicable to a wide range of engineering structures and most recently has been used in the elastic-plastic creep analyses of high-temperature nuclear reactor components and rotating turbine blades. Previous work in this area for elastic-plastic analysis has been demonstrated by Levy et al. In that reference, use of a variable number of stress points within an element to describe elastic-plastic behaviour was demonstrated. These ideas have been extended for combined plasticity and creep behaviour. Thus, within an element, the order of the allowable total kinematic strain distribution is dependent on the number of element nodes (assumed displacement distribution), and the order of the allowable plastic strain distribution (and hence the elastic-plastic boundaries) and/or creep strain distribution is dependent on the number and location of the stress points used to numerically integrate the inelastic effects. This allows for an accurate representation of the elastic-plastic creep behaviour within an element. This higher inelastic representation results in the use of a minimum number of degrees of freedom for a given nonlinear analysis, which is particularly important for combined creep and plasticity behaviour and for cyclic loading, where computer times can be prohibitive. The basic numerical solution procedure for the elastic-plastic creep analysis is an incremental predictor-corrector iterative scheme combined with the ‘initial strain’ approach. Attention has been given to the time step increment strategy for combined plasticity and creep as this governs efficiency and accuracy. The methods have been implemented into the three-dimensional solid element module (HEX) of the Grumman PLANS finite element program. Sample problems are used to demonstrate and investigate the accuracy and efficiency of these methods. Sample problems include combined plasticity and creep analysis of a simple rod under time varying load, stress-relaxation of a simple rod, thermal stress-relaxation of a plate subjected to a temperature variation across the width, and creep analysis of an internally loaded thick-walled pressure vessel.