Stress relaxation and elastic follow-up using a stress range-dependent constitutive model

Despite the availability of detailed nonlinear finite element analysis, some aspects of high temperature design can still be best addressed through more simplified methods. One such simplified method relates to the problem of elastic follow-up where typically in strain-controlled situations, elastic behaviour in one part of a structure can lead to large strain accumulation in another. Over the past thirty years it has been shown that in regions with significant elastic follow-up a plot of maximum stress against strain (a 'stress-strain trajectory') is virtually independent of the constitutive relation - a characteristic which can be used to estimate elastic follow-up for design purposes without detailed nonlinear finite element analysis. The majority of studies which have reported this independence on material behaviour have used simple constitutive models for creep strain, primarily based on power law creep or variations. Recently studies of the behaviour of high temperature structures with a stress range dependent constitutive law have begun to emerge. This paper examines the problem of elastic follow-up using such a constitutive law for a classic two-bar structure and for a more complex structure using finite element analysis. It is found that the independence of the stress-strain trajectory on constitutive equation is lost with a stress range dependent relation.