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

Abstract

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

The creep behavior of simple structures with a stress range-dependent constitutive model

“…Naumenko et al [6] briefly examined relaxation of a bar using the modified creep law, demonstrating that a stress range dependent creep law could have significant effect. That example has been extended by the author [14] to more complex structures undergoing creep relaxation, in particular elastic follow-up: it is shown there that a stress range dependent creep law wholly alters the time dependent structural response, unlike the steady creep cases described herein where familiar features are retained. …”

“…5, which we shall refer to as a 'modified power law' for simplicity, was used by Naumenko, Altenbach and Gorash [6,7] to examine how the stress system in simple components -uniaxial stress relaxation, a beam in bending and a pressurized thick cylinder -would change as compared to purely linear and purely power-law behavior. In this paper the beam and thick cylinder problems will be re-examined in more detail -the stress relaxation problem will be considered elsewhere in the context of a more detailed analysis of elastic follow-up [14].…”

Creep deformation and stress relaxation of a martensitic P92 steel at 650 °C

“…10. A two bar structure is a simple benchmark to investigate the relaxation of residual stress in a range of structural components [48,49]. The model consists of two bars (Bar 1 and Bar 2, as shown schematically in Fig.…”

An in situ thermo-mechanical rig for lattice strain measurement during creep using neutron diffraction

“…Therefore, predicting the effect of elastic follow-up on creep stress relaxation is important for the structural integrity assessment of high temperature critical plant components. The majority of previous work predicted the stress relaxation and elastic follow-up behavior using a constant-load creep model, [6][7][8][9][10][11][12][13][14]…”