Estimation of Elastic Follow-Up in Structures

Abstract

Using simplified benchmark models, representative of the behavior of real structures, a unified framework for quantification of elastic follow-up (EFU) in structures has been provided. Closed form analytical solutions for evaluation of elastic follow-up are presented for model structures. The impact of elastic follow-up on the relaxation i.e. the redistribution of residual stresses has been explored and hence its significance in the integrity assessment of structures in general and in classification of residual stresses in particular has been highlighted.

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

“…6 Simple two-bar structure subject to a fixed axial displacement, more detailed studies of elastic follow-up in other, often more complex, structures. In a recent series of publications by Hadidi-Moud and Smith, summarized in reference [9], this feature is also noted.…”

“…11 Equivalent stress-strain trajectories for evaluation point of Y-piece from ABAQUS FEA with modified power-law creep in Section 3 and it is seen that the linear viscous part of the modified power-law has a significant effect in stress relaxation, more so than what is observed for constant load steady creep [16,22]. The simple twobar structure [4] has long been used as a reference benchmark in studies of elastic follow-up [4][5][6][7][8][9][10]: assuming a creep law based on power-law secondary creep alone, it can be shown that this structure has a stress-strain trajectory which is indeed independent of the power index. However, it is shown in Section 4.3 that the relaxation characteristics of the stressstrain trajectory are radically different when using the modified power-law.…”

“…[6,Section 2.2]. Further, Hadidi-Moud and Smith, following their review paper [7], have written a series of papers [8][9][10] which extend the simple two-bar structure of Boyle and Nakamura [4] to a number of similar simple 'benchmark' bar structures, representative of the behaviour of real structures, as part of a study into the relaxation of residual stress in a range of structural components. The concept of an 'elastic follow-up factor' from R5 [2] is further developed and it is argued that the factor '.…”

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

“…To estimate the elastic follow-up in a structure, there are various models designed so then that complex structures can be described by a set of series and parallel springs. Several benchmark models, discussed in earlier studies [7,10,[43][44][45][46][47][48], adopt series, parallel, and combination systems. In the present work, a combination of bars was employed experimentally (see Section 2.3), while, for simplicity, the simulation was subjected to a series bar model.…”