An Extended Shakedown Theory for Structures That Suffer Cyclic Thermal Loading, Part 1: Theory

Abstract

The paper describes an extension of classical shakedown theory for structural problems involving constant mechanical loads and cyclic variations in temperature. The objective of the theory is to provide a simple means of distinguishing between circumstances where thermal cycling can cause structural ratchetting for small or zero mechanical loads from those where very substantial thermal stresses can occur with no danger of ratchetting. This distinction is of particular importance in the design of Liquid Metal Fast Breeder Reactors and current design codes do not address this problem directly. An extended definition of material shakedown is described that provides a conservative theory, taking into account cyclic strain hardening. Some simple experiments on a two-bar structure demonstrates the relevance of the theory to observed structural behavior.

On material immanent ratchetting of two-phase materials under cyclic purely thermal loading

“…In this case, the Bree diagram should degenerate to a one-dimensional single-axis representation of thermal loading conditions, with region boundaries marked as points on this axis. This disadvantage of Bree diagrams was pointed out in [41], where it is stated that the Bree diagram is a solution for a very particular problem and that there can exist circumstances under which thermal loads have a more severe effect on generation of irreversible strains. Thus, a theory providing a classi®cation to which degree a structure is susceptible to thermal loads can be developed by extending the classical shakedown theory to cases of thermal loads in excess of the yield stress, [41].…”

“…This disadvantage of Bree diagrams was pointed out in [41], where it is stated that the Bree diagram is a solution for a very particular problem and that there can exist circumstances under which thermal loads have a more severe effect on generation of irreversible strains. Thus, a theory providing a classi®cation to which degree a structure is susceptible to thermal loads can be developed by extending the classical shakedown theory to cases of thermal loads in excess of the yield stress, [41]. The linkage of the magnitude of thermal loads responsible for the onset of ratchetting with the possibility of the occurrence of plastic shakedown in the case of low mechanical loads and high thermal ones is emphasised.…”

“…One way to determine the shakedown limit is provided by the upper bound theorem of Koiter [39,27]. It was shown in [41] that the entire ratchetting boundary (in other words, conditions for the onset of ratchetting or plastic collapse) can be determined by means of the extended classic shakedown theory.…”

“…Superposition of these residual stresses with the cyclic stress state initiated by external loading results in a subsequent purely elastic behaviour, [38]. A shakedown theory developed in parallel with a limit theory provides criteria for the occurrence of elastic, [38±40], and plastic shakedown [35,41]. The level of the cyclic load is ± for a given distribution of a steady load ± the main factor responsible for the transition from elastic to plastic shakedown.…”

Recent Progress in Constitutive Modeling for Ratchetting

“…This thermal ratchetting was analyzed first by Goodman [53] and then by Ponter et al [54][55][56] and Wada et al [57]. Their analyses were based on the elastic-perfectly plastic model, which will be indicated as the PP model (a) OW I model Fig.…”