Elastic-plastic behaviour of thin tubes subjected to internal pressure and intermittent high-heat fluxes with application to fast-nuclear-reactor fuel elements

Abstract

A sealed reactor fuel can when subjected to sufficiently high thermal stresses in the presence of an internal pressure will yield plastically. A simple model of the can is used to show that the plastic strains so produced may cause ratchetting or plastic cycling as the temperature gradient across the can wall cycles because of startup and shutdown of the reactor. On the assumption that creep is negligible, approximate criteria are derived for the onset of ratchetting and plastic cycling, simple expressions are obtained for the plastic strains incurred by each cycle, and failure of the can due to the above mechanisms is discussed both for work-hardening and non-work-hardening material. Consideration is then given to the effect of stress relaxation due to creep when the mean temperature of the can is sufficiently high to cause complete relaxation of the thermal stress while the reactor is at power, creep being ignored while the reactor is shut down. Under these conditions, it is found that the criterion for ratchetting is simply the criterion for plastic yielding during the first temperature cycle. Finally, it is shown in an appendix that the results obtained from the simple model also hold, with minor modifications, for the similar problem of a thin spherical shell subjected to an internal pressure and a temperature gradient across the shell wall which is cycled. Use is made of this to discuss the accuracy of the results obtained from the simple model when applied to a thin can.

Implications of shakedown for design of actively cooled thermostructural panels

“…Bree diagrams [Bree 1967] have been used extensively in the nuclear pressure vessel industry to delineate the boundaries between various elastoplastic regimes. In the classic Bree problem, a thin-walled cylinder of an elastic, perfectly plastic material (see inset in Figure 3) is subjected to a fixed internal pressure, P, and a cyclic radial temperature difference T between the inside and .…”

“…Although Bree diagrams can be constructed for simple geometries and loading conditions using analytical models [Bree 1967], numerical techniques are generally required [AbdelKarim 2005]. In the present study, finite element analysis (FEA) is used to apply a methodology initially reported in [Abdalla et al 2007].…”

“…The rationale is that allowing the stresses to locally exceed the yield strength of the material upon the first few cycles, with fully elastic response thereafter (shakedown), can result in substantially lighter designs. For this purpose, a simplified technique [Abdalla et al 2007] is used to conduct numerical Breelike analysis [Bree 1967] of prospective geometries and determine shakedown limits, defined by critical combinations of thermal and mechanical stresses. The geometries selected for numerical analysis are obtained from previous optimizations based on yield-limited design [Valdevit et al 2008].…”

Recent Progress in Constitutive Modeling for Ratchetting

“…This strain accumulation is now known as liquid level induced thermal ratchetting, because it can take place when the level of a high temperature liquid changes cyclically in the cylinder. Since the thermal ratchetting can occur even under no mechanical load, it is in contrast with the classical problem of Bree [3], in which the superposition of mechanical and thermal loads is prerequisite. The Subcommittee on Inelastic Analysis of High Temperature Materials, JSMS, has done a comparative study in the last three years for the purpose of finding appropriate constitutive models to simulate liquid level induced thermal ratchetting [1,2].…”

Shakedown analysis of thick cylinders with multiple radial openings

“…In the nuclear industry, ASME Boiler and Pressure Vessel Code (section III, Div.1, NB-3000) has been widely employed to design safety class-I components [1]. The simplified design assessment methods in ASME code like the Bree diagram were developed for a thin cylinder subjected to constant internal pressure and a cyclic linear through-the-wall temperature distribution [2]. One dimensional analysis with an elasticperfectly plastic material model was used to arrive at the limits for shakedown and ratcheting.…”