Bubble Density Dependent Functionals to Describe Deformation and Stress Equilibrium Evolution for In-Reactor Nuclear Fue
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0981-JJ07-04
Bubble Density Dependent Functionals to Describe Deformation and Stress Equilibrium Evolution for In-Reactor Nuclear Fuel Materials Ray B. Stout Rho Beta Sigma Affaires, Livermore, CA, 94550
ABSTRACT Future designs of nuclear reactors require an increased mechanistic understanding of materials’ responses to develop and evaluate ceramic nuclear fuels in order to operate at higher localized temperatures and fuel burn-ups. At higher temperatures, any given non-elastic/plastic deformation rate will occur at a lower stress state and the transport rate of fission gas atoms to bubbles will also be increased. The higher burn-ups, measured as fissions per unit volume of ceramic nuclear fuel, will locally increase the number density of fission gas atoms that will be transported to existing porosity and/or additionally created fuel bubbles. Based on these facts, pressurized bubble density in nuclear fuels of future reactor designs, as measured by the number of bubbles per size(radius) and per fission gas atom content(moles), will evolve significantly different from the pressurized bubbles densities observed in the existing light-water reactors. The following sections will describe preliminary concepts of nuclear fuel response models that use: (1). a bubble density field equation to describe the time evolution of the discrete bubble species of different size(radius) bubbles and different gas content bubbles; (2). a deformation field equation dependence on fission gas bubble density; and (3). a stress/bubble-pressure equilibrium equation dependence on fission gas bubble density. INTRODUCTION Future dispersion nuclear fuel materials will contain small spatial subsets of high fissile actinide content, and at high burn-up these will contain dense sets of fission gas bubble species. The evolution of dense sets of discrete bubble species(order 1010 to 1018 bubbles per cc) in nuclear materials[NFs] is a stochastic problem that can be described with a generic Boltzmann transport equation[1, 2]. A bubble species is identified by the physical attributes of radius, gas content, and their rates with respect to time. A bubble density function is defined as the number of bubbles per unit bubble species per unit spatial volume at an arbitrary time. The in-reactor nuclear fuel material responses for deformation and stress equilibrium are bubble density dependent, as the radius and gas content of a bubble species will evolve in time and space at rates compatible with the local fission rate, the local temperature, and the local stress state. A spatial volume of NF material that contains a high density of pressurized bubbles is a non-contiguous material; and is not a continuum for applied mathematical operations of derivatives and integrations[2, 3, 4]. However, by using vector path integral concepts for arbitrary spatial paths between any two arbitrary and finitely separated spatial points, two stochastic vectors will be derived that decompose the spatial volume into material and bubble spatial domains at any arbitrary time. This
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