Statistical Analysis of the Oxide Transitions

People involved in the project

Léo Borrel

Credentials: Currently Ph.D. Student in Particle Physics at Caltech

The corrosion of zirconium alloy fuel cladding is a critical issue in current Light Water Reactors (LWRs). The main goal of this cladding is to ensure the fuel rod structural integrity to keep a coolable geometry in both operating conditions and accident scenarios. This project is an extension of the Modeling of Zirconium Alloys Fuel Cladding and aims to add statistical components to the C4 Model for operating condition oxide growth. The oxide transition occurs at the point where the growing oxide “breaks” due to internal stress, and a new oxide starts forming underneath it, restarting the characteristic parabolic or sub-parabolic growth.

Weight gain as a function of time for corrosion of Zr-1.0Nb at 360 °C for 240 days
Weight gain as a function of time for corrosion of Zr-1.0Nb at 360 °C for 240 days

Originally, the transition time is an empirical parameter set in the C4 model. However, in reality, the oxide transition thickness varies between experiments, and also within a sample. This project aims to model these variations using a Monte Carlo type of analysis. A sequence of oxide thickness curves are generated using the C4 model, each with its first transition randomly chosen within a Normal distribution function. The resulting oxide thickness at each time is fitted to a Normal distribution function, which can be used for statistical analysis, such as providing the C4 model with a confidence interval.

Controlling the transitions with a probability function introduces variability into the model of oxide growth and offers a more realistic behavioral explanation of the transition. This allowed for the creation of an oxide thickness heat map which visually shows the probability of the alloy possessing any oxide thickness at a given exposure time.

Normalized Probability Density of Oxide Thickness with Exposure time
The normalized probability density of the total oxide thickness as a function of exposure time for Zr-1.0 Nb.

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