Modelling the Anomalous Oxidation Behavior of Zirconium Alloys

Abstract

Zirconium alloys, widely used as the cladding material for fuel rods in pressurized-water-reactors, undergo oxidation during service. The initial oxidation kinetics is very similar in form to that of a classically passivating layer. However, as the oxide layer reaches a certain critical thickness, a sudden increase in the rate of weight-gain is observed while the oxide layer remains adhered to the substrate. This process repeats itself with an approximately regular period in time. Microscopy images reveal a co-related periodicity in the oxide's microstructure as well. The acceleration in the oxidation kinetics associated with these transitions leads to an increase in the amount of hydrogen entering the Zircaloy, limiting the fuel burn-up in the reactors by causing hydrogen embrittlement. The aim of this thesis, therefore, is to develop physics-based-models to understand the mechanisms which govern this anomalous behavior. Specifics of the three major parts of this work are outlined below.

Mechanistic model for oxide growth stresses: The stresses within the oxide layer have been postulated to play an important role in affecting its protectiveness, for example, by allowing crack formation. Therefore, a mechanistic model for the oxide stresses is presented, showing that the oxide deforms primarily by dislocation glide for $T<900$ K, while the creep of the substrate only becomes significant at higher temperatures. Model predictions also suggest that the transitions in the oxidation kinetics cannot be attributed to a macroscopic fracture of the oxide. Hence, a possible indirect influence of the oxide stresses via a phase transformation is studied next.

Model for the martensitic phase transformation in the oxide: Tetragonal-to-monoclinic phase transformation driven by stress-relaxation has been postulated to affect the porosity of the oxide layer by forming micro-cracks. Therefore, a free-energy-based framework is developed to investigate its favorability using 3-D twinning-based simulations in ABAQUS. Results show that the loss of coherency at the grain-oxide interface plays a crucial role in driving this phase transformation. Furthermore, the stress evolution within the oxide is found to have a negligible effect on the transformation-energy barriers. Therefore, alternate mathematical models for the periodic oxidation kinetics of Zircaloys are proposed next.

Application of Turing's pattern formation theory to oxidation-type systems: Turing's reaction-diffusion theory has provided crucial insights into the periodic behavior of various physical systems. Candidate mathematical models for Zircaloy oxidation based on the application of this theory to a moving-boundary system are proposed. These models consider two species which satisfy the Turing criteria of pattern formation, and a third species which corresponds to the oxygen ion. Model behavior shows periodic spatial distribution of the Turing species, as well as transitions in the oxidation kinetics [hence reproducing all of the prominent features of the experimental data]. An alternative preliminary oxidation model is proposed, based on the stress-dependent interaction that occurs between two immobile species: tetragonal phase of the oxide, and pores. Model predictions show a spatial periodicity in the distribution of both of these species, in addition to the transitions in the boundary kinetics, as observed experimentally.

In summary, this thesis furthers a largely experimental literature on Zircaloy oxidation with a rigorous quantitative understanding of the underlying physical mechanisms. Furthermore, to the best of our knowledge, this is the first time that mathematical models for the oxidation behavior of Zircaloys have been proposed without using the unreasonable assumption of oxide cracking.