Formation path of δ hydrides in zirconium by multiphase field modeling

Abstract

A multiphase field model is developed to study the effects of metastable ζ and γ hydrides on the nucleation and growth of the stable δ hydrides in α zirconium matrix. The model incorporates all the possible phases using the Gibbs free energies of formation for each phase and their available material properties. The multiphase field model is constructed by utilizing one conserved phase-field variable to represent the concentration of hydrogen, and six non-conserved phase-field variables to represent the α phase, ζ phase, three orientation variants of γ phase, and δ phase. The evolution equations are coupled with the mechanical equilibrium equations and solved using the Multiphysics Object Oriented Simulation Environment (MOOSE). Nucleation of hydrides is controlled using classic nucleation theory, inserting nuclei randomly with a probability dependent on the competition between the hydride's volume free energy and the interface's area free energy to form critical sized nuclei. The comparison between the results of the multiphase model and a two-phase model (without metastable phases) indicate that the intermediate phases are influential in the initial formation and evolution of δ phase hydrides. Random seed simulations, both in the basal plane and the (101¯0) plane, also indicate that the intermediate metastable phases play a key role in the shape evolution of δ hydrides. Results suggest that quantitative phase field models of δ hydride growth need to include intermediate phases in order to accurately predict the morphology of hydrides.