A phase-field model to study the effects of temperature change on shape evolution of γ-hydrides in zirconium

A temperature-dependent phase-field model is developed to study the effects of temperature change on shape evolution of γ-hydrides in an α-zirconium matrix. To construct the temperature-dependent free energy functional of the phase-field model, Gibbs free energies of formation from previous experiments are employed, and one conserved and three non-conserved phase-field variables are used for hydrogen concentration and hydride orientations, respectively. The mixed order evolution equations of phase-field variables coupled with mechanical equilibrium equations are solved in a finite element framework. Results from isothermal simulations of seeded and random nucleation in single crystal α-zirconium matrix show that the thickness of non-equilibrium hydrides varies with temperature during evolution, and the hydrides are more rod-like (thinner) at higher temperatures and thicker at lower temperatures. Quench simulations with random nucleation indicate that the majority of precipitation occurs at early stages of quenching, but the size and shape of hydrides change as the temperature decreases. Simulations from random nucleation of hydrides in a polycrystalline α-zirconium matrix show a higher concentration of precipitates along high angle grain boundaries.