Temperature effect on the evolution of hydrides in zirconium

Abstract

Phase field equations considering thermal effect are developed through the theoretical analysis. Some simplifications are made based on the apprehension of phase field theory. Finite element method (FEM) and Finite difference method (FDM) are used to solve the partial differential equation (PDE), which describe hydride embrittlement phenomenon through phase field method. In this work, constitutive equations including the chemical effect, the gradient effect, the elastic effect as well as the thermal effect are developed. The effect of elasticity and temperature gradient is focused based on the previous researches. The results of simulation demonstrate that the codes based on COMSOL can be applied to the investigation of phase transformation, although the calculation is dependent on many factors, such as size of mesh grid, length of time step, values of the phase field parameters. In addition, general calculations through FDM involving the influence of 1D and 2D temperature gradients show that temperature field has great effect on the evolution of hydrides. Hydrides will form at low temperature regions due to thermal drift effect. Finally, quantitative calculations are conducted to provide real scale analysis.