A quantitative phase field model for hydride precipitation in zirconium alloys: Part II. Modeling of temperature dependent hydride precipitation

A quantitative free energy functional developed in Part I (Shi and Xiao, 2014) was applied to model temperature dependent δ-hydride precipitation in zirconium in real time and real length scale. At first, the effect of external tensile load on reorientation of δ-hydrides was calibrated against experimental observations, which provides a modification factor for the strain energy in free energy formulation. Then, two types of temperature-related problems were investigated. In the first type, the effect of temperature transient was studied by cooling the Zr-H system at different cooling rates from high temperature while an external tensile stress was maintained. At the end of temperature transients, the average hydride size as a function of cooling rate was compared to experimental data. In the second type, the effect of temperature gradients was studied in a one or two dimensional temperature field. Different boundary conditions were applied. The results show that the hydride precipitation concentrated in low temperature regions and that it eventually led to the formation of hydride blisters in zirconium. A brief discussion on how to implement the hysteresis of hydrogen solid solubility on hydride precipitation and dissolution in the developed phase field scheme is also presented.