A phase field model was developed to simulate the grain refinement in solids. The model considers the interfacial energies of grain boundaries and bubble surfaces, strain energy associated with dislocations, and the chemical energy of gas atoms. This enables the model to simulate the formation and growth of sub-grains and bubbles in a self-consistent manner. The model results demonstrate strong effects of dislocation density (the magnitude and distribution), grain boundary energy, and bubble radius and number density on the formation of the sub-grains. For polycrystalline ceramic fuel UOv2 and the metallic fuel U-Mo, the model simulated the high burn-up structure (HBS) formation and evolution. In the case of UOv2, the model predicts the average size of the recrystallized grains within the range of 0.3 to 0.5 microns corresponding to a dislocation density range of ? = (2.5'10^15 - 2.65'10^15) m-^2 or equivalently to 70 - 75 GWd/tHM burn-up. For the metallic fuel U-Mo, the HBS was determined to extend within a fission density range of 5.5'10^21 fission/cm^3 or equivalent to approximately 120 GWd/tHM. The corresponding U-Mo newly recrystallized average sub-grain size was concluded to be similar to the UOv2 case. These predictions agree with the reported data in the literature.
