Estimation of the Critical Value of the Second-Phase Particles in the Microstructure of AZ31 Mg Alloy by Phase-Field Methods

In this study, phase-field models were employed to simulate the effects of second-phase particles (SPPs) on grain growth of the AZ31 Mg alloy, under realistic spatial and temporal scales, at 350 °C, during annealing. The particle sizes ranged from 0 to 7 μm, and the particles with large volume fractions were used in the paper. The results reveal that the volume fractions and sizes of the SPP affect grain growth and that the volume fractions and sizes of the SPP on pinning exhibited critical values. When the SPP volume fraction is f = 5%, the SPP is at the maximum critical size, $r{\mathsf{\mu }\mathrm{m}}_{max}$; when the SPP size is $r=1 \mathsf{\mu }\mathrm{m}$, the SPP minimum critical volume fraction is f_min = 0.25% and the maximum critical volume fraction is f_max = 20%. The critical values increase with the increase of the sizes or volume fractions of the second-phase particles. Finally, the average grain size, particle size, and particle volume fraction obtained from the simulation were fitted according to the Zener relationship, and the obtained results showed that the fitting indices were in the range of 0.33–0.50. The results were compared with the experimental results. The simulation results obtained in this study will provide an important academic reference for understanding the mechanism and law of grain growth, an important reference for accurate control of grain size and properties of the material, a reference for the development of the annealing treatment process of Mg alloy, and a theoretical guide for the use of recrystallization process to control the microstructure of Mg alloy and improve the plastic-forming properties.