Numerical simulation of Zener pinning with growing second-phase particles

The Zener pinning effect with growing second-phase particles in Al₂O₃-ZrO₂ composite systems were studied by two-dimensional (2-D) computer simulations using a diffuse-interface field model. In these systems, all second-phase particles are distributed at grain corners and boundaries. The second-phase particles grow continuously, and the motion of grain boundaries of the matrix phase is pinned by the second-phase particles which coarsen through the Ostwald ripening mechanism, i.e., long-range diffusion. It is shown that both matrix grains and secondphase particles grow following the power-growth law, R_t ^m - R₀ ^m = kt with m = 3. It is found that the mean size of the matrix phase (D) depends linearly on the mean size of the second-phase particles (r) for all volume fractions of second phase from 10% to 40%, which agrees well with experimental results. It is shown that D/r is proportional to the volume fraction of the second phase (f) as f ^-1/2 for a volume fraction less than 30%, which agrees with Hillert and Srolovitz's predictions for 2-D systems, while experimental results from 2-D cross sections of three-dimensional (3-D) Al₂O₃-rich systems showed that either a f ^-1/2 or a f ^-1/3 relation might be possible. It is also found that D/r is not proportional to f -1/³ and f ^-1 in 2-D simulations, which suggests that the Zener pinning effect can be very different in 2-D and 3-D systems.