Numerical Simulation of Zener Pinning with Growing Second‐Phase Particles

The Zener pinning effect with growing second‐phase particles in Al 2 O 3 ‐ZrO 2 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 second‐phase particles grow following the power‐growth law, R t m ‐ R 0 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) Al 2 O 3 ‐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.