Finite element simulation of disk-shaped HfB₂ ceramics during spark plasma sintering process

Spark plasma sintering is an interesting manufacturing method, which benefits electric current heating. In the present study, the sintering process of hafnium diboride (HfB₂₎ ceramics was simulated using the finite element method. The governing equations of electric potential, current conservation, and energy conservation were solved using COMSOL Multiphysics software. The electric potential of the whole system versus time and current distribution at different time steps were obtained. The heat generation was calculated using the Joule heating effect, and the needed temperature for sintering was obtained. The required temperature for process progression was 2100°C that achieved after 1380 s. Moreover, the maximum electric current was 5942.863 A, which remained constant until the end of the operation. Since HfB₂ is an electrical conductor, the current easily passed through the sample with an approximately uniform distribution. To provide a better understanding of the sintering mechanisms, an electrically resistive material (Al₂O₃) was also simulated. The results showed a more uniform current distribution in HfB₂ compared to Al₂O₃. It was observed that the needed temperature for sintering of alumina was obtained only by heat conduction from graphite die toward the sample, whereas HfB₂ benefited both mechanisms of heat conduction and Joule heating inside the sample.