Numerical modeling of heat transfer during spark plasma sintering of titanium carbide

Spark plasma sintering (SPS) is an efficient manufacturing method especially for ultra-high temperature ceramics (UHTCs) such as titanium carbides. Heating mechanism in SPS is a result of high electric current in the device including die, punch, and sample powder. Because the temperature distribution in the sintering process has considerable effect on the microstructure of the final sintered sample, in the present work, SPS of a cylindrical sample consist of a titanium carbide was investigated numerically. The governing equations of heat diffusion and electricity distribution in the whole device was solved using finite element method. In the heat diffusion equation, heat generation per volume was considered as a result of electric current in the device. Boundary conditions including radiation heat transfer and convective cooling by water flow were modelled by Stefan-boltzman and Newton cooling laws, respectively. The maximum temperature was observed at the center of the TiC sample. The radial temperature distribution in the sample showed considerable gradient as the minimum and maximum temperatures were 2000 degrees C and 1920 degrees C, respectively. Despite the radial direction, vertical temperature gradient was negligible in TiC sintering. Although the highest current density and consequent heat generation were observed at the die/punch interface with the minimum cross section, the maximum temperature of the whole apparatus was at the punch location.