Spark plasma sintering of zirconium carbide and oxycarbide: Finite element modeling of current density, temperature, and stress distributions

A combined experimental/numerical approach was developed to determine the distribution of current density, temperature, and stress arising within the sample during spark plasma sintering (SPS) treatment of zirconium carbide (ZrCx) or oxycarbide (ZrCxOy). Stress distribution was calculated by using a numerical thermomechanical model, assuming that a slip without mechanical friction exists at the interfaces between the sample and the graphite elements. Heating up to 1950 degrees C at 100 degrees C min(-1) and a constant applied pressure of 100 MPa were retained as process conditions. Simulated temperature distributions were found to be in excellent agreement with those measured experimentally. The numerical model confirms that, during the zirconium oxycarbide sintering, the temperature measured by the pyrometer on the die surface largely underestimates the actual temperature of the sample. This real temperature is in fact near the optimized sintering temperature for hot-pressed zirconium oxycarbide specimens. It is also shown that high stress gradients existing within the sample are much higher than the thermal ones. The amplitude of the stress gradients was found to be correlated with those of temperature even if they are also influenced by the macroscopic sample properties (coefficient of thermal expansion and elastic modulus). At high temperature, the radial and angular stresses, which are much higher than the vertical applied stress, provide the more significant contribution to the stress-related driving force for densification during the SPS treatment. The heat lost by radiation toward the wall chambers controlled both the thermal and stress gradients.