Modeling of SPS apparatus:: Temperature, current and strain distribution with no powders

The mathematical simulation of the spark plasma sintering/synthesis (SPS) apparatus, which represents an effective tool for sintering/synthesizing advanced materials, is addressed. Because several, concomitant physicochemical phenomena-such as heat transfer and generation, electric current transport, and stress-strain mechanics along with chemical transformation and sintering-take place during SPS processes, a step-by-step heuristic procedure is proposed for successful quantitative modeling purposes. First, in this work we consider the SPS behavior of specific sample configurations characterized by the absence of powders. This approach permits detailed analysis of the system from the perspective of electric phenomena. The inductive character is carefully described and properly taken into account when comparing experimental data with model results. The importance of considering rms (root mean squared) electric current for a quantitative determination of the Joule effect is highlighted. Moreover, this approach allows one to determine the electric and thermal resistances experimentally evidenced in the horizontal contacts between stainless steel electrodes and graphite spacers as functions of temperature and applied mechanical load. Horizontal contact resistances between graphite elements are experimentally found to be negligible and, accordingly, they are not modeled. Model reliability is tested by comparing numerical simulations with experimental data obtained at operating conditions far from those adopted during the fitting procedure of unknown parameters. The proposed model can be successfully compared from a quantitative perspective to the measured temperature, voltage, and displacement, once rms current, geometry, and mechanical load are set.