Numerical modelling of Spark Plasma Sintering (SPS) processes is essential to evaluate temperature and stress distributions that can result in sample inhomogeneities. Most of the available literature, however, produced analysis in static conditions. In this work, we focused our attention on the time evolution of current density, temperature and stress distribution during a SPS process using a new approach that includes a PID control in the algorithm, allowing a realistic simulation of experiments performed using a temperature controller. Controlled temperature experiments have been simulated and discussed, with special interest focused on the time evolution of the process. The results showed that stress gradients inside the samples (~40%) are much greater than the temperature gradients (~2%), suggesting that heterogeneities in the microstructure can also be caused by the stress gradient. During the evolution of the process, a peak in stresses is experienced by the alumina sample at the beginning of the cooling stage, caused by differences in contraction between the sample and the die. It has been proved that, using a controlled cooling stage, these peaks in the stresses can be easily eliminated.
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The authors would like to thank T. Holland at the Department of Chemical Engineering and Materials Science at UC Davis for performing the SPS experiments. The first author would like to acknowledge the mobility grant from the “José Castillejo” program, and the financial support from the FEDER/MEC, Madrid (Project MAT2007-61643).