Finite element modeling of spark plasma sintering: Application to the reduction of temperature inhomogeneities, case of alumina Youssef Achenani a, ⁎, Malika Saâdaoui a, ⁎, Abdelkhalek Cheddadi a , Guillaume Bonnefont b , Gilbert Fantozzi b a Mohammed V University in Rabat, Mohammadia School of Engineers, P.O. Box 765, Agdal, Rabat, Morocco b Lyon University, MATEIS, UMR 5510 CNRS, National Institute of Applied Sciences of Lyon, Avenue Jean Capelle, F-69621 Villeurbanne Cedex, France abstract article info Article history: Received 2 August 2016 Received in revised form 16 December 2016 Accepted 19 December 2016 Available online 21 December 2016 Increasing attention is being paid to numerical modeling of spark plasma sintering (SPS) due to its significant im- portance for the comprehension and the optimization of this process. In this study, SPS sintering experiments of alumina were performed and their results were used to develop faithful simulations of the temperature distribu- tion, based on a thermal-electrical finite element model. Particular focus was put on the axial temperature distri- bution within the sample, rarely considered in the literature. The model was used to analyze the influence of various experimental parameters potentially affecting the temperature distribution (axial asymmetry, die loca- tion and insulation) and simple methods, based on the die location andits insulation, are proposed to reduce the temperature inhomogeneities in the sample. © 2016 Elsevier Ltd. All rights reserved. Keywords: Spark plasma sintering Finite element modeling Temperature distribution Die location Die insulation 1. Introduction Spark Plasma Sintering (SPS) is a consolidation process based on Joule heating by the application of a pulsed electrical current to a graph- ite die containing the material powder. Compared to other conventional sintering methods, SPS offers exceptional benefits, including rapid heating rate and reduced sintering temperature and holding time, which allow to avoid grain growth and to improve mechanical or phys- ical properties of the final products. So that, increasing attention is paid to this technique, which has been applied to a variety of advanced ma- terials in a wide range of application fields [1–3]. The sample temperature is of particular importance to the SPS pro- cess, since it determines the structure and properties of the material and their homogeneity. However, it is difficult to control due to inherent experimental difficulties and the large number of the involved parame- ters. In recent years, finite element modeling with consideration of the coupled phenomena involved during SPS sintering played a crucial role in understanding this process. Most of the models considered ther- moelectric coupling [4–7] to determine electrical and temperature fields. Some works integrated mechanical coupling to investigate stress distribution as in [8–12], or a densification model [13–18]. A complex temperature distribution within the tools and the sample has been evidenced, with temperature gradients depending on process parameters such as the heating rate [15,19–21], geometrical aspects of the sample and tools [6,7,15,18,22] and thermophysical parameters, es- pecially material conductivity [3,10,22,23]. A parametric analysis of Muñoz et al. [21] highlighted the difficulty to predict the effect of one parameter independently of the others. However, most of the numerical studies lack of experimental validation and their accuracy depend on the simplifying assumptions related to the device parts taken into ac- count, power or heating conditions, and contact resistances between the graphite tools and between the punches and the sample. Anselmi- Tamburini et al. [24] and Cincotti et al. [25] highlighted the importance of considering the RMS (Root Mean Squared) value of the pulsed cur- rent input to determine the Joule effects. Whereas the first simulations considered a constant applied electric potential or current, Muñoz and Anselmi-Tamburini [10] and Wang et al. [15] introduced a Proportion- al-Integral-Differential (PID) module for better reproduction of the ex- perimental thermal sintering cycle. Moreover, the contact resistances have often been neglected in numerical modeling. Few authors devel- oped calibration or experimental methods to determine them [14,26– 30]. Vertical contact resistances are much larger than horizontal ones [14,26,27] and the influence of the applied pressure has been outlined in [24,29,31,32]. In general, symmetrical thermal boundary conditions are used and the axial temperature distribution within the sample has been barely in- vestigated. In this study, standard sintering experiments were per- formed with alumina, chosen as a model for non-conductive materials, and their results were used to develop faithful simulations with limited approximations. The influence of various experimental pa- rameters on both radial and axial temperature distributions was then investigated, and simple methods based on the die location and its Materials and Design 116 (2017) 504–514 ⁎ Corresponding authors. E-mail addresses: achenaniyoussef@yahoo.fr (Y. Achenani), saadaoui@emi.ac.ma (M. Saâdaoui). http://dx.doi.org/10.1016/j.matdes.2016.12.054 0264-1275/© 2016 Elsevier Ltd. All rights reserved. Contents lists available at ScienceDirect Materials and Design journal homepage: www.elsevier.com/locate/matdes