Numerical optimization of sample and die geometric parameters to increase the attainable temperature during spark plasma sintering of TiC ceramics

  • Saeed Mohammad Bagheri 1
  • Mohsen Naderi 1
  • Mohammad Vajdi 1
  • Farhad Sadegh Moghanlou 1
  • Ali Tarlani Beris 2
  • 1 Department of Mechanical Engineering, University of Mohaghegh Ardabili, Ardabil, Iran
  • 2 Department of Mechanical Engineering, College of Engineering, Boston University, Boston, USA


The present study offers a comprehensive thermal modeling of spark plasma sintering (SPS) for a titanium carbide (TiC) sample. Utilizing COMSOL Multiphysics Software, the research investigates the temperature distribution within the TiC sample, situated within a graphite die. The study employs governing equations for heat diffusion, augmented by terms accounting for Joule heating, to calculate temperature variations. Boundary conditions, particularly at the upper and lower limits of the system, are explicitly accounted for, with cooling mechanisms modeled as convection. Through the application of the Taguchi method and Analysis of Variance (ANOVA), the study identifies the diameter of the sintering sample as the most significant parameter affecting the maximum temperature at the center of the TiC sample, with a significance of about 87%. The outer diameter of the graphite die followed with a significance of slightly more than 10%, and the thickness of the TiC sample had a significance of around 2%. The findings contribute to a nuanced understanding of the SPS process, offering valuable insights for optimizing the sintering parameters. Numerical results further underscore the importance of specific geometric parameters in the SPS process. This study serves as a robust foundation for future research aimed at refining the SPS process for TiC samples and other materials.


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Keywords: Titanium carbide, Spark plasma sintering, Taguchi method, Numerical analysis, Temperature distribution


[1] W.G. Fahrenholtz, G.E. Hilmas, Ultra-high temperature ceramics: Materials for extreme environments, Scr. Mater. 129 (2017) 94–99.
[2] B.R. Golla, A. Mukhopadhyay, B. Basu, S.K. Thimmappa, Review on ultra-high temperature boride ceramics, Prog. Mater. Sci. 111 (2020) 100651.
[3] J.-F. Justin, A. Julian-Jankowiak, V. Guérineau, V. Mathivet, A. Debarre, Ultra-high temperature ceramics developments for hypersonic applications, CEAS Aeronaut. J. 11 (2020) 651–664.
[4] M. Sakkaki, S.M. Arab, In-situ synthesized phases during the spark plasma sintering of g-C3N4 added TiB2 ceramics: A thermodynamic approach, Synth. Sinter. 3 (2023) 73–78.
[5] S. Tang, C. Hu, Design, preparation and properties of carbon fiber reinforced ultra-high temperature ceramic composites for aerospace applications: A review, J. Mater. Sci. Technol. 33 (2017) 117–130.
[6] R. Orrù, G. Cao, Comparison of reactive and non-reactive spark plasma sintering routes for the fabrication of monolithic and composite ultra high temperature ceramics (UHTC) materials, Materials (Basel). 6 (2013) 1566–1583.
[7] W.R. Matizamhuka, Spark plasma sintering (SPS) - an advanced sintering technique for structural nanocomposite materials, J. South. Afr. Inst. Min. Metall. 116 (2016) 1171–1180.
[8] S.-X. Song, Z. Wang, G.-P. Shi, Heating mechanism of spark plasma sintering, Ceram. Int. 39 (2013) 1393–1396.
[9] M. Shahedi Asl, Z. Ahmadi, S. Parvizi, Z. Balak, I. Farahbakhsh, Contribution of SiC particle size and spark plasma sintering conditions on grain growth and hardness of TiB2 composites, Ceram. Int. 43 (2017) 13924–13931.
[10] X.C. Zhong, S.M. Wu, X.T. Dong, Y.X. Li, J.H. Huang, et al., High density La-Fe-Si based magnetocaloric composites with excellent properties produced by spark plasma sintering, Mater. Sci. Eng. B. 280 (2022) 115717.
[11] M. Tokita, Progress of spark plasma sintering (SPS) method, systems, ceramics applications and industrialization, Ceramics. 4 (2021) 160–198.
[12] A.D. Preston, K. Ma, Effect of powder morphology on the microstructure and mechanical property gradients in stainless steels induced by thermal gradients in spark plasma sintering, MRS Adv. 6 (2021) 482–488.
[13] W. Weifeng, X. Kuangdi, Spark plasma sintering, The ECPH Encyclopedia of Mining and Metallurgy, Springer Nature Singapore, Singapore. (2023) 1–2.
[14] J. Diatta, G. Antou, N. Pradeilles, A. Maître, Numerical modeling of spark plasma sintering—Discussion on densification mechanism identification and generated porosity gradients, J. Eur. Ceram. Soc. 37 (2017) 4849–4860.
[15] M. Fattahi, M. Najafi Ershadi, M. Vajdi, F. Sadegh Moghanlou, A. Sabahi Namini, M. Shahedi Asl, On the simulation of spark plasma sintered TiB2 ultra high temperature ceramics: A numerical approach, Ceram. Int. 46 (2020) 14787–14795.
[16] X.Y. Li, Z.H. Zhang, X.W. Cheng, G.J. Huo, S.Z. Zhang, Q. Song, The development and application of spark plasma sintering technique in advanced metal structure materials: A review, Powder Metall. Met. Ceram. 60 (2021) 410–438.
[17] P. Cavaliere, B. Sadeghi, A. Shabani, Spark plasma sintering: process fundamentals, in: Spark Plasma Sinter. Mater., Springer International Publishing, Cham. (2019) 3–20.
[18] A. Cincotti, A.M. Locci, R. Orrù, G. Cao, Modeling of SPS apparatus: Temperature, current and strain distribution with no powders, AIChE J. 53 (2007) 703–719.
[19] E.A. Olevsky, C. Garcia‐Cardona, W.L. Bradbury, C.D. Haines, D.G. Martin, D. Kapoor, Fundamental aspects of spark plasma sintering: II. finite element analysis of scalability, J. Am. Ceram. Soc. 95 (2012) 2414–2422.
[20] L. Cheng, Z. Xie, G. Liu, W. Liu, W. Xue, Densification and mechanical properties of TiC by SPS-effects of holding time, sintering temperature and pressure condition, J. Eur. Ceram. Soc. 32 (2012) 3399–3406.
[21] A. Babapoor, M. Shahedi Asl, Z. Ahmadi, A.S. Namini, Effects of spark plasma sintering temperature on densification, hardness and thermal conductivity of titanium carbide, Ceram. Int. 44 (2018) 14541–14546.
[22] D. Garbiec, V. Leshchynsky, A. García-Junceda, R. Swadźba, P. Siwak, et al., Microstructure and mechanical properties of spark plasma sintered and severely deformed AA7075 alloy, Metals (Basel). 11 (2021) 1433.
[23] S. Jafargholinejad, S. Soleymani, Effects of carbon nano-additives on characteristics of TiC ceramics prepared by field-assisted sintering, Synth. Sinter. 1 (2021) 62–68.
[24] A. Sabahi Namini, Z. Ahmadi, A. Babapoor, M. Shokouhimehr, M. Shahedi Asl, Microstructure and thermomechanical characteristics of spark plasma sintered TiC ceramics doped with nano-sized WC, Ceram. Int. 45 (2019) 2153–2160.
[25] M. Naderi, M. Vajdi, F. Sadegh Moghanlou, H. Nami, Sensitivity analysis of fluid flow parameters on the performance of fully dense ZrB2-made micro heat exchangers, Synth. Sinter. 3 (2023) 88–106.
[26] M. Naderi, M. Vajdi, F. Sadegh Moghanlou, H. Nami, Numerical assessment of ceramic micro heat exchangers working with nanofluids by Taguchi optimization approach, Synth. Sinter. 3 (2023) 166–178.
[27] N.J. Rathod, M.K. Chopra, U.S. Vidhate, N.B. Gurule, U.V. Saindane, Investigation on the turning process parameters for tool life and production time using Taguchi analysis, Mater. Today Proc. 47 (2021) 5830–5835.
[28] S. Mohammad Bagheri, M. Vajdi, F. Sadegh Moghanlou, M. Sakkaki, M. Mohammadi, et al., Numerical modeling of heat transfer during spark plasma sintering of titanium carbide, Ceram. Int. 46 (2020) 7615–7624.
[29] M. Sakkaki, F. Sadegh Moghanlou, M. Vajdi, M. Shahedi Asl, M. Mohammadi, M. Shokouhimehr, Numerical simulation of heat transfer during spark plasma sintering of zirconium diboride, Ceram. Int. 46 (2020) 4998–5007.
[30] A. Pavia, L. Durand, F. Ajustron, V. Bley, G. Chevallier, et al., Electro-thermal measurements and finite element method simulations of a spark plasma sintering device, J. Mater. Process. Technol. 213 (2013) 1327–1336.
[31] G. Molénat, L. Durand, J. Galy, A. Couret, Temperature control in spark plasma sintering: an FEM approach, J. Metall. 2010 (2010) 1–9.
[32] C. Manière, A. Pavia, L. Durand, G. Chevallier, K. Afanga, C. Estournès, Finite-element modeling of the electro-thermal contacts in the spark plasma sintering process, J. Eur. Ceram. Soc. 36 (2016) 741–748.
[33] M. Le Flem, A. Allemand, S. Urvoy, D. Cédat, C. Rey, Microstructure and thermal conductivity of Mo–TiC cermets processed by hot isostatic pressing, J. Nucl. Mater. 380 (2008) 85–92.
[34] N. Durlu, Titanium carbide based composites for high temperature applications, J. Eur. Ceram. Soc. 19 (1999) 2415–2419.
[35] W.S. Williams, The thermal conductivity of metallic ceramics, JOM. 50 (1998) 62–66.

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Numerical optimization of sample and die geometric parameters to increase the attainable temperature during spark plasma sintering of TiC ceramics
How to Cite
Mohammad Bagheri, S., Naderi, M., Vajdi, M., Sadegh Moghanlou, F., & Tarlani Beris, A. (2023). Numerical optimization of sample and die geometric parameters to increase the attainable temperature during spark plasma sintering of TiC ceramics. Synthesis and Sintering, 3(4), 213-225.

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