Modeling and Experimental Study of Pyroplastic Deformation for Ceramic Materials during Liquid Phase Sintering Process


1 Ceramic, Ceramic

2 , Materials and Energy Research Center (MERC)

3 Dear Editorial Board: Enclosed is a manuscript to, Dear Editorial Board: Enclosed is a manuscript to


The effective shear and bulk viscosity, as well as dynamic viscosity, describe the rheological properties of the ceramic body during the liquid phase sintering process. The rheological parameters depend on the physical and thermo-mechanical characteristics of the material such as relative density, temperature, grain size, diffusion coefficient, and activation energy. Thermal behavior of the ceramic body during sintering process including the viscose flow deformation, anisotropic shrinkage, heterogeneous densification, as well as sintering stress, have significant influence on the both final body dimensional precision and densification process. In this paper, the numerical-experimental method has been developed to study both rheological and thermal behavior of hard porcelain ceramic body during liquid phase sintering process. After raw materials analysis, the standard hard porcelain mixture as a ceramic body was designed and prepared. The finite element method for the ceramic specimens during the liquid phase sintering process are implemented in the CREEP user subroutine code in ABAQUS. Densification results confirmed that the bulk viscosity was well-defined with relative density. It has been shown that the shrinkage along the normal axis of slip casting is about 1.5 times larger than that of casting direction. The stress analysis proved that the sintering stress is more than the hydrostatic stress during the entire sintering time so, the sintering process occurs completely. The inhomogeneity in Von-Misses, pressure, and principal stress intensifies the relative density non-uniformity. Dilatometry, SEM, XRD investigations as well as bulk viscosity simulation results confirmed that the “mullitisation plateau” was presented as a very little expansion at the final sintering stage, because of the highly amount of mullite formation.


1. Blaine, D.C., German, R.M. and Park, S.J., "Computer modeling of distortion and densification during LPS of highperformance materials", Proceedings of the International Conference on Powder Metallurgy and Particulate Materials, Metal Powder Industries Federation, Vol. 1, (2005), 29-37.

2. Gasik, M. and Zhang, B., "A constitutive model and FE simulation for the sintering process of powder compacts", Computational Material Science, Vol. 18, (2000), 93-101.

3. Molla, T.T., Bjqrk, R and Olevsky, E., "Multi-scale modeling of shape distortion during sintering of bi-layers", Computational Materials Science, Vol. 88, (2014), 28-36.

4. Bene, P. and Bardaro, D., "Numerical-experimental method to study the viscous behavior of ceramic materials", Journal of the European Ceramic Society, Vol. 34, (2014), 2617-2622.

5. Sarbandi, B., Finite element simulation of ceramic deformation during sintering, Ph.D. thesis, Paris Institute of Technology, Mechanics of materials, (2014).

6. Blaine, D., Chung, S.H., Park, S.J., Suri, P. and German, R.M., "Finite Element Simulation of Sintering Shrinkage and Distortion in Large PIM Parts", PM Science and Technology Briefs, Vol. 6., No. 2., (2004), 13-18.

7. Blaine, D.C. and German, R.M., Sintering simulation of PIM stainless steel, International Conference on the Powder Injection Molding of Metals, Ceramics, and Carbides, San Diego, CA, (2002).

8. Mitsoulis, E., Flows of Viscoplastic Materials: Modeling and Computations, Rheology reviews, (2007).

9. Andreev, D.V. and Zakharov, A.I., "Ceramic Item Deformation during Firing: Effects of Composition and Microstructure", Refractory and Industrial Ceramics, Vol. 50, No. 4, (2009), 45-52.

10. Tuncel, D.Y. and Ozel, E., "Evaluation of pyroplastic deformation in sanitary ware porcelain bodies", Ceramics International, Vol. 38, (2012), 1399-1407.

11. Bernardin, A.M., Medeiros, D.S. and Riella, H.G., "Pyroplasticity in porcelain tiles", Material Science and Engineering A, Vol. 427, (2006), 316-319.

12. Dellert, A., Heunisch, A. and Roosen, A., "The origin of anisotropic shrinkage in tape-cast green tapes", International Journal of Applied Ceramic Technology, Vol. 8, No. 6, (2011), 1312-1319.

13. Sighinolfi, D., "Experimental study of deformations and state of tension in traditional ceramic materials", Ceramic Materials, Vol. 63, No. 2, (2011), 226-232.

14. Martina, S., Guessasma, M., Lechella, J. and Adenota, F. "Simulation of sintering using a non-smooth discrete element method. Application to the study of rearrangement", Computational Materials Science, Vol. 84, (2014), 31-39.

15. Blaine, D.C., Bollina, R. and German, R.M., "Critical use of video-imaging to rationalize computer sintering simulation models", Computer in Industry, Vol. 56, (2005), 867-875.

16. Olevsky, E.A., "Theory of Sintering: from Discrete to Continuum", Materials Science and Engineering, Vol. 23, (1998), 41-100.

17. Arguello, J.G., Tikare, V., Garino, T.J. and Braginsky, M.V., Three-Dimensional simulation of sintering using a continuum modeling approach, Sandia National Laboratories, Chapter 5, (2003).

18. Olevsky, E.A. and German, R.M., "Effect of gravity on dimentional shange during sintering –part two. Shape distortion", Acta Materialia, Vol. 48, (2000), 1167-1180.

19. Shinagawa, K. and Hirashima, Y. "A Constitutive Model for Sintering of Central Powder Compacts with Internal Structure due to Granules", Transactions of the Japan Society of Mechanical Engineers, Vol. 64, No. 617, (1998), 155-161.

20. Shinagawa, K., "Internal Stress Diagrams of Sintering Stress versus Viscosity for Graded Multilayers", JSME International Journal, Vol. 46, No. 3, (2003), 378-383.

21. Mohanram, A., Lee, S., Messing, G. and Green, D., "A novel use of constrained sintering to determine the viscous Poisson’s ratio of densifying materials", Acta Materialia, Vol. 53, (2005), 2413-2418.

22. German, R.M., Chung, S-H. and Blaine, D., "Distortion and Densification Control during Liquid Phase Sintering of High-Performance aterials", Proceedings of 8th International Conference on Numerical Methods in Industrial Forming Processes, Columbus, OH, (2004).

23. Zuo, R., Aulbach, E. and Rodel, J., "Experimental determination of sintering stresses and sintering viscosities", Acta Materialia, Vol. 51, (2003), 4563-4574.

24. Theron, C., Determination of sintering parameters for liquid phase sintering of silicon nitride, Ph.D. thesis, State University of New Jersy, (2008).

25. Tomandl, G. and Varkoly, P., "Three-dimensional computer modeling of grain growth and pore shrinkage during sintering", Materials Chemistry and Physics, Vol. 67, (2001), 12-16.

26. Shima, S. and Oyane, M., "Plasticity theory for porous metals", International Journal of Mechanical Sciences, Vol. 18, (1976), 285-291.

27. Lutgard, C., Jonghe, D. and Rahman, M.N., Sintering of ceramic, Handbook of Advanced Ceramics, Chapter 4, (2003).

28. Blaine, D.C., Bollina, R. and German, R.M., In situ characterization of apparent viscosity for continuum modeling of supersolidus liquid phase sintering, Proceedings of the 4th International Conference on Science, Technology and Applications of Sintering, Institute National Polytechnique de Grenoble, Grenoble, France, (2005).

29. Lee, S., Messing, G. and Green, D., "Bending creep test to measure the viscosity of porous materials during sintering", Journal of American Ceramic Society, Vol. 86, (2003), 877- 882.

30. Porte, F., Brydson, R. and Rand, B., "Creep Viscosity of Vitreous China", Journal of American Ceramic Society, Vol. 87, (2004), 923-928.

31. Zanelli, C., Guarini, G., Raimondo, M. and Dondi, M., "The vitreous phase of porcelain stoneware: composition, evolution during sintering and physical properties", Journal of Non- Crystalline Solids, Vol. 357, (2011), 3251-3260.

32. Cheng, B. and Ngan, A.H.W., "The sintering and densification behavior of many copper nanoparticles: A molecular dynamics

study", Computational Materials Science, Vol. 74, (2013), 1- 11.

33. Fu, Z., Polfer, P., Kraft, T. and Roosen, A., "Correlation between anisotropic green microstructure of spherical-shaped alumina particles and their shrinkage behavior", Journal of American Ceramic Society, Vol. 98, 11, (2015), 3438-3444.

34. Yaghoubi, H., Salahi, E. and Taati, F., "Evaluation of dynamic viscosity and rheological properties of ceramic materials during liquid phase sintering by numerical-experimental procedure", International Journal of Applied Ceramic Technology, Vol. 14, (2017), 1222–1235.