Numerical method for simulating sintering

  • A. V. Galakhov
Scientific Research and Development

A numerical method is proposed in order to simulate sintering, based on fundamental equations of diffusion theory (Fick equation). The method makes it possible to consider actual geometry of particles from which a powder compact is composed, and it may be used for an assembly of particles of another shape, dimensions and reciprocal position. A boundary element method is used for numerical realization. Results are presented for simulating sintering of Al2O3 particles of different shape and sizes. Dependences are presented for the effect of different material characteristics, in particular dihedral angle (it specifies the relationship of free surface energy and intergranular boundary energy), on sintering kinetics and the value of intergranular boundary achieved.


sintering simulation boundary element method dihedral angle 


  1. 1.
    Ya. E. Geguzin, Physics of Sintering [in Russian], Nauka, Moscow (1967).Google Scholar
  2. 2.
    V. V. Skorokhod, Rheological Bases of Sintering Theory [in Russian], Naukova Dumka, Kiev (1972).Google Scholar
  3. 3.
    Ya. I. Frenkel’, “Viscous flow of crystalline bodies under the action of surface tension,” Fiz. Zh., 9, 385–391 (1945).Google Scholar
  4. 4.
    G. C. Kuczinski, “Self-diffusion in sintering of metallic particles,” Trans. Amer. Inst. Min. Met. Eng., 185, 169–178 (1949).Google Scholar
  5. 5.
    M. F. Ashby, “ Afirst report on sintering diagrams,” Acta Metall., 22, 278–289 (1974).Google Scholar
  6. 6.
    F. B. Swinkels and M. F. Ashby, “A second report on sintering diagrams,” Acta Metall., 29, 259–281 (1981).CrossRefGoogle Scholar
  7. 7.
    A. V. Galakhov and E. V. Tsibailo, “Inhomogeneity of powder packing in compacts and the strength of ceramics prepared from them,” Ogneupory. Tekhn. Keram., No. 5, 14–19 (1997).Google Scholar
  8. 8.
    J. Ma and L. C. Lim, “Effect of particle size distribution on sintering of agglomerate-free submicron alumina powder compacts,” J. Eur. Ceram. Soc., 22, 2197–2208 (2008).CrossRefGoogle Scholar
  9. 9.
    E. A. Nichols, “The sintering of wires by surface diffusion,” Acta Metall., 16, 103–113 (1968).CrossRefGoogle Scholar
  10. 10.
    J.W. Ross,W. A. Miller, and G. C.Weatherley, “Dynamic computer simulation of viscous flow sintering,” J. Appl. Phys., 52, 3644–3668 (1981).Google Scholar
  11. 11.
    A. Jagota and P. W. Dawson, “Micromechanical modelling of powder compacts. II. Truss formulation of discrete packing,” Acta Metall., 36, 2563–2873 (1988).CrossRefGoogle Scholar
  12. 12.
    M. P. Anderson, D. J. Srolovitz, G. S. Grest, et al., “Computer simulation of grain growth,” Acta Metall., 32, 783–791 (1984).CrossRefGoogle Scholar
  13. 13.
    G. N. Hassold, I. Chen, and D. J. Srolovitz, “Computer simulation of fine-state sintering. I. Model, kinetics and microstructure,” J. Amer. Ceram. Soc., 73, 2857–2864 (1990).CrossRefGoogle Scholar
  14. 14.
    H. Matsabura, “Computer simulation studies of sintering and grain growth,” J. Ceram. Soc. Jap., 115, 263–268 (2005).CrossRefGoogle Scholar
  15. 15.
    N. Brebbiya and S. Warner, Application of the Boundary Element Method [Russian translation], Mir, Moscow 91982).Google Scholar
  16. 16.
    J. M. Dynys, R. V. Coble and W. S. Coblenz, “Mechanisms of atom transport during initial stage sintering of Al2O3,” Mat. Sci. Res., 13, 391–404 (1979).Google Scholar
  17. 17.
    P. Nicolopoulus, “Surface, grain boundary and interfacial energies in Al2O3 and Al2O3–Sn, Al2O3-Co systems,” J. Mater. Sci., 20, 3993–4000 (1985).CrossRefADSGoogle Scholar
  18. 18.
    C. A. Hnadwerker, J. N. Dynys, R. M. Cannon, et al., “Dihedral angles in magnesia and alumina,” J. Amer. Ceram. Soc., 73, 1371–1377 (1990).CrossRefGoogle Scholar
  19. 19.
    K. E. Easterling, “Electron microscopy study of stresses of contacts between sintered aluminum particles,” Int. J. Powd. Met., 7, 29–37 (1971).Google Scholar
  20. 20.
    R. L. Coble, “Effects of particle size distribution in initial stage sintering,” J. Amer. Ceram. Soc., 56, 461–466 (1973).CrossRefGoogle Scholar
  21. 21.
    B. J. Kellett and F. F. Lange, “Thermodynamics of densification: I. Sintering of simple particle arrays, equilibrium configurations, pore stability and shrinkage,” J. Amer. Ceram. Soc., 72, 725–734 (1989).CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media, Inc. 2009

Authors and Affiliations

  • A. V. Galakhov
    • 1
  1. 1.A. A. Baikov Institute of Metallurgy and Materials ScienceRussian Academy of SciencesMoscowRussia

Personalised recommendations