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.
References
Ya. E. Geguzin, Physics of Sintering [in Russian], Nauka, Moscow (1967).
V. V. Skorokhod, Rheological Bases of Sintering Theory [in Russian], Naukova Dumka, Kiev (1972).
Ya. I. Frenkel’, “Viscous flow of crystalline bodies under the action of surface tension,” Fiz. Zh., 9, 385–391 (1945).
G. C. Kuczinski, “Self-diffusion in sintering of metallic particles,” Trans. Amer. Inst. Min. Met. Eng., 185, 169–178 (1949).
M. F. Ashby, “ Afirst report on sintering diagrams,” Acta Metall., 22, 278–289 (1974).
F. B. Swinkels and M. F. Ashby, “A second report on sintering diagrams,” Acta Metall., 29, 259–281 (1981).
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).
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).
E. A. Nichols, “The sintering of wires by surface diffusion,” Acta Metall., 16, 103–113 (1968).
J.W. Ross,W. A. Miller, and G. C.Weatherley, “Dynamic computer simulation of viscous flow sintering,” J. Appl. Phys., 52, 3644–3668 (1981).
A. Jagota and P. W. Dawson, “Micromechanical modelling of powder compacts. II. Truss formulation of discrete packing,” Acta Metall., 36, 2563–2873 (1988).
M. P. Anderson, D. J. Srolovitz, G. S. Grest, et al., “Computer simulation of grain growth,” Acta Metall., 32, 783–791 (1984).
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).
H. Matsabura, “Computer simulation studies of sintering and grain growth,” J. Ceram. Soc. Jap., 115, 263–268 (2005).
N. Brebbiya and S. Warner, Application of the Boundary Element Method [Russian translation], Mir, Moscow 91982).
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).
P. Nicolopoulus, “Surface, grain boundary and interfacial energies in Al2O3 and Al2O3–Sn, Al2O3-Co systems,” J. Mater. Sci., 20, 3993–4000 (1985).
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).
K. E. Easterling, “Electron microscopy study of stresses of contacts between sintered aluminum particles,” Int. J. Powd. Met., 7, 29–37 (1971).
R. L. Coble, “Effects of particle size distribution in initial stage sintering,” J. Amer. Ceram. Soc., 56, 461–466 (1973).
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).
Author information
Authors and Affiliations
Additional information
Translated from Novye Ogneupory, No. 5 pp. 30–37, May 2009.
Rights and permissions
About this article
Cite this article
Galakhov, A.V. Numerical method for simulating sintering. Refract Ind Ceram 50, 191–197 (2009). https://doi.org/10.1007/s11148-009-9170-3
Received:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11148-009-9170-3