Recent developments in applied mathematics and mechanics: theory, experiment and practice. Devoted to the 80th anniversary of academician N.N.Yanenko

Akademgorodok, Novosibirsk, Russia, June 24 - 29, 2001



Abstracts


NIS participants

Numerical analysis of technological processes with phase transitions

Leshchuk A.A., Novikov N.V.

V. Bakul Institute for Superhard Materials of the National Academy of Sciences of Ukraine (Kiev)

A numerical model of diamond synthesis process in high pressure apparatus (HPA) was developed. A complete coupled system of constitutive equations includes equations of plastic flow theory with due account of finite deformations and phase transitions, an electrical conductivity equation, an equation of nonlinear nonsteady thermal conductivity, a kinetic equation for diamond crystal growth rate, equations for carbon phase equilibrium and solvent-metal melting. The HPA reaction zone is considered as a mechanical mixture of graphite, solvent-metal and diamond, its effective properties being determined by properties and mass concentration of the components. Phase transitions are determined from the changes in properties, concentrations and abrupt changes in the region where diamond synthesis is possible. Based on the procedure developed a problem for determination of temperature, pressure and concentration fields in the reaction zone of HPA under diamond synthesis conditions is solved. Stress and temperature fields in initial state (before phase transition) were taken from the problem solution on the reaction cell compression between HPA anvils with due account of large elasto-plastic deformations of the reaction mixture and the container and from subsequent solution of a problem on the stress redistribution in electric heating of HPA.

Note. Abstracts are published in author's edition



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