Mathematical Modelling of the Sintering Process of Iron-Based Metal-Glass Materials

Abstract

Based on the study of the mechanisms of diffuse coalescence and coagulation, we review mathematical methods of description and construction of models for sintering process of the metal–ceramic materials. These models are represented by a set of nonlinear differential equations including bulk, grain-boundary, and surface diffusion coefficients, and correspond to a sequence of the temperature stage levels increasing with a certain rate and having different durations. By adjusting the levels, rates and durations of temperature regimes, technical parameters of the charge, it is possible to control the sintering process online. The description of the kinetics of liquid-phase sintering under pressure is performed based on the rheological theory of sintering using the diffusion–viscous flow mechanism. According to this mechanism, there are a tangential slippage along the grain boundaries and a decrease of the volume of pores due to the ejection of vacancies to the surface. After the formation of the liquid phase during sintering of the powder solid, (generally) firstly, there is a growth of grains, and then, a compaction of the obtained alloy. The process of sintering of the iron, cast iron, and sitall (glassceramic) powders is considered as the mutual diffusion of two (quasi)binary alloys: cast iron (iron + carbon) and fayalite (iron + sitall). The calculation of the interdiffusion coefficient of the resulting alloy is carried out according to the Darken formula. A number of features characterize sintering of multicomponent systems. The sintering of dissimilar materials (with different melting points) is a complex eutectic process, in which, along with self-diffusion, causing the mass transfer to the region of particle contact, there is an interdiffusion, which provides homogenization of the composition via equalization of the concentrations of dissimilar atoms within the sample. Under conditions of limited solubility or complete insolubility of the components, sintering of the system is complicated by isolating homogeneous particles from mutual contact, hindering the flow of self-diffusion, and thereby, worsening the sintering conditions. For the numerical solution of the problem, a fourth-order Runge–Kutta method with a variable integration step is used. A software package for solving the problem is developed, the calculation results are given on the example of an alloy of a powder mixture of iron, cast iron, and sitallized glass.

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