The physico-mechanical properties of ceramic-matrix Al2O3-based composites are strongly influenced by the particle size of Al2O3, the presence of carbon nanotubes (CNTs), and the temperature regimes of sintering. In order to obtain the very low porosity ceramic composites with high rates of flexural strength and crack resistance, mathematical models were developed for grinding the particles of Al2O3 and spark plasma sintering of the composite. Mathematical models were based on the equations of the balance of the number of particles by size taking into account their grinding (for the grinding stage), the balance of pores in the composite by the size (for the sintering stage). The kinetic parameters of mathematical models were determined and a good agreement was reached between the calculated and experimental results. The developed models were used to determine the optimal modes of grinding and sintering stages, which made it possible to obtain, in particular, the composite Al2O3 - CNT (20 vol. %) with bending strength 540 MPa, and crack resistance 6.3 MPa·m1/2.

Ceramic fibers produced in the form of multi-filament filament fibers are not strong enough to be used directly as a structural material. Factorial experiment planning is used to obtain a regression equation that describes the dependence of the absolute breaking load of a filament with a linear density of 100 tex on the degree of twisting when the initial 10-tex filament is doubled to form two strands and then five strands. The optimum degree of twisting is determined through the use of evolutionary planning.Materials composed of fibers based on high-melting oxides of aluminum and silicon can be effectively used in aggressive media heated to high temperatures [1].Ceramic fibers produced in the form of multi-filament filament fibers are not strong enough to be used directly as a structural material. One technological means of increasing the strength of these products is multiple doubling that involves twisting of the components of the fiber.The goal of the study being discussed here was to optimize twists of filament fibers. The study was performed by conducting a factorial experiment [2] that employed evolutionary planning [3].The breaking load of the fiber was chosen as the optimization criterion. Tests were performed on a mockup of a unit that provides for the doubling, twisting, and lubrication of fibers. The mockup made it possible to regulate the rate of feed of the fiber, the direction of the twists, and the number of twists. The lubrication unit made it possible to control the amount of lubricant that was supplied.The breaking load was determined using an "Instron" instrument on specimens with a test base of 500 mm. Table 1 shows the factors that were varied and their levels (the notation used here and henceforth corresponds to that employed in [2]). Table 2 presents raw data from the tests. The results obtained from calculation of the regression coefficients are shown below: b 0 = 8.36; b 1 = 0.90; b 2 = 1.16; b 12 = -0.06; b 11 = -2.924; b 22 = -0.989.We determine the variance of the absolute breaking load, or the variance of reproducibility:S 2 {Υ} = S ö 2 {Υ} = 2.8145/5 -1 + 0.70.We determine the variances of the regression coefficients:S 2 (b 0 ) = 0.2 ⋅ 0.7 = 0.14; S(b 0 ) = 0.374; S 2 (b i ) = 0.125 ⋅ 0.7 =0.0875; S(b i ) = 0.296;

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