Mathematical modeling of branching of the leading edge of a longitudinal shear crack on a porous inclusion is proposed. The leading edge of the crack is approximated by the δ-neighborhood of the plastic deformation of the material with the front of longitudinal or shear waves, at which the longitudinal or transverse velocities break when passing through the leading edge of the crack. Expressions are obtained and graphs of the relative intensity of the leading edges of the reflected cracks of longitudinal and transverse shear and the conditions for the generation of reflected cracks depending on the angle of intersection of the crack with inclusion and physical parameters of the material are constructed.

In recent years it has become more and more usual to use an acid tamped lining for the walls of steel-smelting arc furnaces, since the resistance of these linings to 7000-13,000 smelts is significantly higher than that of brick (30-40 smelts). The use of the acid tamped lining makes it possible to obtain significant savings in dinas brick, to improve production management in the casting shops, to reduce the area previously required for storing refractories, and to significantly reduce the labor content in maintenance work on the furnace lining.One important characteristic of quartz sand is its grainy composition, which provides the necessary gas-permeability of the refractory mass. It was established in [i] that the most efficient grain composition for a refractory mass is the group-02 (State Standard 2138-74) quartz molding sand with the grains remaining on sieve No. 016-0315. At the same time, fine group-016 sands are used in the steel-casting shops of several plants for the preparation of the molding mixtures; when this sand is sieved most of the grains remain on No. 01-02 sieves. The use of sands of two different groups (for the manufacture of molding mixtures and refractory masses) in a single shop is quite difficult from the point of view of production management. Therefore, the task of the present study includes the development of refractory masses for tamped linings of steel-smelting arc furnaces based on fine sand in order not to make production complicated, and also to use for the preparation of the refractory masses the same materials and equipment that are used to produce molding masses.The experimental studies were carried out at the Kemrov electromechanical plant, the Kuzbasselektromotor, and the Riga Electromachinery Plant.A study of the grain composition of the IKO16A Karasorsk and Novinsk sand used by these plants showed (Table i) that the Karasorsk sand contains 52% of 0.2-0.16-mm grains and 25.5% of 0.315-0.2-mm grains; the Novinsk sand of the same group contains these fractions in smaller (23.4%) and larger amounts (31.8%), respectively.The greater the concentration of fine fractions in the quartz sand, the greater the need to include a refractory clay in order to achieve the specified strength in the crock and plasticity of the mass, and the greater the requirement for water glass to strengthen the lining at high temperatures [2]. At the same time an increased amount of water glass and clay in the refractory mass lowers the mass and correspondingly increases flashing-off of the lining during service [3]. Taking these factors into account, work was also carried out on the selection of an effective composition of the refractory mass for tamped linings on the basis Of fine Karasorsk sand. TABLE i. Characteristics of Experimental SandsMass frac~on, %, of ffac~om, mm SKTB Planning Organization of the Vladimir ll'ich Plant.

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