{'fraction_non_alphanumeric': 0.029542318997060765, 'fraction_numerical': 0.01952492351988483, 'mean_word_length': 4.678303814713897, 'pattern_counts': {'":': 0, '<': 0, '<?xml version=': 0, '>': 0, 'https://': 0, 'lorem ipsum': 0, 'www.': 0, 'xml': 0}, 'pii_count': 0, 'substrings_counts': 0, 'word_list_counts': {'cursed_substrings.json': 1, 'profanity_word_list.json': 0, 'sexual_word_list.json': 0, 'zh_pornsignals.json': 0}}
Modeling of casting technology of large-sized ingots from deformable aluminum alloys

An industrial technology for semi-continuous casting of large-sized ingots from wrought aluminum alloy 1580 has been developed through the use of complex modeling, including computer modeling and physical modeling. The ProCAST and ANSYS software packages equipped with the FLUENT module were used for computer modeling. The physical modeling was carried out on a laboratory semi-continuous casting unit (SCCU), which represents a tenfold reduced physical model of an industrial casting unit for the vertical semi-continuous casting of ingots from aluminum alloys. An aluminum-magnesium alloy with the addition of 0.05% (wt.) of scandium was used as the object of modeling. The results of computer modeling were tested at the SCCU, and then computer modeling was carried out for casting a large ingot. According to the modes obtained in the simulation, an ingot with a section of 1310 × 560 mm was cast under industrial conditions, which had a good surface quality with the absence of casting defects. In the microstructure of an industrial ingot and an ingot cast on the SCCU, there were no primary intermetallic compounds Al3(Sc, Zr), which makes it possible to strengthen the alloy upon annealing. To check the manufacturability during rolling, billets with a size of 40 × 120 × 170 mm were cut from these ingots, which were hot-rolled to a thickness of 5 mm, and then cold rolled to a thickness of 1 mm. The rolling results revealed good workability of the alloy, which was reflected in the high quality of the surface and the absence of cracks at the edges of the rolled stock. The mechanical properties of sheets obtained from both ingots were at the same level, which proves the reliability of casting modes for ingots obtained by complex modeling and the validity of their use for industrial conditions of the semi-continuous casting of large ingots from aluminum alloys.


Introduction
Mastering the technology of casting large-sized ingots from new deformable aluminum alloys of the Al-Mg-Sc system [1][2][3][4][5], obtained in industrial conditions using semicontinuous casting machines [6], requires high energy and material costs. Also, it is dangerous due to the risk of withdrawal from building the operating equipment; therefore, it is considered relevant to carry out modeling before industrial tests [7,8]. In metallurgy, different types of modeling are used; therefore, for each case, it is important to choose the optimal type of modeling in order to obtain the most reliable results at the lowest cost. In this work, to simulate the process of semi-continuous casting of large-sized flat ingots from deformable aluminum alloys, complex modeling, including computer modeling in ESI ProCAST, ANSYS software packages were used, and physical modeling on a laboratory semi-continuous casting unit (SCCU) was applied [6,8].
These modern software systems are based on well-known physical laws and mathematical models and allow to effectively simulating casting processes for static and dynamic models. With their help, the processes of heat and mass transfer and crystallization that occur during continuous casting of ingots from various metals and alloys, including aluminum alloys, have been well studied [9,10]. But despite this, the development of new aluminum alloys and the hydrodynamic modeling of their flow or crystallization in the process of casting ingots require verification of the ProCAST and ANSYS models on the data of a real physical model. Verification is necessary to increase the comparability and accuracy of computer models; however, for the production of large-sized flat ingots, the verification process becomes more complicated due to the scale factor. The choice of modes for casting ingots in an industrial environment, based on data from a computer model that has not passed the verification procedure, can cause significant production costs due to the formation of casting defects and product rejects. Therefore, the verification of computer models, based on the results obtained on reduced physical models, is a good way to reduce production costs and improve the accuracy of modeling, as well as for the subsequent selection of technological modes for casting flat ingots in an industrial environment. To verify the models in this work a casting machine was used that was reduced by a factor of 10 relative to an industrial unit -a semi-continuous casting unit (SCCU). At the same time, the scientific novelty of the work should be attributed to the fact that such studies on integrated modeling were first carried out on a new alloy 1580 of the aluminum-magnesium system with the addition of scandium. There is no information on such studies for alloys of the aluminum-magnesium system with additions of scandium in the literature, although alloys of this type are now becoming more and more popular in many industries.
The purpose of the work was to develop an industrial technology for semi-continuous casting of large-sized ingots from deformable aluminum alloy 1580 through complex modeling, including computer modeling with modeling on a physical model of a casting machine for semi-continuous casting of aluminum alloys.
To achieve this goal, the following tasks were solved in the work: -Computer simulation of semi-continuous casting of flat ingots from deformable aluminum alloy 1580, -Experimental testing of casting modes developed by computer modeling on the physical model of the SCCU and studying the structure of the obtained ingots, -Testing experimental modes of modeling in industrial conditions for casting large-sized ingots and studying their structure, and -Study of manufacturability during rolling of ingots manufactured at the SCCU and ingot cast in industrial conditions and comparison of the quality and mechanical properties of the obtained sheet semi-finished products.

Method of carrying out research
The ESI ProCAST and ANSYS software systems equipped with the FLUENT module were used to carry out the computer modeling work.
Physical modeling was carried out on a laboratory unit for the semi-continuous casting of aluminum alloys, created at the Siberian Federal University (SibFU) with the assistance of RUSAL [6]. The installation is a ten times smaller physical model of an industrial casting unit for the vertical semi-continuous casting of ingots from aluminum alloys. The automated control system of the model ensures the accuracy of adjustment and recording of the main parameters of its operation in a wide range of values, which makes it possible to obtain the structure of cast billets under cooling conditions close to industrial ones. The versatility of the equipment layout makes it possible to use the SCCU for the production of ingots from aluminum alloys by the method of semi-continuous casting into a mold with or without heat packing. The complex also provides ample opportunities for testing prototypes of technological equipment and various technical solutions in the field of foundry production. The layout of the equipment included in the SCCU is shown in Fig. 1.
The main parts of the SCCU are two induction melting furnaces (1), mixer (2), filtration unit (3), vertical casting machine (4), metal track system (5), and a crane, water supply, power supply, control, and control systems. In the furnaces, alloys of given chemical composition are prepared, which in the molten state are sent through a metal path to a mixer for settling, modification, and refining with argon. After the mixer, the alloy is fed through the metal track to the casting machine, in which an ingot with a rectangular section of 60 × 200 mm or a round section with a diameter of up to 190 mm is formed.
The operation of the SCCU is carried out by an automated process control system (APCS); the operation diagram of which is shown in Fig. 2.
An aluminum-magnesium alloy 1580 with the addition of scandium was chosen as the object of modeling; the chemical composition of which is presented in Table 1.
The alloy for the physical modeling of casting was prepared in an IAT-0.16 induction furnace. The mass of the alloy for one simulation cycle was 50 ± 0.1 kg, and for its preparation aluminum of the A85 brand, magnesium of the Mg90 brand, and an aluminum alloy -2% (wt.) scandium were used. The alloy was poured from the mixer into the mold of a casting machine with a rectangular cross section of 60 × 200 mm for further use of the ingot as a billet for sheet rolling. The alloy temperature was in an induction furnace 800 ± 8 °C, in the mixer 750 ± 5 °C, and on the mold of the casting machine 700-705 °C. The analysis of the chemical composition of the alloy was carried out on an optical emission spectrometer Hitachi Foundry master lab.
To study the microstructure of the alloy, an Observer A1m light microscope, Carl Zeiss was used, and the fine structure was studied using a Carl Zeiss EVO 50 scanning electron microscope and a JEM 2100 transmission electron microscope.
Rolling was carried out in the laboratory of the Department of Metal Forming of the Siberian Federal University [6][7][8]11]. For hot rolling, billets with a size of 40 × 120 × 170 mm were milled from the ingot and subjected to homogenization annealing in a two-stage mode: the first heating at 350 °C and holding for 3 h and the second heating for 1 h to 425 °C and holding for 4 h. Billets were heated to 450 °C and rolled to a thickness of 5 mm with a single reduction of 5-10% on a tworoll mill with a roll diameter of 330 mm and a barrel length of 520 mm. The total rolling reduction was 88%. Then the sheets were annealed at 380 °C for 1 h and rolled at room temperature on a two-roll mill LS 400 AUTO manufactured by Mario Di Maio with a roll diameter of 200 mm and a barrel length of 400 mm to a thickness of 1 mm with single reductions of 2-5%. The total reduction rate was 80%. Cold-rolled sheets were annealed at 350 °C for 3 h, and samples were cut from them for mechanical tensile tests.
The mechanical properties of hot-and cold-rolled products were determined by tensile tests at room temperature on a Walter + BaiAG LFM 400-kN universal testing machine in accordance with State Standard 1497-84. The configuration of the samples is shown in Fig. 3.  The tensile test results were subjected to standard statistical processing. Five samples were taken for one experimental point.

Results and discussion
The ESI ProCAST software package is designed for computer modeling of all casting processes and is based on the finite element method, which provides high accuracy in describing the geometry of the casting and the shape of the design model. The complex can be used to calculate most of the processes of thermal, crystallization, metallurgical, and stress-strain character. The program used in the work is based on three main solvers designed to simulate the distribution of the temperature field, hydrodynamic processes, and estimate the stresses in castings [12].
The module for calculating the heat problem allows you to simulate the processes of crystallization and the formation of defects such as shrinkage cavities and macroporosity. Crystallization simulations can be performed under a variety of conditions, such as gravity casting, recharge, low pressure, or high-pressure casting. With the help of the hydrodynamic module, it is possible to simulate the filling of a casting mold with an alloy. The calculation of hydrodynamics in ESI ProCAST is described by the full Navier-Stokes equation and can be carried out in conjunction with the analysis of crystallization, which is especially important when adding metal to large forms when part of the melt has already begun to solidify. The calculation takes into account the stresses arising at all stages of crystallization of the alloy in the form and the likelihood of hot cracking. The hydrodynamic solver also takes into account the toughness of the alloy, depending on its temperature. Alloy toughness can also be calculated in the ESI ProCAST thermodynamic database.
The calculation of the stress-strain state of the casting and metal tooling takes into account thermal stresses obtained during uneven cooling of various parts of the casting, as well as mechanical stresses arising from the contact interaction of the casting and the mold.
Due to the finite element method and the solver algorithm, when calculating the stress-strain state of the casting, the geometry of the computational grid changes with the restructuring and change of the coordinates of its nodes, depending on the shrinkage of the alloy and the stresses obtained, taking into account the stiffness of the form. As a result, it is possible to evaluate the shrinkage processes in the casting that are close to reality, determine the air gap between the casting and the mold, take into account its thermal resistance, and determine the mutual influence of the casting and the mold.
In the described calculation process, the problem of unsteady heat transfer and the hydrodynamic problem of metal flow in a metal path were simultaneously solved, which made it possible to take into account real heat losses when modeling casting on a physical model. Figure 4 shows the finite element mesh of the model under the following conditions: -Casing material -steel 3, -The material of the metal track cartridges is refractory concrete, -Temperature of the cartridges of the metal track (refractory concrete) 300 ± 5 °C, -Thermal insulation material -heat-insulating concrete, -Thermal insulation temperature of the mixer furnace (heat-insulating concrete) 400 ± 5 °C, -Ambient temperature 20 °C, -Alloy material -alloy of the Al-Mg system (Table 1), and -Casting temperature -700 ± 5 °C.
The ESI ProCAST hydrodynamic and thermal modules were used to calculate the dynamics of the metal flow. The problem statement was a solid model of a system of metal tracts and a mixer. At the initial moment of time, the crucible of the induction furnace is filled with metal from a bulk source of mass with a given temperature, and then a special algorithm for tilting the induction furnace into the receiving pocket is applied in the model. Heating of the metal in the mixer furnace is carried out due to the operation of the heaters located in the lid. Heat generation was taken into account in the heater zone. On the surface of the metal casing of the mixer furnace convective heat exchange with the environment was set taking into account the temperature of the casing surface. Figure 5 shows a model of the process of pouring metal from the ladle of an induction furnace into the receiving bowl of the SCCU and the resulting distribution of metal flow rates. The metal flow velocity V in the flow at these technological parameters was 1.5-1.7 m/s. The high value of the melt flow rate in the jet shows that the overflow of the melt from the induction furnace to the mixer furnace through the metal path proceeds dynamically, and the massive receiving bowl of the metal path has the required specified slope and good thermal insulation. These factors guarantee the absence of overcooling of the melt at the beginning of the overflow and the accuracy of the selected temperature and speed regimes. Figure 6 shows the model and the distribution of the velocities of the melt along the metal path when it is moved from the receiving bowl to the mixer. The melt flow rate in this area is 0.2-0.7 m/s. The model shows the uniformity of filling the metal track with melt during the overflow. Figure 7 shows the model and the distribution of the velocities of the melt during the overflow of metal from the metal track into the mixer. The melt flow rate was 0.2-1.0 m/s. The correspondence between the melt flow rate in the taphole of the mixer furnace and the melt flow rate along the length of the metal track shows the correctness of the selected thermal regime and the induction furnace tilt algorithm. This in turn confirms the uniformity of filling the mixer furnace and guarantees the minimum metal remainder in the metal path after overflow from one unit in another. Figure 8 shows the model and the distribution of the speeds of metal movement along the metal track after its removal from the crucible of the induction furnace. The melt flow rate is 0.2-0.6 m/s.   Figure 10 shows a model of a longitudinal section of a mixer furnace and the temperature distribution in it after filling with liquid metal. The melt temperature is approximately 650 °C, the temperature of the heaters is 800 °C, and the temperature on the walls of the mixer body does not exceed 60 °C. Figure 11 shows a model of the cross section of the metal track and the temperature distribution in it. The temperature in the lining is distributed correctly, since the temperature transition is smooth and clear, and the temperature on the walls of the body of the metal track does not exceed 60 °C.  To determine the modes of casting ingots at the SCCU, which could be considered as close as possible to industrial ones, a computer simulation of casting at the SCCU was carried out in the ANSYS program, equipped with the FLU-ENT module. At the same time, such thermal and geometric characteristics as the aspect ratio of the cast billet, the shape, and the depth of the molten metal hole were chosen as the main criteria for the similarity of experimental and industrial types of casting.
The investigated alloy belongs to the Al-Mg system, the alloys of which are not hardened by heat treatment. Recently, however, alloying with transition metals has begun to be used to strengthen these alloys. In [5, it was found that the greatest strengthening effect in alloys of the Al-Mg system is exerted by doping with scandium. Filatov Yu.A. with authors [5] presented data about industrial alloys and show much higher properties (especially yield strength). Works [13,14] have found that the maximum strengthening effect is caused by the precipitation of Al 3 Sc nanoparticles. The paper [15] reports a significant improvement in tensile properties, by addition of small amounts of Sc (0.8 wt%). Zakharov V.V. and authors [16][17][18][19][20]32] have shown that the content of scandium may be reduced without lowering the level of the properties. Studies in [21,30,31,33,36] have shown that precipitation (and discontinuous precipitation) of the Al 3 Sc/Al 3 (Sc, Zr) is generally considered to be a key factor for the excellent mechanical properties in aluminum alloys. Works [22-25, 27, 34, 35, 37] explained the effects of Sc addition on the microstructure and mechanical properties. K. Yan et al. [26] studied morphological characteristics of Al 3 Sc particles with Sc containing 0.6 wt% in aluminum. The recrystallization behavior and Al 3 (Sc, Zr) particles were studied by annealing the samples after cold rolling (CR) and equal channel angular pressing (ECAP) [28]. Hardening behavior during isothermal annealing of aluminum alloys with 0.25 wt% of Sc is discussed in [29]. H. Pouraliakbar and authors [38] studied the dynamic and static softening phenomena in Al-6 Mg alloy with Sc addition 0.12 wt% during two-stage deformation through interrupted hot compression test.
This effect can be explained by the precipitation of nanosized particles of the Al 3 Sc phase from the solid solution upon annealing [29,[39][40][41][42][43][44][45][46][47]. The paper [39] presents the study on mechanical properties of rolled sheet products from a new alloy of the Al-Mg-Sc system in a deformed and heattreated state; presented heat treatment modes give a fairly good ratio of strength and ductility properties. Mechanical properties of cold-rolled, annealed semi-finished products were investigated in work [40,41]. The influence of heat treatment and recrystallization on mechanical properties was studied in the works: for industrial alloy 01570 [42], for alloys Al-0.06Sc and Al-0.06Sc-0.06Zr (at.%) in [43], for aluminum alloy with 0.2 wt% of Sc in [44], for alloys of Al-Mg-Mn-Sc-Zr system in [45,46], for Al-Sc-Zr-based alloy with a small addition of Ti in [47], for Al-0.25Sc and Al-0.25Sc-0.12Zr alloys during isothermal annealing in work [29]. These particles effectively block mobile dislocations, stabilizing the grain structure, and thus have a strong anti-recrystallization effect for all types of semi-finished products from these alloys. During casting, the rate of cooling of the melt in the range of crystallization temperatures of the aluminum-magnesium alloy affects the scandium content in the supersaturated solid solution. The higher the Fig. 9 Model of the temperature distribution of the metal in the trays of the metal track received from the crucible of the induction furnace cooling rate, the more alloying elements, including scandium, remain in the solid solution. Considering the high cost of scandium in magnalia, this element is partially replaced by zirconium. Then the decomposition of the solid solution during subsequent heat treatment proceeds with the release of complex dispersed crystals of intermetallic phases of the Al 3 (Sc, Zr) type, which, like the Al 3 Sc phase, improve the physical and mechanical properties of the alloy [11, 13, 22, 25, 29-32, 37, 39-41, 43, 44, 48, 49]. Therefore, in order to ensure the maximum content of scandium and zirconium in a supersaturated solid solution when casting large-sized ingots from aluminum-magnesium alloys, high crystallization rates of the melt should be used in order to exclude the formation of primary aluminides of scandium and zirconium during crystallization and cooling of the ingot [13,22,26,[47][48][49][50].
The authors [50] have shown that one of the indicators by which the cooling rate during crystallization of aluminum alloys can be estimated is the depth of the dimple of the liquid phase of the alloy in the mold during the main casting period. In [51], it was experimentally established that when casting ingots from aluminum-magnesium alloys doped with scandium and zirconium, the maximum depth of the dimple of the liquid phase of the alloy in the mold during the main casting period must be maintained no more than the value calculated by the formula: where L h is the maximum depth of a hole in liquid metal, mm; H is the ingot width, mm; B is the ingot thickness, mm; and N is an empirical coefficient, which for industrial size ingots is 0.875 (1 ± 0.03) -confidence interval within which the experimental results fit with a reliability of 95%.
The formula is valid for alloys of the Al-Mg system, in which the scandium concentration does not exceed 0.15% (wt.) If the condition for the depth of the hole is met, there is no primary intermetallic compounds Al 3 (Sc, Zr) in the structure of the cast ingot, since all scandium and zirconium are in a supersaturated solid solution. If the depth of the molten alloy cavity in the mold is greater than the value calculated by the formula (1), then primary intermetallic compounds Al 3 (Sc, Zr) appear in the ingot structure, which practically does not have a hardening effect on the alloy. As a result, the concentration of scandium in the supersaturated solid solution decreases and, It should be noted that the claimed parameter -the depth of the molten alloy hole in the mold -is easy to control during the casting of the ingot, for example, using the method of ultrasonic scanning or a metal probe.
The crystallization conditions of ingots obtained at the SCCU differ from industrial ingots due to different cooling rates due to a significant difference in the sizes of their cross sections. Therefore, the modeling of the crystallization process of ingots at the SCCU was carried out in the ANSYS program, equipped with the FLUENT module according to 5 options (Table 2).  In Table 2, the range of 705-636 °C is limited by the casting temperature and the liquidus temperature of the investigated alloy and 636-470 °C is limited by the liquidus temperature and the solidus temperature. The simulation results are presented in Figs. 12, 13, 14, 15, and 16.
To simulate the process of semi-continuous casting with direct cooling of flat ingots from aluminum alloys the initial conditions are functions of temperature, pressure, and speed given in space. At the input, the speed value is set, corresponding to the metal consumption, and this value changes during the casting process and corresponds to the speed of the pallet movement. All external surfaces are set to zero speed. Symmetry planes with zero velocity normal are specified. On the outer surfaces, convection conditions are set corresponding to the intensity of air and water cooling.
The great importance in the simulation of continuous casting is the problem of heat transfer during the The used computer program does not provide for the possibility of setting hole depth markers; therefore, this parameter in operation was determined by manual measurement. As follows from Table 2, the maximum depth of the hole (L h ) corresponded to option no. 4. The casting parameters for this option were tested when casting on the SCCU, which gave the following results. During the crystallization of the ingot, direct measurements of the parameter L h with a probe gave a result of 117 ± 3 mm. The ingot was characterized by good surface quality and no casting defects (Fig. 17).
Investigations of the microstructure of ingots after casting at the SCCU revealed particles of primary phases containing magnesium, iron, silicon, and manganese, such as β(Al 8 Mg 5 ), Al 6 (Fe, Mn), Al 15 (Fe, Mn) 3 Si 2 , and Al 10 (Mg, Mn) 3 . The composition of these phases for alloys of the Al-Mg system has been studied sufficient in detail [52]. In this case, the absence of primary crystals of intermetallic compounds Al 3 (Sc, Zr) in the structure of the ingots is important, indicating that scandium and zirconium dissolve in a solid solution of aluminum and do not precipitate during crystallization (Fig. 18a). Annealing the ingots in a twostage mode provided partial dissolution of nonequilibrium phases. The microstructure of homogenized ingots is represented by crystals of the α-solid solution and inclusions of intermetallic phases of various shapes located along the grain boundaries (Fig. 18b).
The phase composition of the investigated alloy after annealing was determined using a scanning electron microscope (SEM) equipped with an energy-dispersive spectrometer. In the structure of the annealed ingots, light inclusions of intermetallic compounds in the form of polyhedrons containing Al, Mg, Mn, and Cr were revealed, which approximately corresponds to the Al 10 (Mg, Mn, Cr) 3 phase (Fig. 19 spectrum 1), dark inclusions in the form of hieroglyphs containing Mg and Si, which corresponds to the Mg 2 Si phase ( Fig. 19 spectrum 4). Iron forms eutectic phases of irregular shape containing Al, Fe, Si, Mg, Mn, and Cr, corresponding to the Al 15 (Fe, Mn, Cr) 3 Si 2 phase (Fig. 19 spectrums 6,   7). As a result of the decomposition of an aluminum solid solution supersaturated with transition metals, secondary particles of intermetallic compounds containing Cr, Mn are formed in the structure of the alloys (Fig. 19 spectrums 6, 7).
The studies of the fine structure of the ingots after annealing were carried out using transmission electron microscopy to determine the shape, size, and distribution of Al 3 (Sc, Zr) and Al 6 Mn inclusions precipitated from the supersaturated solid solution after its decomposition. The distribution pattern of Al 3 (Sc, Zr) and Al 6 Mn particles over the ingot volume is shown in Fig. 20 in light and dark field. Figure 20a, b show particles of the Al 3 (Sc, Zr) phase with a size of 15-20 nm, which are evenly distributed over the volume of grains, and in Fig. 20c, d, Al6Mn particles are given, having a cylindrical or rectangular shape with a size of ~ 70 × 40 nm.
The results of studies of microstructure and fine structure have confirmed the correctness of the choice of casting modes obtained by computer simulation.
The values of the parameter L h obtained by computer and physical modeling were substituted into Formula (1), the empirical coefficient N was calculated, and it was found that its value for the ingots obtained at the SCCU should be 1.95. It should also be noted that with an increase in the casting speed, the crystallization rate of the ingot increases, which leads to an increase in the temperature on the surface of the ingot. Reducing water consumption will reduce the rate of crystallization. Analysis of computer and physical modeling showed that on an experimental ingot with a cross section of 60 × 200 mm with this tooling, casting with an average crystallization rate in the range from 1.4 to 2.8 °C/s will make it possible to obtain ingots with the structure of which primary intermetallic compounds Al 3 (Sc, Zr) are absent. To achieve this crystallization rate, the casting temperature should be 705 °C; the casting rate should be 85 mm/s with a water flow rate of 2.5 m 3 /h. Thus, we can assume that different values of the empirical coefficient N for ingots are due to the difference in cooling rates when casting large and laboratory ingots.
A computer simulation was carried out for casting an industrial large-sized ingot with a cross section of 1310 × 560 mm from an alloy of chemical composition corresponding to Table 1, according to the modes indicated in Table 3. To speed up the calculations when visualizing the simulation results, a calculation was performed for 1/4 ingot since the boundary conditions during casting remain the same for this design of the mold of the casting tooling. The model has also been verified against physical modeling data. In addition, the following conditions were set for the model: metal level 60 cm, lateral distribution of metal, and metal level in the mold 35 mm. The simulation result is shown in Fig. 21.
Determination of the depth of the model hole showed a value of 275 mm, which is in good agreement with the calculation according to formula (1) at which L h = 280 mm. According to the modes obtained in the simulation, a large-sized ingot with a section of 1310 × 560 mm (Fig. 22) was obtained under industrial conditions, which had a good surface quality and was characterized by the absence of casting defects. In the casting process, the depth of the hole at the ingot was L h = 276 ± 4 mm. In addition, studies of the microstructure of this ingot, as well as of the ingot cast on the SCCU, showed the absence of primary intermetallic compounds Al 3 (Sc, Zr) in its structure, which confirms the correctness of formula (1), as well as the correctness of the casting mode developed by modeling.
To check the manufacturability during subsequent rolling, ingots with a size of 40 × 120 × 170 mm were cut from experimental and industrial ingots, which were hot rolled to a thickness of 5 mm, and then cold rolled to a thickness of 1 mm. The rolling results showed good manufacturability, both in hot and cold rolling, which was reflected in the high quality of the surface and the absence of cracks at the edges of the rolled stock [6, 11, 39-41, 48, 53, 54]. The works [39,[53][54][55] also present the results on the production of welded samples from the investigated alloy, confirming the manufacturability of the obtained semi-finished products. After each type of rolling, annealing and tensile tests were carried out, which gave the following results. The mechanical properties of hot-rolled sheets 5 mm thick, rolled from both ingots, after annealing at 380 °C for 1 h were at the same level: R m = 340 ± 5 MPa, R p = 215 ± 5 MPa, and A    = 22 ± 2%. The mechanical properties of cold-rolled alloy sheets after annealing at 350 °C for 3 h were also similar and amounted to R m = 342 ± 5 MPa, R p = 215 ± 4 MPa, and A = 19 ± 2%. The intersection of the confidence intervals for the parameters of mechanical properties made it possible to conclude that they are practically identical.

Conclusions
Studies carried out on the 1580 alloy of the aluminummagnesium system with the addition of scandium allowed to conclude the following. The use of complex modeling of the process of semi-continuous casting of aluminum alloys including computer modeling and physical modeling on an experimental unit of semi-continuous casting makes it possible to develop industrial modes of casting new alloys. At the same time, one of the important indicators that allow controlling the casting process is the depth of the molten metal hole. Experiments carried out both on a physical model and on an industrial foundry installation have shown that if the depth of the hole does not exceed the critical one, then in the structure of the ingot there are no primary precipitates of the phase containing scandium. Subsequent separation of dispersed particles of phases containing scandium after rolling and subsequent annealing provides strengthening of alloy 1580. Laboratory ingots and industrial ingots showed good manufacturability, both during hot and cold rolling. The mechanical properties of the sheets were practically the same. The foregoing proves the reliability of the modes of casting ingots obtained by complex modeling and the validity of their application for industrial conditions of the semicontinuous casting of ingots from aluminum alloys.