Choice of materials properties and of shell molds structure by investment models

The paper presents a mathematical model optimizing the choice of material and morphological structure of the shell mold (SM), which has the highest resistance to cracking when pouring liquid metal into it. To solve this problem, the theory of small elastoplastic deformations and the heat equation, as well as proven numerical methods, were used. The objective function min – max was constructed from control variables characterizing the properties of the molding material of the shell. The process of heating an axisymmetric shell mold was considered when pouring liquid metal into it. The resistance of the shell form was estimated by the stresses arising in it. An algorithm for solving this problem was compiled. Using numerical schemes and program complexes developed in previous studies, an algorithm for solving the optimization problem was constructed and the values of control variables were found in which the shell mold does not break even in the presence of a rigid process – pouring steel into a cold shell mold. Analysis of the influence of weight of each of the found parameters on the value of the constructed objective function is given. Using a mathematical experiment, the morphological structure of the shell mold was studied. The shell mold of five layers is considered. The corrected system of equations makes it possible to take into account the properties of the layers made of different materials. Calculations were performed when the layer of the shell mold from material found by optimization occupies different positions in its cross section. In this case, the remaining layers of the mold are made of traditional ceramics. The optimal location of this layer was found. It is shown that the presence of several layers with the found properties does not affect the increase in crack resistance of the shell mold.