Modeling and Optimizing the Property Choices of Materials and Structures of Shell Molds for Investment Casting

Abstract

The paper presents a mathematical model for optimizing the choice of material and morphological structure of a shell mold (SM) that has the highest resistance to cracking when liquid metal is poured into it. In order to solve this problem, the theory of small elastoplastic deformations, the heat equation, and proven numerical methods are used. The min–max objective function of control variables characterizing the properties of the SM material is constructed. The process of heating an axisymmetric SM by pouring liquid metal into it is considered. The SM resistance is estimated by the stresses arising in it. An algorithm for solving this problem is constructed. Using numerical schemes and software tools developed in previous studies, an algorithm for solving the optimization problem is constructed, and the values of control variables are found, in which the SM cannot be destroyed even being exposed to a rigid process of pouring steel into the cold SM. The analysis of the weight’s influence of each parameter found on the value of the objective function constructed is performed. A mathematical experiment is used to study the morphological structure of the SM. A five-layer SM is considered. The corrected system of equations makes it possible to consider the properties of the layers made of different materials. Calculations are performed for the cases of different positions of one of the mold layers in the mold section. This layer is made of the material found by optimization, while other mold layers are made of traditional ceramics. The optimal location of this layer is found. It is shown that the presence of several layers with the found properties does not influence the increase in the crack resistance of the SM.