The Influence of External Heat Exposure on the Stress State of Shell Molds by Smelting Models

The problem of determining the force effect of the support filler on the resistance of the shell mold (SM) during the crystallization of liquid metal (steel) in it is formulated and solved. The tensile normal stress that occurs in the outer layers of the mold in the initial time moments when liquid metal is poured into it is taken as the leading physical quantity that affects the crack resistance of the SM. The force factor affecting the stress-strain state (SSS) of the SM is the friction between the SM and the supporting filler (SuFi), which appears during the elastic expansion of the outer layer in the SM as a result of the temperature exposure from the crystallizing liquid metal. The problem of mathematical programming (minmax function) is formulated to determine the coefficient of friction between the SM and SuFi to obtain the smallest value of the normal tensile stress in the SM over the area under consideration in the presence of a system of constraints. An axisymmetric body of rotation is considered, which has four regions: liquid metal, solid metal, SM, and SuFi, which is considered to be a solid body that creates friction at the contact point with the outer layer of the SM. To solve the problem, equations of the linear theory of elasticity, the equation of thermal conductivity and a proven numerical method are used, according to which the area under study is divided into elements by a system of orthogonal surfaces. For each element, the formulated system of equations is written in a difference form. An algorithm for solving the problem is developed and the results of the solution are presented, stress diagrams in the SuFi are constructed using the found value of the friction coefficient. The analysis of the received results is given.