Numerical investigation of isotropic beam crystallization process under nonuniform cooling

Abstract

Abstract-The study is directed to conclusion and approbation of the new defining relations that describe arousal and change of stress fields in isotropic material during crystallization, taking into account temperature strains and structural shrinkage. The statement of the crystallization problem and numerical realization of the process by the example of linear and plane statements have been made. The problem of crystallization of a beam of isotropic material under nonuniform cooling with phase transitions has been considered. The authors removed the defining relations describing the occurrence and change of stress fields in an isotropic material during crystallization, taking into account temperature deformations and structural shrinkage. The numerical realization of the problem of crystallization of a beam was made by two methods: a finite difference method and a finite element method. The tendency of accumulation of an error of the finite difference method has been established. The verification of defining relations by the example of the problem of plate nonuniform controlled cooling from temperature above melting point has been made at the second stage of the study. Displacement, stress and strain fields that satisfy the physics of the process and boundary conditions have been obtained.