Element-Free Galerkin Method Modeling of Thermo-Elastic-Plastic Behavior for Continuous Casting Round Billet

Abstract

When solving the coupled thermal-mechanical problem of the metal solidification, the mesh-based numerical methods suffer from the inconsistency of mesh lines and curved boundaries. Furthermore, the mesh should be continually reconstructed to comply with the interface when dealing with the moving boundary such as phase transition, which brings great difficulties to the numerical calculation. Based on the plane stress assumption, the present work establishes a two-dimensional thermo-elastic-plastic calculation model for continuous casting round billets using the Element-Free Galerkin method, and the correction scheme of elastoplastic transition region has been explored. The results show that the correction scheme has a slight effect on magnitude of the equivalent stress and no impact on the subsequent plastic deformation zone. The elastoplastic transition region of shell surface appears in the range of 100 to 200 mm below the meniscus, and the averaged plastic stress is about 2.27 times of the elastic stress at the mold outlet. Near the interface region of liquid–solid phase exhibits an elastic deformation behavior, while far from the interface region appears plastic deformation in which the elastic stress remains invariable. The Element-Free Galerkin method is discretized by a series of arbitrary nodes, which exhibits high accuracy and great flexibility in dealing with moving interface problems. It provides a powerful approach to calculate and analyze the heat transfer/mechanical behavior with complex geometric boundaries such as round billet, chamfered billet, and beam blank.