| A new, computationally-efficient algorithm has been implemented to solve for thermal stresses, strains, and displacements in realistic solidification processes which involve highly nonlinear constitutive relations. A general form of the transient heat equation including latent-heat from phase transformations such as solidification and other temperature-dependent properties is solved numerically for the temperature field history. The resulting thermal stresses are solved by integrating the highly nonlinear thermoelastic-viscoplastic constitutive equations using a two-level method. First, an estimate of the stress and inelastic strain is obtained at each local integration point by implicit integration followed by a bounded Newton-Raphson iteration of the constitutive law. Then, the global finite element equations describing the boundary value problem are solved using full Newton-Raphson iteration. The procedure has been implemented into the commercial package Abaqus using a user-defined subroutine (UMAT) to integrate the constitutive equations at the local level. Two special treatments for treating the liquid/mushy zone with a fixed grid approach are presented and compared. Other local integration methods as well as the explicit initial strain method used in CON2D for solving this problem are also briefly reviewed and compared.; The model is validated both with a semi-analytical solution from Weiner and Boley as well as with an in-house finite element code CON2D specialized in thermo-mechanical modeling of continuous casting. Both finite element codes are then applied to simulate temperature and stress development of a slice through the solidifying steel shell in a continuous casting mold under realistic operating conditions including a stress state of generalized plane strain and with actual temperature dependent properties. Mechanical results are then used to predict an ideal taper for different casting speeds.; The model is then improved to add coupling of heat flow and stress generation that are increment-wise coupled through the size of the interfacial gap. Coupled results are first verified with a solidifying slice, and then quantitatively against the CON2D 2D model of billet casting by fully employing Abaqus thermal and mechanical contact capabilities. Another coupled 2D model of bloom beam blank casting, known for a very challenging geometry, is solved for the simultaneous evolution of deformation, temperature, and stress. Finally, a large scale 3D simulation of a thin slab caster with a funnel, first of that kind ever conducted, is performed to correctly reproduce the 3D mechanical state in casting process with extremely complex geometry and loading conditions. |
