Thermo-Mechanical Finite Element Model of Shell Behavior In The Continuous Casting of Steel

A finite-element model, CON2D, has been developed to simulate temperature, stress, and shape development during the continuous casting of steel, both in and below the mold. The stress model features an elastic-viscoplastic creep constitutive equation that accounts for the different responses of the liquid, semi-solid, delta-ferrite, and austenite phases. Temperature and composition-dependent functions are also employed for properties such as thermal linear expansion. A contact algorithm is developed to prevent penetration of the shell into the mold wall due to the internal liquid pressure. An efficient two-step algorithm has been developed to integrate these highly non-linear equations. An inelastic strain damage criterion is developed to predict hot tear crack formation, which includes the contribution of pseudo-strain due to the flow of the liquid during feeding of the mushy zone. The model is validated with an analytical solution for both temperature and stress in a solidifying slab. It is then applied to predict the maximum casting speed to avoid crack formation due to bulging below the mold during casting of steel billets. Introduction Computational models are important tools to study the complex process of continuous casting of steel. They can help to understand how defects form and to optimize casting conditions to maximize quality and productivity at low cost. Brimacombe and coworkers applied both heat flow [1] and stress models [2] to study crack formation in slabs. Kristiansson [3] applied a thermal stress model of square billets that featured time-dependent plasticity. Recently, Fachinotti et. al. developed a mixed Eulerian-Lagrangian [4] thermal mechanical model to study round steel billets. A thermal-mechanical finite element model, CON2D, has been developed at the University of Illinois over the past decade [5, 6]. This paper summarizes the features of this model and describes one of its recent applications: prediction of the maximum casting speed to avoid crack formation due to bulging below the mold during continuous casting of square billets. Heat Transfer and Solidification Model The model solves a 2D finite-element discretization of the transient heat conduction equation in a Lagrangian reference frame that moves down through the caster with the solidifying steel shell. The nonlinear enthalpy gradients that accompany latent heat evolution were handled using a spatial averaging method by Lemon [7]. It adopts a three-level time-stepping method by Dupont [8]. Stress Model The force equilibrium, constitutive, and strain displacement equations in this 2-D slice through the shell are solved under a condition of generalized plane strain in the casting direction [5].