Mathematical Modeling of Hot Tearing in the Solidification of Continuously Cast Round Billets

Abstract

Billets produced by continuous casting sometimes show the presence of subsurface cracks that can compromise the quality of the final product. The presence of these cracks is revealed by Baumann prints of billet cross sections in which the chill zone is visible and the short radial cracks are located only where the chill zone thickness is thinner. This experimental finding induces the hypothesis that cracks are formed as a result of the presence of unevenness in the mold heat extraction around the billet perimeter. Cracks start to open in the dendritic front in regions where the shell growth in the mold is slower. The study presented in this article focused on steels with a sulfur content of about 300 ppm. The Baumann prints taken from billet samples of numerous different heats allowed detecting the presence of subsurface cracks and their location nearby visible chill zone thinning areas. To understand the mechanisms of crack formation and to define the possible corrections, a modeling activity has been carried out using the finite element technique on 148-mm diameter billets continuously cast at TenarisDalmine (Dalmine, Italy). The model performs a two-dimensional thermomechanical analysis of the solidification in the mold and within about 4 cm below the mold exit, along which the shell surface is cooled only by radiation to the environment, before the sprays of the first ring impact on the strand. The model includes the contact of the shell with the mold inner surface, which moves according to taper and distortion (this last part is calculated by means of a separate mold model); the steel creep behavior; the calculation of the heat transfer through the gap depending on the local mutual distance between the two surfaces; the effect of the liquid steel fluid dynamics on the solidification growth as a result of the temperature distribution; and the calculation of a hot tearing indicator represented by the porosity fraction caused by mechanical strains applied at the dendrite roots. From the simulation results, it is concluded that subsurface cracks are generated in the space between the mold exit and the first cooling ring; the involved mechanisms of formation also are withdrawn. Nucleation of MnS precipitates of large dimensions is an additional cause of defectiveness in controlled sulfur steels. As a final conclusion of this work, the most important actions to eliminate subsurface cracks are derived.

Review on Modeling and Simulation of Continuous Casting

“…An excellent analytical solution of solidification of an elastic-perfectly-plastic material exists, [171] which has been used for verification of a few thermal-mechanical models of steel continuous casting. [11,34,35,164,165] These studies Figure 18. Simulated narrow face mold shape (curved lines) and inclinometer measurements (straight lines) just after startup and after a width change.…”

“…Unlike models of heat transfer and fluid flow, where such validation has become routine, it is much less common to see proper verification and validation of thermal‐mechanical models prior to their application to practical continuous casting problems. An excellent analytical solution of solidification of an elastic‐perfectly‐plastic material exists, which has been used for verification of a few thermal‐mechanical models of steel continuous casting . These studies reveal that achieving mesh refinement is still an obstacle to accurate modeling, as a much finer mesh is needed for mechanical analysis than for thermal modeling alone.…”

“…Many detailed models have been developed to predict heat transfer across the interfacial gap between the strand and the mold wall in a fundamental manner. [13,[15][16][17]19,22,[30][31][32][33][34][35][36][37] Interfacial heat transfer depends on the thermal conductivity of the interfacial layers and the size of the gap, which requires both detailed models of the gap and measurements. Lab measurements of mold slag thermal conductivity must be interpreted using models to extract the property data from the raw measurements.…”

“…Surface shape problems that have been studied with thermalmechanical computational models include deep oscillation marks and transverse depressions, [151,154] longitudinal depressions, [165,174] off-corner gutters, [174] rhomboidity in square billets, [175] ovalization of round billets, [35,176] and bulging in large blooms and slabs. [3,166,177,178] Unless they are extreme, the shape problems themselves are less important than the cracks and macrosegregation problems that often accompany them.…”

“…[37,174] Coupling them with a detailed model of the interfacial gap model enables better accuracy in the corner regions, by accounting for phenomena such as a larger local air gap decreasing heat transfer across the gap, resulting in lower mold temperature, hotter shell surface temperatures, and a thinner shell. [15,31,[35][36][37]179] Even better accuracy can be achieved if the effects of fluid flow are taken into account by coupling with a thermal-flow model. A few models have demonstrated such multiphysics approaches, which are especially important in the mold, where flow has a large influence on shell growth.…”