A simple, but comprehensive model of heat transfer and solidification of the continuous casting of steel slabs is described, including phenomena in the mold and spray regions. The model includes a one-dimensional (1-D) transient finite-difference calculation of heat conduction within the solidifying steel shell coupled with two-dimensional (2-D) steady-state heat conduction within the mold wall. The model features a detailed treatment of the interfacial gap between the shell and mold, including mass and momentum balances on the solid and liquid interfacial slag layers, and the effect of oscillation marks. The model predicts the shell thickness, temperature distributions in the mold and shell, thickness of the resolidified and liquid powder layers, heat-flux profiles down the wide and narrow faces, mold water temperature rise, ideal taper of the mold walls, and other related phenomena. The important effect of the nonuniform distribution of superheat is incorporated using the results from previous three-dimensional (3-D) turbulent fluid-flow calculations within the liquid pool. The FORTRAN program CONID has a user-friendly interface and executes in less than 1 minute on a personal computer. Calibration of the model with several different experimental measurements on operating slab casters is presented along with several example applications. In particular, the model demonstrates that the increase in heat flux throughout the mold at higher casting speeds is caused by two combined effects: a thinner interfacial gap near the top of the mold and a thinner shell toward the bottom. This modeling tool can be applied to a wide range of practical problems in continuous casters.

http://ccc.illinois.edu/pdf files/publications/03_mtb_meng_con1d_reprint_post.pdf

Heat-transfer and solidification model of continuous slab casting: CON1D

A simple analytical model of microsegregation for the solidification of multicomponent steel alloys is presented. This model is based on the Clyne-Kurz model and is extended to take into account the effects of multiple components, a columnar dendrite microstructure, coarsening, and the δ/γ transformation. A new empirical equation to predict secondary dendrite arm spacing as a function of cooling rate and carbon content is presented, based on experimental data measured by several different researchers. The simple microsegregation model is applied to predict phase fractions during solidification, microsegregation of solute elements, and the solidus temperature. The predictions agree well with a range of measured data and the results of a complete finite-difference model. The solidus temperature decreases with either increasing cooling rate or increasing secondary dendrite arm spacing. However, the secondary dendrite arm spacing during solidification decreases with increasing cooling rate. These two opposite effects partly cancel each other, so the solidus temperature does not change much during solidification of a real casting.

/pdf/simple-model-of-microsegregation-during-solidification-of-19etufzehv.pdf

Simple Model of Microsegregation during Solidification of Steels

A coupled 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 model simulates a transverse section of the strand in generalized plane strain as it moves down at the casting speed. It includes the effects of heat conduction, solidification, nonuniform superheat dissipation due to turbulent fluid flow, mutual dependence of the heat transfer and shrinkage on the size of the interfacial gap, the taper of the mold wall, and the thermal distortion of the mold. The stress model features an elastic-viscoplastic creep constitutive equation that accounts for the different responses of the liquid, semisolid, delta-ferrite, and austenite phases. Functions depending on temperature and composition are employed for properties such as thermal linear expansion. A contact algorithm is used to prevent penetration of the shell into the mold wall due to the internal liquid pressure. An efficient two-step algorithm is used to integrate these highly nonlinear equations. The model is validated with an analytical solution for both temperature and stress in a solidifying slab. It is applied to simulate continuous casting of a 120 mm billet and compares favorably with plant measurements of mold wall temperature, total heat removal, and shell thickness, including thinning of the corner. The model is ready to investigate issues in continuous casting such as mold taper optimization, minimum shell thickness to avoid breakouts, and maximum casting speed to avoid hot-tear crack formation due to submold bulging.

/pdf/thermomechanical-finite-element-model-of-shell-behavior-in-4sxhwpz46b.pdf

Thermomechanical finite-element model of shell behavior in continuous casting of steel

Solidification cracking is a significant problem during the welding of austenitic stainless steels, particularly in fully austenitic and stabilized compositions. Hot cracking in stainless steel welds is caused by low-melting eutectics containing impurities such as S, P and alloy elements such as Ti, Nb. The WRC-92 diagram can be used as a general guide to maintain a desirable solidification mode during welding. Nitrogen has complex effects on weld-metal microstructure and cracking. In stabilized stainless steels, Ti and Nb react with S, N and C to form low-melting eutectics. Nitrogen picked up during welding significantly enhances cracking, which is reduced by minimizing the ratio of Ti or Nb to that of C and N present. The metallurgical propensity to solidification cracking is determined by elemental segregation, which manifests itself as a brittleness temperature range or BTR, that can be determined using the varestraint test. Total crack length (TCL), used extensively in hot cracking assessment, exhibits greater variability due to extraneous factors as compared to BTR. In austenitic stainless steels, segregation plays an overwhelming role in determining cracking susceptibility.

Solidification cracking in austenitic stainless steel welds

To estimate the cracking condition in continuously cast steels, a new model for critical fracture stress given from the measured critical strain has been proposed, which can take into account the brittle temperature range and strain rate. The effects of brittle temperature range and strain rate on critical strain for internal crack formation were analyzed. When the brittle temperature range and strain rate were increased, the possibility of internal crack formation increased due to the decreasing critical strain. To describe the thermomechanical property model of the mushy zone between zero strength temperature (ZST) and zero ductility temperature (ZDT), the yield criterion for porous metals, which can take into account δ/γ transformation, was used. Using the fitting equation for the measured critical strain and the microsegregation analysis, the thermomechanical behavior of the mushy zone could be successfully described by the proposed model, which incorporates the effects of microsegregation of solute elements and δ/γ transformation on hot tear during solidification at the given range of steel compositions and strain rates. A cracking criterion based on the difference of deformation energy in the brittle temperature range is proposed to explain the cracking phenomenon of whole carbon range.

A new criterion for internal crack formation in continuously cast steels

Effects of carbon and sulfur on the longitudinal surface cracks have been investigated by calculating the non-equilibrium pseudo binary Fe-C phase diagram and introducing the strain in brittle temperature range for continuous casting of steels. The cracking tendency as a function of carbon content was well described by the strain in brittle temperature range. The strain in brittle temperature range was influenced by the other solute elements as well as carbon. The carbon content at which longitudinal surface cracking is maximized decreased with increasing sulfur content. At a given carbon content, the possibility of surface cracking increased with increasing sulfur content.

Effect of carbon and sulfur in continuously cast strand on longitudinal surface cracks

The effect of cooling rate on the characteristic temperatures such as liquidus temperature (TL), zero strength temperature (ZST), liquid impenetrable temperature (LIT) and zero ductility temperature (ZDT) has been investigated by calculating the non-equilibrium pseudo binary Fe–C phase diagram. The effect of cooling rate on TL was not significant. The effect of cooling rate on ZST, LIT and ZDT was significant due to segregation of solute elements at the final stage of solidification. Using the microsegregation analysis proposed by Ueshima, the calculated temperatures at the solid fractions of 0.75 and 0.99 corresponded to the experimentally measured ZST and ZDT, respectively. Prediction equation on ZST, LIT and ZDT, which can take into account cooling rate and steel composition, was proposed. At given steel compositions and cooling rates, the suggested prediction equation on ZST, LIT and ZDT could successfully describe the experimentally measured data and the calculated data from microsegregation analysis.

https://www.jstage.jst.go.jp/article/isijinternational1989/38/10/38_10_1093/_pdf

Effect of Cooling Rate on ZST, LIT and ZDT of Carbon Steels Near Melting Point

A mathematical model has been developed for the prediction of cracks in the continuously cast steel beam blank through the fully coupled analysis of fluid flow, heat transfer, and deformation behavior of a solidifying shell. Fluid flow and heat transfer in the strand mold were analyzed with a three-dimensional (3-D) finite-volume method (FVM). For the complex geometry of the beam blank, a body-fitted coordinate (BFC) system was employed. Thermo-elastic-plastic deformation behavior in the strand was analyzed using the finite-element method (FEM) based on the two-dimensional (2-D) slice model. The thermal fields of the strand calculated with the FVM were used in the analysis of the deformation behavior of the strand. Through the iterative analysis of the fluid flow, heat-transfer, and deformation behavior, the coupling parameter of the heat-transfer coefficient between the strand and the mold was obtained. In order to describe the thermophysical properties and thermomechanical behavior of steel in the mushy zone, the microsegregation of solute elements was assessed. Consequently, some characteristic temperatures of steel as well as variations of phase fractions with temperature were determined. The probability of cracking in the strand, originating from an interdendritic liquid film, was quantified as a crack susceptibility coefficient. Recirculating flows were developed in the web and flange-tip regions. The development of a solidifying shell in the flange-center region was retarded by the inlet flow from a submerged entry nozzle (SEN). An air gap was formed mainly near the flange-tip corner. Surface cracks in the web and fillet regions and internal cracks in the flange-tip region were predicted.

Prediction of cracks in continuously cast steel beam blank through fully coupled analysis of fluid flow, heat transfer, and deformation behavior of a solidifying shell

Using a 2-dimensional finite element, the effects of carbon content, slab width, narrow face taper and casting speed on solidification cracking during continuous casting of slabs were analyzed. The possibility of solidification cracking during continuous casting of slabs was predicted using the Specific Crack Susceptibility, s S c . The new proposed parameter, s S c , can represent the averaged possibility of solidification cracking of the strand during continuous casting in the mold. The surface crack formed near corner region of strand at the initial stage of solidification, and the internal crack was found in the internal regions of wide center, corner and off-corner at the middle and final stage of solidification. The carbon range sensitive to solidication cracking is between 0.1 wt% C and 0.14 wt% C steels. At the slab widths of 1900 mm and 2 150 mm, the possibility of solidification cracking increased in the regions of wide center, corner and off-corner in comparison with the slab width of 1 600 mm. With increasing narrow face taper, the possibility of solidification cracking decreased along the region of wide face due to the mechanical compression imposed by the narrow face taper. With increasing casting speed, the possibility of solidification cracking increased in the regions of wide center, corner and off-corner, because the shell thickness is largely decreased due to decrease of dwelling time of strand within the mold. These predictions at various casting conditions were in good agreement with the experimental observations in industry.

Tae-jung Yeo

Papers

A new criterion for internal crack formation in continuously cast steels

Effect of carbon and sulfur in continuously cast strand on longitudinal surface cracks

Effect of Cooling Rate on ZST, LIT and ZDT of Carbon Steels Near Melting Point

Prediction of cracks in continuously cast steel beam blank through fully coupled analysis of fluid flow, heat transfer, and deformation behavior of a solidifying shell

Analysis of Solidification Cracking Using the Specific Crack Susceptibility