IDS tool

OUR TOOL 2. IDS – MULTIPHYSICAL TOOL FOR MODELING OF SOLIDIFICATION, MICROSTRUCTURE DEVELOPMENT AND MATERIAL PROPERTIES IN CASTING PROCESSES OF STEELS INCLUDING THE POSSIBLE SUBSEQUENT COOLING, REHEATING AND ROLLING PROCESSES

General:

The microstructure of steels cover dendrites, grains, phases, inclusions, precipitations, etc. It is characterized by such features like size, morphology, distribution and fraction of grains, phases, inclusions, precipitates, and eventual defects. Material properties in turn are strongly affected by these micro-structural phenomena. The interrelationships between the material properties, the micro-structural features and the process selection and accomplishment are self-evident.

Microstructural modeling has been carried out in various scales from atomic scale to dimensions of macroscopic processes. Although great attention has been put recently on atomistic models, they are hardly applicable to industrial scale processes like continuous casting due to its huge scale and complexity of the system and the different influencing phenomena. For such purposes, physically based fundamental models which can be adjusted by experimental data are today the most realistic and practical approaches. One such simulation tool, IDS, is briefly introduced below.

IDS is a physically based tool even it has also empirical features. We call IDS a thermodynamic-kinetic-empirical tool. It is fast and can applied in online calculations. This is not so general for physically based tools.

IDS is a physically based tool even if it has also empirical features. We call IDS a thermodynamic-kinetic-empirical tool. IDS simulates solidification, phase transformations, compound formation/dissolution (inclusions and precipitates), and solute distribution during the solidification of steels and during their cooling/heating process after solidification including the reheating furnace and even hot rolling. The package also simulates solid state phase transformations related to the austenite decomposition process. Additionally, it calculates important thermophysical material properties (such as enthalpy, thermal conductivity, and density) from the liquid state down to room temperature. The development started in Finland in 1984 in cooperation between universities and the steel industry. Recently, the IDS database has been extended to enable improved simulations for new steel grades. AS mentioned, the tool is computationally so fast that it is suitable for online applications.

There are two different IDS versions. One is a desktop program with a graphical user interface (GUI). Another tool is called OnlineIDS and it is a computing library (DLL) without GUI. OnlineIDS can be coupled with other tools (e.g. heat transfer models) and applied for online applications.

Figure 1: IDS tool – Inputs and main outputs. Inputs are just steel nominal composition and cooling rates. Cooling rates can be given as a profile calculated with another tool or given as two fixed cooling rates, one for solidification and one for austenite decomposition. Advanced user can give more information and own microstructure data as dendrite arm spacing but the tool has default formulas for arm spacing too.

The calculations of the IDS package are made in one volume element set on the side of a dendrite arm (Figure 2). A realistic simulation provides that there are no strong liquid flows capable of transporting solutes to certain parts of the strand (causing macrosegregation).

Figure 2. Calculation domain. Magnified portion of the mushy zone showing a volume element on the side of a dendrite arm and some results of simulation (L=liquid, δ=ferrite (bcc), γ=austenite (fcc), TLIQ= liquidus temperature, TPER=peritectic temperature, TSOL=solidus temperature).

The present IDS package includes the following calculation modules:

· SOL: Simulation of solidification

· ADC: Simulation of austenite decomposition

· MAT: Calculation of material properties

· GAS: Calculation of hydrogen and nitrogen solubility, pressure and diffusivity

· PRF: Simulation of precipitate formation at the austenite/austenite and ferrite/austenite phase interface

· SCA: Simulation of oxide scale formation in the steel surface

· A special model has been developed to determine the diffusion coefficient of hydrogen in different steels – this can be applied to determine optimal conditions for removal of hydrogen from the as-cast steel.

The package also contains a data bank, which includes the material data needed in calculations (parameters for Gibbs energy, enthalpy, diffusion, microstructure, thermal conductivity, density and liquid viscosity). Nowadays IDS is applied also to quality prediction. It is not a separate module, but in the next versions we will collect th emsot important quality indices into one output file.

IDS main instruments

Thermodynamic chemical-potential-equality equations

• Determination of thermodynamic equilibrium at the phase interfaces

• Based on substitutional solution, sublattice and magnetic ordering models

Interfacial material balance equations

• Determination of mass conversion due to interface movement

• Fick’s 1st law of solute diffusion included

Finite difference application of Fick’s 2nd law

• Simulation of solute diffusion in single-phase regions

Empirical regression formulas of austenite decomposition (ADC)

• Based mainly on German and British CCT measurements

• Formulas for temperatures indicating start and end of phase transformations

• Formulas for critical cooling rates of phase transformation noses

Empirical material property formulas

• Based on the experimental measurements of the literature

• Formulas for microstructure (secondary arm spacing and austenite grain size)

• Formulas for the thermal conductivity, density, viscosity, surface tension

• Formulas for fusion entropy of individual solution phases

Main simplifications:

• Hexagonal dendrite arm arrangement

• Complete solute mixing in liquid: Diffusion infinite in liquid, no solute transport in liquid

• Thermodynamic equilibrium at the phase interfaces: Reasonable, widely applied assumption in solidification models

• No undercooling before the formation of a new phase: Real phase formation temperatures are slightly lower, especially below the solidus)

• No solute partition in low-alloy steels below 900°C (except for interstitial atoms C, B and N): Reasonable assumption due to the low solute diffusivities of substitutional atoms at low temperatures

• No solute partition and movement of / interface in high-alloy steels (stainless) below 600°C: Reasonable assumption due to the low solute diffusivities at low temperatures.

• Diffusion of solutes small interstitial atoms B,C,H,N,O extremely rapid at high temperatures : Reasonable assumption during cooling rates of conventional solidification processes

Alloying elements included Fe, C, Si, Mn, P, S, Cr, Mo, Ni, Nb, Ti, V, B, Al, Ca, Cu, N, Ce, Mg, O, H (note: not all elements in all modules).

Phases: α-ferrite, Δ-ferrite, eutectic ferrite, austenite, cementite, pearlite, bainite, α-martensite (bct structure), ɛ-martensite (hcp structure).

The tool includes the formation and evolution of stoichiometric and semistoichiometric inclusions and precipitates. The possible inclusions/compounds of simulation are:

• Stoichiometric binaries: AlN, BN, CrN, Cr2N, Si3N4, TiB2, CaS, MgS, H2(g), N2(g), CO(g), Fe2B, Fe3C, CNb, CTi, CV, Graphite, Al2O3, B2O3 (liquid), CaO, Ce2O3, Cr2O3, FeO, MgO, MnO, SiO2, Ti2O3.

• Stoichiometric ternaries: FeMo2B2, Fe3Mo3C (M6C, simplified), FeNbB, Ti2CS, Al2CaO4 (spinel), Al2MgO4 (spinel).

• Semistoichiometric ternaries: (Mn,Fe)SL (liquid), (Mn,Fe)S, (C,N)Nb, (C,N)Ti, (C,N)V, (Cr,Fe)2B, (Fe,X)2B (X=Cr,Mn,Ni,V), (Fe,X)3C (X=Cr,Mn,Mo), (Cr,Fe)7C3, (Cr,Fe)23C6, (BC)6Fe23, (Cr,Ni)8Fe9 (sigma).

IDS databank

During the years, a great number of material data needed in IDS simulations has been restored to the IDS databank. All these data have been verified with experimental measurements. Most of that data is the Gibbs energy data of solution phases and compounds taken from thermodynamic assessments of iron-based alloys. The contents of the databank are presented below.

· Thermodynamic Gibbs energy data. Phases: liquid, ferrite, austenite, compounds and cementite. Components: Fe, C, Si, Mn, P, S, Cr, Mo, Ni, Cu, Al, N, Nb, Ti, V, Ca, Ce, Mg, B, O, H

· Diffusion coefficients of solutes. Phases: ferrite and austenite. Solutes: Si, Mn, P, Cr, Mo, Ni, Cu, Al, Nb, Ti, V, Ca (diffusion of B, C, H, N, O, S assumed extremely rapid)

· Microstructure data. Parameters for calculating primary dendrite arm spacing, DAS1, secondary dendrite arm spacing, DAS2, and austenite grain size, Dgra. Calculated DAS2 is used as a default value for the SOL simulation (can be accepted or rejected by the user). It is also used as the initial value for the size of austenite grains, whose growth is then calculated during the SOL and ADC simulations. The value of DAS2 is applied in SOL simulation and values of Dgra are applied in ADC simulation.

· Thermophysical material data:

1. Enthalpy, specific heat and latent heat (derived from the Gibbs energy data)

2. Thermal conductivity. Phases: liquid and solid. Components: Fe, C, Si, Mn, Cr, Mo, Ni (liquid) and Fe, C, Si, Mn, Cr, Mo, Ni, Al, Cu, Nb, Ti, V (solid).

3. Density. Phases: liquid, ferrite, austenite, cementite, graphite, sigma. Components: Fe, C, Si, Mn, P, S, Cr, Mo, Ni, Al, Cu, Nb, Ti, V, B.

4. Dynamic liquid viscosity. Components: Fe, C, Si, Mn, P, S, Cr, Mo, Ni, Al, Cu, Nb, Ti, V, B, N, O. 11

5. Surface tension between liquid and air. Components: Fe, C, Si, Mn, P, S, Cr, Mo, Ni, Al, Cu, Ti, N, O.

6. Fusion entropy. Phases: ferrite and austenite. Components: Fe, C, Cr, Mo, Ni. For the calculation of solid/liquid interface energy.

· CCT data. Parameters of CCT regression formulas. Components: C, Si, Mn, Cr, Mo, Ni, Al, Cu, B, Applied in ADC simulations.

Table 1: Recommended minimum and maximum solute compositions of IDS. We are extending these ranges all the time. The next version includes high Mn stainless steels.

Figure 3. IDS main window

Figure 4. IDS composition window. Example steel EXA1 with composition 0.15%C-0.3%Si-0.8%Mn-0.02%Nb-0.005%N-0.001%S

Figure 5. IDS Run parameters window for a composition/steel grade EXA2. Constant cooling rates for solidification SOL (1.0 C/s) and austenite cooling rate ADC (0.1 C/s), and default oxygen pressure (0.21 atm),

Figure 6. IDS example results: Solidification diagram for composition 0.15%C-0.3%Si-0.8%Mn-0.02%Nb-0.005%N-0.001%S with solidification cooling rate 1°C/sec and cooling rate for austenite decomposition 0.1°C/sec.

Figure 7. Comparison of enthalpy for steels: Low-alloyed steel and High-alloyed steel Both cases use constant cooling rates for SOL (1.0 C/s) and ADC (0.1 C/s).

IDS CASE EXAMPLE: SCALE MODULE

SCA module is applied to simulate the oxide scale formation at the continuous casting strand surface and/or in the subsequent processes. So, the simulation can be extended from the start of continuous casting to the end of the possible reheating or rolling processes. The model applies a databank containing thermodynamic, diffusion and material property data, and it has been validated with numerous literature measurements.

The scale formation tendency is described by the driving forces of different oxides calculated at a given temperature and O2 pressure of the furnace. At each temperature, equilibrium ferrite and austenite fractions and compositions are first calculated for the given steel composition, and then, based on the prevailing O2 pressure of the atmosphere, driving forces of 15 oxides, i.e., FeO, Fe3O4, Al2O3, B2O3, Ce2O3, Cr2O3, Cu2O, MnO, MoO2, NbO2, NiO, SiO2, Ti2O3, V2O3, Fe2SiO4, are calculated from both the ferrite and austenite steel matrices. These driving forces are then weighted by the calculated ferrite and austenite fractions to get the oxide driving forces for the whole steel composition. Finally, these driving forces, at a certain temperature, are summarized to get the total oxide driving force. The model was developed further to calculate approximate amounts of different oxides as a function of temperature. Also, the characterization of the oxides, whether they are detrimental or not, is given. The outputs are:

• Metal loss (mg/cm2)

• Oxide weight gain (mg/cm2)

• Different oxide fractions (%)

Figure shows how a too-high holding temperature and oxygen pressure of the furnace clearly increase the metal loss in plain carbon steel (0.15%C), but not so much in stainless steels (AISI 410 and 316). The weaker oxidation in the latter steels is due to the formation of protective Cr2O3 and MoO2 layers.

Figure 8. Calculation example - scale model. The metal loss in plain carbon steel (0.15%C) and stainless steels AISI 410 and AISI 316. The weaker oxidation in the latter steels is due to the formation of protective Cr2O3 and MoO2 layers.

IDS CASE: QUALITY PREDICTION

IDS calculates many fundamental phenomena taking place during casting and during the subsequent cooling and reheating processes. Many of these phenomena can be correlated with sensitivities to different kinds of defects. Because the IDS inputs are steel composition and cooling patterns, then these can be correlated with defect sensitivities via these calculated fundamental phenomena. Also, the root causes for defect formations will be obtained and so, as an example, to give feedback to the operators to make necessary corrections. The computational efficiency of IDS ensures that the tool is applicable in the real-time operation.

By way of examples, IDS calculates many indices/criteria and writes them to a file *.SI, but the user can define also own criteria using data from the IDS output data files. The following criteria are automatically calculated in the present IDS version: QIstr, QIshe, QIsoB, QIsoP, QIsoS, QIsul, QIaus, QIgra, QIHzst, QINzst, QIOzst, QIHsol, QINsol, QIOsol, QIexcN, QIexcH, QIfpcFer, QIfpcMar and QIfpcBai.

Explanations:

· QISTR = Maximum change of delta ferrite (fraction) caused by the phase transformation from ferrite to austenite (during peritectic reaction) between the zero-strength temperature (TZST) and the final solidification (TSOL). Tzst = temperature at solid fraction, fs = 0.75.

· QISHE = Maximum change of delta-ferrite (fraction) between Tsol and Tsol-30°C

· QIsoB = Dissolved amount (wt%) of B in the last liquid drop at Tsol

· QIsoP = Dissolved amount (wt%) of P in the last liquid drop at Tsol

· QIsoS = Dissolved amount (wt%) of S in the last liquid drop at Tsol

· QIsul = Fraction of liquid (Mn,Fe)S at Tsol

· QIAUS = Volumetric shrinkage caused by the phase transformation above solidus from liquid to austenite after peritectic reaction

· QIgra = Austenite grain size at Tsol-200°C

· QIHzst = H2 gas amount (micro moles) formed in liquid between Tliq and Tzst

· QINzst = N2 gas amount (micro moles) formed in liquid between Tliq and Tzst

· QIOzst = CO gas amount (micro moles) formed in liquid between Tliq and Tzst

· QIHsol = H2 gas amount (micro moles) formed in liquid between Tzst and Tsol

· QINsol = N2 gas amount (micro moles) formed in liquid between Tzst and Tsol

· QIOsol = CO gas amount (micro moles) formed in liquid between Tzst and Tsol

· QIexcN = Excess (insoluble) N (ppm) at 25°C

· QIexcH = Excess (insoluble) H (ppm) at 25°C

· QIfpcFer = Fraction of ferrite at final phase constitution (25°C)

· QIfpcMar = Fraction of martensite at final phase constitution (25°C)

· QIfpcBai = Fraction of bainite at final phase constitution (25°C)

The criteria presented above are steel composition and cooling rate based. Some notes about the criteria are below:

QIstr and QIshe criteria. QIstr criterion calculates the maximal transformation from δ-ferrite to austenite during the last stage of solidification, i.e., between Tzst (zero-strength temperature) and Tsol. QIshe is the maximal transformation from δ-ferrite to austenite just after the solidification, i.e., between Tsol and Tsol-30°C. These phase transformations and the related volume changes cause stresses and strains in the structure and so increase the sensitivities to many kinds of defects. If the QIshe value is high, as with steels Ceq=0.1%, an air gap forms between the mold and the steel shell because of the δ-ferrite to austenite transformation just below the solidus. Figure shows the phenomenon with Ceq=0.1% steels schematically). Figure shows the criteria QIshe and QIstr calculated for the binary Fe-C system using a solidification rate of 1 °C/s. If the value QIshe or QIstr is high, the steel is very prone to many kinds of surface quality problems including bleeding defects. The sum of these two criteria is high for the binary Fe-C system at about Ceq.=0.13%. It could be expected that the steel is then also prone to surface defects.

Figure 9. Schematic picture. Beginning of solidification of steel 0.1 Ceq (%) in the mold with air gap formation which causes reduced heat transfer and grain growing at the surface.

Figure 10. The criteria QIshe and QIstr were calculated for the binary Fe-C system. Solidification rate 1 °C/s. Typically, QIshe is highest at around C=0.1% and QIstr at around C=0.18% compositions but alloying elements may change these values. The highest top values should be avoided by chemical composition adjustment if the steel grade is sensitive to surface quality problems.

Criteria QIsoS, QIsoP, QIsoB. It is well known that high microsegregation of for instance P, S and B strongly increases the sensitivities to hot cracking, bleeding, and some surface defects too. IDS calculates the dissolved amounts of S, P, B, and the sum of them in the last liquid just above the solidus temperature. Inclusions forming is considered and they reduce the dissolved amounts, as (MnFe)S. The sum of these indices (QIsoS, QIsoP, QIsoB) can also be useful in quality prediction.

Two industrial case examples (published in steel research Int. 2024, 2300529)

IDS was coupled with a steady-state heat transfer model, known as Tempsimu, to simulate the continuous casting process. Measured compositions are utilized in the simulations and defects reported at a steelmaking plant are used as labels in classification. Logistic regression, decision tree, and Gaussian Naïve Bayes classifiers are developed to predict transverse cracking in peritectic C–Mn and low-carbon B–Ti micro-alloyed steels. For these two cases, the decision tree gave the best results. So mainly composition and cooling rate-based criteria were applied. The results are very good. Now also some process data will be applied.

1. Prediction of transverse cracking in peritectic C-Mn steel in vertical-bending slab caster

Figure 11. The final decision tree predicting transverse cracking in the peritectic C–Mn steel. Only two IDS criteria are used to get good results: 1) Amount of AlN precipitates during straightening and 2) QIstr criterion.

Table 2. Performance of classifiers predicting transverse cracking in the peritectic C–Mn steel.

Figure 12. The normalized confusion matrix of predictions for the best classifier predicting transverse cracking in the peritectic C–Mn steel. 95.7% of slabs without defects could be predicted correctly and 88.7% of slabs with defects.

To avoid the defects:

· Reduce AlN during straightening, i.e. reduce N or change the secondary cooling

· And/or reduce the QIstr criterion (by for instance reducing a bit C%, if possible)

2. Prediction of transverse cracking in low-carbon B–Ti micro-alloyed steel in vertical bending slab caster

Figure 13. The final decision tree predicting transverse cracking in the low-carbon B–Ti micro-alloyed steel. Only two IDS criteria are again used to get good results, QIaus and the temperature difference between Tzst and Tsol (= QIsol (Tzst-Tsol).

Table 3. Performance of classifiers predicting transverse cracking in the low-carbon B–Ti micro-alloyed steel.

Figure 14. The normalized confusion matrix of predictions for the best classifier predicting transverse cracking in the low-carbon B–Ti micro-alloyed steel. 91.2% of slabs without defects could be predicted correctly and 98% of slabs with defects.