cooling rate optimization of as-cast...

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Iranian Journal of Materials Science & Engineering Vol. 9, Number 3, September 2012

1. INTRODUCTION

One of the challenging subjects in the steelproduction industry has been optimizing thecooling rate of quenching as-cast steel to roomtemperature to have higher productivity withoutlowering the quality of the cast steel. When steelcools from a high temperature, residual stresses aredeveloped due to thermal, mechanical ortransforming austenite to other phaseconfigurations. The products of the phasetransformation depend on the austenitecomposition and cooling rate. Stresses developedduring quenching of as cast steel can raise fromdifferent sources such as, thermal stresses,volumetric stress, internal stresses, phasetransformation stresses, post phase transformationstresses (interaction among the phases) and etc.These stress concentration zones are vulnerableregions to the formation of microcracks or growthof the flaws in these regions. Qualitativeinformation about temperature evolution, coolingrate, residual stresses and distortion, assist therealistic modeling. Smolijan [1] predicted the strainand residual stress evolution within a geometricallycomplex specimen (e.g. cylinder, cones, spheres,etc) dealing with estimation of microstructure and

hardness distribution after quenching using amathematical method based on the finite volumemethod and Jominy tests results. He did notconsider in his simulations any existence orformation of anomalies or defects before or afterquenching. A quenching simulation for morecomplex geometry such as stepped cylinder andaxially symmetric steel workpiece were publishedby other software programmers [2-3]. Chen andMeekisho [4] developed the model of a quenchingprocess to study the effect of actual servicecondition aspects such as the presence of holes ornotches using temperature dependent materialsproperties. Reti et al. [5], developed aphenomenological kinetic model flexible for bothisothermal and non-isothermal conditions todescribe the multiphase diffusional austenitedecomposition which occurs during quenching oflow alloy hypoeutectoid steel after austenizationthrough pseudo-autonomous differential equations.Many publications are available on the simulationof the phase transitions in steel [6-14]. Someresearchers implement the classical nucleation andgrowth theory to model the microstructure of agiven austenite grain size cooling down withdifferent rates to the ferrite- transformationtemperature range [15-18]. Gur and Tekkaya [19]

COOLING RATE OPTIMIZATION OF AS-CAST CONSCIOUSLY CASTSTEELM. R. Allazadeh* [email protected]: January 2012 Accepted: August 2012

University of Pittsburgh, Mechanical Engineering Department, Pittsburgh PA, 15261.

Abstract: Combination of a finite element method (FEM) algorithm with ANSYS codes and post image processing ofNDT ultrasonic images along with laboratory cooling experiments and microstructural analysis provides a guidelineto determine the optimum cooling rate for any grade of steel in which the highest productivity can be achieved withoutany degradation of the cast steel products. The suggested FEM algorithm with ANSYS codes is introduced to developa quasi real models to simulate quenching of as-cast steel with any cooling rate from any initial temperature belowsteel’s melting point. The algorithm builds a model which is capable to approximate the thermodynamic stressesgenerated by thermal strain and possible solid-solid phase transformation for as-cast steel with any chemicalcomposition. The model is applicable for any casting geometry (slab, billet and bloom, bar, etc.) and adaptable for anymethod of cooling (unidirectional or multidirectional). Cooling with any cooling agent can be simulated with thealgorithm in an ideal case. The phase transformation of the steel in the algorithm can be controlled by ContinuousCooling Transformation (CCT) Diagram obtained from analytical calculation or real time-temperature-transformation experiments for the cast steel. A function for optimizing cooling rate is suggested.

Keywords: Cooling rate, Optimization of production rate, Cast steel, continually casting steel, FEM algorithm, ANSYS

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combined thermal analysis and microstructuralanalysis with small strain elastic-plastic analysis topredict the temperature distribution, the progress ofphase transformation, the evolution of internalstresses and residual stresses during quenching foraxisymmetric steel components. Wang et aldeveloped an FEM process model of quenching ofsteel 1080 steel cylinder in water to demonstrateaustenite-pearlite and austenite-martensitetransformation and suggested an elastic-plasticstress analysis [20]. Different researchers [21-25]investigated the effect of phase transformation onthe residual stresses within quenched bodies. Theseresidual stresses have an important role in changingthe soundness of the steel during cooling.Nevertheless, many theoretical models weresuggested to prescribe the steel quenching byresearchers. Most of them, if not all, relied on thesimplifications that rendered the unrealisticoutcomes [1]. A wide range of cooling processanalyses is based on the FEM and finite volumemethod (FVM) computer simulations. However,researchers [26] focused mainly on the followingfour basic analyses in their simulations: (a) heattransfer analysis during the cooling process (b)microstructural composition analysis via materialproperties, which mainly refer to thermal andmechanical properties (c) thermoplastic stress-strain analysis (d) fracture and debonding as well asvoid nucleation or growth analysis for computationof damage tolerance.

The objective of this paper is to introduce amethod to define the optimum cooling rate forcooling continuously as-cast steel on industriallevel. An FEM algorithm developed with theANSYS codes is introduced in this research workto simulate the cooling of as-cast steel from anytemperature below the solidification temperature.The algorithm is capable of being customized tosimulate the thermodynamic behavior of as-caststeel microstructure with any chemicalcomposition and any casting geometry imposedto desired cooling method. The ultimate intentionof this research work is to provide a guideline oncooling process set up in continuous casting steelproduction for different steel compositionsthrough NDT tests, cooling experiment tests andFEM numerical analyses. Therefore, this workwill help to improve the efficiency of the casting

of steel by increasing the productivity anddecreasing the inventory period of solidifiedcontinuously casting steel strand (slabs, blooms,and billets) in the production line withoutdegrading the quality.

2. OPTIMIZATION TECHNIQUE OF THECOOLING RATE ON CONTINUOUSLYCAST STEEL PRODUCTION LINE

Solidification is a major source of creation ofanomalies in the bulk material. Kianfar et al. [27]claimed to simulate three dimensional simulationof solidification in a horizontal billet continuouscasting for an industrial billet caster. In addition,residual and local stresses around anomalies or inthe vicinity of grain boundaries are the source ofmicrocrack or crack propagation during heattreatment and cooling of solidified hot steel [28].Additive elements to molten steel duringcontinuous casting may introduce inclusions tothe microstructure of the strand, which maychange the defect density of the hot as-cast steelduring cooling. Author has discussed the effect ofthe chemical composition of the inclusion on thedistribution of the stress concentration zone in thesteel microstruture during cooling in [29] by twodimensionless parameters. These parameters arethe stress concentration factors and the inclusionrigidity factor.

Therefore, to determine the maximum coolingrate, it is essential to extract the information ofthe as-cast steel microstructure and defectscharacterizations on production line. Theextracted data should include the density, size,type and location of all inclusions, voids andflaws or cracks within the as-cast steel. Theultrasonic NDT post image processing developedby author, whose detail was published in [30],coupled with the DT microstructural analysis,provides information to decode further theinformation embedded in the NDT tests images.In this NDT post image processing technique, aMicrosoft Excel program was coupled with acommercial software ultrasonic image processingprocess and analyzes the NDT parameters tospecify the type of the anomalies in themicrostructure and the three dimensionalobjective Cartesian coordinate position of the

M. R. Allazadeh

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defect in the microstructure. Thereby, it canprovide a three dimensional image of themicrostructure of the as-cast steel after secondarycooling stage on continuously cast productionline. These images are used by an FEM algorithmto approximate the stress configuration of themicrostructure and predict the characteristic dateof all existing anomalies after cooling hot as-caststeel to room temperature with different coolingrate. An FEM algorithm developed with theANSYS codes introduced in this paper simulatesthe cooling of as-cast steel from any temperaturebelow solidification temperature. The algorithmis capable to be customized to simulate thethermodynamic behavior of as-cast steelmicrostructure with any chemical compositionand any casting geometry for a desired coolingmethod. The phase transformation simulationswere based on the CCT diagram and, therefore,they were quasi-real models. The models predict,numerically, the generation of the stressconcentration regions due to the thermodynamicstrains during cooling a sample from the austenitetemperature range with different cooling rates.The correction factors for the computationparameters and FEM variables reserved withinthe algorithm provide adjusting tools for differentsimulation case to increase the precision of theresults in industry.

3. THE FEM ALGORITHM TO PREDICTSTRESS DISTRIBUTION WITHIN COOLINGAS-CAST STEEL

A mathematical model requires three types offormulation to simulate the cooling process of theas-cast steel with austenitic microstructure: thetransformation process, cooling rate and elastic-plastic deformation within the microstructure.The simulation of a cooling process is formulatedby the heat transfer governing equations definedin many academic course books. All the heattransfer mathematical models follow two mainsteps, first, establish a stress strain relationshipbased on thermodynamic constitutive laws, and,second, develop a proper method to demonstratereal heat data evolution [1]. A quasi real ANSYSprogram is developed to approximate the stressdistribution during cooling through thickness of

cast steel with different cooling rate and definedboundary conditions the same as those imposedin the experimental process in an ideal case (nobubble formation, homogenous constanttemperature, etc.). The level of complexity of theeffective factor on cooling rate depends on thenumber of different phenomena contributing tomodify the microstructure of the steel duringcooling from the austenite temperature. Some ofthese phenomena are phase transformation,diffusion and impurity segregation, modifyingthe unit cell and atoms arrangement during phasetransformation, localized stresses due to thermalvolume changes and many other factors.

The algorithm presented in the Figure 1computes the thermal gradient within themicrostructure and thermal structural contractionresulted from temperature drop in the coolingprocess within the acceptable precision fordefined thermal and mechanical properties ofsteel. Unlike most of the numerical simulationswhich calculate the change of phase fractionduring simulation, the cooling curve-phasetransformation data are based on theexperimental results from CCT diagrams in thealgorithm presented in Figure 1. Therefore, thenumerical model introduced in this paper isquasi-real since not only the material properties,geometrical information and boundary conditionsare based on the experimental model but also thedecomposition of austenite into product phases ofthe phase transformation is read from a databaseprovided to the program by the user. The CCTdiagram furnishes this information for the modelto be able to simulate the cooling of a steel slabwith different cooling rates for given chemicalcompositions. The CCT diagram can be providedto the algorithm by commercial software such asJMATPRO whose graph is an analyticalapproximation or experimental results performedfor a given steel grade (i.e. steel with definedchemical composition). Therefore, the model cansimulate both a simple cooling curve and acomplicated cooling path process for a widerange of different types of steel. Nevertheless, thepriority of phase transformation is determined bythe CCT diagram introduced into the program.ANSYS Parametric Design Language (APDL) isutilized to introduce the CCT diagram into the

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FEM code and couple the thermal and dynamicanalysis. The qualitative and quantitativeinformation about the elements in themicrostructures of each sample can give theapproximate phase transformation temperature asa function of alloy content, time and temperature.The block specified for the decision of phasetransformation judges the necessity of the phasetransformation and furnishes the information fordata sorting to introduce the phase configurationof the microstruture after each load step. Themodel was designed to be controlled with thevolume fraction of phases presented in the final

microstructure after cooling to room temperatureto increase the accuracy of the stress analysis.The volume fraction phases presented in themicrostructure after transformation of austeniteto the other phases follow the unity percentagerule in the algorithm as next;

(%ferrite+%pearlite+%bainite+%martensite+%austenite+%otherphase) /100=1 (1)

The experimental kinetics of the isothermalphase transformation for ferrite, pearlite, andbainite can be calculated by Johnson-Mehl-

M. R. Allazadeh

Fig. 1. Flow chart of the FEM algorithm proposed to simulate cooling of as-cast steel slab.

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Avrami governing equation as [6-8];

(2)

where Vk and Vy are the volume fraction beforeand after transformation. t is the quenching time,b and n are temperature dependent phaseconstants. Then Koistimen and Marburger [31]deployed the same method to define therelationship between volume fraction before (Vm)and after (Vn) the martensite transformation asshown in Equation 3;

(3)

where Ms is the martensite start temperature inthe CCT diagram and T(t) is the temperature ofthe material at given time, t. The value of theconstant, c, is given in the literature as 0.011 [19].If the final product of the cooling is known, theprogram can be set to mimic the experimentaldata for final volume fractions of different phasesin the microstructure. Therefore, instead ofestimating the phase fractions with Equations 2and 3, the actual volume fracture for the phasesare embedded in the program as a function of thethermal expansion coefficient. It reduces thecalculation of the residual stress within the finalmicrostructure.

The structure deformation within the elementdue to the solid-solid transformation carries out byintroducing thermo-elastic strain into the elementssubjected to the phase transformation in anisothermal condition. The nodal and elementoutcomes of the proposed algorithm in the ANSYSprovide the final phase configuration of themicrostructure and thermal distributions andaccumulation stress concentration zones. Thereby,the results can mark the vulnerable region to theformation of microcracks or the growth of flaws.The models were designed for thermally inducedstresses (such as those resulting from cooling)rather than mechanically applied stress models.The maximum stress concentration zone usuallyappears at the interface of two phases in themicrostructural configuration. It was observedfrom the results of the numerical computation thatthe shape of the grains changes the distribution ofstress concentration zones [28, 32]. The algorithm

can simulate the cooling and solid-solid phasetransformation processes for used defined grainshape. The collection of the numerical simulations,resulting from different steps of the acceleratedcooling simulation, indicates that the stressconcentration zones generated by solid-solid phasetransformation were stored in the microstructurewhich some example of such numerical results willbe presented in this paper. The properties of thegrain boundaries (GB) play important roles in theintensity of the accumulated residual stressesduring accelerated cooling of as-solidified steel.This fact can be observed in the results of thenumerical simulations in the other publications [28,32]. Four different methods are available in thedeveloped ANSYS program to build interfacialregion between grains representing GB. These fourintergranular interaction methods built in thepresented algorithm are;• Interfaces formed by glued grains: ANSYS

merge the nodes at contact surfaces of twoadjunct grains so there is not anydiscontinuity for thermodynamic fields atgrain boundaries by other word the grainboundary is ignored in the simulations.

• Thin layer bodies: they are built bymeshing interspaces regions betweenadjacent grains surfaces, these elementspossess complete set of thermo-dynamicmaterial properties, this GB model can betuned up to provide GB properties withbetter accuracy in compare to other GBmodels.

• Contact element interface method: ANSYSdefined master-slave interaction among thenodes at the interfacial surfaces of theadjacent grains by giving dynamicproperties to the nodes of the contactsurfaces.

• Cohesive zone interface method: ANSYSgenerates interfacial elements withcohesion properties built by the nodes ofcontact surfaces of adjacent grains.

In the numerical model presented in this work,the inter-granular cracks are simulated byincluding the properties defined for the grainboundary of the microstructure. This increasesthe precision of the simulation. However, itcauses discontinuity and convergence problems

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in the mathematical calculation in the code.Interaction of atoms and metallurgical behaviorof unit cells in a crystal are more complicatedthan the continuum model used in the FEMsimulations, many factors were also neglected inthese simulations to simplify the model.However, the models are able to present theresidual stress concentration within themicrostructure during cooling. In the model, theheat was considered to transfer due to threemodes of the heat transferring of conduction,convection and radiation. The material wasassumed to be perfectly isotropic, which for multicrystal material is a reliable assumption. It isimportant to note that the computation time wasnot the same as real time in the coolingexperiment. The relation between real time in theCCT diagram and computational time was setthrough a number of time steps per second. Thisvalue was set in a time correction factor, (TCF),whose value is a function of different factors ofthe steel sample microstructure. Some of thesefactors are steel chemical composition, size of thesample of the model, method of building grainboundaries, meshing size and type of elementsused in the model as well as microstructureinformation such as grain size, quantity anddistribution of anomalies in the microstructureand degree of homogeneity. Therefore, the valueof the TCF should be set experimentally toemploy the phase transformation in the modelaccurately. The proposed algorithm builds themodel based on the chosen type of the steel

composition from the material library and steelproduct geometry library. Then it applies thecomputational parameters and FEM parametersto the model.

Three types of the controls were embeddedwithin the algorithm to adjust the precision aftereach time step. These thermodynamic controlsare transformation control, cooling rate controland thermodynamic strain induced control. Phasetransformation control mimics the behavior ofthe unite cells in the solid-solid phasetransformation and the dynamic changes in thestructural bodies by applying the phasetransformation deformation on the atomic crystalcell in the meshing elements to represent thetransformation of the grain phases as a result ofdiffusion and diffusionless atomistic movementsin the steel microstructure. This crystal celldeformation was formulated in the materialproperties by Heaviside step function to inducethe deformation of solid-solid transformationbehavior of the unit cell and grain boundaries inthe model.

The Heaviside function was implemented in thedefinition of the heat expansion coefficient. Thedefinition of the heat expansion coefficient for eachphase is based on the experimental data of the CCTdiagram for a given steel composition. Figure 2 is ageneral definition for temperature dependentHeaviside type thermal expansion coefficientfunction. The algorithm utilizes the thermodynamicchanges and Heaviside function duringtransformation of the austenite phase to the product

M. R. Allazadeh

Fig. 2. Heaviside function introduced in the definition of the thermal expansion coefficient for specific steel grade tosimulate the phase transformation numerically;

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of solid-solid phase transformation via transientphase corresponding for each type of the austenitephase transformation. The transient phase performsthe changes in the size of the unit cells in theisothermal condition. The cooling curve in thequasi-real mathematical models given in thealgorithm is calculated by a linear function definedbetween the range of the temperatures known for agiven phase fraction. It can also be noticed inFigure 2 that the isothermal solid-solid phasetransformation is considered over a smalltemperature range rather than at criticaltemperature. This is required for the convergencecondition of the program which results in an ill-function of the equation and it also is a requirementfor the incubation time of the transformation.

The desired cooling rate is adjusted with coolingrate control designed in the suggested FEMalgorithm: A more efficient solution of controllingthe cooling rate is to introduce the cooling rate viathe behavior of the thermal properties of thematerial. A material control rate of heat flux isproposed in the algorithm based on the classicalconductivity equation. Thermodynamic straininduced control was inserted in the FEM algorithmto monitor the strains generated during the coolingprocess of the as-cast steel. Cooling steel slabsfrom the austenite temperature range, creates bothstrain induced due to thermodynamic effects on themicrostructure and solid to solid phasetransformation phenomena resulting fromformation of other phases (ferrite, bainite,martensite,….) out of the austenite phase. Thestrain developed in the microstructure may resultin increasing the density of cracks and flaws inwhich they are modeled by fracture constitutivelaws. The thermal induced strain exists becauseof the heat flux out of the body during quenchingand it calculated as a function of secantcoefficient of the thermal expansion, as below[33];

(4)

where To and Tn are temperatures at which αsecis evaluated and defined, respectively. Tref is thezero thermal strain temperature which in most

cases in the calculation is equal to To. Thisvariation in the coefficient of thermal expansionis defined by defined temperature at criticalpoints of the Heaviside function. ANSYS definedthe values between the defined temperature by alinear function and constant for the temperaturebelow and above the defined temperature rangein the table by extreme points of minimum andmaximum temperature in the data table,respectively.

4. VALIDATION OF THE FINITE ELEMENTMODEL

The ANSYS meshing element designated asplane 223 was used for the thermo-elasticanalysis during cooling. The plane 223 elementhas eight nodes with up to four degrees offreedom per node and capability of couplingfields.

To verify the cooling process of the FEMmodel experimentally under laboratoryconditions, a block of 75 x 75 x 50 millimetersfrom the continuous cast steel slab AISI-1010was cut. The sample was verified by the pretestultrasonic NDT images to be nearly anomaly-free. The NDT method and results wereexplained in detail in [30]. To monitor thetemperature variation through the samplethickness during cooling experiments, allsamples are drilled with a 3 mm drill bit, almosttwice the diameter of the thermocouple, to avoidsticking the thermocouple inside the hole becauseof volume changes due to high temperatureduring heat treatment. The holes were drilled at6.25, 12.5 and 25 millimeters from the topsurface (cut surface from the slab), at midsectionof the sample. Figure 3 shows the dimensions ofthe samples used for this experiment. The furnacewas set to the austenite temperature rangebetween 900 °C -1100 °C and was kept for 15 to30 minutes at this temperature to eliminate thetemperature gradient across the furnace beforeputting the specimen inside the furnace. A threechannel Lab view interface program recorded thedata from the sample in real time. The programpresented the data in both real time and averageover 50 points’ samples data in two differentgraphs as the experiment proceeded. The

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program is set with data acquisition (DAQ) rateof 1000 Hz, effective DAQ 20 sample/second.The Lab view program runs in a desktop PCcomputer and DAQ channels were connected tothree thermocouples, which were inserted intothe sample holes. The sample is put in and out ofthe furnace using tongs. A conveyer facilitatedsmooth sliding of the sample between the ovenand the quenching table to avoid removing thethermocouple from its place and to ensure thecontinuous contact of the thermocouple with thesample during the experiment. The furnace wasadjusted to the desired temperature. Figure 4 isthe picture of the system set up used in theexperiment. Both heating and cooling processesof the steel samples needed predefined data andprocedures. The purpose of the heating process inthis experiment was to obtain the austenite phase.During austenization, the samples were heatedabove the austenite temperature and the coolingrate was monitored from the austenite phase. Thestart and the end range of the solid-solid phasetransformation in the experiment, which was thetemperature range falling between A1 and A3 inthe Fe-FeC phase diagram, was estimated byJMATPRO. Data were set to be stored in realtime in Excel files during the heating and coolingprocesses for post processing and analyzing.Before putting the samples in the furnace, thethermocouples were placed in the holes inside thesample and fixed on the sample. The testedsample was kept for two hours at this temperatureaccording to ASTM standards to have a uniformtemperature all over the specimen. The coolingrate recording was stopped near ambient

temperature. The experiment is the cold chargingof the slab into the hot furnace and holding theslab until the microstructure has only austenitephase. The cooling rate at the first 1500 s portionof the cooling process can be observed in Figure5. The through-thickness cooling rate from thesurface to the center plane is shown in Figure 5 atfour checking point cooling from 900 °C to near100 °C by ambient temperature air. Thecheckpoints are measured from the top surface ofthe sample at quarter, middle and center planes.The cooling rate at these check points shows, asit was expected, the slowest cooling rate belongsto the center plane while the surface has thefastest cooling rate and is decreasing fromsurface to the center plane.

The FEM program was used to model the 1010steel AISI grade to simulate the cooling processanalytically with the sample size similar to theone used in the laboratory cooling experiment.

M. R. Allazadeh

Fig. 3. Schematic view of the sample used for the coolingrate experiment;

Fig. 4. Experimental set up.

Fig. 5. Cooling rate graph related to air cooling of Steel1010.

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The film or convection coefficient in the modelwas 25 Wm-2K-1 [34], which is the same as air-cooling. Figure 6 is the cooling curve of themodel at the middle plane based on the FEMnumerical calculation. The cooling rate in Figure5 is almost 0.4 C/s but in Figure 6 is about 1 C/s,however, both curves show same behavior.Applying a constant factor to shift the curve inFigure 6 over Figure 5 shows the correlationbetween numerical results computed by FEM andexperimental results obtained during the coolingexperiment. It is important to note no curvefitting has been deployed in Figures 5 and 6;therefore, the comparison is a legitimateverification of the cooling model and the programcan be used for modeling the cooling process. Itis only comparison between a continuumnumerical model and experimental results toverify the thermodynamic calculation of thealgorithm and the algorithm ignores some of thedetail of microstructural events taken place

during the experiments such as grain coarsening.A more complicated simulation was modeled

to show the stress accumulation due to strainintroduced to the microstructure using theproposed algorithm in Figure 1. Then the resultswere compared with the crack formation in thesteel grade 1010 in the described laboratorycooling test. It can be seen from Figure 7 that thestress concentration plane is the more vulnerableplate within the sample for the formation of thedefect. Figure 7 is the evidence that the proposedalgorithm can predict the stress concentrationzone imposed to the steel microstructure by thestress generating sources and, consequently, itcan give valuable information about the locationof the formation of the defect, if the inputinformation and adjusting correction factors aredefined accurately.

5. OPTIMIZATION OF THE COOLING RATEUSING THE SUGGESTED NUMERICALALGORITHM

A series of simulations designed to investigatethe relationship between the residual stressesdeveloped within the microstructure with phaseconfiguration of the cast steel. In the models, thephase transformation of the steel is based on theCCT diagram suggested by JMATPRO foraverage grain size of 1000 mm for the steel withchemical composition in Table 1, quenched withdifferent cooling rates from 1200 °C.

The heat is transferred from the top surface of a2-dimensional model with no heat exchange fromother surfaces with the environment (i.e. adiabaticthermal conditions). Cooling rate can be controlledwith three different methods as: the appliedconvection film coefficient, environmenttemperature and time parameters of the FEMcomputation. In these simulations, in order to havebetter control over changing the rate of cooling,the latter method was used. The model isconstrained from the bottom. It is to simulate thehalf section of a 30 mm thick slab, usingsymmetric conditions, cooling using coolingagents from top and bottom surfaces in an idealcase (no bubble formation, homogenous constanttemperature, etc.). The boundary conditionsapplied to the models are shown in the Figure 8.

Fig. 6. through thickness cooling rate of sample 1010 inthe cooling model of the sample at middle section of the

slab, ¼ and 1/8 depth measured from top surface.

Fig. 7. Comparison of the defect formation in thelaboratory cooing test sample with the result of the model

simulated by the proposed algorithm.

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The material properties of all phase productsformed after cooling the steel model were obtainedfrom JMATPRO. The film or convectioncoefficient in the model was 500 Wm-2K-1. Theemmisitivity coefficient is considered to be 0.8 forreddish to grey color of the sample from 1200 °C toroom temperature. The grains are represented bybody entity in the models and elements within thebody are unit cells in the grains. The graindiameters are considered to be 1000 µm in the

model. The grains are homogenous and isotropicwithout any dislocations or any type of anomalies.The interaction between contact grains is a contactproblem and, like all other contact problems, ishighly nonlinear and requires significant computerresources to resolve. The solution may convergeafter a number of iterations or totally diverge orcontact surfaces may overlap each other in a largelyunpredictable and abrupt manner, depending on theloads, material, boundary conditions, and otherfactors [35]. The grain boundaries were defined asatoms in non-lattice sites. In this model, the grainboundaries were built with thin layer bodies’method. The material properties defined for thegrain boundaries in the model are close to thematerial properties of the phases of adjacent grainsbefore and after phase transformation.

Figure 9 is a summary of a series of thesimulation with different time computationalparameters, to impose different cooling rates. Thestrain induced by the austenite to martensitetransformation was considered slightly smallerthan the strain induced by the austenite to ferritephase transformation. This fact was applied in the

M. R. Allazadeh

Element % Element % Element % Element %

C 0.114 Cu 0.005 Nb 0.001 N 0.0042

Mn 0.489 Ni 0.003 Sn 0.001 As 5 e-4

P 0.009 Cr 0.005 Al-total 0.0329 Ti 0.0007

S 0.0039 V 0.001 Al-soluble 0.0303 B 1e-4

Si 0.041 Mo 0.001 Ca 0.0025 Si 0.041

Table 1. Chemical composition of steel grade 1010 used in the FEM simulations.

Fig. 8. Boundary conditions of the models used for

studying the stress accumulation at the interface.

Fig. 9. Variation in the stress accumulation at the grain boundary interface due to application of different cooling rates aftercompletion of the solid-solid phase transformation.

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algorithm based on the equation developed byOnink et al. [36] and Lee et al. [37] formulation.

The first section in Figure 9 is the austenite toferrite transformation and it shows that theresidual stress accumulation is increasing as thecooling rate accelerated. However, a slightdecline in the stress accumulation can beobserved in the two phase formation as themartensite formation took place with highercooling rates. This can be a direct result of thelower strain of the martensite formationcompared to the ferrite formation. The decreaseof the maximum stress concentration in the thirdsection is due to the effect of the time parameterin transforming the austenite to its solid-solid

phase transformation products. The results inFigure 10 were collected after completion of thephase transformation. It can be understood byinvestigating the gradual transformation imagesin Figure 10 that in the case of a higher coolingrate the high stress concentration band is closer tothe top surface and the chance for relaxation ishigher. When the phase transformation iscompleted before the end of the load step, theadditive residual stresses to the microstructureare only the result of the thermodynamic strainswithout influence of the phase transformationstrains. It shows the importance of applying TCFparameters to assure accuracy of the results forsimulation to obtain the optimum cooling rate.

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2

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Fig. 10. Stress distributions for results of the graph in the Figure 9.

Fig. 11. Presentation of the void and initiation of flaw formation using the deletion element block in the algorithm.

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The last block in the proposed algorithm inFigure 1 is to present the void and flaw initiationin the final results. If this block is placed in thetime process cycle, the accuracy could beincreased. However, the probability of thedivergent solution and crash of the simulationgets higher as mentioned before. Figure 11 is anexample of the simulation of a model withelement deletion block in the algorithm. Itpresents the void and flaw initiation in the model.The image on the bottom right side of the Figure2 shows that the final product of the phasetransformation is martensite. In this model, thecooling was applied from the top and the left sidesurfaces.

The models presented in this research workdemonstrated the potential concentration ofresidual stresses around two phase material suchas iron-carbon alloys produced from solid-solidphase transformation and, on a smaller scale, dueto the thermal gradient within the microstructuredeveloped by the cooling process (e.g. aroundinclusions in the results presented in [29] ).

The algorithm in Figure 1was used to simulatemany models with focus on influence of differentparameter on cooling rate. Some of thesesimulations can be found in previous publicationsof the author [28, 32]. From different simulationsusing the suggested algorithm, it could beconcluded that the critical cooling rate dependson the following,• Cleanliness of the microstructure (pre-

existing flaws and voids),• Initial stress state of the microstructure (σi),• Chemical composition of the steel (c%),• Thermodynamic material properties of

each phases,• Microstructural configuration (single phase

or multi phase),• Grain size and grain shape (Dcγ),• Size of the slabs (Vs),• Cooling procedure • Shape of the slabs,• Initial temperature of the as-cast slab at the

start of the accelerated cooling process (Tt),• Grain boundary properties (σcoh)

To obtain a critical cooling rate, the abovefactors can be formulated in a cooling rateequation as:

(5)

The information about the cleanliness of themicrostructure on production line can beextracted from the developed NDT test publishedin [29]. Analytical formula embedded withinJMATPRO gives the thermodynamic materialproperties. The rest of the parameters depend onthe designed casting production line and desiredcast product. The proposed algorithm can be usedwith different models to study different aspects ofcontinuum behavior of microstruture duringcooling process.

6. CONCLUTIONS

The main goal of this paper was to introduce afingerprint guideline to optimize the cooling rateof continually cast steel as casting is in progresson production line. This increase the productivityof the casting line, reduce the cost of the productand increase the quality of the cast steel. Theguideline suggested for this purpose includes,• Microstructural analysis using different

optical observation and investigation of theanomalies in the microstructure

• NDT tests and developed post imageprocessing developed for this guideline,

• Laboratory data of CCT diagram for thecast steel on production line,

• Experimental results (cooling experiments,thermal expansion determination,…) todetermine thermodynamic materialproperties of the steel with the samechemical composition as the cast steel

• The developed algorithm for the FEMprogram.

The algorithm could be used to study thefactors influence the optimum cooling rate forquenching as-cast continuously cast steel. Afunction to optimize cooling rate was suggestedbased on the simulations generated by the FEMalgorithm introduced in this paper. The steelmaking industries can use this fingerprints as aguide line to predict the following • The possibility of crack formation or

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M. R. Allazadeh

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propagation for the applied cooling rate,• Information about the size of the crack for

the applied cooling rate,• A platform to investigate the relationship

between the crack formation and the steelcomposition for a given cooling rate.

• Connection between CCT diagram andaltering the defect density for a given steelcomposition,

• The residual stress distribution within theknown microstructural configuration,

The accuracy of the steps proposed in thesuggested guidelines can be increased if differentadvanced steps are added to it. For example, inthis work, the criteria to present the flaw

initiation was based on having quenching stresshigher than a constant critical value considered ascohesive stress at the grain boundary. However,the adhesion force at grain boundary varies fordifferent steel chemical composition by thesegregation of different alloying elements or thegrain boundary resistance to flaw formation.Figure 12 shows that competition between tensileresidual stress and grain boundary resistance tothe formation of flaw as a function ofsegregation, determines the critical optimumcooling rate for specific grade of steel.

The correction factors in the algorithm controlthe accuracy of the results. The precise value ofthese correction factors must be obtained for each

Fig. 12. Increasing the accuracy of the algorithm by including the effect of segregation elements at the grain boundary to theflaw formation.

Fig. 13. Encapsulating method applied to determine the phase transformation product for each cooling rate.

14

case of the cast steel via cooling experiments inthe laboratory and on industrial scales. Arranginga set of encapsulating steel sample to be used inthe cooling tests with different cooling ratesprovides the samples for microstructuralinvestigation to determine the formation of thedefect and volume fraction of the phasesproduced in the microstructure. Laboratorycasting of steel with different compositions canregulate the correction factors designed in thealgorithm to increase the accuracy of the resultsfor the prediction of the crack formation in thecontinuously cast steel. Figure 13 and Figure 14suggest these laboratories experiments whichenhance the accuracy of the algorithm.

The growing demand for new steel productsand competition to produce steel with higherquality and optimum production rate, will keepthis research field open for many new ideas andresearchers.

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M. R. Allazadeh

cooling rate optimization of as-cast...

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