FIELD OF THE INVENTION
The invention relates to segregation in cast steel product. Particularly the invention relates to a device and a method for determining and controlling steel segregation in a cast steel product.
BACKGROUND OF THE INVENTION
During solidification of liquid metals and alloys, redistribution of solutes occurs between liquid and solid phases leading to non-uniformity of composition. Segregation of solute elements is an inherent characteristic of alloy solidification. The solubility of solutes in the solid phase is relatively small in comparison to the liquid phase at a given temperature during solidification. Therefore, solidifying phase rejects excess solutes in the coexisting liquid phase at the solid-liquid interface, leading to gradual solute buildup/enrichment in the residual liquids with progress of solidification. Consequently, the portion of liquid which solidifies in the final stage contains significantly higher solute contents as compared to the nominal composition of alloy/steel.
Segregation can be classified into micro-segregation and macro-segregation. Micro-segregation is mostly confined to the microscopic area i.e. within the inter-dendritic spaces of the solidifying melt. They have much lower scale of segregation (few micron size), can be relatively less harmful as some of the segregated elements (only small atoms) get homogenized up to some extent during subsequent reheating and thermo-mechanical working (i.e. hot rolling) of cast sections.
On the other hand, macro-segregation in castings is non-uniformity of composition over macroscopic or large areas, and their size can vary from few hundred to several thousand microns. They can be extended throughout the length of castings i.e. they can be so large that their size can be equal to the size of castings. Due to large sizes, macro-segregation is considered more harmful to finished steel properties, as they cannot be eliminated even with prolonged heat treatments.

Segregation in continuously cast (CC) sections essentially originates from solute rejection at the solid-liquid interface (zone refining action) coupled with movement of residual solute enriched liquid and coexisting solid phases in the mushy zone during solidification. Flow of residual solute enriched liquid in the mushy zone is induced by suction created by the solidification shrinkage, solutal convection, sedimentation of free crystallites (almost pure and denser), bulging of solidifying strands between the support rolls, deformation of dendrites, etc. Macro-segregation poses serious quality problems in continuously cast products, which may exhibit high degree of segregation in the central region of cast sections (centreline segregation), unless proper measures are adopted for its minimisation.
Commonly, centerline segregation (CLS) becomes more pronounced in case of high carbon steels cast at relatively higher superheats and at high casting speeds in narrow cross-sections. High centerline segregation gives rise to undue phase transformations (bainite or martensite etc.), which may lead to cracks or failure during subsequent thermo-mechanical working of cast section or premature failure of the finished steel products in service. They are largely responsible for the anisotropic mechanical properties, hydrogen induced cracking (corrosion resistance), cracking during welding, etc. Pronounced segregation leads to banding in the hot rolled sheets and heavy plates, where cracks can run easily parallel to the banded region of cast section. Problem of macro-segregation becomes more acute in case of high carbon steels, in high strength low alloy (HSLA) steels, as well as in high alloy steels.
Following are some of the work done in this regard
1) G. Lesoult, Mat. Sc. Eng. A, Vol. 413, pp. 19-29, 2005
2) F. Mayer, M. Wu, and A. Ludwig: Steel Research Int.,vol. 81, pp.660-667, 2010
3) M. C. Flemings: ISIJ Int., vol. 40, pp. 833-841, 2000.
4) C. Ciccuti and R. Boeri: Scripta Materialia, vol. 45, pp. 1455-1460, 2001

However they do not disclose a comprehensive method of determining segregation of multicomponent cast product. Also the prior arts cater to only a specific grade of cast product and do not disclose for both high carbon grade and low carbon grade steel. Also the prior arts do not quantify segregation through an expression which is intinsically related to the physical phenomena pertaining to the solidification physics and resultant segregation process
OBJECT OF THE INVENTION
In view of the foregoing limitations inherent in the prior-art, it is an object of the invention to establish a device and method for determining and controlling cast steel segregation along with its severity in a steel while being casted in slab caster.
SUMMARY OF THE INVENTION
In one aspect, the invention provides a cast steel segregation predicting device for determining and controlling cast steel segregation in a steel product while being cast in a slab caster, the cast steel segregation predicting device comprises a plurality of sensors placed at various location in the slab caster, the plurality of sensors are configured to sense values corresponding to parameters of superheat temperature (ΔT), diffusion coefficient of solute (DS), solidification temperature (tS), composition of solidified steel (CS) and composition of liquid steel (CL) and forward the sensed values to a data storage means, the data storage means is coupled to the plurality of sensors, the data storage means are configured to store and forward the sensed values to a calculating means, the calculating means are coupled to the data storage means, and is configured to
receive and feed the sensed values in an equation thereby
determining the value of Ψ and forward the value of “Ψ” to a decision making means, the decision making means are coupled to the calculating means, and is configured to receive the output of “Ψ” and judge the output of “Ψ” and thereby

an action needed, the action needed is forwarded to a user interface, the action needed being decided based on following assumptions:
if no macro-segregation would have occurred, thereby no
value alteration of the parameters is needed
if negative segregation would have occurred, thereby value
alteration of the parameters is needed to bring Ψ = 1 and
if positive segregation would have occurred, thereby value
alteration of the parameters is needed to bring the value of Ψ = 1; and
the user interface is coupled to the decision making means, the user interface is configured to display the action needed.
In another aspect, a method for determining and controlling cast steel segregation in a steel product while being cast in a slab caster comprises steps of sensing values corresponding to parameters of superheat temperature (ΔT), diffusion coefficient of solute (DS), solidification temperature (tS), composition of solidified steel (CS) and composition of liquid steel (CL), storing the sensed
values, feeding the sensed values in an equation thereby
determining the value of judging the value of “Ψ” and thereby an action
needed, the action needed is decided based on following assumptions:
if no macro-segregation would have occurred, thereby no
value alteration of the parameters is needed
if negative segregation would have occurred, thereby value
alteration of the parameters is needed to bring and
if positive segregation would have occurred, thereby value
alteration of the parameters is needed to bring and
displaying the action needed.
BRIEF DESCRIPTION OF THE ACCOMPANYING DRAWINGS
FIG. 1a shows a block diagram of a cast steel segregation predicting device with its various components in accordance with an embodiment of the invention.

FIG. 1b shows block diagram of a user interface comprising a screen and a plurality of value buttons in accordance with an embodiment of the invention.
FIG. 2 illustrates a flow diagram depicting various steps for determining and controlling cast steel segregation in a steel while being casted in slab caster in accordance with an embodiment of the invention.
DETAILED DESCRIPTION OF THE INVENTION
Various embodiments of the invention provide a cast steel segregation predicting device for determining and controlling cast steel segregation in a steel product while being cast in a slab caster, the cast steel segregation predicting device comprising a plurality of sensors, the plurality of sensors being placed at various location in the slab caster, the plurality of sensors being configured to sense values corresponding to parameters of superheat temperature (ΔT), diffusion coefficient of solute (DS), solidification temperature (tS), composition of solidified steel (CS) and composition of liquid steel (CL) and forward the sensed values to a data storage means, the data storage means being coupled to the plurality of sensors, the data storage means being configured to store and forward the sensed values to a calculating means, the calculating means being coupled to the data storage means, the calculating means being configured to
receive and feed the sensed values in an equation thereby
determining the value of Ψ and forwarding the value of to a decision making means, the decision making means being coupled to the calculating means, the decision making means being configured to receive the output of and judge the output of and thereby an action needed, the action needed being
forwarded to a user interface, the action needed being decided based on following assumptions:
if no macro-segregation ,would have occurred, thereby no
value alteration of the parameters is needed

if negative segregation would have occurred, thereby value
alteration of the parameters is needed to bring and
if positive segregation would have occurred, thereby value
alteration of the parameters is needed to bring the value of and
the user interface being coupled to the decision making means, the user interface being configured to display the action needed.
Another embodiment of the invention provide a method for determining and controlling cast steel segregation in a steel product while being cast in a slab caster, the method comprising steps of: sensing values corresponding to parameters of superheat temperature (ΔT), diffusion coefficient of solute (DS), solidification temperature (tS), composition of solidified steel (CS) and composition of liquid steel (CL), storing and forwarding the sensed values for evaluation, receiving and feeding the sensed values in an
equation thereby determining the value of “Ψ”, judging the
value of “Ψ” and thereby an action needed, the action needed being decided based on following assumptions:
if no macro-segregation would have occurred, thereby no
value alteration of the parameters is needed
if negative segregation would have occurred, thereby value
alteration of the parameters is needed to bring and
if positive segregation would have occurred, thereby value
alteration of the parameters is needed to bring and
displaying the action needed.
Shown in FIG. 1a is a block diagram of a cast steel segregation predicting device hereinafter (device (100)) with various components for determining and controlling cast steel segregation in a steel product while being cast in a slab caster.

The device (100) comprises a plurality of sensors (S1, S2, S3………….S6), a data storage means (104), a calculating means (108), a decision making means (112) and a user interface (116). The plurality of sensors are coupled to the data storage means (104). The data storage means (104) is coupled to the calculating means (108). The calculating means (108) is coupled to the decision making means (112). The decision making means (112) is further coupled to the user interface (116).
The plurality of sensors (S1, S2, S3………….S6) are located at various locations in the slab caster. These sensors are located at such locations so as to sense the values of various parameters such as superheat temperature (ΔT), diffusion coefficient of solute (DS), solidification temperature (tS), composition of solidified steel (CS) and composition of liquid steel (CL).
It is to be noted that mode of coupling between various means is electrical. In an embodiment the various other means can also be used.
The user interface (116) comprises a screen (120) and a plurality of value buttons (124) coupled to each other shown in FIG. 1b. Some of the value buttons correspond to parameters of superheat temperature (ΔT), diffusion coefficient of solute (DS), solidification temperature (tS), Casting speed, tundish temperature, compositions of liquid and solid steel etc. These value buttons are configured to change the values of the parameters to affect the cast steel operation. The screen (120) is configured to display various parameters value and attributes related to cast steel operation. These parameters can be superheat temperature, diffusion coefficient, solidification temperature, casting speed, tundish temperature, compositions of liquid and solid steel etc.
The values captured by the sensors are forwarded to the data storage means (104). The data storage means (104) is configured to store and further forward the values to the calculating means (108).
The calculating means (108) operates on the platform of the equation:


where ΔT is superheat temperature, DS is diffusion coefficient of solute, tS is solidification temperature, CS is composition of solidified steel and CL is composition of liquid steel.
The calculating means (108) is configured to receive the sensed values from the data storage means (104) and feed in the eq. 1 and therby value of “Ψ” is calculated.
The calculated value of is forwarded to the decision making means
(112). The decision making means (112) receives the value of judge the
value of and thereby imparts an action needed. The action needed is based
on following assumptions:
If no macro-segregation would have occurred. Since this condition is
most favorable therefore no value alteration/action of the parameters is needed.
If Ψ>1, negative segregation would have occurred. Therefore, value alteration/action needed of the parameters is needed so as to bring the value of Ψ favorably i.e.
If positive segregation would have occurred. Therefore, value
alteration/action needed of the parameters is needed so as to bring the value of Ψ favorably i.e.
As the value of Ψ increases, the severity of the segregation increases.
The action needed/value alteration needed from the decision making means (112) is forwarded to the user interface (116) and subsequently reflected on the screen (120) of the user interface (116). On the basis of decision reflected on the screen (120), values corresponding to value buttons (124) can be altered by the operator so as to bring the value of “Ψ”=1.

The decision from the decision making means is real time in nature and the variations in the parameter can be done in real time operation so as to control cast steel segregation.
A method (200) is shown in FIG. 2 illustrates a flow diagram depicting various steps for determining and controlling cast steel segregation in the steel product while being cast in slab caster in accordance with an embodiment of the invention.
At step (204) various values corresponding to parameters of superheat temperature diffusion coefficient of solute (Ds), solidification temperature
(ts), composition of solidified steel (Cs) and composition of liquid steel (Cl) are sensed. The sensing is done by means of the sensors (S1, S2……..S6). Various sensors are positioned at various locations in the slab caster to fetch these values.
At step (208) the sensed values are stored. The values are stored in data storage means (104).

to determine the value of Ψ. This feeding is done by means of the calculating means (108).
At step (216) the value of is judged and thereby the action
needed/value alteration of parameters. The action needed is decided based on following assumptions:
If no macro-segregation would have occurred. Since this condition is
most favorable therefore no action/value alteration of parameters is needed.




If Ψ>1, negative segregation would have occurred. Therefore, value alteration of the parameters is needed so as to bring the value of Ψ favorably i.e.


If 0<Ψ<1, positive segregation would have occurred. Therefore, value alteration of the parameters is needed so as to bring the value of Ψ favorably i.e.

The step (216) is processed by the decision making means (112).
At step (220) the action needed is displayed. The display is on the screen (120) of the user interface (116). The operator can change the values of parameters by value buttons (124) so as to bring value of Ψ favorably i.e.1.
Generation of Formula
In continuous casting process, solidification of liquid steel begins in a water-cooled copper mold. The steel shell which forms in the mold contains a core of liquid steel which gradually solidifies as the strand moves through the caster guided by a large number of roll pairs. At the exit of the mold, the steel strand is cooled by a water based spray system. Assuming that the solidified layer thickness is small compared to the thickness of the cast product, the condition of linear flow of heat in a semi-infinite domain holds and thermal history and the progress of the solidification front can be estimated by using the generalized Neumann‟s solution.
For linear flow of heat, the temperatures TS in the solid region satisfy the following relation:


The equation governing the conduction of heat in the moving liquid is given by,

where, Tl denotes temperature in liquid, x denotes the distance, ρl density in liquid phase, ρs density in solid phase, t denotes time and al and as are thermal diffusivity in the liquid phase and solid phase respectively, X denotes solidification frontal and as are given by

cps and cpl are specific heat of steel in the solid phase and liquid phase respectively and Ks and Kl are the thermal conductivity of solid and liquid steel, ρ l density in liquid phase, ρS density in solid phase.
Application of adjoint-gradient correlation theory produces the following solutions of heat transfer,

where A and B are constants. TS and Tl are the temperatures in solid region and liquid region respectively. To is initial temperature and Tc is cooling temperature.
The „error function‟ solution derived for the above-mentioned equations is mathematically expressed as,


The rate (R) at which the dendrite tip is growing can be found by examining the rate of movement of solidification front and is given by the following expression,



where Tl is the temperatures in liquid region.
MORPHOLOGY OF CAST STRUCTURE
Nearly all of the solidification microstructures which can be exhibited by a pure metal or an alloy can be divided into two groups: single-phase primary crystals and polyphase structures. The most important growth form is the tree¬like primary crystal, i.e. the dendrite. Under industrial conditions, metallic alloys usually solidify in dendritic interfaces. The microstructural scale of dendrites, such as primary and secondarydendrite arm spacings, control the
segregation profiles and determines the properties of cast structures. Primary dendrite arm spacing is related to the solidification rate R and thermal
gradient G in the solidifying domain, and can be expressed in a general form according to the following equation,

where m, n, c1 are equation constants
With regard to secondary dendrites, a ripening process causes the dendrite arms to change with time into coarser, less branched dendrites growing perpendicularly to the primary trunk.
Secondary dendrite arm spacing (λ2) can be represented as a function of time, and can be given as below

where C2 is a constant ts and is the local solidification time.


where is the difference between the liquidus temperature and solidus
temperature.
ANALYSIS OF SEGREGATION
The level of segregation along the centerline of continuously cast (CC) products is called centerline macro-segregation, and is known to be the prime cause of subsurface cracks and porosity in the continuously cast products. Macro-segregation is generally evaluated by:
Degree of segregation,
where Ci is concentration of solute i at the location under consideration, Ci0 is
nominal concentration of solute i.
Macro-segregation depends on partition coefficient (k) of solute elements, growth rate (R), morphology of cast structure e.g. dendrite arm spacings movement of solid and liquid phases during solidification.
For the purpose of analysis over a small segregated region such as spot segregation in center of the slabs, Scheil equation (no diffusion in solid, and complete mixing in the liquid) can be applied as follows,

where fs is the fraction of solute in the solid phase, where k is partition coefficient. For the case of finite diffusion in the solid following equation has been
proposed


where is superheat temperature, Ds is the diffusion coefficient in the solid
phase, ts is the local solidification time, and is the dendrite arm spacing, Cs is solute composition in solid and Cl is solute composition in liquid.
Advantages:
The cast steel segregation predicting device is easy to use and has high mathematical accuracy. This device very useful for cast steel operation.

I / We claim:
1. A cast steel segregation predicting device (100) for determining and
controlling cast steel segregation in a steel product while being cast in a slab caster, the cast steel segregation predicting device comprising:
a plurality of sensors (S1, S2, S3………….S6), the plurality of sensors being placed at various location in the slab caster, the plurality of sensors being configured to sense values corresponding to parameters of superheat temperature (ΔT), diffusion coefficient of solute (DS), solidification temperature (tS), composition of solidified steel (CS) and composition of liquid steel (CL) and forward the sensed values to a data storage means (104);
the data storage means (104) being coupled to the plurality of sensors (S1, S2, S3………….S6), the data storage means (104) being configured to store and forward the sensed values to a calculating means (108);
the calculating means (108) being coupled to the data storage means (104), the calculating means (108) being configured to receive and
feed the sensed values in an equation thereby
determining the value of Ψ and forwarding the value of “Ψ” to a decision making means (112);
the decision making means (112) being coupled to the calculating means (108), the decision making means being configured to receive the output of and judge the output of and thereby an action needed,
the action needed being forwarded to a user interface (116), the action needed being decided based on following assumptions:
if no macro-segregation would have occurred, thereby no
value alteration of the parameters is needed
if negative segregation would have occurred, thereby value
alteration of the parameters is needed to bring and

if positive segregation would have occurred, thereby value
alteration of the parameters is needed to bring the value of Ψ = 1; and
the user interface (116) being coupled to the decision making means (112), the user interface (116) being configured to display the action needed.
2. The cast steel segregation predicting device (100) as claimed in claim 1, wherein the user interface (116) comprises a screen (120) and a plurality of value buttons (124).
3. The cast steel segregation predicting device (100) as claimed in claim 3, wherein the plurality of value buttons (124) are configured to do value alteration of the parameters.
4. The cast steel segregation predicting device (100) as claimed in claim 1, wherein the cast steel segregation is controlled during real time operation.
5. A method for determining and controlling cast steel segregation in a steel product while being cast in a slab caster, the method comprising steps of:
sensing values corresponding to parameters of superheat temperature (ΔT), diffusion coefficient of solute (DS), solidification temperature (tS), composition of solidified steel (CS) and composition of liquid steel (CL);
storing the sensed values;
feeding the sensed values in an equation thereby determining the value of
judging the value of “Ψ” and thereby an action needed, the action needed being decided based on following assumptions:
if , no macro-segregation would have occurred, thereby no
value alteration of the parameters is needed

if negative segregation would have occurred, thereby value
alteration of the parameters is needed to bring and
if , positive segregation would have occurred, thereby value
alteration of the parameters is needed to bring and
displaying the action needed.