Real-time prediction method for proeutectoid ferrite growth during continuous casting

Abstract

The present invention provides a real-time prediction method for the growth of proeutectoid ferrite during continuous casting, which relates to the technical field of prediction of slab microstructure. The present invention takes into account the temperature change during the actual cooling process of the slab, and improves the phase transformation model under a constant cooling rate by using the integral method to make it applicable to the actual production process of the slab. Only by inputting the temperature history during the continuous casting process of the slab can the real-time prediction of the growth law of proeutectoid ferrite in the entire cross-section of the slab be realized. Through the prediction of the growth of proeutectoid ferrite in the entire cross-section of the slab, the present invention can guide the factory to dynamically adjust the cooling process, and at the same time, the temperature history after the process adjustment can be used as an input condition to continue calculating the growth of proeutectoid ferrite under the new process, realizing the mutual feedback between theoretical calculation and on-site process.

Description

Technical Field

[0001] The present invention relates to the technical field of prediction of continuous casting billet structure, and particularly to a real-time prediction method for the growth of proeutectoid ferrite during continuous casting. Background Art

[0002] During continuous casting, due to the combined action of external cooling water and heat transfer of the high-temperature billet inside, the cooling rate of the billet surface in the austenite / ferrite two-phase region is very slow, resulting in the full precipitation of film-like proeutectoid ferrite on austenite. Since the hardness of ferrite is only 1 / 4 of that of austenite, stress concentration will occur at the ferrite film during the bending and straightening deformation process, reducing the hot plasticity of the billet, and further inducing surface defects such as corner cracks, transverse surface cracks and longitudinal surface cracks. As the main surface defect of the billet, surface cracks will expand into more serious cracks during the feeding and rolling processes, causing billet breakage or reducing the properties of rolled products, and cutting off the surface crack part will also reduce the metal yield. If the real-time prediction of the growth of proeutectoid ferrite film during the phase transformation process of the billet can be achieved, it can provide important data for the optimization of the continuous casting cooling process and fundamentally control the generation of surface cracks.

[0003] Some researchers have conducted some studies on the precipitation law of proeutectoid ferrite in continuous casting billets. Patent CN201810964557.5 performs linear analysis based on the microstructure evolution law during the solidification process of the billet and combines a large amount of on-site data. By optimizing the casting speed and secondary cooling water distribution system of the continuous casting machine, the best conditions are provided for the transformation of austenite to ferrite, avoiding the precipitation of film-like ferrite and achieving the purpose of eliminating transverse corner cracks.

[0004] Patent CN202010592850.0 controls the surface temperature of the billet by using cooling water before the straightening section of the continuous casting machine, so that the surface of the billet is kept constant near the phase transformation temperature of the steel grade from austenite to ferrite for a long time. A ferrite layer is formed on the surface of the billet through long-term temperature constancy, increasing the proportion of ferrite in the surface structure of the billet, and using the high plasticity of ferrite to improve the plasticity of the surface structure of the billet, thereby reducing the cracks generated under the action of tensile stress in the straightening area of the inner arc surface of the billet.

[0005] Liu Huasong et al. from the University of Science and Technology Beijing studied the formation of intergranular and intragranular ferrite in microalloyed steel under continuous casting conditions through modeling and experiments. By adopting the classical Johnson-Mehl-Avrami theory, a model for predicting the volume fraction of ferrite with different nucleation configurations was developed. For the volume fraction and half thickness of film-like ferrite, a series of thermal expansion tests were carried out using a Gleeble-3500 thermal simulation testing machine and a laser confocal scanning high-temperature microscope, verifying the accuracy of the model.

[0006] However, most of the existing studies predict the precipitation law of proeutectoid ferrite in the continuous casting billet through experimental means or empirical formulas. During the calculation process, the billet is regarded as cooling at a constant cooling rate in the austenite / ferrite two-phase region, which does not conform to the temperature change law in the actual cooling process of the billet. Moreover, the previous technical means cannot realize the real-time prediction of the growth of proeutectoid ferrite during the phase change process, making it difficult to guide the on-site production. Based on the ferrite growth kinetics and the finite difference method, combined with the full-section temperature history of the billet calculated by the finite element method, the present invention realizes the real-time prediction of the precipitation law of proeutectoid ferrite in the full section of the billet. Summary of the Invention

[0007] Aiming at the deficiencies of the existing technology, the present invention provides a real-time prediction method for the growth of proeutectoid ferrite during continuous casting. Based on the ferrite growth kinetics and the finite difference method, combined with the full-section temperature history of the billet calculated by the finite element method, the present invention realizes the real-time prediction of the precipitation law of proeutectoid ferrite in the full section of the billet. The purpose is to provide timely guidance for the optimization of the cooling process on the continuous casting site, fundamentally control the occurrence of surface cracks, improve the metal yield, reduce production losses, and improve the performance of rolled products at the same time.

[0008] A real-time prediction method for the growth of proeutectoid ferrite during continuous casting includes the following steps:

[0009] Step 1: Establish a heat transfer finite element model for the continuous casting process, calculate the temperature history of the full section of the billet according to the heat transfer finite element model, and the time interval of the temperature data is Δt;

[0010] The heat transfer finite element model is: a full-section heat transfer model of a two-dimensional slice is established based on finite element analysis software. The initial temperature of the model is the actual pouring temperature. The heat transfer coefficients of the wide and narrow faces of the billet are determined according to the on-site water distribution system as boundary conditions. According to the casting speed of the billet and the position distribution of the secondary cooling zone, the heat transfer boundary of the model is updated to simulate the temperature field distribution of the billet during the entire continuous casting process.

[0011] The temperature history is: the relationship between the temperature change of each grid node with time after the heat transfer finite element model is meshed;

[0012] Step 2: Determine the phase change incubation period at different temperatures according to the phase change thermal expansion experiment, and fit the relationship formula τ(T) between the phase change incubation period and the temperature:

[0013]

[0014] In the formula, A and m are constants; R is the gas constant; Q k is the activation energy of carbon diffusion in austenite; T is the phase change temperature; A e3 The starting temperature of the austenite-to-ferrite transformation;

[0015] The variable-temperature process is regarded as an isothermal process within the incremental step Δt. The incubation period is accumulated through Equation (2). When the accumulated value equals 1, the phase transformation begins.

[0016]

[0017] Where i represents the incremental step number of the finite element heat transfer model, s represents the incremental step number when the accumulated value of the formula equals 1, and T i represents the nodal temperature value at the i-th incremental step.

[0018] Step 3: Calculate the solute resistance ΔG of alloying element Mn to interface migration dis , as shown in Equation (3):

[0019]

[0020] Parameter Parameter Where is the diffusion coefficient of Mn element in the phase interface, V int is the interface migration rate, is the initial molar fraction of Mn in the continuous casting slab, Parameter Parameter Parameter δ is half of the austenite / ferrite phase interface, and E0 represents the binding energy, represents half of the sum of the chemical potentials of Mn element on the austenite side and the ferrite side. Among them, represents the chemical potential of Mn element on the ferrite side, represents the chemical potential of Mn element on the austenite side.

[0021] Step 4: Calculate the chemical driving force ΔG per mole of atoms according to the following formula chem :

[0022]

[0023] In the formula, i is the alloying element of the steel grade; k is the number of elements, is the composition of element i transported at the phase interface; and are the molar fractions of element i on the austenite side and the ferrite side; and are the chemical potentials of element i on the austenite side and the ferrite side of the phase interface.

[0024] The frictional force ΔG during the interface migration process friction depends on the interface migration rate V int and the intrinsic mobility M of the austenite / ferrite interface int ;

[0025] ΔGfriction = V int V m / M int (5)

[0026] M int = 2.7×10 18 exp(-145000 / RT) (6)

[0027] where V m is the molar volume of Fe element;

[0028] Step 5: Use the Gibbs energy balance method to solve for the interface migration rate V under specific conditions according to the following formula int , and when there are multiple solutions to the equation, take the minimum solution as the final solution;

[0029] ΔG chem = ΔG friction + ΔG dis (7)

[0030] where the specific conditions refer to a certain temperature and a certain carbon concentration on the austenite side, and both of these conditions change in real time during the calculation process. According to the real-time situation, automatically solve for the current interface migration rate V int ;

[0031] Step 6: Take the austenite radius length as the calculation domain, and use the finite difference method to divide the calculation domain into n micro-elements. At time t, the position of the phase interface is The number of micro-elements on the austenite side at time t is Micro-element length The number of micro-elements on the ferrite side is The carbon mole fraction of the micro-elements on the ferrite side is all X t,α / γ , and the carbon mole fraction of the micro-element near the interface in the austenite is The carbon mole fraction inside the austenite is Then, calculate the interface migration rate at the current time t according to Steps 3 and 4

[0032] where n is the three elements of Fe, C, and Mn, n takes 3, R is the gas constant, and round() is the rounding function;

[0033] Step 7: At time t + Δt, the distance of interface migration The phase interface position at this time The number of micro-elements on the austenite side is Micro-element length The number of micro-elements on the ferrite side is The carbon mole fraction of the micro-elements on the ferrite side is all X t+Δt,α / γ, after the microelement is re-divided, it is necessary to calculate the carbon mole fraction on the austenite side at the moment of t+Δt according to the carbon mole fraction at the moment of t:

[0034]

[0035] where Δt represents the time interval between the previous moment and the next moment in the node temperature history, that is, the time step, and Δy t represents the size of the microelement on the austenite side at the moment of t;

[0036] Step 8: Calculate the carbon enrichment at the phase interface and the carbon diffusion on the austenite side at the moment of t+Δt according to Fick's first law.

[0037] During the carbon diffusion on the austenite side within the time of Δt, the adjacent microelements satisfy Fick's first law:

[0038]

[0039] where, represents the diffusion flux between two adjacent microelements at the moment of t+Δt, and D γ is the diffusion coefficient of carbon in austenite. The carbon mole fraction after diffusion is obtained based on the carbon diffusion flux:

[0040]

[0041] At the same time, due to the different carbon concentrations on the austenite side and ferrite, carbon enrichment at the phase interface will occur, and equations (11) and (12) are used for calculation:

[0042]

[0043]

[0044] where, represents the carbon diffusion flux at the phase interface at the moment of t, represents the phase interface migration velocity at the moment of t, represents the carbon concentration at the phase interface at the moment of t+Δt.

[0045] Step 9: Calculate in a cycle with the time step of Δt to obtain the thickness of the proeutectoid ferrite film at different casting positions of the continuous casting slab;

[0046] The distance of the interface migration at the moment of t+Δt Since the thickness of the ferrite film at the start time of the phase transformation is 0, the time history of the continuous casting slab reaching different casting positions is divided by the incremental step of Δt, and the thickness of the ferrite film is obtained by superimposing using the integral principle:

[0047]

[0048] where, Represents the interface migration rate corresponding to the i-th increment step, and m represents the number of the increment step when reaching the specified casting stream position.

[0049] The beneficial effects produced by adopting the above technical solution are as follows:

[0050] The present invention provides a real-time prediction method for the growth of proeutectoid ferrite during continuous casting. When calculating the growth of proeutectoid ferrite in the continuous casting billet, the present invention fully considers the temperature change situation in the actual cooling process of the continuous casting billet, optimizes and improves the phase transformation model under a constant cooling rate through the integral method, so that the calculation result is more in line with the actual situation on site. Only using the temperature field distribution of the continuous casting billet as the input, the real-time prediction of the precipitation law of proeutectoid ferrite in the whole cross-section of the continuous casting billet can be realized, guiding the dynamic adjustment of the cooling process in the production site. At the same time, the growth situation of ferrite under the new process can be calculated, realizing the two-way feedback between theoretical prediction and on-site process, fundamentally controlling the generation of surface cracks, improving the metal yield, reducing production losses, and improving the performance of the rolled material. Brief Description of the Drawings

[0051] Figure 1 It is the temperature history diagram of the 1 / 2 cross-section and characteristic points of the continuous casting billet in the embodiment of the present invention;

[0052] Figure 2 It is the parameter fitting diagram of the phase transformation incubation period in the embodiment of the present invention;

[0053] Figure 3 It is the phase interface migration rate diagram at a specific carbon content at 685°C in the embodiment of the present invention;

[0054] Figure 4 It is the schematic diagram of carbon diffusion during the phase transformation process in the embodiment of the present invention;

[0055] Figure 5 It is the experimental calculation result diagram in the embodiment of the present invention;

[0056] Among them, Figure (a) - Experimental thermal history and calculation results of the corner ferrite film thickness; Figure (b) - Experimental metallographic structure;

[0057] Figure 6 It is the calculation result diagram of the corner temperature and ferrite film thickness of the continuous casting billet in the embodiment of the present invention;

[0058] Figure 7 It is the carbon molar fraction distribution diagram on the austenite side of the corner at different positions from the meniscus in the embodiment of the present invention;

[0059] Figure 8 It is the prediction result diagram of the ferrite film thickness of the 1 / 2 cross-section of the continuous casting billet at the exit of the straightening zone in the embodiment of the present invention; Detailed Embodiments

[0060] The specific embodiments of the present invention will be further described in detail below in conjunction with the accompanying drawings and embodiments. The following embodiments are used to illustrate the present invention, but are not used to limit the scope of the present invention.

[0061] A real-time prediction method for the growth of proeutectoid ferrite in the continuous casting process, comprising the following steps:

[0062] Step 1: Establish a heat transfer finite element model for the continuous casting process, calculate the temperature history of the entire cross-section of the slab according to the heat transfer finite element model, and the time interval of the temperature data is Δt;

[0063] The heat transfer finite element model is: a full cross-section heat transfer model of a two-dimensional slice is established based on finite element analysis software. In this embodiment, Marc software is used. The initial temperature of the model is the actual pouring temperature. The heat transfer coefficients of the wide and narrow faces of the slab are determined according to the on-site water distribution system as boundary conditions. According to the casting speed of the slab and the position distribution of the secondary cooling zone, the heat transfer boundary of the model is updated to simulate the temperature field distribution of the slab during the entire continuous casting process.

[0064] The temperature history is: the relationship between the temperature of each grid node and time after the heat transfer finite element model is meshed;

[0065] In this embodiment, the growth of proeutectoid ferrite in a Q345 slab with a cross-section of 280×2000 mm of a certain steel plant is calculated. The main components of the steel grade and the mass percentage of each component are: C: 0.17%, Mn: 1.5%, and the balance is Fe. According to the nozzle and cooling water distribution of the casting machine on the steel plant site, the casting temperature of the slab is 1542 °C, and the drawing speed is 0.9 m / min. The temperature field distribution results of the entire cross-section of the slab during the entire casting process are calculated. According to the symmetry of the geometric model and boundary conditions, here, the 1 / 2 cross-section of the slab is taken for temperature field calculation, as Figure 1 shown.

[0066] Step 2: Determine the phase transformation incubation period at different temperatures according to the phase transformation thermal expansion experiment, and fit the relationship formula τ(T) between the phase transformation incubation period and temperature:

[0067]

[0068] In the formula, A and m are constants obtained by fitting through experimental data; R is the gas constant; Q k is the activation energy for carbon diffusion in austenite, with the unit of J; T is the phase transformation temperature, with the unit of K; A e3 The starting temperature of the transformation from austenite to ferrite;

[0069] In this embodiment, the influence of the phase transformation nucleation incubation period on the precipitation of proeutectoid ferrite is fully considered. The phase transformation incubation period at different temperatures is determined by the phase transformation thermal expansion experiment, and the experimental data is brought into the formula 1 for parameter fitting. The results are asFigure 2 as shown

[0070] The variable temperature process is regarded as an isothermal process within the increment step Δt, and the incubation period is accumulated through formula (2). When the accumulated value equals 1, the phase transformation begins.

[0071]

[0072] This formula performs iterative calculations on the results of the nodal temperature history, where i represents the increment step number of the finite element heat transfer model, s represents the increment step number when the accumulated value of the formula equals 1, and T i represents the nodal temperature value at the i-th increment step.

[0073] Step 3: Calculate the solute resistance ΔG of alloying element Mn to interface migration dis , as shown in formula (3):

[0074]

[0075] Parameter Parameter where is the diffusion coefficient of Mn element in the phase interface, μm 2 / s; V int is the interface migration rate, μm / s, is the initial molar fraction of Mn in the continuous casting slab, Parameter Parameter Parameter δ is half of the austenite / ferrite phase interface, δ = 0.0005 μm, and E0 represents the binding energy, taking 9900 J / mol; represents half of the sum of the chemical potentials of the Mn element on the austenite side and the ferrite side, where represents the chemical potential of the Mn element on the ferrite side, represents the chemical potential of the Mn element on the austenite side.

[0076] Step 4: Calculate the chemical driving force ΔG per mole of atoms according to the following formula chem :

[0077]

[0078] In the formula, i is the alloying element of the steel grade; k is the number of elements, here k = 3; is the composition of element i transported at the phase interface; and are the molar fractions of element i on the austenite side and the ferrite side; and are the chemical potentials of element i on the austenite side and the ferrite side of the phase interface.

[0079] Frictional force ΔG during interface migration process friction depends on the interface migration rate V int and the intrinsic mobility M of the austenite / ferrite interface int , μm 4 J -1 s -1 :

[0080] ΔG friction = V int V m / M int (5)

[0081] M int = 2.7×10 18 exp(-145000 / RT) (6)

[0082] where V m is the molar volume of Fe element; take V m = 7.1×10 12 μm 3 mol -1

[0083] Step 5: Adopt the Gibbs energy balance method to solve the interface migration rate V under specific conditions according to the following formula int , and take the minimum solution as the final solution when there are multiple solutions to the equation;

[0084] ΔG chem = ΔG friction +ΔG dis (7)

[0085] where the specific conditions refer to a certain temperature and a certain carbon concentration on the austenite side, and both of these conditions change in real time during the calculation process. According to the real-time situation, the current interface migration rate V is automatically solved int ; where Equation 7 is a univariate nonlinear equation about the interface migration rate V int , first find the approximate range of the solution of Equation 7 according to the graphical method, as Figure 3 shown, and then use the bisection method to approximate and solve Equation 7. When there are multiple solutions to Equation 7, take the minimum solution as the final solution.

[0086] Step 6: Take the austenite radius length as the calculation domain, divide the calculation domain into n micro-elements by the finite difference method. At time t, the position of the phase interface is The number of micro-elements on the austenite side at time t is Micro-element length The number of micro-elements on the ferrite side is The carbon mole fraction of the micro-elements on the ferrite side is all X t,α / γ, the carbon mole fraction of the microelement near the interface in austenite is The carbon mole fraction inside austenite is Then, calculate the interface migration rate at the current moment t according to Steps 3 and 4

[0087] where n is three elements of Fe, C, and Mn, n takes 3, and R is the gas constant, taking 8.314 J·mol -1 .K -1 . round() is a rounding function, which is a program function indicating rounding the value in the parentheses and retaining the integer part.

[0088] Step 7: At the moment t+Δt, the distance of interface migration The phase interface position at this time The number of microelements on the austenite side is Microelement length The number of microelements on the ferrite side is The carbon mole fraction of the microelements on the ferrite side is all X t+Δt,α / γ , after the microelements are re-divided, it is necessary to calculate the carbon mole fraction on the austenite side at the moment t+Δt according to the carbon mole fraction at the moment t:

[0089]

[0090] where Δt represents the time interval between the previous moment and the next moment in the node temperature history, that is, the time step, and Δy t represents the size of the microelement on the austenite side at the moment t;

[0091] Step 8: Calculate the carbon enrichment at the phase interface and the carbon diffusion on the austenite side at the moment t+Δt according to Fick's first law.

[0092] During the carbon diffusion on the austenite side within the time of Δt, the adjacent microelements satisfy Fick's first law:

[0093]

[0094] where, represents the diffusion flux between two adjacent microelements at the moment t+Δt, and D γ is the diffusion coefficient of carbon in austenite. Based on the carbon diffusion flux, the carbon mole fraction after diffusion is obtained:

[0095]

[0096] Meanwhile, due to the different carbon concentrations on the austenite side and the ferrite, the situation of carbon enrichment at the phase interface will occur, and it is calculated using Equations (11) and (12):

[0097]

[0098]

[0099] in, represents the carbon diffusion flux at the interface at time t, represents the migration velocity of the phase interface at time t, Represents the carbon concentration at the interface at time t+Δt. Figure 4 shown.

[0100] Step 9: Calculate cyclically with a time step length of Δt to obtain the thickness of the proeutectoid ferrite film at different casting strand positions on the entire cross section of the ingot;

[0101] The distance of interface migration at time t+Δt The ferrite film thickness at the beginning of phase transformation is 0. The time history of the ingot reaching different casting strand positions is divided by the incremental step Δt and superimposed using the integration principle. The ferrite film thickness is:

[0102]

[0103] in, represents the interface migration rate corresponding to the i-th incremental step, and m represents the number of the incremental step when the specified casting strand position is reached.

[0104] according to Figure 1 The experimental thermal history of the temperature history of the corner of the billet is designed. First, the temperature is raised to 1550℃ and kept for 1 minute to melt the sample. Then the temperature is lowered to 800℃ at a cooling rate of 7.5℃ / s, then raised to 900℃ at a cooling rate of 2.5℃ / s, and finally lowered to 680℃ at a cooling rate of 0.1℃ / s. It is quenched to room temperature. The calculation results of the pre-eutectoid ferrite film are consistent with the experimental metallographic analysis results. Figure 5 As shown, the relative error is 3.3%, which verifies the accuracy of the method for predicting the growth of proeutectoid ferrite in the casting billet according to the present invention.

[0105] according to Figure 1 The temperature history of the corner of the billet is shown in the figure. The growth of the proeutectoid ferrite film in the corner of the billet is calculated by combining formulas (1)(2)(7)(13). Figure 6 shown.

[0106] According to equations (1)(2)(7)(8) and Fick's first law, the volume fraction of proeutectoid ferrite, carbon enrichment at the phase interface and carbon diffusion on the austenite side at different positions of the casting strand from the meniscus are calculated as follows: Figure 7 shown.

[0107] According to the calculation method of proeutectoid ferrite film growth at the corner of the ingot, Figure 1Based on the temperature history data of the 1 / 2 cross-section, the growth of the proeutectoid ferrite film at each node of the 1 / 2 cross-section of the continuous casting slab is calculated, and the predicted results of the ferrite film thickness of the entire 1 / 2 cross-section of the continuous casting slab at the exit of the straightening zone are as follows Figure 8 shown.

[0108] The above description is only a preferred embodiment of the present disclosure and an explanation of the applied technical principles. Those skilled in the art should understand that the scope of the invention involved in the embodiments of the present disclosure is not limited to the technical solutions formed by the specific combination of the above technical features, and should also cover other technical solutions formed by any combination of the above technical features or their equivalent features without departing from the above inventive concept. For example, the technical solutions formed by mutually replacing the above features with the technical features (but not limited to) disclosed in the embodiments of the present disclosure that have similar functions.

Claims

1. A real-time prediction method for the growth of proeutectoid ferrite during continuous casting, characterized in that, Including the following steps: Step 1: Establish a finite element model for heat transfer in the continuous casting process, calculate the temperature history of the entire cross-section of the slab according to the finite element model for heat transfer, and the time interval of the temperature data is Δt; Step 2: Determine the phase transformation incubation period at different temperatures according to the phase change thermal expansion experiment, and fit the relationship between the phase transformation incubation period and the temperature; Step 3: Calculate the solute drag ΔG of alloying element Mn on interface migration dis , as shown in formula (3): Parameter Parameter wherein is the diffusion coefficient of Mn element in the phase interface, V int is the interface migration rate, is the initial molar fraction of Mn in the continuous casting billet, Parameter Parameter Parameter δ is half of the austenite / ferrite phase interface, E0 represents the binding energy, T is the phase transformation temperature, represents half of the sum of the chemical potentials of the Mn element on the austenite side and the ferrite side, wherein, represents the chemical potential of the Mn element on the ferrite side, represents the chemical potential of the Mn element on the austenite side; Step 4: Calculate the chemical driving force per mole of atoms according to the following formula: where i is the alloying element of the steel grade; k is the number of elements, is the composition of element i transported at the phase interface; and are the mole fractions of element i on the austenite side and the ferrite side; and are the chemical potentials of element i on the austenite side and the ferrite side of the phase interface; The frictional force ΔG during the interface migration process friction depends on the interface migration rate V int and the inherent mobility M of the austenite / ferrite interface int ; ΔG friction = V int V m / M int (5) M int = 2.7×10 18 exp(-145000 / RT) (6) Among which V m is the molar volume of Fe element; Step 5. Using the Gibbs energy balance method, solve for the interface migration rate V under specific conditions according to the following formula int , and when the equation has multiple solutions, take the minimum solution as the final solution; ΔG chem = ΔG friction + ΔG dis (7) Wherein the specific conditions refer to a certain temperature and a certain carbon concentration on the austenite side. Both of these conditions change in real time as the calculation process progresses. According to the real-time situation, the current interface migration rate V is automatically solved int ; Step 6: Take the austenite radius length as the computational domain, and use the finite difference method to divide the computational domain into n micro-elements. At time t, the position of the phase interface is The number of micro-elements on the austenite side at time t is Micro-element length The number of micro-elements on the ferrite side is The carbon mole fraction of each micro-element on the ferrite side is X t ,α / γ , and the carbon mole fraction of the micro-element near the interface in the austenite is The carbon mole fraction inside the austenite is Then, calculate the interface migration rate at the current time t according to Steps 3 and 4 where n is the three elements Fe, C, and Mn, n takes 3, R is the gas constant, and round() is the rounding function; Step 7: At time t + Δt, the distance of interface migration The position of the phase interface at this time The number of infinitesimals on the austenite side is The infinitesimal length The number of infinitesimals on the ferrite side is The carbon mole fraction of each infinitesimal on the ferrite side is X t+Δt,α / γ , after re - dividing the infinitesimals, calculate the carbon mole fraction on the austenite side at time t + Δt according to the carbon mole fraction at time t; Step 8: Calculate the carbon enrichment at the phase interface and the carbon diffusion on the austenite side at the moment of t+Δt according to Fick's first law; Step 9: Calculate cyclically with a time step of Δt to obtain the thickness of the proeutectoid ferrite film at different casting positions of the entire cross-section of the slab.

2. The real-time prediction method for the proeutectoid ferrite growth during the continuous casting process according to claim 1, wherein The finite element model for heat transfer described in Step 1 is: Establish a full cross-section heat transfer model of a two-dimensional slice based on finite element analysis software. The initial temperature of the model is the actual pouring temperature. Determine the heat transfer coefficients of the wide and narrow faces of the slab as boundary conditions according to the on-site water distribution system. Update the heat transfer boundary of the model according to the casting speed of the slab and the position distribution in the secondary cooling zone to simulate the temperature field distribution of the slab during the entire continuous casting process; The temperature history is: After dividing the finite element model for heat transfer into grids, the relationship between the temperatures of each grid node and time.

3. The real-time prediction method for proeutectoid ferrite growth during continuous casting according to claim 1, characterized in that The relationship between the phase transformation incubation period and the temperature τ(T) described in Step 2: where A and m are constants; R is the gas constant; Q k is the activation energy for carbon diffusion in austenite; T is the phase transition temperature; A e3 The starting temperature of the transformation from austenite to ferrite; Regard the variable temperature process as an isothermal process within the increment step Δt, and accumulate the incubation period through formula (2). When the accumulated value is equal to 1, the phase transformation starts; where i represents the increment step number of the finite element heat transfer model, s represents the increment step number when the cumulative value of the formula is equal to 1, and T i represents the nodal temperature value at the i-th increment step.

4. A real-time prediction method for the growth of proeutectoid ferrite during continuous casting according to claim 1, characterized in that, The carbon mole fraction on the austenite side described in Step 7 is: where Δt represents the time interval between the previous and the next moments in the nodal temperature history, i.e., the time step, and Δy t represents the size of the infinitesimal element on the austenite side at time t.

5. A real-time prediction method for proeutectoid ferrite growth during continuous casting according to claim 1, characterized in that The specific content of Step 8 is that during the Δt time of carbon diffusion on the austenite side, adjacent micro-elements satisfy Fick's first law: Among them, represents the diffusion flux of two adjacent micro-elements at time t+Δt, and D γ is the diffusion coefficient of carbon in austenite. The mole fraction of carbon after diffusion is obtained based on the carbon diffusion flux: At the same time, due to the different carbon concentrations on the austenite side and ferrite, carbon enrichment at the phase interface will occur, and formulas (11) and (12) are used for calculation: Among them, represents the carbon diffusion flux at the phase interface at time t, represents the migration velocity of the phase interface at time t, represents the carbon concentration at the phase interface at time t + Δt.

6. The real-time prediction method for proeutectoid ferrite growth during continuous casting according to claim 1, characterized in that, Specifically, the step 9 is the distance of interface migration at the moment of t+Δt Since the thickness of the ferrite film at the start of the phase change is 0, the time history of the slab reaching different casting positions is segmented by the incremental step Δt, and superimposed using the integral principle. The thickness of the ferrite film is as follows: Among them, represents the interface migration rate corresponding to the i-th increment step, and m represents the number of the increment step when reaching the specified casting stream position.

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