A method for predicting the size of TiN precipitates in Ti microalloyed steel continuous casting slabs

Abstract

The invention provides a method for predicting the size of TiN precipitates in Ti microalloyed steel continuous casting billet, and relates to the technical field of steel continuous casting. The method firstly constructs a solidification heat transfer model of a 1 / 4 billet for the problem of solidification heat transfer in billet continuous casting; then, based on the Ueshima model theory, a solute microsegregation model in the steel solidification process is constructed to calculate the microsegregation ratio of the solute element; and in view of the problem of TiN inclusion precipitation in the Ti microalloyed steel solidification process, a TiN precipitation and growth model is coupled on the basis of the solute microsegregation model; finally, the solute microsegregation and TiN precipitation behavior in the Ti microalloyed steel under the continuous casting solidification condition are determined by using the billet continuous casting solidification heat transfer model, the solute microsegregation model and the TiN precipitation and growth model. The method effectively combines the continuous casting process parameters with TiN precipitation, and reveals the solute microsegregation and TiN precipitation behavior under the continuous casting solidification condition.

Description

Technical Field

[0001] The invention relates to the technical field of steel continuous casting, and in particular to a method for predicting the size of TiN precipitates in a Ti microalloy steel continuous casting billet. Background Art

[0002] At present, Ti microalloying technology has been widely used. Adding a trace amount of Ti element to ordinary high-strength low-alloy steel can significantly improve the yield strength and tensile strength of the steel, thereby obtaining low-cost and high-performance steel. The nano-scale carbonitride precipitation phase formed by the combination of Ti element and C and N elements pins the austenite grain boundary, which can play a role in fine grain strengthening and precipitation strengthening. Since the content of Ti element in the earth's crust is very rich, my country's proven Ti reserves account for about half of the world's total, so my country's Ti element has a great advantage in raw material costs. With the increasingly urgent demand for the research and development of low-cost high-strength steel, titanium microalloyed steel has become more and more popular, and Ti microalloying technology has become increasingly mature and has very significant economic and social benefits and bright application prospects.

[0003] Since the solute redistribution coefficients of Ti and N elements are both less than 1, during the solidification process of molten steel, Ti and N elements are continuously enriched at the solidification front, which inevitably leads to the precipitation of TiN. This type of TiN is mostly micron-sized, mainly square, and has hard edges and corners. Due to their relatively large size, these TiN can neither pin the grain boundaries to prevent the growth of austenite grains during carburization, nor play the role of precipitation strengthening. They even often become the source of cracks in steel that endanger the quality of the steel, and will not be eliminated in subsequent heat treatments. Therefore, it is necessary to reveal the precipitation and growth behavior of TiN during steel solidification, which is of great significance for refining the size of TiN in the ingot and controlling the cracks in the ingot.

[0004] The premise of exploring the precipitation behavior of inclusions is to clarify the microscopic segregation behavior of solute elements during solidification. The Chinese patent "A method for predicting the precipitation of TiN inclusions in welding wire steel and welding wire steel production process" with document number CN 114743604A proposes a prediction method for the precipitation of TiN inclusions in welding wire steel, and determines whether the thermodynamic conditions for TiN precipitation are met by activity calculation. However, the patent sets the Ti and N solute contents as the initial components of the steel grade, and fails to consider the influence of the solute microscopic segregation behavior on the Ti and N solute contents. Furthermore, MaW J (International Journal of Minerals Metallurgy and Materials, 2014, 21 (3): 234-239) used the lever model and Scheil model to explore the segregation behavior of Ti and N elements in 20CrMnTi and coupled the TiN precipitation model to clarify the precipitation and growth behavior of TiN. However, in the actual solidification process, the diffusion of solute elements in the solid phase is limited diffusion, and the lever model's assumption of complete diffusion of solute elements in the solid phase and the Scheil model's assumption of complete non-diffusion of solute elements in the solid phase are both inaccurate. Based on the above problems, Wang P (Metallurgical and Materials Transactions B, 2021, 52 (4): 2056-2071) used the Clyne-Kurz model and Ohnaka model to consider the limited diffusion of solute elements in the solid phase, explored the segregation behavior of Ti and N elements in high-carbon cord steel, and coupled the TiN precipitation model to illustrate the precipitation and growth behavior of TiN. However, the Clyne-Kurz model and the Ohnaka model cannot consider the transition between the δ, γ, and L phases, and the solidification rate needs to be set manually, resulting in an inability to accurately describe the actual solidification process of steel. In addition, current studies generally set the cooling rate calculated by the model to a fixed value. In fact, due to the dynamic competition between the latent heat release during solidification and the cooling conditions in each continuous casting zone, the cooling rate during the continuous casting solidification process changes in real time. Setting the cooling rate to a fixed value cannot be effectively linked to the continuous casting solidification cooling conditions. Summary of the invention

[0005] The technical problem to be solved by the present invention is to provide a method for predicting the size of TiN precipitates in Ti microalloyed steel continuous casting billets in view of the above-mentioned deficiencies in the prior art, so as to realize the prediction of the size of TiN precipitates in Ti microalloyed steel continuous casting billets.

[0006] In order to solve the above technical problems, the technical solution adopted by the present invention is: a method for predicting the size of TiN precipitates in Ti microalloyed steel continuous casting billet, comprising the following steps:

[0007] Step 1: Aiming at the solidification heat transfer problem of billet continuous casting, a solidification heat transfer model of 1 / 4 billet is constructed;

[0008] Step 1.1: Establish a two-dimensional slice model of the 1 / 4 cross section of the billet;

[0009] The solidification heat transfer control equation of the two-dimensional slice model is shown in the following formula:

[0010]

[0011] Where ρ is the density of the molten steel; T is the temperature of the molten steel; c is the specific heat capacity of the molten steel; k eff is the thermal conductivity of the molten steel; t is the time; L is the latent heat of solidification of the molten steel; f s is the solid phase ratio of the molten steel; x and y are the coordinate axes of the Cartesian coordinate system;

[0012] Step 1.2: Set the initial conditions and boundary conditions of the 1 / 4 billet solidification heat transfer model;

[0013] At the initial moment of solidification of the 1 / 4 billet, the temperature of the two-dimensional slice is the casting temperature T c The boundary conditions between the crystallizer and the secondary cooling zone are determined according to their water cooling conditions, and the boundary conditions of the air cooling zone are determined by the Stefan-Boltzmann law, that is:

[0014] The initial conditions of the mathematical model for solidification heat transfer of 1 / 4 billet are shown in the following formula:

[0015] T(x≥0,y≥0,t=0)=T c (2)

[0016] Among them, t = 0 represents the initial time of solidification heat transfer calculation of 1 / 4 billet;

[0017] The boundary conditions of the crystallizer, secondary cooling zone, and air cooling zone are shown in the following formula:

[0018]

[0019] h w =1.57W 0.55 (1-0.0075T w ) / α (4)

[0020] h e =[(T sur +T K ) 2 +(T amb +T K ) 2 ](T sur +T amb +2T K ) (5)

[0021] Where, T c is the casting temperature; q mold is the heat flux density of the crystallizer; A and B are coefficients, which depend on the cooling water flow rate and the inlet and outlet temperature difference of the crystallizer; h w is the cooling water convection heat transfer coefficient; W is the cooling water flow density; T w is the cooling water temperature; α is the coefficient related to the cooling of the nip roll; h e is the equivalent convection heat transfer coefficient of the billet surface radiation; T sur is the billet surface temperature; T amb is the ambient temperature; T K is the Celsius temperature corresponding to the absolute temperature 0K;

[0022] Step 2: Based on the Ueshima model theory, a solute microsegregation model during steel solidification is constructed to calculate the microsegregation ratio of the solute elements;

[0023] Step 2.1: Based on the Ueshima model theory, determine the calculation domain of the solute microsegregation model during steel solidification;

[0024] According to the Ueshima model theory, the solidification structure is approximated as a regular hexagonal prism with adjacent edges, and the axial diffusion of the solute along the dendrite is ignored; the cross-sectional area of ​​the dendrite is assumed to expand outward in the form of a regular hexagon during the solidification process, and an equilateral triangle of 1 / 6 of the regular hexagon is selected as the calculation domain of the solute microsegregation model according to the principle of symmetry; the calculation domain is evenly divided into Node_n calculation nodes; the distance between two adjacent nodes is Δx; j is the node number; A j represents the area of ​​node j; L j Represents the interface length between node j and node j+1; Delt_n is the total number of nodes in the δ phase; Solid_n is the total number of nodes in the solid phase; Since the calculation domain of the dendrite size belongs to the micrometer scale, at the same time, it is assumed that there is no temperature difference in the calculation domain; The solute microsegregation model assumes that the solute atoms are uniformly mixed in the liquid phase, and the limited diffusion in the solid phase satisfies Fick's second law;

[0025] Step 2.2: Determine the migration of the phase interface during the steel solidification process by using the steel solidification characteristic temperature criterion;

[0026] The steel solidification characteristic temperature includes the liquidus temperature T L ,δ / γ transition temperature T Ar4 and virtual liquidus temperature T L ′, by comparing the real-time temperature T during steel solidification with the liquidus temperature T L ,δ / γ transition temperature T Ar4 , virtual liquidus temperature T L / The relative size relationship between them can be used to judge the movement of the phase interface during the solidification process of steel;

[0027] The calculation formula of the steel solidification characteristic temperature is as follows:

[0028]

[0029]

[0030]

[0031] Among them, m i and n i are the slopes of the liquidus line and the δ / γ phase transition line of element i in the pseudo-binary Fe-i equilibrium phase diagram; represents the solute content of element i in the last node of the δ phase and the liquid phase at the solidification front, respectively; k δ / L represents the solute redistribution coefficient at the δ / L interface;

[0032] For the solid-liquid interface, when T≤T L When T≤T L And T≤T Ar4 When T≤T, the total number of nodes in the δ phase decreases by one and the total number of nodes in the solid phase increases by one. For the δ / γ interface and the complete δ phase, when T≤T L ′ and T≤T Ar4 When , the total number of nodes in the δ phase decreases by one node;

[0033] Step 2.3: Based on the solute element redistribution and solute conservation law, determine the solute element redistribution at the phase interface during steel solidification;

[0034] The solute distribution at different interfaces during steel solidification is as follows:

[0035] The δ / γ interface satisfies:

[0036]

[0037]

[0038] Among them, k γ / δ represents the solute redistribution coefficient at the γ / δ interface; A Delt_n Represents the area between the Delt_n node and the Delt_n+1 node; They represent the solute contents of element i in the δ and γ nodes at the δ / γ interface before solute redistribution occurs; They represent the solute contents of element i in the δ and γ nodes at the δ / γ interface after solute redistribution occurs;

[0039] The δ / L interface satisfies:

[0040]

[0041]

[0042] Among them, k L / δ represents the solute redistribution coefficient at the L / δ interface; A Solid_n Represents the area between the Solid_n node and the Solid_n+1 node; They represent the solute content of element i in node j before and after solute redistribution occurs; They represent the solute contents of element i in the δ node at the δ / L interface before and after solute redistribution occurs;

[0043] The γ / L interface satisfies:

[0044]

[0045]

[0046] Among them, k γ / L represents the solute redistribution coefficient at the γ / L interface;

[0047] Step 2.4: Based on Fick's second law, determine the back diffusion of solute elements in the solid phase;

[0048] Fick's second law is expressed as follows:

[0049]

[0050] in, Represents the change in the solute content of element i in the solid phase; represents the solute diffusion coefficient in the solid phase;

[0051] The single-phase diffusion of solute elements in the δ phase or γ phase can be solved by the explicit difference method of Fick's second law. The change of solute i at the j node within the δ phase or γ phase within the Δt time is The following relationship is satisfied:

[0052]

[0053] At the dendrite center with j=1, the solute change within Δt time The following relationship is satisfied:

[0054]

[0055] Among them, Δx represents the horizontal distance between two adjacent nodes, L jrepresents the interface length between node j and node j+1, D i represents the diffusion coefficient of element i in the solid phase;

[0056] Step 2.5: Calculate the solute content in the solidification front and divide it by the initial solute content to obtain the microsegregation ratio of the solute element;

[0057] Step 3: To solve the problem of TiN inclusion precipitation during the solidification of Ti microalloyed steel, a TiN precipitation and growth model is coupled based on the solute microsegregation model;

[0058] Step 3.1: Based on the premise that TiN is precipitated when the Ti and N solute contents at the solidification front meet the thermodynamic conditions for TiN precipitation, determine the thermodynamic conditions for TiN precipitation;

[0059] The reaction equation for the formation of TiN in molten steel and the corresponding standard Gibbs free energy change are shown in the following formula:

[0060] [Ti]+[N]=TiN(s) (18)

[0061] ΔG θ =-RT·lnK TiN =-291000+107.91T (J·mol -1 ) (19)

[0062] Among them, ΔG θ represents the standard Gibbs free energy change, K TiN represents the reaction equilibrium constant; R is the ideal gas constant, T is the temperature of the molten steel, and (s) represents the state of a solid phase;

[0063] The thermodynamic conditions for TiN precipitation are shown in the following formula:

[0064]

[0065] Among them, K TiN represents the equilibrium constant of TiN formation reaction; f [Ti] 、f [N] represents the activity coefficient of Ti and N elements, They represent the contents of Ti and N solute elements in the solidification front, respectively;

[0066] Step 3.2: Calculate the size of TiN inclusions based on the principle that the difference between the real-time concentration and the equilibrium concentration of N element at the solidification front is the driving force for TiN growth;

[0067] The TiN inclusion size is determined by the following TiN growth calculation formula:

[0068]

[0069] Where P represents the limiting element in TiN; r represents the radius of the TiN inclusion; ρ Fe , TiN represent the density of molten steel and TiN respectively; represents the diffusion coefficient of the limiting element P in the molten steel, M TiN represents the molar mass of TiN, M P represents the molar mass of the limiting element P, ΔC P Represents the difference between the concentration of limiting element P at the solidification front and the equilibrium concentration of inclusion precipitation;

[0070] Step 4: Determine the solute microsegregation and TiN precipitation behavior in Ti microalloyed steel under continuous casting solidification conditions using the billet continuous casting solidification heat transfer model, solute microsegregation model and TiN precipitation and growth model;

[0071] Step 4.1: Read the Ti microalloy steel grade information, continuous casting machine structural parameters, continuous casting process parameters, and solidus temperature and liquidus temperature;

[0072] Step 4.2: Use the solidification heat transfer model to calculate the temperature field of the continuous casting billet during the continuous casting solidification process, extract the temperature history of the continuous casting billet at the characteristic position under the inner arc skin of the small square billet, and transfer the temperature history to the solute microsegregation model through the Lagrangian linear interpolation method;

[0073] The real-time temperature of the solute microsegregation model determined by the Lagrange linear interpolation method at any time in the corresponding heat transfer calculation temperature history is shown in the following formula:

[0074]

[0075] Among them, the two adjacent time steps of the solidification heat transfer model are t1 and t2, and the corresponding temperatures are T1 and T2; t represents any time in the time period of t1 to t2 in the solute microsegregation model, and T is the temperature corresponding to the calculation domain of the solute microsegregation model at time t;

[0076] Step 4.3: Read the chemical composition of the steel grade and the calculation domain size of the solute microsegregation model;

[0077] The calculation domain size of the solute microsegregation model refers to half of the dendrite arm spacing in the continuous casting billet, which is statistically determined after the billet corrosion experiment;

[0078] Step 4.4: Calculate the microsegregation ratio of solute elements under continuous casting solidification conditions using the solute microsegregation model;

[0079] Step 4.5: Use the TiN precipitation and growth model to calculate the precipitation timing and precipitation size of TiN under continuous casting solidification conditions.

[0080] The beneficial effect of adopting the above technical solution is that: the method for predicting the size of TiN precipitates in Ti microalloyed steel continuous casting billet provided by the present invention is based on the Ueshima model theory, and a solute microsegregation model is established to explore the microsegregation behavior of solute elements. The Ueshima model approximates the cross section of the dendrite to a regular hexagon, assumes that the limited diffusion of solute elements in the solid phase satisfies Fick's second law, and uses the characteristic temperature criterion controlled by the segregation degree of the solute elements to judge whether the δ, γ, and L phase transitions occur, which is more in line with the actual solidification process of steel. In addition, in order to make the cooling rate calculated by the model fit the actual continuous casting cooling rate, a solidification heat transfer model is established, the temperature field of the continuous casting billet is calculated, and the temperature history of the continuous casting billet is used as the cooling condition calculated by the solute microsegregation and TiN precipitation model, which is more in line with the actual solidification temperature history of steel.

[0081] The method of the present invention effectively combines the continuous casting process parameters with TiN precipitation, and reveals the solute micro-segregation and TiN precipitation behavior under the continuous casting solidification conditions. The actual continuous casting process is fully considered, and the connection between the macroscopic solidification heat transfer behavior and the microscopic solute segregation and TiN precipitation behavior is established, providing theoretical guidance for optimizing the quality of Ti micro-alloyed steel products. BRIEF DESCRIPTION OF THE DRAWINGS

[0082] Figure 1 A flow chart of a method for predicting the size of TiN precipitates in a Ti microalloyed steel continuous casting billet provided in an embodiment of the present invention;

[0083] Figure 2 A schematic diagram of a two-dimensional slice model of a 1 / 4 cross section of a 20CrMnTi billet provided in an embodiment of the present invention;

[0084] Figure 3 Schematic diagram of the Ueshima solute microsegregation theoretical model provided in an embodiment of the present invention, wherein (a) is the three-dimensional morphology of dendrite growth, (b) is the cross-sectional morphology of the dendrite, and (c) is the calculation domain of the solute microsegregation model;

[0085] Figure 4 A solidification thermal history curve at a specific position of the inner arc of a 20CrMnTi billet provided in an embodiment of the present invention;

[0086] Figure 5 A graph showing the statistical results of the dendrite arm spacing at different positions provided by an embodiment of the present invention;

[0087] Figure 6 A prediction curve diagram of Ti and N solute segregation ratios at the solidification front provided by an embodiment of the present invention, wherein (a) is a prediction curve diagram of Ti solute segregation ratio, and (b) is a prediction curve diagram of N solute segregation ratio;

[0088] Figure 7A comparison diagram of TiN precipitation size provided in an embodiment of the present invention, wherein (a) is a diagram showing the predicted result of TiN precipitation size, and (b) is a diagram showing an example of TiN size distribution in a casting. DETAILED DESCRIPTION

[0089] The specific implementation of the present invention is further described in detail below in conjunction with the accompanying drawings and examples. The following examples are used to illustrate the present invention, but are not intended to limit the scope of the present invention.

[0090] This embodiment takes the continuous casting and solidification process of a 160mm×160mm small square billet of 20CrMnTi gear steel in a steel plant as an example, and adopts a prediction method for the size of TiN precipitates in a Ti microalloyed steel continuous casting billet of the present invention to predict the solute microsegregation and TiN precipitation behavior under the continuous casting and solidification conditions of 20CrMnTi gear steel.

[0091] In this embodiment, a method for predicting the size of TiN precipitates in Ti microalloyed steel continuous casting billet is as follows: Figure 1 As shown, the following steps are included:

[0092] Step 1: Aiming at the solidification heat transfer problem of billet continuous casting, a solidification heat transfer model of 1 / 4 billet is constructed;

[0093] Step 1.1: Establish a two-dimensional slice model of the 1 / 4 cross section of the 20CrMnTi billet;

[0094] The 2D slice model of the 1 / 4 cross section of the 20CrMnTi billet in this embodiment is as follows: Figure 2 As shown in the figure, the model uses a 1 mm square grid and refines the grid at the corners and edges of the model. The number of nodes in this model is 7366 and the number of elements is 7200.

[0095] Considering that the heat transfer along the billet drawing direction only accounts for 3% to 6% and the symmetry of heat transfer, a 1 / 4 cross section of a 20CrMnTi billet was selected as the research object, and a two-dimensional slice solidification heat transfer model was established. Its control equation is shown in the following formula:

[0096]

[0097] Where ρ is the density of molten steel, kg / m 3 ; T is the temperature of the molten steel, ℃; c is the specific heat capacity of the molten steel, J / (kg·℃); k eff is the thermal conductivity of the molten steel, W / (m·℃); t is the time, s; L is the latent heat of solidification of the molten steel, J / kg; f s is the solid phase ratio of the molten steel; x and y are the coordinate axes of the Cartesian coordinate system;

[0098] Step 1.2: Set the initial conditions and boundary conditions of the 1 / 4 billet solidification heat transfer model;

[0099] At the initial moment of solidification of the 1 / 4 billet, the temperature of the two-dimensional slice is the casting temperature T c The boundary conditions between the crystallizer and the secondary cooling zone are determined according to their water cooling conditions, and the boundary conditions of the air cooling zone are determined by the Stefan-Boltzmann law, that is:

[0100] The initial conditions of the mathematical model for solidification heat transfer of 1 / 4 billet are shown in the following formula:

[0101] T(x≥0,y≥0,t=0)=T c (2)

[0102] Among them, t = 0 represents the initial time of solidification heat transfer calculation of 1 / 4 billet;

[0103] The boundary conditions of the crystallizer, secondary cooling zone, and air cooling zone are shown in the following formula:

[0104]

[0105] h w =1.57W 0.55 (1-0.0075T w ) / α (4)

[0106] h e =[(T sur +T K ) 2 +(T amb +T K ) 2 ](T sur +T amb +2T K ) (5)

[0107] Where, T c is the casting temperature, °C; q mold is the heat flux density of the crystallizer, W / m 2 ; A and B are coefficients, which depend on the cooling water flow rate and the inlet and outlet temperature difference of the crystallizer; h w is the cooling water convection heat transfer coefficient, W / (m 2 ·℃); W is the flow density of cooling water, L / (m 2 ·s); T w is the cooling water temperature, °C; α is the coefficient related to the cooling of the nip roll; h e is the equivalent convection heat transfer coefficient of the billet surface radiation, W / (m 2 ℃); T sur is the billet surface temperature, °C; T amb is the ambient temperature, °C; T K is the Celsius temperature corresponding to the absolute temperature 0K, 273.15℃;

[0108] Step 2: Based on the Ueshima model theory, a solute microsegregation model during steel solidification is constructed to calculate the microsegregation ratio of the solute elements;

[0109] Step 2.1: Based on the Ueshima model theory, determine the calculation domain of the solute microsegregation model during steel solidification;

[0110] According to the Ueshima model theory, the solidification structure is approximated as a regular hexagonal prism with adjacent edges, such as Figure 3 As shown, the axial diffusion of the solute along the dendrite is ignored; the cross-sectional area of ​​the dendrite is set to expand outward in the form of a regular hexagon during the solidification process, and an equilateral triangle of 1 / 6 of the regular hexagon is selected as the calculation domain of the solute microsegregation model according to the principle of symmetry; the calculation domain is evenly divided into Node_n calculation nodes. In this embodiment, the calculation domain is evenly divided into 200 calculation nodes, that is, the total number of nodes Node_n = 200; the distance between two adjacent nodes is Δx; j is the node number; A j represents the area of ​​node j; L j Represents the interface length between node j and node j+1; Delt_n is the total number of nodes in the δ phase; Solid_n is the total number of nodes in the solid phase; Since the calculation domain of the dendrite size belongs to the micrometer scale, at the same time, it is assumed that there is no temperature difference in the calculation domain; The solute microsegregation model assumes that the solute atoms are uniformly mixed in the liquid phase, and the limited diffusion in the solid phase satisfies Fick's second law;

[0111] Step 2.2: Determine the migration of the phase interface during the steel solidification process by using the steel solidification characteristic temperature criterion;

[0112] The steel solidification characteristic temperature includes the liquidus temperature T L ,δ / γ transition temperature T Ar4 and virtual liquidus temperature T L ′, by comparing the real-time temperature (T) during steel solidification with the liquidus temperature T L ,δ / γ transition temperature T Ar4 , virtual liquidus temperature T L / The relative size relationship between them can be used to judge the movement of the phase interface during the solidification process of steel;

[0113] The calculation formula of the steel solidification characteristic temperature is as follows:

[0114]

[0115]

[0116]

[0117] Among them, m i and n i are the slopes of the liquidus line and the δ / γ phase transition line of element i in the pseudo-binary Fe-i equilibrium phase diagram; represents the solute content of element i in the last node of the δ phase and the liquid phase at the solidification front, respectively; k δ / L represents the solute redistribution coefficient at the δ / L interface;

[0118] For the solid-liquid interface (δ / L and γ / L), when T≤T L When T≤T L And T≤T Ar4 When T≤T, the total number of nodes in the δ phase decreases by one and the total number of nodes in the solid phase increases by one. For the δ / γ interface and the complete δ phase, when T≤T L ′ and T≤T Ar4 When , the total number of nodes in the δ phase decreases by one node;

[0119] Step 2.3: Based on the solute element redistribution and solute conservation law, determine the solute element redistribution at the phase interface during steel solidification;

[0120] The solute distribution at different interfaces during steel solidification is as follows:

[0121] The δ / γ interface satisfies:

[0122]

[0123]

[0124] Among them, k γ / δ represents the solute redistribution coefficient at the γ / δ interface; A Delt_n Represents the area between the Delt_n node and the Delt_n+1 node; They represent the solute contents of element i in the δ and γ nodes at the δ / γ interface before solute redistribution occurs; They represent the solute contents of element i in the δ and γ nodes at the δ / γ interface after solute redistribution occurs;

[0125] The δ / L interface satisfies:

[0126]

[0127]

[0128]

[0129] Among them, A Solid_nRepresents the area between the Solid_n node and the Solid_n+1 node; They represent the solute content of element i in node j before and after solute redistribution occurs; They represent the solute contents of element i in the δ node at the δ / L interface before and after solute redistribution occurs;

[0130] The γ / L interface satisfies:

[0131]

[0132]

[0133] Among them, k γ / L represents the solute redistribution coefficient at the γ / L interface;

[0134] Step 2.4: Based on Fick's second law, determine the back diffusion of solute elements in the solid phase;

[0135] Fick's second law is expressed as follows:

[0136]

[0137] in, Represents the change in the solute content of element i in the solid phase; represents the solute diffusion coefficient in the solid phase;

[0138] The single-phase diffusion of solute elements in the δ phase or γ phase can be solved by the explicit difference method of Fick's second law. The change of solute i at the j node within the δ phase or γ phase within the Δt time is The following relationship is satisfied:

[0139]

[0140] Solute change at the dendrite center (j=1) within Δt time The following relationship is satisfied:

[0141]

[0142] Among them, Δx represents the horizontal distance between two adjacent nodes, L j represents the interface length between node j and node j+1, D i represents the diffusion coefficient of element i in the solid phase;

[0143] Step 2.5: Calculate the solute content in the solidification front and divide it by the initial solute content to obtain the microsegregation ratio of the solute element;

[0144] In this embodiment, the solute redistribution coefficient k between different phases is δ / L , kγ / L , k γ / δ , the diffusion coefficient D of different solute elements in the solid phase i , the slope m of the liquidus line and the δ / γ phase transition line of element i in the pseudo-binary Fe-i equilibrium phase diagram i 、n i They are summarized in Table 1.

[0145] Table 1 Redistribution coefficient of solute elements, solid phase diffusion coefficient, and slope of temperature line

[0146]

[0147] Note: R = 1.987 cal / mol·K.

[0148] Step 3: To solve the problem of TiN inclusion precipitation during the solidification of Ti microalloyed steel, a TiN precipitation and growth model is coupled based on the solute microsegregation model;

[0149] Step 3.1: Based on the premise that TiN is precipitated when the Ti and N solute contents at the solidification front meet the thermodynamic conditions for TiN precipitation, determine the thermodynamic conditions for TiN precipitation;

[0150] The reaction equation for the formation of TiN in molten steel and the corresponding standard Gibbs free energy change are shown in the following formula:

[0151] [Ti]+[N]=TiN(s) (18)

[0152] ΔG θ =-RT·lnK TiN =-291000+107.91T (J·mol -1 ) (19)

[0153] Among them, ΔG θ represents the standard Gibbs free energy change, K TiN represents the reaction equilibrium constant; R is the ideal gas constant, whose value is 8.314 J / (mol·K); T is the temperature of the molten steel, K; (s) represents the state of a solid phase;

[0154] For pure TiN inclusions, the activity of TiN is TiN = 1. Therefore, the Gibbs free energy change of the TiN formation reaction can be expressed as formula (21):

[0155]

[0156]

[0157] Among them, a TiN 、a Ti 、a Nrepresent the activities of TiN, Ti, and N, respectively; Respectively represent the solute content of Ti and N elements in the molten steel; f [Ti] 、f [N] Represent the activity coefficients of Ti and N respectively. [Ti] 、f [N] The value of can be calculated by the following formula:

[0158]

[0159]

[0160] in, They represent the activity coefficients of Ti and N at 1873K respectively, and their values ​​can be calculated using the following formula:

[0161]

[0162]

[0163] in, are the interaction coefficients between Ti, N and solute element j, respectively.

[0164] Since the mass fraction of Fe in the molten steel is greater than 90%, the influence of the second-order interaction coefficient is ignored, and only the first-order interaction coefficient is considered. The values ​​of the first-order interaction coefficients of Ti, N and solute element j are shown in Table 2.

[0165] Table 2187 The first-order interaction coefficients of elements in molten steel at 3K

[0166]

[0167] When the concentration relationship between Ti and N in the residual molten steel satisfies the following formula, TiN inclusions will immediately precipitate from the molten steel (i.e., the thermodynamic condition for TiN precipitation):

[0168]

[0169] After the TiN inclusions precipitate, the Ti and N element contents will decrease, so the solute concentration in the residual liquid phase needs to be updated in time:

[0170]

[0171]

[0172] in, Respectively represent the concentrations of Ti and N elements in the residual liquid phase after renewal; Respectively represent the concentrations of Ti and N elements in the residual liquid before renewal; ΔC Ti , ΔC NThey represent the consumption of Ti and N elements in the residual liquid phase due to TiN precipitation, and the two have the following proportional relationship:

[0173]

[0174] Among them, M Ti 、M N 、M TiN are the molar masses of Ti, N and TiN respectively.

[0175] Assuming that during the solidification process, the consumption of Ti and N elements in the residual liquid phase is all used for the precipitation of TiN inclusions, the mass percentage of TiN inclusions precipitated is w TiN for:

[0176]

[0177] Step 3.2: Calculate the size of TiN inclusions based on the principle that the difference between the real-time concentration and the equilibrium concentration of N element at the solidification front is the driving force for TiN growth;

[0178] When the concentration product of Ti and N elements in the residual liquid phase satisfies formula (26), TiN inclusions precipitate in the residual liquid phase and gradually grow. The size of TiN inclusions is determined by the following TiN growth calculation formula:

[0179]

[0180] Where P represents the limiting element in TiN; r represents the radius of the TiN inclusion, μm; ρ Fe , TiN Represent the density of molten steel and TiN, respectively, and their values ​​are 7070kg / m 3 、5430kg / m 3 ; represents the diffusion coefficient of the limiting element P in the molten steel, M TiN represents the molar mass of TiN, M P represents the molar mass of the limiting element P, ΔC P Represents the difference between the concentration of limiting element P at the solidification front and the equilibrium concentration of inclusion precipitation;

[0181] For Ti and N elements,

[0182]

[0183]

[0184] It can be found that the diffusion coefficients of Ti and N in molten steel are not much different. Therefore, it is believed that when the initial content of Ti is greater than that of N, N is the limiting element, and vice versa, Ti is the limiting element.

[0185] In order to consider the solidification process As t changes, in this embodiment, the trapezoidal integral formula is used to integrate equation (31):

[0186]

[0187] Among them, r i+1 、r i They represent the TiN inclusion radius before and after calculation at a certain moment respectively; They represent the product of the diffusion coefficient and consumption of N element in molten steel at two adjacent time steps at a certain moment.

[0188] Step 4: Determine the solute microsegregation and TiN precipitation behavior in Ti microalloyed steel under continuous casting solidification conditions using the billet continuous casting solidification heat transfer model, solute microsegregation model and TiN precipitation and growth model;

[0189] Step 4.1: Read the Ti microalloy steel grade information, continuous casting machine structural parameters, continuous casting process parameters, and solidus temperature and liquidus temperature;

[0190] The steel grade information includes steel grade and chemical composition; the continuous casting machine structural parameters include mold height, secondary cooling zone structural parameters and air cooling zone length; the secondary cooling zone structural parameters include the number and length of secondary cooling zones; the continuous casting process parameters include casting temperature, casting speed, water flow in each of the mold and secondary cooling zones, and electromagnetic stirring current and frequency;

[0191] In this embodiment, the steel grade is 20CrMnTi, and the chemical composition, structural parameters of the continuous casting machine and continuous casting process parameters of the steel are shown in Tables 3, 4 and 5 respectively.

[0192] Table 3 Main chemical composition of 20CrMnTi (wt%)

[0193] C Si Mn P S Cr Ti N 0.19 0.24 0.89 0.016 0.01 1.08 0.069 0.0047

[0194] Table 4 Continuous casting machine parameters

[0195] Crystallizer height / m Second cooling zone 1 / m Second cooling zone 2 / m Second cooling zone three / m Second cooling zone 4 / m Air cooling area / m 0.8 0.31 2.73 2.57 2.89 10.7

[0196] Table 5 20CrMnTi continuous casting process parameters

[0197]

[0198] In this embodiment, the corresponding liquidus-solidus temperature calculation formula is selected for 20CrMnTi steel:

[0199] T L =1536-{65[C]+8[Si]+5[Mn]+30[P]+25[S]+20[Ti]+1.5[Cr]} (35)

[0200] T S =1536-{175[C]+20[Si]+30[Mn]+280[P]+575[S]+40[Ti]} (36)

[0201] Among them, T L is the liquidus temperature; T S is the solidus temperature; [C], [Si], [Mn], [P], [S], [Cr], and [Ti] are the mass fractions of the corresponding elements.

[0202] Step 4.2: Use the solidification heat transfer model to calculate the temperature field of the continuous casting billet during the continuous casting solidification process, extract the temperature history of the continuous casting billet at the characteristic position under the inner arc skin of the small square billet, and transfer the temperature history to the solute microsegregation model through the Lagrangian linear interpolation method;

[0203] In this embodiment, the time step used in the solidification heat transfer model is set to 0.1s, and the time step used in the solute microsegregation model is set to 1e -6 s, the temperature history of the solidification heat transfer model is transferred to the solute microsegregation model by linear Lagrangian interpolation. The corresponding formula is as follows:

[0204]

[0205] Among them, the two adjacent time steps of the solidification heat transfer model are t1 and t2, and the corresponding temperatures are T1 and T2; t represents any time in the time period of t1 to t2 in the solute microsegregation model, and T is the temperature corresponding to the calculation domain of the solute microsegregation model at time t;

[0206] This embodiment provides a solidification heat history curve at a specific position of the inner arc of a 20CrMnTi billet, such as Figure 4 As shown, from Figure 4It can be seen that in the early stage of solidification, the release of latent heat of solidification alleviates the heat loss caused by cooling to a certain extent, and the cooling rate is slow. As the solidification proceeds, the liquid phase is gradually consumed, and the amount of latent heat of solidification released also decreases, which is increasingly insufficient to replenish the lost heat, and the cooling rate gradually accelerates. During the entire solidification process, the cooling rate at the 20mm position always remains the largest compared to the 40 and 60mm positions. This is because the strong cooling area near the foot roll section enters the mushy zone, and the thermal resistance of the solidified billet shell is small, and the heat conduction to the outside is most significant. At the same time, it can be judged from the inclination of the curve that in the middle and late stages of solidification, the cooling rate at the 60mm position near the center of the billet is higher than that at the 40mm position. This is because when the billet solidifies near the center, its surroundings are already completely solidified, and no additional latent heat is transferred to the center of the billet.

[0207] Step 4.3: Read the chemical composition of the steel grade and the calculation domain size of the solute microsegregation model;

[0208] The calculation domain size of the solute microsegregation model refers to half of the dendrite arm spacing in the continuous casting billet, which is statistically determined after the billet corrosion experiment;

[0209] In order to clarify the dendrite arm spacing at different positions of the gear steel ingot, this embodiment carried out a ingot corrosion experiment, statistically analyzed the dendrite arm spacing (DAS) results at different positions, and then determined the solute microsegregation model calculation domain size (MCDS), the specific method is:

[0210] The wire cutting machine was used to cut the gear steel ingot from the inner arc surface to the center (0-80 mm), and the sample was placed in 100 ml saturated picric acid + Seagull detergent solution at a constant temperature of 80 ° C for 2 minutes after grinding and polishing. The corroded surface of the sample was photographed using a metallographic microscope. The DAS data at 10-65 mm from the ingot surface were randomly measured and polynomial fitting was performed. Figure 5 The DAS results at 10 to 65 mm are shown. The results show that the closer to the center of the billet, the larger the DAS, especially after entering the equiaxed crystal zone, this trend is more obvious. Among them, the CET transformation position of columnar crystal to equiaxed crystal is 42.06 mm, and the functional relationship between the upper and lower limits of DAS and the distance from the billet surface (loc) is:

[0211] DAS max =-37.2643+19.28896loc-0.51714loc 2 +0.0057loc 3 R 2 =0.956 (38)

[0212] DAS min=-13.4867+11.11188loc-0.29313loc 2 +0.00318loc 3 R 2 =0.952 (39)

[0213] The larger the DAS, the more sufficient the space for TiN precipitation and the less sufficient the back diffusion of solute elements in the solid phase, resulting in a relatively larger TiN precipitation size. It should be pointed out that the TiN precipitation thermodynamic and kinetic model assumes that when the Ti and N concentration product at the solidification front meets the TiN precipitation thermodynamic conditions, TiN will precipitate and begin to grow immediately. Therefore, in this embodiment, DAS is taken as max To investigate the maximum precipitation size of TiN. DAS at 20, 40, and 60 mm max They correspond to 187.26, 271.67, and 489.57 μm respectively, so the MCDS are 93.63, 135.835, and 244.785 μm respectively.

[0214] Step 4.4: Calculate the microsegregation ratio of solute elements under continuous casting solidification conditions using the solute microsegregation model;

[0215] In this embodiment, the prediction curve of Ti and N solute segregation ratio at the solidification front is as follows: Figure 6 As shown in the figure, since the initial concentration of N is one order of magnitude lower than that of Ti during the solidification of 20CrMnTi, N is considered to be the limiting element for TiN precipitation. The segregation ratio of Ti continues to increase after TiN precipitation, while the segregation ratio of N begins to decrease until it is lower than the initial N concentration level. Solid phase ratio f s When =0.99, the segregation ratios of Ti element at 20, 40 and 60 mm are 9.461, 9.667 and 10.830 respectively; the segregation ratios of N element at 20, 40 and 60 mm are 0.544, 0.530 and 0.463 respectively.

[0216] Step 4.5: Use the TiN precipitation and growth model to calculate the precipitation timing and precipitation size of TiN under continuous casting solidification conditions.

[0217] In this embodiment, the TiN precipitation size predicted by the TiN precipitation and growth model and the actual TiN size in the ingot are compared. Figure 7 As shown by Figure 7 (a) It can be seen that the precipitation solid phase ratios of TiN at 20, 40, and 60 mm are 0.675, 0.676, and 0.669, respectively, and the predicted maximum precipitation sizes of TiN at 20, 40, and 60 mm are 6.128, 7.836, and 7.593 μm, respectively. Figure 7(b) shows an example of the distribution of TiN size in the billet. The results show that the maximum TiN size measured in the continuous casting billet at 20, 40, and 60 mm is 4.758, 7.552, and 6.679 μm, respectively. It can be found that the maximum TiN precipitation size predicted by the TiN precipitation and growth model is in good agreement with the actual measured results of the billet. It can be seen that the above model can provide theoretical guidance for refining the TiN size in the billet and improving the billet quality.

[0218] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, rather than to limit it. Although the present invention has been described in detail with reference to the aforementioned embodiments, those skilled in the art should understand that they can still modify the technical solutions described in the aforementioned embodiments, or make equivalent replacements for some or all of the technical features therein. However, these modifications or replacements do not cause the essence of the corresponding technical solutions to deviate from the scope defined by the claims of the present invention.

Claims

1. A method for predicting the size of TiN precipitates in Ti microalloyed steel continuous casting billets, characterized in that: The following steps are involved: Step 1: Aiming at the solidification heat transfer problem of billet continuous casting, a solidification heat transfer model of 1 / 4 billet is constructed; Step 2: Based on the Ueshima model theory, a solute microsegregation model during steel solidification is constructed to calculate the microsegregation ratio of the solute elements; Step 3: To solve the problem of TiN inclusion precipitation during the solidification of Ti microalloyed steel, a TiN precipitation and growth model is coupled based on the solute microsegregation model; Step 3.1: Based on the premise that TiN is precipitated when the Ti and N solute contents at the solidification front meet the thermodynamic conditions for TiN precipitation, determine the thermodynamic conditions for TiN precipitation; The reaction equation for the formation of TiN in molten steel and the corresponding standard Gibbs free energy change are shown in the following formula: [Ti]+[N]=TiN(s) (18) ΔG θ =-RT·lnK TiN =-291000+107.91T (J·mol -1 ) (19) Among them, ΔG θ represents the standard Gibbs free energy change, K TiN represents the reaction equilibrium constant; R is the ideal gas constant, T is the temperature of the molten steel, and (s) represents the state of a solid phase; The thermodynamic conditions for TiN precipitation are shown in the following formula: Among them, K TiN represents the equilibrium constant of TiN formation reaction; f [Ti] 、f [N] represents the activity coefficient of Ti and N elements, They represent the contents of Ti and N solute elements in the solidification front, respectively; Step 3.2: Calculate the size of TiN inclusions based on the principle that the difference between the real-time concentration and the equilibrium concentration of N element at the solidification front is the driving force for TiN growth; The TiN inclusion size is determined by the following TiN growth calculation formula: Where P represents the limiting element in TiN; r represents the radius of the TiN inclusion; ρ metal , TiN represent the density of molten steel and TiN respectively; represents the diffusion coefficient of the limiting element P in the molten steel, M TiN represents the molar mass of TiN, M P represents the molar mass of the limiting element P, △C P Represents the difference between the concentration of limiting element P at the solidification front and the equilibrium concentration of inclusion precipitation; Step 4: Use the billet continuous casting solidification heat transfer model, solute microsegregation model and TiN precipitation and growth model to determine the solute microsegregation and TiN precipitation behavior in Ti microalloyed steel under continuous casting solidification conditions.

2. The method for predicting the size of TiN precipitates in Ti microalloyed steel continuous casting billet according to claim 1, characterized in that: The specific method of step 1 is: Step 1.1: Establish a two-dimensional slice model of the 1 / 4 cross section of the billet; The solidification heat transfer control equation of the two-dimensional slice model is shown in the following formula: Where ρ is the density of the molten steel; T is the temperature of the molten steel; c is the specific heat capacity of the molten steel; k eff is the thermal conductivity of the molten steel; t is the time; L is the latent heat of solidification of the molten steel; f s is the solid phase ratio of the molten steel; x and y are the coordinate axes of the Cartesian coordinate system; Step 1.2: Set the initial conditions and boundary conditions of the 1 / 4 billet solidification heat transfer model; At the initial moment of solidification of the 1 / 4 billet, the temperature of the two-dimensional slice is the casting temperature T c The boundary conditions between the crystallizer and the secondary cooling zone are determined according to their water cooling conditions, while the boundary conditions of the air cooling zone are determined by the Stefan-Boltzmann law.

3. The method for predicting the size of TiN precipitates in Ti microalloyed steel continuous casting billet according to claim 2, characterized in that: The initial conditions of the mathematical model of solidification heat transfer of 1 / 4 small square billet described in step 1.2 are shown in the following formula: T(x≥0, y≥0, t=0)=T c (2) Among them, t = 0 represents the initial time of solidification heat transfer calculation of 1 / 4 billet; The boundary conditions of the crystallizer, secondary cooling zone, and air cooling zone are shown in the following formula: h w =1.57W 0.55 (1-0.0075T w ) / a (4) h e =[(T sur +T K ) 2 +(T amb +T K ) 2 ](T sur +T amb +2T K ) (5) Where, T c is the casting temperature; q mold is the heat flux density of the crystallizer; A and B are coefficients, which depend on the cooling water flow rate and the inlet and outlet temperature difference of the crystallizer; h w is the cooling water convection heat transfer coefficient; W is the cooling water flow density; T w is the cooling water temperature; α is the coefficient related to the cooling of the nip roll; h e is the equivalent convection heat transfer coefficient of the billet surface radiation; T sur is the billet surface temperature; T amb is the ambient temperature; T K is the Celsius temperature corresponding to absolute temperature 0K.

4. The method for predicting the size of TiN precipitates in Ti microalloyed steel continuous casting billet according to claim 3, characterized in that: The specific method of step 2 is: Step 2.1: Based on the Ueshima model theory, determine the calculation domain of the solute microsegregation model during steel solidification; According to the Ueshima model theory, the solidification structure is approximated as a regular hexagonal prism with adjacent edges, and the axial diffusion of the solute along the dendrite is ignored; the cross-sectional area of ​​the dendrite is assumed to expand outward in the form of a regular hexagon during the solidification process, and an equilateral triangle of 1 / 6 of the regular hexagon is selected as the calculation domain of the solute microsegregation model according to the principle of symmetry; the calculation domain is evenly divided into Node_n calculation nodes; the distance between two adjacent nodes is Δx; j is the node number; A j represents the area of ​​node j; L j Represents the interface length between node j and node j+1; Delt_n is the total number of nodes in the δ phase; Solid_n is the total number of nodes in the solid phase; Since the calculation domain of the dendrite size belongs to the micrometer scale, at the same time, it is assumed that there is no temperature difference in the calculation domain; The solute microsegregation model assumes that the solute atoms are uniformly mixed in the liquid phase, and the limited diffusion in the solid phase satisfies Fick's second law; Step 2.2: Determine the migration of the phase interface during the steel solidification process by using the steel solidification characteristic temperature criterion; The steel solidification characteristic temperature includes the liquidus temperature T L ,δ / γ transition temperature T Ar4 and virtual liquidus temperature T L ′, by comparing the real-time temperature T during steel solidification with the liquidus temperature T L ,δ / γ transition temperature T Ar4 , virtual liquidus temperature T L / The relative size relationship between them can be used to judge the movement of the phase interface during the solidification process of steel; For the solid-liquid interface, when T≤T L When T≤T L And T≤T Ar4 When T≤T, the total number of nodes in the δ phase decreases by one and the total number of nodes in the solid phase increases by one. For the δ / γ interface and the complete δ phase, when T≤T L ′ and T≤T Ar4 When , the total number of nodes in the δ phase decreases by one node; Step 2.3: Based on the solute element redistribution and solute conservation law, determine the solute element redistribution at the phase interface during steel solidification; Step 2.4: Based on Fick's second law, determine the back diffusion of solute elements in the solid phase; Step 2.5: Calculate the solute content in the solidification front and divide it by the initial solute content to obtain the microsegregation ratio of the solute element.

5. The method for predicting the size of TiN precipitates in Ti microalloyed steel continuous casting billet according to claim 4, characterized in that: The calculation of the characteristic temperature of steel solidification in step 2.2 is shown in the following formula: Among them, m i and n i are the slopes of the liquidus line and the δ / γ phase transition line of element i in the pseudo-binary Fe-i equilibrium phase diagram; represents the solute content of element i in the last node of the δ phase and the liquid phase at the solidification front, respectively; k δ / L Represents the solute redistribution coefficient at the δ / L interface.

6. The method for predicting the size of TiN precipitates in Ti microalloyed steel continuous casting billet according to claim 5, characterized in that: The solute distribution at different interfaces during the steel solidification process determined in step 2.3 is specifically: The δ / γ interface satisfies: Among them, k γ / δ represents the solute redistribution coefficient at the γ / δ interface; A Delt_n Represents the area between the Delt_n node and the Delt_n+1 node; They represent the solute contents of element i in the δ and γ nodes at the δ / γ interface before solute redistribution occurs; They represent the solute contents of element i in the δ and γ nodes at the δ / γ interface after solute redistribution occurs; The δ / L interface satisfies: Among them, A Solid_n Represents the area between the Solid_n node and the Solid_n+1 node; They represent the solute content of element i in node j before and after solute redistribution occurs; They represent the solute contents of element i in the δ node at the δ / L interface before and after solute redistribution occurs; The γ / L interface satisfies: Among them, k γ / L represents the solute redistribution coefficient at the γ / L interface.

7. The method for predicting the size of TiN precipitates in Ti microalloyed steel continuous casting billet according to claim 6, characterized in that: Fick's second law described in step 2.4 is expressed as follows: in, Represents the change in the solute content of element i in the solid phase; represents the solute diffusion coefficient in the solid phase; The single-phase diffusion of solute elements in the δ phase or γ phase can be solved by the explicit difference method of Fick's second law. The change of solute i at the j node within the δ phase or γ phase within the Δt time is The following relationship is satisfied: At the dendrite center with j=1, the solute change within Δt time The following relationship is satisfied: Among them, Δx represents the horizontal distance between two adjacent nodes, L j represents the interface length between node j and node j+1, D i represents the diffusion coefficient of element i in the solid phase.

8. The method for predicting the size of TiN precipitates in Ti microalloyed steel continuous casting billet according to claim 7, characterized in that: The specific method of step 4 is: Step 4.1: Read the Ti microalloy steel grade information, continuous casting machine structural parameters, continuous casting process parameters, and solidus temperature and liquidus temperature; Step 4.2: Use the solidification heat transfer model to calculate the temperature field of the continuous casting billet during the continuous casting solidification process, extract the temperature history of the continuous casting billet at the characteristic position under the inner arc skin of the small square billet, and transfer the temperature history to the solute microsegregation model through the Lagrangian linear interpolation method; Step 4.3: Read the chemical composition of the steel grade and the calculation domain size of the solute microsegregation model; The calculation domain size of the solute microsegregation model refers to half of the dendrite arm spacing in the continuous casting billet, which is statistically determined after the billet corrosion experiment; Step 4.4: Calculate the microsegregation ratio of solute elements under continuous casting solidification conditions using the solute microsegregation model; Step 4.5: Use the TiN precipitation and growth model to calculate the precipitation timing and precipitation size of TiN under continuous casting solidification conditions.

9. The method for predicting the size of TiN precipitates in Ti microalloyed steel continuous casting billet according to claim 8, characterized in that: The step 4.2 determines the real-time temperature of the solute micro-segregation model corresponding to the heat transfer calculation temperature history at any time by the Lagrange linear interpolation method, as shown in the following formula: Among them, the two adjacent time steps of the solidification heat transfer model are t1 and t2, and the corresponding temperatures are T1 and T2; t represents any time in the time period of t1 to t2 in the solute microsegregation model, and T is the corresponding temperature of the calculation domain of the solute microsegregation model at time t.

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