A method for predicting precipitation and growth of TiN particles in continuous casting billets considering complex changing cold speed

Abstract

The application provides a continuous casting billet TiN particle precipitation growth and distribution prediction method considering complex change cold speed, and relates to the field of steel continuous casting solidification. The method is based on the prediction model of V-B segregation model and Fick first law, considers the complex cooling change of different billet parts and different casting distances in the continuous casting solidification process, accurately predicts and calculates the precipitation growth and size evolution of TiN particles according to the actual cooling speed change history of the billet, considers the cooling speed change difference of each part of the billet section, predicts and calculates the distribution state of the TiN particle size on the billet section, and considers the influence of the initial nucleation size on the subsequent grain size growth. The method can more accurately predict the size and distribution of TiN particles on the billet section, and provide guidance for the control of TiN. The method can also be extended and applied to the TiN particle precipitation growth and distribution prediction of other casting solidification processes or other alloy casting processes.

Description

Technical Field

[0001] This invention relates to the field of solidification in continuous casting of steel, and provides a method for predicting the precipitation, growth, and distribution of TiN particles in continuously cast billets, taking into account complex variations in cooling rates. This method can also be extended to predicting the precipitation, growth, and distribution of TiN particles in other casting solidification processes or other alloy casting processes. Background Technology

[0002] Continuous casting is a widely used technology in steel production. TiN particles are a common inclusion in continuously cast billets, and their size and distribution directly affect the surface quality and subsequent processing performance of the billet. Currently, the size of TiN particles in continuous casting is mainly determined by sampling, which is costly, time-consuming, and inefficient. Using mathematical models to quickly and accurately predict the size of TiN particles in continuous casting offers advantages for controlling TiN precipitates, improving billet quality, and optimizing process parameters. While some mathematical models exist for predicting the growth size of TiN precipitates, these methods use a fixed cooling rate. However, due to the complexity of cooling conditions, the cooling rate varies and changes in real-time at different stages of continuous casting (initial, intermediate, and final stages) and at different parts of the billet cross-section (center, surface, and corners). Models that do not consider these cooling rate variations cannot objectively reflect the size of TiN particles in the continuously cast billet. Furthermore, current prediction methods do not consider the influence of the initial nucleation size, leading to inaccurate prediction results. To address the above issues, based on the complex cooling rate variations at different locations and drawing distances during continuous casting solidification, an accurate and reliable method for predicting the precipitation, growth, and distribution of TiN particles in continuously cast billets, taking into account the complex variations in cooling rate, is provided.

[0003] Currently, methods for predicting the size of TiN inclusions are scarce. A search using a patent search engine yielded two relevant patent applications: "A method for predicting TiN inclusion precipitation in welding wire steel and a welding wire steel production process" [CN 114743604 A], filed in 2022, and "A method for predicting TiN inclusion precipitation during steel solidification" [CN 109785907A], filed in 2019. Other related patents mainly concern the suppression of TiN precipitation in molten steel, statistical analysis of TiN separation, and research on TiN coatings, which are unrelated to this patent. [CN 114743604 A] uses the Wanger model to calculate the precipitation temperature of TiN particles and then compares it with the actual liquidus temperature of the molten steel to determine whether TiN particles precipitate. The difference between this invention and the aforementioned technology lies in that the latter does not consider the influence of real-time cooling rate changes on TiN particle size; this invention also uses the actual activity product and equilibrium activity product of TiN at different temperatures to determine whether TiN particles precipitate, thus avoiding repetitive content. [CN 109785907 A] establishes a mathematical model for TiN precipitation based on the nucleation and growth process in metal solidification theory, using data analysis and visualization software to predict TiN precipitation and growth. The difference between this invention and the aforementioned technology lies in that this invention derives a TiN particle size prediction model based on real-time cooling rate using the VB segregation model and Fick's first law, predicting the TiN size at different cooling histories and locations in the cast billet, thus avoiding repetitive content.

[0004] Unlike the methods described above, this invention, based on the VB segregation model and Fick's first law, considers the initial nucleation size of TiN particles. According to the complex changes in cooling rate at different parts of the billet and different drawing distances during continuous casting solidification, it provides an accurate and reliable method for predicting the precipitation, growth, and distribution of TiN particles in continuously cast billets, taking into account the complex changes in cooling rate. This provides guidance for controlling and predicting TiN size. Summary of the Invention

[0005] This invention provides a method for predicting the precipitation, growth, and distribution of TiN particles in continuously cast billets, taking into account complex variations in cooling rates, and predicting the size of the largest TiN particles during continuous casting. Based on the VB segregation model and Fick's first law, this method incorporates complex cooling variations at different locations within the continuously cast billet and at different casting distances during different continuous casting solidification processes.

[0006] This invention includes the following steps:

[0007] Step 1): Determination of the solidus temperature and liquidus temperature of the steel grade

[0008] The solidus and liquidus temperatures of a steel grade are calculated using simulation software, empirical formulas, or actual measurements.

[0009] Step 2): Determining the actual cooling curves of various parts of the continuous casting billet cross-section

[0010] By grouping the billets into groups with the same cooling curve, the actual cooling curves of different parts of the billet are simulated and calculated using a solidification heat transfer model to obtain the temperature changes during the continuous casting process of the billet; at the same time, the differences in cooling rates of different parts of the billet cross section can be compared.

[0011] Step 3): Calculation of enrichment and segregation of Ti and N elements at the solidification front of the continuously cast billet during solidification.

[0012] The enrichment and segregation concentration changes of Ti and N elements in the solidification front interface were calculated based on different cooling curves, and the calculation formulas are (1)-(6).

[0013]

[0014]

[0015]

[0016]

[0017]

[0018]

[0019] Where w[j] is the concentration of element j at the interface front, wt%; w o [j] represents the initial concentration of element j in the molten steel, in wt%; f s τ is the solid fraction; τ is the local solidification time during the solidification process of molten steel, in seconds; K j Dj is the equilibrium distribution coefficient of element j; Dj is the diffusion coefficient of element j in the solid phase, in cm2 2 / s; L is the secondary dendrite arm spacing, μm; T is the temperature at the steel melt interface front, K; T L The liquidus temperature of molten steel, in K; T S T0 is the solidus temperature of molten steel, K; T0 is the melting point temperature of pure iron, K; Rct is the cooling rate at time t, K / s; [C] is the concentration of carbon in molten steel, wt%.

[0020] Step 4): Calculation of TiN precipitation thermodynamics and initial nucleation size

[0021] The actual concentration product of TiN at the leading edge interface of the continuously cast billet is calculated by selecting points in the cooling curve from high to low, and compared with the equilibrium activity product at that temperature to determine whether the precipitation conditions are met, as expressed in formulas (7)-(8); the initial nucleation size is determined according to the different nucleation modes of TiN particles, denoted as r0, as expressed in formula (9).

[0022]

[0023] Q TiN K is the actual activity product of TiN; TiN This is the equilibrium activity product of TiN.

[0024]

[0025] σ is the specific interfacial energy at the interface between the new phase and the parent phase; ΔG V The phase transition free energy per unit volume; ΔG EV r is the elastic change energy per unit volume caused by the formation of a new phase. h The core size for heterogeneous nucleation;

[0026] Step 5): Calculation of TiN particle size growth at different cooling rates

[0027] Based on the particle size prediction model derived from Fick's first law, which includes temperature and cooling rate, the size of TiN in different parts of the billet is calculated. Furthermore, the distribution of TiN particle size across the billet cross-section can be analyzed based on the concentration changes of Ti and N at the leading edge interface. The R values ​​at times t and t-1 are used to determine the particle size distribution. c Instantaneous changes reflect the growth of TiN particles under instantaneous changes.

[0028] The predicted TiN particle growth size based on real-time cooling rate is derived from Fick's first law as follows:

[0029]

[0030] Where, r t M represents the size of the TiN particles at time t (in μm); T iN ρ is the relative atomic mass of TiN; TiN The density of TiN is 5.43 g / cm³. 3 ;ρ metal The density of molten steel is 7.07 g / cm³. 3 M N D is the relative atomic mass of element N; L-N The diffusion coefficient in the liquid phase is denoted as cm. 2 / sec; Let K be the difference between the liquidus temperature of the molten steel and the temperature at the leading edge. Let K be the difference between the liquid phase temperature of the molten steel and the front temperature at time t-1. Let T be the radius of the TiN particle at time t-1, in μm. * T is the liquidus temperature of molten steel. L The difference between the temperature of the leading edge and the temperature T: T L -T=T * , through Rct and Calculate the instantaneous change in TiN size at time t, and sum the instantaneous changes to obtain the TiN particle size r at time t. t .

[0031] Step 6): Calculation of TiN particle distribution in different parts of the continuously cast billet

[0032] Using the TiN particle growth prediction model derived in step 5), combined with the cooling curves of different parts of the continuous casting billet in step 2), the precipitation growth and distribution state of TiN particles in different parts of the continuous casting billet cross-section were calculated.

[0033] The present invention has the following beneficial effects:

[0034] 1. The method for predicting the precipitation growth and distribution of TiN particles in continuous casting billets provided by this invention can take into account the complex changes in cooling rate at different parts of the billet and different drawing distances during the continuous casting solidification process. Based on the actual cooling rate change history of the billet, it can accurately predict and calculate the precipitation growth and size evolution of TiN particles.

[0035] 2. The prediction method provided by this invention can take into account the differences in cooling rate at various parts of the billet cross-section and predict and calculate the distribution of TiN particle size on the billet cross-section.

[0036] 3. The prediction method provided by this invention can take into account the initial nucleation size of uniform or heterogeneous nucleation, and the prediction model results are more accurate and more in line with reality. Attached Figure Description

[0037] Figure 1 This is a flowchart of a method for predicting the precipitation and growth size of TiN grains in a continuous casting process based on real-time cooling rate.

[0038] Figure 2 The concentration changes of Ti and N elements at the front interface with different solid fractions during the solidification process.

[0039] Figure 3 The equilibrium concentration product and actual concentration product of TiN precipitation vary with the solid fraction.

[0040] Figure 4 The maximum size of TiN particles at different locations on the billet varies with the solid fraction. Detailed Implementation

[0041] This invention provides a method for predicting the precipitation, growth, and distribution of TiN particles in continuously cast billets, taking into account complex variations in cooling rate. The invention is further described in detail below with examples. The calculation process uses the center portion of the outer arc surface of the billet as an example.

[0042] Step 1): Determination of the solidus temperature and liquidus temperature of the steel grade

[0043] The solidus temperature of the molten steel is determined to be 1727 K, and the liquidus temperature is determined to be 1784 K.

[0044] Step 2): Determining the actual cooling curves of various parts of the continuous casting billet cross-section

[0045] The cooling process of different parts of the billet is shown in Table 1 below.

[0046] Table 1 Cooling rates of different parts

[0047]

[0048] Step 3): Calculation of enrichment and segregation of Ti and N elements at the solidification front of the continuously cast billet during solidification.

[0049] The concentrations of Ti and N elements at the front interface under different solid fractions were calculated using formulas (1)-(6).

[0050]

[0051]

[0052]

[0053]

[0054]

[0055]

[0056] Where w[j] is the concentration of element j at the interface front, wt%; w o [j] represents the initial concentration of element j in the molten steel, in wt%; f s τ is the solid fraction; τ is the local solidification time during the solidification process of molten steel, in seconds; K j is the equilibrium distribution coefficient of element j; Dj is the diffusion coefficient of element j in the solid phase, cm² / s; L is the secondary dendrite arm spacing, μm; T is the temperature at the steel-molten interface front, K; T L The liquidus temperature of molten steel, K; T S T0 is the solidus temperature of molten steel, in K; T0 is the melting point temperature of pure iron; Rct is the cooling rate at time t, in K / s; [C] is the concentration of carbon in molten steel, in wt%.

[0057] The calculation result is Figure 2 As shown.

[0058] Step 4): Calculation of TiN precipitation thermodynamics and initial nucleation size

[0059] The Q values ​​of this steel grade at different temperatures can be calculated using formulas (7)-(8). TiN K TiN .

[0060] Q TiN =w[Ti]·w[N] (7)

[0061]

[0062] Q TiN K is the actual activity product of TiN; TiN This is the equilibrium activity product of TiN;

[0063]

[0064] σ is the specific interfacial energy at the interface between the new phase and the parent phase; ΔG V The phase transition free energy per unit volume; ΔG EV r is the elastic change energy per unit volume caused by the formation of a new phase. h The core size for heterogeneous nucleation;

[0065] The calculation result is Figure 3 As shown. The calculation results show that at 1742K, Q of this steel grade... TiN =0.00089 is greater than K TiN =0.00088, at which point TiN particles begin to precipitate. The initial nucleation size r0 of the TiN particles is calculated to be 0.002 μm by formula (9).

[0066] Step 5): Calculation of TiN particle size growth at different cooling rates

[0067] The TiN particle size at different locations was calculated using the data in Table 1 and formula (9).

[0068]

[0069] Where, r t M represents the size of the TiN particles at time t (in μm); T iN ρ is the relative atomic mass of TiN; TiN The density of TiN is 5.43 g / cm³. 3 ;ρ metal The density of molten steel is 7.07 g / cm³. 3 M ND is the relative atomic mass of element N; L-N The diffusion coefficient in the liquid phase is denoted as cm. 2 / sec; Let K be the difference between the liquidus temperature of the molten steel and the temperature at the leading edge. Let r be the temperature difference between the liquid phase temperature and the frontal temperature of the molten steel at time t, expressed in K. t-1 Let be the radius of the TiN particle at time t-1, in μm;

[0070] Step 6): Calculation of TiN particle distribution in different parts of the continuously cast billet

[0071] Using the TiN particle growth prediction model derived in step 5, and combined with the cooling curves of different parts of the continuously cast billet, the precipitation growth and distribution state of TiN particles in different parts of the continuously cast billet cross section were calculated.

[0072] The calculation results are as follows Figure 4 As shown.

[0073] It should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and not to limit the technical solutions. They have revealed the technical content and features of the present invention. Those skilled in the art should understand that any modifications or equivalent substitutions to the technical solutions of the present invention without departing from the spirit and scope of the present invention should be covered within the scope of the claims of the present invention.

Claims

1. A method for predicting the precipitation, growth, and distribution of TiN particles in continuously cast billets considering complex variations in cooling rate, characterized in that, Includes the following steps: Step 1): Determination of the solidus temperature and liquidus temperature of the steel grade The solidus and liquidus temperatures of steel grades are calculated using simulation software, empirical formulas, or actual measurements. Step 2): Determining the actual cooling curves of various parts of the continuous casting billet cross-section. Grouping by the same cooling curve, the actual cooling curves of different parts of the billet are simulated and calculated using a solidification heat transfer model to obtain the temperature changes during the continuous casting process of the billet; at the same time, the differences in cooling rates of different parts of the billet cross section can be compared. Step 3): Calculation of enrichment and segregation of Ti and N elements at the solidification front of the continuously cast billet during solidification. The enrichment and segregation concentration changes of Ti and N elements in the solidification front interface are calculated according to different cooling curves, and the calculation formulas are (1)-(6). (1) (2) (3) (4) (5) (6) Among them, w[ j [ ] represents the concentration of element j at the interface front, in wt%; w o [ j [ ] represents the initial concentration of element j in the molten steel, in wt%; f s K is the solid fraction; φ is the local solidification time during the solidification process of molten steel, in seconds; K j The balancing distribution coefficient for element j; 𝐷 𝑗 Let be the diffusion coefficient of element j in the solid phase, cm. 2 / s; 𝐿 is the secondary dendrite arm spacing, μm; T is the temperature at the steel-molten interface front, K; T L The liquidus temperature of steel is K; T S T0 is the solidus temperature of molten steel, in K; T0 is the melting point temperature of pure iron, in K. R ct Let be the cooling rate at time t, in K / s; C [ ] represents the concentration of carbon element in the molten steel, in wt% Step 4): Calculation of TiN precipitation thermodynamics and initial nucleation size The actual concentration product of TiN at the leading edge interface of the continuously cast billet is calculated by selecting points in the cooling curve from high to low, and compared with the equilibrium activity product at that temperature to determine whether the precipitation conditions are met. This is expressed as formula (7)-(8). The initial nucleation size is determined according to the different nucleation modes of TiN particles and is denoted as r0. This is expressed as formula (9). (7) Q TiN This represents the actual activity product of TiN; K TiN This is the equilibrium activity product of TiN; (9) The specific interfacial energy at the interface between the new phase and the parent phase; The phase transition free energy per unit volume; This refers to the elastic change energy per unit volume caused by the formation of a new phase. This refers to the core size of heterogeneous nucleation. Step 5): Calculation of TiN particle size growth at different cooling rates Based on the particle size prediction model derived from Fick's first law, which includes temperature and cooling rate, the size of TiN in different parts of the billet is calculated. Furthermore, the distribution of TiN particle size across the billet cross-section can be analyzed based on the concentration changes of Ti and N at the leading edge interface. The difference between the liquid phase temperature of the molten steel and the leading edge temperature at times t and t-1 is also considered. Cooling rate at time t R ct The instantaneous effect of the instantaneous cooling rate change on the growth size of TiN particles is shown in formula (10); (10) in, r t Let t be the size of the TiN particle in μm. M TiN Here is the relative atomic mass of TiN; ρ TiN The density of TiN is 5.43 g / cm³. 3 ; ρ metal The density of molten steel is 7.07 g / cm³. 3 ; M N D is the relative atomic mass of element N; L-N The diffusion coefficient in the liquid phase is denoted as cm. 2 / sec; T t * Let K be the difference between the liquid phase temperature of the molten steel and the front temperature at time t; Let be the radius of the TiN particle at time t-1, in μm; Step 6): Calculation of TiN particle distribution in different parts of the continuously cast billet Using the TiN particle growth prediction model derived in step 5), combined with the cooling curves of different parts of the continuous casting billet in step 2), the precipitation growth and distribution state of TiN particles in different parts of the continuous casting billet cross-section were calculated.

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