Method and device for predicting behavior of inclusions during solidification of molten steel

Abstract

The application discloses a kind of inclusions precipitation behavior prediction method in molten steel solidification process, belong to metallurgical technical field.The method of the present application is based on the reaction generation of various inclusions in molten steel solidification process and the concentration variation of corresponding solute elements are analyzed in real time, and the prediction results of V-B microscopic segregation model coupled with kinetic precipitation consumption are updated and corrected in real time according to the analysis results, so that the precipitation type, precipitation size and solute element microscopic segregation of various inclusions in molten steel can be accurately predicted.The application also discloses a kind of inclusions precipitation behavior prediction device in molten steel solidification process.Compared with prior art, the technical scheme of the present application is suitable for various inclusions, and the prediction result is more accurate, so as to provide scientific guidance for scientific research and production process improvement.

Description

Technical Field

[0001] This invention relates to a method for predicting the precipitation behavior of inclusions during the solidification process of molten steel, belonging to the field of metallurgical technology. Background Technology

[0002] Adding trace amounts of alloying elements to steel can significantly improve its yield strength and tensile strength, thereby obtaining low-cost, high-performance steel. For example, the submicron-sized oxide precipitates formed by the combination of Ti and O elements pin the austenite grain boundaries, thus playing a role in grain refinement and precipitation strengthening.

[0003] Compositional segregation during solidification is an inherent characteristic of alloys. Some solute elements, due to their small redistribution coefficients, continuously accumulate at the solidification front. This makes it possible for inclusions that would otherwise be difficult to form directly in the liquid phase to form as solidification progresses, or it causes fine inclusions that would normally form directly in the liquid phase to coarsen. These inclusions formed during solidification are often micron-sized oxides, spherical in shape. As solidification proceeds, they undergo a coarsening stage, causing the fine inclusions to become larger. Coarsened inclusions reduce the pinning effect of submicron oxides on grain boundaries and are less effective at precipitation strengthening. Therefore, it is necessary to reveal the precipitation behavior of inclusions during steel solidification, which is of great significance for refining inclusion size and improving steel properties.

[0004] The key to investigating inclusion precipitation behavior is accurately predicting the microscopic segregation behavior and precipitation consumption of each solute element participating in the precipitation reaction during steel solidification. Patent CN 110970094A, "A Prediction Method for VN Precipitation During Steel Solidification," provides a mathematical model for VN precipitation during the solidification of a quaternary alloy, using activity calculations to determine whether the thermodynamic conditions for VN precipitation are met. Patent CN 114722626A, "A Prediction and Simulation Method for Macroscopic Segregation and Precipitated Inclusions in Ingots," provides a prediction and simulation method for precipitated inclusions in ingots, considering the influence of macroscopic segregation. However, neither of these patents considers the influence of the microscopic segregation behavior of solute elements on inclusion precipitation, which may underestimate the amount of inclusions precipitated or even make it difficult to estimate the precipitation amount. Furthermore, patent CN 115862766A, "Prediction of MnS and MnS-M steel grades based on solidification segregation model,"... x O yThe paper presents a method for predicting inclusion size based on the Clyne-Kurz segregation model. This segregation model has a certain accuracy in predicting segregation, but it does not couple the consumption of solute elements caused by inclusion precipitation, thus overestimating the solute element content in the solidification region. The patent CN 116011229A, "A Method for Predicting the Size of TiN Precipitates in Ti Microalloyed Steel Continuous Casting Billets", and Gui Lintao et al. (Journal of Materials Research and Technology, 2020, 9(3): 5499-5514) comprehensively consider the above problems and respectively give a model that couples TiN precipitation and growth based on the solute microsegregation model. This is currently a more accurate model in the field of research on the precipitation behavior of single inclusions. However, in reality, the formation process of inclusions in the liquid phase is a competitive formation process of multiple inclusions, involving the competitive precipitation of many types of inclusions such as TixO, TiN, and MnS. Due to the influence of mechanisms such as solute element segregation and competition for precipitation during solidification, simply relying on reaction equilibrium thermodynamics to predict the composition of the precipitated phase at the end of solidification is clearly insufficient. This is because reaction equilibrium thermodynamics can only calculate the change in Gibbs free energy of the precipitate based on a specific temperature and concentration, while during solidification, the concentration and temperature of the solute elements change over time rather than remaining constant.

[0005] Therefore, traditional thermodynamic models and the other models mentioned above are usually difficult to accurately predict the composition of the final precipitated phase. However, by using a coupled model that combines solute element segregation with the competitive precipitation of inclusions, the composition and coarsening size of the precipitated phase can be predicted more accurately. Summary of the Invention

[0006] The technical problem to be solved by the present invention is to overcome the shortcomings of the prior art and provide a method for predicting the precipitation behavior of inclusions in the solidification process of molten steel. Based on the competitive precipitation model, the VB microsegregation model is corrected in real time to more accurately predict the precipitation type, precipitation size and microsegregation of solute elements of inclusions in molten steel, and to provide more accurate guidance for the type composition and size control of inclusions.

[0007] The present invention specifically adopts the following technical solutions to solve the above-mentioned technical problems:

[0008] A method for predicting inclusion precipitation behavior during the solidification process of molten steel includes the following steps:

[0009] Step 1: Use the following VB microsegregation model coupled with kinetic precipitation consumption to predict the solidification coefficient f during solidification. s The uncorrected content of each solute element at that time:

[0010]

[0011]

[0012] t f =(T L -T S ) / R C

[0013]

[0014] in, The solidification coefficient is f s The uncorrected content of solute element i, in wt.%; The solidification coefficient is f s -Δf s The corrected content of solute element i after the reaction for inclusion formation is completed, in wt.%; [%i] 0 This is the initial concentration of solute element i, in wt.%; k i β is the solute partition coefficient of solute element i; i D is the back diffusion coefficient of solute element i; S,i It is the diffusion coefficient of solute element i in the solid phase, with units of cm. 2 / s;t f L1 is the local solidification time, in seconds; L2 is the secondary dendrite spacing, in μm; R C Cooling rate, unit: K / s; T L T S These are the liquidus temperature and solidus temperature of steel, respectively, in K; [%C] represents the concentration of carbon in the liquid phase, in wt.%.

[0015] Step 2: Determine the solidification coefficient of each inclusion under study based on the competitive precipitation model. s The determination of precipitation type, precipitation amount, and coarsening size at that time includes the following sub-steps:

[0016] Step 2.1: Calculate the change in Gibbs free energy of each inclusion under the current conditions. If there are inclusions with a change in Gibbs free energy less than 0, sort the n inclusions with a change in Gibbs free energy less than 0 in ascending order, and set k=1 before proceeding to step 2.2; otherwise, proceed to step 2.4.

[0017] Step 2.2: Calculate the solidification coefficient of the kth inclusion in the sorted sequence at f. s The amount of precipitation at time was calculated, and the solidification coefficient of the k-th inclusion was calculated according to Fick's first law. sThe coarsening size at that time; then, based on the equilibrium concentration of the solute element participating in the reaction to form the inclusion, the corresponding solute element at a solidification coefficient of f. s Content before correction Updated and corrected to Then determine whether k = n is satisfied. If yes, proceed to step 2.4; otherwise, proceed to step 2.3.

[0018] Step 2.3: Let k = k + 1, then go to step 2.2;

[0019] Step 2.4: Output the solidification coefficient of each inclusion at f. s The amount of precipitation, the coarsening size, and the various solute elements at the solidification coefficient f s Corrected content after the inclusion formation reaction is completed Using the above data as initial parameters, the solidification coefficient is f s +Δf s The precipitation behavior of inclusions is predicted.

[0020] Preferably, in step 2.2, inclusion A is calculated according to the following formula. x B y When the solidification coefficient is f s Precipitation amount at time:

[0021]

[0022]

[0023]

[0024] in, Indicates inclusion A x B y The standard Gibbs free energy is expressed in J / mol; R is the gas constant; T is the solid-liquid front temperature in K; f A f B These are the activity coefficients of solute elements A and B, respectively; These represent solidification coefficients f and f, respectively. s The concentration of solute elements A and B at the solid-liquid interface, expressed in wt.%. A respectively x B y The equilibrium concentrations of solute elements A and B during precipitation, expressed in wt.%; M A M B These are the atomic weights of solute elements A and B, respectively. It is the inclusion A precipitated from the reaction. x B y The content is expressed in wt.%.

[0025] Preferably, in step 2.2, inclusion A x B y When the solidification coefficient is f s The coarsening dimension is calculated according to the following formula:

[0026]

[0027] In the formula, r represents inclusion A. x B y The radius of the precipitate, in μm; M B Inclusion A x B y Atomic weight of solute element B; ρ Fe , Fe and inclusion A, respectively x B y The density, in g / cm³ 3 ;D L,B This represents the diffusion coefficient of solute element B in the liquid phase, expressed in cm. 2 / s; Solute element B in a solidification coefficient of f s Content before correction and content after correction.

[0028] Based on the same inventive concept, the following technical solutions can also be obtained:

[0029] A device for predicting inclusion precipitation behavior during the solidification process of molten steel includes a computer storage medium on which a computer program is stored for performing the method described in any of the above technical solutions.

[0030] Compared with the prior art, the technical solution of the present invention has the following beneficial effects:

[0031] This invention uses a competitive precipitation model to analyze in real time the reaction and formation of various inclusions and the corresponding concentration changes of solute elements during the solidification of molten steel. Based on the analysis results, the prediction results of the VB microsegregation model coupled with kinetic precipitation consumption are updated and corrected in real time. This enables real-time and accurate prediction of the precipitation behavior of various inclusions and the microsegregation of solute elements during the solidification process of molten steel, thereby providing scientific guidance for process optimization. Attached Figure Description

[0032] Figure 1 This is a flowchart illustrating the method for predicting inclusion precipitation behavior during the solidification process of molten steel according to the present invention.

[0033] Figure 2 This is a schematic diagram showing the change of N content with solidification coefficient during the solidification process obtained by the method of the present invention.

[0034] Figure 3 The results of the prediction of the precipitation behavior of Ti-containing inclusions in 347H steel with three different compositions using the method of the present invention are shown.

[0035] Figure 4 The results show the prediction of the precipitation behavior of Ti-containing inclusions in 430 steel using the method of the present invention. Detailed Implementation

[0036] To address the shortcomings of existing technologies, the present invention addresses this issue by using a competitive precipitation model to analyze in real time the reaction and formation of various inclusions and the corresponding concentration changes of solute elements during the solidification of molten steel. Based on the analysis results, the prediction results of the VB microsegregation model coupled with kinetic precipitation consumption are updated and corrected in real time, thereby enabling real-time and accurate prediction of the precipitation behavior of various inclusions and the microsegregation of solute elements during the solidification process of molten steel.

[0037] To facilitate public understanding, the technical solution of the present invention will be described in detail below with reference to the accompanying drawings:

[0038] The method for predicting inclusion precipitation behavior during the solidification process of molten steel proposed in this invention, such as... Figure 1 As shown, it includes the following steps:

[0039] Step 1: Use the VB microsegregation model coupled with kinetic precipitation consumption to predict the solidification coefficient f during the solidification process. s The uncorrected content of each solute element at that time:

[0040] Solute elements typically segregate into the residual liquid phase during steel solidification, leading to an increase in solute element concentration in the liquid phase and thus promoting precipitation of precipitates. Therefore, solute element segregation should be considered when predicting precipitate formation to obtain the solute element concentration at each moment; simultaneously, solute elements are also consumed and reduced due to the precipitation of inclusions. Based on this consideration, this invention uses a VB microsegregation model coupled with kinetic precipitation consumption to predict solute segregation during solidification. The model can be simply described as follows:

[0041]

[0042]

[0043] t f =(T L -T S ) / R C (3)

[0044]

[0045] in, The solidification coefficient is fs The uncorrected content of solute element i, in wt.%; The solidification coefficient is f s -Δf s The corrected content of solute element i after the reaction for inclusion formation is completed, in wt.%; [%i] 0 This is the initial concentration of solute element i, in wt.%; k i β is the solute partition coefficient of solute element i; i D is the back diffusion coefficient of solute element i; S,i It is the diffusion coefficient of solute element i in the solid phase, with units of cm. 2 / s;t f L1 is the local solidification time, in seconds; L2 is the secondary dendrite spacing, in μm; R C Cooling rate, unit: K / s; T L T S These are the liquidus temperature and solidus temperature of steel, respectively, in K; [%C] represents the concentration of carbon in the liquid phase, in wt.%.

[0046] Step 2: Determine the solidification coefficient of each inclusion under study based on the competitive precipitation model. s The determination of precipitation type, precipitation amount, and coarsening size at that time includes the following sub-steps:

[0047] Step 2.1: Calculate the change in Gibbs free energy of each inclusion under the current conditions. If there are inclusions with a change in Gibbs free energy less than 0, sort the n inclusions with a change in Gibbs free energy less than 0 in ascending order, and set k=1 before proceeding to step 2.2; otherwise, proceed to step 2.4.

[0048] The calculation of Gibbs free energy plays a very important role in metallurgical and materials thermodynamic analysis. It is an important parameter for judging and controlling the trend, direction and equilibrium of reaction. Van't Hoff is usually used to calculate the change in Gibbs free energy (ΔG) of chemical reaction under isothermal and isobaric conditions. For the inclusion precipitation reaction shown in equation (5), the Gibbs free energy of the inclusion under specific concentration and temperature conditions during solidification is calculated based on the relationship between Gibbs free energy and temperature. The calculation formulas are (6) and (7).

[0049] x[A]+y[B]=A x B y (s)(5)

[0050]

[0051] lgfi =f(T)·lgf i (1873K) (7)

[0052] Where [%A] and [%B] are the liquid phase concentrations of elements A and B during the solidification process, respectively, in wt.%; R is the gas constant, 8.314 J / (mol·K); T is the solid-liquid front interface temperature, in K; f i f is the activity coefficient of solute element [i]; s It is the solidification coefficient, which reflects the degree of solidification; T is the temperature of the solid-liquid interface, in K; ΔG Θ Standard Gibbs free energy; is the interaction coefficient.

[0053] Based on the above calculation of Gibbs free energy, the change in Gibbs free energy of a certain composition of molten metal undergoing a chemical reaction at a certain temperature can be obtained. By comparing the changes in Gibbs free energy of different chemical reactions, the order of chemical reactions can be obtained. This invention innovatively proposes this method to determine the dominant inclusions precipitated during solidification, achieving the prediction of complex precipitation of various inclusions during the solidification of molten steel, which other models cannot do. According to this method, the precipitation order of inclusions in molten steel under a certain given condition can be obtained. By sorting the changes in Gibbs free energy, the order of reactions is obtained, as shown in equation (8):

[0054]

[0055] In the formula This indicates that the reaction produces inclusion I. n The change in Gibbs free energy, (n) is the sort number; I n In order for a reaction to occur (i.e.) ) inclusions.

[0056] Step 2.2: Calculate the solidification coefficient of the kth inclusion in the sorted sequence at f. s The amount of precipitation at time was calculated, and the solidification coefficient of the k-th inclusion was calculated according to Fick's first law. s The coarsening size at that time; then, based on the equilibrium concentration of the solute element participating in the reaction to form the inclusion, the corresponding solute element at a solidification coefficient of f. s Content before correction Updated and corrected to Then determine whether k = n is satisfied. If yes, proceed to step 2.4; otherwise, proceed to step 2.3.

[0057] For the reaction precipitates, assuming the solute element ratio is an ideal chemical ratio, therefore, at a solidification coefficient of f... s The solidification time of inclusion A x By The amount of precipitation can be calculated using the following formula:

[0058]

[0059]

[0060]

[0061] in, Indicates inclusion A x B y The standard Gibbs free energy is expressed in J / mol; R is the gas constant, with a value of 8.314 J / (mol·K); T is the solid-liquid front temperature, expressed in K; f A f B These are the activity coefficients of solute elements A and B, respectively; These represent solidification coefficients f and f, respectively. s The concentration of solute elements A and B at the solid-liquid interface, expressed in wt.%. A respectively x B y The equilibrium concentrations of solute elements A and B during precipitation, expressed in wt.%; M A M B These are the atomic weights of solute elements A and B, respectively. It is the inclusion A precipitated from the reaction. x B y The content is expressed in wt.%.

[0062] After the precipitation reaction is complete, the concentration of the solute element participating in the reaction is its equilibrium concentration, i.e. It should be noted that if the thermodynamic condition (i.e., ΔG>0) is not met, no reaction will occur, therefore the amount of precipitation will be zero, and the concentration will not change after the reaction is complete. That is, the concentration of the solute element after the reaction can be expressed as equation (12):

[0063]

[0064] It should be noted that, unlike traditional models that calculate precipitation during solidification, this is not the difference between the final predicted segregation concentration and the final equilibrium concentration, but rather the difference between the segregation concentration and the equilibrium concentration at each solidification moment. This more accurately reflects the changes in solute elements during solidification, thereby improving the accuracy of predicting precipitate size.

[0065] During solidification, for precipitates where the difference between solute element content and equilibrium concentration is the driving force for precipitate coarsening, according to Fick's first law, solute elements with fast diffusion rates are relatively less likely to accumulate at the solidification front. Therefore, solute elements with fast diffusion rates are the limiting factor for precipitate coarsening. Let's assume [B] is the diffusion-limiting element; it's easy to deduce that inclusion A... x B y The coarsened size model is expressed as formula (13):

[0066]

[0067] In the formula, r represents inclusion A. x B y The radius of the precipitate, in μm; M B Inclusion A x B y Atomic weight of solute element B; ρ Fe , Fe and inclusion A, respectively x B y The density, in g / cm³ 3 ;D L,B This represents the diffusion coefficient of solute element B in the liquid phase, expressed in cm. 2 / s; Solute element B in a solidification coefficient of f s Content before correction and content after correction.

[0068] Step 2.3: Let k = k + 1 and then go to step 2.2.

[0069] Step 2.4: Output the solidification coefficient of each inclusion at f. s The amount of precipitation, the coarsening size, and the various solute elements at the solidification coefficient f s Corrected content after the inclusion formation reaction is completed Using the above data as initial parameters, the solidification coefficient is f s +Δf s To predict the precipitation behavior of inclusions;

[0070] After calculating the content and size of each of the n reactive inclusions in sequence, the results are recorded in matrix C(f) s ) and R(f s The content of solute elements after the reaction for inclusion formation is corrected. Together as the next solidification time (i.e., solidification coefficient f) s +Δf s The initial parameters (the solidification time).

[0071] To verify the technical effect of the present invention, two embodiments are used for verification:

[0072] Example 1

[0073] This embodiment takes 347H stainless steel as an example, uses the method of the present invention to predict the precipitation behavior of Ti-containing inclusions during the solidification of molten steel, and provides experimental verification results.

[0074] First, the composition and solidification rate of this steel grade were collected: In this embodiment, the composition of the 347H stainless steel used is shown in Table 1, and the solidification rate is 5 K / s. The parameters required for subsequent calculations are as follows:

[0075]

[0076]

[0077]

[0078] Among them, f i (1873K) [i] represents the activity coefficient of solute element [i] at 1873 K; [%j] is the liquid phase concentration of element j during solidification, in wt.%; T0 is the melting point temperature of pure iron, taken as 1809 K; T L It is the liquidus temperature of steel used for calculation, in K; T S It is the solidus temperature, K; ΔT L,i and ΔT S,i The values ​​of the reduction in liquidus and solidus temperatures by solute elements in molten steel are shown in Table 2. The interaction coefficients are shown in Table 3.

[0079] Table 1 Chemical composition of 347H, wt.%

[0080]

[0081] Table 2. Values ​​of reduction in liquidus and solidus temperatures (K) of solute elements in molten steel.

[0082]

[0083] Table 3. Interaction coefficients of element j with Ti, N, and O at 1873 K

[0084]

[0085] Step 1: Use the following VB microsegregation model coupled with kinetic precipitation consumption to predict the solidification coefficient f during solidification. s The uncorrected content of each solute element at that time:

[0086]

[0087]

[0088] t f =(T L -T S ) / R C

[0089]

[0090] in, The solidification coefficient is f s The uncorrected content of solute element i, in wt.%; The solidification coefficient is f s -Δf s The corrected content of solute element i after the reaction for inclusion formation is completed, in wt.%; [%i] 0 This is the initial concentration of solute element i, in wt.%; k i β is the solute partition coefficient of solute element i; i D is the back diffusion coefficient of solute element i; S,i It is the diffusion coefficient of solute element i in the solid phase, with units of cm. 2 / s;t f L1 is the local solidification time, in seconds; L2 is the secondary dendrite spacing, in μm; R C Cooling rate, unit: K / s; T L T S These are the liquidus temperature and solidus temperature of steel, respectively, in K; [%C] represents the concentration of carbon in the liquid phase, in wt.%; some of the parameters involved in the calculation in this embodiment are given in Table 4.

[0091] Table 4. Equilibrium partition coefficients and diffusion coefficients of solute elements

[0092]

[0093] *R: 1.987 cal / (mol·K)

[0094] Step 2: Determine the solidification coefficient of each inclusion under study based on the competitive precipitation model. s The determination of precipitation type, precipitation amount, and coarsening size at that time includes the following sub-steps:

[0095] Step 2.1: Calculate the change in Gibbs free energy of each inclusion under the current conditions. If there are inclusions with a change in Gibbs free energy less than 0, sort the n inclusions with a change in Gibbs free energy less than 0 in ascending order, and set k=1 before proceeding to step 2.2. Otherwise, proceed to step 2.4.

[0096] Based on the relationship between Gibbs free energy and temperature, the Gibbs free energy of inclusions undergoing chemical reactions under specific concentration and temperature conditions during solidification is calculated using the following formula:

[0097]

[0098]

[0099]

[0100]

[0101]

[0102]

[0103] Where R is the gas constant, 8.314 J / (mol·K); T is the solid-liquid front interface temperature, K; f i f is the activity coefficient of solute element [i]; s It is the solidification coefficient that determines the degree of solidification of the reaction; ΔG Θ The standard Gibbs free energy is shown in Table 5.

[0104] Table 5 Standard Gibbs free energy changes of different elements reacting with 1 mol of dissolved titanium

[0105]

[0106] By ranking the Gibbs free energy, the order of reactions is obtained. Furthermore, based on the research of Hou Yuyang et al. on titanium-containing precipitates in stainless steel, TiN only forms TiN-Ti2O3 composite inclusions by encapsulating Ti2O3 cores. Therefore, when TiN reacts and precipitates, the Ti2O3 cores are isolated from the solid-liquid interface and exit the reaction. For this reason, in this embodiment, when ΔG first appears in the calculation... TiN If the value is less than 0, it is assumed that Ti2O3 will no longer form, and no Ti2O3 precipitation judgment is performed.

[0107] Step 2.2: Calculate the solidification coefficient of the kth inclusion in the sorted sequence at f. s The amount of precipitation at time was calculated, and the solidification coefficient of the k-th inclusion was calculated according to Fick's first law.s The coarsening size at that time, and then, based on the equilibrium concentration of the solute element that participates in the reaction to form the inclusion, the corresponding solute element at a solidification coefficient of f. s Content before correction Updated and corrected to Then determine whether k = n is satisfied. If yes, proceed to step 2.4; otherwise, proceed to step 2.3.

[0108] This invention couples reaction precipitation prediction with real-time solute element segregation. For reaction precipitates, it is assumed that their solute element ratio is an ideal stoichiometric ratio. Therefore, at a solidification coefficient of f... s The amount of TiN and TiOx precipitated at the solidification time is calculated using the following formula:

[0109]

[0110]

[0111]

[0112]

[0113] in, The values ​​are the equilibrium concentrations of Ti and N during TiN precipitation, in wt.%. TiO x Equilibrium concentrations of Ti and O during precipitation, wt.%. M i It is the atomic weight of the solute element; It represents the content of inclusions precipitated from the reaction, in wt.%.

[0114] After the precipitation reaction is complete, the concentration of the solute element is its equilibrium concentration, i.e. Therefore, the concentration of the solute element after the reaction is complete can be expressed as:

[0115]

[0116] To address the precipitation and coarsening of Ti-containing inclusions during stainless steel solidification, a model for Ti-containing inclusion precipitation and coarsening is constructed based on the Goto inclusion coarsening kinetic model. This model calculates the solute element consumption and size evolution caused by inclusion precipitation. The coarsening size model for TiN and TiOx can be expressed by the following formula:

[0117]

[0118]

[0119] In the formula, r is the radius of the precipitate, in μm; M is the atomic weight; and ρ is the density, in g / cm³. 3 ; It is the driving force for coarsening of precipitates at the solidification coefficient of fs; the specific parameter values ​​required for the calculation are shown in Table 6.

[0120] Table 6. Relevant atomic weights and density values

[0121]

[0122] Step 2.3: Let k = k + 1 and then go to step 2.2.

[0123] Step 2.4: Output the solidification coefficient of each inclusion at f. s The amount of precipitation, the coarsening size, and the various solute elements at the solidification coefficient f s Corrected content after the inclusion formation reaction is completed Using the above data as initial parameters, the solidification coefficient is f s +Δf s To predict the precipitation behavior of inclusions;

[0124] After all precipitation calculations are completed (i.e., k = n), the calculation results of the content and size of each inclusion are recorded in matrix C(f s ) and R(f s The content of solute elements after the reaction for inclusion formation is corrected. Together as the next solidification time (i.e., solidification coefficient f) s +Δf s The initial parameters (the solidification time).

[0125] A numerical simulation program was developed based on the Matlab R2021a platform to simulate the precipitation process of Ti-containing inclusions during the solidification of molten steel. To further clarify the VB microsegregation model coupled with kinetic precipitation consumption proposed in this invention, the microsegregation of N element during solidification was calculated using sample #0. The calculation results are as follows: Figure 2 As shown. In the absence of inclusions precipitating (f s When <0.6), the model described in this invention yields the same results as the VB microsegregation model in calculating solute element concentration. Furthermore, when inclusions precipitate, this model can not only calculate precipitation consumption (dC) L Furthermore, this result can be used to update the solute element concentration and predict subsequent microsegregation. It is important to emphasize that, just as... Figure 2 The solidification coefficient is f s As shown in the case where = 0.8, unlike traditional models, this model calculates not only the difference between the final predicted segregation concentration and the final equilibrium concentration, but also considers the difference between the segregation concentration and the equilibrium concentration at every moment. This more accurately reflects the changes in solute elements during solidification, thereby improving the accuracy of precipitate size prediction.

[0126] Table 7 shows a comparison between the statistical values ​​of the average size of inclusions in 347H and the calculated values ​​of the coupled model of this invention. It can be seen that the predicted size of the precipitates from the technical solution of this invention matches the actual values ​​well.

[0127] Table 7. Statistical values ​​of average size of 347H precipitates and calculated values ​​using the coupled model.

[0128]

[0129] In this embodiment, several types of inclusions with different areal densities were found in all three samples. EDS analysis was performed on the inclusions, and the results were compared with... Figure 3 The precipitation amount and precipitate radius of the three samples obtained by the prediction method of the present invention are compared. Figure 3 In the figure, a and b represent the precipitate radius and precipitate amount of sample 1, respectively; c and d represent the precipitate radius and precipitate amount of sample 2, respectively; and e and f represent the precipitate radius and precipitate amount of sample 3, respectively. The EDS analysis results are consistent with... Figure 3 The prediction results shown are highly consistent, proving the technical effectiveness of the present invention.

[0130] Example 2

[0131] This embodiment takes 430 stainless steel as an example and uses the method of the present invention to predict the influence of cooling rate on the size of Ti-containing inclusions during the solidification process of molten steel.

[0132] This embodiment follows the same steps as Embodiment 1, with only some parameters changed. Therefore, the process description will not be repeated; only the changed parameters, prediction results, and experimental verification results will be shown. The changed parameters are shown in Tables 8 and 9.

[0133] Table 8 Chemical composition of 430, wt.%

[0134]

[0135] Table 9. Equilibrium partition coefficients and diffusion coefficients of solute elements

[0136]

[0137] *R: 1.987 cal / (mol·K)

[0138] This embodiment uses the method of the present invention to predict the evolution of the size of Ti-containing inclusion precipitates under both high and low cooling rates. Figure 4As shown in the figure, a represents the condition under high cooling rate, and b represents the condition under low cooling rate. The prediction results of the method of this invention and the average statistical size of the precipitates measured experimentally are shown in Table 10. It can be seen that the technical solution of this invention can accurately predict the effect of cooling rate on the size of Ti-containing precipitates.

[0139] Table 10. Statistical values ​​of average size of 430 precipitates and calculated values ​​from the coupled model.

[0140]

Claims

1. A method for predicting the precipitation behavior of inclusions during the solidification process of molten steel, characterized in that, Includes the following steps: Step 1: Use the following VB microsegregation model coupled with kinetic precipitation consumption to predict the solidification coefficient f during solidification. s The uncorrected content of each solute element at that time: b i =2a i [1-exp(-1 / a i )]-exp(-1 / (2a i )), t f =(T L -T S ) / R C in, The solidification coefficient is f s The uncorrected content of solute element i, in wt.%; The solidification coefficient is f s -Δf s The corrected content of solute element i after the reaction for inclusion formation is completed, in wt.%; [%i] 0 This is the initial concentration of solute element i, in wt.%; k i It is the solute partition coefficient of solute element i; β i D is the back diffusion coefficient of solute element i; S,i It is the diffusion coefficient of solute element i in the solid phase, with units of cm. 2 / s;t f L1 is the local solidification time, in seconds; L2 is the secondary dendrite spacing, in μm; R C Cooling rate, unit: K / s; T L T S These are the liquidus temperature and solidus temperature of steel, respectively, in K; [%C] represents the concentration of carbon in the liquid phase, in wt.%. Step 2: Determine the solidification coefficient of each inclusion under study based on the competitive precipitation model. s The determination of precipitation type, precipitation amount, and coarsening size at that time includes the following sub-steps: Step 2.1: Calculate the change in Gibbs free energy of each inclusion under the current conditions. If there are inclusions with a change in Gibbs free energy less than 0, sort the n inclusions with a change in Gibbs free energy less than 0 in ascending order, and set k=1 before proceeding to step 2.2; otherwise, proceed to step 2.

4. Step 2.2: Calculate the solidification coefficient of the kth inclusion in the sorted sequence at f. s The amount of precipitation at time was calculated, and the solidification coefficient of the k-th inclusion was calculated according to Fick's first law. s The coarsening size at that time; then, based on the equilibrium concentration of the solute element participating in the reaction to form the inclusion, the corresponding solute element at a solidification coefficient of f. s Content before correction Updated and corrected to Then determine whether k = n is satisfied. If yes, proceed to step 2.4; otherwise, proceed to step 2.

3. Step 2.3: Let k = k + 1, then go to step 2.2; Step 2.4: Output the solidification coefficient of each inclusion at f. s The amount of precipitation, the coarsening size, and the various solute elements at the solidification coefficient f s Corrected content after the inclusion formation reaction is completed Using the above data as initial parameters, the solidification coefficient is f s +Δf s The precipitation behavior of inclusions is predicted.

2. The method for predicting inclusion precipitation behavior during the solidification process of molten steel as described in claim 1, characterized in that, In step 2.2, inclusion A is calculated according to the following formula. x B y When the solidification coefficient is f s Precipitation amount at time: in, Indicates inclusion A x B y The standard Gibbs free energy is expressed in J / mol; R is the gas constant; T is the solid-liquid front temperature in K; f A f B These are the activity coefficients of solute elements A and B, respectively; These represent solidification coefficients f and f, respectively. s The concentration of solute elements A and B at the solid-liquid interface, expressed in wt.%. A respectively x B y The equilibrium concentrations of solute elements A and B during precipitation, expressed in wt.%; M A M B These are the atomic weights of solute elements A and B, respectively. It is the inclusion A precipitated from the reaction. x B y The content is expressed in wt.%.

3. The method for predicting inclusion precipitation behavior during the solidification process of molten steel as described in claim 1, characterized in that, In step 2.2, inclusion A x B y When the solidification coefficient is f s The coarsening dimension is calculated according to the following formula: In the formula, r represents inclusion A. x B y The radius of the precipitate, in μm; M B Inclusion A x B y Atomic weight of solute element B; ρ Fe , Fe and inclusion A, respectively x B y The density, in g / cm³ 3 ; D L,B This represents the diffusion coefficient of solute element B in the liquid phase, expressed in cm. 2 / s; Solute element B in a solidification coefficient of f s Content before correction and content after correction.

4. A device for predicting inclusion precipitation behavior during the solidification process of molten steel, characterized in that, It includes a computer storage medium having a computer program stored thereon for performing the method as described in any one of claims 1 to 3.

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