A method, device, medium and equipment for predicting second phase separation of a continuous casting billet

Abstract

The application discloses a continuous casting billet second phase precipitation prediction method, device, medium and equipment. The method comprises the following steps: determining each target phase zone experienced by target metal liquid in a solidification process and a second phase precipitate; determining a target solute distribution coefficient of a metal element in the second phase precipitate in each target phase zone; for the target solute distribution coefficient corresponding to the metal element in the same target phase zone, using a predetermined first solute concentration calculation formula, calculating the actual solute concentration of the metal element in a liquid phase state to obtain the actual solute concentration of the metal element in the liquid phase state in each target phase zone; and based on at least the actual solute concentration of the metal element in the liquid phase state in each target phase zone and the equilibrium solute concentration of a non-metal element in the second phase precipitate in the liquid phase state in each target phase zone, using a precipitation amount superposition method to predict the total precipitation amount of the second phase precipitate in the solidification process.

Description

Technical Field

[0001] This invention relates to the field of continuous casting production, and in particular to a method, apparatus, medium and equipment for predicting the precipitation of the second phase in a continuously cast billet. Background Technology

[0002] Microalloyed steel, which is ordinary low-carbon steel with the addition of microalloying elements, possesses excellent properties such as good weldability, high yield strength, and good cold and hot formability. Microalloying technology has developed rapidly, and the development of low-alloy high-strength steel has formed a completely new category of microalloyed steel. During the solidification of molten steel, alloying elements undergo solute redistribution at the solid-liquid interface; this phenomenon is called segregation. High levels of segregation inevitably lead to the precipitation of second-phase inclusions. These inclusions may precipitate in large quantities at grain boundaries, becoming stress concentration sources, thereby deteriorating the steel's plasticity and increasing its crack susceptibility.

[0003] Taking titanium microalloyed steel as an example, nanoscale titanium carbide precipitates in the steel can pin the austenite grain boundaries, refine the austenite grains, and improve the strength of the steel matrix. However, during continuous casting, titanium and nitrogen gradually accumulate in the dendritic liquid phase. This provides sufficient thermodynamic and kinetic conditions for the precipitation of titanium nitride, leading to the formation of micron-sized titanium nitride (TiN) precipitates. Titanium nitride (TiN) is very hard and has sharp edges and corners. Therefore, during continuous casting, due to the mismatch between deformation and the matrix, large-sized titanium nitride (TiN) precipitates easily induce microcracks in the matrix. The thermal and mechanical stresses generated during continuous casting, bending, straightening, or rolling further promote the propagation of these cracks. Large-sized titanium nitride (TiN) cannot be effectively eliminated by subsequent heat treatment. Furthermore, large-sized titanium nitride (TiN) can cause failure during material use.

[0004] Solute microsegregation in dendritic regions is a key factor in the formation of second-phase precipitates. Therefore, when studying the precipitation and growth behavior of precipitates during steel solidification, a combination of thermodynamic and kinetic models and solute microsegregation models is typically used. However, existing prediction methods suffer from inaccurate prediction results, meaning they cannot accurately predict the precipitation of second phases. Summary of the Invention

[0005] In view of this, the present invention provides a method, apparatus, medium and equipment for predicting the precipitation of the second phase in continuously cast billets, the main purpose of which is to solve the problem that the prediction of the second phase precipitation is not accurate enough.

[0006] To address the above problems, this application provides a method for predicting the precipitation of the second phase in continuously cast billets, comprising:

[0007] The target phase regions and second-phase precipitates that the target molten metal undergoes during solidification are identified; each target phase region includes a first target phase region L+δ, a second target phase region L+δ+γ, and a third target phase region γ.

[0008] Determine the target solute partition coefficient of the metal element in the second phase precipitate within each of the target phase regions;

[0009] For the target solute distribution coefficient corresponding to the metal element in the same target phase region, the actual solute concentration of the metal element in the liquid phase is calculated using a predetermined first solute concentration calculation formula, so as to obtain the actual solute concentration of the metal element in the liquid phase in each target phase region.

[0010] Based at least on the actual solute concentration of metal elements in the liquid phase within each target phase region and the equilibrium solute concentration of non-metal elements in the liquid phase within each target phase region of the second phase precipitate, the total precipitation amount of the second phase precipitate during the solidification process is predicted using the precipitation amount superposition method.

[0011] Optionally, the formula for calculating the concentration of the first solute is:

[0012]

[0013] Among them, C L This indicates the actual solute concentration of the metal element in the liquid phase within the target phase region;

[0014] C0 represents the initial concentration of the metal element within the target phase region;

[0015] C i This indicates the solute concentration of the metallic element in cell i;

[0016] A i Represents the area of ​​dendrite cell i;

[0017] k v This indicates the target solute partition coefficient of the metal element within the target phase region.

[0018] A M This represents the area of ​​cell M.

[0019] Optionally, before predicting the total amount of the second phase precipitate during the solidification process using the precipitation amount superposition method, the method further includes: determining the equilibrium solute concentration of non-metallic elements in the liquid phase within each target phase region of the second phase precipitate, specifically including:

[0020] Based on the actual temperature corresponding to each target phase region, the equilibrium solute concentration of the non-metallic element in the liquid phase in each target phase region is calculated using the second solute concentration calculation formula.

[0021] Optionally, before predicting the total amount of the second phase precipitate during the solidification process using the precipitation amount superposition method, the method further includes:

[0022] The solidification time of the target molten metal is divided into several equal time steps;

[0023] Based on the target phase region corresponding to each time step, the actual solute concentration of metal elements in each target phase region, and the equilibrium solute concentration of non-metal elements in each target phase region, the actual solute concentration of metal elements and the equilibrium solute concentration of non-metal elements corresponding to each time step are determined.

[0024] For each target phase region, the equilibrium mass fraction of metal elements in the liquid phase and the equilibrium mass fraction of non-metal elements in the liquid phase are determined to obtain the equilibrium mass fraction of metal elements in the liquid phase and the equilibrium mass fraction of non-metal elements in the liquid phase corresponding to each time step.

[0025] The total precipitation amount of the second phase precipitate during the solidification process is predicted using a precipitation amount superposition method, based at least on the actual solute concentration of metal elements in the liquid phase within each target phase region and the equilibrium solute concentration of non-metal elements in the second phase precipitate within each target phase region in the liquid phase. Specifically, this includes:

[0026] Based on the actual solute concentration of the metal element in the liquid phase, the equilibrium solute concentration of the non-metal element in the liquid phase, the equilibrium mass fraction of the metal element in the liquid phase, and the equilibrium mass fraction of the non-metal element in the liquid phase corresponding to the same time step, the precipitation amount corresponding to each time step is calculated.

[0027] The total amount of precipitation is obtained by superimposing the precipitation amounts corresponding to each time step.

[0028] Optionally, the method further includes: determining a target cooling rate corresponding to each time step based on each time step;

[0029] Based on the target cooling rate corresponding to each time step, the diffusion coefficient of non-metallic elements in the liquid phase of the second phase precipitate corresponding to each time step and the mass fraction of the non-metallic elements in the steel are determined.

[0030] Based on the diffusion coefficient of non-metallic elements in the liquid phase, the relative molecular mass of the second-phase precipitate, the density of steel, the density of the second-phase precipitate, the relative molecular mass of non-metallic elements, the mass fraction of non-metallic elements in steel, and the mass fraction of non-metallic elements in the second-phase precipitate, the size of the second-phase precipitate corresponding to each time step is calculated.

[0031] The total size of the second-phase precipitates is obtained by superimposing the sizes of the second-phase precipitates at each time step.

[0032] To address the aforementioned problems, this application provides a device for predicting the precipitation of the second phase in continuously cast billets, comprising:

[0033] The first determining module is used to determine the target phase regions and the second phase precipitates that the target molten metal undergoes during the solidification process; the target phase regions include the first target phase region L+δ, the second target phase region L+δ+γ, and the third target phase region γ.

[0034] The second determining module is used to determine the target solute partition coefficient of the metal element in the second phase precipitate in each of the target phase regions;

[0035] The calculation module is used to calculate the actual solute concentration of the metal element in the liquid phase state based on the target solute distribution coefficient corresponding to the metal element in the same target phase region using a predetermined first solute concentration calculation formula, so as to obtain the actual solute concentration of the metal element in the liquid phase state in each target phase region.

[0036] The prediction module is used to predict the total amount of the second phase precipitate during the solidification process by using the precipitation amount superposition method, based at least on the actual solute concentration of metal elements in the liquid phase in each target phase region and the equilibrium solute concentration of non-metal elements in the second phase precipitate in the liquid phase in each target phase region.

[0037] To address the aforementioned problems, this application provides a storage medium storing a computer program that, when executed by a processor, implements the steps of the prediction method for second phase precipitation in continuously cast billets as described above.

[0038] To address the aforementioned problems, this application provides an electronic device, comprising at least a memory and a processor, wherein the memory stores a computer program, and the processor, when executing the computer program in the memory, implements the steps of the prediction method for the precipitation of the second phase in the continuously cast billet as described above.

[0039] This application discloses a method, apparatus, medium, and equipment for predicting the precipitation of the second phase in continuously cast billets. By determining the solute distribution coefficient of the metal element corresponding to each phase region, the determination of the solute distribution coefficient of the metal element can be made more reasonable and accurate. This lays the foundation for the subsequent reasonable and accurate determination of the actual solute concentration of the metal element in the liquid phase corresponding to each phase region based on the solute distribution coefficient of the metal element. Subsequently, based on the actual solute concentration of the metal element in each phase region and the equilibrium solute concentration of the non-metal element, a superposition and accumulation calculation method can be used to accurately calculate the total precipitation amount of the second phase precipitate. This avoids the problem that the determination of the target element solute concentration is not reasonable and accurate due to the use of a uniform fixed solute distribution coefficient for solute concentration calculation, which in turn leads to the inaccurate and unreasonable calculation of the subsequent precipitation amount.

[0040] The above description is merely an overview of the technical solution of the present invention. In order to better understand the technical means of the present invention and to implement it in accordance with the contents of the specification, and in order to make the above and other objects, features and advantages of the present invention more apparent and understandable, specific embodiments of the present invention are described below. Attached Figure Description

[0041] Various other advantages and benefits will become apparent to those skilled in the art upon reading the following detailed description of preferred embodiments. The accompanying drawings are for illustrative purposes only and are not intended to limit the invention. Furthermore, the same reference numerals denote the same parts throughout the drawings. In the drawings:

[0042] Figure 1 This is a flowchart illustrating a method for predicting the precipitation of the second phase in a continuously cast billet, according to an embodiment of this application.

[0043] Figure 2 The curve showing the change in the equilibrium distribution coefficient of Ti element during the solidification process of titanium microalloyed steel;

[0044] Figure 3 The image shows the predicted results of TiN precipitates in the cross-section of the slab.

[0045] Figure 4 (a) represents the actual amount of TiN precipitated on the surface of the slab;

[0046] Figure 4 (b) is the actual amount of TiN precipitated at the 1 / 4 position of the slab;

[0047] Figure 4 (c) Actual TiN precipitation at the center of the slab;

[0048] Figure 5 Figure showing the predicted results of Ti(C,N) precipitates in the cross-section of the slab;

[0049] Figure 6(a) represents the actual amount of Ti(C,N) precipitated on the surface of the slab;

[0050] Figure 6 (b) is the actual amount of Ti(C,N) precipitated at the 1 / 4 position of the slab;

[0051] Figure 6 (c) represents the actual amount of Ti(C,N) precipitated at the center of the slab;

[0052] Figure 7 This is a structural block diagram of a device for predicting the precipitation of the second phase in a continuously cast billet, according to another embodiment of this application.

[0053] Figure 8 This is a structural block diagram of an electronic device according to another embodiment of this application. Detailed Implementation

[0054] Various embodiments and features of this application are described herein with reference to the accompanying drawings.

[0055] It should be understood that various modifications can be made to the embodiments described herein. Therefore, the above description should not be considered as limiting, but merely as an example of embodiments. Other modifications within the scope and spirit of this application will be apparent to those skilled in the art.

[0056] The accompanying drawings, which are included in and form part of this specification, illustrate embodiments of the present application and, together with the general description of the present application given above and the detailed description of the embodiments given below, serve to explain the principles of the present application.

[0057] These and other features of this application will become apparent from the following description of preferred forms of embodiments given as non-limiting examples, with reference to the accompanying drawings.

[0058] It should also be understood that although this application has been described with reference to some specific examples, those skilled in the art can certainly implement many other equivalent forms of this application.

[0059] The above and other aspects, features and advantages of this application will become more apparent when taken in conjunction with the accompanying drawings and in view of the following detailed description.

[0060] Specific embodiments of this application are described thereafter with reference to the accompanying drawings; however, it should be understood that the claimed embodiments are merely examples of this application, which can be implemented in various ways. Well-known and / or repeated functions and structures are not described in detail to avoid unnecessary or redundant details that could obscure the application. Therefore, the specific structural and functional details claimed herein are not intended to be limiting, but merely serve as the basis and representative basis for the claims to teach those skilled in the art to use this application in a variety of substantially any suitable detailed structures.

[0061] This specification may use the phrases “in one embodiment,” “in another embodiment,” “in yet another embodiment,” or “in other embodiments,” all of which may refer to one or more of the same or different embodiments according to this application.

[0062] This application provides a method for predicting the precipitation of the second phase in continuously cast billets, such as... Figure 1 As shown, it includes the following steps:

[0063] Step S101: Determine the target phase regions and second phase precipitates that the target molten metal undergoes during solidification; the target phase regions include the first target phase region L+δ, the second target phase region L+δ+γ, and the third target phase region L+γ.

[0064] Step S102: Determine the target solute partition coefficient of the metal element in the second phase precipitate within each target phase region;

[0065] In this step, taking titanium nitride (TiN) as the second phase precipitate as an example, the metal element is titanium (Ti) and the non-metal element is nitrogen (N).

[0066] Step S103: For the target solute distribution coefficient corresponding to the metal element in the same target phase region, calculate the actual solute concentration of the metal element in the liquid phase using a predetermined first solute concentration calculation formula, so as to obtain the actual solute concentration of the metal element in the liquid phase in each target phase region.

[0067] Step S104: Based at least on the actual solute concentration of metal elements in the liquid phase in each target phase region and the equilibrium solute concentration of non-metal elements in the liquid phase of the second phase precipitate in each target phase region, the total precipitation amount of the second phase precipitate during the solidification process is predicted by the precipitation amount superposition method.

[0068] This embodiment presents a method for predicting the precipitation of the second phase in continuously cast billets. By determining the solute distribution coefficient of the metal element corresponding to each phase region, the determination of the solute distribution coefficient of the metal element can be made more reasonable and accurate. This lays the foundation for the subsequent reasonable and accurate determination of the actual solute concentration of the metal element in the liquid phase corresponding to each phase region based on the solute distribution coefficient of the metal element. Subsequently, based on the actual solute concentration of the metal element in each phase region and the equilibrium solute concentration of the non-metal element, a superposition and accumulation calculation method can be used to accurately calculate the total precipitation amount of the second phase precipitate. This avoids the problem that the determination of the target element solute concentration is not reasonable and accurate due to the use of a uniform fixed solute distribution coefficient for solute concentration calculation, which in turn leads to the inaccurate and unreasonable calculation of the subsequent precipitation amount.

[0069] Another embodiment of this application provides a method for predicting the precipitation of the second phase in continuously cast billets. Based on the above embodiments, in this embodiment, when performing step S102, that is, when determining the target solute distribution coefficient of the metal element in each target phase region in the second phase precipitate, the target solute distribution coefficient k of the metal element in each target phase region can be calculated using Thermo Calc software. v (where v represents element v), the specific first calculation formula is as follows:

[0070]

[0071] Where, k v This represents the target solute partition coefficient of the metallic element within the target phase region. β is the activity coefficient in an infinitely diluted solution system. ε is the activity interaction coefficient. i, m, ..., n are the solute elements in the steel throughout the solidification process. C s Indicates the solute concentration in the solid state; C L This indicates the concentration of the solute in the liquid state.

[0072] In other words, taking an example where the second-phase precipitate contains elements x and y, where x is a metallic element and y is a non-metallic element, the target solute partition coefficient of metallic element x within the first target phase region L+δ can be calculated using the first calculation formula described above. And the target solute partition coefficient of metal element x in the third target phase region γ Then, based on the solute partition coefficient of metallic element x in the first phase region L+δ... Solute partition coefficient of metal element x in the third target phase region γ The target solute partition coefficient of metal element x in the second target phase region L+δ is calculated using the following second calculation formula. The second calculation formula is as follows:

[0073]

[0074] Where v represents the target element. g δ It means that g γ This represents the proportion of the δ phase and the γ phase. That is, using the second calculation formula mentioned above, the target solute partition coefficient of the target element x within the second target phase region L+δ can be calculated. Right now

[0075] In this embodiment, by using the above method to calculate the target solute distribution coefficient of the metal element in each target phase region, the determination of the target solute distribution coefficient is reasonable and accurate, laying the foundation for the subsequent accurate determination of the actual solute concentration of the metal element in the liquid phase in each target phase region based on the target solute distribution coefficient of each metal element in each target phase region.

[0076] Another embodiment of this application provides a method for predicting the precipitation of the second phase in a continuously cast billet. Based on the above embodiment, in this embodiment, when performing step S103, that is, for the target solute distribution coefficient corresponding to the metal element in the same target phase region, the actual solute concentration of the metal element in the liquid phase is calculated using a predetermined first solute concentration calculation formula. The first solute concentration calculation formula used to obtain the actual solute concentration of the metal element in the liquid phase in each target phase region is as follows:

[0077]

[0078] Among them, C L C represents the solute concentration of the metal element in the liquid phase within the target phase region; C0 represents the initial concentration of the metal element within the target phase region; C i A represents the solute concentration of the element in cell i; i Let A be the area of ​​cell i; M k is the area of ​​cell M; v This represents the target solute partition coefficient of the metal element within the target phase region.

[0079] In this embodiment, the solute partition coefficient of metal element x in the first phase region L+δ is used. The target solute partition coefficient of metal element x within the second target phase region L+δ+γ And the solute partition coefficient of metal element x in the third target phase region γ Using the above formula for calculating the first solute concentration, the actual solute concentration of metal element x in the liquid phase within the first phase region L+δ can be calculated. The actual solute concentration of metal element x in the liquid phase within the second phase region L+δ+γ The actual solute concentration of metal element x in the liquid phase within the third phase region γ

[0080] In this embodiment, by calculating the actual solute concentration of metal elements in the liquid phase within each target phase region, a foundation is laid for subsequent accurate prediction of precipitation based on the actual solute concentration.

[0081] Specifically, in this embodiment, the reasoning process for the first solute concentration calculation formula is as follows:

[0082] According to Ueshima's regular hexagonal dendrite model, the cross-section can be approximated as a regular hexagon. The governing equation for solute diffusion in the dendritic cross-section of steel during solidification is as follows:

[0083]

[0084] (1) Initial conditions: t = 0,

[0085] (2) Boundary conditions: x = 0, λ / 2,

[0086] In the above formula, λ is the secondary dendrite spacing, in meters (m). 0 L,v C L,v and C s,v , respectively, represent the initial concentrations (%) of element v in molten steel, liquid phase l, and solid phase s. s,v (T) is the diffusion coefficient of solute element v in solid phase s, m² / s. t is time, in seconds. k v s / l k v δ / l and k v γ / l These are the equilibrium distribution coefficients of solute element v at the s / l interface, δ / l, and γ / l, respectively.

[0087] This model utilizes 1 / 6 of a regular hexagon as the computational domain, further dividing it into 200 computational units to ensure computational accuracy. In this application, i represents the number of units, and L... i A represents the length of the adjacent interfaces between unit i and unit i+1. i Let represent the area of ​​element i, and Δx represent the width of the element along the x-direction. Therefore, 1≤i≤H, H+1≤i≤M, and M+1≤i≤N represent the δ phase, γ phase, and liquid phase, respectively.

[0088] The diffusion of solute elements in solid and liquid phases can be quantified within a time step Δt using the following basic equation.

[0089] In the δ phase (1≤i≤H) and γ phase (H+1≤i≤M), the solute concentration is expressed as:

[0090]

[0091] In the formula, j represents the δ phase and γ phase respectively; D is the diffusion coefficient of the solute in different phases; and C is the percentage of solute mass concentration.

[0092] At the dendrite center (δ phase, i = 1),

[0093]

[0094] δ / γ at the interface (δ phase, i=H; γ phase, i=H+1),

[0095]

[0096] Solute mass flux J in and J out The control units representing solute inflow and outflow near the δ / γ interface can be determined using the following formulas:

[0097]

[0098]

[0099] According to the principle of mass conservation of the control unit near the δ / γ interface, we can obtain:

[0100]

[0101] The above formula can be transformed into the following equation.

[0102]

[0103] Based on the principle of solid-liquid solute conservation in a two-phase system, the following results were obtained at the γ / l interface (γ phase i = M, liquid phase i = M+1).

[0104]

[0105]

[0106] Where C l C is the solute concentration of the element in the liquid phase. C0 is the initial concentration of the element. i Let A be the solute concentration of the element in cell i. i Let A be the area of ​​cell i. M Let k be the area of ​​cell M. γ / l This represents the target solute partition coefficient of the target element at the γ / l interface, which is also the target solute partition coefficient of the γ target element in the third target phase region.

[0107] Another embodiment of this application provides a method for predicting the precipitation of the second phase in a continuously cast billet. Based on the above embodiment, before executing step S104, that is, before predicting the total precipitation amount of the second phase precipitate during the solidification process using the precipitation amount superposition method, the method further includes: determining the equilibrium solute concentration of non-metallic elements in the liquid phase within each target phase region of the second phase precipitate, specifically including:

[0108] Based on the actual temperature corresponding to each target phase region, the equilibrium solute concentration of the non-metallic element in the liquid phase within each target phase region is calculated using the second solute concentration calculation formula.

[0109] In this example, the reasoning process for calculating the second solute concentration is as follows:

[0110] Taking titanium microalloyed steel as an example (applicable but not limited to titanium microalloyed steel), the Gibbs free energy generated by TiN during the solidification process of molten steel can be expressed by the following formula (I):

[0111] ΔG Θ = -291000 + 107.91 T, J·mol -1 (one)

[0112]

[0113] Where αTiN, αTi, and αN represent the activity coefficients of TiN, Ti, and N, respectively. w(Ti) and w(N) represent the mass amounts of Ti and N reacted, respectively.

[0114]

[0115]

[0116]

[0117] Formula (VI) can be derived using formulas (I) to (V).

[0118]

[0119]

[0120] ΔG=-289641+107.62T-RTln[w(Ti)·w(N)] (VIII)

[0121] Based on the chemical composition of the steel, the critical conditions for precipitation are determined as follows:

[0122] ΔG=0 (IX)

[0123] The calculation formula uses the composition of steel 1:

[0124] ΔG = -289641 + 187.16T (x)

[0125]

[0126] By performing logarithmic operations on both sides of equation (XI), equation (XII) can be obtained.

[0127] lgC=-(lgf [Ti] +lgf [N] )-(lgw [Ti] +lgw [N] ) (twelve)

[0128] Taking the logarithm of 10 from formula (12) yields formula (13).

[0129]

[0130] From C = w[Ti]·w[N], we can obtain:

[0131]

[0132] Therefore, obtain

[0133] in, This represents the equilibrium solute concentration of non-metallic elements in the liquid phase within the target phase region; T represents the actual temperature corresponding to the target phase region. In this embodiment, the actual temperature T of each target phase region refers to the real-time temperature value corresponding to the interface (phase interface) of different phase regions during the phase transformation process of the target metal liquid.

[0134] Therefore, when the second phase precipitate is TiN, the formula for calculating the second solute concentration is:

[0135]

[0136] Another embodiment of this application provides a method for predicting the precipitation of the second phase in a continuously cast billet. Based on the above embodiment, in this embodiment, when performing step S104, that is, when predicting the total precipitation amount of the second phase precipitate during the solidification process using a precipitation amount superposition method based at least on the actual solute concentration of the metal element in the liquid phase within each target phase region and the equilibrium solute concentration of the non-metal element in the second phase precipitate within each target phase region, the solidification time of the target metal liquid can first be divided into several equal time steps; then, based on the target phase region corresponding to each time step, the actual solute concentration of the metal element within each target phase region, and the equilibrium solute concentration of the non-metal element within each target phase region, the actual solute concentration of the metal element corresponding to each time step is determined, and so on... The equilibrium solute concentration of non-metallic elements at each time step is determined. For each target phase region, the equilibrium mass fraction of metallic elements and the equilibrium mass fraction of non-metallic elements in the liquid phase are determined to obtain the equilibrium mass fraction of metallic elements and the equilibrium mass fraction of non-metallic elements in the liquid phase at each time step. Finally, based on the actual solute concentration of metallic elements, the equilibrium solute concentration of non-metallic elements, the equilibrium mass fraction of metallic elements, and the equilibrium mass fraction of non-metallic elements in the liquid phase at the same time step, the precipitation amount at each time step is calculated, and the precipitation amounts at each time step are superimposed to obtain the total precipitation amount.

[0137] Specifically, the calculation process for the total amount of precipitation is as follows:

[0138] Step 1: First, determine the solidification time t, and then divide the solidification time t into several equal time steps Δt.

[0139] Step 2: Based on the time period of each time step Δt, determine the target phase region corresponding to each time step Δt, thereby determining the actual solute concentration C of the metal element in the liquid phase corresponding to each time step Δt. Δt,L And the equilibrium solute concentration of nonmetallic elements in the liquid phase.

[0140] That is, the actual solute concentration of metal element x in the liquid phase within each time step Δt can be determined. And the equilibrium solute concentration of nonmetallic element y in the liquid phase within each time step Δt.

[0141] Step 3: For each target phase region, determine the equilibrium mass fraction of the metal element and the equilibrium mass fraction of the non-metal element in the liquid phase, to obtain the equilibrium mass fraction of the metal element and the equilibrium mass fraction of the non-metal element in the liquid phase corresponding to each time step.

[0142] That is, to obtain the mass fraction of metallic element x in equilibrium state within each time step Δt. and the mass fraction of nonmetallic element y in equilibrium state within each time step Δt.

[0143] Step 4: Based on the solute concentration of each target element in the liquid phase and the mass fraction of each target element in equilibrium at the same time step Δt, calculate the precipitation amount corresponding to each time step; then, sum the precipitation amounts corresponding to each time step to obtain the total precipitation amount. That is, the precipitation amount of the (i+1)th unit can be accumulated using the following formula to obtain the total precipitation amount of the (i+1)th unit.

[0144] In this step, the formula for calculating the amount of precipitation is as follows:

[0145]

[0146] Where x represents a metallic element, y represents a nonmetallic element, L represents the liquid phase, Eq represents the equilibrium state, and Δt represents the time step. This represents the actual solute concentration of metal element x in the liquid phase within a time step Δt. A i+1 This represents the area corresponding to dendritic cell i+1 in the liquid phase, which is a known value. It represents the equilibrium mass fraction of metal element x in the liquid phase within a time step Δt. This represents the equilibrium solute concentration of nonmetallic element y in the liquid phase within a step size Δt. It represents the equilibrium mass fraction of nonmetallic element y in the liquid phase within a time step Δt.

[0147] This is because commonly used microsegregation models typically treat the solute partition coefficient as a constant when dealing with solute diffusion within the solid phase. However, in actual cooling processes, the solute segregation coefficient is a variable that varies with temperature, inclusion precipitation, and phase composition. Therefore, using a constant solute partition coefficient undoubtedly leads to calculation errors. This application, by employing a solute partition coefficient corresponding to each target phase region, enables more accurate prediction of subsequent precipitation amounts.

[0148] Meanwhile, the cooling rate affects the distribution, size, and quantity of second-phase particles. During continuous casting, the cooling rate of the billet varies with the position of the casting stream, and even at the same casting stream position, the cooling rates at the surface, corners, and core of the billet differ. Commonly used calculation models employ constant cooling rates, which cannot accurately calculate second-phase precipitation during variable cooling rates in continuous casting. Therefore, in this application, after determining the actual concentration values ​​of each target phase region, the metallic element, and the equilibrium concentration values ​​of the non-metallic element, the solidification time is divided into several sufficiently small time intervals to obtain several time steps. Then, the actual solute concentration values ​​of the metallic element and the equilibrium solute concentration values ​​of the non-metallic element within each time step are determined. This allows for the acquisition of the solute concentration corresponding to each time step, thereby simulating the solute concentration values ​​at each time point under variable cooling rates and improving the accuracy of precipitation prediction.

[0149] In this embodiment, the reasoning process for the precipitation calculation formula is as follows:

[0150] Establish the coupled separation model and the segregation model:

[0151] Variables M and N represent the number of solid-phase nodes and the total number of nodes, respectively. The solidification time t can be expressed as...

[0152]

[0153] Among them, T liq T is the liquidus temperature. solid Rc is the solid-state temperature; Rc is the cooling rate.

[0154] Assuming a constant cooling rate, each time step is currently represented as t' = t / M. When the second-phase precipitate reaches equilibrium at node i, and the solute element concentration product equals the equilibrium value, it can be deduced that:

[0155]

[0156] in, This represents the actual solute concentration of metal element x in the liquid phase. This represents the mass fraction of the nonmetallic element y in the liquid phase. This represents the mass fraction of metallic element x in the liquid phase; This represents the equilibrium mass fraction of nonmetallic element y in the liquid phase. A i Let i be the area of ​​cell i.

[0157] Based on the above equation, the time and temperature associated with the precipitation of the second phase can be determined. Furthermore, accumulation begins at (x+1)Δt, and the actual precipitation amount can be expressed as:

[0158]

[0159] To accurately calculate the amount of carbon nitride precipitation at different cooling rates, this application employs the micro-element superposition method. By utilizing sufficiently small time intervals, a uniform cooling rate can be achieved. That is, the cooling rate is the same within a set time step; therefore, the amount of second-phase precipitation at different locations on the slab is determined by the superposition of precipitation amounts within each unit time. The specific calculation formula is as follows:

[0160]

[0161] in, This represents the actual solute concentration of metal element x in the liquid phase. This represents the equilibrium mass fraction of metallic element x in the liquid phase. The equilibrium solute concentration of nonmetallic element y in the liquid phase. This represents the equilibrium mass fraction of nonmetallic element y in the liquid phase. A i+1 Let i be the area of ​​cell i+1, which is a known range of values.

[0162] In this application, the temperature change of the continuous casting process was simulated using MSC.Marc finite element software. The amount of precipitation of the second phase per unit time was calculated based on the temperature change of each node of the slab and superimposed until the temperature reached the solidus temperature, at which point the iteration stopped.

[0163] Another embodiment of this application provides a method for predicting the precipitation of the second phase in a continuously cast billet. In this embodiment, the size of the second phase precipitate can also be predicted. The specific prediction process is as follows:

[0164] Step 1: Determine the target cooling rate corresponding to each time step based on each time step;

[0165] In this step, the first cooling rate corresponding to the start time and the second cooling rate corresponding to the end time can be determined based on the start and end times of the time step. Then, the average cooling rate corresponding to the time step is obtained by averaging the first and second cooling rates, and the average cooling rate is used as the target cooling rate for the time step.

[0166] Step 2: Based on the target cooling rate corresponding to each time step, determine the diffusion coefficient D of the non-metallic elements in the liquid phase of the second phase precipitate corresponding to each time step. L-y and the mass fraction w of the non-metallic elements in the steel. L-y ;

[0167] Step 3: Based on the diffusion coefficient D of non-metallic elements in the liquid phase corresponding to the same time step. L-y The relative molecular mass M of the second phase precipitate xyThe density of steel ρmetal and the density of the second phase precipitate ρ xy The relative molecular mass M of nonmetallic elements y The mass fraction w of non-metallic elements in steel L-y and the mass fraction w of nonmetallic elements in the second phase precipitate. e-y The size of the second phase precipitate corresponding to each time step is calculated; the total size of the second phase precipitate is obtained by superimposing the sizes of the second phase precipitates corresponding to each time step.

[0168] In this step, the formula for calculating the overall size of the second-phase precipitate is as follows:

[0169]

[0170] Where x represents a metallic element in the second phase, and y represents a nonmetallic element in the second phase. D L-y The value represents the diffusion coefficient of element y in the liquid phase, in cm² / s. Mxy represents the relative molecular mass of compound xy. My represents the relative molecular mass of element y. ρmetal represents the density of steel, in units of 7.86 g / cm³. ρ represents the density of the second phase. w L-y w represents the mass fraction of element y in steel. e-y It is the mass fraction of element y in the second phase.

[0171] In this embodiment, by using the above method to predict the precipitation size of the second phase precipitate, the final prediction result can be more accurate.

[0172] The following example uses titanium microalloyed steel as the target molten metal. The prediction method for second-phase precipitation in this application is used to predict the precipitation of the second phase. The specific process is as follows:

[0173] The Gibbs free energy generated by TiN during the solidification of molten steel can be expressed by formula (1):

[0174] ΔG Θ = -291000 + 107.91 T, J·mol -1 (1)

[0175]

[0176] Where αTiN, αTi, and αN represent the activity coefficients of TiN, Ti, and N, respectively. w(Ti) and w(N) represent the mass amounts of Ti and N reacted, respectively.

[0177]

[0178]

[0179]

[0180] Formula (6) can be derived using formulas (1) to (5).

[0181]

[0182]

[0183] ΔG=-289641+107.62T-RTln[w(Ti)·w(N)] (8)

[0184] Table 1 lists the chemical composition of the steel. The critical conditions for precipitation are as follows:

[0185] ΔG=0 (9)

[0186] Table 1:

[0187] wt% C Mn Ti N Si Al Steel 1 0.15 1.3 0.02 0.0035 0.2 0.04 Steel 2 0.15 1.3 0.04 0.0035 0.2 0.04 Steel 3 0.15 1.3 0.06 0.0035 0.2 0.04 Steel 4 0.15 1.3 0.08 0.0035 0.2 0.04

[0188] The calculation formula uses the composition of steel 1:

[0189] ΔG=-289641+187.16T (10)

[0190]

[0191] Simultaneously, by performing logarithmic operations on both sides of equation (11), equation (12) can be obtained.

[0192] lgK=-(lgf [Ti] +lgf [N] )-(lgw [Ti] +lgw [N] (12)

[0193] Taking the logarithm of 10 of formula (13) yields formula (13).

[0194]

[0195] K equ =w[Ti]·w[N] gives:

[0196]

[0197] Right now,

[0198] Therefore, based on the actual temperature corresponding to each target phase region, the formula can be used respectively. The equilibrium solute concentration of the nonmetallic element nitrogen in the liquid phase within each target phase region was calculated.

[0199] During the solidification process, the liquid phase becomes enriched with elements such as Ti and N, resulting in selective crystallization and microsegregation at the solid-liquid interface. At this stage, the concentrations of Ti and N at the solidification front can be represented by the solid fraction fs, as shown in equations (15) and (16).

[0200]

[0201]

[0202] At the solidification front, the actual concentrations of Ti and N can be represented by Q. TiN express:

[0203]

[0204]

[0205] Where T is the actual temperature; Tm = 1873 K; Tl is the liquidus temperature, which is known; Ts is the solidus temperature, which is known; and fs is the solid fraction.

[0206] The Gibbs free energy of TiN during solidification varies with different titanium contents. When the Gibbs free energy is negative, TiN will precipitate.

[0207] (2) This application uses Thermo Calc software to calculate the solute concentration in the solid and liquid phases. ThermoCalc can be used to determine the phase transformations during the solidification process of titanium microalloyed steel, obtaining the various phase regions the steel undergoes throughout the cooling process, including the L phase region, L+δ phase region, L+δ+γ phase region, and γ phase region. From each phase region, the target phase region where the second phase precipitation occurs is determined, i.e., the first target phase region L+δ, the second target phase region L+δ+γ, and the third target phase region γ are determined.

[0208] The equilibrium partition coefficient ki (where i represents the solute element) in different phase regions is affected by their unique chemical and physical properties. ki is determined using the solute partition coefficient model described below.

[0209]

[0210] Where, k v This represents the target solute partition coefficient of the metallic element within the target phase region. β is the activity coefficient in an infinitely diluted solution system. ε is the activity interaction coefficient. i, m, ..., n are the solute elements in the steel throughout the solidification process. C s Indicates the solute concentration in the solid state; C L This indicates the concentration of the solute in the liquid state.

[0211] In the L+δ+γ phase region, the solute partition coefficient of δ+γ can be defined as:

[0212]

[0213] In other words, if the second phase precipitate is TiN, it contains both the metallic element titanium (Ti) and the non-metallic element nitrogen (N). Using the first calculation formula described above, the target solute partition coefficient of the metallic element Ti within the first target phase region L+δ can be calculated. And the target solute partition coefficient of the metallic element Ti in the third target phase region γ Then, based on the solute partition coefficient of metallic element Ti in the first phase region L+δ... Solute partition coefficient of metallic element Ti in the third target phase region γ The target solute partition coefficient of metallic element Ti in the second target phase region L+δ was calculated using formula (20).

[0214] Then, further utilization Based on the solute partition coefficient of metallic element Ti in the first phase region L+δ The target solute partition coefficient of metallic element Ti in the second target phase region L+δ+γ And the solute partition coefficient of metallic element Ti in the third target phase region γ Using the above formula for calculating the first solute concentration, the actual solute concentration of metallic element Ti in the liquid phase within the first phase region L+δ can be calculated. The actual solute concentration of metallic element Ti in the liquid phase within the second phase region L+δ+γ The actual solute concentration of metallic element Ti in the liquid phase within the third phase region γ

[0215] In this embodiment, the liquid phase temperature and the onset temperature of the δ / γ phase transition (TAr4) can be determined using Thermo Calc software, and the solute concentrations of different elements in the liquid phase can be calculated, such as... Figure 2 As shown.

[0216] (3) A precipitation model for liquefied carbonitrides was established by coupling elemental segregation, where variables M and N represent the number of solid-phase nodes and the total number of nodes in this study, respectively. The solidification time t can be expressed as:

[0217]

[0218] Among them, T liq T is the liquidus temperature. solid Rc is the solid-state temperature; Rc is the cooling rate.

[0219] Assuming a constant cooling rate, each time step is currently represented by t' = t / M. When TiN reaches equilibrium at node i and the product of solute element concentrations equals the equilibrium value, we can deduce that:

[0220]

[0221] Where Liquid represents the liquid phase and Eq represents the equilibrium state.

[0222] Based on the above formula, the time and temperature associated with the onset of TiN precipitation can be determined. TiN begins to accumulate at (x+1)Δt, and the actual amount of TiN precipitated at t can be expressed as follows:

[0223]

[0224] Similarly, once the critical solid solubility of Ti(C,N) precipitate is reached, the total amount of Ti(C,N) precipitate can be determined using this method, which will not be elaborated further here.

[0225] (4) To accurately calculate the amount of titanium nitride precipitation at different cooling rates, a micro-element superposition method was adopted. By utilizing sufficiently small time intervals, a uniform cooling rate can be achieved. Currently, the cooling rate is the same within the set time step; therefore, the amount of titanium nitride precipitation at different locations on the slab is determined by the superposition of precipitation amounts within each unit time. The specific calculation formula is as follows:

[0226] concentration The actual solute concentration of metallic element Ti in the liquid phase within the first phase region L+δ The actual solute concentration of metallic element Ti in the liquid phase within the second phase region L+δ+γ The actual solute concentration of metallic element Ti in the liquid phase within the third phase region γ Then, the solidification time can be divided into several time steps Δt, and the actual solute concentration of the metallic element Ti in the liquid phase within each time step Δt can be determined. Equilibrium solute concentration of nonmetallic element N in the liquid phase within each time step Δt Then, the equilibrium mass fraction of the metallic element Ti in the liquid phase within the step size Δt can be further obtained. Obtain the equilibrium mass fraction of nonmetallic element N in the liquid phase within a time step Δt. And obtain the area A corresponding to dendrite cell i+1 in the liquid phase. i+1 Finally, the amount of titanium nitride (TiN) precipitated in the second phase can be calculated using the above formula (24).

[0227] In this embodiment, the temperature changes during the continuous casting process were simulated using MSC.Marc finite element software, and the temperature change process at each node was obtained. When the temperature is below the liquidus temperature and reaches the critical state for titanium nitride precipitation, the amount of nitride precipitation per unit time is calculated based on the temperature changes at each node of the slab, and the results are superimposed until the temperature reaches the solidus temperature, at which point the iteration stops.

[0228] (5) The error between the predicted and actual values ​​was verified by selecting samples from different locations on the slab for testing and analysis. Using a scanning electron microscope, a 50μm×50μm field of view was selected, and a total of 49 fields of view were systematically selected from left to right and from top to bottom for statistical analysis. EDS analysis was used to determine the precipitation components. Then, the scanned images were binarized and merged into the final image, and the observed quantities were compared with the predicted values.

[0229] Figures 3-4 The cross-sectional precipitation cloud diagrams and actual test results of TiN are shown when the superheat is 25℃ and the casting speed is 1.0 m / min. Table 2 lists the errors between the experimental and predicted values. The minimum deviation is 6.63%, the maximum deviation is 9.72%, and the average deviation is 7.76%.

[0230] Table 2:

[0231] <![CDATA[ TiN wt%]]> surface 1 / 4 center Predicted value 0.00482 0.0139 0.0232 Measured values 0.00452 0.0128 0.0257 mistake 6.63％ 6.92％ 9.72％

[0232] Figures 5-6 The cross-sectional precipitation cloud diagrams and actual test results of Ti(C,N) at a superheat of 25℃ and a casting speed of 1.0 m / min are shown. Table 3 lists the errors between the experimental and predicted values. The minimum deviation is 8.97%, the maximum deviation is 5.85%, and the average deviation is 7.34%.

[0233] Table 3:

[0234] Ti(C,N)wt% surface 1 / 4 center Predicted value 0.00362 0.00983 0.0142 Measured values 0.00342 0.00917 0.0156 mistake 5.85％ 7.19％ 8.97％

[0235] The experimental results above demonstrate that the method described in this application can accurately predict the amount of second-phase precipitates.

[0236] Another embodiment of this application provides a device for predicting the precipitation of the second phase in a continuously cast billet, such as... Figure 7 As shown, it includes:

[0237] The first determining module 11 is used to determine the target phase regions and the second phase precipitates that the target molten metal undergoes during the solidification process; the target phase regions include the first target phase region L+δ, the second target phase region L+δ+γ, and the third target phase region γ.

[0238] The second determining module 12 is used to determine the target solute partition coefficient of the metal element in the second phase precipitate in each of the target phase regions;

[0239] Calculation module 13 is used to calculate the actual solute concentration of the metal element in the liquid phase state based on the target solute distribution coefficient corresponding to the metal element in the same target phase region using a predetermined first solute concentration calculation formula, so as to obtain the actual solute concentration of the metal element in the liquid phase state in each target phase region.

[0240] The prediction module 14 is used to predict the total amount of precipitation of the second phase precipitate during the solidification process by using the precipitation amount superposition method, based at least on the actual solute concentration of metal elements in the liquid phase in each target phase region and the equilibrium solute concentration of non-metal elements in the second phase precipitate in the liquid phase in each target phase region.

[0241] In this embodiment, the formula for calculating the first solute concentration is as follows:

[0242]

[0243] Among them, C L C0 represents the actual solute concentration of the metal element in the liquid phase within the target phase region; C0 represents the initial concentration of the metal element ... i Indicates the solute concentration of the metallic element in cell i; A i Represents the area of ​​dendrite cell i; k v Indicates the target solute partition coefficient of the metal element within the target phase region; A M This represents the area of ​​cell M.

[0244] In this embodiment, the prediction device for the second phase precipitation of the continuously cast billet further includes an equilibrium solute concentration determination module. This module is used to: determine the equilibrium solute concentration of non-metallic elements in the liquid phase of the second phase precipitates within each target phase region before predicting the total precipitation amount of the second phase precipitates using the precipitation amount superposition method. Specifically, the equilibrium solute concentration determination module is used for:

[0245] Based on the actual temperature corresponding to each target phase region, the equilibrium solute concentration of the non-metallic element in the liquid phase in each target phase region is calculated using the second solute concentration calculation formula.

[0246] The formula for calculating the concentration of the second solute is:

[0247]

[0248] in, This represents the equilibrium solute concentration of nonmetallic elements in the liquid phase within the target phase region; T represents the actual temperature corresponding to the target phase region.

[0249] In this embodiment, the prediction device for the precipitation of the second phase in the continuously cast billet further includes a third determining module. This third determining module is used to: before predicting the total precipitation amount of the second phase precipitate during the solidification process using the precipitation amount superposition method, divide the solidification time of the target molten metal into several equal time steps; based on the target phase region corresponding to each time step, the actual solute concentration of the metal element in each target phase region, and the equilibrium solute concentration of the non-metal element in each target phase region, determine the actual solute concentration of the metal element and the equilibrium solute concentration of the non-metal element corresponding to each time step; for each target phase region, determine the equilibrium mass fraction of the metal element in the liquid phase and the equilibrium mass fraction of the non-metal element in the liquid phase, to obtain the equilibrium mass fraction of the metal element in the liquid phase and the equilibrium mass fraction of the non-metal element in the liquid phase corresponding to each time step;

[0250] The prediction module is specifically used to: calculate the precipitation amount corresponding to each time step based on the actual solute concentration of the metal element in the liquid phase, the equilibrium solute concentration of the non-metal element in the liquid phase, the equilibrium mass fraction of the metal element in the liquid phase, and the equilibrium mass fraction of the non-metal element in the liquid phase corresponding to the same time step; and perform superposition calculation based on the precipitation amounts corresponding to each time step to obtain the total precipitation amount.

[0251] In this embodiment, the prediction module is further used for:

[0252] The target cooling rate corresponding to each time step is determined based on the target cooling rate corresponding to each time step. The diffusion coefficient of non-metallic elements in the liquid phase and the mass fraction of non-metallic elements in the steel in the second phase precipitate corresponding to each time step are determined based on the diffusion coefficient of non-metallic elements in the liquid phase, the relative molecular mass of the second phase precipitate, the density of the steel, the density of the second phase precipitate, the relative molecular mass of non-metallic elements, the mass fraction of non-metallic elements in the steel, and the mass fraction of non-metallic elements in the second phase precipitate. The size of the second phase precipitate corresponding to each time step is calculated by superimposing the sizes of the second phase precipitates corresponding to each time step.

[0253] This embodiment provides a predictive device for the precipitation of the second phase in continuously cast billets. By determining the solute distribution coefficient of the metal element corresponding to each phase region, the determination of the solute distribution coefficient of the metal element is made more reasonable and accurate. This lays the foundation for the subsequent reasonable and accurate determination of the actual solute concentration of the metal element in the liquid phase corresponding to each phase region based on the solute distribution coefficient of the metal element. Subsequently, based on the actual solute concentration of the metal element in each phase region and the equilibrium solute concentration of the non-metal element, the total precipitation amount of the second phase precipitate can be accurately calculated using a superposition and accumulation method. This avoids the problem that the determination of the target element solute concentration is not reasonable and accurate due to the use of a uniform fixed solute distribution coefficient for solute concentration calculation, which in turn leads to the inaccurate and unreasonable calculation of the subsequent precipitation amount.

[0254] Another embodiment of this application provides a storage medium storing a computer program, which, when executed by a processor, implements the following method steps:

[0255] Step 1: Determine the target phase regions and second-phase precipitates that the target molten metal undergoes during solidification; the target phase regions include the first target phase region L+δ, the second target phase region L+δ+γ, and the third target phase region γ.

[0256] Step 2: Determine the target solute partition coefficients of the metal elements in the second phase precipitate within each target phase region;

[0257] Step 3: For the target solute distribution coefficient corresponding to the metal element in the same target phase region, calculate the actual solute concentration of the metal element in the liquid phase using the predetermined first solute concentration calculation formula, so as to obtain the actual solute concentration of the metal element in the liquid phase in each target phase region.

[0258] Step 4: Based at least on the actual solute concentration of metal elements in the liquid phase within each target phase region and the equilibrium solute concentration of non-metal elements in the second phase precipitate in the liquid phase within each target phase region, the total precipitation amount of the second phase precipitate during the solidification process is predicted using the precipitation amount superposition method.

[0259] The specific implementation process of the above method steps can be found in the embodiment of the above-mentioned prediction method for the precipitation of the second phase in any continuously cast billet, which will not be repeated here.

[0260] The storage medium in this application, by determining the solute partition coefficient of the metal element corresponding to each phase region, enables a more reasonable and accurate determination of the solute partition coefficient of the metal element. This lays the foundation for the subsequent reasonable and accurate determination of the actual solute concentration of the metal element in the liquid phase corresponding to each phase region based on the solute partition coefficient of the metal element. Subsequently, based on the actual solute concentration of the metal element in each phase region and the equilibrium solute concentration of the non-metal element, a superposition and accumulation calculation method can be used to accurately calculate the total precipitation amount of the second phase precipitate. This avoids the problem that the determination of the target element solute concentration is not reasonable and accurate due to the use of a uniform fixed solute partition coefficient for solute concentration calculation, which in turn leads to the inaccurate and unreasonable calculation of the subsequent precipitation amount.

[0261] Another embodiment of this application provides an electronic device, such as... Figure 8 As shown, it includes at least a memory 1 and a processor 2. The memory 1 stores a computer program, and the processor 2 performs the following method steps when executing the computer program in the memory 1:

[0262] Step 1: Determine the target phase regions and second-phase precipitates that the target molten metal undergoes during solidification; the target phase regions include the first target phase region L+δ, the second target phase region L+δ+γ, and the third target phase region γ.

[0263] Step 2: Determine the target solute partition coefficients of the metal elements in the second phase precipitate within each target phase region;

[0264] Step 3: For the target solute distribution coefficient corresponding to the metal element in the same target phase region, calculate the actual solute concentration of the metal element in the liquid phase using the predetermined first solute concentration calculation formula, so as to obtain the actual solute concentration of the metal element in the liquid phase in each target phase region.

[0265] Step 4: Based at least on the actual solute concentration of metal elements in the liquid phase within each target phase region and the equilibrium solute concentration of non-metal elements in the second phase precipitate in the liquid phase within each target phase region, the total precipitation amount of the second phase precipitate during the solidification process is predicted using the precipitation amount superposition method.

[0266] The specific implementation process of the above method steps can be found in the embodiment of the above-mentioned prediction method for the precipitation of the second phase in any continuously cast billet, which will not be repeated here.

[0267] The electronic device in this application, by determining the solute partition coefficient of the metal element corresponding to each phase region, enables a more reasonable and accurate determination of the solute partition coefficient of the metal element. This lays the foundation for the subsequent reasonable and accurate determination of the actual solute concentration of the metal element in the liquid phase corresponding to each phase region based on the solute partition coefficient of the metal element. Subsequently, based on the actual solute concentration of the metal element in each phase region and the equilibrium solute concentration of the non-metal element, a superposition and accumulation calculation method can be used to accurately calculate the total precipitation amount of the second phase precipitate. This avoids the problem that the determination of the target element solute concentration is not reasonable and accurate due to the use of a uniform fixed solute partition coefficient for solute concentration calculation, which in turn leads to the inaccurate and unreasonable calculation of the subsequent precipitation amount.

[0268] The above embodiments are merely exemplary embodiments of this application and are not intended to limit this application. The scope of protection of this application is defined by the claims. Those skilled in the art can make various modifications or equivalent substitutions to this application within its substance and scope of protection, and such modifications or equivalent substitutions should also be considered to fall within the scope of protection of this application.

Claims

1. A method for predicting the precipitation of the second phase in continuously cast billets, characterized in that, include: The target phase regions and second-phase precipitates that the target molten metal undergoes during solidification are identified; each target phase region includes a first target phase region L+δ, a second target phase region L+δ+γ, and a third target phase region γ. Determine the target solute partition coefficient of the metal element in the second phase precipitate within each of the target phase regions; For the target solute distribution coefficient corresponding to the metal element in the same target phase region, the actual solute concentration of the metal element in the liquid phase is calculated using a predetermined first solute concentration calculation formula, so as to obtain the actual solute concentration of the metal element in the liquid phase in each target phase region. Based at least on the actual solute concentration of metal elements in the liquid phase within each target phase region and the equilibrium solute concentration of non-metal elements in the liquid phase within each target phase region of the second phase precipitate, the total precipitation amount of the second phase precipitate during the solidification process is predicted using the precipitation amount superposition method. Before predicting the total amount of the second phase precipitate during the solidification process using the precipitation amount superposition method, the method further includes: determining the equilibrium solute concentration of non-metallic elements in the liquid phase within each target phase region of the second phase precipitate, specifically including: Based on the actual temperature corresponding to each target phase region, the equilibrium solute concentration of the non-metallic element in the liquid phase in each target phase region is calculated using the second solute concentration calculation formula. The formula for calculating the concentration of the first solute is: in, This indicates the actual solute concentration of the metal element in the liquid phase within the target phase region; This indicates the initial concentration of the metal element within the target phase region; C i This indicates the solute concentration of the metallic element in cell i; A i Represents the area of ​​dendrite cell i; This indicates the target solute partition coefficient of the metal element within the target phase region. A M This represents the area of ​​cell M; The formula for calculating the concentration of the second solute is: in, This represents the equilibrium solute concentration of nonmetallic elements in the liquid phase within the target phase region; T represents the actual temperature corresponding to the target phase region.

2. The method as described in claim 1, characterized in that, Before using the precipitation amount superposition method to predict the total precipitation amount of the second phase precipitate during the solidification process, the method further includes: The solidification time of the target molten metal is divided into several equal time steps; Based on the target phase region corresponding to each time step, the actual solute concentration of metal elements in each target phase region, and the equilibrium solute concentration of non-metal elements in each target phase region, the actual solute concentration of metal elements and the equilibrium solute concentration of non-metal elements corresponding to each time step are determined. For each target phase region, the equilibrium mass fraction of metal elements in the liquid phase and the equilibrium mass fraction of non-metal elements in the liquid phase are determined to obtain the equilibrium mass fraction of metal elements in the liquid phase and the equilibrium mass fraction of non-metal elements in the liquid phase corresponding to each time step. The total precipitation amount of the second phase precipitate during the solidification process is predicted using a precipitation amount superposition method, based at least on the actual solute concentration of metal elements in the liquid phase within each target phase region and the equilibrium solute concentration of non-metal elements in the second phase precipitate within each target phase region in the liquid phase. Specifically, this includes: Based on the actual solute concentration of the metal element in the liquid phase, the equilibrium solute concentration of the non-metal element in the liquid phase, the equilibrium mass fraction of the metal element in the liquid phase, and the equilibrium mass fraction of the non-metal element in the liquid phase corresponding to the same time step, the precipitation amount corresponding to each time step is calculated. The total amount of precipitation is obtained by superimposing the precipitation amounts corresponding to each time step.

3. The method as described in claim 1, characterized in that, The method further includes: The solidification time of the target molten metal is divided into several equal time steps; The target cooling rate corresponding to each time step is determined based on each time step. Based on the target cooling rate corresponding to each time step, the diffusion coefficient of non-metallic elements in the liquid phase of the second phase precipitate corresponding to each time step and the mass fraction of the non-metallic elements in the steel are determined. Based on the diffusion coefficient of non-metallic elements in the liquid phase, the relative molecular mass of the second-phase precipitate, the density of steel, the density of the second-phase precipitate, the relative molecular mass of non-metallic elements, the mass fraction of non-metallic elements in steel, and the mass fraction of non-metallic elements in the second-phase precipitate, the size of the second-phase precipitate corresponding to each time step is calculated. The total size of the second-phase precipitates is obtained by superimposing the sizes of the second-phase precipitates at each time step.

4. An apparatus for implementing the method for predicting the precipitation of the second phase in a continuously cast billet as described in any one of claims 1-3, characterized in that, include: The first determining module is used to determine the target phase regions and the second phase precipitates that the target molten metal undergoes during the solidification process; the target phase regions include the first target phase region L+δ, the second target phase region L+δ+γ, and the third target phase region γ. The second determining module is used to determine the target solute partition coefficient of the metal element in the second phase precipitate in each of the target phase regions; The calculation module is used to calculate the actual solute concentration of the metal element in the liquid phase state based on the target solute distribution coefficient corresponding to the metal element in the same target phase region using a predetermined first solute concentration calculation formula, so as to obtain the actual solute concentration of the metal element in the liquid phase state in each target phase region. The prediction module is used to predict the total amount of the second phase precipitate during the solidification process by using the precipitation amount superposition method, based at least on the actual solute concentration of metal elements in the liquid phase in each target phase region and the equilibrium solute concentration of non-metal elements in the second phase precipitate in the liquid phase in each target phase region.

5. A storage medium, characterized in that, The storage medium stores a computer program, which, when executed by a processor, implements the steps of the method for predicting the precipitation of the second phase in a continuously cast billet as described in any one of claims 1-3.

6. An electronic device, characterized in that, It includes at least a memory and a processor, wherein the memory stores a computer program, and the processor, when executing the computer program in the memory, implements the steps of the method for predicting the precipitation of the second phase in the continuously cast billet as described in any one of claims 1-3.

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