Method for determining thermal physical parameters during solidification of an alloy

Abstract

The application discloses a method for determining thermal physical parameters in an alloy solidification process, and relates to the establishment of a solute segregation model of an alloy solidification two-phase region, the acquisition of a relational database of different alloy element compositions and different process parameters and phase fractions, the mapping of the alloy element compositions and the process parameters into factor vectors with different weights through a tensor CP decomposition method, and the determination of the quantitative relationship between the thermal physical parameters and the process parameters and the alloy element compositions through a fitting method. The method can conveniently and accurately acquire the thermal physical parameters under non-equilibrium solidification conditions, determine the thermal physical parameters in the metal solidification process, and solve the model error problem caused by the thermal physical parameters.

Description

Technical Field

[0001] This invention belongs to the field of metal solidification thermophysical property testing technology, specifically relating to a method for determining thermophysical parameters of the metal solidification process. Background Technology

[0002] Metal solidification processes are mostly described by established solidification heat transfer models, and thermophysical parameters are important factors affecting the accuracy of these models. Modeling using experimental methods to determine thermophysical parameters is difficult to implement due to operational challenges and compositional variations at temperatures exceeding 1000℃. Using empirical formulas and database methods is also problematic because mismatches between production process conditions and parameters affect the accuracy of model calculations. Thermophysical parameters calculated based on pseudo-binary phase diagrams are obtained under equilibrium solidification conditions, which also introduces calculation errors. While segregation models can obtain thermophysical parameters under non-equilibrium solidification conditions, the coupling between the segregation model and the solidification model makes them difficult to solve. Summary of the Invention

[0003] This invention proposes a novel method for determining the thermal properties of metal solidification processes. This method aims to avoid the complex calculations required for coupled models while obtaining the thermal properties of non-equilibrium solidification conditions, thereby solving the model error problem caused by thermal properties.

[0004] To achieve the objectives of this invention, the following technical solution is specifically adopted:

[0005] A method for determining the thermophysical parameters of an alloy solidification process, used for determining the thermophysical parameters of a multi-alloy element molten metal solidification process, characterized by comprising the following steps:

[0006] Step 1: Establish the solute diffusion equation in the two-phase region of alloy solidification;

[0007] Step 2: Establish a non-metallic inclusion precipitation model to correct the phase fractions of the two-phase microsegregation model;

[0008] Step 3: Establish a database of process parameters and phase fractions;

[0009] Step 4: Analyze and explore the relationship between process parameters and phase fraction using the tensor CP decomposition method;

[0010] Step 5: Calculate the thermophysical parameters under non-equilibrium solidification conditions.

[0011] The beneficial effects of this invention are as follows:

[0012] This invention discloses a method for determining thermophysical parameters during alloy solidification. It establishes a solute segregation model in the two-phase region of alloy solidification to obtain a database of relationships between different alloy element compositions, process parameters, and phase fractions. The method then maps alloy element compositions and process parameters into factor vectors with different weights using tensor CP decomposition, and determines the quantitative relationship between thermophysical parameters, process parameters, and alloy element compositions through a fitting method. This method avoids the complex computational solutions to coupled models, enabling convenient and accurate acquisition of thermophysical parameters under non-equilibrium solidification conditions, determining the thermophysical parameters of the metal solidification process, and solving the model error problem caused by thermophysical parameters. Attached Figure Description

[0013] Figure 1 This outlines the process for determining thermophysical parameters based on mechanistic and data mining methods.

[0014] Figure 2 Establish a process for micro-segregation models.

[0015] Figure 3 The equilibrium / non-equilibrium density of Q235 varies with temperature. Detailed Implementation

[0016] A method for determining the thermophysical parameters of an alloy solidification process includes the following steps:

[0017] (1) Based on Fick's second law and the solute diffusion in the dendrite cross section, derive the equations for solute diffusion at the dendrite center, local equilibrium at the interfaces of the liquid phase and δ phase, the liquid phase and γ phase, and the δ phase and γ phase, and determine the initial and boundary conditions according to the actual situation. The diffusion coefficient D is calculated according to the following formula (1):

[0018]

[0019] In the formula, D0 is the diffusion constant, R is the gas constant with a value of 8.314 J / (mol·K), Q represents the activation energy per mole of atoms, and T is the absolute temperature in K.

[0020] (2) Establish a model for the precipitation of non-metallic inclusions.

[0021] Because solute elements have different solubilities in different phases, they redistribute and accumulate at the solid / liquid solidification front as the temperature decreases. When the solute element concentration exceeds the dissolution equilibrium value, non-metallic inclusions precipitate. Therefore, it is necessary to consider coupling a non-metallic inclusion precipitation model and correct the phase fractions of the microsegregation model.

[0022] Based on the current interface temperature and Gibbs free energy, the standard Gibbs free energy is calculated. Then, based on the relationship between Gibbs free energy and equilibrium solubility product, the equilibrium activity product of the two different solute elements at the solid-liquid interface is calculated. Finally, based on the actual solubility product and equilibrium solubility product at the solid / liquid front, it is determined whether there are inclusions formed by the above two different solute elements precipitating. If so, the amount of precipitation is further calculated, and then the phase fractions of the above two different solute elements at the current temperature are corrected.

[0023] (3) Establish a database of process parameters and phase fractions.

[0024] Based on the established two-phase microsegregation model, the phase fractions and solute element segregation rates at the solidification front are calculated under different alloy compositions and processing conditions, providing data for constructing higher-order tensors. Initial conditions, initial elemental compositions of the steel grade, local cooling rate V, and temperature T are used as inputs, and the phase fractions f are calculated. δ f γ f s Solute element segregation rate was used as the output of the database to construct a process condition-microsegregation database. Data was filtered at equal intervals, and the corresponding database was constructed. The matrix representation of the database is as follows:

[0025]

[0026] Among them, elemental composition and process parameters are used The fractions of each phase and the elemental segregation rate are expressed as follows: This indicates that the superscript 'l' represents the sample index in the database, the total number of samples is L, and the subscript 'd' represents the parameter dimension index, with the input parameter dimension being D. in The output parameter dimension is D out .

[0027] (4) Analyze and explore the relationship between process parameters and phase fraction based on the tensor CP decomposition method.

[0028] The database is converted into tensor data according to equation (3), and accessed using an index-based method. The index of the tensor data X is... The corresponding input parameters have a dimension of D. in The output parameter dimension is D out Each set of indices corresponds to a localized cooling and solidification condition.

[0029]

[0030] In the formula y dout This represents the output phase fractions and solute element segregation rates, where d out This corresponds to the output dimension number.

[0031] Tensor decomposition methods can reduce data dimensionality and extract data features without destroying the data structure. CP decomposition essentially decomposes a high-order tensor into a summation of multiple rank-one tensor outer products. For example, an N-dimensional tensor... The CP decomposition is shown in equation (4), where R is a positive integer, and

[0032]

[0033] Using the CP decomposition method, the concentrations of each solute element (C1, C2, ..., Cn), temperature T, and local cooling rate V are mapped to different factor matrices. Considering normalizing the columns of the factor matrices, the weights can be denoted as... The CP decomposition model can be expressed as equation (5), where:

[0034]

[0035] The high-order tensor data of the dimension reduction is decomposed and filled by alternating least squares (ALS) to obtain the tensor CP decomposition result, which maps the process parameters into factor vectors of different dimensions and their corresponding weight coefficients.

[0036] (5) Calculate the thermophysical parameters under non-equilibrium solidification conditions

[0037] The tensor CP decomposition method maps process parameters into factor vectors, but because the process parameters are selected based on an equal-interval method when the database is built, the tensor decomposition result is discrete data.

[0038] Discrete input-output data are used as training samples to input into the neural network, training the neural network weights and reducing the fitting bias. The continuous phase fraction variation law under any process parameters within a certain range is obtained by fitting using the neural network method. Then, the thermophysical parameters under non-equilibrium solidification conditions in the two-phase region are calculated using the two-phase region mixing average formula (6). The specific process parameter ranges are: cooling rate range is 0.1℃ / s~0.7℃ / s, temperature range is 1520℃~1200℃, initial C element content is 0.12~0.36 (%), initial Si element content is 0.1~0.4 (%), initial Mn element content is 0.3~1.2 (%), initial P element content is 0.005~0.025 (%), and initial S element content is 0.002~0.01 (%).

[0039] φ=∑f i φ i =f L φ L +f δ φ δ +f γ φγ (6) Where φ represents physical properties, including density, thermal conductivity, specific heat capacity, etc. i These are the corresponding phase properties, f i These are the phase fractions.

[0040] Example 2

[0041] Taking the solidification of molten steel in the continuous casting process of iron and steel production as an example, this paper analyzes the process of determining the density of molten metal during solidification. A process for microsegregation is established. Figure 2 As shown, the precipitated non-metallic inclusions are MnS. A database is constructed, with input parameters including elemental composition: C, Si, Mn, S, P, and process parameters temperature T and local cooling rate V; the output parameter is: f s f δ f γ These represent the solid fraction, delta phase fraction, and gamma phase fraction, respectively. The resulting higher-order tensor structure index is as follows:

[0042]

[0043] The established database involves the following parameter ranges: cooling rate of 0.1℃ / s to 0.7℃ / s, temperature range of 1520℃ to 1200℃, and equidistant screening. By weight percentage, the initial composition of C element is 0.12 to 0.36%, the initial composition of Si element is 0.1 to 0.4%, the initial composition of Mn element is 0.3 to 1.2%, the initial composition of P element is 0.005 to 0.025%, and the initial composition of S element is 0.002 to 0.01%.

[0044] Based on the process described above, the density of Q235 steel in the solidification two-phase region is calculated. When the contents of elements C, Si, Mn, S, and P in the molten liquid are 0.14%, 0.16%, 0.54%, 0.016%, and 0.003%, respectively, the temperature range of the two-phase region is 1510.5℃~1348.6℃, and the cooling rate is 0.25℃ / s. The solidification path of this steel is as follows: first, the δ phase is formed; when the temperature drops to around 1480℃, a peritectic reaction occurs, and the γ phase is formed on the surface of the δ phase. The δ phase completely transforms into the γ phase, and the γ phase precipitates directly in the molten steel. According to the present invention, the calculated density of the two-phase region is shown below. Figure 3 The density determined by this invention is closer to the experimental value.

[0045] According to this technical solution, the density of Q235 steel in the solidification two-phase region is calculated. When the contents of elements C, Si, Mn, S, and P in the molten liquid are 0.14%, 0.16%, 0.54%, 0.016%, and 0.003%, respectively, the temperature range of the two-phase region is 1510.5℃~1348.6℃, and the cooling rate is 0.25℃ / s. The solidification path of this steel is as follows: first, the δ phase is formed; when the temperature drops to around 1480℃, a peritectic reaction occurs, and the γ phase is formed on the surface of the δ phase. The δ phase completely transforms into the γ phase, and the γ phase precipitates directly in the molten steel. According to this invention, the calculated density of the two-phase region is shown in [reference needed]. Figure 3 The density determined by this invention is closer to the experimental value.

Claims

1. A method for determining the thermophysical parameters of an alloy solidification process, used for determining the thermophysical parameters of a multi-alloy element molten metal solidification process, characterized in that... Includes the following steps: Step 1: Establish the solute diffusion equation in the two-phase region of alloy solidification; Step 2: Establish a non-metallic inclusion precipitation model to correct the phase fractions of the two-phase microsegregation model; Step 3: Establish a database of process parameters and phase fractions; Step three includes: Based on the established two-phase microsegregation model, the phase fractions and solute element segregation rates at the solid / liquid solidification fronts under different alloy compositions and process conditions are calculated, providing data for constructing higher-order tensors. The database is constructed by using initial conditions, initial composition of each element in the steel grade, and local cooling rate as inputs, and phase fractions, solute element segregation rates, and thermodynamic temperatures as outputs. Step 4: Analyze and explore the relationship between process parameters and phase fraction using the tensor CP decomposition method; Step four includes: The database is converted into tensor data and designed to be accessed by subscript index. Each set of indexes corresponds to a local cooling solidification condition. The high-order tensor is decomposed into multiple rank-tensor outer products and summation forms by tensor CP decomposition, and the concentration of each solute element, temperature, and local cooling rate are mapped to different factor matrices. The high-order tensor data of the dimension reduction is decomposed and filled by alternating least squares method to obtain tensor decomposition results, that is, process parameters are mapped into factor vectors of different dimensions and corresponding weight coefficients. Step 5: Calculate the thermophysical parameters under non-equilibrium solidification conditions.

2. The method for determining the thermophysical parameters of the alloy solidification process as described in claim 1, characterized in that... Step one includes: Based on Fick's second law and the solute diffusion across the dendrite cross section, equations for solute diffusion at the dendrite center, local equilibrium at the interfaces of the liquid phase and δ phase, the liquid phase and γ phase, and the δ phase and γ phase are derived. Initial and boundary conditions are determined according to actual conditions, and the diffusion coefficient D varies with temperature and elemental composition as shown in equation (1). （1） In the formula, D0 is the diffusion constant, R is the gas constant, Q is the activation energy per mole of atoms, and T is the absolute temperature.

3. The method for determining the thermophysical parameters of the alloy solidification process as described in claim 1, characterized in that... Step two includes: Calculate the standard Gibbs free energy based on the current interface temperature and Gibbs free energy; Based on the relationship between standard Gibbs free energy and equilibrium solubility product, calculate the equilibrium activity product of two different solute elements at the solid-liquid interface. Based on the actual solubility product and equilibrium solubility product at the solid / liquid solidification front, it is determined whether inclusions formed by two different solute elements are precipitating. If so, the amount of inclusions precipitated is further calculated, and the phase fractions of the two different solute elements at the current temperature are corrected.

4. The method for determining the thermophysical parameters of the alloy solidification process as described in claim 1, characterized in that... Build a database by filtering data at equal intervals.

5. The method for determining the thermophysical parameters of the alloy solidification process as described in claim 1, characterized in that... Step five includes: The neural network method is used to calculate the continuous variation law of each phase fraction under arbitrary process parameters; The thermophysical parameters under non-equilibrium solidification conditions in the two-phase region are calculated using the mixing-average formula for the two-phase region. This formula describes the relationship between process parameters and thermophysical parameters under non-equilibrium solidification conditions in the two-phase region in functional form. The mixing-average formula for the two-phase region is as follows: in, Physical properties include density, thermal conductivity, and specific heat capacity. These are the corresponding phase properties. These are the phase fractions.

Images