A calculation method for solidification thermodynamics of alloy steel multi-component system

Abstract

The present invention provides a method for calculating the solidification thermodynamics of a multi-component system of alloy steel, and relates to the technical field of steel continuous casting. The method first calculates the pseudo-binary phase diagram of solute elements at different contents of multi-alloy steel, obtains a δ / γ phase transition temperature data set, establishes a δ / γ phase transition temperature Bp neural network prediction model, and trains the Bp neural network prediction model; and optimizes the liquidus temperature solution formula, and then couples the Bp neural network prediction model and the liquidus temperature solution formula to the Ueshima model to obtain the Bp-Ueshima model; establishes the relationship between different cooling rates and secondary branch arm spacing during solidification; and then realizes the calculation of the phase change characteristic temperature and solute microsegregation of multi-alloy steel according to the Bp-Ueshima model. The method uses the Bp neural network prediction model and the optimized liquidus temperature solution formula as a criterion to judge whether the δ, γ, and L phase transitions occur, which is more in line with the actual solidification process of steel.

Description

Technical Field

[0001] The invention relates to the technical field of steel continuous casting, and in particular to a calculation method for solidification thermodynamics of a multi-component system of alloy steel. Background Art

[0002] With the increase in the types and quantities of alloying elements in alloy steel, the corrosion resistance, high temperature resistance, thermal cracking resistance and wear resistance of steel have been improved. Therefore, it is used in aerospace, high-speed rail, ships and other fields. The working conditions are relatively complex, so the quality requirements for alloy steel parts are particularly strict. Since alloy steel undergoes peritectic phase transformation during the continuous casting solidification process, it is easy to cause uneven growth of the solidified shell of the continuous casting billet, inducing surface longitudinal cracks. In addition, the segregation of alloy elements during the solidification process will also produce large-sized carbides, and often become the source of cracks in the steel that endanger the quality of the steel, and will not be completely eliminated in the subsequent heat treatment. Therefore, the calculation of the characteristic temperature of the phase transformation and the solute microsegregation of alloy steel is of great significance for its continuous casting solidification quality control.

[0003] Early research used numerical methods to calculate the solidification process of multi-element alloy steels and numerically calculated the segregation behavior of multiple solute elements during the solidification process. In the model that describes the thermodynamic behavior of the solidification process, MaW J (International Journal of Minerals Metallurgy and Materials, 2014, 21 (3): 234-239) used the lever model and the Scheil model to explore the segregation behavior of elements in 20CrMnTi. However, in the actual solidification process, the diffusion of solute elements in the solid phase is limited diffusion, and the lever model assumes that the solute elements in the solid phase are completely diffused and the Scheil model assumes that the solute elements in the solid phase are completely non-diffused. Both are inaccurate. Brody-Fleming (Transaction of American Institute of Mining, Metallurgical, and Petroleum Engineers, 1966 (236): 615-624) established the BF model based on the Scheil model. The BF model takes into account the back diffusion process of solute elements in the solid phase, but the BF model is limited to elements that diffuse limitedly in the solid phase. Clyne and Kurz (Metallurgical and Materials Transactions A-process Metallurgy and Materials Science, 1981, 12 (6): 965-971) corrected the coefficient of the reverse diffusion process based on the BF model, which was widely used by later scholars to calculate the solute concentration of the element microsegregation process. The above numerical models did not consider the influence of dendrite morphology on the solidification process. Kobayashi (Transactions of the Iron and Steel Institute of Japan, 1988, 28 (7): 535-542) et al. assumed that the dendrite morphology grown during the solidification process was plate-like and columnar, and derived and proposed a new solute redistribution analytical model. The typical dendrite morphology in the continuous casting process is dendritic, and the plate-like and columnar morphologies are significantly different from the typical dendrite morphology. However, the weak flow between the secondary dendrite arms has little effect on the solute distribution, and the diffusion coefficient of the solute in the solid phase determines the diffusion rate of the solute.Ueshima Y (Metallurgical and Materials Transactions B-process Metallurgy and Materials Processing Science, 1986, 17 (4): 845-859) used the Ueshima model to analyze the solidification process of peritectic steel for the first time. The solidification process takes into account the back diffusion of elements in the solid phase. The model assumes that the cross section of the dendrite maintains a regular hexagon and grows outward during the coarsening process until it fits with the adjacent growing dendrite and the solidification process is completely completed, thereby stopping growth, and the solute is completely mixed in the molten steel, and the solute diffuses limitedly in the solid phase. Therefore, the diffusion of solute elements in the region is controlled by the one-dimensional second-order Fick equation. The model uses the liquidus temperature and the δ / γ phase transition temperature solution formula to judge when judging the movement of the phase interface. Its parameters are the phase transition line slope in the pure binary Fe-i (C, Si, Mn, P and S) phase diagram, which is approximated as a constant in most cases, and it is assumed that it is not affected by the type and content of other solute elements during the solidification process. Although this treatment has been successful in calculating the phase transformation characteristic temperature and solute microsegregation of plain carbon steel and microalloyed steel, the validity of the temperature discriminant is usually limited to a narrow composition range and a specific alloy system. Compared with plain carbon steel and microalloyed steel, the increase in the types and contents of alloying elements in multi-alloyed steels leads to a more serious reliance on the validity of thermodynamic data for the simulation of the solidification process. According to the pseudo-binary phase diagram Fe-i of multi-alloyed steel, compared with the pure binary phase diagram Fe-i, the liquidus temperature changes linearly with the change of solute elements, and its slope changes with the type and content of solute elements. However, the δ / γ phase transition temperature does not change linearly with the change of solute elements. Therefore, with the increase of the types and contents of alloying elements, it is obvious that once the interaction between solute elements is ignored. The calculation of the phase transformation characteristic temperature and solute microsegregation of multi-alloyed steel will be wrong. As a result, the study of the solidification process of multi-alloyed steel has been increasingly valued by scholars, among which thermodynamic data is the key basis for studying the solidification behavior and controlling its solidification defects during the casting process of multi-alloyed steel.

[0004] In summary, although the Ueshima model can calculate the phase transformation characteristic temperature and solute microsegregation of plain carbon steel and microalloyed steel, with the increase of the types and contents of alloying elements, the existing model fails to fully consider the influence of the interaction between solute elements on the calculation of phase transformation characteristic temperature and solute microsegregation of multi-alloyed steel. Summary of the invention

[0005] The technical problem to be solved by the present invention is to provide a calculation method for the solidification thermodynamics of a multi-component system of alloy steel in view of the deficiencies in the above-mentioned prior art, calculate the pseudo-binary phase diagram Fe-i of the multi-alloy steel under different solute element contents, obtain a δ / γ phase transition temperature data set, establish a δ / γ phase transition temperature Bp neural network prediction model, and optimize the liquidus temperature solution formula to solve the technical problem of the interaction between solute elements when solving the phase transition temperature, couple the Bp neural network prediction model and the liquidus temperature solution formula to the Ueshima model, and realize the calculation of the phase transition characteristic temperature and solute microsegregation of the multi-alloy steel.

[0006] In order to solve the above technical problems, the technical solution adopted by the present invention is: a calculation method for the solidification thermodynamics of a multi-component system of alloy steel, firstly calculating the pseudo-binary phase diagram Fe-i of the solute elements at different contents of the multi-alloy steel, obtaining a δ / γ phase transition temperature data set, establishing a δ / γ phase transition temperature Bp neural network prediction model, and training the Bp neural network prediction model; optimizing the liquidus temperature solution formula, and then coupling the Bp neural network prediction model and the liquidus temperature solution formula to the Ueshima model to obtain the Bp-Ueshima model; establishing the relationship between different cooling rates and secondary branch arm spacing during solidification; and then realizing the calculation of the phase transition characteristic temperature and solute microsegregation of the multi-alloy steel according to the Bp-Ueshima model; the specific method is:

[0007] Step 1: Calculate the pseudo-binary phase diagram of each solute element at different contents of multi-alloy steel, and process the pseudo-binary phase diagram to obtain a δ / γ phase transition temperature data set. Based on this data set, establish a δ / γ phase transition temperature Bp neural network prediction model, and train the model;

[0008] Step 1.1: Calculate the pseudo binary phase diagram of solute elements at different contents of multi-alloy steel, and extract the δ / γ phase transition temperature and the corresponding content of different solute elements from the pseudo binary phase diagram;

[0009] Step 1.2: Establish a Bp neural network prediction model; determine the number of neurons in the input layer and the output layer based on the data characteristics in the δ / γ phase transition temperature data set; in addition, determine the number of neurons in the hidden layer; the number of neurons in the input layer is determined by the type of solute elements, and the output layer has only one characteristic signal, temperature, so the output layer has only one neuron;

[0010] According to the Bp neural network structure, the input signal entering the zth neuron node in the hidden layer is net z , as shown below:

[0011]

[0012] The output signal o of the neuron node z :

[0013]

[0014] The input signal net entering the gth neuron node of the output layer g :

[0015]

[0016] The output signal of the neuron node in the output layer is d g :

[0017]

[0018] Among them, w kz is the weight value from the kth neuron node in the input layer to the zth neuron node in the hidden layer; x k is the input signal of the kth neuron in the input layer; b kz is the threshold from the kth neuron node in the input layer to the zth neuron node in the hidden layer; N is the type of solute element; is the activation function; M is the number of neurons in the hidden layer; w zg is the weight value from the zth neuron node in the hidden layer to the gth neuron node in the output layer; b zg It is the threshold from the zth neuron node in the hidden layer to the gth neuron node in the output layer;

[0019] Step 1.3: Use the δ / γ phase transition temperature dataset to train the Bp neural network prediction model;

[0020] According to the established Bp neural network structure, the δ / γ phase transition temperature data set is classified, and the training data set, validation data set and test data set are randomly classified in a certain proportion, and then the Bp neural network is trained; the mean square error function MSE is used to compare the expected value T and the output value d g Calculate and determine whether the output value of the output layer of the Bp neural network meets the requirements, as shown in the following formula:

[0021]

[0022] Where p is the number of input signals in the δ / γ phase transition temperature dataset;

[0023] Step 2: Based on the Ueshima model theory, a solute microsegregation model during the solidification process of alloy steel is constructed to calculate the microsegregation ratio of the solute elements and the phase transition characteristic temperature;

[0024] Step 2.1: Based on the Ueshima model theory, determine the calculation domain of the solute microsegregation model during steel solidification;

[0025] According to the Ueshima model theory, the solidification structure is approximated as a regular hexagonal prism with adjacent edges, and the axial diffusion of the solute along the dendrite is ignored; the cross-sectional area of ​​the dendrite is assumed to expand outward in the form of a regular hexagon during the solidification process, and an equilateral triangle of 1 / 6 of the regular hexagon is selected as the calculation domain of the solute microsegregation model according to the principle of symmetry; the calculation domain is evenly divided into Node_n calculation nodes; the distance between two adjacent nodes is Δx; j is the node number; A j represents the area of ​​node j; L j Represents the interface length between node j and node j+1; Delt_n is the total number of nodes in the δ phase; Solid_n is the total number of nodes in the solid phase; Since the calculation domain of the dendrite size belongs to the micrometer scale, at the same time, it is assumed that there is no temperature difference in the calculation domain; The solute microsegregation model assumes that the solute atoms are uniformly mixed in the liquid phase, and the limited diffusion in the solid phase satisfies Fick's second law;

[0026] Step 2.2: Determine the migration of the phase interface during the steel solidification process by using the steel solidification characteristic temperature criterion;

[0027] The steel solidification characteristic temperature includes the liquidus temperature T L ,δ / γ transition temperature T Ar4 and virtual liquidus temperature T L ′,δ / γ transition temperature T Ar4 The Bp neural network prediction model in step 1 is used to obtain the liquidus temperature T according to the solute content of the last node of the δ phase in the calculation domain. L and virtual liquidus temperature T L ' is calculated based on the slope of the liquidus line in the pseudo-binary phase diagram, as shown in the following formula:

[0028]

[0029]

[0030] Among them, m i is the liquidus slope of element i in the pseudo-binary phase diagram; represents the solute content of element i in the last node of the δ phase and the liquid phase at the solidification front, respectively; k δ / L represents the solute redistribution coefficient at the δ / L interface;

[0031] Through the steel solidification characteristic temperature criterion, the migration of the phase interface during steel solidification is determined as follows:

[0032] When the δ phase exists and T≤T Ar4When T≤T L When T≤T L And T≤T Ar4 When T≤T, the total number of nodes in the δ phase decreases by one and the total number of nodes in the solid phase increases by one. For the δ / γ interface and the complete δ phase, when T≤T L ′ and T≤T Ar4 When , the total number of nodes in the δ phase decreases by one node;

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

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

[0035] The δ / γ interface satisfies:

[0036]

[0037]

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

[0039] The δ / L interface satisfies:

[0040]

[0041]

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

[0043] The γ / L interface satisfies:

[0044]

[0045]

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

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

[0048] The single-phase diffusion of the solute element in the δ phase or γ phase is solved by the explicit difference method of Fick's second law:

[0049] The change of element i at node j within the δ phase or γ phase within the Δt time The following relationship is satisfied:

[0050]

[0051] At the center of the dendrite with j=1, the change of element i within Δt The following relationship is satisfied:

[0052]

[0053] Among them, Δx represents the horizontal distance between two adjacent nodes, L j represents the interface length between node j and node j+1, A 1 Represents the area of ​​1 node; D i represents the diffusion coefficient of element i in the solid phase; and represent the solute contents of element i at 2 nodes and 1 node respectively;

[0054] Step 2.5: Calculate the solute content in the solidification front and divide it by the initial solute content to obtain the microsegregation ratio of the solute element;

[0055] Step 3: Establish the relationship between cooling rate and dendrite secondary branch arm spacing to determine the calculation domain size of the solute microsegregation model;

[0056] The calculation domain size of the solute microsegregation model refers to half of the dendrite arm spacing in the continuous casting billet, and the solidification structure under different cooling rates is obtained by experimental means, and is determined by statistics after corrosion experiments or by an empirical formula between cooling rate and dendrite secondary arm spacing;

[0057] Step 4: Determine the phase transformation characteristic temperature and solute microsegregation in the multi-alloy steel during the solidification process using the solute microsegregation model;

[0058] Step 4.1: Read the chemical composition of the steel grade and the calculation domain size of the solute microsegregation model;

[0059] Step 4.2: Use the solute microsegregation model to calculate the microsegregation ratio and phase transition characteristic temperature of the solute elements during the solidification process at different cooling rates.

[0060] The beneficial effect of adopting the above technical solution is that: the present invention provides a method for calculating the solidification thermodynamics of a multi-component system of alloy steel. With the increase of the types and contents of alloy elements, the traditional Ueshima model uses the thermodynamic data of the Fe-i binary equilibrium phase diagram to determine the phase transition, which is no longer applicable. In order to solve the limitations of the solute microsegregation model in the discriminant of the phase interface temperature during the solidification process, the interaction between the solute elements must be considered. With the help of the thermodynamic software Thermo-Calc, the pseudo-binary phase diagram of the solute elements at different contents was calculated, and the δ / γ phase transition temperature data set was obtained. The δ / γ phase transition temperature Bp neural network prediction model was established, and the neural network prediction model was trained. The liquidus temperature solution formula was optimized and then coupled to the Ueshima model to obtain the Bp-Ueshima model. Based on the Bp-Ueshima model theory, a solute microsegregation model is established to explore the microsegregation behavior of solute elements. The Bp-Ueshima model approximates the cross section of the dendrite to a regular hexagon, assumes that the limited diffusion of solute elements in the solid phase satisfies Fick's second law, and uses the Bp neural network prediction model and the optimized liquidus temperature solution formula as the criterion for judging whether the δ, γ, and L phase transitions occur, which is more in line with the actual solidification process of steel. In short, with the help of the Bp neural network, the thermodynamic software Thermo-Calc is effectively combined with the Ueshima model to obtain the phase transition characteristic temperature and solute microsegregation of the multi-alloy steel solidification process, providing theoretical guidance for optimizing the quality of multi-alloy steel products. BRIEF DESCRIPTION OF THE DRAWINGS

[0061] Figure 1 A flow chart of a method for calculating solidification thermodynamics of a multi-component system of alloy steel provided in an embodiment of the present invention;

[0062] Figure 2 The topological structure of the Bp neural network prediction model provided by the embodiment of the present invention;

[0063] Figure 3 The algorithm structure of the Bp neural network prediction model provided by the embodiment of the present invention;

[0064] Figure 4 Output fitting verification of the Bp neural network prediction model provided by the embodiment of the present invention;

[0065] Figure 5The fitting verification of the Bp neural network prediction model provided in the embodiment of the present invention for each data set, wherein (a) is the fitting verification of the training data set, (b) is the fitting verification of the test data set, (c) is the fitting verification of the verification data set, and (d) is the fitting verification of the total data set;

[0066] Figure 6 Schematic diagram of the Ueshima solute microsegregation theoretical model provided in an embodiment of the present invention, wherein (a) is the three-dimensional morphology of dendrite growth, (b) is the cross-sectional morphology of the dendrite, and (c) is the calculation domain of the solute microsegregation model;

[0067] Figure 7 The dendrite morphology at different cooling rates provided by the embodiments of the present invention, wherein (a) is the solidification structure morphology at 10°C / min, (b) is the solidification structure morphology at 15°C / min, and (c) is the solidification structure morphology at 20°C / min;

[0068] Figure 8 A diagram showing how the secondary dendrite arm spacing changes with cooling rate provided in an embodiment of the present invention. DETAILED DESCRIPTION

[0069] The specific implementation of the present invention is further described in detail below in conjunction with the accompanying drawings and examples. The following examples are used to illustrate the present invention, but are not intended to limit the scope of the present invention.

[0070] This embodiment takes H13 multi-alloy steel as an example, and adopts the calculation method of the alloy steel multi-component system solidification thermodynamics of the present invention to calculate the solute micro-segregation behavior and phase change characteristic temperature during the solidification process of H13 multi-alloy steel.

[0071] In this embodiment, a method for calculating the solidification thermodynamics of a multi-component system of alloy steel is provided. First, a pseudo-binary phase diagram Fe-i of solute elements at different contents in the multi-alloy steel is calculated to obtain a δ / γ phase transition temperature data set, a δ / γ phase transition temperature Bp neural network prediction model is established, and the Bp neural network prediction model is trained; and the liquidus temperature solution formula is optimized, and then the Bp neural network prediction model and the liquidus temperature solution formula are coupled to the Ueshima model to obtain the Bp-Ueshima model; then, the relationship between different cooling rates and secondary branch arm spacing during the solidification process is established; finally, the phase transition characteristic temperature and solute microsegregation of the multi-alloy steel are calculated according to the Bp-Ueshima model; Figure 1 As shown, the specific method is:

[0072] Step 1: The pseudo-binary phase diagram of each solute element (C, Si, Mn, P, S, Cr, Mo, V) at different contents of multi-alloy steel is calculated with the help of thermodynamic software Thermo-Calc (TCFE9 database), and the pseudo-binary phase diagram is processed to obtain a δ / γ phase transition temperature data set. Based on this data set, a δ / γ phase transition temperature Bp neural network prediction model is established, and the model is trained;

[0073] Step 1.1: Calculate the pseudo-binary phase diagram of solute elements at different contents of multi-alloy steel with the help of thermodynamic software Thermo-Calc (TCFE9 database), and extract the δ / γ phase transition temperature and the corresponding content of different solute elements from the pseudo-binary phase diagram;

[0074] Step 1.2: Establish a Bp neural network prediction model; determine the number of neurons in the input layer and the output layer and the number of neurons in the hidden layer based on the data characteristics in the δ / γ phase transition temperature data set; wherein the number of neurons in the input layer is determined by the type of solute element, and the output layer has only one characteristic signal, namely temperature, so the output layer has only one neuron; in this embodiment, a Bp neural network prediction model is created with the aid of the software Matlab.

[0075] The calculation process of the Bp neural network consists of two processes: forward information feedback and error back propagation. The forward propagation process is to process from the input layer to the hidden layer layer by layer and then turn to the output layer. The state of each layer of neurons only affects the state of the next layer of neurons. If the expected output cannot be obtained in the output layer, it will turn to back propagation and return the error signal along the original connection path. By modifying the weight value and threshold of each neuron, the error signal is minimized. The trained Bp neural network learns and stores a large number of input-output pattern mapping relationships without revealing the mathematical equations describing this mapping relationship in advance. According to the pseudo-binary phase diagram Fe-i, the δ / γ phase transition temperature data set is obtained. The number of neurons in the input layer and the output layer is determined based on the characteristics of the data set. The number of neurons in the input layer is equal to the type of solute elements (8), and the number of neurons in the output layer is only 1, corresponding to the characteristic temperature of the δ / γ phase transition. In addition, a hidden layer containing 10 neuron nodes is used to create a Bp neural network with the help of the software Matlab. The corresponding input layer, output layer and hidden layer are created based on the δ / γ phase transition temperature data set. The topological structure of the Bp neural network is as follows Figure 2 As shown;

[0076] According to the Bp neural network structure, the input signal entering the zth neuron node in the hidden layer is net z , as shown below:

[0077]

[0078] The output signal o of the neuron node z :

[0079]

[0080] The input signal net entering the gth neuron node of the output layer g :

[0081]

[0082] The output signal of the neuron node in the output layer is d g :

[0083]

[0084] Among them, w kz is the weight value from the kth neuron node in the input layer to the zth neuron node in the hidden layer; x k is the input signal of the kth neuron in the input layer; b kz is the threshold from the kth neuron node in the input layer to the zth neuron node in the hidden layer; N is the type of solute element; is the activation function; M is the number of neurons in the hidden layer; w zg is the weight value from the zth neuron node in the hidden layer to the gth neuron node in the output layer; b z1 It is the threshold from the zth neuron node in the hidden layer to the gth neuron node in the output layer;

[0085] Step 1.3: Use the δ / γ phase transition temperature dataset to train the Bp neural network prediction model;

[0086] According to the established Figure 3 The Bp neural network structure shown classifies the δ / γ phase transition temperature data set, randomly classifies the training data set, the validation data set and the test data set in a ratio of 7:1.5:1.5, and performs model training; the training set is used to train the Bp neural network prediction model, obtain model parameters, and adjust the network according to its error; the validation set is used to evaluate the generalization ability of the neural network model, that is, the accuracy of the model, and the training is stopped when the generalization stops improving; the test set has no effect on the training and is only used to measure the network performance of the final model; in this embodiment, the training data set uses the Levenberg-marquardt algorithm for model training, and the training automatically stops when the generalization stops improving.

[0087] This embodiment uses the mean square error function MSE to compare the expected value T and the output value d g Calculate and determine whether the output value of the output layer of the Bp neural network meets the requirements, as shown in the following formula:

[0088]

[0089] Where p is the number of input signals in the δ / γ phase transition temperature dataset;

[0090] In this embodiment, after the Bp neural network prediction model is trained 1000 times, the mean square errors of the training data set, the validation data set, and the test data set are 0.0056, 0.0047, and 0.0059, respectively, indicating that after the Bp neural network prediction model is trained through deep learning, the error between the model input value and the expected value is small enough, proving the effectiveness of the Bp neural network prediction model. Figure 4 The output fitting verification of the Bp neural network prediction model. In addition, the phase change characteristic temperature predicted by the Bp neural network prediction model is compared with the actual phase change characteristic temperature. It can be seen that the linear fitting equation of the simulated temperature and the actual temperature of the training data set, the verification data set and the test data set is y=x+0.011(R 2 =1), y = x + 0.012 (R 2 =1) and y = x + 0.043 (R 2 =1). The Bp neural network prediction model was used to perform a fitting verification on all data. The linear fitting equation of the simulated phase transition temperature and the actual phase transition temperature was y=x+0.017(R 2 =1), which once again proves the reliability of the Bp neural network prediction model. The results are as follows Figure 5 As shown;

[0091] Step 2: Based on the Ueshima model theory, a solute microsegregation model during the solidification process of alloy steel is constructed to calculate the microsegregation ratio of the solute elements and the phase transition characteristic temperature;

[0092] Step 2.1: Based on the Ueshima model theory, determine the calculation domain of the solute microsegregation model during steel solidification;

[0093] According to the Ueshima model theory, the solidification structure is approximated as a regular hexagonal prism with adjacent edges, such as Figure 6 As shown, the axial diffusion of the solute along the dendrite is ignored; the cross-sectional area of ​​the dendrite is set to expand outward in the form of a regular hexagon during the solidification process, and an equilateral triangle of 1 / 6 of the regular hexagon is selected as the calculation domain of the solute microsegregation model according to the principle of symmetry; the calculation domain is evenly divided into Node_n calculation nodes; in this embodiment, the calculation domain is evenly divided into 200 calculation nodes, that is, the total number of nodes Node_n = 200; the distance between two adjacent nodes is Δx; j is the node number; A j represents the area of ​​node j; L jRepresents the interface length between node j and node j+1; Delt_n is the total number of nodes in the δ phase; Solid_n is the total number of nodes in the solid phase; Since the calculation domain of the dendrite size belongs to the micrometer scale, at the same time, it is assumed that there is no temperature difference in the calculation domain; The solute microsegregation model assumes that the solute atoms are uniformly mixed in the liquid phase, and the limited diffusion in the solid phase satisfies Fick's second law;

[0094] Step 2.2: Determine the migration of the phase interface during the steel solidification process by using the steel solidification characteristic temperature criterion;

[0095] The steel solidification characteristic temperature includes the liquidus temperature T L ,δ / γ transition temperature T Ar4 and virtual liquidus temperature T L ′,δ / γ transition temperature T Ar4 The Bp neural network prediction model in step 1 is used to obtain the liquidus temperature T according to the solute content of the last node of the δ phase. L and virtual liquidus temperature T L ' is calculated based on the slope of the liquidus line in the pseudo-binary phase diagram, as shown in the following formula:

[0096]

[0097]

[0098] Among them, m i is the liquidus line of element i in the pseudo-binary phase diagram; represents the solute content of element i in the last node of the δ phase and the liquid phase at the solidification front, respectively; k δ / L represents the solute redistribution coefficient at the δ / L interface;

[0099] The traditional Ueshima model compares the real-time temperature T during the solidification process of steel with the liquidus temperature T L ,δ / γ transition temperature T Ar4 , virtual liquidus temperature T L The relative size relationship between ′ can be used to judge the movement of the phase interface during the solidification process of steel; in addition, the traditional Ueshima model uses the liquidus line of element i and the slope of the δ / γ phase transition line in the binary Fe-i equilibrium phase diagram. In order to consider the interaction between solute elements in the solidification process on T Ar4 The present invention uses the Bp neural network prediction model in step 1 to obtain the δ / γ transition temperature T according to the solute content of the last node of the δ phase. Ar4 , no longer using the formula To determine the δ / γ transition, n i is the slope of the δ / γ phase transition line. In addition, the liquidus temperature T L and virtual liquidus temperature TL m in ′ i is the slope of the liquidus line of element i in the pseudo-binary phase diagram; the present invention optimizes the liquidus line temperature solution formula based on the liquidus line slope in the pseudo-binary phase diagram.

[0100] Through the steel solidification characteristic temperature criterion, the migration of the phase interface during steel solidification is determined as follows:

[0101] When the δ phase exists and T≤T Ar4 When T≤T L When T≤T L And T≤T Ar4 When T≤T, the total number of nodes in the δ phase decreases by one and the total number of nodes in the solid phase increases by one. For the δ / γ interface and the complete δ phase, when T≤T L ′ and T≤T Ar4 When , the total number of nodes in the δ phase decreases by one node;

[0102] Step 2.3: Based on the solute element redistribution and solute conservation law, determine the solute element redistribution at the phase interface during steel solidification;

[0103] The solute distribution at different interfaces during steel solidification is as follows:

[0104] The δ / γ interface satisfies:

[0105]

[0106]

[0107] Among them, k γ / δ represents the solute redistribution coefficient at the γ / δ interface; A Delt_n Represents the area of ​​the Delt_n node; They represent the solute contents of element i in the δ and γ nodes at the δ / γ interface before solute redistribution occurs; They represent the solute contents of element i in the δ and γ nodes at the δ / γ interface after solute redistribution occurs;

[0108] The δ / L interface satisfies:

[0109]

[0110]

[0111] Among them, A j represents the area of ​​node j; k L / δ represents the solute redistribution coefficient at the L / δ interface; ASolid_n Represents the area of ​​Solid_n node; They represent the solute content of element i in node j before and after solute redistribution occurs; They represent the solute contents of element i in the δ node at the δ / L interface before and after solute redistribution occurs;

[0112] The γ / L interface satisfies:

[0113]

[0114]

[0115] Among them, k γ / L represents the solute redistribution coefficient at the γ / L interface;

[0116] Step 2.4: Based on Fick's second law, determine the back diffusion of solute elements in the solid phase;

[0117] Fick's second law is expressed as follows:

[0118]

[0119] in, represents the solute content of element i in the solid phase; Represents the change in the solute content of element i in the solid phase; represents the solute diffusion coefficient in the solid phase;

[0120] The single-phase diffusion of the solute element in the δ phase or γ phase is solved by the explicit difference method of Fick's second law:

[0121] The change of element i at node j within the δ phase or γ phase within the Δt time The following relationship is satisfied:

[0122]

[0123] At the center of the dendrite with j=1, the change of element i within Δt The following relationship is satisfied:

[0124]

[0125] Among them, Δx represents the horizontal distance between two adjacent nodes, L j represents the interface length between node j and node j+1, A 1 Represents the area of ​​1 node; D i represents the diffusion coefficient of element i in the solid phase; and represent the solute contents of element i at 2 nodes and 1 node respectively;

[0126] Step 2.5: Calculate the solute content in the solidification front and divide it by the initial solute content to obtain the microsegregation ratio of the solute element;

[0127] In this embodiment, the solute redistribution coefficient k between different phases is δ / L , k γ / L , k γ / δ , the diffusion coefficient D of different solute elements in the solid phase i , the slope m of the liquidus line of element i in the pseudo-binary phase diagram Fe-i of H13 multi-alloy steel i As shown in Table 1.

[0128] Table 1 Redistribution coefficient of solute elements, solid phase diffusion coefficient, slope of phase transition temperature line

[0129]

[0130] Wherein, R = 1.987 cal / mol·K.

[0131] Step 3: Establish the relationship between cooling rate and dendrite secondary branch arm spacing to determine the calculation domain size of the solute microsegregation model;

[0132] The calculation domain size of the solute microsegregation model refers to half of the dendrite arm spacing in the continuous casting billet, and the solidification structure under different cooling rates is obtained by experimental means, and is determined by statistics after corrosion experiments or by an empirical formula between cooling rate and dendrite secondary arm spacing;

[0133] In this embodiment, a solidified sample at different cooling rates during solidification is obtained by means of a differential scanning calorimeter (DSC), and the sample is polished and etched. The secondary dendrite arm spacing on the surface of the sample after etching is measured to establish a relationship between the cooling rate and the secondary dendrite arm spacing, which specifically includes the following steps:

[0134] Step S1: taking a H13 multi-alloy steel ingot sample and processing the sample;

[0135] Before the DSC experiment, the H13 multi-alloy steel was first processed into a Φ5mm×1mm cylindrical sample, and the surface was ground to about 50mg with sandpaper. Then it was placed in a beaker containing anhydrous ethanol and cleaned with ultrasonic oscillation for 3 to 5 minutes, and finally dried with a hair dryer and dried in a vacuum drying oven;

[0136] Step S2: using DSC to test the H13 multi-alloy steel sample at cooling rates of 10, 15, and 20°C / min;

[0137] The treated samples were tested using a DSC404F3 differential scanning calorimeter manufactured by NETZSCH, Germany. The samples were analyzed in a corundum crucible (Al2O3) with a lid. The reference sample for all measurements was an empty alumina crucible. The measurements were carried out in an inert atmosphere of pure argon (>99.9999%). Before each measurement, the furnace chamber was evacuated and filled with inert gas twice to avoid decarburization and oxidation of the steel sample in the presence of residual oxygen at high temperatures. The gas flow rate during the experiment was 50mL / min. First, the sample was heated from room temperature to 50°C for temperature calibration, and then heated to 1500°C at a rate of 20°C / min. The sample was kept at 1500°C for 2 minutes to ensure that the sample was completely melted. Then it was cooled to 1200°C at cooling rates of 10, 15, and 20°C / min, and the DSC thermal signal was recorded in real time during the high-temperature solidification process. Then it was quickly cooled to room temperature;

[0138] Step S3: performing a corrosion test on the solidified sample after the experiment to establish the relationship between the cooling rate and the distance between the secondary branches of the dendrite;

[0139] The sample surface was polished and then corroded in a saturated picric acid solution at a constant temperature (80°C) in a water bath. The top surface morphology of the sample was photographed using an optical microscope. Figure 7 The secondary branch arm spacing of dendrites at different cooling rates was statistically analyzed using ImageJ software, as shown in Figure 2. Figure 8 As shown, the relationship between the cooling rate and the secondary branch arm spacing of the dendrite is established as shown in the following formula:

[0140]

[0141] Where, λ is the secondary dendrite arm spacing (μm), R c is the cooling rate during solidification (℃·min -1 ).

[0142] Step 4: Determine the phase transformation characteristic temperature and solute microsegregation in the multi-alloy steel during the solidification process using the solute microsegregation model;

[0143] Step 4.1: Read the chemical composition of the steel grade and the calculation domain size of the solute microsegregation model; the calculation domain size of the solute microsegregation model refers to half of the secondary dendrite arm spacing, which is obtained through step S3;

[0144] Step 4.2: Use the solute microsegregation model to calculate the microsegregation ratio and phase transition characteristic temperature of the solute elements during the solidification process at different cooling rates.

[0145] In this embodiment, the Bp-Ueshima model is used to calculate the final solidification period at cooling rates of 10°C / min, 15°C / min, and 20°C / min: the segregation ratios of the solute element C are 4.265, 4.261, and 4.259, respectively; the segregation ratios of the solute element Si are 5.33, 5.31, and 5.30, respectively; the segregation ratios of the solute element Mn are 2.534, 2.531, and 2.529, respectively; The segregation ratios of element P are 37.161, 36.953 and 36.805 respectively; the segregation ratios of solute element S are 62.84, 65.50 and 62.26 respectively; the segregation ratios of solute element Cr are 1.6207, 1.6203 and 1.6200 respectively; the segregation ratios of solute element Mo are 4.46, 4.45 and 4.44 respectively; the segregation ratios of solute element V are 3.37, 3.36 and 3.35 respectively.

[0146] In this embodiment, the Bp-Ueshima model is used to calculate that the liquidus temperature is 1473.35°C at cooling rates of 10°C / min, 15°C / min and 20°C / min, peritectic reactions occur at 1420.31°C, 1420.35°C and 1420.37°C, respectively, ferrite is completely transformed into austenite at 1376.2°C, 1376.40°C and 1376.52°C, respectively, and the liquid phase completely disappears at 1306.12°C, 1306.89°C and 1307.43°C.

[0147] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, rather than to limit it. Although the present invention has been described in detail with reference to the aforementioned embodiments, those skilled in the art should understand that they can still modify the technical solutions described in the aforementioned embodiments, or make equivalent replacements for some or all of the technical features therein. However, these modifications or replacements do not cause the essence of the corresponding technical solutions to deviate from the scope defined by the claims of the present invention.

Claims

1. A method for calculating the solidification thermodynamics of a multi-component system of alloy steel, characterized by: Firstly, the pseudo-binary phase diagram of solute elements at different contents in multi-alloy steel is calculated to obtain the δ / γ phase transition temperature data set, and the δ / γ phase transition temperature Bp neural network prediction model is established and trained. The liquidus temperature solution formula is optimized, and then the Bp neural network prediction model and the liquidus temperature solution formula are coupled to the Ueshima model to obtain the Bp-Ueshima model. The relationship between different cooling rates and secondary branch arm spacing during solidification is established. Then, the phase transition characteristic temperature and solute microsegregation of multi-alloy steel are calculated based on the Bp-Ueshima model. The method comprises the following steps: Step 1: Calculate the pseudo-binary phase diagram of each solute element at different contents in multi-alloy steel, and process the pseudo-binary phase diagram to obtain a δ / γ phase transition temperature data set. Based on this data set, establish a δ / γ phase transition temperature Bp neural network prediction model and train the model; Step 2: Based on the Ueshima model theory, a solute microsegregation model during the solidification process of alloy steel is constructed to calculate the microsegregation ratio of the solute elements and the phase transition characteristic temperature; Step 2.1: Based on the Ueshima model theory, determine the calculation domain of the solute microsegregation model during steel solidification; Step 2.2: Determine the migration of the phase interface during the steel solidification process by using the steel solidification characteristic temperature criterion; The steel solidification characteristic temperature includes the liquidus temperature T L ,δ / γ transition temperature T Ar4 and virtual liquidus temperature T L ′,δ / γ transition temperature T Ar4 The Bp neural network prediction model in step 1 is used to obtain the liquidus temperature T according to the solute content of the last node of the δ phase in the calculation domain. L and virtual liquidus temperature T L 'Calculated based on the slope of the liquidus line in the pseudo-binary phase diagram; Through the steel solidification characteristic temperature criterion, the migration of the phase interface during steel solidification is determined as follows: When the δ phase exists and T≤T Ar4 When T≤T L When T≤T L And T≤T Ar4 When T≤T, the total number of nodes in the δ phase decreases by one and the total number of nodes in the solid phase increases by one. For the δ / γ interface and the complete δ phase, when T≤T L ′ and T≤T Ar4 When , the total number of nodes in the δ phase decreases by one node; Step 2.3: Based on the solute element redistribution and solute conservation law, determine the solute element redistribution at the phase interface during steel solidification; Step 2.4: Based on Fick's second law, determine the back diffusion of solute elements in the solid phase; Step 2.5: Calculate the solute content in the solidification front and divide it by the initial solute content to obtain the microsegregation ratio of the solute element; Step 3: Establish the relationship between cooling rate and dendrite secondary branch arm spacing to determine the calculation domain size of the solute microsegregation model; The calculation domain size of the solute microsegregation model refers to half of the dendrite arm spacing in the continuous casting billet. The solidification structure at different cooling rates is obtained by experimental means, and is determined by statistics after corrosion experiments or by an empirical formula between the cooling rate and the dendrite secondary arm spacing; Step 4: Determine the phase change characteristic temperature and solute microsegregation in the multi-alloy steel during the solidification process using the solute microsegregation model; Step 4.1: Read the chemical composition of the steel grade and the calculation domain size of the solute microsegregation model; Step 4.2: Use the solute microsegregation model to calculate the microsegregation ratio and phase transition characteristic temperature of the solute elements during the solidification process at different cooling rates.

2. The method for calculating solidification thermodynamics of a multi-component system of alloy steel according to claim 1, characterized in that: The specific method of step 1 is: Step 1.1: Calculate the pseudo binary phase diagram of solute elements at different contents of multi-alloy steel, and extract the δ / γ phase transition temperature and the corresponding content of different solute elements from the pseudo binary phase diagram; Step 1.2: Establish a Bp neural network prediction model; determine the number of neurons in the input layer and the output layer based on the data characteristics in the δ / γ phase transition temperature data set; in addition, determine the number of neurons in the hidden layer; the number of neurons in the input layer is determined by the type of solute elements, and the output layer has only one characteristic signal, temperature, so the output layer has only one neuron; Step 1.3: Use the δ / γ phase transition temperature dataset to train the Bp neural network prediction model.

3. The method for calculating solidification thermodynamics of a multi-component system of alloy steel according to claim 2, characterized in that: The Bp neural network prediction model is specifically: According to the Bp neural network structure, the input signal entering the zth neuron node in the hidden layer is net z , as shown below: The output signal o of the neuron node z : The input signal net entering the gth neuron node of the output layer g : The output signal of the neuron node in the output layer is d g : Among them, w kz is the weight value from the kth neuron node in the input layer to the zth neuron node in the hidden layer; x k is the input signal of the kth neuron in the input layer; b kz is the threshold from the kth neuron node in the input layer to the zth neuron node in the hidden layer; N is the type of solute element; is the activation function; M is the number of neurons in the hidden layer; w zg is the weight value from the zth neuron node in the hidden layer to the gth neuron node in the output layer; b zg It is the threshold from the zth neuron node in the hidden layer to the gth neuron node in the output layer.

4. The method for calculating solidification thermodynamics of a multi-component system of alloy steel according to claim 3, characterized in that: In step 1.3, the δ / γ phase transition temperature data set is classified according to the established Bp neural network structure, and the training data set, the validation data set and the test data set are randomly classified according to a certain proportion, and then the Bp neural network is trained; the mean square error function MSE is used to train the expected value T ar and the output value d g Calculate and determine whether the output value of the output layer of the Bp neural network meets the requirements, as shown in the following formula: where p is the number of input signals in the δ / γ phase transition temperature dataset.

5. The method for calculating solidification thermodynamics of a multi-component system of alloy steel according to claim 4, characterized in that: In step 2.1, according to the Ueshima model theory, the solidification structure is approximated as a regular hexagonal prism with adjacent edges, and the axial diffusion of the solute along the dendrite is ignored; the cross-sectional area of ​​the dendrite is set to expand outward in the form of a regular hexagon during the solidification process, and an equilateral triangle of 1 / 6 of the regular hexagon is selected as the calculation domain of the solute microsegregation model according to the principle of symmetry; the calculation domain is evenly divided into Node_n calculation nodes; the distance between two adjacent nodes is Δx; j is the node number; A j represents the area of ​​node j; L j Represents the interface length between the j node and the j+1 node; Delt_n is the total number of δ phase nodes; Solid_n is the total number of solid phase nodes; Since the calculation domain of the dendrite size belongs to the micron scale, at the same time, it is set that there is no temperature difference in the calculation domain; the solute microsegregation model sets the solute atoms to be uniformly mixed in the liquid phase, and the limited diffusion in the solid phase satisfies Fick's second law.

6. The method for calculating solidification thermodynamics of a multi-component system of alloy steel according to claim 5, characterized in that: Step 2.2: Liquidus temperature T L and virtual liquidus temperature T L ′ is shown in the following formula: Among them, m i is the liquidus slope of element i in the pseudo-binary phase diagram; represents the solute content of element i in the last node of the δ phase and the liquid phase at the solidification front, respectively; k δ / L Represents the solute redistribution coefficient at the δ / L interface.

7. The method for calculating solidification thermodynamics of a multi-component system of alloy steel according to claim 6, characterized in that: The specific method of step 2.3 is: The solute distribution at different interfaces during steel solidification is as follows: The δ / γ interface satisfies: Among them, k γ / δ represents the solute redistribution coefficient at the γ / δ interface; A Delt_n Represents the area of ​​the Delt_n node; They represent the solute contents of element i in the δ and γ nodes at the δ / γ interface before solute redistribution occurs; They represent the solute contents of element i in the δ and γ nodes at the δ / γ interface after solute redistribution occurs; The δ / L interface satisfies: Among them, A j represents the area of ​​node j; k L / δ represents the solute redistribution coefficient at the L / δ interface; A Solid_n Represents the area of ​​Solid_n node; They represent the solute content of element i in node j before and after solute redistribution occurs; They represent the solute contents of element i in the δ node at the δ / L interface before and after solute redistribution occurs; The γ / L interface satisfies: Among them, k γ / L represents the solute redistribution coefficient at the γ / L interface.

8. The method for calculating solidification thermodynamics of a multi-component system of alloy steel according to claim 7, characterized in that: The specific method of step 2.4 is: The single-phase diffusion of the solute element in the δ phase or γ phase is solved by the explicit difference method of Fick's second law: The change of element i at node j within the δ phase or γ phase within the Δt time The following relationship is satisfied: At the center of the dendrite with j=1, the change of element i within Δt The following relationship is satisfied: Among them, Δx represents the horizontal distance between two adjacent nodes, L j represents the interface length between node j and node j+1, A 1 Represents the area of ​​1 node; D i represents the diffusion coefficient of element i in the solid phase; and Represent the solute content of element i at 2 nodes and 1 node respectively.

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