Method for Dynamically Predicting Tensile Properties of Superalloys Based on Grain Size Variation

Abstract

The present invention relates to a method for dynamically predicting the tensile properties of superalloys based on grain size changes, including the steps of establishing a relationship model between the γ-phase grain size of superalloys and the solution treatment process parameters of superalloys, establishing the relationship between the tensile properties of superalloys and the heat treatment process parameters of superalloys, and establishing a neural network model of the heat treatment process parameters, γ-phase grain size and tensile properties of the superalloys. The present invention has established a theoretical calculation formula for the γ-phase grain size of superalloys considering the influence of the initial γ-phase grain size D0, temperature and time. When establishing the tensile property prediction model, the dynamic evolution of the microstructure parameters is used as the input of the Pi-sigma fuzzy neural network model, and a neural network model for mapping the relationship among the heat treatment process parameters, microstructure and tensile properties of superalloys is constructed, so as to realize the prediction of the tensile properties of superalloys according to the heat treatment process parameters and microstructure, which is not available in other methods.

Description

Technical Field

[0001] The present invention relates to the field of heat treatment of metal materials, and particularly to a method for predicting the tensile properties of superalloys. Background Art

[0002] Heat treatment is an important means to regulate the microstructure of superalloys and improve the alloy properties. Different heat treatment processes can obtain different γ-phase grain sizes, strengthening phase morphologies and quantities, and different microstructures have an important influence on the tensile properties of materials. Therefore, it is necessary to establish a microstructure-property prediction model of the material to obtain the mapping relationship between the heat treatment process parameters, microstructure and tensile properties of superalloys, so as to optimize the heat treatment parameters to achieve the purpose of accurately regulating the microstructure properties.

[0003] The literature "Prediction of Mechanical Properties of TC4 Alloy by HIP Heat Treatment Using BP Artificial Neural Network, Cheng Jiahao, Jin Shuzheng, Du Xiaoyi, etc., World Nonferrous Metals, 2020, 552(12): 156-157." discloses a method for predicting the tensile strength and elongation of materials under hot isostatic pressing heat treatment based on a BP artificial neural network model. This method takes the temperature, holding time and pressure of hot isostatic pressing heat treatment as input parameters, establishes a three-layer neural network model including an input layer, a hidden layer and an output layer, and predicts the tensile strength and elongation of the alloy after hot isostatic pressing heat treatment with high precision. However, in the modeling process, the literature only considers the influence of heat treatment process parameters on tensile properties, and does not consider the influence of the dynamic evolution of the material microstructure during heat treatment on tensile properties. However, as Figure 1 shown, the γ-phase grain size of superalloys will change significantly during heat treatment. Especially when the solution temperature is close to the solvus temperature of the γ' phase, the dissolution of the γ' phase will cause the γ-phase grain size to coarsen significantly, and finally the tensile properties of the alloy will be significantly reduced. Therefore, the modeling method in the literature cannot identify the microstructure evolution of the material, nor can it predict the tensile properties of the alloy according to the processing parameters and microstructure, nor can it dynamically predict the mapping relationship among the heat treatment process parameters, microstructure and tensile properties, which has great limitations. Summary of the Invention

[0004] The purpose of the present invention is to avoid the deficiencies of the prior art. Aiming at the complex evolution of the γ-phase grain size during the heat treatment of superalloys, and the material characteristics that this evolution has a significant impact on the tensile properties, a calculation formula for the γ-phase grain growth during the heat treatment of superalloys is established based on heat treatment process experiments and tissue quantitative results, and a neural network relationship model between heat treatment process parameters, microstructure parameters and the tensile properties of superalloys is established, and finally a method for dynamically predicting the tensile properties of superalloys based on grain size change is provided, which can predict the tensile properties of superalloys.

[0005] To achieve the above object, the technical solution adopted by the present invention is as follows: A method for dynamically predicting the tensile properties of superalloys based on grain size changes, comprising the following steps:

[0006] Step 1: Establish a relationship model between the γ-phase grain size of the superalloy and the solution treatment parameters of the superalloy.

[0007] The superalloy is solution-treated at different solution temperatures and solution times, and the γ-phase grains of the solution-treated superalloy specimens are quantitatively analyzed by metallography, so as to obtain the experimental values of the γ-phase grain size after solution treatment at different solution temperatures and solution times, and thus establish a correspondence table between the solution temperature, solution time and the γ-phase grain size of the superalloy; Then, based on the Anelli model, a mathematical model between the initial size of the γ-phase grains of the superalloy, the γ-phase grain size after solution treatment, the solution temperature and the solution time is established, expressed as model formula (1):

[0008]

[0009] In the formula, D0 and D t are the initial grain size of the γ-phase and the γ-phase grain size after solution treatment, respectively, with the unit of μm; t is the solution time, with the unit of min; T is the solution temperature, with the unit of K; Q is the diffusion activation energy, with the unit of kJ·mol -1 ; R is the gas constant, which is 8.3145 J·mol -1 ·K -1 ; n is the γ-phase grain growth index, m is the time index, and A is the alloy material parameter;

[0010] That is, a relationship model of the influence of the solution temperature and solution time on the γ-phase grain size of the superalloy is obtained;

[0011] Step 2: Establish the relationship between the tensile properties of the superalloy and the heat treatment process parameters of the superalloy.

[0012] The solution-treated superalloy specimens described in Step 1 are subjected to a tensile test, so as to establish a correspondence table of the tensile properties of the superalloy after solution treatment at different solution temperatures and solution times, that is, to obtain the influence law of the solution temperature and solution time on the tensile properties of the superalloy.

[0013] Step 3: Establish a neural network model of the heat treatment process parameters, γ-phase grain size and tensile properties of the superalloy:

[0014] Based on the relationships established in Step 1 and Step 2 respectively and using the hybrid Pi-sigma fuzzy neural network model, a neural network model is established with the solution temperature, solution time, and γ-phase grain size as the model inputs, and the yield strength, tensile strength, elongation, and reduction of area of the superalloy in tension as the model outputs. That is, the mapping relationship among the γ-phase grain size of the superalloy, the heat treatment process parameters of the superalloy, and the tensile properties of the superalloy is obtained, and the dynamic prediction of the tensile properties of the superalloy based on the change of grain size is realized.

[0015] Further, it also includes the optimization steps for the alloy material parameters in the model formula (1):

[0016] a) Transpose the model formula (1) and take the logarithm of both ends to obtain the quantitative model formula (3):

[0017]

[0018] In the quantitative model formula (3), select at least six numbers from 0 to 6 as the initial values of the γ-phase grain growth index n. Substitute each initial value of the γ-phase grain growth index n, the initial γ-phase grain size value in the corresponding table in Step 1, the experimental value of the γ-phase grain size after solution treatment, and the solution time t value into the quantitative model formula (3), and then obtain the alloy material parameter lnA, time index m, and diffusion activation energy Q values corresponding to each initial value of the γ-phase grain growth index n through the multiple linear regression method;

[0019] b) Substitute the alloy material parameter lnA, γ-phase grain time index m, and diffusion activation energy Q values corresponding to each initial value of the γ-phase grain growth index n obtained in Step a) into the model formula (1), so as to obtain the calculated value of the γ-phase grain size after solution treatment at different solution temperatures and solution times; Take the average relative error between the experimental value and the calculated value of the γ-phase grain size after solution treatment in Step 1 as the objective function AARE, and its expression is formula (4):

[0020]

[0021] In the formula, N is the number of groups of solution treatment experiments, E i is the experimental value of the γ-phase grain size after solution treatment, C i is the calculated value of the γ-phase grain size after solution treatment;

[0022] c) Calculate the objective function AARE corresponding to each γ-phase grain growth index n value, establish the relationship between the objective function AARE and the γ-phase grain growth index n value through polynomial fitting, and find the minimum value of the fitted polynomial, that is, obtain the γ-phase grain growth index n value when the average relative error is the smallest;

[0023] Substitute the value of the γ-phase grain growth index \(n\) when the average relative error is minimized into the quantitative model formula (3) described in step b), and repeat step b), then the alloy material parameters \(\ln A\), the γ-phase grain time index \(m\), and the diffusion activation energy \(Q\) corresponding to the value of \(n\) when the average relative error is minimized can be obtained; and substitute the alloy material parameters \(\ln A\), the γ-phase grain time index \(m\), the diffusion activation energy \(Q\), and the γ-phase grain growth index \(n\) at this time as the final corresponding relationship parameters into the model formula (1) to obtain the predicted value of the γ-phase grain size after solution treatment, that is, accurately obtain the relationship model between the solution temperature and solution time and the γ-phase grain size of the superalloy, ensuring the accurate prediction of the γ-phase grain size after solution treatment with different solution temperatures and solution times by the model formula (1).

[0024] Furthermore, it also includes the step of verifying the accuracy of the predicted value of the γ-phase grain size after solution treatment calculated by the model formula (1):

[0025] Take the average relative error between the predicted value of the γ-phase grain size after solution treatment and the experimental value of the γ-phase grain size after solution treatment as the objective function \(ARE\) and the correlation coefficient \(R\) as the measurement index of the model prediction accuracy. The calculation formulas are shown in formulas (5) and (6) respectively:

[0026]

[0027]

[0028] In the formula, \(N\) is the number of groups of solution treatment experiments, \(E\) i is the experimental value of the γ-phase grain size after solution treatment, and \(C\) i is the predicted value of the γ-phase grain size after solution treatment; the smaller the value of the objective function \(ARE\) calculated by the formulas (5) and (6) and the closer the value of \(R\) is to 1, the higher the accuracy of the prediction of the γ-phase grain size after solution treatment, and the verification of the calculation accuracy of the γ-phase grain size after solution treatment by the model formula (1) is realized.

[0029] Furthermore, in step one, at least 5 - 20 groups of solution treatments with solution temperatures and solution times are carried out, and the corresponding relationship values of the solution temperature, solution time, and the γ-phase grain size of the superalloy are obtained. Select 5 - 10 groups of corresponding relationship values as the experimental values of the γ-phase grain size after solution treatment, and the remaining groups of corresponding relationship values are used to verify the accuracy of the predicted value of the γ-phase grain size after solution treatment.

[0030] Furthermore, the neural network model specifically established in step three at least includes the following parts:

[0031] The input layer of the neural network model. The three input parameters included in the input layer are: solution temperature T, in °C, solution time t, in min, and γ-phase grain size d, in μm.

[0032] The middle layer of the neural network model. The said middle layer includes the second to fifth layers of the model.

[0033] The second layer is to normalize the parameters input by the input layer. Then, the input parameters are divided into three fuzzy intervals UL, UM, and US as three fuzzy variables respectively. The activation functions of each fuzzy interval all adopt the Gaussian function expression (2).

[0034]

[0035] In the formula, x j is the input value, and are the mean and variance of the activation function respectively.

[0036] Then, the initial activation function expressions of the three input parameters in different fuzzy intervals are as follows:

[0037] For the solution temperature:

[0038]

[0039]

[0040]

[0041] In the formula, T min is the lower limit of the solution temperature; T median is the middle value of the solution temperature; T max is the upper limit of the solution temperature, and their units are all °C;

[0042] For the solution time:

[0043]

[0044]

[0045]

[0046] In the formula, t min is the lower limit of the solution time; t median is the middle value of the solution time; t max is the upper limit of the solution time, and their units are all min;

[0047] For the γ-phase grain size:

[0048]

[0049]

[0050]

[0051] where d min is the lower limit of the γ-phase grain size; d median is the median value of the γ-phase grain size; d max is the upper limit of the γ-phase grain size, and their units are all μm;

[0052] The third layer assigns a set of fuzzy rules to the three input parameters input from the second layer. After different interval divisions, they are linearly combined again through the activation function to obtain the output y of the middle layer i and the weight w of the fuzzy rule i ;

[0053] The fourth layer is the multiplication operation layer in the Pi-sigma fuzzy neural network, which performs a multiplication operation on the output of the third layer. Then the output value q i of this layer is the product of the output y i of the middle layer and the weight w i of the fuzzy rule. Its node output function is:

[0054]

[0055] where [x1, x2…x n are the input parameters, μ i is the activation function, and p i is the weight vector;

[0056] The fifth layer is the summation operation layer in the Pi-sigma fuzzy neural network, which performs a summation operation on the output of the fourth layer; then its node output function s i is:

[0057]

[0058] It also includes the output layer of the neural network. The output layer represents the final output of the fuzzy neural network as the weighted average of the output node output function s i of the middle layer according to the operation method of the Takagi-Sugeno fuzzy system. The expression of the final output value Y is:

[0059]

[0060] where m is the number of fuzzy rules, x = [x1, x2…x n are the input parameter values, y i is the output of the middle layer, p i is the weight vector, and wi is the weight of the fuzzy rule, μ i is the activation function; that is, the mapping relationship between the grain size of the γ-phase of the superalloy, the heat treatment process parameters of the superalloy, and the tensile properties of the superalloy is obtained, and the prediction of the grain size of the γ-phase of the superalloy and the heat treatment process parameters of the superalloy on the tensile properties of the superalloy is realized.

[0061] Further, the obtaining of the output y of the intermediate layer i and the weight w i The specific fuzzy rules involved in the steps are as follows:

[0062] R 1 : If x1 is UL, x2 is UL, …, x n is UL,

[0063] Then

[0064]

[0065] …

[0066] R m : If x1 is US, x2 is US, …, x n is US,

[0067] Then

[0068]

[0069] In the formula, m is the number of fuzzy rules, x = [x1, x2 … x n is the input parameter, and the vector p i is the weight vector in the process of linearly combining the input values to obtain the output y of the intermediate layer i , w i is the weight, μ i is the activation function described above.

[0070] Further, the initial activation function expressions of the three input parameters in different fuzzy intervals are as follows:

[0071] Taking the solution temperature as 1100 °C to 1165 °C, the initial activation function expression of the solution temperature is:

[0072]

[0073]

[0074]

[0075] Taking the solution treatment time as 30 - 240 min, the initial activation function expression of the solution treatment time is as follows:

[0076]

[0077]

[0078]

[0079] According to the test results, the γ-phase grain size range is 4.0 - 87.8 μm, and the initial activation function expression of the γ-phase grain size is as follows:

[0080]

[0081]

[0082]

[0083] Furthermore, in the second step, there are at least 15 - 30 sets of corresponding relationship values of solution treatment temperature, solution treatment time and the tensile properties of the superalloy.

[0084] Furthermore, it also includes selecting at least 10 sets from the corresponding relationship table of the tensile properties of the superalloy established in the second step under different solution treatment temperatures and solution treatment times as teacher samples for training, and using the yield strength, tensile strength, elongation and reduction of area data of the remaining corresponding groups as non-sample data to verify the neural network model established in the third step. During the training process, the error backpropagation algorithm is used to optimize the weight vectors, weights and intermediate layer outputs in the above neural network model to obtain the prediction model with the highest accuracy.

[0085] Furthermore, the superalloy is GH4175.

[0086] The beneficial effects of the present invention are as follows: Before constructing the correlation relationship between the heat treatment process parameters and the tensile properties of the superalloy, a theoretical calculation formula for the γ-phase grain size of the superalloy considering the influence of the initial γ-phase grain size D0, temperature and time is established, which can dynamically predict the quantitative relationship between the heat treatment process parameters and the microstructure parameters of the superalloy, reflect the evolution history of the microstructure under different heat treatment process parameters, and when establishing the tensile property prediction model, the dynamic evolution of the microstructure parameters is used as the input of the Pi-sigma fuzzy neural network model, and then the influence of the evolution of the microstructure parameters on the tensile properties can be reflected. On the basis of these two models, a neural network model for the mapping relationship among the heat treatment process parameters, microstructure and tensile properties of the superalloy can be further constructed, so as to realize the prediction of the tensile properties of the superalloy according to the heat treatment process parameters and microstructure, which is not possessed by other methods. Description of the Drawings

[0087] Figure 1 It is a diagram showing the influence of the solution treatment process parameters of the present invention on the microstructure of GH4175 alloy;

[0088] Figure 2 It is a comparison diagram between the experimental values and calculated values of the γ-phase grain size of GH4175 alloy in the experimental example of the present invention;

[0089] Figure 3 It is a structure diagram of the tensile property prediction fuzzy neural network established by the present invention. Detailed Embodiments

[0090] The principles and features of the present invention will be described below with reference to the accompanying drawings. The examples given are only for explaining the present invention and are not intended to limit the scope of the present invention.

[0091] To achieve the above object, the present invention provides the following detailed embodiments:

[0092] Example 1: A method for dynamically predicting the tensile properties of superalloys based on grain size changes, comprising the following steps:

[0093] 1) Solution-treat the superalloy at different solution temperatures and solution times, and perform metallographic quantification on the γ-phase grains of the solution-treated superalloy specimens, so as to obtain the experimental values of the γ-phase grain sizes after solution treatment at different solution temperatures and solution times, and thus establish a correspondence table between the solution temperature, solution time and the γ-phase grain size of the superalloy;

[0094] 2) Based on the Anelli model, establish a corresponding calculation model between the initial size of the γ-phase grains of the superalloy, the size of the γ-phase grains after solution treatment, the solution temperature and the solution time, expressed as model formula (1):

[0095]

[0096] In the formula, D0 and D t are respectively the initial size of the γ-phase grains and the size of the γ-phase grains after solution treatment with a duration of t, in μm; t is the solution time, in min; T is the solution temperature, in K; Q is the diffusion activation energy, in kJ·mol -1 ; R is the gas constant, which is 8.3145 J·mol -1 ·K -1 ; n is the γ-phase grain growth index, m is the time index, and A is the alloy material parameter;

[0097] 3) Transpose model formula (1) and take the logarithm of both ends to obtain quantitative model formula (3):

[0098]

[0099] In the quantitative model formula (3), at least six numbers are selected from 0 to 6 as the initial value of the γ-phase grain growth index n. Substitute each initial value of the γ-phase grain growth index n, the initial γ-phase grain size value obtained from the corresponding table in step 1, the experimental value of the γ-phase grain size after solution treatment, and the solution time t value into the quantitative model formula (3). Then, the alloy material parameters lnA, time index m, and diffusion activation energy Q values corresponding to each initial value of the γ-phase grain growth index n are obtained through the multiple linear regression method.

[0100] 4) Substitute the alloy material parameters lnA, γ-phase grain time index m, and diffusion activation energy Q values corresponding to each initial value of the γ-phase grain growth index n obtained in step 3) into the model formula (1), so as to calculate the calculated value of the γ-phase grain size after solution treatment at different solution temperatures and solution times; Take the average relative error between the experimental value and the calculated value of the γ-phase grain size after solution treatment described in step 1 as the objective function AARE, and its expression is formula (4):

[0101]

[0102] In the formula, N is the number of groups of the corresponding table of the solution temperature and solution time and the γ-phase grain size of the superalloy, E i is the experimental value of the change size of the γ-phase grain, C i is the calculated value of the γ-phase grain size after solution treatment;

[0103] 5) Calculate the objective function AARE corresponding to each value of the γ-phase grain growth index n. Establish a corresponding relationship list between the objective function AARE and the value of the γ-phase grain growth index n through polynomial fitting. Take the minimum value of the fitted polynomial to obtain the value of the γ-phase grain growth index n when the average relative error is the smallest; Substitute the value of the γ-phase grain growth index n when the average relative error is the smallest into the quantitative model formula (3) described in step 3), and repeat step 3), that is, obtain the alloy material parameters lnA, γ-phase grain time index m, and diffusion activation energy Q values corresponding to the n value when the average relative error is the smallest; And substitute the alloy material parameters lnA, γ-phase grain time index m, and diffusion activation energy Q values and the γ-phase grain growth index n value at this time as the final corresponding relationship parameters into the model formula (1) to obtain the predicted value of the γ-phase grain size after solution treatment, that is, accurately obtain the corresponding relationship between the solution temperature and solution time and the γ-phase grain size of the superalloy, ensuring the accurate prediction of the γ-phase grain size after solution treatment at different solution temperatures and solution times by the model formula (1).

[0104] Substitute the value of the γ-phase grain growth index n when the average relative error is the smallest into the quantitative model formula (3) described in step 3), and repeat step 3), that is, obtain the alloy material parameters lnA, γ-phase grain time index m, and diffusion activation energy Q values corresponding to the n value when the average relative error is the smallest; And substitute the alloy material parameters lnA, γ-phase grain time index m, and diffusion activation energy Q values and the γ-phase grain growth index n value at this time as the final corresponding relationship parameters into the model formula (1) to obtain the predicted value of the γ-phase grain size after solution treatment, that is, accurately obtain the corresponding relationship between the solution temperature and solution time and the γ-phase grain size of the superalloy, ensuring the accurate prediction of the γ-phase grain size after solution treatment at different solution temperatures and solution times by the model formula (1).

[0105] In the established corresponding table of solution temperature and solution time and the γ-phase grain size of the superalloy, that is, in step 1), at least 5-20 sets of corresponding relationship values of solution temperature and solution time and the γ-phase grain size of the superalloy are included, and 5-10 sets of corresponding relationship values are selected as the test values of the γ-phase grain size after solution treatment.

[0106] 6) Verify the prediction accuracy of the γ-phase grain size after solution treatment calculated by the model formula (1).

[0107] Take the average relative error between the predicted value of the γ-phase grain size after solution treatment and the test value of the γ-phase grain size after solution treatment as the objective function ARE and the correlation coefficient R as the measurement index of the model prediction accuracy. The calculation formulas are shown in formulas (5) and (6) respectively:

[0108]

[0109]

[0110] In the formula, N is the number of groups of solution treatment tests, E i is the test value of the γ-phase grain size after solution treatment, and C i is the predicted value of the γ-phase grain size after solution treatment; the smaller the value of the objective function ARE and the closer the value of R is to 1 calculated by the formulas (5) and (6), the higher the prediction accuracy of the γ-phase grain size after solution treatment, and the verification of the calculation accuracy of the γ-phase grain size by the model formula (1) is realized.

[0111] In the established corresponding table of solution temperature and solution time and the γ-phase grain size of the superalloy, at least 5-20 sets of corresponding relationship values of solution temperature and solution time and the γ-phase grain size of the superalloy are included. Select 5-10 sets of corresponding relationship values as the test values of the γ-phase grain size after solution treatment, and the corresponding relationship values of the remaining groups are used to verify the prediction accuracy of the γ-phase grain size after solution treatment.

[0112] That is, a relationship model between the γ-phase grain size of the superalloy and the solution process parameters of the superalloy is established, and an accurate corresponding relationship between the solution temperature, solution time and the γ-phase grain size of the superalloy is obtained.

[0113] 7) Perform a tensile test on the solution-treated superalloy specimen described in step 1) to establish a tensile property correspondence table of the superalloy at different solution temperatures and solution times, that is, obtain the correspondence between the solution temperature, solution time and the tensile properties of the superalloy, namely, establish the relationship between the tensile properties of the superalloy and the heat treatment process parameters of the superalloy; the established tensile property correspondence table of the superalloy at different solution temperatures and solution times includes at least 15 - 30 sets of correspondence values of the solution temperature, solution time and the tensile properties of the superalloy.

[0114] 8), Based on the correspondence between the γ-phase grain size, tensile properties of the superalloy specimen obtained in steps 1) - 7) and the solution temperature and solution time, a neural network model with the solution temperature, solution time and γ-phase grain size as the model inputs and the yield strength, tensile strength, elongation and reduction of area of the superalloy tensile as the model outputs is established based on the hybrid Pi-sigma fuzzy neural network model, that is, the mapping relationship between the γ-phase grain size of the superalloy, the heat treatment process parameters of the superalloy and the tensile properties of the superalloy is obtained, and the dynamic prediction of the tensile properties of the superalloy based on the change of grain size is realized.

[0115] The established neural network model specifically includes the following parts:

[0116] The input layer of the neural network model, the three input parameters included in the input layer are: solution temperature T, unit: °C, solution time t, unit: min, and γ-phase grain size d, unit: μm;

[0117] The middle layer of the neural network model, the middle layer includes the second to fifth layers of the model;

[0118] The second layer is to normalize the parameters input to the input layer, and then divide the input parameters into three fuzzy intervals UL, UM and US as three fuzzy variables respectively, and the activation functions of each fuzzy interval all adopt the Gaussian function expression (2);

[0119]

[0120] In the formula, x j is the input value, and are the mean and variance of the activation function respectively;

[0121] Then, the initial activation function expressions of the three input parameters in different fuzzy intervals are as follows:

[0122] For the solution temperature:

[0123]

[0124]

[0125]

[0126] Wherein T min is the lower limit of the solution temperature; T median is the intermediate value of the solution temperature; T max is the upper limit of the solution temperature, and their units are all °C;

[0127] For the solution time:

[0128]

[0129]

[0130]

[0131] Wherein t min is the lower limit of the solution time; t median is the intermediate value of the solution time; t max is the upper limit of the solution time, and their units are all min;

[0132] For the γ-phase grain size:

[0133]

[0134]

[0135]

[0136] Wherein d min is the lower limit of the γ-phase grain size; d median is the intermediate value of the γ-phase grain size; d max is the upper limit of the γ-phase grain size, and their units are all μm;

[0137] The third layer mentioned above gives a set of fuzzy rules to the three input parameters input by the second layer, and after different interval divisions, it is linearly recombined through the activation function mentioned above to obtain the output y of the intermediate layer i and the weight w of the fuzzy rule i ;

[0138] The fourth layer mentioned above is the multiplication operation layer in the Pi-sigma fuzzy neural network, which performs a multiplication operation on the output of the third layer. Then the output value q i of this layer is the product of the output y i of the intermediate layer and the weight w i of the fuzzy rule, and its node output function is:

[0139]

[0140] In the formula, [x1, x2…x n are input parameters, μ i is the activation function, p i is the weight vector;

[0141] The fifth layer mentioned above is the summation layer in the Pi-sigma fuzzy neural network, which performs a summation operation on the output of the fourth layer; then its node output function s i is:

[0142]

[0143] It also includes the output layer of the neural network. The output layer represents the final output of the fuzzy neural network as the weighted average of the output node output function s i of the middle layer according to the operation method of the Takagi-Sugeno fuzzy system. The expression of the final output value Y is:

[0144]

[0145] In the formula, m is the number of fuzzy rules, x = [x1, x2…x n is the input parameter value, y i is the output of the middle layer, p i is the weight vector, w i is the weight of the fuzzy rule, μ i is the activation function; that is, the mapping relationship between the γ-phase grain size of the superalloy, the heat treatment process parameters of the superalloy, and the tensile properties of the superalloy is obtained, and the prediction of the γ-phase grain size of the superalloy and the heat treatment process parameters of the superalloy on the tensile properties of the superalloy is realized.

[0146] The specific fuzzy rules involved in the step of obtaining the output y i of the middle layer and the weight w i are as follows:

[0147] R 1 : If x1 is UL, x2 is UL,…,x n is UL

[0148] Then

[0149]

[0150] …

[0151] R m : If x1 is US, x2 is US,…,x n is US

[0152] Then

[0153]

[0154] In the formula, m is the number of fuzzy rules, x = [x1, x2... x n is the input parameter, and the vector p i is the weight vector in the process of linearly combining the input values to obtain the output y of the middle layer i , w i is the weight value, and μ i is the activation function described above.

[0155] 9) Select at least 10 groups from the corresponding relationship table of the tensile properties of the superalloy at different solution temperatures and solution times established in step 7) as the teacher samples for training, and use the yield strength, tensile strength, elongation and reduction of area data of the remaining corresponding groups as non-sample data to verify the neural network model established in step 8). During the training process, the error backpropagation algorithm is used to optimize the weight vector, weight value and the output of the middle layer in the above neural network model to obtain the prediction model with the highest accuracy.

[0156] Experimental example: Taking the prediction model of the tensile strength of GH4175 alloy at 750 °C as an example, the content of the present invention is described in more detail. The described examples are only part of the examples of the present invention, not all examples. Other examples obtained based on the method described in the present invention also belong to the scope of protection of the present invention.

[0157] First, the solution and aging process experiments of the superalloy were carried out, and combined with the quantitative metallography technology, the influence of the solution temperature and solution time on the grain size of the γ-phase of the superalloy was studied, and a theoretical calculation formula for the grain size of the γ-phase of the superalloy considering the influence of the initial γ-phase grain size D0, temperature and time was established. Then, the tensile strength data was collected through the tensile test at 750 °C, and a prediction fuzzy neural network model of the tensile strength was established.

[0158] Through heat treatment experiments and microstructure quantification, the change law of the γ-phase grain size at a solution temperature of 1120 °C to 1160 °C and a solution time of 15 min to 120 min was obtained. Based on the Anelli model, considering the influence of the initial γ-phase grain size D0, temperature and time, a theoretical calculation formula for the grain size of the γ-phase of the superalloy was established, and the grain growth behavior was expressed as:

[0159]

[0160] In the formula, t is the solution time (min); D tis the grain size (μm) of γ-phase at solution time t; D0 is the initial grain size (μm) of γ-phase; T is the solution temperature (K); Q is the diffusion activation energy (kJ·mol -1 ); R is the gas constant (8.3145 J·mol -1 ·K -1 ); n, m and A are material parameters.

[0161] By transposing Equation (3) and taking the logarithm of both sides, it can be expressed as:

[0162]

[0163] By obtaining the values of the parameters in the equation through quantitative results, when the parameter n is from 0 to 6, the relationship between ln(D t -D0) and lnt and 1000 / RT during solution treatment of GH4175 alloy at 1120 °C to 1150 °C was determined. Substituting the experimental values of D t , D0 and t, the values of lnA, m and Q were obtained through multiple linear regression.

[0164] After determining the values of lnA, m and Q under different n values, with the minimum average relative error between the calculated value and the experimental value of the γ-phase grain size as the objective function, the relationship between the average relative error and the n value was determined through polynomial fitting, and the n value when the average relative error was the smallest was 1.6.

[0165] In the same way, the calculation formula for the grain size at a solution temperature of 1150 °C to 1160 °C can be obtained. The calculation formula for the average relative error is as follows:

[0166]

[0167] Table 1 is the corresponding table of the influence of solution process parameters on the γ-phase grain size of GH4175 alloy, and Table 2 is the table of material parameters in the theoretical calculation equation of the γ-phase grain size of GH4175 alloy. Figure 2 The comparison between the experimental value and the calculated value of the γ-phase grain size is shown. The maximum relative error of the obtained theoretical calculation formula is 15.5%, and the average relative error is 7.0%, indicating that the prediction accuracy of this theoretical calculation formula is relatively high and can accurately predict the γ-phase grain size at a solution temperature of 1120 °C to 1160 °C and a solution time of 15 min to 120 min.

[0168] Table 1 Influence of solution process parameters on the γ-phase grain size of GH4175 alloy (μm)

[0169]

[0170] Table 2 Material parameters in the theoretical calculation equation of the γ-phase grain size of GH4175 alloy

[0171]

[0172]

[0173] Through the tensile test at 750 °C, 15 groups of tensile property data under different solution temperatures and solution times were obtained. The test results show that when the solution temperature is higher than 1150 °C, the strength and plasticity of the alloy are significantly reduced. This is mainly because the re-solution of the γ′ phase will cause significant coarsening of the γ-phase grain size. When establishing the tensile property prediction model, only considering the influence of process parameters cannot dynamically predict the mapping relationship among heat treatment process parameters, microstructure, and tensile properties. Therefore, the present invention combines the theoretical calculation formula of the γ-phase grain size and uses the γ-phase grain size as the model input.

[0174] The fuzzy neural network structure of the present invention is as Figure 3 shown. The three input parameters of the first layer of the fuzzy neural network are the solution temperature (T, °C), solution time (t, min), and γ-phase grain size (d, μm). The second layer normalizes the input parameters to determine the division of the fuzzy subsets of the input variables and the corresponding activation functions. The ranges of the solution temperature, solution time, and γ-phase grain size of the GH4175 alloy of the present invention are 1100 - 1165 °C, 30 - 240 min, and 4.0 - 87.8 μm, respectively. Then the three fuzzy variables are respectively divided into three intervals UL, UM, and US, and the activation functions of each fuzzy interval are all taken as Gaussian functions. The initial activation function expressions of the three variables in different fuzzy intervals are as follows:

[0175] For the solution temperature:

[0176]

[0177]

[0178]

[0179] For the solution time:

[0180]

[0181]

[0182]

[0183] For the γ-phase grain size:

[0184]

[0185]

[0186]

[0187] The third layer linearly combines the parameters input from the previous layer again through an activation function after dividing them into different intervals according to the given fuzzy rules. The fourth layer is the multiplication operation layer in the Pi-sigma fuzzy neural network, and the fifth layer corresponds to the summation operation layer in the Pi-sigma fuzzy neural network, which performs a summation operation on the output of the previous layer. The sixth layer represents the final output of the fuzzy neural network with the weighted average value of the output of the middle layer according to the operation method of the Takagi-Sugeno fuzzy system.

[0188] Among the 15 groups of tensile strength test data obtained from the tensile test, 12 groups are selected as teacher samples to train the model, and the other 3 groups are used as non-sample data for model verification. The neural network is trained multiple times with different learning parameters, and finally, appropriate neural network training parameters can be determined. The learning rate and step size are taken as 2×10 -5 and 1.9×10 -4 , and the initial value of the weight is randomly assigned by the program. When the cumulative output error of all teacher samples is less than 2%, it is considered that the model has converged, and then the trained model is used to predict the 3 groups of non-sample data.

[0189] Table 3 Comparison of experimental values and predicted values of partial sample data of tensile strength of GH4175 alloy at 750℃

[0190]

[0191] Table 4 Comparison of experimental values and predicted values of non-sample data of tensile strength of GH4175 alloy at 750℃

[0192]

[0193] Table 3 shows the comparison results of experimental values and predicted values of partial sample data of tensile strength at 750℃, and its maximum relative error is 0.72%. Table 4 shows the comparison results of experimental values and predicted values of non-sample data of tensile strength at 750℃, and its maximum relative error is 3.18%.

[0194] It can be seen from this that the model has a high prediction accuracy for the tensile strength of GH4175 alloy. This method can accurately construct the mapping relationship among the heat treatment process parameters, microstructure, and tensile properties of superalloys, so as to realize the dynamic prediction of the tensile properties of superalloys.

[0195] The above are only the preferred embodiments of the present invention and are not intended to limit the present invention. Any modifications, equivalent replacements, improvements, etc. made within the spirit and principle of the present invention shall be included in the protection scope of the present invention.

Claims

1. A method for dynamically predicting the tensile properties of superalloys based on the change of grain size, characterized in that Including the following steps: Step 1: Establish a relationship model between the γ-phase grain size of the superalloy and the solution treatment process parameters of the superalloy. Subject the superalloy to solution treatment at different solution temperatures and solution times, and conduct metallographic quantification on the γ-phase grains of the superalloy specimens after solution treatment, so as to obtain the experimental values of the γ-phase grain size after solution treatment at different solution temperatures and solution times, and thus establish a correspondence table between the solution temperature, solution time and the γ-phase grain size of the superalloy. Then, based on the Anelli model, establish a mathematical model between the initial size of the γ-phase grains of the superalloy, the γ-phase grain size after solution treatment, the solution temperature and the solution time, expressed as model formula (1): That is, obtain a relationship model for the influence of the solution temperature and solution time on the γ-phase grain size of the superalloy; where, D0 and D t are the initial grain size of γ-phase and the grain size of γ-phase after solution treatment, with the unit of μm; t is the solution time, with the unit of min; T is the solution temperature, with the unit of K; Q is the diffusion activation energy, with the unit of kJ·mol -1 ; R is the gas constant, which is 8.3145 J·mol -1 ·K -1 ; n is the grain growth index of γ-phase, m is the time index, and A is the alloy material parameter; Step 2: Establish the relationship between the tensile properties of the superalloy and the heat treatment process parameters of the superalloy. Conduct a tensile test on the superalloy specimens after the solution treatment in Step 1, so as to establish a correspondence table of the tensile properties of the superalloy after solution treatment at different solution temperatures and solution times, that is, obtain the influence law of the solution temperature and solution time on the tensile properties of the superalloy; Step 3: Establish a neural network model for the heat treatment process parameters, γ-phase grain size and tensile properties of the superalloy: According to the relationships established in Step 1 and Step 2 respectively and based on the hybrid Pi-sigma fuzzy neural network model, establish a neural network model with the solution temperature, solution time and γ-phase grain size as the model inputs and the yield strength, tensile strength, elongation and reduction of area of the superalloy in tension as the model outputs, that is, obtain the mapping relationship between the γ-phase grain size of the superalloy, the heat treatment process parameters of the superalloy and the tensile properties of the superalloy, and realize the dynamic prediction of the tensile properties of the superalloy based on the change of grain size. It also includes an optimization step for the alloy material parameters in the model formula (1): a) Transpose the model formula (1) and take the logarithm of both ends to obtain the quantitative model formula (3):

2. The method for dynamically predicting the tensile properties of superalloys based on grain size change according to claim 1, characterized in that, In the quantitative model formula (3), select at least six numbers from 0 to 6 as the initial values of the γ-phase grain growth index n. Substitute each initial value of the γ-phase grain growth index n, the initial γ-phase grain size value, the experimental value of the γ-phase grain size after solution treatment and the solution time t value in the corresponding table in Step 1 into the quantitative model formula (3), and then obtain the alloy material parameter lnA, time index m and diffusion activation energy Q values corresponding to each initial value of the γ-phase grain growth index n through the multiple linear regression method; b) Substitute the alloy material parameter lnA, γ-phase grain time index m and diffusion activation energy Q values corresponding to each initial value of the γ-phase grain growth index n obtained in Step a) into the model formula (1), so as to obtain the calculated values of the γ-phase grain size after solution treatment at different solution temperatures and solution times. Take the average relative error between the experimental value and the calculated value of the γ-phase grain size after solution treatment in Step 1 as the objective function AARE, and its expression is formula (4): ​ ​ where N is the number of groups of solution treatment tests, and E i is the test value of the grain size of the γ-phase grains after the solution treatment, and C i is the calculated value of the grain size of the γ-phase grains after the solution treatment; c) Calculate the objective function AARE corresponding to each value of the γ-phase grain growth index n, establish the relationship between the objective function AARE and the γ-phase grain growth index n through polynomial fitting, and find the minimum value of the polynomial obtained by fitting, that is, obtain the value of the γ-phase grain growth index n when the average relative error is the smallest; Substitute the value of the γ-phase grain growth index n when the average relative error is the smallest into the quantitative model formula (3) in step b), and repeat step b), that is, obtain the alloy material parameters lnA, the γ-phase grain time index m, and the diffusion activation energy Q corresponding to the value of n when the average relative error is the smallest; and substitute the alloy material parameters lnA, the γ-phase grain time index m, the diffusion activation energy Q, and the γ-phase grain growth index n at this time as the final corresponding relationship parameters into the model formula (1) to obtain the predicted value of the γ-phase grain size after solution treatment, that is, accurately obtain the relationship model between the solution temperature and the solution time and the γ-phase grain size of the superalloy, ensuring the accurate prediction of the γ-phase grain size after solution treatment at different solution temperatures and solution times by the model formula (1).

3. The method for dynamically predicting the tensile properties of superalloys based on grain size changes according to claim 2, wherein It also includes the step of verifying the accuracy of the predicted value of the γ-phase grain size after solution treatment calculated by the model formula (1): Take the average relative error between the predicted value of the γ-phase grain size after solution treatment and the experimental value of the γ-phase grain size after solution treatment as the objective function ARE and the correlation coefficient R as the measurement index of the model prediction accuracy. The calculation formulas are shown in formulas (5) and (6) respectively: Where N is the number of groups of solution treatment tests, and E i is the experimental value of the γ-phase grain size after the solution treatment, and C i is the predicted value of the γ-phase grain size after the solution treatment; the smaller the value of the objective function ARE and the closer the value of R is to 1 calculated from the formulas (5) and (6) above, the higher the prediction accuracy of the γ-phase grain size after the solution treatment, and the verification of the calculation accuracy of the γ-phase grain size after the solution treatment by the model formula (1) is realized.

4. The method for dynamically predicting the tensile properties of superalloys based on grain size changes according to claim 3, wherein In step one, at least 5 - 20 groups of solution treatments of solution temperature and solution time are carried out, and the corresponding relationship values of solution temperature, solution time, and the γ-phase grain size of the superalloy are obtained. Select 5 - 10 groups of corresponding relationship values as the experimental values of the γ-phase grain size after solution treatment, and the remaining groups of corresponding relationship values are used to verify the accuracy of the predicted value of the γ-phase grain size after solution treatment.

5. The method for dynamically predicting the tensile properties of superalloys based on grain size changes according to claim 1, characterized in that The neural network model specifically established in step three includes at least the following parts: The input layer of the neural network model, and the three input parameters included in the input layer are: solution temperature T, unit: °C, solution time t, unit: min, and γ-phase grain size d, unit: μm; The middle layer of the neural network model, and the middle layer includes the second to fifth layers of the model; The second layer is to normalize the parameters input by the input layer. Then, the input parameters are divided into three fuzzy intervals UL, UM, and US as three fuzzy variables respectively, and the activation functions of each fuzzy interval all adopt the Gaussian function expression (2); where x j is the input value, and are the mean and variance of the activation function, respectively; Then, the initial activation function expressions of the three input parameters in different fuzzy intervals are as follows: For the solution temperature: where T min is the lower limit of the solution temperature; T median is the intermediate value of the solution temperature; T max is the upper limit of the solution temperature, and their units are all °C; For the solution time: where t min is the lower limit of the solution treatment time; t median is the median value of the solution treatment time; t max is the upper limit of the solution treatment time, and their units are all min; For the γ-phase grain size: where d min is the lower limit of the γ-phase grain size; d median is the median value of the γ-phase grain size; d max is the upper limit of the γ-phase grain size, and their units are all μm; The third layer mentioned above assigns a set of fuzzy rules to the three input parameters input by the second layer. After different interval divisions, they are linearly combined again through the activation function mentioned above, so as to obtain the output y of the middle layer i and the weight w of the fuzzy rule i ; The fourth layer described above is the multiplication operation layer in the Pi-sigma fuzzy neural network, which performs a multiplication operation on the output of the third layer. Then the output value q of this layer i is the output y of the intermediate layer i and the weight w of the fuzzy rule i The product of, and its node output function is: wherein, [x1, x2…x n are input parameters, μ i is an activation function, and p i is a weight vector; The fifth layer described above is the summation layer in the Pi-sigma fuzzy neural network, which performs a summation operation on the output of the fourth layer; then the node output function s i is as follows: It also includes the output layer of the neural network. The output layer is based on the operation method of the Takagi-Sugeno fuzzy system, and the weighted average of the output function s of the output nodes of the intermediate layer represents the final output of the fuzzy neural network. The expression of the final output value Y is as follows: i The weighted average represents the final output of the fuzzy neural network, and the expression of the final output value Y is: Where m is the number of fuzzy rules, x = [x1, x2... x n is the input parameter value, y i is the output of the middle layer, p i is the weight vector, w i is the weight of the fuzzy rule, μ i is the activation function; that is, the mapping relationship between the γ-phase grain size of the superalloy, the heat treatment process parameters of the superalloy, and the tensile properties of the superalloy is obtained, and the prediction of the γ-phase grain size of the superalloy and the heat treatment process parameters of the superalloy on the tensile properties of the superalloy is realized.

6. The method for dynamically predicting the tensile properties of superalloys based on grain size changes as described in claim 5, characterized in that, The obtaining of the intermediate layer output y i and the weight w i The fuzzy rules involved in the steps are specifically as follows: R 1 : If x1 is UL, x2 is UL, …, x n is UL, … R m : If x1 is US, x2 is US, …, x n is US, where m is the number of fuzzy rules, x = [x1, x2... x n is the input parameter, and the vector p i is the weight vector in the process of linearly combining the input values to obtain the output y of the middle layer i , w i is the weight value, and μ i is the activation function described above.

7. The method for dynamically predicting the tensile properties of superalloys based on grain size change according to claim 5, wherein The initial activation function expressions of the three input parameters in different fuzzy intervals are as follows: Take the solution temperature as 1100 °C - 1165 °C, then the initial activation function expression of the solution temperature is: Take the solution time as 30 - 240 min, then the initial activation function expression of the solution time is: According to the test results, the γ-phase grain size range is 4.0 - 87.8 μm, and the initial activation function expression of the γ-phase grain size is as follows:

8. The method for dynamically predicting the tensile properties of superalloys based on the change of grain size according to claim 1, characterized in that, In the second step, there are at least 15 - 30 sets of corresponding relationship values of solution temperature, solution time and tensile properties of the superalloy.

9. The method for dynamically predicting the tensile properties of superalloys based on grain size change according to claim 8, characterized in that, It also includes selecting at least 10 sets from the corresponding relationship table of the tensile properties of the superalloy at different solution temperatures and solution times established in the second step as teacher samples for training, and using the yield strength, tensile strength, elongation and reduction of area data of the remaining corresponding groups as non-sample data to verify the neural network model established in the third step. During the training process, the error backpropagation algorithm is used to optimize the weight vectors, weights and intermediate layer outputs in the above neural network model to obtain the prediction model with the highest accuracy.

10. The method for dynamically predicting the tensile properties of superalloys based on the change in grain size according to any one of claims 1-9, characterized in that, The superalloy described is GH4175.

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