A method for predicting superalloy properties based on coupled microstructural damage using ANN and UMAT

Abstract

The present invention discloses a method for predicting the performance of high-temperature alloys with coupled microstructural damage based on artificial neural networks (ANNs) and unified method for automated mechanical attribute (UMATs), which belongs to the field of high-temperature nickel-based alloy materials. The present invention establishes a constitutive model for high-temperature nickel-based alloys with coupled microstructural sequential damage. The microstructural sequential damage includes γ′ strengthening phase, γ matrix phase, carbides, creep cavities, and the like. Compared with damage variables that only consider a single damage, this constitutive model has better applicability. Furthermore, a user-defined material library (UMAT) is constructed based on the constitutive model of high-temperature nickel-based alloys with coupled microstructural sequential damage. Specifically, a neural network prediction model for microstructural damage variables is constructed based on ANNs and UMAT. The neural network prediction model for coupled microstructural damage variables is applied to the user-defined material library (UMAT) to perform finite element simulation prediction of the mechanical properties of materials with coupled microstructural damage. This method utilizes the excellent nonlinear processing capabilities of neural networks to improve the accuracy and efficiency of performance prediction for high-temperature alloys with coupled microstructural damage.

Description

Technical Field

[0001] The present invention relates to a high-temperature alloy performance prediction method based on coupled microstructure damage of an artificial neural network and a user-defined material library UMAT, and in particular to a high-temperature nickel-based alloy material performance prediction method based on a neural network and a user-defined material library UMAT, belonging to the field of high-temperature nickel-based alloy materials. Background Art

[0002] The constitutive equation of a material describes the basic information about its deformation. Traditional constitutive model construction methods rely on mathematical modeling, where regression analysis of material performance test results is performed on the model to derive the constants within the model. Traditional constitutive models fall into two categories: phenomenological models and models based on physical mechanisms. It is often impossible to describe all materials using a single constitutive equation that satisfies the range of deformation and thermodynamic parameters of these materials. Currently, a wide range of software programs are available for numerical simulation of material stress-strain responses. Abaqus, with its excellent secondary development capabilities and user subroutine design capabilities, is widely used in alloy material design. Abaqus' user material subroutine, UMAT, is one such subroutine for programming material constitutive relations. Existing constitutive modeling methods combined with finite element simulation yield low accuracy in predictive calculations, particularly in the simulation of large three-dimensional models. Furthermore, existing constitutive modeling methods limit the scope of application of the models. Due to the large and complex number of material parameters, they are difficult to control in practice.

[0003] To address these issues and considering the rapid development of neural networks in the fields of material design and performance prediction, a combination of neural network methods and numerical simulation has been applied to constitutive material modeling. This effectively addresses the limitations of constitutive modeling and the complexity of finite element simulation calculations, while also significantly improving model computational efficiency. Currently, researchers have compared the predictive capabilities of neural network constitutive models with those using mathematical methods and found that neural network constitutive models outperform mathematical models in both computational speed and prediction accuracy. Summary of the Invention

[0004] In order to solve the problems of high prediction cost, low accuracy and complex modeling process in the existing high-temperature alloy performance prediction methods, the main purpose of the present invention is to provide a coupled microstructure damage high-temperature alloy performance prediction method based on ANN and UMAT. By establishing a constitutive model of a high-temperature nickel-based alloy material with coupled microstructure time-series damage and constructing a user-defined material library UMAT based on this constitutive model, that is, constructing a neural network prediction model of microstructure damage variables based on ANN and UMAT, the neural network prediction model of the coupled microstructure damage variables is applied in the user-defined material library UMAT to perform finite element simulation prediction of the mechanical properties of materials with coupled microstructure damage, thereby improving the accuracy and efficiency of the performance prediction of high-temperature nickel-based alloys with coupled microstructure damage.

[0005] The purpose of the present invention is achieved through the following technical solutions.

[0006] The method for predicting the performance of high-temperature alloys with coupled microstructure damage based on ANN and UMAT disclosed in the present invention comprises the following steps:

[0007] Step 1: Construct the Chaboche unified viscoplastic constitutive model of high-temperature nickel-based alloys. Given the total strain rate of high-temperature nickel-based alloys Including elastic strain rate and inelastic strain rate Given the yield function F in the Chaboche viscoplastic constitutive model, this yield function F is related to stress, temperature and internal variables; given the flow law of the model, the flow law is related to the yield function F, and the inelastic strain rate in the Chaboche unified viscoplastic constitutive model is obtained. Establish the flow law of coupled micro-tissue time-series damage to characterize the effect of coupled micro-tissue time-series damage on inelastic strain rate The influence of the flow law is taken into account, and the flow law is modified to obtain the Chaboche unified viscoplastic constitutive model with coupled microstructure time-sequential damage. The prediction accuracy of the mechanical properties of high-temperature nickel-based alloys is improved by using this Chaboche unified viscoplastic constitutive model with coupled microstructure time-sequential damage. The internal variable evolution equations including isotropic hardening and kinematic hardening are respectively given. The stress, strain, strain rate, and temperature in the constitutive model are obtained through mechanical property tests, the damage variable is calculated from the results of material microstructure observation tests, and the other material parameters in the model are obtained by fitting the mechanical property test data. The mechanical property tests include monotonic tensile tests and cyclic fatigue tests.

[0008] The S11 high-temperature nickel-based alloy uses the Chaboche unified viscoplastic constitutive model, and the total strain rate expression is:

[0009]

[0010] in, is the total strain rate tensor, is the elastic strain rate tensor, Inelastic strain rate tensor.

[0011] The yield function in the S12 Chaboche viscoplastic constitutive model is related to the flow law as shown in the following equation:

[0012]

[0013] Λ=Λ(F), is a non-negative plastic multiplier, F is a function related to stress, temperature and internal variables, and the expression is:

[0014] F=J(σ ij -X ij )-R(p)-σ y

[0015] R is the scalar of isotropic hardening, which represents the stress caused by isotropic hardening, and X ij is the back stress, which represents the hardening related to the movement of the center of the yield surface, σ y is the yield stress, J(σ ij -X ij ) represents the second invariant of the effective stress deviator, which is expressed as:

[0016]

[0017] Among them, σ' ij and X' ij are σ ij and X ij Bias.

[0018] The flow law of the S13 constitutive model is expressed as follows:

[0019]

[0020] Among them, when the internal value of <·> is negative, its value is zero; M ijkl is the anisotropy matrix; K, k0, and n are temperature-dependent material parameters; and D is the damage variable for coupled microstructural temporal damage. The damage variable D includes the temporal evolution characteristics of the superalloy's γ' strengthening phase, the γ matrix phase, carbides, and creep cavities. The value of the damage variable D is calculated from microstructural observation experiments, based on the morphology and dimensions of these temporal microstructural evolutions.

[0021] The evolution equation of the S14 isotropic hardening or softening model is as follows:

[0022]

[0023] Q, b, γ and m are material parameters, Q r is the asymptotic value of R.

[0024] The S15 kinematic hardening model uses inelastic strain rate and cumulative inelastic strain rate to describe nonlinear kinematic hardening in the following form:

[0025]

[0026] k, c, a, Φ, β, r are material parameters, is the cumulative inelastic strain rate.

[0027] Step 2: Add the Chaboche unified viscoplastic constitutive model of coupled microstructure temporal damage obtained in step 1 to the user-defined material library UMAT, so as to facilitate the subsequent step 5 of calling the Chaboche unified viscoplastic constitutive model of coupled microstructure temporal damage in the finite element simulation software for finite element simulation prediction.

[0028] Preferably, the user-defined material library UMAT is a user-defined material module in Abaqus. The Chaboche unified viscoplastic constitutive model of coupled microstructure temporal damage obtained in step 1 is constructed using the user-defined material module UMAT in Abaqus / Standard, and the constructed model is added to the user-defined material library UMAT.

[0029] Step three: Construct a neural network prediction model for damage variables coupled to microstructural damage. Build a neural network framework, including an input layer, a hidden layer, and an output layer. Determine the number of nodes in each layer of the neural network. Determine the training function and transfer function of the neural network. Determine hyperparameters such as the neural network learning rate, batch size, weight initialization method, optimization algorithm, and number of iterations. Using the microstructural observation test data from step one, including the size of the high-temperature alloy γ' strengthening phase, γ matrix phase, carbide size, and creep hole size, construct a training dataset for the damage variable D. The dataset is then divided into a training set and a test set for training.

[0030] Considering that the damage variable D is a time series related variable, in order to more accurately describe the impact of time-related damage on the mechanical properties of high-temperature alloys, as a preference, the neural network uses an LSTM long short-term memory neural network. Through the time series prediction ability of the LSTM long short-term memory neural network, the model's prediction accuracy for microstructure time series damage is improved.

[0031] S31 constructs a neural network data set for training the coupled microstructure temporal damage D in the Chaboche unified viscoplastic constitutive model of coupled microstructure temporal damage obtained in step 1, and each microstructure parameter and damage variable serves as the data set of the LSTM neural network, wherein the time-varying morphological dimensions of the high-temperature alloy γ' strengthening phase, γ matrix phase, carbide, creep holes, etc. and the damage variable D are simultaneously input data, and the damage variable D is output data.

[0032] S32: Loading the training set. The data set in step S31 is used as the training data set of the neural network, with 70% of the data set used as the training set and 30% of the data set used as the test set.

[0033] S33 builds an LSTM neural network prediction model based on the Keras framework:

[0034] Forget Gate:

[0035] f t =σ(W xf x t +W hf h t-1 +b f )

[0036] Where x is the input data set of LSTM, h is the state value, W is the weight matrix, b is the bias matrix, σ represents the activation function sigmoid, and f is the forget gate.

[0037] Update Gate:

[0038] i t =σ(W xi x t +W hi h t-1 +b i )

[0039] g t =tanh(W xg x t +W hg h t-1 +b g )

[0040] Where i and g are the two function operations of the update gate, and tanh represents the activation function tanh.

[0041] Memory storage unit (i.e. memory cell): In each time step of LSTM, there is a memory cell, which selects the memory function through LSTM.

[0042] c t =c t-1 ⊙f t +g t⊙i t

[0043] Where ⊙ is the Hadamard product and c is the memory cell.

[0044] Output gate:

[0045] O t =σ(W xo x t +W ho h t-1 +b o )

[0046] m t =tanh(c t )

[0047] h t =o t ⊙m t

[0048] y t =W gh h t +b g

[0049] Where O is the output gate, m is the tanh calculation between the memory cell and the output gate, m can convert the useful memory content in the memory cell into output, and y is the output value, which is the damage variable D.

[0050] S34 compiles the LSTM neural network prediction model and defines the mean absolute error as the loss function:

[0051]

[0052] Where y i is the predicted value, x i are the true values, that is, the predicted value and actual value of the damage variable D respectively.

[0053] The neural network prediction model constructed by S35 is used to predict the material's time-series damage variables, serving as a replacement for the damage variable D in the constitutive model. The neural network-based coupled microstructure damage prediction model enables the constitutive model to better characterize the effects of various microstructure damages on the mechanical properties of high-temperature nickel-based alloys.

[0054] Step 4: Apply step 3 to the Chaboche unified viscoplastic constitutive model of coupled microstructure temporal damage in the user-defined material library UMAT, combine the given high-temperature nickel-based alloy application conditions, predict the mechanical properties of the high-temperature nickel-based alloy according to the finite element simulation software, and use the neural network prediction model to supplement the missing data in the experimental data set in step 3, thereby reducing the experimental cost of constructing the Chaboche unified viscoplastic constitutive model of coupled microstructure temporal damage; train the Chaboche unified viscoplastic constitutive model of coupled microstructure temporal damage according to the neural network constructed in step 3, and iteratively optimize the damage variable D in the Chaboche unified viscoplastic constitutive model of coupled microstructure temporal damage in the user-defined material library UMAT described in step 2, until a neural network for predicting the damage variable D is called in the trained Chaboche unified viscoplastic constitutive model of coupled microstructure temporal damage.

[0055] Preferably, the user-defined material library UMAT is a user-defined material module for the finite element simulation software Abaqus / Standard. Simulation calculations are performed using Abaqus finite element simulation software, whose secondary development capabilities make the simulation calculation process for the mechanical properties of high-temperature nickel-based alloys more flexible and applicable.

[0056] S41 applies the damage variable neural network prediction model of coupled microtissue damage in step three to the damage variable in the Chaboche unified viscoplastic constitutive model of coupled microtissue temporal damage through Python language, replacing the damage variable D in the flow law of the Chaboche unified viscoplastic constitutive model of coupled microtissue temporal damage.

[0057] S42 uses the neural network prediction model to supplement the missing data in the experimental data set in step three, trains the Chaboche unified viscoplastic constitutive model of coupled microstructure temporal damage according to the neural network constructed in step three, and iteratively optimizes the damage variable D in the Chaboche unified viscoplastic constitutive model of coupled microstructure temporal damage in the user-defined material library UMAT described in step two until a trained neural network prediction model is obtained.

[0058] Step 5: Apply the neural network trained in Step 4 for coupled microstructure temporal damage D to the user-defined material library UMAT for the Chaboche unified viscoplastic constitutive model of coupled microstructure temporal damage. Based on a given high-temperature nickel-based alloy application, the neural network generates an optimal Chaboche unified viscoplastic constitutive model for coupled microstructure temporal damage. This model can better characterize the impact of the evolution of coupled microstructure temporal damage on the mechanical properties of the alloy. Combined with finite element simulation software, the Chaboche unified viscoplastic constitutive model of coupled microstructure temporal damage is used to predict the mechanical properties of the alloy, improving the accuracy of mechanical property predictions.

[0059] Preferably, the user-defined material library UMAT is a user material subroutine module of the finite element simulation software Abaqus / Standard. This module, as a secondary development function module of Abaqus, makes the simulation calculation process of the mechanical properties of high-temperature nickel-based alloys more flexible and more applicable.

[0060] In step S51, a structural model is constructed in the Abaqus finite element simulation software, and user material parameters, boundary conditions, and load characteristics identical to those used in the actual working conditions are added. The user material parameters are the material parameters of the Chaboche unified viscoplastic constitutive model for coupled microstructure time-sequential damage, obtained based on the experimental data fit described in step 1.

[0061] S52 calls the user-defined material library UMAT of the Chaboche unified viscoplastic constitutive model of coupled microstructure temporal damage containing the trained damage variable neural network prediction model described in step 4 in the post-processing module of the Abaqus finite element simulation software to perform finite element simulation calculations.

[0062] S53 The user-defined material UMAT of the Chaboche unified viscoplastic constitutive model of coupled micro-tissue temporal damage is called at the integration point of the unit body described in step S52. When the incremental step starts, Abaqus will enter the UMAT module through the interface of the user-defined material library UMAT. The neural network of the micro-tissue temporal damage D will perform an iterative operation synchronously with each call of the user-defined material library UMAT.

[0063] The initial values ​​of the necessary variables of the current integration point of the S54 unit body, including stress, strain, strain rate and internal variables, will be passed to the corresponding variables of UMAT.

[0064] Each time Abaqus calls the user-defined material library UMAT and finishes the calculation, S55 recalculates the constant variables passed into it to obtain a new Jacobian matrix and strain increment vector and returns it to the incremental step. The incremental step then uses the equilibrium judgment equation to determine whether the result meets the judgment rules. If it meets the requirements, it enters a new incremental step until the simulation ends.

[0065] The method further includes step 6, applying the simulation prediction results of step 5 to analyze and obtain simulated predicted values ​​for the mechanical properties of the high-temperature nickel-based alloy. The methods described in steps 1 to 5 can reduce the complexity of the Chaboche unified viscoplastic constitutive model for coupled microstructural damage, improve the model's adaptability, and increase the speed and accuracy of the constitutive model's prediction of the mechanical properties of the high-temperature nickel-based alloy with coupled microstructural damage. This can also reduce the testing cost of the high-temperature nickel-based alloy.

[0066] Beneficial effects:

[0067] 1. The present invention discloses a Chaboche unified viscoplastic constitutive model for coupled microstructural damage, in which the microstructural damage includes γ' strengthening phase, γ matrix phase, carbide, creep voids, etc. Compared with the damage variable that only considers a single damage, this constitutive model has better applicability and can more accurately describe and predict the performance of high-temperature nickel-based alloy materials with coupled microstructural damage.

[0068] 2. The present invention discloses a method for predicting the mechanical properties of high-temperature nickel-based alloys based on an artificial neural network. By utilizing the excellent nonlinear processing capabilities of neural networks, the method can quickly and accurately predict the mechanical properties of high-temperature nickel-based alloys.

[0069] 3. The present invention discloses a method for predicting the mechanical properties of high-temperature nickel-based alloys based on an artificial neural network. The method is a finite element simulation calculation method embedded with a neural network prediction model. The damage variable neural network prediction model of coupled microstructure damage is applied in the user-defined material library UMAT in the Abaqus finite element simulation software. This method combines the user-defined capabilities of the finite element simulation software with the nonlinear data processing capabilities of the neural network, effectively improving the speed and accuracy of calculating the mechanical properties of high-temperature nickel-based alloys with coupled microstructure damage using the finite element simulation software. BRIEF DESCRIPTION OF THE DRAWINGS

[0070] Figure 1 Flowchart of the artificial neural network-based method for predicting the mechanical properties of high-temperature nickel-based alloys.

[0071] Figure 2 Displacement cloud diagram of constitutive model based on neural network.

[0072] Figure 3Comparison of simulation results of uniaxial tensile stress-strain curves based on neural network constitutive model. DETAILED DESCRIPTION

[0073] The embodiments of the present invention are described in further detail below with reference to the accompanying drawings and examples.

[0074] like Figure 1 As shown, the constitutive modeling method of high-temperature alloys based on coupled microstructure damage of ANN and UMAT disclosed in this embodiment is specifically implemented as follows:

[0075] Step 1: Construct the Chaboche unified viscoplastic constitutive model of high-temperature nickel-based alloys. Given the total strain rate of high-temperature nickel-based alloys Including elastic strain rate and inelastic strain rate Given the yield function F in the Chaboche viscoplastic constitutive model, this yield function F is related to stress, temperature and internal variables; given the flow law of the model, the flow law is related to the yield function F, and the inelastic strain rate in the Chaboche unified viscoplastic constitutive model is obtained. Establish the flow law of coupled micro-tissue time-series damage to characterize the effect of coupled micro-tissue time-series damage on inelastic strain rate The influence of the flow law is taken into account, and the flow law is modified to obtain the Chaboche unified viscoplastic constitutive model with coupled microstructure time-sequential damage. The prediction accuracy of the mechanical properties of high-temperature nickel-based alloys is improved by using the Chaboche unified viscoplastic constitutive model with coupled microstructure time-sequential damage. The internal variable evolution equations including isotropic hardening and kinematic hardening are respectively given. The stress, strain, strain rate, and temperature in the constitutive model are obtained through mechanical property tests. The damage variable is obtained by calculation based on the test results of material microstructure observation. The other material parameters in the model are obtained by fitting the mechanical property test data. The mechanical property tests include monotonic tensile tests and cyclic fatigue tests.

[0076] The S11 high-temperature nickel-based alloy uses the Chaboche unified viscoplastic constitutive model, and the total strain rate expression is:

[0077]

[0078] in, is the total strain rate tensor, is the elastic strain rate tensor, Inelastic strain rate tensor.

[0079] The yield function in the S12 Chaboche unified viscoplastic constitutive model is related to the flow law as shown below:

[0080]

[0081] Λ=Λ(F), is a non-negative plastic multiplier, F is a function related to stress, temperature and internal variables, and the expression is:

[0082] F=J(σ ij -X ij )-R(p)-σ y

[0083] R is the scalar of isotropic hardening, which represents the stress caused by isotropic hardening, and X ij is the back stress, which represents the hardening related to the movement of the center of the yield surface, σ y is the yield stress, J(σ ij -X ij ) represents the second invariant of the effective stress deviator, which is expressed as:

[0084]

[0085] Among them, σ' ij and X' ij are σ ij and X ij Bias.

[0086] The flow law of the S13 constitutive model is expressed as follows:

[0087]

[0088] Among them, when the internal value of <·> is negative, its value is zero; M ijkl is the anisotropy matrix; K, k0, and n are temperature-dependent material parameters; and D is the damage variable for coupled microstructural temporal damage. The microstructural damage included in the damage variable D includes the temporal evolution characteristics of the γ' strengthening phase in high-temperature nickel-based alloys, the temporal evolution characteristics of the γ matrix phase, the temporal evolution characteristics of carbides, and the temporal evolution characteristics of creep cavities. The damage variable D is calculated by microscopic observation of the morphological and dimensional characteristics of the temporal evolution of these various microstructural processes.

[0089] The evolution equation of the S14 isotropic hardening or softening model is as follows:

[0090]

[0091] Q, b, γ and m are material parameters, Q r is the asymptotic value of R.

[0092] The S15 kinematic hardening model uses inelastic strain rate and cumulative inelastic strain rate to describe nonlinear kinematic hardening in the following form:

[0093]

[0094] k, c, a, φ, β, r are material parameters, is the cumulative inelastic strain rate.

[0095] Step 2: Add the Chaboche unified viscoplastic constitutive model of coupled microstructure time-sequential damage obtained in step 1 to the user-defined material library UMAT module in Abaqus. Construct the Chaboche unified viscoplastic constitutive model of coupled microstructure time-sequential damage obtained in step 1 through the user-defined material module UMAT of Abaqus / Standard, and add the constructed model to the user-defined material library UMAT to facilitate the subsequent step 5 of calling the Chaboche unified viscoplastic constitutive model of coupled microstructure time-sequential damage in the finite element simulation software for finite element simulation prediction.

[0096] Step three: Construct a damage variable neural network prediction model for coupled microstructural damage. Considering that the damage variable D is a time-series variable, an LSTM (Long Short-Term Memory) neural network is used to predict the damage variable D to more accurately describe the impact of time-dependent damage on the mechanical properties of the superalloy. The LSTM neural network's time-series prediction capabilities improve the model's accuracy in predicting microstructural time-series damage. The LSTM neural network comprises three gating units: a forget gate, an update gate, and an output gate, as well as a memory storage unit, also known as a memory cell. The activation function of the selected neural network is determined to be either sigmoid or tanh; and hyperparameters such as the neural network learning rate, batch size, weight initialization method, optimization algorithm, and number of iterations are determined. Through the microstructural observation experiments in step one, a database of microstructural damage information for high-temperature nickel-based alloys is obtained. Microstructural damage information for high-temperature nickel-based alloys is obtained through laboratory electron microscopy observations and image digital processing and analysis software. Microstructural damage information parameters for high-temperature nickel-based alloys include the equivalent diameter of the γ' strengthening phase, the width of the γ matrix phase, the equivalent diameter of carbides, and the equivalent diameter of creep voids. The damage variable D is calculated from the microtissue damage characteristic parameters and a training data set of the damage variable D is constructed. The training data set is then divided into a training set and a test set for neural network training.

[0097] S31 constructs a neural network dataset for training the coupled microstructure temporal damage D in the Chaboche unified viscoplastic constitutive model of coupled microstructure temporal damage obtained in step 1, and each microstructure parameter and damage variable serves as the dataset of the LSTM neural network. The microstructure pre-damage treatment conditions of high-temperature nickel-based alloy materials are set based on the turbine blade overhaul time and actual operating conditions. The pre-damage time nodes are 0h, 300h, 600h, 900h and 1200h, respectively, thereby obtaining microstructure damage information data, including the morphological and dimensional evolution characteristics of the high-temperature alloy γ' strengthening phase equivalent diameter, γ matrix phase width, carbide equivalent diameter, creep hole equivalent diameter, etc. that change with the pre-damage time, and the damage variable D is used as input data, and the damage variable D is output data.

[0098] S32: Loading the training set. The data set in step S31 is used as the training data set of the neural network, with 70% of the data set used as the training set and 30% of the data set used as the test set.

[0099] S33 builds an LSTM neural network prediction model based on the Keras framework:

[0100] Forget Gate:

[0101] f t =σ(W xf x t +W hf h t-1 +b f )

[0102] Where x is the input data set of LSTM, h is the state value, W is the weight matrix, b is the bias matrix, σ represents the activation function sigmoid, and f is the forget gate.

[0103] Update Gate:

[0104] i t =σ(W xi x t +W hi h t-1 +b i )

[0105] g t =tanh(W xg x t +W hg h t-1 +b g )

[0106] Where i and g are the two function operations of the update gate, and tanh represents the activation function tanh.

[0107] Memory storage unit (i.e. memory cell): In each time step of LSTM, there is a memory cell, which selects the memory function through LSTM.

[0108] c t =c t-1 ⊙f t +g t ⊙i t

[0109] Where ⊙ is the Hadamard product and c is the memory cell.

[0110] Output gate:

[0111] O t =σ(W xo x t +W ho h t-1 +b o )

[0112] m t =tanh(c t )

[0113] h t =o t ⊙m t

[0114] y t =W gh h t +b g

[0115] Where O is the output gate, m is the tanh calculation between the memory cell and the output gate, m can convert the useful memory content in the memory cell into output, and y is the output value, which is the damage variable D.

[0116] S34 compiles the LSTM neural network prediction model and defines the mean absolute error as the loss function:

[0117]

[0118] Where y i is the predicted value, x i are the true values, that is, the predicted value and actual value of the damage variable D respectively.

[0119] The neural network prediction model constructed by S35 is used to predict the material's time-series damage variable D, serving as a proxy for the damage variable D in the constitutive model. Using the various microstructural morphological parameters and damage variable D obtained experimentally at 0h, 300h, 600h, and 900h pre-damage, the damage variable D at 1200h is predicted. The LSTM-based coupled microstructural damage neural network prediction model enables the constitutive model to better characterize the effects of various microstructural damages on the mechanical properties of high-temperature nickel-based alloys.

[0120] Step 4: Apply step 3 to the Chaboche unified viscoplastic constitutive model for coupled microstructure temporal damage in the user-defined material library UMAT module of the finite element simulation software Abaqus / Standard. The simulation calculations are performed using Abaqus finite element simulation software, whose secondary development capabilities make the simulation calculation process for the mechanical properties of high-temperature nickel-based alloys more flexible and applicable. Based on the given high-temperature nickel-based alloy application conditions, the mechanical properties of the high-temperature nickel-based alloy are predicted using the finite element simulation software. A neural network prediction model is used to supplement the missing data in the experimental dataset in step 3, reducing the experimental cost of constructing the Chaboche unified viscoplastic constitutive model for coupled microstructure temporal damage. The neural network constructed in step 3 is used to train the Chaboche unified viscoplastic constitutive model for coupled microstructure temporal damage, and the damage variable D in the Chaboche unified viscoplastic constitutive model for coupled microstructure temporal damage in the user-defined material library UMAT described in step 2 is iteratively optimized until a neural network is obtained that calls the microstructure temporal damage D in the trained Chaboche unified viscoplastic constitutive model for coupled microstructure temporal damage.

[0121] S41 applies the damage variable neural network prediction model of coupled microtissue damage in step three to the damage variable in the Chaboche unified viscoplastic constitutive model of coupled microtissue temporal damage through Python language, and uses the damage variable value at 1200h predicted by the LSTM neural network to replace the damage variable D in the flow law of the Chaboche unified viscoplastic constitutive model of coupled microtissue temporal damage.

[0122] S42 uses the LSTM neural network prediction model to supplement the missing damage variable D time series data in the experimental data set in step three, trains the Chaboche unified viscoplastic constitutive model of coupled microstructure time series damage according to the neural network constructed in step three, and iteratively optimizes the damage variable D in the Chaboche unified viscoplastic constitutive model of coupled microstructure time series damage in the user-defined material library UMAT described in step two until a trained neural network prediction model is obtained.

[0123] Step five, apply the neural network of coupled microstructure temporal damage D trained in step four to the user-defined material library UMAT module of the finite element simulation software Abaqus / Standard for the Chaboche unified viscoplastic constitutive model of coupled microstructure temporal damage. According to the given application conditions of high-temperature nickel-based alloys, the corresponding optimal Chaboche unified viscoplastic constitutive model of coupled microstructure temporal damage is given by the LSTM neural network, which can better characterize the influence of the evolution of coupled microstructure temporal damage on the mechanical properties of high-temperature nickel-based alloys. Combined with finite element simulation software, the mechanical properties of high-temperature nickel-based alloys are predicted based on the Chaboche unified viscoplastic constitutive model of coupled microstructure temporal damage, thereby improving the prediction accuracy of the mechanical properties of high-temperature nickel-based alloys. The finite element simulation calculation results using the user-defined material library UMAT embedded with the LSTM neural network are as follows. Figure 2 shown.

[0124] In step S51, a unit cell model is constructed in the Abaqus finite element simulation software, and user material parameters, boundary conditions, and load characteristics for the high-temperature nickel-based alloy are added, identical to those used in the actual operating conditions. The user material parameters are the various material parameters in the Chaboche unified viscoplastic constitutive model for coupled microstructural time-sequential damage of the high-temperature nickel-based alloy, obtained based on the experimental data fit described in step 1.

[0125] S52 calls the user-defined material library UMAT of the Chaboche unified viscoplastic constitutive model of coupled microstructure temporal damage containing the trained damage variable LSTM neural network prediction model described in step 4 in the post-processing module of the Abaqus finite element simulation software to perform finite element simulation calculations.

[0126] S53 The user-defined material UMAT of the Chaboche unified viscoplastic constitutive model of coupled micro-tissue temporal damage is called at the integration point of the unit body described in step S52. When the incremental step starts, Abaqus will enter the UMAT module through the interface of the user-defined material library UMAT module. The LSTM neural network prediction model of micro-tissue temporal damage D will perform an iterative operation synchronously with each call of the user-defined material library UMAT.

[0127] The initial values ​​of the necessary variables of the current integration point of the S54 unit body, including stress, strain, strain rate and internal variables, will be passed to the corresponding variables of UMAT.

[0128] Each time Abaqus calls the user-defined material library UMAT, S55 recalculates the constant variables passed into it to obtain a new Jacobian matrix and strain increment vector and returns it to the incremental step. The incremental step then uses the equilibrium judgment equation method to determine whether the result meets the judgment rules. If it meets the requirements, it enters a new incremental step until the end of the simulation.

[0129] Apply the simulation prediction results of step 5 to analyze and obtain the simulation prediction values ​​of the mechanical properties of high-temperature nickel-based alloys. Comparison of the stress and strain response simulation results of high-temperature nickel-based alloys with and without LSTM neural networks Figure 3 As shown in the examples, it can be seen that the method proposed in the present invention is feasible, and the method described in steps 1 to 5 can reduce the complexity of the Chaboche unified viscoplastic constitutive model for coupled microstructure time-sequential damage, improve the adaptability of the model, and improve the prediction speed and accuracy of the constitutive model for the mechanical properties of high-temperature nickel-based alloys with coupled microstructure damage, while reducing the testing cost of high-temperature nickel-based alloy materials.

[0130] The above specific description further illustrates the purpose, technical solutions and beneficial effects of the invention in detail. It should be understood that the above description is only a specific embodiment of the present invention and is not intended to limit the scope of protection of the present invention. Any modifications, equivalent substitutions, improvements, etc. made within the spirit and principles of the present invention should be included in the scope of protection of the present invention.

Claims

1. A coupled microstructure-damaged superalloy performance prediction method based on ANN and UMAT is characterized by: The following steps are included: Step 1: Construct the Chaboche unified viscoplastic constitutive model of high-temperature nickel-based alloys. Given the total strain rate of high-temperature nickel-based alloys Including elastic strain rate and inelastic strain rate Given the yield function F in the Chaboche viscoplastic constitutive model, this yield function F is related to stress, temperature and internal variables; given the flow law of the model, the flow law is related to the yield function F, and the inelastic strain rate in the Chaboche unified viscoplastic constitutive model is obtained. Establish the flow law of coupled micro-tissue time-series damage to characterize the effect of coupled micro-tissue time-series damage on inelastic strain rate The influence of the flow law is taken into account and the flow law is modified to obtain the Chaboche unified viscoplastic constitutive model coupled with the time-sequential damage of microstructures. In step one, The S11 high-temperature nickel-based alloy uses the Chaboche unified viscoplastic constitutive model, and the total strain rate expression is: in, is the total strain rate tensor, is the elastic strain rate tensor, inelastic strain rate tensor; The yield function in the S12 Chaboche viscoplastic constitutive model is related to the flow law as shown in the following equation: Λ=Λ(F), is a non-negative plastic multiplier, F is a function related to stress, temperature and internal variables, and the expression is: F=J(σ ij -X ij )-R(p)-σ y R is the isotropic hardening scalar, which represents the stress caused by isotropic hardening, and X ij is the back stress, which represents the hardening related to the movement of the yield surface center, σ y is the yield stress, J(σ ij -X ij ) represents the second invariant of the effective stress deviator, which is expressed as: Among them, σ′ ij and X′ ij are σ ij and X ij Bias; The flow law of the S13 constitutive model is expressed as follows: Among them, when the internal value of <·> is negative, its value is zero; M ijkl is an anisotropic matrix; K, k0, and n are temperature-dependent material parameters; D is the damage variable of coupled microstructural temporal damage; the microstructural damage contained in the damage variable D includes the temporal evolution of the γ′ strengthening phase of the high-temperature alloy, the temporal evolution of the γ matrix phase, the temporal evolution of carbides, and the temporal evolution of creep cavities; the value of the damage variable D is obtained by calculating the morphology and size of the above-mentioned microstructural temporal evolution through microstructural observation test observation results; The evolution equation of the S14 isotropic hardening or softening model is as follows: Q, b, γ and m are material parameters, Q r is the asymptotic value of R; The S15 kinematic hardening model uses inelastic strain rate and accumulation to describe nonlinear kinematic hardening in the following form: k, c, a, Φ, β, r are material parameters, is the cumulative inelastic strain rate; Step 2: Add the Chaboche unified viscoplastic constitutive model of coupled microstructure temporal damage obtained in step 1 to the user-defined material library UMAT, so as to facilitate the subsequent step 5 of calling the Chaboche unified viscoplastic constitutive model of coupled microstructure temporal damage in the finite element simulation software for finite element simulation prediction; Step three, construct a damage variable neural network prediction model for coupled microstructure damage and build a neural network framework; through the microstructure observation test data in step one, including the size of the γ′ strengthening phase, the size of the γ matrix phase, the size of the carbide, and the size of the creep hole of the high-temperature alloy, construct a training data set for the damage variable D, and divide the data set into a training set and a test set for training.

2. The method for predicting properties of high-temperature alloys with coupled microstructure damage based on ANN and UMAT according to claim 1, characterized in that: Step 4: Apply step 3 to the Chaboche unified viscoplastic constitutive model of coupled microstructure temporal damage in the user-defined material library UMAT, combine the given high-temperature nickel-based alloy application conditions, predict the mechanical properties of the high-temperature nickel-based alloy according to the finite element simulation software, and use the neural network prediction model to supplement the missing data in the experimental data set in step 3, thereby reducing the experimental cost of constructing the Chaboche unified viscoplastic constitutive model of coupled microstructure temporal damage; train the Chaboche unified viscoplastic constitutive model of coupled microstructure temporal damage according to the neural network constructed in step 3, and iteratively optimize the damage variable D in the Chaboche unified viscoplastic constitutive model of coupled microstructure temporal damage in the user-defined material library UMAT described in step 2, until a neural network that calls the microstructure temporal damage D in the trained Chaboche unified viscoplastic constitutive model of coupled microstructure temporal damage is obtained.

3. The method for predicting properties of high-temperature alloys with coupled microstructure damage based on ANN and UMAT according to claim 1, characterized in that: Step 5: Apply the neural network of coupled microstructure temporal damage D trained in step 4 to the user-defined material library UMAT of the Chaboche unified viscoplastic constitutive model of coupled microstructure temporal damage. According to the given application conditions of high-temperature nickel-based alloys, the corresponding optimal Chaboche unified viscoplastic constitutive model of coupled microstructure temporal damage is given by the neural network, which can better characterize the influence of the evolution of coupled microstructure temporal damage on the mechanical properties of high-temperature nickel-based alloys. Combined with finite element simulation software, the mechanical properties of high-temperature nickel-based alloys are predicted based on the Chaboche unified viscoplastic constitutive model of coupled microstructure temporal damage, thereby improving the prediction accuracy of the mechanical properties of high-temperature nickel-based alloys.

4. The method for predicting properties of high-temperature alloys with coupled microstructure damage based on ANN and UMAT according to claim 1, characterized in that: The method also includes step six, applying the simulation prediction results obtained in step five to analyze and obtain the simulation prediction values ​​of the mechanical properties of the high-temperature nickel-based alloy; using the methods described in steps one to five, the complexity of the Chaboche unified viscoplastic constitutive model of coupled microstructure time-sequential damage can be reduced, the adaptability of the model can be improved, and the prediction speed and prediction accuracy of the constitutive model for the mechanical properties of the high-temperature nickel-based alloy with coupled microstructure damage can be improved, while the testing cost of the high-temperature nickel-based alloy material can be reduced.

5. The method for predicting properties of high-temperature alloys with coupled microstructure damage based on ANN and UMAT according to claim 1, characterized in that: The user-defined material library UMAT is a user-defined material module in Abaqus. The Chaboche unified viscoplastic constitutive model of coupled microstructure temporal damage obtained in step 1 is constructed through the user-defined material module UMAT of Abaqus / Standard, and the constructed model is added to the user-defined material library UMAT.

6. The method for predicting properties of high-temperature alloys with coupled microstructure damage based on ANN and UMAT according to claim 5, characterized in that: The neural network uses an LSTM long short-term memory neural network. Through the time series prediction ability of the LSTM long short-term memory neural network, the prediction accuracy of the model for microtissue time series damage is improved. The implementation method of step three is: S31 constructs a neural network data set for training the coupled microstructure time-series damage D in the Chaboche unified viscoplastic constitutive model of coupled microstructure time-series damage obtained in step 1, wherein each microstructure parameter and damage variable serves as the data set of the LSTM neural network, wherein the morphology and size of the high-temperature alloy γ′ strengthening phase, γ matrix phase, carbide, and creep voids that change with time and the damage variable D are simultaneously input data, and the damage variable D is output data; S32 loads the training set; uses the data set in step S31 as the training data set of the neural network, 70% of the data set as the training set, and 30% of the data set as the test set; S33 builds an LSTM neural network prediction model based on the Keras framework: Forget Gate: f t =σ(W xf x t +W hf h t-1 +b f ) Where x is the input data set of LSTM, h is the state value, W is the weight matrix, b is the bias matrix, σ represents the activation function sigmoid, and f is the forget gate; Update Gate: i t =σ(W xi x t +W hi h t-1 +b i ) g t =tanh(W xg x t +W hg h t-1 +b g ) Where i and g are the two function operations of the update gate, and tanh represents the activation function tanh; Memory storage unit: In each time step of LSTM, there is a memory cell, which selects the memory function through LSTM; c t =c t-1 ⊙f t +g t ⊙i t Where ⊙ is the Hadamard product, c is the memory cell; Output gate: O t =σ(W xo x t +W ho h t-1 +b o ) m t =tanh(c t ) h t =o t ⊙m t y t =W gh h t +b g Where O is the output gate, m is the tanh calculation between the memory cell and the output gate, m can convert the useful memory content in the memory cell into output, and y is the output value, which is the damage variable D; S34 compiles the LSTM neural network prediction model and defines the mean absolute error as the loss function: Where y j is the predicted value, x j are the true values, i.e., the predicted value and actual value of the damage variable D respectively; The neural network prediction model constructed by S35 is used to predict the material's time-series damage variables as a substitute for the damage variable D in the constitutive model; the LSTM-based coupled microstructure damage neural network prediction model can enable the constitutive model to better characterize the influence of various microstructure damages on the mechanical properties of high-temperature nickel-based alloys.

7. The method for predicting properties of high-temperature alloys with coupled microstructure damage based on ANN and UMAT according to claim 6, characterized in that: The user-defined material library UMAT is a user-defined material module of the finite element simulation software Abaqus / Standard; the simulation calculation is performed using the Abaqus finite element simulation software, and the secondary development capability of the Abaqus finite element simulation software is utilized to make the simulation calculation process of the mechanical properties of the high-temperature nickel-based alloy more flexible and more applicable; the implementation method of step four is, S41 applies the damage variable neural network prediction model of coupled microtissue damage in step 3 to the damage variable in the Chaboche unified viscoplastic constitutive model of coupled microtissue time-series damage by using Python language, replacing the damage variable D in the flow law of the Chaboche unified viscoplastic constitutive model of coupled microtissue time-series damage; S42 uses the neural network prediction model to supplement the missing data in the experimental data set in step three, trains the Chaboche unified viscoplastic constitutive model of coupled microstructure temporal damage according to the neural network constructed in step three, and iteratively optimizes the damage variable D in the Chaboche unified viscoplastic constitutive model of coupled microstructure temporal damage in the user-defined material library UMAT described in step two until a trained neural network prediction model is obtained.

8. The method for predicting properties of high-temperature alloys with coupled microstructure damage based on ANN and UMAT according to claim 7, characterized in that: The user-defined material library UMAT is a user material subroutine module of the finite element simulation software Abaqus / Standard; this module, as a secondary development function module of Abaqus, makes the simulation calculation process of the mechanical properties of high-temperature nickel-based alloys more flexible and more applicable; the implementation method of step five is, S51 builds a structural model in Abaqus finite element simulation software, adding user material parameters, boundary conditions and load characteristics that are the same as those in the actual working conditions; The user material parameters are the material parameters in the Chaboche unified viscoplastic constitutive model of coupled microstructure time-series damage obtained based on the experimental data fitting in step 1; S52 calls the user-defined material library UMAT of the Chaboche unified viscoplastic constitutive model of coupled microstructure temporal damage containing the trained damage variable neural network prediction model in step 4 in the post-processing module of the Abaqus finite element simulation software to perform finite element simulation calculations; The user-defined material UMAT of the Chaboche unified viscoplastic constitutive model coupled with micro-tissue temporal damage in step S53 is called at the integration point of the unit body in step S52. At the beginning of the increment, Abaqus will enter the UMAT module through the interface of the user-defined material library UMAT. The neural network of the micro-tissue temporal damage D will perform an iterative operation synchronously with each call of the user-defined material library UMAT. The initial values ​​of the necessary variables of the S54 unit body at the current integration point, including stress, strain, strain rate and internal variables, will be passed to the corresponding variables of UMAT; Each time Abaqus calls the user-defined material library UMAT, S55 recalculates the constant variables passed in to obtain a new Jacobian matrix and strain increment vector and returns it to the incremental step. The incremental step then uses the equilibrium judgment equation to determine whether the result meets the judgment rules. If it meets the requirements, it enters a new incremental step until the end of the simulation.

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