A method for obtaining parameters of a polycrystal plastic finite element constitutive model based on a convolutional neural network

Abstract

The present application relates to a kind of polycrystal plastic finite element constitutive model parameter acquisition methods based on convolutional neural network, comprising (1) the stress-strain response matrix obtained by normalization conversion of crystal plastic finite element simulation and material mechanics test is stress-strain matrix training image set and stress-strain matrix prediction image set;(2) with the aid of the identification ability of convolutional neural network to image feature, the regression relationship between stress-strain matrix training image set and polycrystal plastic finite element constitutive model parameter is established, and the trained convolutional neural network is obtained;(3) stress-strain matrix prediction image set is input into the trained convolutional neural network, and the polycrystal plastic finite element constitutive model parameter corresponding to the stress-strain response of material mechanics test is obtained.The present application improves the prediction accuracy, and can be applied to the model parameter acquisition of more cyclic tensile, cyclic tensile and other various test data.

Description

TECHNICAL FIELD

[0001] The application belongs to the field of material mechanical property prediction and strength evaluation, and relates to a method for obtaining parameters of a polycrystal plastic finite element constitutive model based on a convolutional neural network. BACKGROUND

[0002] The deformation behavior of a metal material is closely related to the crystal morphology, and the traditional elastic-plastic and viscoplastic constitutive models are difficult to reflect the influence of the crystal morphology and the grain size on the mechanical properties of the material. The crystal plastic finite element constitutive model establishes a finite element model related to the crystal morphology, and performs volume averaging on the stress and strain of all the grains in the finite element model to describe the overall stress-strain relationship of the polycrystalline material.

[0003] The stress-strain relationship in a single crystal is described by using a single crystal slip system constitutive model, and a set of fitting parameters P is used to represent the stress in the single crystal, i.e., σ=f(P,ε). Since the overall stress-strain of the polycrystalline material is obtained by volume averaging of the finite element model, the change relationship between the stress and the strain cannot be explicitly or implicitly represented by σ=f(P,ε), which brings difficulties to the parameter acquisition of the polycrystal plastic finite element constitutive model.

[0004] The commonly used parameter acquisition methods include the trial-and-error method and the surrogate model method. The trial-and-error method first uses several sets of trial parameters for simulation, compares the obtained results with the test data, and gradually narrows down the parameter range by using the bisection method to improve the fitting accuracy. However, when the model parameters are large, the above method has a huge workload, and the parameter combination is easily trapped in a local optimum, which is difficult to achieve satisfactory results. The surrogate model method performs finite element simulation in a certain parameter range by batch finite element simulation to obtain a more comprehensive stress-strain response. Then, a suitable surrogate model is used to establish the relationship between the stress-strain and the corresponding model parameters, and only a small amount of finite element calculation is required to obtain the model parameters.

[0005] When the surrogate model method is used to obtain the parameters, the quality of the surrogate model determines the accuracy of the correlation between the stress-strain and the parameters of the polycrystal plastic finite element model. The published Chinese invention patent CN202011426575.1 "A method for determining material parameters of a crystal plastic finite element model" uses a deep belief neural network to construct a surrogate model with the model parameters as the input and the stress-strain as the output, and the fitting accuracy reaches R 2 =0.9984. However, since the number of elements in the stress-strain is often greater than the number of model parameters, the method adopts a model structure with fewer inputs and more outputs, which makes it difficult to further improve the fitting accuracy to R 2 >0.9999.

[0006] When the experimental data consists of cyclic tension and cyclic compression, the amount of stress and strain data increases, making it difficult for existing methods of obtaining model parameters to establish a sufficiently accurate surrogate model with few inputs and many outputs.

[0007] This invention transforms the stress-strain matrix into an image and uses a convolutional neural network to establish the relationship between its model parameters and stress-strain. Its structure is multi-input and few-output. At the same time, it utilizes the advantages of convolutional neural networks in image feature recognition, which improves accuracy to a certain extent. Summary of the Invention

[0008] To address the aforementioned technical problems, this invention provides a method for obtaining parameters of a polycrystalline plastic finite element constitutive model based on a convolutional neural network. Utilizing the advantages of convolutional neural networks in image feature recognition, a surrogate model is established between material stress-strain and model parameters, achieving high-precision fitting between model parameters and predicted parameters. This method can be used for obtaining polycrystalline plastic finite element model parameters corresponding to mechanical test data of metallic materials.

[0009] To achieve the above objectives, the technical solution adopted by the present invention is as follows:

[0010] A method for obtaining parameters of a polycrystalline plastic finite element constitutive model based on a convolutional neural network includes the following steps:

[0011] (1) Based on the finite element model with randomly generated parameter set, crystal plasticity finite element simulation is performed to obtain the corresponding stress-strain response matrix;

[0012] (2) Using the characteristic stress of the target material as a reference, normalize the elements in the stress response matrix to the range of [0,1] to obtain the normalized stress matrix;

[0013] (3) Based on the characteristic strain of the target material, normalize the elements in the strain response matrix to the range of [0,1] to obtain the normalized strain matrix;

[0014] (4) Merge the normalized stress and strain matrices to form a stress-strain matrix training image set;

[0015] (5) Establish a deep convolutional neural network, using the stress-strain matrix training image set as the training input and the crystal plastic finite element constitutive model parameters as the training output to train the deep convolutional neural network. Adjust the hyperparameters in the network so that the prediction accuracy of the training set reaches R. 2 >0.999, resulting in the trained deep convolutional neural network;

[0016] (6) Using steps (2) and (3), the test stress-strain response matrix for which parameters need to be obtained is normalized, and the normalized stress and strain matrices are merged to form a stress-strain matrix prediction image set. The stress-strain matrix prediction image set is used as input, and the trained deep convolutional neural network is used for prediction to obtain the polycrystalline plastic finite element constitutive model parameters corresponding to the test stress-strain response matrix for which parameters need to be obtained.

[0017] Furthermore, the parameter acquisition method transforms the merged normalized stress and strain matrices into a stress-strain matrix image set as input for building a deep convolutional neural network.

[0018] Furthermore, in step (2) of the parameter acquisition method, the characteristic stress is selected from the tensile limit stress of the material.

[0019] Furthermore, the characteristic strain in step (3) is selected as 5 times the material yield strain.

[0020] Furthermore, the parameter acquisition method utilizes the deep convolutional neural network's ability to recognize image features to acquire parameters.

[0021] Furthermore, the deep convolutional neural network comprises the following layers: ① input layer; ② convolutional layer; ③ batch normalization layer; ④ activation function layer; ⑤ fully connected layer; ⑥ regression layer.

[0022] Furthermore, using different numbers and orders of interlayer combinations can improve the accuracy of prediction results. The number of layers and the order of combination include, but are not limited to, the following structure: ① Input layer → ② Convolutional layer → ③ Batch normalization layer → ④ Activation function layer → Repeating ②③④ as units → ② Convolutional layer → ③ Batch normalization layer → ④ Activation function layer → ⑤ Fully connected layer → ⑥ Regression layer.

[0023] Furthermore, the size of the input layer is the same as the size of the stress-strain matrix image set, and the fully connected layer eventually converges to the neurons of the established deep convolutional neural network regression layer.

[0024] The advantages of this invention compared to existing model parameter acquisition methods are:

[0025] (1) This invention converts the stress-strain matrix into an image, and utilizes the advantages of convolutional neural networks in image feature recognition to improve prediction accuracy;

[0026] (2) The present invention uses stress and strain as input and model parameters as output. This multi-input-few-output structure makes the surrogate model have strong interpolation ability within a given parameter range and has strong applicability.

[0027] (3) The present invention converts the stress-strain matrix into an image, which can be applied to various situations such as uniaxial tension, cyclic tension, and cyclic tension-compression. It can be done simply by expanding the dimension of the image matrix, while still ensuring accuracy.

[0028] In summary, compared with existing methods, this invention utilizes the superior image feature recognition capabilities of convolutional neural networks and adopts a surrogate model structure with multiple inputs and fewer outputs, thereby improving prediction accuracy. Furthermore, it can be applied to the acquisition of model parameters for various experimental data such as cyclic stretching and cyclic tension and compression, which involve larger datasets. Attached Figure Description

[0029] Figure 1 This is a flowchart of the method for obtaining parameters of a polycrystalline plastic finite element constitutive model based on a convolutional neural network according to the present invention.

[0030] Figure 2 This invention uses a convolutional neural network as a surrogate model to improve the prediction accuracy of model parameters. Detailed Implementation

[0031] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative and not intended to limit the invention. Furthermore, the technical features involved in the various embodiments of this invention described below can be combined with each other as long as they do not conflict with each other.

[0032] The present invention will now be described in detail with reference to the accompanying drawings and specific examples. For example... Figure 1 As shown, the method for obtaining parameters of a polycrystalline plastic finite element constitutive model based on a convolutional neural network according to the present invention includes the following steps:

[0033] (1) Based on the finite element model with randomly generated parameter set, crystal plasticity finite element simulation is performed to obtain the corresponding stress-strain response matrix;

[0034] (2) Using the characteristic stress of the target material as a reference, normalize the elements in the stress response matrix to the range of [0,1] to obtain the normalized stress matrix;

[0035] (3) Based on the characteristic strain of the target material, normalize the elements in the strain response matrix to the range of [0,1] to obtain the normalized strain matrix;

[0036] (4) Merge the normalized stress and strain matrices to form a stress-strain matrix training image set;

[0037] (5) Establish a deep convolutional neural network, using the stress-strain matrix training image set as the training input and the crystal plastic finite element constitutive model parameters as the training output to train the deep convolutional neural network. Adjust the hyperparameters in the network so that the prediction accuracy of the training set reaches R. 2 >0.999, resulting in the trained deep convolutional neural network;

[0038] (6) Using steps (2) and (3), the test stress-strain response matrix for which parameters need to be obtained is normalized, and the normalized stress and strain matrices are merged to form a stress-strain matrix prediction image set. The stress-strain matrix prediction image set is used as input, and the trained deep convolutional neural network is used for prediction to obtain the polycrystalline plastic finite element constitutive model parameters corresponding to the test stress-strain response matrix for which parameters need to be obtained.

[0039] Furthermore, the parameter acquisition method transforms the merged normalized stress and strain matrices into a stress-strain matrix image set as input for building a deep convolutional neural network.

[0040] Furthermore, in step (2) of the parameter acquisition method, the characteristic stress is selected from the tensile limit stress of the material.

[0041] Furthermore, the characteristic strain in step (3) is selected as 5 times the material yield strain.

[0042] Furthermore, the parameter acquisition method utilizes the deep convolutional neural network's ability to recognize image features to acquire parameters.

[0043] Furthermore, the deep convolutional neural network comprises the following layers: ① input layer; ② convolutional layer; ③ batch normalization layer; ④ activation function layer; ⑤ fully connected layer; ⑥ regression layer.

[0044] Furthermore, using different numbers and orders of interlayer combinations can improve the accuracy of prediction results. The number of layers and the order of combination include, but are not limited to, the following structure: ① Input layer → ② Convolutional layer → ③ Batch normalization layer → ④ Activation function layer → Repeating ②③④ as units → ② Convolutional layer → ③ Batch normalization layer → ④ Activation function layer → ⑤ Fully connected layer → ⑥ Regression layer.

[0045] Furthermore, the size of the input layer is the same as the size of the stress-strain matrix image set, and the fully connected layer eventually converges to the neurons of the established deep convolutional neural network regression layer.

[0046] The parameters of the classical crystal slip system constitutive model are obtained by taking the nickel-based superalloy GH4169 as an example.

[0047] The classical constitutive formula for the crystal slip system used in the example is as follows:

[0048]

[0049] in: Let be the slip ratio on the α-th slip system. The reference slip ratio is typically taken as 0.0001, m is the rate sensitivity factor, typically taken as 20, and τ a Let g be the shear stress in the α-th slip system. a Let Γ be the resistive stress on the α-th slip system, and Γ be the sum of the shear strains on all slip systems. Let h be the rate of change of resistive stress on the α-th slip system. αβ Let be the potential hardening coefficient between the α-th slip system and the β-th slip system. Let h0 be the slip ratio on the β-th slip system, and the other parameters be h0, h... s τ s These are the model parameters to be obtained.

[0050] Then, select the above three parameters h0, h s τ s The initial range, in this example, is selected as h0∈

[10] . 3 10 5 ]、h s ∈[200,400]、τ s ∈[100,200]. Within the above range, 5000 sets of parameters are randomly generated for finite element simulation.

[0051] The crystal slip constitutive model was integrated into the Umat subroutine for calculation in the finite element software ABAQUS. Then, a randomly oriented crystal plastic finite element model was established, and calculations were performed using 5000 pre-generated parameter sets, generating 5000 sets of corresponding stress-strain response matrix data.

[0052] The experimental curves of the nickel-based superalloy GH4169 were obtained through uniaxial tensile tests, with a characteristic stress of 1800 MPa and a characteristic strain of 0.01. Using these characteristic stresses and strains, the tensile curves at different temperatures were normalized to form a stress-strain matrix prediction image set. 5000 sets of stress-strain response matrix data were normalized to form a stress-strain matrix training image set. Since the selected strain was 0.01 and the finite element simulation step size was 0.001, the dimension of the stress-strain matrix was 2×11, resulting in an image set size of 2×11 pixels.

[0053] Then, a convolutional neural network was built to describe the relationship between model parameters and stress-strain.

[0054] (1) First, create an image input layer with a size of 2×11 and 1 channel;

[0055] (2) Establish the first convolutional layer with a kernel size of 1×4 and a kernel number of 64. The edge pixels are filled by copying.

[0056] (3) Establish batch normalization layer and activation function layer, perform batch normalization on the structure after convolution, and use ReLU activation function for nonlinear activation.

[0057] (4) Establish a second convolutional layer with a kernel size of 1×8 and a kernel number of 48. The edge pixels are filled by copying.

[0058] (5) Establish batch normalization layer and activation function layer, perform batch normalization on the structure after convolution, and use ReLU activation function for nonlinear activation.

[0059] (6) Establish a third convolutional layer with a kernel size of 2×4 and a kernel number of 64. Edge pixels are filled by copying.

[0060] (7) Establish batch normalization layer and activation function layer, perform batch normalization on the structure after convolution, and use ReLU activation function for nonlinear activation.

[0061] (8) Establish a fourth convolutional layer with a kernel size of 2×8 and a kernel number of 48. Edge pixels are filled by copying.

[0062] (9) Establish batch normalization layer and activation function layer, perform batch normalization on the structure after convolution, and use ReLU activation function for nonlinear activation.

[0063] (10) Establish a fifth convolutional layer with a kernel size of 2×11 and a kernel number of 64. Edge pixels are filled by copying.

[0064] (11) Establish a batch normalization layer and an activation function layer to perform batch normalization on the convolutional structure and use the ReLU activation function for nonlinear activation.

[0065] (12) Establish a fully connected layer, connect it to three neurons, and add a regression layer at the end to realize the regression processing of stress and strain data with model parameters.

[0066] After establishing the above convolutional neural network model, it is trained using a stress-strain matrix training image set and the corresponding model parameters. The training parameters are as follows:

[0067] The MiniBatchSize (number of mini-samples) is 64, with 200 iterations. The initial learning rate is 0.001, decaying to 10% every 90 steps. The training data comprises 80% of the sample size, and the validation data comprises the remaining 20%. The model is trained on a GPU (GTX 1050), and its validation accuracy is as follows. Figure 2 The present invention uses a convolutional neural network as a surrogate model to predict the accuracy of model parameters, as shown in the R... 2 =0.9999.

[0068] The stress-strain matrix prediction image set generated from two uniaxial tensile curves of GH4169 at different temperatures is input into a trained convolutional neural network to obtain the corresponding model parameters. These model parameters are then substituted into a polycrystalline plastic finite element model to obtain the corresponding simulated curves, such as... Figure 1 As shown in process (6), the simulation results agree well with the experimental results, proving the effectiveness and accuracy of the method proposed in this invention.

[0069] The present invention has been illustratively described above with reference to the accompanying drawings. However, the present invention is not limited to the specific implementation process described above. The specific embodiments described above are merely examples. Any invention that does not exceed the scope of the claims of the present invention is within the protection scope of the present invention.

Claims

1. A method for obtaining parameters of a polycrystalline plastic finite element constitutive model based on a convolutional neural network, characterized in that, Includes the following steps: (1) Based on the finite element model with randomly generated parameter set, crystal plasticity finite element simulation is performed to obtain the corresponding stress-strain response matrix; (2) Using the characteristic stress of the target material as a reference, normalize the elements in the stress response matrix to the range of [0,1] to obtain the normalized stress matrix; (3) Based on the characteristic strain of the target material, normalize the elements in the strain response matrix to the range of [0,1] to obtain the normalized strain matrix; (4) Merge the normalized stress and strain matrices to form a stress-strain matrix training image set; (5) Establish a deep convolutional neural network, using the stress-strain matrix training image set as the training input and the crystal plastic finite element constitutive model parameters as the training output to train the deep convolutional neural network. Adjust the hyperparameters in the network to achieve the desired prediction accuracy of the training set. R 2 >0.999, resulting in the trained deep convolutional neural network; (6) Using steps (2) and (3), the test stress-strain response matrix for which parameters need to be obtained is normalized, and the normalized stress and strain matrices are merged to form a stress-strain matrix prediction image set. The stress-strain matrix prediction image set is used as input, and the trained deep convolutional neural network is used for prediction to obtain the polycrystalline plastic finite element constitutive model parameters corresponding to the test stress-strain response matrix for which parameters need to be obtained.

2. The method for obtaining parameters of a polycrystalline plastic finite element constitutive model based on a convolutional neural network according to claim 1, characterized in that: The parameter acquisition method converts the merged normalized stress and strain matrices into a stress-strain matrix image set as input for building a deep convolutional neural network.

3. The method for obtaining parameters of a polycrystalline plastic finite element constitutive model based on a convolutional neural network according to claim 1, characterized in that: The characteristic stress in step (2) of the parameter acquisition method is the tensile limit stress of the material.

4. The method for obtaining parameters of a polycrystalline plastic finite element constitutive model based on a convolutional neural network according to claim 1, characterized in that: The characteristic strain in step (3) is selected to be 5 times the material yield strain.

5. The method for obtaining parameters of a polycrystalline plastic finite element constitutive model based on a convolutional neural network according to claim 1, characterized in that: The parameter acquisition method utilizes the deep convolutional neural network's ability to recognize image features to acquire parameters.

6. The method for obtaining parameters of a polycrystalline plastic finite element constitutive model based on a convolutional neural network according to claim 1, characterized in that: The deep convolutional neural network includes the following layers: ① Input layer; ② Convolutional layer; ③ Batch normalization layer; ④ Activation function layer; ⑤ Fully connected layer; ⑥ Regression layer.

7. The method for obtaining parameters of a polycrystalline plastic finite element constitutive model based on a convolutional neural network according to claim 6, characterized in that: Using different numbers and orders of interlayer combinations can improve the accuracy of prediction results. The number of interlayers and the order of combination include the following structure: ① Input layer → ② Convolutional layer → ③ Batch normalization layer → ④ Activation function layer → Repeating ②③④ as units → ② Convolutional layer → ③ Batch normalization layer → ④ Activation function layer → ⑤ Fully connected layer → ⑥ Regression layer.

8. The method for obtaining parameters of a polycrystalline plastic finite element constitutive model based on a convolutional neural network according to claim 6 or 7, characterized in that: The size of the input layer is the same as the size of the stress-strain matrix image set, and the fully connected layer eventually converges to the neurons of the established deep convolutional neural network regression layer.

Images