Tungsten symmetric tilt grain boundary performance classification method based on BP whale neural network algorithm

Abstract

This invention relates to a method for classifying the properties of tungsten symmetric tilted grain boundaries based on the BP whale neural network algorithm. It belongs to the field of metallic materials technology and addresses the problem of how to predict and classify the properties of tungsten symmetric tilted grain boundaries using the BP whale neural network algorithm. Based on CLS theory, a database of tungsten symmetric tilted grain boundary models is obtained. LAMMPS software is used to model the grain boundaries, and a tensile simulation model is established under ambient temperature and pressure and subjected to tensile testing to obtain a tensile properties database. Five parameters of CLS are selected as input items, and three categories based on the number of inflection points in the stress-strain curve of tungsten materials are selected as output items. The tensile properties database is trained, and the classification is performed based on the number of inflection points in the stress-strain curve. The technical solution of this invention uses the BP whale neural network algorithm to predict the classification of the plastic deformation mechanism of materials and classifies material properties by the number of inflection points in the stress-strain curve, thereby achieving the goal of directly predicting the mechanical properties of tungsten materials.

Description

Technical Field

[0001] This invention belongs to the field of metallic materials technology and relates to a method for classifying the properties of tungsten symmetric tilted grain boundaries based on the BP whale neural network algorithm. Background Technology

[0002] Multi-scale calculation and simulation of material properties under irradiation conditions is a key challenge in nuclear science for national defense basic research. Tungsten is the top-performing material under irradiation, possessing high hardness, high density, high melting point, and high ductile-brittle transition temperature, making it a preferred material system for future fusion reactors. Improving the mechanical properties of tungsten products to produce high-quality tungsten products that meet the requirements of ITER (Island-Thermal Experimental Reactor) has been a research hotspot in this field. Grain boundaries have a significant impact on the plastic deformation of materials; grain boundary sliding and migration are the main microscopic mechanisms of superplastic deformation. In the field of grain boundary engineering, the mechanical properties of materials can be improved by altering the number and distribution of specific grain boundaries.

[0003] Research on grain boundaries has been ongoing for many years, with in-depth studies on grain boundary energy and mechanical properties. Studies on grain boundary energy have shown that symmetric tilted grain boundaries have lower grain boundary energies than asymmetric tilted grain boundaries, thus exhibiting higher grain boundary stability. For grain boundary energy research, laboratories worldwide have large-scale databases and have implemented machine learning algorithms for predicting grain boundary energies. These machine learning algorithms can predict grain boundary energies without making assumptions about the grain boundary structure, significantly reducing the time required for grain boundary structure modeling.

[0004] The Chinese invention patent application document "Automatic Modeling Method for Constructing Interactive Tilted Grain Boundaries Based on Coincident Location Lattice Model" with a publication date of December 7, 2021 and publication number CN113761731A discloses a tilted grain boundary model that can be obtained by calculating the grain interface normal vector using an arbitrary exponential rotation axis vector and an arbitrary coincident location density ∑, and is written in an interactive mode for easy use.

[0005] Studies on the mechanical properties of grain boundaries have largely focused on uniaxial, single-overlap density indices, or the mechanical properties of a few typical tilted grain boundaries, resulting in a limited research framework. Consequently, compared to grain boundary energy, there are fewer studies discussing the tensile mechanical properties of grain boundaries, and existing research frameworks lack a systematic analysis or prediction of the tensile mechanical properties of grain boundaries. Summary of the Invention

[0006] The technical problem to be solved by this invention is how to use the BP whale neural network algorithm to predict and classify the properties of tungsten symmetric tilted grain boundaries.

[0007] The present invention solves the above-mentioned technical problems through the following technical solutions:

[0008] A method for classifying the properties of tungsten symmetric tilted grain boundaries based on the BP whale neural network algorithm includes the following steps:

[0009] A database of tungsten symmetric tilted grain boundary models was obtained based on CLS theory. The grain boundaries were modeled using LAMMPS software. An MD simulation tensile model was established at room temperature and pressure and the model was stretched to obtain a tensile performance database.

[0010] Five parameters of the coincident point matrix CLS are selected as input terms for the BP whale neural network algorithm: coincident position density Σ, rotation angle θ of the coincident point matrix CLS, and rotation axis vector. model and the rotation axis vector Two orthogonal vectors model These five parameters serve as inputs to the BP whale neural network algorithm;

[0011] Three categories based on the number of inflection points in the stress-strain curve of tungsten material were selected as output terms of the BP whale neural network algorithm.

[0012] The tensile property database is trained, and the number of inflection points on the stress-strain curve is used for prediction and classification, so as to achieve the purpose of predicting and classifying the mechanical properties of tungsten grain boundaries after tensile testing.

[0013] Furthermore, the specific method for selecting the five parameters of the phase overlap point matrix CLS as input terms for the BP whale neural network algorithm is as follows:

[0014] (1) Set the rotation axis vector The proportion of the number of lattice points in the heavy point lattice is defined as Σ represents the density of coincident positions; calculate the corresponding CLS rotation angle θ.

[0015] (2) Rotate the axis vector Unitized

[0016] Define g=cosθ, h=sinθ, i=1-cosθ,

[0017]

[0018] The rotation matrix is ​​obtained as R = ∑·R θ Among them, r is required ij All are integers;

[0019] (3) Based on the rotation axis vector Construct using orthogonal relations and make Pairwise orthogonal, then by transformation formula Calculate Calculations revealed that determining grain boundaries is equivalent to determining... and And It is by Obtained through matrix transformation, and for vectors Modulo operation is used to obtain

[0020] Furthermore, the hidden layer of the BP whale neural network algorithm is:

[0021]

[0022] Where m refers to the number of input layer nodes, n refers to the number of output layer nodes, and h is the number of hidden layer nodes; a refers to the adjustment constant between [1, 10]. With m = 5, n = 3, and a = 7, rounding results in 10 hidden layers. The corresponding penalty function is the ReLU function.

[0023] Relu = max{0, x}

[0024] To determine the weights and thresholds, backpropagation of the error is used to iteratively obtain the weighting coefficients. Let the error signal output by neuron i at the current time m be defined as δ. i ;

[0025] To make the BP whale neural network algorithm closer to the actual value, the sum of squared errors of all outputs should be minimized.

[0026]

[0027] Where S is the set of output layer neurons, and N is the number of output layer neurons.

[0028] The advantages of this invention are:

[0029] A database of tungsten symmetric tilted grain boundary models was obtained based on CLS theory. LAMMPS software was used to model the grain boundaries, and a tensile MD simulation model was established under ambient temperature and pressure. The model was then stretched to obtain a tensile properties database. Five parameters of the phase overlap matrix CLS were selected as input terms for the BP whale neural network algorithm, and three categories based on the number of inflection points in the stress-strain curve of tungsten materials were selected as output terms. The tensile properties database was trained, and the mechanical properties of tungsten after grain boundary stretching were predicted and classified based on the number of inflection points in the stress-strain curve. The technical solution of this invention uses the BP whale neural network algorithm to predict the classification of material plastic deformation mechanisms and classifies material properties based on the number of inflection points in the stress-strain curve, thereby achieving the goal of directly predicting the mechanical properties of tungsten materials. Attached Figure Description

[0030] Figure 1 This is a flowchart of a tungsten symmetric tilted grain boundary property classification method based on the BP whale neural network algorithm according to an embodiment of the present invention;

[0031] Figure 2 (a) To establish a grain boundary model based on CLS theory, Figure 2 (b) The stretching model for the established MD simulation;

[0032] Figure 3 For comparison of stress-strain curves of different volumes, big is a volume of 150*150*300 (units). Small refers to a volume of 100*100*200 (unit). );

[0033] Figure 4 A schematic diagram showing the inflection point markings and stage classifications of the stress-strain curve;

[0034] Figure 5 The stress-strain curve of the Σ5

[100] (013) type tungsten symmetric tilted grain boundary;

[0035] Figure 6 The stress-strain curve of the Σ3

[210] (125) type tungsten symmetric tilted grain boundary;

[0036] Figure 7 A schematic diagram of the FCC phase transformation and dislocation phenomenon generated during the stretching of Σ5

[100] (013) type tungsten symmetrical tilted grain boundary;

[0037] Figure 8 A schematic diagram of the FCC phase transformation to HCP phase transformation process and dislocation phenomenon generated during the stretching of Σ3

[210] (125) type tungsten symmetric tilted grain boundary;

[0038] Figure 9 The stress-strain curves of Σ3

[110] (112) type tungsten symmetric tilted grain boundaries;

[0039] Figure 10 The stress-strain curve of the Σ13

[100] (023) type tungsten symmetric tilted grain boundary;

[0040] Figure 11 The stress-strain curve of the Σ41

[100] (054) type tungsten symmetric tilted grain boundary;

[0041] Figure 12 A schematic diagram of various FCC phase transformations generated during the stretching process of Σ3

[110] (112) type tungsten symmetric tilted grain boundaries;

[0042] Figure 13 A schematic diagram of various complex phenomena such as FCC phase transformation, HCP phase transformation, and dislocations generated during the stretching process of Σ13

[100] (023) type tungsten symmetric tilted grain boundary;

[0043] Figure 14 A schematic diagram of various complex phenomena such as dislocations, FCC phase transitions, and HCP phase transitions generated during the stretching process of Σ41

[100] (054) type tungsten symmetric tilted grain boundaries;

[0044] Figure 15 The stress-strain curves without a strengthening stage and without a yielding stage are generated during the tensile process of Σ29

[100] (025) type tungsten symmetrical tilted grain boundaries;

[0045] Figure 16 A schematic diagram of various complex phenomena such as dislocations, FCC phase transitions, and HCP phase transitions generated during the stretching process of Σ29

[100] (025) type tungsten symmetric tilted grain boundaries;

[0046] Figure 17 The classification error diagram for the stress-strain curve of tungsten after tensile stress at symmetric tilted grain boundaries predicted by the BP neural network algorithm;

[0047] Figure 18 The classification error diagram shows the stress-strain curves of tungsten after tensile stress at symmetric tilted grain boundaries, predicted by the BP whale neural network algorithm. Detailed Implementation

[0048] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions of the embodiments of the present invention will be clearly and completely described below in conjunction with the embodiments of the present invention. Obviously, the described embodiments are only some embodiments of the present invention, not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0049] The technical solution of the present invention will be further described below with reference to the accompanying drawings and specific embodiments:

[0050] Example 1

[0051] like Figure 1 As shown, the tungsten symmetric tilt grain boundary property classification method based on the BP whale neural network algorithm includes the following steps:

[0052] A database of tungsten symmetric tilted grain boundary models was obtained based on the CLS (Coincidence Site Lattice) theory. The grain boundaries were modeled using LAMMPS software. A molecular dynamics (MD) simulation tensile model was established under ambient temperature and pressure and the model was stretched to obtain a database of tensile properties.

[0053] Five parameters of the coincident point matrix CLS are selected as input terms for the BP whale neural network algorithm: coincident position density Σ, rotation angle θ of the coincident point matrix CLS, and rotation axis vector. model and the rotation axis vector Two orthogonal vectors model These five parameters serve as inputs to the BP whale neural network algorithm;

[0054] Three categories based on the number of inflection points in the stress-strain curve of tungsten material were selected as output terms of the BP whale neural network algorithm.

[0055] The tensile property database is trained, and the number of inflection points on the stress-strain curve is used for prediction and classification, so as to achieve the purpose of predicting and classifying the mechanical properties of tungsten grain boundaries after tensile testing.

[0056] 1. Molecular dynamics simulation process

[0057] like Figure 2 As shown in (a), a cell database of symmetric tilted grain boundaries in tungsten materials was obtained based on CLS theory, and the grain boundaries were modeled using LAMMPS software. Figure 2 As shown in (b), an MD model was established and stretched under the premise of simulating a tensile model at room temperature and pressure (tensile conditions, total strain: 0.4, temperature: 295K, pressure: 0PA, time step: 0.001ps, tensile rate: 0.01A / ps).

[0058] like Figure 3As shown, a comparative experiment was conducted to determine whether the size would affect the performance. It was found that the size of the size would not affect the change of the stress-strain curve. Therefore, the size can be selected as 100*100*200. This size can save MD simulation time, and at the same time, it will not cause the defect phenomenon to disappear due to excessive shape deviation caused by the volume being too small.

[0059] like Figure 4 As shown, through analysis of stress-strain curves, it can be found that stress-strain curves can be divided into three categories:

[0060] Category 1: Curves with a strengthening phase have 3 inflection points;

[0061] The second type: curves without a strengthening phase, but with a yielding phase, and the curve has two inflection points;

[0062] Category 3: No strengthening phase, no yielding phase, and the curve has one inflection point.

[0063] 2. Classification of different plastic deformations after tensile stretching of symmetrical grain boundaries in tungsten materials

[0064] Different stress-strain curves correspond to different plastic deformation mechanisms in molecular dynamics simulations. By using the common nearest neighbor analysis (CNA) method, defect structures are identified (see Chinese invention patent document "Defect Retrieval Method and System Based on the Extension of Common Nearest Neighbor Method to Multiple Crystal Systems" with application number 202110975207.0). The original phase is BCC phase, the phase transformation is FCC phase, and the stacking fault is HCP phase. At the same time, the corresponding stress-strain curves are found to identify the corresponding number of inflection points.

[0065] Type 1: Tensile structure with stress-strain curve containing three inflection points

[0066] like Figure 5 and Figure 6 As shown, the stress-strain curves of Σ5

[100] (013) and Σ3

[210] (125) type tungsten symmetric tilted grain boundaries are respectively. This type of tungsten symmetric tilted grain boundary exhibits a strengthening stage during tensile testing, with a long strain duration and excellent plasticity. Simultaneously, a large area of ​​FCC phase transformation occurs during deformation, placing the entire process in the yielding stage and prolonging the entire deformation process. For example... Figure 7 The figure shows the FCC phase transformation and dislocation phenomenon generated during the stretching process of the Σ5

[100] (013) type tungsten symmetrical tilted grain boundary. It can be seen from the figure that Σ5

[100] (013) fractures at the grain boundary. Figure 8 The figure shows the FCC phase transformation to HCP phase transformation process and dislocation phenomenon generated during the stretching process of Σ3

[210] (125) type tungsten material. It can be seen from the figure that the Σ3

[210] (125) type tungsten material fractures at the crystal interface pores.

[0067] Type 2: Tensile structures with stress-strain curves containing two inflection points

[0068] like Figures 9 to 11 The figures shown are the stress-strain curves of tungsten materials of type Σ3

[110] (112), Σ13

[100] (023), and Σ41

[100] (054), respectively. These types of tungsten materials exhibit a yielding stage but no strengthening stage during the tensile process of symmetrical grain boundaries. Figure 12 The figure shows various FCC phase transformations that occur during the tensile process of Σ3

[110] (112) type tungsten material. The fracture direction is not the direction of the crystal interface. It can be seen from the figure that the Σ3

[110] (112) type tungsten material fractures at the point where the phase transformation converges, as shown in the figure. Figure 13 The figure shows various complex phenomena such as FCC phase transformation, HCP phase transformation, and dislocations that occur during the tensile process of Σ13

[100] (023) type tungsten material. It can be seen from the figure that the Σ13

[100] (023) type tungsten material fractures at the grain interface. For example... Figure 14 The figure shows a variety of complex phenomena such as dislocations, FCC phase transformation, and HCP phase transformation that occur during the stretching process of Σ41

[100] (054) type tungsten material. The fracture direction is not the direction of the crystal interface. It can be seen from the figure that the Σ41

[100] (054) type tungsten material fractures at the crystal interface due to pores.

[0069] Type 3: Tensile structures with a stress-strain curve containing an inflection point

[0070] like Figure 15 The figure shows the stress-strain curve of Σ29

[100] (025) type tungsten material. This type of tungsten material has no strengthening stage or yielding stage during the tensile process of symmetrical grain boundaries. Figure 16 The figure shows a variety of complex phenomena such as dislocations, FCC phase transitions, and HCP phase transitions that occur during the stretching process of Σ29

[100] (025) type tungsten material. It can be seen from the figure that the Σ29

[100] (025) type tungsten material has pore fractures at the crystal interface.

[0071] 3. Determine the input and output terms of the neural network algorithm platform.

[0072] Analysis of tensile phenomena reveals complex and diverse grain boundary phenomena, with no discernible pattern in fracture locations. However, a comparison in Table 1 shows that the fractures can be categorized into three types based on the number of inflection points. Therefore, a neural network algorithm platform can be established to classify the determined curve inflection points as output items.

[0073] Table 1. Defect classification of symmetric tilted grain boundaries in tungsten materials after MD simulation stretching.

[0074]

[0075] For a given input, based on the CSL (coincidence site lattice) model, if one of two infinitely extended crystals with the same lattice structure is rotated by a specific angle relative to the other crystal around a low-index crystal axis, some lattice points in the two crystals will regularly coincide. These coinciding lattice points will form a three-dimensional superlattice in space, known as the coincidence site lattice (CLS).

[0076] (1) Set the rotation axis vector The ratio of the rotation axis vector to the number of lattice points of the heavy point lattice is defined as... Σ represents the density of coincident positions, and the rotation angle θ of the phase coincident point matrix CLS is calculated.

[0077] (2) Rotate the axis vector Unitized Define g=cosθ, h=sinθ, i=1-cosθ,

[0078]

[0079] The rotation matrix is ​​obtained as R = ∑·R θ , where r ij All are integers;

[0080] (3) Based on the rotation axis vector Constructing vectors using orthogonal relations and make Pairwise orthogonal, then by transformation formula Calculate

[0081] Calculations revealed that determining grain boundaries is equivalent to determining vectors. and And It is by It is obtained through matrix transformation. Therefore, the input terms for the entire process can be determined to be only 5 terms, namely Σ, θ, And here They are pairwise orthogonal, so choose As three of the input quantities.

[0082] 4. Build a BP whale neural network algorithm platform to predict the classification of stress-strain curves.

[0083] The BP whale neural network algorithm was chosen as the performance prediction algorithm platform, with input layers Σ and θ respectively. The output layer selects 3 categories, and the hidden layers of the BP whale neural network algorithm are:

[0084]

[0085] Where m refers to the number of input layer nodes, n refers to the number of output layer nodes, and h is the number of hidden layer nodes; a refers to the adjustment constant between [1, 10]. Here, m = 5, n = 3, a = 7, which, after rounding, results in 10 hidden layers. The corresponding penalty function is the ReLU function.

[0086] Relu = max{0, x}

[0087] To determine the weights and thresholds, an error backpropagation algorithm is used to iteratively obtain the weighting coefficients. Let the error signal output by neuron i at the current time m be defined as δ. i .

[0088] To make the BP whale neural network closer to the actual value, the sum of squared errors of all outputs must be minimized.

[0089]

[0090] Where S is the set of output layer neurons, and N is the number of output layer neurons.

[0091] 5. Experimental Results

[0092] like Figure 17 The figure shows the stress-strain curves after tensile testing at tungsten symmetrical tilted grain boundaries, obtained through direct classification and prediction. It can be seen from the figure that direct classification and prediction will result in significant errors. Figure 18 The figure shows the stress-strain curve type of tungsten after symmetric tilting grain boundary stretching as predicted by the BP whale neural network algorithm. It can be seen from the figure that the prediction and classification accuracy obtained by the method of the present invention is greatly improved.

[0093] The above embodiments are only used to illustrate the technical solutions of the present invention, and are not intended to limit it. Although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some of the technical features. Such modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the spirit and scope of the technical solutions of the embodiments of the present invention.

Claims

1. A method for classifying the properties of tungsten symmetric tilted grain boundaries based on the BP whale neural network algorithm, characterized in that, Includes the following steps: A database of tungsten symmetric tilted grain boundary models was obtained based on CLS theory. The grain boundaries were modeled using LAMMPS software. A molecular dynamics simulation tensile model was established under ambient temperature and pressure, and the model was stretched to obtain a tensile performance database. Five parameters of the phase overlap point matrix CLS are selected as input terms for the BP whale neural network algorithm, namely the overlap position density. The rotation angle θ and rotation axis vector of the phase overlap point matrix CLS model and the rotation axis vector Two orthogonal vectors , model , These five parameters serve as inputs to the BP whale neural network algorithm; Three categories based on the number of inflection points in the stress-strain curve of tungsten material were selected as output terms of the BP whale neural network algorithm. The three categories of the number of inflection points in the stress-strain curve of the tungsten material are as follows: Category 1: Curves with a strengthening phase, having 3 inflection points; Category 2: Curves without a strengthening phase, but with a yielding phase, and the curve has 2 inflection points; Category 3: No strengthening stage, no yielding stage, the curve has 1 inflection point; The tensile property database is trained, and the number of inflection points on the stress-strain curve is used for prediction and classification, so as to achieve the purpose of predicting and classifying the mechanical properties of tungsten grain boundaries after tensile testing.

2. The tungsten symmetric tilted grain boundary property classification method based on the BP whale neural network algorithm according to claim 1, characterized in that, The specific method for selecting the five parameters of the phase overlap point matrix CLS as input terms for the BP whale neural network algorithm is as follows: (1) Set the rotation axis vector The proportion of the number of lattice points in the heavy point lattice is defined as , For the density of coincident positions, calculate the corresponding CLS rotation angle θ; (2) Rotate the axis vector Unitized ; definition , ； Obtain the rotation matrix Among the requirements All are integers; (3) Based on the rotation axis vector Construct using orthogonal relations and ,make Pairwise orthogonal, then by transformation formula Calculate ; Calculations revealed that determining grain boundaries is equivalent to determining... , , and , , , and , , It is by , , Obtained through matrix transformation, and for vectors , , Modulo operation is used to obtain , , .

3. The tungsten symmetric tilted grain boundary property classification method based on the BP whale neural network algorithm according to claim 2, characterized in that, The hidden layer of the BP whale neural network algorithm is: Where m refers to the number of input layer nodes, n refers to the number of output layer nodes, and h is the number of hidden layer nodes; a refers to the adjustment constant between [1, 10]. With m = 5, n = 3, and a = 7, rounding results in 10 hidden layers, and the corresponding penalty function is the ReLU function. To determine the weights and thresholds, backpropagation of the error is used to iteratively obtain the weighting coefficients. Let the error signal output by neuron i at the current time m be defined as... ; To make the BP whale neural network algorithm closer to the actual value, the sum of squared errors of all outputs should be minimized. Where S is the set of output layer neurons, and N is the number of output layer neurons.

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