A method for predicting crack propagation paths in metal materials

Abstract

The present invention discloses a method for predicting crack propagation paths in metal materials, comprising: introducing a continuous phase field damage coefficient and strain energy history variable describing a diffuse array based on phase field fracture theory, and performing finite element calculation on the phase field damage coefficient; processing the obtained damage coefficient to obtain a target matrix and a neural network input matrix for neural network training, and then importing a pre-trained time-delay neural network with a timing prediction function to perform machine learning on the phase field damage variable; outputting a dynamic crack propagation path when a mean square error value is met, and converting the output result into the form of 0 and 1.

Description

Technical Field

[0001] The present invention relates to the field of metal material crack path propagation prediction algorithms, and in particular to a metal material crack propagation path prediction method based on a phase field method and a time delay neural network. Background Art

[0002] In practical engineering problems, the causes of permanent damage in metal materials can be divided into two main categories: fracture and plastic deformation. Fracture is the most common failure mode in metal engineering materials. In most cases, design specifications set high safety factors to avoid dangerous brittle fracture in metal components. In practical engineering problems, due to the severe stress singularity at the crack tip (the stress at the crack tip is infinite), a certain range of plastic damage occurs at the crack tip, which in turn causes a large amount of dislocation damage in the crystal, positively stimulating the propagation and evolution of the crack. In summary, whether it is brittle fracture of metal components or fatigue crack propagation under fatigue loads, the damage and fracture process is complex, making it difficult to study beyond phenomenological methods, and even more difficult to accurately predict the crack propagation path. Therefore, accurately predicting the initiation location and propagation path of fracture in metal materials is of great guiding and reference significance for solving practical engineering safety problems.

[0003] Researchers and scientists in the field of fracture mechanics around the world often use three types of numerical analysis methods to solve the problem of crack propagation path prediction: the Quasi Static Method, the Cohesive Element Method, and the Extended Finite Element Method (XFEM). These three methods are widely used in mature commercial finite element analysis software. Take ABAQUS as an example:

[0004] The singular element method uses singular elements at the crack tip, calculates the fracture parameters at the crack tip through interactive integration, and then re-meshes the crack according to the fracture criterion and crack growth criterion. This method is only suitable for calculating the stress intensity factor at the quasi-static crack tip, that is, for static crack problems. Simulating the crack path requires constantly updating the complex singular mesh at the crack tip, which is extremely complex and makes it difficult to predict the crack growth path.

[0005] Cohesion method: The crack propagation path needs to be known in advance. Cohesive elements with a thickness of 0 are set on the crack propagation path to simulate the discontinuous fracture displacement field caused by structural fracture. The disadvantage of this method is that the crack propagation path needs to be set in advance, which is not suitable for complex crack propagation problems.

[0006] The extended finite element method (EFM), currently the most widely used method, is based on the fracture energy release rate criterion in fracture mechanics. It uses a level set function at the crack tip to describe the crack propagation path of the mesh discontinuity, thereby simulating crack growth. In this method, the accuracy of the crack propagation path calculation is heavily dependent on the accuracy of the finite element mesh, resulting in high computational cost and low accuracy.

[0007] The above three methods are currently the most widely used methods for calculating fracture. However, due to the complexity of fracture problems, each method has obvious shortcomings and disadvantages. In the problem of predicting crack initiation location and crack propagation path, they cannot accurately simulate the crack propagation path. Summary of the Invention

[0008] The purpose of the present invention is to overcome the defects of the prior art. By constructing the fracture equilibrium equation through the fracture variation principle to solve the phase field damage variables, the phase field damage variables are used to describe the expansion process of diffuse cracks, that is, the crack expansion path, instead of using complex phase field method calculations.

[0009] The purpose of the present invention is achieved through the following technical solutions:

[0010] A method for predicting crack propagation paths of metal materials based on phase field method and time delay neural network, including

[0011] Step 1: Establish a finite element model for the component to be tested; construct a fracture equilibrium equation based on phase field fracture theory and obtain the phase field fracture governing equation. Finite element calculations are then performed to solve for the diffuse crack damage variable by introducing key parameters for phase field fracture calculations. These key parameters include the damage coefficient describing the continuous scalar field of the diffuse series and the strain energy history variable that prevents crack closure.

[0012] Step 2: Process the phase field damage variables obtained in step 1 to obtain the target matrix and neural network input matrix for neural network training; import the neural network input matrix and target matrix into a pre-trained time delay neural network with time series prediction function to perform machine learning on the phase field damage variables; the forward process is the neural network training process, and the reverse process is the process of updating the neural network learning parameters; at the same time, iterative prediction is performed using the mean square error as the performance evaluation function until the crack propagation path is output when the mean square error value is met; the neural network layer is a three-layer neural network layer, and the last layer uses a Hardlin output layer to convert the output result into the form of 0 and 1, and then the trained data is visualized and output as a grayscale image;

[0013] Step 3: Use the accuracy coefficient to evaluate the cumulative deviation between the predicted crack growth path and the actual crack growth path

[0014] In the local coordinate system with the tip of the mechanical notch as the origin, the dimensionless accuracy coefficient η, that is, the prediction accuracy, is calculated:

[0015]

[0016] where x pi represents the transverse coordinate value of the dynamic crack propagation path obtained in step 2, x ti Expressed as the transverse coordinate of the real crack under the same vertical coordinate, l t Indicates the true crack length;

[0017] Furthermore, a phase-field fracture UEL subroutine was written in Fortran to perform finite element calculations, and boundary conditions, load information, and material property information were defined in the calculations.

[0018] Furthermore, the step 1 includes:

[0019] Establish a finite element model for the component to be tested;

[0020] According to the energy conservation relationship in the material fracture process, the fracture equilibrium equation is constructed (still: calculating the overall potential energy of the finite element model):

[0021] Π int =E(u,d)+W(d)

[0022] Where d is the damage variable describing the continuous scalar field of the diffuse series; when d = 0, the material is intact; when d = 1, the material is completely destroyed, u is the displacement vector, E(u, d) is the elastic strain energy considering the damage, and W(d) is the fracture energy consumed by the crack surface formation.

[0023] According to the energy conservation relationship generated by the crack surface, the Galerkin equivalent integral form is constructed to calculate the elastic strain energy and the fracture energy during the material fracture process, and the strain energy history variable is introduced. According to the principle that the fracture path is extended along the minimum free energy, the first-order variation of the energy conservation equation is obtained to obtain the phase field control equation.

[0024]

[0025] Using the phase field governing equation, the function has an extreme value when the stationary value is equal to zero to solve the phase field governing equation and calculate the diffuse crack damage variable

[0026] Furthermore, before the neural network training, the crack propagation area of ​​the finite element model constructed in step 1 is subjected to mesh refinement processing, that is, the minimum mesh and the overall mesh size are adjusted, and a linear transition is used in the middle.

[0027] Furthermore, obtaining the target matrix for neural network training in step 2 includes the following steps: binarizing the phase field damage variables obtained in step 1 as target values ​​for time series neural network training, reconstructing the target values ​​into a target matrix with the same dimension as the input matrix, and then constructing the neural network input matrix;

[0028] The construction of the neural network input matrix includes the following steps: constructing a three-dimensional matrix with the specimen size, prefabricated crack position, constraint position, load position, constraint form, and load size as input conditions, and then converting the matrix into a one-dimensional ordered array through the reshape function.

[0029] Furthermore, the iterative prediction conditions in step 2 are: the upper limit of the number of iterative calculations is 10,000 times, and the mean square error is less than 1e-5.

[0030] Compared with the prior art, the technical solution of the present invention has the following beneficial effects:

[0031] The present invention uses the finite element method (FEM) to implement phase-field fracture simulation of metal materials, and Matlab programming to implement machine learning using a neural network (ANN) to output the crack propagation path. Finally, a Q420 SENB (single-edge notch three-point bend) specimen was produced for experimental verification, and the crack propagation path prediction results of the proposed algorithm were compared with the actual test results. The comparison results show that the cumulative error between the proposed algorithm and the actual crack propagation path is less than 8%, demonstrating the extremely high prediction accuracy of the present invention. BRIEF DESCRIPTION OF THE DRAWINGS

[0032] Figure 1 This is a flow chart of an algorithm for predicting crack growth paths based on the combination of phase field method and time-delay neural network;

[0033] Figure 2 shows the plane stress finite element models of three SENB models with geometric dimensions. Figure 2a This is a SENB1 specimen with a crack located in the center of the bottom of the specimen. Figure 2b This is a SENB2 specimen with a crack at the bottom of the specimen, 30 mm from the middle. Figure 2c The SENB3 specimen has two cracks located at the bottom of the specimen, 30 mm from the middle.

[0034] Figure 3 shows the finite element calculation results of three SENB models. Figures 3a-3c The results of SENB1\SENB2\SENB3 specimens are shown respectively;

[0035] Figure 4 is the finite element simulation phase field cloud diagram of three SENB models. Figures 4a-4c The cloud diagrams of SENB1\SENB2\SENB3 specimens are shown respectively;

[0036] Figure 5 It is the neural network structure and training graph;

[0037] Figure 6 is a neural network training accuracy graph used in an embodiment of the present invention;

[0038] Figure 7 shows the grayscale image of the data after neural network training. Figures 7a-7c The comparison diagrams of finite element calculation and neural network prediction results of SENB1\SENB2\SENB3 specimens are shown respectively;

[0039] Figure 8 1. A dimensional diagram of a SENB2 specimen prepared according to the finite element model of step 1 is shown, showing the front view, side view, and mechanical notch of SENB2 from left to right;

[0040] Figure 9 FIG2 shows a crack propagation path diagram of the SENB2 specimen prepared according to the finite element model of step 1, showing the front view, side view and mechanical notch of the SENB2 specimen from left to right;

[0041] Figure 10 a shows a comparison of the crack propagation paths of the SENB2 specimen obtained during the test, by XFEM, and by the method of the present invention. Figure 10 b Comparison of the accuracy of crack propagation paths obtained by the test, XFEM, and the method according to the present invention. DETAILED DESCRIPTION

[0042] In order to make the purpose, technical solutions, beneficial effects and significant improvements of the embodiments of the present invention clearer, the technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the embodiments and the drawings provided in the embodiments of the present invention. Obviously, all the described embodiments are only partial embodiments of the present invention, rather than all embodiments; based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without making creative work are within the scope of protection of the present invention.

[0043] like Figure 1 As shown, a method for predicting the crack propagation path of metal materials based on phase field method and time delay neural network includes the following steps:

[0044] Step 1: Build a finite element model

[0045] As shown in Figure 2, three different SENB (single-edge notch three-point bending specimens, i.e., SENB1\SENB2\SENB3 specimens) plane stress finite element models were designed. The standard three-point bending loading form was adopted. The geometric dimensions of the three SENB models are as follows: Figure 2a, 2b, 2c. The basic constants of the material are E = 210 GPa, μ = 0.3, lc = 1 mm, gc = 2.7e-3 kN / mm, and F = 9.5 kN.

[0046] Based on the energy conservation relationship in the material fracture process, the fracture equilibrium equation is constructed; the key parameters of phase field fracture calculation are introduced, including the damage coefficient d describing the continuous scalar field of the diffuse column and the strain energy history variable to prevent crack closure.

[0047] Step 2: Use Fortran to write a phase field fracture UEL subroutine to solve the diffuse crack damage variable d and the strain energy history variable

[0048] In ABAQUS, the UEL (user-defined element subroutine) subroutine is used to solve the diffuse crack damage variable d and the strain energy history variable through the Depvar custom variable SDV-14 (phase field variable). UEL is written in Fortran to implement the calculation. It includes the following two calculations: Core calculation 1: Through Fortran programming, using the Abaqus: UEL subroutine Depvar custom variable, set SDV-14 equal to the phase field variable, construct the fracture equilibrium equation based on the phase field fracture theory and obtain the phase field control equation, solve the phase field control equation, and calculate the diffuse crack damage variable d i Core Calculation 2: Calculate strain energy history variables using Abaqus:UEL via Fortran programming The purpose is to avoid crack closure and retain the maximum variable in the calculation history. The specific steps include the following (Formula (1) - Formula (5) are theoretical descriptions):

[0049] S201: Calculate the overall potential energy of the model, where d is a continuous scalar field (phase field) describing the degree of damage to the material, and d is a damage variable describing the dynamic growth of diffuse cracks. When d = 0, the material is intact; when d = 1, the material is completely destroyed. u is the displacement vector, E(u, d) is the elastic strain energy considering the damage, and W(d) is the fracture energy consumed by the crack surface formation:

[0050] Π int =E(u, d)+W(d) Formula (1)

[0051] S202: Based on the energy conservation relationship generated by the crack surface, the Galerkin equivalent integral form is constructed to calculate the elastic strain energy E(u, d). The elastic strain energy density is obtained by integrating ψ0(ε) in the Ω region:

[0052] E(u, d) = ∫ Ω (1-d 2 )·ψ0(ε)dV Formula (2)

[0053] Where dV is the differential variable in the integral Ω domain, and ε is the strain tensor. For two-dimensional problems, the strain tensor is a second-order tensor, which can be expressed by the index method. ij (i, j = 1, 2) or in the following matrix form:

[0054]

[0055] S203: Calculate the fracture energy during the material fracture process, where g c is the critical fracture energy release rate, is the width of the diffuse crack, is the Nabla operator, is the fracture surface energy, is the unit vector in the x and y directions.

[0056]

[0057]

[0058]

[0059] S204: Solve the fracture topology problem, where It is a strain energy history variable, and its function is to avoid crack closure and compression cracking problems.

[0060]

[0061]

[0062] S205: According to the principle that the fracture path is extended along the minimum free energy, the first-order variation of formula (6) is obtained, and δΠ d = 0, we get the phase field governing equation (Formula 8), where is the diffusion width of the crack, and Δ is the Laplace operator.

[0063]

[0064]

[0065] S206: Using the phase field governing equation, the function has an extreme value when the stationary value is equal to zero, and solve formula (8) to calculate the diffuse crack damage variable d i (crack propagation path), where d = 0, the material is intact; d = 1, the material is completely destroyed;

[0066]

[0067] Step 3: Refine the mesh of the finite element model and perform binarization

[0068] S301: Under the premise of improving the accuracy of finite element calculation and ensuring the time cost of calculation, the meshes of the three SENB specimens are appropriately refined, with the minimum mesh size set to 0.2mm and the overall mesh size to 5mm, with linear transition in the middle. The mesh division results are as follows: Figures 3a-3c shown.

[0069] FEM finite element analysis is performed on three SENB models (SENB1\SENB2\SENB3), and the phase field variables d in SENB1\SENB2\SENB3 are plotted respectively. i Cloud map Figures 4a-4c As shown in Figure 3, the crack propagation path of Q420 in the three-point bending test is simulated.

[0070] S302: The phase field damage variable d calculated in S206 is i (where i = element label, i.e., the number of each grid in the grid division, i = 1 to N × M) The calculation results are binarized and output as a binary matrix TAR N×M , TAR N×M As the target value for time series neural network training.

[0071] Step 4: Reconstruct the phase field calculation results in Abaqus through Matlab, and use the advantages of the time-delay neural network (FTDNN) in nonlinear relationship fitting to transform the complex problem of phase field fracture simulation into a function fitting problem. Figure 5 The neural network training shown in Figure 2 is based on the data processing of SENB2. The neural network training is based on the data processing of SENB2 as an example, and the other two categories can be obtained similarly.

[0072] S401: Obtaining input matrices and target matrices suitable for neural network machine learning

[0073] Obtaining the neural network input matrix INP:

[0074] The size of the specimen and the position of the prefabricated crack are converted into an N×M feature point matrix GEO N×M ;

[0075] Convert the Dirichlet boundary conditions (constraint positions, load application positions) into the N×M characteristic matrix BC N×M ;

[0076] GEON×M +BC N×M Forming the neural network input matrix INP N×M , and then use the reshape function to convert the matrix into a one-dimensional ordered array, filling it with logical values ​​0 and 1 to meet the 1×3959016 row vector form required by the neural network input, that is, to construct a 563×2344×3 three-dimensional logical type feature matrix.

[0077] Input matrix INP 1×3959016 =GEO 563×2344 +BC 563×2344

[0078] Neural network training target matrix TAR

[0079] Calculate the phase field variable d using ABAQUS i As input, output target matrix TAR 1×3959016

[0080] S402: Perform neural network training based on the input matrix and target matrix obtained in S401, such as Figure 5 As shown:

[0081] Three hidden layers are set up. The first hidden layer uses 7 Tanh-Sigmoid activation functions; the second hidden layer uses 4 Tanh-Sigmoid activation functions; the third hidden layer uses 2 Hardlin output layers. Because of the use of Hardlin activation function, the output results are converted to 0 and 1.

[0082] The LM (Levenberg-Marquardt) learning function is used to learn the neural network. The forward process is the neural network training process, and the reverse process is the process of updating the neural network learning parameters. The mean square error (MSE) is used as the performance evaluation function. The maximum number of iterations is 10,000. Another criterion for stopping iterations is that the performance function MSE is less than 1e-5.

[0083]

[0084] Pureline:f(D i )=D i Formula (12)

[0085]

[0086] When the MSE is less than 1e-5, the predicted crack propagation path is output, and the trained neural network is output as a time delay neural network (CPPFTDNN) for subsequent prediction of crack propagation path.

[0087] In order to improve the prediction accuracy of FTDNNCPP, the input matrix INP data is divided into training set, validation set and test set, where the proportions of the three sets are 70%, 20% and 10%, respectively. The training accuracy is as follows: Figure 6 As shown, the overall training accuracy of the pattern recognition neural network is 99.8%.

[0088] Since the third hidden layer uses the Hardlin activation function, the output results are converted into 0 and 1. After visualizing the trained data, it is shown as follows Figures 7a-7c The comparison chart of finite element calculation and neural network prediction results of SENB1\SENB2\SENB3 is shown.

[0089] Step 5: Use the accuracy coefficient to evaluate the cumulative deviation between the predicted crack growth path and the actual crack growth path

[0090] Taking the crack propagation path of the SENB2 fracture specimen as an example, Matlab was used to extract the crack propagation paths of the SENB2 specimen obtained in the experiment, by XFEM (finite element analysis), and according to the method of the present invention, and the simulation prediction deviation was calculated according to formula (12).

[0091] The present invention proposes a dimensionless accuracy coefficient η, which represents the cumulative deviation between the predicted crack propagation path and the actual crack propagation path, and represents the prediction accuracy. In the local coordinate system with the mechanical notch tip as the origin, where x pi Indicates the transverse coordinate value of the predicted crack extension, x ti Expressed as the transverse coordinate of the real crack under the same vertical coordinate, l t Indicates the length of the crack.

[0092]

[0093] Step 6: Conduct a comparative test

[0094] According to the finite element model constructed in step 1, the SENB2 specimen was made of Q420 material, and the fatigue crack growth test was carried out using a high-frequency fatigue testing machine GPS300 to obtain the crack growth path. The stress ratio was 0.5, that is, F min / F max =0.5, F max = 9.5kN, and crack growth tests were conducted on three types of SENB (single edge notch three-point bend specimens). When the specimens showed obvious plastic deformation and could not be subjected to resonance fatigue testing, the test was stopped and the specimens were polished. Figure 8 As shown in the figure, the actual crack propagation path is as follows Figure 9 shown.

[0095] Since XFEM is a highly nonlinear calculation, under the same boundary conditions and external loads, the XFEM method will stop calculating due to severe distortion of the crack tip unit. The method of the present invention is used to predict the crack propagation path. After calculation, the maximum cumulative error is less than 8%. Figure 10 As shown in a-10b, the method of the present invention clearly shows prediction convergence. At the same time, since the method is based on phase field fracture theory, it overcomes the calculation non-convergence caused by the distortion of the crack tip unit body and stops the calculation. In the process of future applications, combined with the Paris formula, the crack propagation life can be effectively calculated, and it can also be applied to the field of evaluation and prediction of crack propagation life.

[0096] The present invention employs the finite element method (FEM) to implement phase-field fracture simulation of metal materials, and employs Matlab programming to implement machine learning using a neural network (ANN) to output dynamic crack propagation paths. Finally, a Q420 SENB (single-edge notch three-point bend) specimen was fabricated for experimental verification, and the crack propagation path predictions of the proposed algorithm were compared with the actual test results. The comparison results show that the cumulative error between the proposed algorithm and the actual crack propagation path is less than 8%, demonstrating the present invention's extremely high prediction accuracy.

[0097] The above embodiments are only used to illustrate the technical solutions of the present invention, rather than to limit the same. Although the present invention has been described in detail with reference to the aforementioned embodiments, those skilled in the art should understand that they can still modify the technical solutions described in the aforementioned embodiments, or replace some or all of the technical features therein with equivalents, and these modifications or replacements do not cause the essence of the corresponding technical solutions to deviate from the scope of the technical solutions of the embodiments of the present invention. Non-essential improvements, adjustments or replacements made by those skilled in the art based on the contents of this specification are all within the scope of protection claimed by the present invention.

Claims

1. A method for predicting crack propagation paths in metal materials, comprising: Step 1: Establish a finite element model for the component to be tested; construct a fracture equilibrium equation based on phase field fracture theory and obtain the phase field fracture governing equation. Finite element calculations are then performed to solve for the diffuse crack damage variable by introducing key parameters for phase field fracture calculations. These key parameters include the damage coefficient describing the continuous scalar field of the diffuse series and the strain energy history variable that prevents crack closure. Step 2: Process the phase field damage variables obtained in step 1 to obtain the target matrix and neural network input matrix for neural network training; import the neural network input matrix and target matrix into a pre-trained time delay neural network with time series prediction function to perform machine learning on the phase field damage variables; the forward process is the neural network training process, and the reverse process is the process of updating the neural network learning parameters; at the same time, the mean square error is used as the performance evaluation function for iterative prediction until the crack propagation path is output when the mean square error value is met; the neural network layer is a three-layer neural network layer, and the last layer uses a Hardlin output layer to convert the output result into the form of 0 and 1, and then the trained data is visualized and a grayscale image is output; Step 3: Use the accuracy coefficient to evaluate the cumulative deviation between the predicted crack propagation path and the actual crack propagation path; in the local coordinate system with the mechanical notch tip as the origin, calculate the dimensionless accuracy coefficient η, that is, the prediction accuracy: where x pi represents the transverse coordinate value of the dynamic crack propagation path obtained in step 2, x ti Expressed as the transverse coordinate of the real crack under the same vertical coordinate, l t Indicates the true crack length; The step 1 specifically includes: Establish a finite element model for the component to be tested; According to the energy conservation relationship in the material fracture process, the fracture equilibrium equation is constructed or the overall potential energy of the finite element model is calculated: Π int E(u,d)+W(d) Where d is the damage variable describing the continuous scalar field of the diffuse series; when d = 0, the material is intact; when d = 1, the material is completely destroyed, u is the displacement vector, E(u, d) is the elastic strain energy considering the damage, and W(d) is the fracture energy consumed by the crack surface formation. According to the energy conservation relationship generated by the crack surface, the Galerkin equivalent integral form is constructed to calculate the elastic strain energy and the fracture energy during the material fracture process, and the strain energy history variable is introduced. According to the principle that the fracture path is extended along the minimum free energy, the first-order variation of the energy conservation equation is obtained to obtain the phase field control equation. Using the phase field governing equation, the function has an extreme value when the stationary value is equal to zero to solve the phase field governing equation and calculate the diffuse crack damage variable 2. The method for predicting crack propagation paths of metal materials according to claim 1, characterized in that: The phase field fracture UEL subroutine was written in Fortran for finite element calculation, and boundary conditions, load information and material property information were defined in the calculation.

3. The method for predicting crack propagation paths of metal materials according to claim 1, characterized in that: Refinement processing is to adjust the minimum grid and the overall grid size, using linear transition in the middle.

4. The method for predicting crack propagation paths of metal materials according to claim 1, characterized in that: The acquisition of the target matrix for neural network training in step 2 includes the following steps: The phase field damage variable obtained in step 1 is binarized and used as the target value for time series neural network training. The target value is reconstructed into a target matrix with the same dimension as the input matrix, and then the neural network input matrix is ​​constructed. The construction of the neural network input matrix includes the following steps: constructing a three-dimensional matrix with the specimen size, prefabricated crack position, constraint position, load position, constraint form, and load size as input conditions, and then converting the matrix into a one-dimensional ordered array through the reshape function.

5. The method for predicting crack propagation paths of metal materials according to claim 4, characterized in that: The iterative prediction conditions in step 2 are: the upper limit of the number of iterative calculations is 10,000 times, and the mean square error is less than 1e-5.

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