Parameter calibration method of finite element model capable of predicting PLC effect of alloy material

Abstract

The invention discloses a parameter calibration method of a finite element model capable of predicting a PLC (Programmable Logic Controller) effect of an alloy material based on a particle swarm optimization BP (Back Propagation) neural network, which can realize accurate and rapid calibration of parameters of the finite element model and accurate prediction of spatio-temporal behaviors of the PLC effect of the alloy material and sawtooth rheological instability intervals of the spatio-temporal behaviors. Comprising the following steps: performing a uniaxial tensile test; constructing a corrected MC constitutive model; establishing a uniaxial tension finite element model; and determining to-be-calibrated parameters of the uniaxial tension finite element model and the like. By constructing the BP neural network model optimized based on the particle swarm optimization, the parameters of the uniaxial tension finite element model of the PLC effect can be accurately and quickly calibrated, the manual trial and error rate and the calibration workload are remarkably reduced, the parameter calibration precision and efficiency are improved, the simulation precision of the finite element model of the PLC effect of the alloy material can be predicted, and the method is suitable for popularization and application. The method has important guiding significance and engineering value for the integrated design of alloy components and process parameters and the inhibition of the sawtooth-shaped plasticity instability phenomenon in the machining process.

Description

Technical Field

[0001] The invention relates to the technical field of mechanical behavior prediction research of alloy materials, and in particular to a parameter calibration method of a finite element model capable of predicting a PLC effect of an alloy material. Background Art

[0002] Tensile test is a common mechanical experimental technique used to measure the tensile properties and deformation characteristics of materials. When alloy materials are subjected to tensile tests under certain strain rates, deformation temperatures and pre-deformation conditions, a plastic instability phenomenon will occur. This phenomenon is called the Portevin-Le Chatelier effect, or PLC effect for short, which is usually manifested as a zigzag yield of stress in the time domain and localization of strain in the air domain. The PLC effect is a cluster phenomenon, and its essence stems from the dynamic strain aging phenomenon during the evolution of the material's microstructure. The generation of the PLC effect can lead to problems such as rough surface, reduced toughness, weakened ductility and shortened fatigue cycle, which seriously affects the service reliability and life of alloy materials and their components.

[0003] With the development of computer technology and calculation methods, finite element simulation has been more and more widely valued and applied in the field of engineering design and scientific research, and has become an effective way to solve complex engineering analysis and calculation problems. Almost all design and manufacturing from automobiles to space shuttles are inseparable from finite element simulation calculations. Its wide use in various fields such as machinery manufacturing, material processing, aerospace, automobiles, civil construction, electronics, national defense and military industry, ships, railways, petrochemicals, energy and scientific research has made a qualitative leap in the design level. However, it must be pointed out that the accuracy of finite element simulation results mainly depends on the accuracy of the finite element model and its parameters, especially the correctness of the constitutive model in the finite element model and the accuracy of its parameters.

[0004] At present, the constitutive models used to describe the PLC effect are mainly divided into two categories: one is the dislocation dynamics model that considers the mutual transformation between mobile dislocations, forest dislocations and Cottrell dislocations, and the other is the solute dynamics model that considers the change in solute atom concentration. Among them, the Mccormick (MC) constitutive model, as a solute dynamics model, considers the interaction between solute atoms and mobile dislocations and is widely used for quantitative prediction of the spatiotemporal behavior of the PLC effect.

[0005] However, there are many parameters in the MC constitutive model used for numerical simulation fitting of PLC effects. The existing MC constitutive parameter calibration method is complicated, time-consuming, and has the disadvantage of insufficient parameter calibration accuracy, which leads to large simulation errors in the calibrated MC constitutive model during simulation. Experienced personnel are required to adjust and optimize the calibrated constitutive parameters through trial and error combined with finite element simulation technology. For example, "Yu Hengxu, Experimental and Simulation Study on Dynamic Strain Aging Behavior of Additively Manufactured GH4169 Alloy, Harbin Institute of Technology, 2021" calibrated the corresponding parameters of its MC model by least squares fitting, and compared and verified them with the experimental results, but this method is cumbersome and computationally intensive. Some parameters to be calibrated have a large range of values, and continuous trial and error adjustment and optimization are required to obtain a better solution. For example, "Guillermin N, et al. Experimental and numerical analysis of the Portevin–Le Chatelier effect in a nickel-base superalloy for turbine disks application. International Journal of Solids and Structures, 2023, 264, 112076" (Experimental and numerical analysis of the Portevin–Le Chatelier effect in a nickel-base superalloy for turbine disks application, International Journal of Solids and Structures, 2023, 264, 112076) uses the Levenberg-Marquardt algorithm to determine the calibration of all parameters in the model by considering the fitting experimental strain rate sensitivity curve, critical plastic strain, and plastic strain increment in the band when calibrating the MC model. However, this calibration method still has a complex calculation process and a large amount of calculation, and also requires continuous trial and error to adjust the parameters for optimization. For example, "Liao Junwei, Numerical Simulation of Dynamic Strain Aging in Aluminum-Magnesium Alloys, Huazhong University of Science and Technology, 2018" calibrates the PLC effect MC model of aluminum-magnesium alloys, and determines the parameters by referring to the parameter values ​​of the aluminum alloy MC model in other literature. Although referring to other literature can effectively reduce the amount of calculation, due to the different spatiotemporal behaviors of the PLC effect of different materials, their constitutive material parameters cannot be universal and need to be recalibrated according to the PLC effect characteristics of each material.

[0006] The Levenberg-Marquardt algorithm is an optimization algorithm for solving nonlinear least squares problems. It combines the advantages of the gradient descent method and the Gauss-Newton method by introducing a damping factor λ to balance the search direction and step size. When the damping parameter λ is large, the algorithm tends to the gradient descent method, with a small step but a stable direction; when λ is small, the algorithm tends to the Gauss-Newton method, using second-order information to accelerate convergence. The Levenberg-Marquardt algorithm has the advantages of fast convergence and good stability, and is particularly suitable for parameter estimation and function fitting problems. It is suitable for situations where the function form is known but the parameters are unknown, such as in 3D reconstruction, parameter optimization in machine learning, and other fields. However, the algorithm has high requirements for the initial value and may not be suitable for use when the function form is complex or there are many parameters.

[0007] Particle swarm optimization (PSO) is an optimization algorithm based on swarm intelligence. In the algorithm, each particle corresponds to a fitness value determined by the fitness function. The speed of the particle determines the direction and distance of the particle's movement. The speed is dynamically adjusted according to the movement experience of itself and other particles, thereby achieving individual optimization in the solvable space.

[0008] BP neural network is a multi-layer feedforward neural network based on the error back propagation algorithm, which has powerful nonlinear mapping ability and excellent multi-dimensional function mapping ability. BP neural network consists of input layer, hidden layer (can have multiple) and output layer. Each neuron is connected to all neurons in the previous layer, transmits signals through weighted sum, and undergoes nonlinear transformation through activation function. The calculation process consists of forward calculation process and reverse calculation process. In the forward propagation process, the input pattern is processed layer by layer from the input layer through the hidden layer and then transferred to the output layer. The state of each layer of neurons only affects the state of the next layer of neurons. If the expected output cannot be obtained in the output layer, it will turn to back propagation, return the error signal along the original connection path, and minimize the error signal by modifying the weights of each neuron. Its core algorithm is the error back propagation algorithm (Error Backpropagation), which calculates the error between the network output and the target value, and uses the gradient descent method to adjust the network weights to minimize the error. The principle of PSO optimization of BP neural network is to apply PSO algorithm to the optimization process of BP neural network. The core idea of ​​PSO algorithm optimization of BP neural network is to optimize the weights and thresholds in the neural network through particle swarm. Each particle represents a set of weights and biases in the BP neural network, and the PSO search mechanism is used to find the global optimal solution, thereby improving the prediction performance of the BP neural network.

[0009] Latin Hypercube Sampling (LHS) is a method for approximating random sampling from a multivariate parametric distribution. This method reduces the correlation between input variables by dividing the range of each component into equal intervals and sampling uniformly in each interval.

[0010] ABAQUS finite element software is a powerful finite element analysis software, mainly used to solve engineering problems from simple to highly complex, including multi-physics nonlinear problems. ABAQUS is well-known for its rich unit and material model library, which can simulate the performance of metals, rubber, polymer materials, composite materials, reinforced concrete, compressible hyperelastic foam materials, and geological materials such as soil and rock. As a general simulation tool, ABAQUS finite element software can not only solve structural (stress / displacement) problems, but also perform multi-physics coupling analysis such as heat conduction, mass diffusion, thermoelectric coupling analysis, acoustic analysis, geotechnical mechanics analysis and piezoelectric medium analysis. ABAQUS provides two solvers: ABAQUS / Standard and ABAQUS / Explicit, and also includes a human-computer interaction pre- and post-processing module: ABAQUS / CAE, which allows users to model, analyze and display results in a unified interface. In addition, ABAQUS also supports secondary development through user subroutines and Python scripts. Through the secondary development of Abaqus, the efficiency and quality of simulation analysis can be greatly improved, thereby playing a greater role in engineering design and scientific research.

[0011] The fmincon function is a MATLAB function used to solve the minimum value of nonlinear multivariate functions, especially suitable for constrained optimization problems. It is a nonlinear programming solver that can handle linear and nonlinear constraints and is suitable for optimization problems in engineering, science, and finance. Summary of the invention

[0012] The purpose of the present invention is to provide a parameter calibration method of a finite element model that can predict the PLC effect of alloy materials based on a particle swarm optimization BP neural network, which can achieve accurate and rapid calibration of the parameters of the finite element model and accurate prediction of the spatiotemporal behavior of the PLC effect of the alloy material and its sawtooth rheological instability range.

[0013] The present invention adopts the following technical scheme to achieve its invention purpose, a method for calibrating parameters of MC constitutive model of PLC effect of alloy material, which comprises the following steps:

[0014] Step (1): perform a uniaxial tensile test;

[0015] Take the alloy specimen and conduct a uniaxial tensile test under set conditions, record the load-time curve and strain-time curve, convert them into true stress-strain curve, then observe the sawtooth fluctuation of the plastic part on the true stress-strain curve, and count its stress level, average stress drop amplitude, and total stress drop times;

[0016] Step ⑵: construct a modified MC constitutive model;

[0017] The expression of the modified MC constitutive model is:

[0018]

[0019] In the expression: σ is the equivalent stress;

[0020] is the equivalent plastic strain rate;

[0021] R0 is a material parameter related to the initial yield stress;

[0022] p is the equivalent plastic strain;

[0023] Q, b, and K are material parameters;

[0024] P1, P2, α, and n are parameters related to dynamic strain aging;

[0025] C m1 and C m2 It is a parameter related to the concentration of phase particles or solute atoms around mobile dislocations;

[0026] t a (p) is the statute of limitations period;

[0027] w1 and w2 are parameters related to the plastic strain increment generated when mobile dislocations break free from phase particles or solute atom pinning;

[0028] E is Young's elastic modulus;

[0029] Step (3): establishing a uniaxial tensile finite element model;

[0030] Couple the modified MC constitutive model, that is, use the UMAT subroutine to embed the modified MC constitutive model into the ABAQUS finite element software simulation platform to build a uniaxial tensile finite element model that can predict the PLC effect of alloy materials;

[0031] Step (4): determining the parameters to be calibrated of the uniaxial tension finite element model described in step (3);

[0032] The parameters to be calibrated of the uniaxial tensile finite element model include the stiffness S of the sample fixture used in the uniaxial tensile test in step (1), the expression of the modified MC constitutive model in step (2), K, P1, P2, α, C m1 , C m2 , w1, w2, E, Q, b, R0, n; and the Poisson's ratio v of the alloy material required in the uniaxial tensile finite element model for predicting the PLC effect of the alloy material described in step (3);

[0033] Since the MC constitutive model can only simulate the plastic part of the stress-strain curve of alloy materials, the relevant parameters of the elastic part of the stress-strain curve of alloy materials, such as Young's elastic modulus E and Poisson's ratio υ, are also needed in the finite element model;

[0034] Since the stiffness of the uniaxial tensile test specimen fixture has a certain influence on the PLC effect of the alloy material, the stiffness S of the uniaxial tensile test specimen fixture is selected as the parameter to be calibrated; step (5): calibrating the values ​​of some parameters to be calibrated of the uniaxial tensile finite element model;

[0035] The part of the parameters to be calibrated include parameters E, Q, b, R0, n, υ;

[0036] The parameters E, Q, b and R0 described in step (4) are calibrated by fitting the actual stress-strain curve of the test, and the parameters υ and n are determined according to the properties of the alloy material;

[0037] Step (6): Build and train a neural network model;

[0038] Construct a BP neural network model based on particle swarm optimization and set relevant initial parameters;

[0039] Determine the value range of the remaining parameters to be calibrated of the uniaxial tension finite element model; use Latin hypercube sampling to obtain different combinations of the remaining parameters to be calibrated of the uniaxial tension finite element model;

[0040] Finite element simulation calculation is performed according to the Latin hypercube sampling results to obtain sample data of the training set; the sample data of the training set is used to train the BP neural network model optimized by the particle swarm algorithm; that is, the Latin hypercube sampling results (the combination of the remaining parameters to be calibrated of the uniaxial tension finite element model) are used as input, and are put into the uniaxial tension finite element model for finite element simulation calculation, and the stress level, average stress drop amplitude, and total stress drop times in the real stress-strain curve under different parameters are obtained by statistical simulation, and these three values ​​are used as output to obtain the input and output combination as the sample data of the training set, and the sample data of the training set is used to train the BP neural network model optimized by the particle swarm algorithm;

[0041] The remaining parameters to be calibrated include parameters S, K, P1, P2, α, C m1 , C m2 , w1, w2;

[0042] The neural network includes a BP neural network and a particle swarm algorithm; wherein the particle swarm algorithm is used to optimize the weights and thresholds of the BP neural network; the parameters to be determined include the inertia weight, maximum speed, acceleration constant, maximum number of generations, group size in the particle swarm algorithm, and the number of hidden layers and neurons in the BP neural network;

[0043] Step ⑺: Test the effectiveness of the BP neural network model optimized based on the particle swarm algorithm;

[0044] In addition, the remaining parameters to be calibrated (S, K, P1, P2, α, C m1 , C m2 , w1, w2) as the input of the test set sample data, and respectively input them into the uniaxial tensile finite element model that can predict the PLC effect of alloy materials and the BP neural network model optimized based on the particle swarm algorithm for calculation, that is, the uniaxial tensile finite element model that can predict the PLC effect of alloy materials is input for finite element simulation calculation to obtain the finite element simulation results, and the stress level, average stress drop amplitude, and total stress drop times in the real stress-strain curve in the statistical simulation results are used as outputs to obtain the input-output combination as the sample data of the test set; in the BP neural network model optimized based on the particle swarm algorithm, the sample data of the test set is input for prediction calculation to obtain the prediction result of the neural network model;

[0045] By comparing the finite element simulation results with the prediction results of the neural network model, the effectiveness of the BP neural network model optimized by the particle swarm algorithm is tested;

[0046] If the error is greater than the set value, it means that the accuracy of the established neural network is not enough, and the parameters of the neural network model need to be adjusted and retried; if the error is less than the set value, it means that the established neural network model has a higher accuracy, and the parameters of this neural network model are determined to be used for the next prediction; Step ⑻: Use the effective neural network model to solve the remaining parameters to be calibrated (S, K, P1, P2, α, C m1 , C m2 , w1, w2) optimal values;

[0047] Based on the effective neural network model, the fmincon function is used to solve the remaining parameters of the uniaxial tensile finite element model when the fitness function is the minimum value. This set of parameters is put into the uniaxial tensile finite element model that can predict the PLC effect of alloy materials for finite element simulation calculation to obtain its true stress-strain curve, and its stress level, average stress drop amplitude and total stress drop times are counted.

[0048] The error value is obtained by comparing the stress level, average stress drop amplitude, and total stress drop times in the test results, and the error value is compared with the set value (the set maximum error value) to determine whether it is necessary to obtain a new solution set or determine the optimal values ​​of the remaining parameters to be calibrated of the uniaxial tensile finite element model that can predict the PLC effect of the alloy material under the tensile test conditions;

[0049] If the error is greater than the set value, it means that the fmincon function needs to be used again to solve the minimization fitness function to obtain a new solution set; if the error is less than the set value, this set of parameters is used as the optimal values ​​of the remaining parameters to be calibrated of the uniaxial tensile finite element model that can predict the PLC effect of the alloy material under the tensile test conditions, and finally the finite element model that can accurately predict the PLC effect of the alloy material is constructed.

[0050] The stress level described in step (1) of the present invention is the average value of the maximum and minimum stress values ​​of the sawtooth yield portion on the true stress-strain curve;

[0051] The average stress drop amplitude is the average value obtained by dividing the sum of the amplitudes (peak minus trough) of each stress sawtooth fluctuation in the sawtooth yielding part on the true stress-strain curve by the number of stress sawtooth fluctuations;

[0052] The total number of stress drops is the total number of stress zigzag fluctuations in the zigzag yield portion on the true stress-strain curve.

[0053] The phase particles or solute atoms described in step (2) of the present invention are phase particles or solute atoms precipitated during the aging treatment of the alloy.

[0054] In step (5) of the present invention, the Young's elastic modulus E is obtained by fitting the elastic part of the true stress-strain curve obtained by the tensile test of the alloy material;

[0055] After smoothing the plastic part of the true stress-strain curve obtained from the tensile test of the alloy material, the plastic hardening part y=R0+Q(1-exp(-bp)) in the expression of its MC constitutive model is used to fit the Q, b, and R0 parameters;

[0056] The parameter υ is determined by consulting the literature based on the properties of the alloy material;

[0057] The parameter n (related to the type of diffusion of phase particles or solute atoms) is determined by the properties of the alloy material, namely bulk diffusion (value 0.66) or tubular diffusion (value 0.33).

[0058] In the step (6), the parameters K, P1, P2, α, C m1 , C m2 , w1, and w2 are calibrated by the BP neural network model optimized based on the particle swarm algorithm.

[0059] The initial parameters set in step (6) of the present invention include the number of hidden layers, the number of neurons in each layer, inertia weight, maximum speed, acceleration constant, maximum number of generations, and group size.

[0060] In step (6) of the present invention, since the neural network model in the present invention is relatively complex, the number of hidden layers is set to 3, the number of neurons in each layer is less than twice the number of the input layer, and the difference decreases layer by layer, according to the formula Count the number of neurons;

[0061] in, is the number of neurons in the lth layer, and the reduction amplitude k is set to a fixed value greater than 0.

[0062] In step (8) of the present invention, the sum of the squared differences between the test results and the prediction results of the trained neural network model is used as the fitness function.

[0063] Where N is the number of output results. is the prediction result of the neural network model trained for the i-th sample, y i is the result of the ith test.

[0064] Due to the adoption of the above-mentioned technical scheme, the present invention has better achieved the purpose of the invention. It completes the prediction mapping relationship from the parameters to be calibrated to the real stress-strain curve results by constructing a BP neural network model optimized based on the particle swarm algorithm, and realizes the optimal values ​​of the remaining parameters to be calibrated of the uniaxial tension finite element model that can predict the PLC effect of alloy materials from the test results, thereby obtaining the optimal parameters to be calibrated of the uniaxial tension finite element model. Compared with the existing parameter calibration method of the uniaxial tension finite element model that can predict the PLC effect of alloy materials, the uniaxial tension finite element model parameters of the PLC effect can be accurately and quickly calibrated, significantly reducing the human trial and error rate and calibration workload, improving the parameter calibration accuracy and efficiency, and improving the simulation accuracy of the finite element model prediction that can predict the PLC effect of alloy materials. It has important guiding significance and engineering value for the integrated design of alloy composition and process parameters and the suppression of the sawtooth plastic instability phenomenon during processing. BRIEF DESCRIPTION OF THE DRAWINGS

[0065] Figure 1 It is a schematic block diagram of the process principle of the present invention;

[0066] Figure 2 is a comparison diagram of the actual stress-strain curves of the finite element model prediction results and the test results in the embodiment of the present invention;

[0067] Figure 3 It is an error comparison diagram between the finite element model prediction result and the test result in the embodiment of the present invention. DETAILED DESCRIPTION

[0068] The present invention will be further described below in conjunction with the accompanying drawings and embodiments.

[0069] Depend on Figures 1 to 3 It can be seen that a parameter calibration method of a finite element model that can predict the PLC effect of an alloy material includes the following steps:

[0070] Step (1): perform a uniaxial tensile test;

[0071] Take the alloy specimen (the alloy specimen in this embodiment is a Ti-12Mo alloy plate specimen) and place it under the set conditions (350°C, 1×10 -3 A uniaxial tensile test is performed at a strain rate of 10000 strains, and the load-time curve and strain-time curve are recorded and converted into a true stress-strain curve. Then, the sawtooth fluctuation of the plastic part of the true stress-strain curve is observed, and its stress level, average stress drop amplitude, and total stress drop times are counted;

[0072] Step ⑵: construct a modified MC constitutive model;

[0073] The expression of the modified MC constitutive model is:

[0074]

[0075] In the expression: σ is the equivalent stress;

[0076] is the equivalent plastic strain rate;

[0077] R0 is a material parameter related to the initial yield stress;

[0078] p is the equivalent plastic strain;

[0079] Q, b, and K are material parameters;

[0080] P1, P2, α, and n are parameters related to dynamic strain aging;

[0081] C m1and C m2 It is a parameter related to the concentration of phase particles or solute atoms around mobile dislocations;

[0082] t a (p) is the statute of limitations period;

[0083] w1 and w2 are parameters related to the plastic strain increment generated when mobile dislocations break free from phase particles or solute atom pinning;

[0084] E is Young's elastic modulus;

[0085] Step (3): establishing a uniaxial tensile finite element model;

[0086] Couple the modified MC constitutive model, that is, use the UMAT subroutine to embed the modified MC constitutive model into the ABAQUS finite element software simulation platform to build a uniaxial tensile finite element model that can predict the PLC effect of alloy materials;

[0087] Step (4): determining the parameters to be calibrated of the uniaxial tension finite element model described in step (3);

[0088] The parameters to be calibrated of the uniaxial tensile finite element model include the stiffness S of the sample fixture used in the uniaxial tensile test in step (1), the expression of the modified MC constitutive model in step (2), K, P1, P2, α, C m1 , C m2 , w1, w2, E, Q, b, R0, n; and the Poisson's ratio υ (0.33 in this embodiment) of the alloy material required in the uniaxial tensile finite element model for predicting the PLC effect of the alloy material described in step (3);

[0089] Since the MC constitutive model can only simulate the plastic part of the stress-strain curve of alloy materials, the relevant parameters of the elastic part of the stress-strain curve of alloy materials, such as Young's elastic modulus E and Poisson's ratio υ, are also needed in the finite element model;

[0090] Since the stiffness of the uniaxial tensile test specimen fixture has a certain influence on the PLC effect of the alloy material, the stiffness S of the uniaxial tensile test specimen fixture is selected as the parameter to be calibrated; step (5): calibrating the values ​​of some parameters to be calibrated of the uniaxial tensile finite element model;

[0091] The part of the parameters to be calibrated include parameters E, Q, b, R0, n, υ;

[0092] The parameters E, Q, b and R0 described in step (4) are calibrated by fitting the actual stress-strain curve of the test, and the parameters υ and n are determined by the properties of the alloy material;

[0093] Step (6): Build and train a neural network model;

[0094] Construct a BP neural network model based on particle swarm optimization and set relevant initial parameters;

[0095] Determine the value range of the remaining parameters to be calibrated for the uniaxial tension finite element model, as shown in Table 1:

[0096] Table 1. Range of values ​​of other parameters to be calibrated for the uniaxial tension finite element model

[0097]

[0098] Using Latin hypercube sampling, different combinations of other parameters to be calibrated for the uniaxial tension finite element model are obtained (60 groups in this embodiment);

[0099] Finite element simulation calculations were performed based on the Latin hypercube sampling results to obtain the sample data of the training set, as shown in Table 2:

[0100] Table 2. Sample data of the training set required for the neural network model (the last three columns in the table use 1, 2, and 3 to represent the stress level, the average stress drop amplitude, and the total number of stress drops, respectively)

[0101]

[0102]

[0103]

[0104] The sample data of the training set is used to train the BP neural network model optimized by the particle swarm algorithm; the combination of the remaining parameters to be calibrated of the uniaxial tensile finite element model of the Latin hypercube sampling results (60 groups) is used as input, and is put into the uniaxial tensile finite element model for finite element simulation calculation, and the stress level, average stress drop amplitude, and total stress drop times in the real stress-strain curve under different parameters are obtained by statistical simulation, and these three values ​​are used as output, and the input and output combinations are obtained as sample data of the training set to train the BP neural network model optimized by the particle swarm algorithm;

[0105] The remaining parameters to be calibrated include parameters S, K, P1, P2, α, C m1 , C m2 , w1, w2;

[0106] The neural network includes a BP neural network and a particle swarm algorithm; wherein the particle swarm algorithm is used to optimize the weights and thresholds of the BP neural network; the parameters to be determined include the inertia weight, maximum speed, acceleration constant, maximum number of generations, group size in the particle swarm algorithm, and the number of hidden layers and neurons in the BP neural network;

[0107] Step ⑺: Test the effectiveness of the BP neural network model optimized based on the particle swarm algorithm;

[0108] In addition, the remaining parameters to be calibrated (S, K, P1, P2, α, C m1 , C m2 , w1, w2) as the input of the sample data of the test set, and respectively input them into the uniaxial tensile finite element model that can predict the PLC effect of the alloy material and the BP neural network model optimized based on the particle swarm algorithm for calculation, that is, the uniaxial tensile finite element model that can predict the PLC effect of the alloy material is input for finite element simulation calculation to obtain the finite element simulation results, and the stress level, average stress drop amplitude, and total stress drop times in the real stress-strain curve in the statistical simulation results are used as outputs, and (15 groups) of input and output combinations are obtained as the sample data of the test set, as shown in Table 3:

[0109] Table 3. Sample data of the test set required for the neural network model (the last three columns in the table use 1, 2, and 3 to represent the stress level, the average stress drop amplitude, and the total number of stress drops, respectively)

[0110]

[0111]

[0112] In the BP neural network model optimized by the particle swarm algorithm, the sample data of the test set is input to perform prediction calculations to obtain the prediction results of the neural network model;

[0113] By comparing the finite element simulation results with the prediction results of the neural network model, the effectiveness of the BP neural network model optimized by the particle swarm algorithm is tested;

[0114] If the error is greater than the set value, it means that the accuracy of the established neural network is not enough, and the parameters of the neural network model need to be adjusted and retried; if the error is less than the set value, it means that the established neural network model has a higher accuracy, and the parameters of this neural network model are determined to be used for the next prediction (in this example, the number of hidden layer neurons is 15-10-6, the acceleration constants c1 and c2 are set to 2, and other values ​​remain unchanged from the initial settings);

[0115] Step ⑻: Use the effective neural network model to solve the remaining parameters to be calibrated (S, K, P1, P2, α, C m1 , C m2 , w1, w2) optimal values;

[0116] Based on the effective neural network model, the fmincon function is used to solve the remaining parameters of the uniaxial tensile finite element model when the fitness function is the minimum value. This set of parameters is put into the uniaxial tensile finite element model that can predict the PLC effect of alloy materials for finite element simulation calculation to obtain its true stress-strain curve, and its stress level, average stress drop amplitude and total stress drop times are counted.

[0117] The error value is obtained by comparing the stress level, average stress drop amplitude, and total stress drop times in the test results. The error value is compared with the set value (the set maximum error value) to determine whether it is necessary to obtain a new solution set or determine the optimal values ​​of the remaining parameters to be calibrated of the uniaxial tensile finite element model that can predict the PLC effect of the alloy material under the tensile test conditions, as shown in Table 4:

[0118] Table 4 Optimal values ​​of other parameters to be calibrated for the uniaxial tension finite element model

[0119]

[0120] If the error is greater than the set value, it means that the fmincon function needs to be used again to solve the minimization fitness function to obtain a new solution set; if the error is less than the set value, this set of parameters is used as the optimal values ​​of the remaining parameters to be calibrated of the uniaxial tensile finite element model that can predict the PLC effect of the alloy material under the tensile test conditions, and finally the finite element model that can accurately predict the PLC effect of the alloy material is constructed.

[0121] The stress level described in step (1) of the present invention is the average value of the maximum and minimum stress values ​​of the sawtooth yield portion on the true stress-strain curve;

[0122] The average stress drop amplitude is the average value obtained by dividing the sum of the amplitudes of each stress sawtooth fluctuation (peak minus trough) of the sawtooth yield portion on the true stress-strain curve by the number of stress sawtooth fluctuations;

[0123] The total number of stress drops is the total number of stress zigzag fluctuations in the zigzag yield portion on the true stress-strain curve.

[0124] The phase particles or solute atoms described in step (2) of the present invention are phase particles or solute atoms precipitated from the alloy during the aging treatment process (in this example, the ω precipitated phase particles precipitated from the Ti-12Mo alloy during the aging treatment process).

[0125] In step (5) of the present invention, the Young's modulus of elasticity E (92980 MPa in this embodiment) is obtained by fitting the elastic part of the true stress-strain curve obtained by the tensile test of the alloy material;

[0126] After smoothing the plastic part of the true stress-strain curve obtained from the tensile test of the alloy material, the plastic hardening part y=R0+Q(1-exp(-bp)) in the expression of its MC constitutive model is used to fit the parameters Q, b, and R0 (in this embodiment, Q is 27.075MPa; b is 220.458; R0 is 570MPa);

[0127] The parameter υ is determined by consulting the literature and the properties of the alloy material (the determined value of the parameter υ in this embodiment is 0.33);

[0128] The parameter n (related to the diffusion type of phase particles or solute atoms) is determined by the properties of the alloy material, namely, bulk diffusion or tube diffusion (in this embodiment, it is determined to be bulk diffusion by the properties of the alloy material, and the value of n is 0.66).

[0129] In the step (6), the parameters K, P1, P2, α, C m1 , C m2 , w1, and w2 are calibrated by a BP neural network model optimized by a particle swarm algorithm (parameters in this embodiment are K, P1, P2, α, C m1 , C m2 , w1, w2 see Table 4).

[0130] The initial parameters set in step (6) of the present invention include the number of hidden layers, the number of neurons in each layer, inertia weight, maximum speed, acceleration constant, maximum number of generations, and group size.

[0131] In step (6) of the present invention, since the neural network model in the present invention is relatively complex, the number of hidden layers is set to 3, the number of neurons in each layer is less than twice the number of the input layer, and the difference decreases layer by layer, according to the formula Count the number of neurons;

[0132] in, is the number of neurons in the lth layer, and the reduced amplitude value k is set to a fixed value greater than 0 (the number of neurons in this embodiment is initially set to 10-5-4 with reference to the number of input parameters, the inertia weight is initially set to the default value 1, the maximum speed is initially set to 1, the acceleration constant is initially set to 2, the maximum number of generations is initially set to 200, and the group size is initially set to 100).

[0133] In step (8) of the present invention, the sum of the square differences between the test results and the prediction results of the trained neural network model is used as the fitness function:

[0134] Where N is the number of output results. is the prediction result of the neural network model trained for the i-th sample, yi is the result of the ith test.

[0135] Conclusion: Based on the BP neural network model optimized by particle swarm algorithm, the parameters to be calibrated of the uniaxial tensile finite element model that can predict the PLC effect of alloy materials are solved, and the uniaxial tensile finite element model is input for finite element simulation calculation to obtain the comparison between the simulated real stress-strain curve and the experimental results. Figure 2 As shown in FIG. 1 , it can be seen that the uniaxial tensile finite element model constructed by the present invention can accurately simulate the elastic-plastic mechanical behavior of the alloy material. Figure 3 It can be seen from the error comparison diagram that after the parameters calibrated by the BP neural network model optimized based on the particle swarm algorithm are input into the uniaxial tension finite element model, the uniaxial tension finite element model can accurately simulate the PLC effect of the alloy material.

[0136] The above is an embodiment of the best technical solution of the present invention, but the technical solution to be protected by the present invention is not limited to the contents disclosed in the embodiment and the drawings. Therefore, any equivalent or modification completed without departing from the spirit disclosed by the present invention shall fall within the protection scope of the present invention.

[0137] In summary, the present invention obtains the stress level, average stress drop amplitude and total stress drop times in the real stress-strain curve of the test through a uniaxial tensile test, and constructs a modified MC constitutive model; couples the modified MC constitutive model to establish a uniaxial tensile finite element model that can predict the PLC effect of the alloy material and determines the parameters to be calibrated of the uniaxial tensile finite element model; after calibrating some parameters to be calibrated of the finite element model; performs Latin hypercube sampling on the remaining parameters to be calibrated of the uniaxial tensile finite element model, and performs finite element simulation calculation on the sampling results to determine the sample data of the training set required for the neural network model, and constructs and trains the BP neural network model optimized based on the particle swarm algorithm; and then randomly selects the remaining parameters to be calibrated of the uniaxial tensile finite element model. A certain parameter combination is used as the sample data of the test set to test the effectiveness of the BP neural network model optimized by the particle swarm algorithm, and an effective prediction mapping relationship is constructed from the remaining parameters to be calibrated of the uniaxial tension finite element model to the stress level, average stress drop amplitude, and total stress drop times in the real stress-strain curve results; the BP neural network model optimized by the particle swarm algorithm is used to solve the test results to obtain the optimal values ​​of the remaining parameters to be calibrated of the uniaxial tension finite element model that can predict the PLC effect of the alloy material, so that the parameters of the uniaxial tension finite element model can be accurately and quickly calibrated, which significantly reduces the human trial and error rate and calibration workload, effectively improves parameter calibration and efficiency, and improves the accuracy of the finite element model prediction of the PLC effect.

Claims

1. A parameter calibration method for a finite element model capable of predicting the PLC effect of alloy materials, characterized in that The following steps are involved: Step (1): perform a uniaxial tensile test; Take the alloy specimen and conduct a uniaxial tensile test under set conditions, record the load-time curve and strain-time curve, convert them into true stress-strain curve, then observe the sawtooth fluctuation of the plastic part on the true stress-strain curve, and count its stress level, average stress drop amplitude, and total stress drop times; Step ⑵: construct a modified MC constitutive model; The expression of the modified MC constitutive model is: In the expression: σ is the equivalent stress; is the equivalent plastic strain rate; R0 is a material parameter related to the initial yield stress; p is the equivalent plastic strain; Q, b, and K are material parameters; P1, P2, α, and n are parameters related to dynamic strain aging; C m1 and C m2 It is a parameter related to the concentration of phase particles or solute atoms around mobile dislocations; t a (p) is the statute of limitations period; w1 and w2 are parameters related to the plastic strain increment generated when mobile dislocations break free from phase particles or solute atom pinning; E is Young's elastic modulus; Step (3): establishing a uniaxial tensile finite element model; By coupling the modified MC constitutive model, a uniaxial tensile finite element model that can predict the PLC effect of alloy materials is constructed; Step (4): determining the parameters to be calibrated of the uniaxial tension finite element model described in step (3); The parameters to be calibrated of the uniaxial tensile finite element model include the stiffness S of the uniaxial tensile test specimen fixture described in step (1), the expression of the modified MC constitutive model described in step (2), K, P1, P2, α, C m1 , C m2 , w1, w2, E, Q, b, R0, n; and the Poisson's ratio υ of the alloy material required in the uniaxial tensile finite element model for predicting the PLC effect of the alloy material described in step ⑶; Step (5): calibrating the values ​​of some parameters to be calibrated of the uniaxial tension finite element model; The part of the parameters to be calibrated include parameters E, Q, b, R0, n, υ; The parameters E, Q, b and R0 described in step (4) are calibrated by fitting the actual stress-strain curve of the test, and the parameters υ and n are determined according to the properties of the alloy material; Step (6): Build and train a neural network model; Construct a BP neural network model based on particle swarm optimization and set relevant initial parameters; Determine the value range of the remaining parameters to be calibrated of the uniaxial tension finite element model; use Latin hypercube sampling to obtain different combinations of the remaining parameters to be calibrated of the uniaxial tension finite element model; Finite element simulation calculation is performed based on the Latin hypercube sampling results to obtain sample data of the training set; the sample data of the training set is used to train the BP neural network model optimized based on the particle swarm algorithm; The remaining parameters to be calibrated include parameters S, K, P1, P2, α, C m1 , C m2 , w1, w2; Step ⑺: Test the effectiveness of the BP neural network model optimized based on the particle swarm algorithm; In addition, the remaining combinations of parameters to be calibrated of the uniaxial tensile finite element model are randomly selected as sample data of the test set, and are respectively input into the uniaxial tensile finite element model that can predict the PLC effect of the alloy material and the BP neural network model optimized based on the particle swarm algorithm for calculation, that is, the uniaxial tensile finite element model that can predict the PLC effect of the alloy material is input for finite element simulation calculation to obtain the finite element simulation result; the prediction calculation is performed in the BP neural network model optimized based on the particle swarm algorithm to obtain the prediction result of the neural network model; Compare the finite element simulation results with the prediction results of the neural network model to test the effectiveness of the BP neural network model optimized based on the particle swarm algorithm; Step (8): using the tested effective neural network model to solve the optimal values ​​of the remaining parameters to be calibrated of the uniaxial tension finite element model; Based on the effective neural network model, a set of remaining parameters to be calibrated of the uniaxial tension finite element model is obtained when the fitness function is the minimum value; the set of parameters is put into the uniaxial tension finite element model that can predict the PLC effect of the alloy material for finite element simulation calculation; The error value is obtained by comparing the test results, and the error value is compared with the set value to determine whether it is necessary to obtain a new solution set or to determine the optimal values ​​of the remaining parameters to be calibrated of the uniaxial tensile finite element model that can predict the PLC effect of the alloy material under the tensile test conditions; Finally, a finite element model was constructed that can accurately predict the PLC effect of alloy materials.

2. A parameter calibration method for a finite element model capable of predicting the PLC effect of an alloy material according to claim 1, characterized in that The stress level described in step (1) is the average of the maximum and minimum stress values ​​of the sawtooth yield portion on the true stress-strain curve; The average stress drop amplitude is the average value obtained by dividing the sum of the amplitudes of the stress sawtooth fluctuations in the sawtooth yielding part on the true stress-strain curve by the number of stress sawtooth fluctuations; The total number of stress drops is the total number of stress zigzag fluctuations in the zigzag yield portion on the true stress-strain curve.

3. A parameter calibration method for a finite element model capable of predicting the PLC effect of an alloy material according to claim 2, characterized in that The phase particles or solute atoms described in step (2) are phase particles or solute atoms precipitated from the alloy during the aging treatment process.

4. The method for calibrating parameters of a finite element model capable of predicting the PLC effect of an alloy material according to claim 2, characterized in that In the step (5), the Young's elastic modulus E is obtained by fitting the elastic part of the true stress-strain curve obtained by the tensile test of the alloy material; After smoothing the plastic part of the true stress-strain curve obtained from the tensile test of the alloy material, the plastic hardening part y=R0+Q(1-exp(-bp)) in the expression of its MC constitutive model is used to fit the Q, b, and R0 parameters; The parameter υ is determined by consulting the literature based on the properties of the alloy material; The parameter n, i.e., bulk diffusion or tube diffusion, is determined by the material properties of the alloy; In the step (6), the parameters K, P1, P2, α, C m1 , C m2 , w1, and w2 are calibrated by the BP neural network model optimized based on the particle swarm algorithm.

5. The parameter calibration method of a finite element model capable of predicting the PLC effect of alloy materials according to claim 3, characterized in that In the step (5), the Young's elastic modulus E is obtained by fitting the elastic part of the true stress-strain curve obtained by the tensile test of the alloy material; After smoothing the plastic part of the true stress-strain curve obtained from the tensile test of the alloy material, the plastic hardening part y=R0+Q(1-exp(-bp)) in the expression of its MC constitutive model is used to fit the Q, b, and R0 parameters; The parameter υ is determined by consulting the literature based on the properties of the alloy material; The parameter n, i.e., bulk diffusion or tube diffusion, is determined by the material properties of the alloy; In the step (6), the parameters K, P1, P2, α, C m1 , C m2 , w1, and w2 are calibrated by the BP neural network model optimized based on the particle swarm algorithm.

6. A parameter calibration method for a finite element model capable of predicting the PLC effect of an alloy material according to claim 4, characterized in that The initial parameters set in step (6) include the number of hidden layers, the number of neurons in each layer, inertia weight, maximum speed, acceleration constant, maximum number of generations, and group size.

7. The parameter calibration method of a finite element model capable of predicting the PLC effect of an alloy material according to claim 5, characterized in that The initial parameters set in step (6) include the number of hidden layers, the number of neurons in each layer, inertia weight, maximum speed, acceleration constant, maximum number of generations, and group size.

8. A parameter calibration method for a finite element model capable of predicting the PLC effect of an alloy material according to claim 1 or 2 or 3 or 4 or 5 or 6 or 7, characterized in that In the step (6), the number of hidden layers is set to 3, the number of neurons in each layer is less than twice the number of the input layer, and the difference decreases layer by layer, according to the formula Count the number of neurons; in, is the number of neurons in the lth layer, and the reduction amplitude k is set to a fixed value greater than 0.

9. A parameter calibration method for a finite element model capable of predicting the PLC effect of an alloy material according to claim 1 or 2 or 3 or 4 or 5 or 6 or 7, characterized in that In the step (8), the sum of the squared differences between the test results and the prediction results of the trained neural network model is used as the fitness function: Where N is the number of output results. is the prediction result of the neural network model trained for the i-th sample, y i is the result of the ith test.

10. The method for calibrating parameters of a finite element model capable of predicting the PLC effect of alloy materials according to claim 8, characterized in that In the step (8), the sum of the squared differences between the test results and the prediction results of the trained neural network model is used as the fitness function: Where N is the number of output results. is the prediction result of the neural network model trained for the i-th sample, y i is the result of the ith test.

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