Method and device for identifying j-c constitutive parameters of manganese aluminum bronze

Abstract

The application belongs to the technical field of material modeling and simulation, and discloses a method and device for identifying J-C constitutive parameters of manganese aluminum bronze, which comprises the following steps: obtaining the real stress-strain curve of the material through a quasi-static compression experiment, and performing a thermal-mechanical coupling compression experiment under different temperature and strain rate conditions, extracting the stress-strain response under the corresponding state, and estimating the initial parameter set of the model; then constructing stress-strain response verification data through the thermal-mechanical coupling compression experiment; constructing a parameter optimization space based on the initial parameter set, and performing iterative optimization based on the fusion optimization algorithm of the genetic algorithm, the grey wolf algorithm and the particle swarm algorithm; the fitness function is weighted based on variable weights on the basis of the average relative error of the experimental data curve and the fitted data curve, wherein the variable weight is determined according to the fitting deviation at the yield point and the plastic section. The J-C constitutive model obtained by the application can accurately simulate the mechanical behavior of manganese aluminum bronze.

Description

Technical Field

[0001] This invention belongs to the field of materials modeling and simulation technology, and in particular relates to a method and device for identifying constitutive parameters of manganese aluminum bronze JC. Background Technology

[0002] The statements in this section are merely background information related to the present invention and do not necessarily constitute prior art.

[0003] The JC constitutive model is a constitutive relation model used to describe the stress-strain response of metallic materials under different strain rates, temperatures, and other loading conditions. It characterizes the mechanical behaviors of materials, such as yielding, work hardening, and thermal softening, and is one of the core models used in material modeling and simulation in engineering fields such as aerospace, shipbuilding, and weaponry. Currently, the conventional method for parameter inversion in this model involves conducting numerous grouped tensile and compression experiments under different strain rates and temperatures to complete a series of mechanical property tests. After obtaining the material's stress-strain data, stepwise linear fitting or the least squares method is used to estimate the five core parameters of the JC constitutive model, thus achieving preliminary acquisition of the JC constitutive model parameters and providing basic parameter support for simulating the mechanical behavior of materials. However, this method relies on numerous grouped experiments to obtain parameters, requiring coverage of different strain rate and temperature combinations. Furthermore, the experimental process requires high-precision control, leading to a significant increase in experimental costs and a substantial extension of the parameter acquisition cycle. Simultaneously, the fitting results are extremely sensitive to the accuracy of the experimental data, and experimental errors are easily directly transmitted to the parameter results, resulting in poor technical and economic efficiency. Moreover, the parameter accuracy is limited by experimental conditions, making it difficult to meet the needs of efficient and high-precision engineering applications.

[0004] Another existing technology involves obtaining macroscopic stress-strain response data of materials under typical loading conditions and then using optimization algorithms such as genetic algorithms to inversely calculate parameters, replacing the traditional method of fitting with a large number of grouped experiments. This can reduce experimental costs and improve parameter solution efficiency to some extent. However, there are significant nonlinear coupling relationships among the five parameters of the JC constitutive model. This is especially true for alloys such as manganese aluminum bronze, which contain α, β, and κ multiphase states. Their strain rate dependence and temperature sensitivity are stronger, and the parameter coupling effect is more prominent. Optimization based on existing optimization algorithms can easily lead to excessively long optimization cycles or getting trapped in local optima. Summary of the Invention

[0005] To overcome the shortcomings of the prior art, the present invention provides a method and apparatus for identifying constitutive parameters of manganese aluminum bronze JC, enabling the constitutive model to more accurately simulate the mechanical behavior of manganese aluminum bronze.

[0006] To achieve the above objectives, one or more embodiments of the present invention provide a method for identifying the constitutive parameters of JC in manganese aluminum bronze, comprising the following steps:

[0007] The true stress-strain curve of the material is obtained by quasi-static compression experiments, and thermo-mechanical coupled compression experiments are carried out under different temperatures and strain rates. The stress-strain response under the corresponding conditions is extracted, and the initial parameter set of the model is estimated.

[0008] A thermo-mechanical coupling compression experiment was conducted under set temperature and strain rate conditions, and the stress-strain response under the corresponding conditions was extracted as verification data.

[0009] A parameter optimization space is constructed based on the initial parameter set. An iterative optimization algorithm based on the fusion of genetic algorithm, gray wolf algorithm and particle swarm algorithm is used to obtain the optimal parameter set. The fitness function used in the optimization process is: based on the average relative error between the experimental data curve and the fitted data curve, a weighted average is applied. The variable weight is determined based on the fitting deviation between the yield point and the plastic segment.

[0010] In some embodiments, the process of estimating the initial set of parameters for the model includes:

[0011] The strain hardening term was isolated from the constitutive model, and a compression experiment was conducted under quasi-static, room temperature conditions to obtain the first stress-strain curve. The yield strength, strain hardening modulus and strain hardening exponent were obtained by fitting the strain hardening term.

[0012] The strain hardening term and strain rate hardening term were separated from the constitutive model. Compression experiments were conducted under high strain rate and room temperature conditions to obtain the second stress-strain curve. The yield strain and yield stress of the material were determined, and the strain rate hardening index was calculated.

[0013] Compression experiments were conducted under high strain rate and high temperature conditions to obtain the third stress-strain curve, determine the yield strain and yield stress of the material, and calculate the thermal softening index.

[0014] In some embodiments, the iterative optimization based on the fusion optimization algorithm of genetic algorithm, gray wolf algorithm and particle swarm optimization includes:

[0015] An initial population is randomly generated within the search interval, and each individual in the population corresponds to a set of parameters.

[0016] A global coarse search is performed on the initial population based on the genetic algorithm to obtain the optimal individual in the GA and generate a set of optimal individuals in the GA.

[0017] The best individual in GA is used as the initial α wolf candidate. The gray wolf algorithm is used to perform directional convergence within the set of best individuals in GA to obtain the best individual in GWO and generate the set of GWO individuals.

[0018] Using the best individual in the GWO as the central initial value of the particle swarm optimization algorithm, and taking a portion of the best individual set in the GA and the best individual set in the GWO as the search range, local optimization is performed to obtain the globally optimal parameter set.

[0019] In some embodiments, the fitness function used by the fusion optimization algorithm is:

[0020]

[0021] Where P represents the combination of parameters to be optimized. This indicates the number of sample points in the experimental data. This represents the weight in the t-th iteration, with an initial value of 1. Let represent the experimental stress value of the i-th sample point, k denote the optimization stage (identified by GA, GWO, and PSO), and m be the starting point of the continuous sample points corresponding to the yield point and the plastic segment. To fit the stress values ​​at the yield point and in the plastic segment of the curve, This is for fine-tuning the weights.

[0022] In some embodiments, the position update formula in the Grey Wolf algorithm is:

[0023]

[0024] in, These represent the α, β, and δ wolf pack leaders, respectively. Indicates the position of the gray wolf in the current round. This represents the position of a randomly selected gray wolf from the current group. Used to control the approximation speed and direction. Used to control the amount of disturbance and the range of contraction.

[0025] In some embodiments, the method further includes:

[0026] Substitute the optimal parameter set into the constitutive model, conduct simulation experiments, and obtain the simulated stress-strain curves;

[0027] Based on the average relative error between the simulated stress-strain curve and the actual experimental curve, it is determined whether the accuracy requirement is met. If it is met, the optimal parameter set is output. If it is not met, the optimal parameter set is used as the starting individual for the search, and iterative optimization is performed again based on the fusion optimization algorithm of genetic algorithm, gray wolf algorithm and particle swarm algorithm.

[0028] A second aspect of the present invention provides a device for identifying constitutive parameters of manganese aluminum bronze JC, comprising:

[0029] The initial parameter acquisition module is configured to obtain the true stress-strain curve of the material through quasi-static compression experiments, and to conduct thermo-mechanical coupling compression experiments under different temperatures and strain rates to extract the stress-strain response under the corresponding conditions and estimate the initial parameter set of the model.

[0030] The verification data acquisition module is configured to conduct a thermo-mechanical coupling compression experiment under set temperature and strain rate conditions, and extract the stress-strain response under the corresponding conditions as verification data.

[0031] The fusion optimization module is configured to construct a parameter optimization space based on the initial parameter set, and perform iterative optimization based on a fusion optimization algorithm of genetic algorithm, gray wolf algorithm and particle swarm algorithm to obtain the optimal parameter set. The fitness function used in the optimization process is: based on the average relative error between the experimental data curve and the fitted data curve, a weighted average is applied, and the variable weight is determined according to the fitting deviation at the yield point and the plastic segment.

[0032] A third aspect of the present invention provides an electronic device including a processor and a memory, wherein the memory stores computer instructions that, when executed by the processor, cause the electronic device to perform the method described thereon.

[0033] A fourth aspect of the present invention provides a computer-readable storage medium having a computer program stored thereon, which, when executed by a processor, implements the method.

[0034] A fifth aspect of the present invention provides a computer program product comprising a computer program that, when executed by a processor, implements the method described herein.

[0035] The above one or more technical solutions address the material properties of manganese aluminum bronze by introducing variable weights based on the fitting deviation between the yield point and the plastic segment into the fitness function. They also employ an iterative optimization algorithm based on a fusion of genetic algorithm, gray wolf algorithm, and particle swarm optimization algorithm. This approach combines the advantages of multiple algorithms, ensuring a global search range to avoid local optima while improving convergence efficiency. Furthermore, the optimization process focuses on key mechanical property regions of manganese aluminum bronze, such as the yield point and plastic segment, thus improving fitting accuracy. The optimized constitutive model can more accurately simulate the mechanical behavior of manganese aluminum bronze. Attached Figure Description

[0036] The accompanying drawings, which form part of this invention, are used to provide a further understanding of the invention. The illustrative embodiments of the invention and their descriptions are used to explain the invention and do not constitute an improper limitation of the invention.

[0037] Figure 1This is a flowchart of the method for identifying constitutive parameters of JC in manganese aluminum bronze in an embodiment of the present invention;

[0038] Figure 2 This is a flowchart illustrating the solution process of the fusion optimization algorithm for the constitutive model in this embodiment of the invention.

[0039] Figure 3 The stress-strain curves and their preliminary fitting curves from the compression experiment;

[0040] Figure 4 The stress-strain curves at 6500 s⁻¹ and 600 °C and the verification of the preliminary fitting curves were obtained.

[0041] Figure 5 The result diagram of the fusion optimization algorithm iteration;

[0042] Figure 6 The graph shows the fitting curve of the optimal parameters obtained by the fusion algorithm.

[0043] Figure 7 The stress-strain curves from the compression experiment and their fitting curves using a genetic algorithm;

[0044] Figure 8 This is a comparison chart of the stress-strain curves from finite element simulation and the experimental stress-strain curves. Detailed Implementation

[0045] Embodiments of this application will now be described in more detail with reference to the accompanying drawings. While some embodiments of this application are shown in the drawings, it should be understood that this application can be implemented in various forms and should not be construed as limited to the embodiments set forth herein. Rather, these embodiments are provided to provide a more thorough and complete understanding of this application. It should be understood that the drawings and embodiments of this application are for illustrative purposes only and are not intended to limit the scope of protection of this application.

[0046] In the description of the embodiments of this application, the term "comprising" and similar terms should be understood as open-ended inclusion, i.e., "including but not limited to". The term "based on" should be understood as "at least partially based on".

[0047] To address the shortcomings of existing technologies in identifying JC constitutive parameters of manganese-aluminum bronze, this invention acquires data through quasi-static compression experiments combined with multi-temperature, multi-strain-rate thermo-mechanical coupling compression experiments. This avoids the high cost and long cycle of traditional techniques involving numerous group experiments. Furthermore, a fusion optimization strategy employing genetic algorithms, gray wolf algorithms, and particle swarm optimization (PSO) is used. The genetic algorithm's global search capability avoids local optima, the gray wolf algorithm's directional convergence capability compresses the parameter space, and the PSO algorithm's local refinement capability balances global exploration and convergence speed, overcoming the limitations of single algorithms in strongly coupled manganese-aluminum bronze parameter scenarios. Simultaneously, a variable weight based on the fitting deviation between the yield point and the plastic segment is introduced into the fitness function, focusing the optimization on the key mechanical region dominated by the multiphase states of manganese-aluminum bronze. This solves the problem of low fitting accuracy caused by existing technologies not specifically adapting to core characteristics, ultimately achieving efficient and high-precision identification of JC parameters for manganese-aluminum bronze.

[0048] The JC constitutive model is as follows:

[0049]

[0050] σ is the flow strain, and ε is the plastic strain. Here, T is the strain rate, and T is the actual temperature. The material flow behavior is defined by five parameters A, B, C, n, and m, which are the yield strength, strain hardening modulus, strain rate hardening coefficient, strain hardening exponent, and thermal softening exponent, respectively. Furthermore, T r and T m These represent the reference strain rate, room temperature, and melting temperature, respectively. For this manganese-aluminum bronze alloy, these are taken as 0.001 s. -1 20℃, 1400℃.

[0051] Regarding the aforementioned JC constitutive model, one or more embodiments of the present invention provide a method for identifying JC constitutive model parameters adapted to manganese aluminum bronze, such as... Figure 1 and Figure 2 As shown, it includes the following steps:

[0052] S101. Obtain the true stress-strain curve of the material through quasi-static compression experiments, and conduct thermo-mechanical coupling compression experiments under different temperatures and strain rates to extract the stress-strain response under the corresponding conditions and estimate the initial parameter set of the model.

[0053] S102. Conduct a thermo-mechanical coupling compression experiment under set temperature and strain rate conditions, and extract the stress-strain response under the corresponding state as verification data.

[0054] S103. Construct a parameter optimization space based on the initial parameter set, and use the error between the validation data and the fitted data as the fitness function. Iteratively optimize using a fusion optimization algorithm based on genetic algorithm, gray wolf algorithm and particle swarm algorithm to obtain the optimal parameter set. The fitness function used in the optimization process is: based on the average relative error between the experimental data curve and the fitted data curve, a weighted average is applied based on variable weights. The variable weights are determined according to the fitting deviation at the yield point and the plastic segment.

[0055] The above technical solution addresses the material properties of manganese aluminum bronze by introducing variable weights based on the fitting deviation between the yield point and the plastic segment into the fitness function. It then uses a fusion optimization algorithm based on genetic algorithm, gray wolf algorithm, and particle swarm optimization to iteratively optimize the model. This approach combines the advantages of multiple algorithms, ensuring a global search range to avoid local optima while improving convergence efficiency. Furthermore, the optimization process focuses on key mechanical property regions of manganese aluminum bronze, such as the yield point and plastic segment, thus improving fitting accuracy. The resulting constitutive model can more accurately simulate the mechanical behavior of manganese aluminum bronze.

[0056] Furthermore, by combining quasi-static compression experiments with thermo-mechanical coupling compression experiments at different temperatures and strain rates, an initial parameter set for estimating stress-strain response under multiple working conditions is obtained. Then, the Genetic-Grey Wolf-Particle Swarm fusion optimization algorithm (GA-GWO-PSO) is introduced for global optimization. Under limited experimental conditions, constitutive parameters that are highly consistent with the measured curves can be obtained. This overcomes the shortcomings of traditional term-by-term fitting methods, such as poor applicability to complex multiphase materials and severe error accumulation. It has the advantages of high accuracy, high efficiency, and strong versatility, and can be extended to constitutive parameter inversion and simulation modeling of other high-strength copper-based and multiphase alloys.

[0057] Step S101 specifically includes:

[0058] S1011. The strain hardening term is isolated from the constitutive model. A compression test is conducted under quasi-static, room temperature conditions to obtain the first stress-strain curve. The yield strength, strain hardening modulus, and strain hardening exponent are obtained by fitting the strain hardening term. It can be understood that under extremely low strain rate and room temperature conditions, the strain rate term and the thermal softening term are approximately 1, and their contribution to the total stress is negligible.

[0059] Specifically, the metal material to be tested is subjected to a strain rate of 0.001 s⁻¹. -1 A Hopkinson bar experiment was conducted under quasi-static conditions at room temperature, denoted as Experiment 1, to obtain the true stress-strain curves under these conditions. The constitutive model formula can then be simplified to:

[0060]

[0061] The yield strength A of the material was obtained from the stress-strain curve in Experiment 1 as 315.98 MPa. Then, by combining the simplified formula and fitting the least squares method, the strain hardening modulus B was found to be 828.82 MPa and the strain hardening exponent n was 0.4079, denoted as A0, B0, and n0.

[0062] S1012. The strain hardening and strain rate hardening terms are separated from the constitutive model. A compression test is conducted at high strain rate and room temperature to obtain a second stress-strain curve. The yield strain and yield stress of the material are determined, and the strain rate hardening index is calculated. It is understandable that, since the temperature remains room temperature, the thermal softening term is still 1. At this point, the difference in stress compared to Experiment 1 is mainly caused by the strain rate effect. By comparing the stress values ​​of Experiment 2 and Experiment 1 at the same strain but different strain rates, the strain rate hardening index C0 can be calculated.

[0063] Specifically, the metal material to be tested is subjected to a strain rate of 4000 s⁻¹. -1 The Hopkinson column test was conducted at a temperature of 20℃, denoted as Experiment 2, to obtain the true stress-strain curves under these conditions. The constitutive model formula can then be simplified to:

[0064]

[0065] Experiment 2 shows that the yield strain of the material is 0.0591 MPa and the yield strength A is 739.77 MPa. The strain rate hardening index C is calculated to be 0.0185, denoted as C0.

[0066] S1013. A compression test was conducted under high strain rate and high temperature conditions to obtain the third stress-strain curve, determine the yield strain and yield stress of the material, and calculate the thermal softening index. It can be understood that by comparing the stress values ​​of Experiment 3 and Experiment 2 under the same strain, similar strain rate, and different temperatures, the thermal softening index m0 can be calculated.

[0067] Specifically, the metal material to be tested is subjected to a strain rate of 4500 s. -1 The Hopkinson column test was conducted at a temperature of 600℃, designated Experiment 3, to obtain the actual stress-strain curves under these conditions. The constitutive model formula can then be written as:

[0068]

[0069] Experiment 3 shows that the yield strain of the material is 0.02984 MPa and the yield strength A is 537.87 MPa. The calculated thermal softening index m is 1.9509, denoted as m0.

[0070] Based on this, an initial parameter set P0=[A0,B0,C0,n0,m0] is obtained. This estimate is based on approximations obtained after decoupling the three effects, and may not be the globally optimal solution. In the following steps, a search interval is constructed based on this initial parameter set, and then the optimal parameter set is found through iterative optimization.

[0071] In step S102, a thermo-mechanical coupling compression experiment is conducted based on temperature and strain rate conditions different from those in the previous experiment, and the stress-strain response under the corresponding conditions is extracted as verification data.

[0072] For example, the metal material to be tested is subjected to a strain rate of 6500 s. -1 A Hopkinson compression test was conducted at 600℃, designated Experiment 4, to obtain the actual stress-strain curves under this condition. Using an independent set of data to evaluate the quality of the parameter set ensures that the identified parameters not only fit known data but also predict the material's behavior under unknown conditions, thereby enhancing the model's generalization and reliability.

[0073] As shown in Table 1, the JC constitutive parameters were initially fitted and solved using the first three sets of specific experimental data. The fitting curves for experiments 1-3 are shown in Table 1. Figure 3 As shown, they correspond to Figure 3 The fitting curves for Experiment 4 are as follows: (a, b, and c are given in the original text.) Figure 4 As shown, the initial constitutive parameters are then extended by ±30%, and the optimal parameters are obtained by fitting the parameters using a fusion optimization algorithm within the new interval. Finally, finite element simulation is performed using Abaqus to verify the results.

[0074] Table 1 Experimental Conditions

[0075]

[0076] In step S103, the parameter values ​​in the initial parameter set are expanded to obtain the search space. The error between the validation data and the fitted data is used as the fitness function. The optimal parameter set is obtained by iterative optimization based on the fusion optimization algorithm of genetic algorithm (GA), gray wolf algorithm (GWO) and particle swarm optimization (PSO).

[0077] For example, let P0 = [A0, B0, C0, n0, m0]. Expanding P0 by ±30% yields the intervals A = [221.186, 410.774], B = [580.174, 1077.466], C = [0.01295, 0.02405], n = [0.28553, 0.53027], m = [1.36563, 2.53617], and the search space P = [A, B, C, n, m].

[0078] Based on the characteristics of manganese-aluminum bronze—its high strain rate sensitivity, high-temperature softening properties, and yield characteristics sensitive to working conditions—a fitness function is established. Specifically, a weighted average is applied based on the average relative error between the experimental and fitted data curves. The variable weights are determined according to the fitting deviation between the yield point and the plastic segment, with an initial value of 1. The function is defined as follows:

[0079]

[0080] Where P = [A, B, C, n, m], This indicates the number of sample points in the experimental data. This represents the weight in the t-th iteration, with an initial value of 1. The stress-strain curve for Experiment 4 is shown. Let represent the experimental data for the i-th sample point, and k represent the optimization stage, identified by GA, GWO, and PSO. When k=GA, ... This represents the fitting curve corresponding to the parameter combination during the optimization process within the search space based on the genetic algorithm, when k=GWO. The fitting result of the gray wolf optimization algorithm is given when k=PSO. This is the fitting result of the particle swarm optimization algorithm. The critical transition region and the plastic segment where the yield point is located on the experimental curve both correspond to continuous data sample points, and these data sample points are generally continuous. The data sample points corresponding to the yield point and the plastic segment are mN. This represents the stress values ​​at the yield point and plastic segment of the fitted curve. The weights are then fine-tuned. The value can be 1.4.

[0081] In the fitness function above, variable weights are set on the basis of traditional average relative error to address the high strain rate sensitivity and high temperature softening characteristics of manganese aluminum bronze. The weights are driven by the fitting deviation of the yield point and plastic segment, and the variable weights are amplified in a directional manner to avoid overestimating stress in the high temperature phase transformation region. This better reflects the characteristics of high temperature softening and avoids the model overestimating stress in the high temperature phase transformation region. It also makes the weights automatically tilt towards high strain rate conditions without additional manual intervention.

[0082] The iterative optimization based on the fusion algorithm of genetic algorithm (GA), gray wolf algorithm (GWO) and particle swarm optimization (PSO) specifically includes:

[0083] (1) Randomly generate an initial population within the search interval, with each individual in the population corresponding to a set of parameters. The total population size is 1000, which serves as the initial population for the GA population.

[0084] (2) Perform a global coarse search on the initial population based on the genetic algorithm (GA) to obtain the GA optimal individuals and generate a set of GA optimal individuals. For example, the set of GA optimal individuals retains the first 500 individuals.

[0085] Specifically, a global coarse search using a genetic algorithm is performed on the GA population. The population size is 1000, and the maximum number of iterations is 200. A tournament selection mechanism is used to select superior individuals for reproduction. Simulated binary crossover (SBX) is used to generate new individuals. Gaussian mutation is used to perturb individual genes with a certain probability to maintain population diversity. During the optimization process, the fitness convergence criterion is set to a relative error of less than 10. -4 To ensure computational accuracy, the best individual in each generation is retained for the next generation, and its output best individual is used as the initial solution for the next stage. At this point, the solution is obtained. Corresponding The optimal individual is then written into both the GWO and PSO populations to achieve information sharing. Leveraging the diversity advantage of the GA population, the solution space can be quickly covered, avoiding local optima traps.

[0086] (3) The best individual in GA is used as the initial α wolf candidate. The best individual in GA is then converged directionally using the gray wolf algorithm within the set of best individuals in GA to obtain the best individual in GWO and generate the set of GWO individuals. For example, the set of best individuals in GWO retains the first 150 individuals.

[0087] Specifically, the Grey Wolf Algorithm is used to achieve directional convergence of the GWO population, with the output of the GA stage as the basis. As the initial alpha wolf candidates for GWO, the new population was subjected to 200 iterations. Every 50 generations, the three individuals with the best fitness were reselected to determine the alpha, beta, and delta wolf pack leaders. The position of ω wolf is updated using the prey-encircling behavior of gray wolves. Let P(t) be the position of a randomly selected gray wolf in the current population. This is to prevent the population from excessively shrinking around individuals α, β, and δ, thus avoiding getting trapped in a local optimum. The solution obtained is... Corresponding The position update formula is:

[0088]

[0089] in, Used to control the approximation speed and direction. Used to control the amount of disturbance and the range of contraction. , , where a is a constant that decreases linearly from 2 to 0, and r1 and r2 are random numbers between [0,1].

[0090] The Grey Wolf Algorithm, by simulating the cooperative search mechanism of the social hierarchy of grey wolves, enables the population to converge quickly to the region indicated by the GA optimal solution, compressing the optimization range and improving the quality of the solution. Furthermore, by introducing... Random individual perturbations enable the optimization process to guide the population towards the optimal parameter region based on the α, β, and δ leader wolves, while also preventing excessive aggregation of the population due to strong coupling of manganese aluminum bronze parameters, thus maintaining the diversity of population parameters and adapting to the characteristics of high strain rate strengthening and high temperature softening.

[0091] (4) Using the GWO optimal individual as the central initial value of the particle swarm algorithm, and using a portion of the GA optimal individual set and the GWO optimal individual set as the search range, perform local optimization to obtain the global optimal parameter set.

[0092] Specifically, the PSO population is locally refined using the particle swarm optimization algorithm, and the output of the GWO stage is... As the central initial value for PSO, an initial population of PSO is constructed and refined iteratively is performed using the standard formula of the particle swarm optimization algorithm. The adaptive inertia ω decreases linearly from 0.9 to 0.4, the weights of individual c1 and population experience c2 are both 1.6, and r1 and r2 are random numbers between [0,1]. The initial velocity of the particle is 0. This is the optimal solution in the initial population of PSO. This represents the currently calculated particle position in the PSO population. The solution obtained at this point is... Corresponding The standard formula for the particle swarm optimization algorithm is:

[0093]

[0094] By iteratively updating particle velocity and position, and leveraging the strong local exploitation capabilities of PSO, the system searches within a local region near the GWO optimal solution to achieve precise parameter fine-tuning and obtain the globally optimal parameter set.

[0095] (5) The constitutive parameters are used in finite element simulation to conduct simulation experiments, and the simulated stress-strain curves are obtained. It is then determined whether the accuracy requirements are met, specifically whether the average relative error between the simulated curve and the actual experimental curve is less than 2%. If this requirement is met, then... Let be the constitutive parameter of JC, and if it is not satisfied, let Optimize again.

[0096] The iteration terminated when the average relative error was less than 2% during the third iteration, indicating that the JC constitutive model at this point was the optimal parameter combination model selected by the optimization algorithm. Figure 5 As shown, the objective function value reaches 0.0135, satisfying the model conditions. The fitted curve obtained with these optimal parameters is compared with the experimental curve, as shown below. Figure 6As shown, it can accurately reflect the mechanical behavior of materials under different strain, strain rate, and temperature conditions. The values ​​of its parameters (such as initial yield stress, strain hardening coefficient, strain rate sensitivity coefficient, temperature softening coefficient, etc.) have achieved a high degree of fit to the experimental data through multiple generations of evolutionary iterations. The final JC constitutive parameters are A=312.77MPa, B=771.71MPa, n=0.38, C=0.0219, and m=1.892.

[0097] like Figure 7 As shown, the stress-strain curves of the plastic stage under four typical experimental conditions (different combinations of strain rate and temperature) were fitted and verified. Experiments 1-4 correspond to... Figure 7 a, b, c, and d in the figure represent the degree of fit (coefficient of determination) before and after optimization. The comparison results are shown in Table 2.

[0098] Table 2 Comparison of Fit Before and After Optimization

[0099]

[0100] The results show that the fusion optimization algorithm can improve the overall fitting accuracy between the model prediction curve and the experimental curve under different thermo-mechanical loading conditions. Especially under high strain rate and high temperature conditions, the optimized model describes the stress response of the material in the plastic stage more accurately, and the coefficient of determination of the curve is higher. The maximum increase reached 0.0353, and the average increase reached 0.0169. For example... Figure 8 As shown, the obtained JC model parameters are in good agreement with the experimental stress-strain curves in the finite element simulation, and the obtained parameters can predict the mechanical behavior of the material. This optimization strategy significantly improves the stability and versatility of the J-C model parameters under complex thermo-mechanical coupling conditions, and provides a reliable parameter basis for accurate modeling of manganese-aluminum bronze-like multiphase alloys in high-performance cutting, impact, and high-temperature deformation simulations.

[0101] The above one or more embodiments obtain real stress-strain data under different temperatures and strain rates through quasi-static and high-strain-rate compression experiments to establish an initial J-C model parameter set. Then, a Genetic-Grey Wolf-Particle Swarm Optimization (GA-GWO-PSO) fusion optimization algorithm is introduced into the parameter space for global optimization. Combined with dynamic crossover mutation probability adjustment, elite retention, parallel cooperative evolution, adaptive error weighting, and a center-encircling mechanism, efficient identification of five parameters—yield strength, strain hardening modulus, strain rate sensitivity coefficient, strain hardening exponent, and thermal softening exponent—is achieved. Subsequently, through finite element simulation feedback correction and error re-optimization mechanisms, the physical consistency and prediction accuracy of the parameters are further improved. Through multi-intelligent algorithm collaborative optimization and adaptive feedback correction mechanisms, the high-dimensional coupling and convergence instability problems existing in the traditional parameter solution process are solved, significantly enhancing the model's predictive ability under strain rate, temperature, and microstructure effects.

[0102] Furthermore, one or more of the above embodiments can obtain constitutive parameters that are highly consistent with the measured curves under limited experimental conditions, overcoming the shortcomings of traditional term-by-term fitting methods, such as poor applicability to complex multiphase materials and severe error accumulation. They have the advantages of high precision, high efficiency and strong versatility, and can be extended to the field of constitutive modeling and thermo-mechanical coupling simulation calibration of titanium alloys, aluminum alloys and high-temperature structural materials, providing highly reliable theoretical and computational support for the design simulation of complex alloy materials in the fields of shipbuilding, aviation and marine engineering.

[0103] Based on the above method, one or more embodiments of the present invention also provide a device for identifying the constitutive parameters of manganese aluminum bronze JC, comprising:

[0104] The initial parameter acquisition module is configured to obtain the true stress-strain curve of the material through quasi-static compression experiments, and to conduct thermo-mechanical coupling compression experiments under different temperatures and strain rates to extract the stress-strain response under the corresponding conditions and estimate the initial parameter set of the model.

[0105] The verification data acquisition module is configured to conduct a thermo-mechanical coupling compression experiment under set temperature and strain rate conditions, and extract the stress-strain response under the corresponding conditions as verification data.

[0106] The fusion optimization module is configured to construct a parameter optimization space based on the initial parameter set, and perform iterative optimization based on a fusion optimization algorithm of genetic algorithm, gray wolf algorithm and particle swarm algorithm to obtain the optimal parameter set. The fitness function used in the optimization process is: based on the average relative error between the experimental data curve and the fitted data curve, a weighted average is applied, and the variable weight is determined according to the fitting deviation at the yield point and the plastic segment.

[0107] One or more embodiments of the present invention also provide an electronic device that can be used to implement the method for identifying the constitutive parameters of manganese aluminum bronze (JC) described in the above embodiments. The electronic device includes one or more processors, one or more memories coupled to the processors, and a communication module coupled to the processors.

[0108] The memory may include one or more non-volatile memories and one or more volatile memories. Examples of non-volatile memories include, but are not limited to, at least one of the following: read-only memory (ROM), erasable programmable read-only memory (EPROM), flash memory, hard disk, compact disc (CD), digital video disc (DVD), or other magnetic and / or optical storage. Examples of volatile memories include, but are not limited to, at least one of the following: random access memory (RAM), or other volatile memories that do not persist during power-off periods. The computer program may be stored in the ROM. When the processor executes the computer program, it implements the above-described method for identifying the constitutive parameters of JC in manganese aluminum bronze.

[0109] In some embodiments, the program may be tangibly contained in a computer-readable medium, which may include in a device (such as in memory) or other storage device accessible by the device. The program may be loaded from the computer-readable medium into RAM for execution. The computer-readable medium may include any type of tangible non-volatile memory, such as ROM, EPROM, flash memory, hard disk, whereby the computer-readable storage medium stores a computer program that, when executed by a processor, implements the aforementioned method for identifying constitutive parameters of manganese aluminum bronze JC.

[0110] In the above embodiments, implementation can be achieved entirely or partially through software, hardware, firmware, or any combination thereof. When implemented using software, it can be implemented entirely or partially in the form of a computer program product. The computer program product includes one or more computer instructions. When these computer program instructions are loaded and executed on a server or terminal, they generate, in whole or in part, the processes or functions described in the embodiments of this application. The computer instructions can be stored in a computer-readable storage medium or transmitted from one computer-readable storage medium to another. For example, the computer instructions can be transmitted from one website, computer, server, or data center to another website, computer, server, or data center via wired (e.g., coaxial cable, fiber optic cable, digital subscriber line) or wireless (e.g., infrared, wireless, microwave, etc.) means. The computer-readable storage medium can be any available medium accessible to the server or terminal, or a data storage device such as a server or data center that integrates one or more available media. The available medium can be a magnetic medium (e.g., floppy disk, hard disk, and magnetic tape), an optical medium (e.g., digital video disk (DVD), etc.), or a semiconductor medium (e.g., solid-state drive).

[0111] Furthermore, although the operations are described in a specific order, this should be understood as requiring that such operations be performed in the specific order shown or in sequential order, or requiring that all illustrated operations be performed to achieve the desired result. In certain environments, multitasking and parallel processing may be advantageous. Similarly, although several specific implementation details are included in the above discussion, these should not be construed as limiting the scope of this application. Certain features described in the context of individual embodiments may also be implemented in combination in a single implementation. Conversely, various features described in the context of a single implementation may also be implemented individually or in any suitable sub-combination in multiple implementations.

[0112] Although the subject matter has been described using language specific to structural features and / or methodological logic, it should be understood that the subject matter defined in the appended claims is not necessarily limited to the specific features or actions described above. Rather, the specific features and actions described above are merely illustrative examples of implementing the claims.

Claims

1. A method for identifying constitutive parameters of JC in manganese aluminum bronze, characterized in that, Includes the following steps: The true stress-strain curve of the material is obtained by quasi-static compression experiments, and thermo-mechanical coupled compression experiments are carried out under different temperatures and strain rates. The stress-strain response under the corresponding conditions is extracted, and the initial parameter set of the model is estimated. A thermo-mechanical coupling compression experiment was conducted under set temperature and strain rate conditions, and the stress-strain response under the corresponding conditions was extracted as verification data. A parameter optimization space is constructed based on the initial parameter set. An iterative optimization algorithm based on the fusion of genetic algorithm, gray wolf algorithm and particle swarm algorithm is used to obtain the optimal parameter set. The fitness function used in the optimization process is: based on the average relative error between the experimental data curve and the fitted data curve, a weighted average is applied based on variable weights. The variable weights are determined according to the fitting deviation between the yield point and the plastic segment. Iterative optimization based on a fusion optimization algorithm of genetic algorithm, gray wolf algorithm and particle swarm optimization includes: An initial population is randomly generated within the search interval, and each individual in the population corresponds to a set of parameters. A global coarse search is performed on the initial population based on the genetic algorithm to obtain the optimal individual in the GA and generate a set of optimal individuals in the GA. The best individual in GA is used as the initial α wolf candidate. The gray wolf algorithm is used to perform directional convergence within the set of best individuals in GA to obtain the best individual in GWO and generate the set of GWO individuals. Using the best individual in GWO as the central initial value of the particle swarm algorithm, and taking a portion of the best individual set in GA and the best individual set in GWO as the search range, local optimization is performed to obtain the globally optimal parameter set. The fitness function used in the fusion optimization algorithm is: Where P represents the combination of parameters to be optimized. This indicates the number of sample points in the experimental data. This represents the weight in the t-th iteration, with an initial value of 1. Let represent the experimental stress value of the i-th sample point, k denote the optimization stage (identified by GA, GWO, and PSO), and m be the starting point of the continuous sample points corresponding to the yield point and the plastic segment. To fit the stress values ​​at the yield point and in the plastic segment of the curve, This is for fine-tuning the weights.

2. The method for identifying constitutive parameters of JC in manganese-aluminum bronze as described in claim 1, characterized in that, The process of estimating the initial parameter set of the model includes: The strain hardening term was isolated from the constitutive model, and a compression experiment was conducted under quasi-static, room temperature conditions to obtain the first stress-strain curve. The yield strength, strain hardening modulus and strain hardening exponent were obtained by fitting the strain hardening term. The strain hardening term and strain rate hardening term were separated from the constitutive model. Compression experiments were conducted under high strain rate and room temperature conditions to obtain the second stress-strain curve. The yield strain and yield stress of the material were determined, and the strain rate hardening index was calculated. Compression experiments were conducted under high strain rate and high temperature conditions to obtain the third stress-strain curve, determine the yield strain and yield stress of the material, and calculate the thermal softening index.

3. The method for identifying constitutive parameters of JC in manganese-aluminum bronze as described in claim 1 or 2, characterized in that, In the Grey Wolf Algorithm, the position update formula is: in, These represent the α, β, and δ wolf pack leaders, respectively. Indicates the position of the gray wolf in the current round. This represents the position of a randomly selected gray wolf from the current group. Used to control the approximation speed and direction. Used to control the amount of disturbance and the range of contraction.

4. The method for identifying constitutive parameters of JC bronze as described in claim 1, characterized in that, The method further includes: Substitute the optimal parameter set into the constitutive model, conduct simulation experiments, and obtain the simulated stress-strain curves; Based on the average relative error between the simulated stress-strain curve and the actual experimental curve, it is determined whether the accuracy requirement is met. If it is met, the optimal parameter set is output. If it is not met, the optimal parameter set is used as the starting individual for the search, and iterative optimization is performed again based on the fusion optimization algorithm of genetic algorithm, gray wolf algorithm and particle swarm algorithm.

5. A device for identifying constitutive parameters of JC in manganese-aluminum bronze, characterized in that, include: The initial parameter acquisition module is configured to obtain the true stress-strain curve of the material through quasi-static compression experiments, and to conduct thermo-mechanical coupling compression experiments under different temperatures and strain rates to extract the stress-strain response under the corresponding conditions and estimate the initial parameter set of the model. The verification data acquisition module is configured to conduct a thermo-mechanical coupling compression experiment under set temperature and strain rate conditions, and extract the stress-strain response under the corresponding conditions as verification data. The fusion optimization module is configured to construct a parameter optimization space based on an initial parameter set, and perform iterative optimization based on a fusion optimization algorithm of genetic algorithm, gray wolf algorithm and particle swarm algorithm to obtain the optimal parameter set. The fitness function used in the optimization process is: based on the average relative error between the experimental data curve and the fitted data curve, a weighted average is applied based on variable weights, and the variable weights are determined according to the fitting deviation between the yield point and the plastic segment. Iterative optimization based on a fusion optimization algorithm of genetic algorithm, gray wolf algorithm and particle swarm optimization includes: An initial population is randomly generated within the search interval, and each individual in the population corresponds to a set of parameters. A global coarse search is performed on the initial population based on the genetic algorithm to obtain the optimal individual in the GA and generate a set of optimal individuals in the GA. The best individual in GA is used as the initial α wolf candidate. The gray wolf algorithm is used to perform directional convergence within the set of best individuals in GA to obtain the best individual in GWO and generate the set of GWO individuals. Using the best individual in GWO as the central initial value of the particle swarm algorithm, and taking a portion of the best individual set in GA and the best individual set in GWO as the search range, local optimization is performed to obtain the globally optimal parameter set. The fitness function used in the fusion optimization algorithm is: Where P represents the combination of parameters to be optimized. This indicates the number of sample points in the experimental data. This represents the weight in the t-th iteration, with an initial value of 1. Let represent the experimental stress value of the i-th sample point, k denote the optimization stage (identified by GA, GWO, and PSO), and m be the starting point of the continuous sample points corresponding to the yield point and the plastic segment. To fit the stress values ​​at the yield point and in the plastic segment of the curve, This is for fine-tuning the weights.

6. An electronic device, characterized in that, It includes a processor and a memory, the memory storing computer instructions that, when executed by the processor, cause the electronic device to perform the method of any one of claims 1 to 4.

7. A computer-readable storage medium having a computer program stored thereon, characterized in that, When the program is executed by the processor, it implements the method according to any one of claims 1 to 4.

8. A computer program product, the computer program product comprising a computer program, characterized in that, When the computer program is executed by a processor, it implements the method as described in any one of claims 1 to 4.

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