An improved Chaboche model and its parameter identification method for friction stir welding.

Abstract

This invention provides an improved Chaboche model suitable for friction stir welding. The improved Chaboche model distinguishes tensile and compressive responses by the difference between the elastic trial stress and the total back stress; it introduces equivalent plastic strain and historical peak residual strain to characterize elastic modulus degradation and isotropic soft hardening behavior; it uses the superposition of multiple independent nonlinear components to characterize kinematic hardening; and it calibrates the elastic modulus degradation, isotropic soft hardening, and kinematic hardening parameters in both the tensile and compressive domains to achieve selectable tensile and compressive response asymmetry modeling. This invention also provides a parameter identification method for the improved Chaboche model suitable for friction stir welding. By improving the multi-mechanism coupling characterization capability of the Chaboche model and combining it with swarm intelligence optimization algorithms, this invention provides an efficient tool for fatigue life prediction and structural optimization of friction stir welded joints, significantly enhancing the engineering application value of numerical simulation.

Description

Technical Field

[0001] This invention relates to the field of friction stir welding technology, and in particular to an improved Chaboche model and its parameter identification method suitable for friction stir welding. Background Technology

[0002] Friction stir welding (FSW) is a solid-state joining process. Its basic principle involves the friction and compression between a high-speed rotating stirring head and the workpiece to rapidly heat the material in the joint area to a viscoplastic state. As the stirring head moves along the joint path at a certain forward speed, a stable zone of plastic material flow forms behind it. Under the compression of the stirring head shoulder, the plasticized material is recompacted and cooled, forming a dense, continuous, and firmly bonded weld. Compared to traditional fusion welding processes, such as TIG or MIG welding, FSW significantly reduces the risk of welding deformation and hot cracking due to its lower heat input and temperature gradient. Its welded joints exhibit advantages such as high strength, low residual stress, fewer defects, and no need for filler material. It has been successfully applied in aerospace, automotive manufacturing, and industrial construction, showing broad application prospects in the joining of aluminum-based materials.

[0003] In actual service, friction stir welded aluminum alloy butt joints are often subjected to low-cycle cyclic loading, and their mechanical response significantly depends on the existing plastic loading history. To accurately characterize the nonlinear mechanical response of metallic materials under low-cycle cyclic loading in numerical simulations, existing techniques typically utilize cyclic constitutive models for finite element modeling and analysis, such as the Dafalias-Popov hyperboloid model and the traditional Chaboche model. A reasonable cyclic constitutive model can not only characterize the nonlinear behaviors of materials under low-cycle cyclic loading, such as strain soft hardening, temperature effects, and strain rate effects, but also effectively capture complex mechanical phenomena such as memory effects, Bauschinger effects, and ratcheting effects. The construction of cyclic constitutive models is of great significance for the design optimization of structural components, providing a reliable numerical basis for high-precision simulation of structural mechanical responses under complex service conditions, thereby improving material utilization efficiency and reducing manufacturing costs.

[0004] The hysteresis curve of friction stir welded aluminum alloy butt joints exhibits a full, spindle-shaped characteristic. During cyclic loading, it shows significant loading path correlation due to the coupling effect of multiple mechanisms, including dislocation density evolution and material microstructure damage accumulation. Under different loading regimes, friction stir welded aluminum alloy butt joints exhibit significant differences in mechanical characteristics, including elastic modulus degradation, isotropic soft hardening, and asymmetric tensile and compressive responses. Traditional Chaboche models are insufficient to effectively characterize these complex properties. With the rapid development of simulation technology, although various improved cyclic constitutive models have been proposed, they generally face problems such as complex model structures, low computational efficiency, limited accuracy, and cumbersome parameter identification, making it difficult to meet the actual needs of rapid prediction and performance evaluation in engineering. Therefore, it is urgent to construct a cyclic constitutive model suitable for friction stir welded aluminum alloy butt joints with clear physical mechanisms, high computational performance, and a simple parameter identification process to support the numerical simulation and engineering applications of this type of connection structure in aerospace, automotive, and construction fields. Summary of the Invention

[0005] To address the aforementioned issues, this invention aims to propose an improved Chaboche model and its parameter identification method suitable for friction stir welding. By improving the multi-mechanism coupling characterization capability of the Chaboche model and combining it with an intelligent parameter optimization method, this invention provides an efficient tool for fatigue life prediction and structural optimization of friction stir welded joints, significantly enhancing the engineering application value of numerical simulation.

[0006] To achieve the above objectives, the technical solution of the present invention is implemented as follows:

[0007] An improved Chaboche model suitable for friction stir welding is proposed. The improved Chaboche model distinguishes the tensile and compressive responses by the difference between the elastic trial stress and the total back stress; it introduces equivalent plastic strain and the history peak residual strain to characterize the elastic modulus degradation and isotropic soft hardening behavior; it uses the superposition of multiple independent nonlinear components to characterize kinematic hardening; and it calibrates the elastic modulus degradation, isotropic soft hardening, and kinematic hardening parameters in the tensile and compressive domains respectively to achieve optional tensile and compressive response asymmetry modeling.

[0008] Furthermore, the elastic stiffness matrix of the improved Chaboche model is:

[0009]

[0010] Where C is the elastic stiffness matrix; λ is the first Lamé parameter; G is the shear modulus; v is the Poisson's ratio; E n E is the current elastic modulus; E0 is the initial elastic modulus; E sat ω represents the saturation value of the elastic modulus degradation; ω and μ are parameters that control the rate of elastic modulus degradation. For equivalent plastic strain; ε p,m ε is the peak residual strain; σ is the total strain; and σ is the Von Mises stress.

[0011] Furthermore, the yield criterion and hardening criterion of the improved Chaboche model are as follows:

[0012]

[0013] Where f is the yield function; σ e σ is the equivalent stress; σ|0 is the initial yield stress; S is the deviatoric stress tensor; α is the back stress tensor; R is the isotropic soft hardening component; α i C represents the i-th back stress component; N is the number of back stress groups, and increasing the value of N can improve the accuracy of kinematic hardening; i and γ i Q represents the kinematic hardening parameter. ∞ and D ∞ , respectively, represent the hardening saturation value and the softening saturation value; b and a represent the isotropic hardening rate and the softening rate, respectively; k and r are material parameters that control the soft hardening saturation value; This represents the equivalent plastic strain increment.

[0014] Furthermore, the flow criterion of the improved Chaboche model is as follows:

[0015]

[0016] Where, dε p dη is the plastic strain increment tensor; σ′ is the plastic multiplier; σ′ is the stress tensor.

[0017] Furthermore, the tensile and compressive response criterion of the improved Chaboche model is:

[0018]

[0019] Where, σ trial α represents the current elastic test stress; α represents the total back stress.

[0020] Furthermore, the improved Chaboche model adopts a dual-domain definition method for its parameter system, with a total of 22+4N parameters, where N is the number of back stress groups. The specific composition of the model parameters is as follows: Tensile domain parameters (11+2N): E 0,拉 E sat,拉 ω 拉 μ 拉 , b 拉 a 拉 k 拉 r拉 σ| 0,拉 and N groups C i,拉 and γ i,拉 (i = 1, 2, 3…N); Compression domain parameter (11 + 2N): E 0,压 E sat,压 ω 压 μ 压 , b 压 a 压 k 压 r 压 σ| 0,压 and N groups C i,压 and γ i,压 (i = 1, 2, 3…N).

[0021] Furthermore, for materials exhibiting symmetric tensile-compressive response characteristics—centered on the back stress—the improved Chaboche model is simplified to be defined using only the tensile domain parameters, with the compressive domain parameters set to be the same as the tensile domain parameters, i.e., E. 0,拉 =E 0,压 E sat,拉 =E sat,压 ω 拉 =ω 压 μ 拉 =μ 压 , b 拉 =b 压 a 拉 =a 压 k 拉 =k 压 r 拉 =r 压 σ| 0,拉 =σ| 0,压 and C i,拉 =C i,压 and γ i,拉 =γ i,压 (i = 1, 2, 3…N).

[0022] Furthermore, for materials that exhibit compressive buckling and tension-compression asymmetry, the improved Chaboche model establishes a dual-domain constitutive relation by independently defining parameter sets for the tension and compression domains to achieve differentiated characterization of compressive and tensile behaviors.

[0023] To achieve the above objectives, the present invention also provides a parameter identification method for an improved Chaboche model suitable for friction stir welding, comprising the following steps:

[0024] S1: Low-cycle cyclic loading tests were conducted on aluminum alloy butt joint test specimens subjected to friction stir welding under various load conditions, and complete hysteresis curve data were collected.

[0025] S2: Based on equivalent plastic strain, historical peak residual strain, elastic trial stress and total back stress, an improved Chaboche cyclic constitutive model with elastic modulus degradation, kinematic hardening, isotropic soft hardening and optional tension-compression response asymmetry characteristics is constructed, and the model parameter set to be identified is determined accordingly.

[0026] S3: Based on the hysteresis curve data obtained from the experiment, the improved Chaboche model is inverted using the sparrow search algorithm to minimize the deviation between the model's predicted stress and the experimental stress, and finally obtains the optimal model parameter solution set; its fitness function is:

[0027]

[0028] Where, σ opt Predict stress for the model; σ exp For stress measurement in the experiment, K is the total number of measurement points for all test pieces or the total number of data points after data noise reduction processing;

[0029] During the global optimization process, the explorer's position is updated as follows:

[0030]

[0031] Among them, X i,j Let κ be the position of the i-th sparrow in the j-th dimension; n is the current iteration number; κ max α is the maximum number of iterations. s A random number between 0 and 1 that satisfies α s ≠ 0; Q is a random number following a normal distribution; L is a row vector containing d elements of 1; W T and S T These are the warning value and the safe value, respectively.

[0032] During the global optimization process, the joiner's position is updated as follows:

[0033]

[0034] Among them, X p The optimal position for the current explorer; X W This represents the current worst-case position globally; A + Let A be a row vector containing d elements of 1 or -1, and satisfy A + =A T (AA T ) -1 ;

[0035] During the global optimization process, the location of the vigilant is updated as follows:

[0036]

[0037] Among them, X b The current global optimal position; β and η are random numbers; f i f g and f w These are the fitness values ​​for the current individual, the current global best solution, and the current global worst solution, respectively; Ψ is a non-zero decimal.

[0038] Furthermore, the parameter range of the improved Chaboche model is determined by trial and error, and the improved Chaboche model uses Latin hypercube sampling and initializes the population in a multidimensional parameter space.

[0039] Beneficial effects: By improving the multi-mechanism coupling representation capability of the Chaboche model and combining it with swarm intelligence optimization algorithms, this invention provides an efficient tool for fatigue life prediction and structural optimization of friction stir welded joints, significantly enhancing the engineering application value of numerical simulation. Attached Figure Description

[0040] 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 undue limitation of the invention. In the drawings:

[0041] Figure 1 This is an overall flowchart of the parameter identification method for the improved Chaboche model applicable to friction stir welding as described in an embodiment of the present invention.

[0042] Figure 2 The parameter identification method for the improved Chaboche model applicable to friction stir welding, under the condition that N=3 and the compression domain parameter is equal to the tensile domain parameter, is used to compare the hysteresis curves and experimental data of the 6061-T6 friction stir welded aluminum alloy butt joint test specimens under three low-cycle cyclic loading regimes.

[0043] Figure 3 For the parameter identification method of the improved Chaboche model applicable to friction stir welding, under the condition that N=3 and the compression domain parameter is not equal to the tensile domain parameter, the hysteresis curve of the 7075-T6 friction stir welded aluminum alloy butt joint test piece under three low-cycle cyclic loading regimes is compared with the experimental measured data.

[0044] Figure 4A schematic diagram of the friction stir welding process for aluminum alloy plates, to which the parameter identification method for the improved Chaboche model applicable to friction stir welding is described.

[0045] Figure 5 A schematic diagram of the test specimen sampling locations for which the parameter identification method for the improved Chaboche model applicable to friction stir welding is applicable;

[0046] Figure 6 for Figure 2 Schematic diagram of loading regime for test specimens of friction stir welded aluminum alloy butt joints of China 6061-T6;

[0047] Figure 7 for Figure 3 Schematic diagram of loading regime for test specimens of friction stir welded aluminum alloy butt joints of China 7075-T6;

[0048] Figure 8 Based on Figure 2 Elastic modulus degradation surface and isotropic soft hardening evolution surface of the improved Chaboche cyclic constitutive model for hysteresis curve calibration of 6061-T6 aluminum alloy butt joint test specimens by friction stir welding.

[0049] Figure 9 When the compression domain parameters are taken as 0 times, 1 / 4 times, 1 / 2 times, 3 / 4 times, 1 time, and 1.5 times the stretching domain parameters, the following is adopted: Figure 6 The hysteresis curve plotted under loading regime 3;

[0050] Figure 10 This is a schematic diagram of the residual strain at the peak of the process. Detailed Implementation

[0051] It should be noted that, unless otherwise specified, the embodiments and features described in the present invention can be combined with each other.

[0052] The present invention will now be described in detail with reference to the accompanying drawings and embodiments.

[0053] Example 1

[0054] An improved Chaboche model suitable for friction stir welding is proposed. The improved Chaboche model distinguishes the tensile and compressive responses by the difference between the elastic trial stress and the total back stress; it introduces equivalent plastic strain and the history peak residual strain to characterize the elastic modulus degradation and isotropic soft hardening behavior; it uses the superposition of multiple independent nonlinear components to characterize kinematic hardening; and it calibrates the elastic modulus degradation, isotropic soft hardening, and kinematic hardening parameters in the tensile and compressive domains respectively to achieve optional tensile and compressive response asymmetry modeling.

[0055] In a specific example, the elastic stiffness matrix of the improved Chaboche model is:

[0056]

[0057] Where C is the elastic stiffness matrix; λ is the first Lamé parameter; G is the shear modulus; v is the Poisson's ratio; E n E is the current elastic modulus; E0 is the initial elastic modulus; E sat ω represents the saturation value of the elastic modulus degradation; ω and μ are parameters that control the rate of elastic modulus degradation. For equivalent plastic strain; ε p,m ε is the peak residual strain; σ is the total strain; and σ is the Von Mises stress.

[0058] In a specific example, the yield criterion and hardening criterion of the improved Chaboche model are:

[0059]

[0060] Where f is the yield function; σ e σ is the equivalent stress; σ|0 is the initial yield stress; S is the deviatoric stress tensor; α is the back stress tensor; R is the isotropic soft hardening component; α i C represents the i-th back stress component; N is the number of back stress groups, and increasing the value of N can improve the accuracy of kinematic hardening; i and γ i Q represents the kinematic hardening parameter. ∞ and D ∞ , respectively, represent the hardening saturation value and the softening saturation value; b and a represent the isotropic hardening rate and the softening rate, respectively; k and r are material parameters that control the soft hardening saturation value; This represents the equivalent plastic strain increment.

[0061] In a specific example, the flow criterion of the improved Chaboche model is:

[0062]

[0063] Where, dε p dη is the plastic strain increment tensor; σ′ is the plastic multiplier; σ′ is the stress tensor.

[0064] In a specific example, the tensile and compressive response criterion of the improved Chaboche model is:

[0065]

[0066] Where, σ trial α represents the current elastic test stress; α represents the total back stress.

[0067] In a specific example, the improved Chaboche model adopts a tension-compression dual-domain definition for its model parameter system, with a total of 22+4N parameters, where N is the number of back stress groups. The specific composition of the model parameters is as follows: Tensile domain parameters (11+2N): E 0,拉 E sat,拉 ω 拉 μ 拉 , b 拉 a 拉 k 拉 r 拉 σ| 0,拉 and N groups C i,拉 and γ i,拉 (i = 1, 2, 3…N); Compression domain parameter (11 + 2N): E 0,压 E sat, Pressure, ω pressure, μ pressure b-pressure, a-pressure, k-pressure, r-pressure, σ| 0, Pressure and N group C i, Pressure and γ i, Pressure (i=1,2,3...N).

[0068] In a specific instance, for materials exhibiting symmetric tensile-compressive response characteristics (centered on the back stress), the improved Chaboche model is simplified to be defined using only the tensile domain parameters, with the compressive domain parameters set to be the same as the tensile domain parameters, i.e., E. 0,拉 =E 0,压 E sat,拉 =E sat,压 ω 拉 =ω 压 μ 拉 =μ 压 , b 拉 =b 压 a 拉 =a 压 k 拉 =k 压 r 拉 =r 压 σ| 0,拉 =σ| 0,压 and C i,拉 =C i,压 and γ i,拉 =γ i,压 (i = 1, 2, 3…N).

[0069] In a specific instance, for materials exhibiting compressive buckling and tension-compression asymmetry, the improved Chaboche model establishes a dual-domain constitutive relation by independently defining parameter sets for the tension and compression domains to achieve differentiated characterization of compressive and tensile behaviors.

[0070] In summary, this embodiment achieves:

[0071] Elastic modulus degradation: By introducing equivalent plastic strain and history peak residual strain, the elastic modulus is dynamically adjusted to characterize the stiffness decay characteristics of the material under cyclic loading.

[0072] Isotropic soft hardening: The soft hardening behavior of yield stress is described by dual-domain parameters (tension / compression), which solves the problem that traditional models cannot reflect the asymmetric response of tension and compression.

[0073] Kinematic hardening: Enhances adaptability to complex back stress paths by superimposing multiple sets of nonlinear back stress components.

[0074] Tension-compression response criterion: Based on the difference between the elastic test stress and the total back stress, the mechanical behavior in the tensile and compressive domains is dynamically distinguished.

[0075] Example 2

[0076] To achieve the above objectives, see Figure 1-10 This embodiment also provides a parameter identification method for an improved Chaboche model suitable for friction stir welding, including the following steps:

[0077] S1: Low-cycle cyclic loading tests were conducted on aluminum alloy butt joint test specimens subjected to friction stir welding under various load conditions, and complete hysteresis curve data were collected.

[0078] S2: Based on equivalent plastic strain, historical peak residual strain, elastic trial stress and total back stress, an improved Chaboche cyclic constitutive model with elastic modulus degradation, kinematic hardening, isotropic soft hardening and optional tension-compression response asymmetry characteristics is constructed, and the model parameter set to be identified is determined accordingly.

[0079] S3: Based on the hysteresis curve data obtained from the experiment, the improved Chaboche model is inverted using the sparrow search algorithm to minimize the deviation between the model's predicted stress and the experimental stress, and finally obtains the optimal model parameter solution set; its fitness function is:

[0080]

[0081] Where, σ opt Predict stress for the model; σ expFor stress measurement in the experiment, K is the total number of measurement points for all test pieces or the total number of data points after data noise reduction processing;

[0082] During the global optimization process, the explorer's position is updated as follows:

[0083]

[0084] Among them, X i,j Let κ be the position of the i-th sparrow in the j-th dimension; n is the current iteration number; κ max α is the maximum number of iterations. s A random number between 0 and 1 that satisfies α s ≠ 0; Q is a random number following a normal distribution; L is a row vector containing d elements of 1; W T and S T These are the warning value and the safe value, respectively.

[0085] During the global optimization process, the joiner's position is updated as follows:

[0086]

[0087] Among them, X p The optimal position for the current explorer; X W This represents the current worst-case position globally; A + Let A be a row vector containing d elements of 1 or -1, and satisfy A + =A T (AA T ) -1 ;

[0088] During the global optimization process, the location of the vigilant is updated as follows:

[0089]

[0090] Among them, X b The current global optimal position; β and η are random numbers; f i f g and f w These are the fitness values ​​for the current individual, the current global best solution, and the current global worst solution, respectively; Ψ is a non-zero decimal.

[0091] This embodiment effectively solves the problem that traditional single constitutive models cannot accurately reflect the differences in mechanical characteristics exhibited by friction stir welded aluminum alloy butt joints under different loading regimes, including behaviors such as elastic modulus degradation, isotropic soft hardening, and tension-compression response asymmetry. The proposed improved Chaboche cyclic constitutive model has a clear physical mechanism, clear meaning of each parameter, and good computational efficiency. The sparrow search algorithm is used to inversely optimize the model parameters, effectively avoiding the problem of getting trapped in local optima in high-dimensional parameter identification. Through this method, a cyclic constitutive model applicable to multiple loading regimes and capable of accurately characterizing the tension-compression response asymmetry mechanism can be established, enabling the analysis and application of friction stir welded aluminum alloy structures in advanced analysis and engineering fields. This embodiment has the advantages of being fast, accurate, easy to operate, and effective.

[0092] In a specific example, to improve recognition efficiency and stability, the parameter range of the improved Chaboche model is determined by trial and error. The improved Chaboche model uses Latin hypercube sampling and initializes the population in a multidimensional parameter space.

[0093] It should be noted that this embodiment calculates the peak residual strain using the forward Euler method. When computational resources are insufficient, the dimensionality of the search space can be selectively reduced by fixing some parameters. All test specimens of friction stir welded aluminum alloy butt joints under all load conditions should be measured using extensometers with the same gauge length. The aluminum alloy base material can also use a modified Chaboche cyclic constitutive model as the material model for numerical simulation. During numerical simulation, the modified Chaboche cyclic constitutive model of the friction stir welded aluminum alloy butt joint test specimen is input for the region within the gauge length of the extensometer, and the modified Chaboche cyclic constitutive model of the aluminum alloy base material is input for the region outside the gauge length of the extensometer to improve simulation accuracy.

[0094] In summary, the Sparrow Optimization Algorithm (SSA) of this embodiment uses the experimental hysteresis curve as a benchmark to construct a fitness function that minimizes the error between the predicted and measured stress.

[0095] Explorer, Joiner, and Watcher Position Update: The position update strategy integrates random factors and early warning mechanisms to achieve a balance between global exploration and local development; by referring to the current best and worst individual positions to guide the population search direction, it effectively improves the ability to escape local optima.

[0096] Parameter initialization: Latin hypercube sampling is used to optimize the efficiency of parameter space search and support high-dimensional (22+4N) parameter inversion.

[0097] Parameter simplification: If computational resources are limited, some parameters (such as the compression domain parameters of symmetric materials) can be fixed to reduce the dimensionality.

[0098] Experimental verification and application:

[0099] In specific implementation, this embodiment can use test data from 6061-T6 friction stir welded aluminum alloy butt joint test specimens and 7075-T6 friction stir welded aluminum alloy butt joint test specimens under three low-cycle cyclic loading regimes to further illustrate this embodiment. Schematic diagrams of the friction stir welding process for all aluminum alloy plates are shown below. Figure 4 As shown in the diagram, the sampling location and shape of the test specimen are as follows: Figure 5 As shown.

[0100] The specific operating method is as follows:

[0101] S1: For three groups of 6061-T6 friction stir welded aluminum alloy butt joint test pieces, under the following conditions... Figure 6 Low-cycle cyclic loading tests were conducted on three groups of 7075-T6 friction stir welded aluminum alloy butt joint test specimens under the load conditions shown. Figure 7 A low-cycle cyclic loading test was conducted under the load condition shown, and complete hysteresis curve data were collected.

[0102] S2: Based on the assumption of volume conservation, the formula σ is adopted. true =σ eng (1+ε eng ) and ε true =ln(1+ε eng The engineering stress-strain data of the hysteresis curves of the 6061-T6 and 7075-T6 friction stir welded aluminum alloy butt joint test specimens were converted into actual stress-strain data. Among them, σ true and ε true These represent the true stress and the true strain, respectively, σ eng and ε eng These are engineering stress and engineering strain, respectively.

[0103] S3: Based on equivalent plastic strain, historical peak residual strain, elastic trial stress, and total back stress, an improved Chaboche cyclic constitutive model is constructed, possessing elastic modulus degradation, kinematic hardening, isotropic soft hardening, and a symmetric tensile-compressive response mechanism. For 6061-T6 friction stir welded aluminum alloy butt joint test specimens, with N=3 selected and the compression and tensile parameters set to be the same, the model parameter set to be identified includes 17 sets of tensile parameters: E 0,拉 E sat,拉 ω 拉 μ 拉 , b 拉 a拉 k 拉 r 拉 σ| 0,拉 C 1,拉 C 2,拉 C 3,拉 γ 1,拉 γ 2,拉 γ 3,拉 For 7075-T6 friction stir welded aluminum alloy butt joint test specimens, selecting N=3, and setting the compression domain parameters and tensile domain parameters respectively, the model parameter set to be identified includes 17 sets of tensile domain parameters: E 0,拉 E sat,拉 ω 拉 μ 拉 , b 拉 a 拉 k 拉 r 拉 σ| 0,拉 C 1,拉 C 2,拉 C 3,拉 γ 1,拉 γ 2,拉 γ 3,拉 ; and 17 sets of compression domain parameters: E 0,压 E sat,压 ω 压 μ 压 , b 压 a 压 k 压 r 压 σ| 0,压 C 1,压 C 2,压 C 3,压 γ 1,压 γ 2,压 γ 3,压 A total of 34 sets of model parameters.

[0104] S4: Based on the hysteresis curve data obtained from the experiment, the sparrow search algorithm is used to perform parameter inversion calculation on the improved Chaboche cyclic constitutive model, minimize the deviation between the model predicted stress and the experimental stress, and finally obtain the optimal model parameter solution set.

[0105] The hysteresis curves plotted by the method for 6061-T6 friction stir welded aluminum alloy butt joint test specimens under three low-cycle cyclic loading regimes are compared with the experimentally measured data. Figure 2 The final recognition model parameters are shown in Table 1:

[0106] Table 1

[0107]

[0108]

[0109] The hysteresis curves plotted by the method for 7075-T6 friction stir welded aluminum alloy butt joint test specimens under three low-cycle cyclic loading regimes are compared with the experimentally measured data. Figure 3 The final recognition model parameters are shown in Table 2:

[0110] Table 2

[0111]

[0112] To visually demonstrate the constitutive model's ability to describe elastic modulus degradation and isotropic soft hardening, the elastic modulus degradation surface and isotropic soft hardening evolution surface of the improved Chaboche cyclic constitutive model, calibrated by the hysteresis curves of the 6061-T6 friction stir welded aluminum alloy butt joint test specimens, were plotted according to Table 1. Figure 8 As shown.

[0113] To visually demonstrate the tension-compression response asymmetry achievable by the improved Chaboche cyclic constitutive model, the compression domain parameters in Table 1 are... b 压 a 压 k 压 r 压 σ| 0,压 C 1,压 C 2,压 C 3,压 γ 1,压 γ 2,压 γ 3,压 When the stretching domain parameter is set to 0, 1 / 4, 1 / 2, 3 / 4, 1, and 1.5 times, the following method is adopted: Figure 6 As shown in the figure, the hysteresis curve of loading regime 3 is plotted as follows. Figure 9 As shown.

[0114] In summary:

[0115] This embodiment uses experimental design to conduct low-cycle cyclic loading under multiple working conditions on 6061-T6 and 7075-T6 friction stir welded joints and collect hysteresis curve data.

[0116] Model validation:

[0117] Figure 2 The simulation and experimental curves of the 6061-T6 joint under symmetric parameters show a high degree of agreement, verifying the model's ability to characterize elastic modulus degradation and isotropic soft hardening.

[0118] Figure 3The model demonstrates the difference in tensile and compressive response of the 7075-T6 joint under asymmetric parameters, proving the advantages of the model in handling complex asymmetries.

[0119] Parameter Influence Analysis: Figure 9 This demonstrates the impact of compression domain parameter scaling on the hysteresis curve shape, providing an intuitive basis for engineering parameter tuning.

[0120] The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the protection scope of the present invention.

Claims

1. A method for constructing an improved Chaboche model suitable for friction stir welding, characterized in that, The improved Chaboche model distinguishes the tensile and compressive responses by the difference between the elastic trial stress and the total back stress; it introduces equivalent plastic strain and historical peak residual strain to characterize the elastic modulus degradation and isotropic soft hardening behavior; it uses the superposition of multiple independent nonlinear components to characterize kinematic hardening; and it calibrates the elastic modulus degradation, isotropic soft hardening, and kinematic hardening parameters in the tensile and compressive domains respectively to achieve optional tensile and compressive response asymmetry modeling. The elastic stiffness matrix of the improved Chaboche model is: in, C Here is the elastic stiffness matrix; Lamé's first parameter; G Shear modulus; Poisson's ratio; E n The elastic modulus at the current moment; E 0 represents the initial elastic modulus; E sat This represents the saturation value of the elastic modulus due to degradation. ω and μ Parameters used to control the rate of degradation of the elastic modulus; Equivalent plastic strain; The residual strain represents the peak value of the process. For total strain; For Von Mises stress.

2. The method for constructing the improved Chaboche model suitable for friction stir welding according to claim 1, characterized in that, The yield criterion and hardening criterion of the improved Chaboche model are as follows: in, f Let be the yield function; Equivalent stress; This is the initial yield stress; S It is the deviatoric stress tensor; α For back stress tensor; R For isotropic soft hardening components; α i For the first i One back stress component; N To determine the number of back stress groups, by increasing... N This value can improve the accuracy of motion hardening; C i and These are the parameters for kinematic hardening. and These are the hardening saturation value and the softening saturation value, respectively. b and a These are the isotropic hardening rate and softening rate, respectively; k and r These are the material parameters that control the soft hardening saturation value; This represents the equivalent plastic strain increment.

3. The method for constructing the improved Chaboche model suitable for friction stir welding according to claim 1, characterized in that, The flow criterion for the improved Chaboche model is as follows: in, For the plastic strain increment tensor; For shaping multipliers; Let be the stress tensor.

4. The method for constructing the improved Chaboche model suitable for friction stir welding according to claim 1, characterized in that, The tensile and compressive response criteria for the improved Chaboche model are as follows: in, The current elastic test stress; This represents the total back stress.

5. The method for constructing the improved Chaboche model suitable for friction stir welding according to claim 1, characterized in that, The improved Chaboche model adopts a tension / compression dual-domain parameter system, with a total of 22+4 parameters. N ,in N The number of back stress groups; The specific composition of the model parameters is as follows: 11+2 N One stretching domain parameter: E 0,拉 , E sat,拉 , ω 拉 , μ 拉 , , , b 拉 , a 拉 , k 拉 , r 拉 , and N Group C i,拉 and , i =1,2,3… N ;11+2 N One compression domain parameter: E 0,压 , E sat,压 , ω 压 , μ 压 , , , b 压 , a 压 , k 压 , r 压 , and N Group C i,压 and , i =1,2,3… N .

6. The method for constructing the improved Chaboche model suitable for friction stir welding according to claim 5, characterized in that, For materials exhibiting symmetric tensile-compressive response characteristics—centered on the back stress—the improved Chaboche model is simplified to be defined using only the tensile domain parameters, with the compressive domain parameters set to be the same as the tensile domain parameters. E 0,拉 = E 0,压 , E sat,拉 = E sat,压 , ω 拉 = ω 压 , μ 拉 = μ 压 , = , = , b 拉 = b 压 , a 拉 = a 压 , k 拉 = k 压 , r 拉 = r 压 , = and C i,拉 = C i,压 and = , i =1,2,3… N .

7. The method for constructing the improved Chaboche model suitable for friction stir welding according to claim 5, characterized in that, For materials that exhibit compressive buckling and tension-compression asymmetry, the improved Chaboche model establishes a dual-domain constitutive relation by independently defining parameter sets for the tension and compression domains to achieve differentiated characterization of compressive and tensile behaviors.

8. A parameter identification method for constructing an improved Chaboche model suitable for friction stir welding as described in any one of claims 1-7, characterized in that, Includes the following steps: S1: Low-cycle cyclic loading tests were conducted on aluminum alloy butt joint test specimens subjected to friction stir welding under various load conditions, and complete hysteresis curve data were collected. S2: Based on equivalent plastic strain, historical peak residual strain, elastic trial stress and total back stress, an improved Chaboche cyclic constitutive model with elastic modulus degradation, kinematic hardening, isotropic soft hardening and optional tension-compression response asymmetry characteristics is constructed, and the model parameter set to be identified is determined accordingly. S3: Based on the hysteresis curve data obtained from the experiment, the improved Chaboche model is inverted using the sparrow search algorithm to minimize the deviation between the model's predicted stress and the experimental stress, and finally obtains the optimal model parameter solution set; its fitness function is: in, σ opt Predict stress for the model; σ exp To test and measure stress, K This refers to the total number of measurement points for all test pieces or the total number of data points after data noise reduction processing. During the global optimization process, the explorer's position is updated as follows: in, X i,j For the first i The sparrow in the first j The position of the dimension; n This represents the current iteration number; κ max This represents the maximum number of iterations. α s A random number between 0 and 1 that satisfies α s ≠ 0; Q These are random numbers that follow a normal distribution. L For a containing d A row vector with 1 element; W T and S T These are the warning value and the safe value, respectively. During the global optimization process, the joiner's position is updated as follows: in, X p This is the optimal position for the current explorer; X W This is the worst position globally at present; A + For inclusion d A row vector with elements 1 or -1, satisfying ; During the global optimization process, the location of the vigilant is updated as follows: in, X b This is the current globally optimal position; β and It is a random number; f i , f g and f w These are the fitness values ​​for the current individual, the current global best solution, and the current global worst solution, respectively. Ψ It is a non-zero decimal.

9. The parameter identification method for the improved Chaboche model applicable to friction stir welding according to claim 8, characterized in that, To improve recognition efficiency and stability, the parameter range of the improved Chaboche model is determined by trial and error. The improved Chaboche model uses Latin hypercube sampling and initializes the population in a multidimensional parameter space.

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