Viscoplastic constitutive model parameter identification method based on fusion of multi-strategy black-wing plinary algorithm

Abstract

The invention relates to a viscoplastic constitutive model parameter identification method based on a fusion multi-strategy black wing plinary algorithm, and the method comprises the steps: fusing multiple factors, constructing an improved damage coupling viscoplastic model, and determining the parameters of a to-be-identified model; wherein the multiple factors comprise a transient softening modulus, a relaxation factor, static recovery, a fatigue-creep interaction damage model and a traditional Chaboch viscoplastic constitutive framework; based on the improved damage coupling viscoplastic model, a weighting method is adopted to construct a single-target optimization model; and based on the single-target optimization model, performing inversion solution on the to-be-identified model parameters by using a multi-strategy fused black-wing plinary algorithm to obtain optimal constitutive model parameters. The model parameters identified based on the fusion multi-strategy black wing plinary algorithm are high in precision and high in convergence speed, and the reasonability of the constitutive model and the high efficiency and reliability of parameter identification are fully explained.

Description

Technical Field

[0001] The present invention relates to the technical field of material constitutive models, and particularly to a method for identifying the parameters of a viscoplastic constitutive model based on a multi-strategy black-winged kite algorithm. Background Art

[0002] Under the condition of long-term exposure to extreme temperature and complex stress environments, high-temperature components are extremely vulnerable to low-cycle fatigue and creep-fatigue interactive failures. This phenomenon has prompted extensive and in-depth research on their deformation behavior and constitutive modeling methods. Previous studies have revealed that high-temperature heat-resistant materials such as 2.25CrMoV steel and carbide-free bainitic steel exhibit behaviors such as continuous strain softening, strain range memory effect, transient Bauschinger effect, and decelerated stress relaxation when subjected to low-cycle fatigue and creep-fatigue loads. Accurately describing these characteristics is crucial for evaluating the reliability of high-temperature structural components and implementing structural optimization, and this requires a comprehensive constitutive model that can accurately simulate the stress-strain response of materials. In addition, the method of combining continuum damage mechanics with traditional constitutive models has been proven to be a promising strategy for solving the problem that traditional models cannot accurately predict the cyclic plastic deformation of materials throughout their life cycle. However, the construction of advanced models inevitably leads to an increase in model parameters, and at the same time, some parameters with unclear physical meanings and high sensitivity are introduced, making traditional parameter identification methods based on trial and error or user experience no longer applicable. With the rapid development of artificial intelligence technology, the importance of meta-heuristic optimization algorithms in the field of inverse identification of constitutive model parameters has been increasing. However, numerous studies have shown that the calibration of constitutive models is a complex inverse problem, and traditional meta-heuristic optimizations are often prone to falling into local optimal solutions when applied. As a newly emerging meta-heuristic algorithm, the black-winged kite optimization algorithm is inspired by the survival strategy of black-winged kites and has advantages such as strong robustness, high search efficiency, and easy programming implementation. However, there is still much room for improvement in the convergence speed, convergence accuracy, and ability to jump out of local optima of the traditional black-winged kite algorithm. Summary of the Invention

[0003] In view of the difficulties in calibrating the parameters of constitutive models in the prior art and the deficiencies of the traditional black-winged kite algorithm in terms of convergence accuracy and convergence speed, the present invention proposes a method for identifying the parameters of a viscoplastic constitutive model based on a multi-strategy black-winged kite algorithm to solve the problems existing in the above prior art.

[0004] To achieve the above object, the present invention provides the following solutions:

[0005] A method for identifying the parameters of a viscoplastic constitutive model based on a multi-strategy black-winged kite algorithm, comprising:

[0006] Integrate multiple factors to construct an improved damage-coupled viscoplastic model and determine the model parameters to be identified; among them, the multiple factors include: transient softening modulus, relaxation factor, static recovery, fatigue-creep interaction damage model, and traditional Chaboche viscoplastic constitutive model framework;

[0007] Based on the improved damage-coupled viscoplastic model, use the weighted method to construct a single-objective optimization model;

[0008] Based on the single-objective optimization model, use the black-winged kite algorithm integrating multiple strategies to inversely solve the model parameters to be identified and obtain the optimal constitutive model parameters; among them, the multiple strategies include: initialization strategy based on symmetric Latin hypercube sampling and opposition-based learning, diversity-driven adaptive strategy, and golden sine strategy.

[0009] Optionally, the improved damage-coupled viscoplastic model includes:

[0010] Master equation:

[0011] ε = ε e + ε in #(1)

[0012]

[0013] Kinematic hardening rule:

[0014]

[0015] φ(p,q) = φ ∞ (q) + [1 - φ ∞ (q)]·e -ω(q)p + κ(q)p#(7)

[0016]

[0017] Isotropic hardening rule of coupled damage:

[0018]

[0019] Cyclic update of kinematic hardening parameters with strain range:

[0020]

[0021] Damage equation:

[0022]

[0023] Among them, ε, ε e , ε in are the total strain, elastic strain, and inelastic strain respectively; I is the second-order unit tensor; v is the Poisson's ratio; E is the elastic modulus; σy0 is the initial yield stress; K and n c are material parameters describing viscous deformation; is the rate of the plastic strain multiplier; is the cumulative inelastic strain rate; σ and α are the Cauchy stress tensor and the back stress tensor respectively; f y is the Von-Mises yield function; σ′ and α' are the deviatoric stress tensor and the deviatoric back stress tensor respectively; is the rate of change of the i-th back stress component; is the linear hardening term obtained from the stable cycles, is the coefficient of the dynamic recovery term obtained from the stable cycles; γ r and m c are material parameters controlling the amount and rate of static recovery respectively; φ(p,q) is the relaxation factor related to the cumulative inelastic strain and the maximum inelastic strain amplitude; q is the radius of the strain memory surface; φ ∞ (q), ω(q) and κ(q) are variables controlling the radius q of the memory surface respectively, and their evolution laws are controlled by three third-order material parameters I kin 、S kin and R kin control; Schur product operator; δ i is the i-th component of the second-order transient softening modulus δ; δ0 and V are the initial value of δ and the rate of evolution towards its asymptotic value respectively; R is the isotropic hardening variable; Q s and b are the asymptotic value of R and its evolution rate respectively, H is the linear softening modulus describing the stable softening stage of the material; D, and are the total damage, the total damage rate, the fatigue damage rate and the creep damage rate respectively; R v is the multiaxial coefficient; σ hyd and σ eq are the hydrostatic pressure and the equivalent stress respectively; D crit 、Ω、β f and r f are the fatigue damage model parameters; λ, β c and r c are the creep damage model parameters.

[0024] Optionally, the model parameters to be identified include: elastic modulus, initial yield stress, material parameters describing viscous deformation, linear hardening term and dynamic recovery term coefficient obtained from stable cycles, material parameters controlling the amount and rate of static recovery, asymptotic value of the isotropic hardening variable R and its evolution rate, linear softening modulus describing the stable softening stage of the material, fatigue damage model parameters, creep damage model parameters, vector parameters.

[0025] Optionally, the single-objective optimization model is:

[0026]

[0027] subject to: lb ≤ x ≤ ub

[0028] where and are the simulated values and the corresponding observed values of each optimization objective respectively; M is the total number of objective functions, and the optimization objectives include: maximum / minimum stress, stress-strain relationship, stress relaxation, and fatigue life; N i is the total number of data sets for the i-th objective; O ij is the total number of sampling points for the j-th data set of the i-th objective; w i is the weight coefficient used to adjust the contribution of each objective; ζ is an arbitrarily small constant used to avoid division by zero; lb and ub are the lower and upper boundaries of the model parameters to be identified respectively.

[0029] Optionally, using the black-winged kite algorithm integrating multiple strategies, the inversion solution of the model parameters to be identified includes:

[0030] Setting algorithm parameters; where the algorithm parameters include: the number of populations, the maximum number of iterations, the probability threshold for the selection of the predation behavior of the black-winged kite, the parameter for controlling the adaptive parameter of the predation behavior, and the parameter for avoiding invalid golden sine search;

[0031] Initializing the population (initial viscoplastic constitutive model parameters) using symmetric Latin hypercube sampling and reverse learning strategy;

[0032] Updating the step coefficients of the predation behavior, migration behavior, and golden positive strategy according to the group diversity;

[0033] Updating the individual positions and fitness values according to the predation behavior model and the single-objective optimization model;

[0034] Updating the individual positions and fitness values according to the migration behavior model and the single-objective optimization model;

[0035] Perturbing the position X best (current optimal viscoplastic constitutive model parameters) of the current optimal black-winged kite individual according to the golden sine strategy, and updating the position of the worst black-winged kite individual using the greedy strategy;

[0036] Updating the position X best (optimal viscoplastic constitutive model parameters) and fitness value F best ;

[0037] Judging whether the maximum number of iterations is reached. If t > T, output the position X of the optimal solution best(Optimal viscoplastic constitutive model parameters) and fitness value F best On the contrary, continue to update the predation behavior, migration behavior, and step size coefficient of the golden positive strategy according to the group diversity.

[0038] Optionally, initializing the population using symmetric Latin hypercube sampling and opposition-based learning strategy includes:

[0039] Initialize the position of the black-winged kite using symmetric Latin hypercube sampling;

[0040] Conduct opposition-based learning on the initial individuals;

[0041] Calculate the fitness values of the initial individuals and the opposition individuals;

[0042] Adopt the elite strategy to screen N elite individuals from the set of initial individuals and opposition individuals to construct the initial population.

[0043] Optionally, updating the predation behavior, migration behavior, and step size coefficient of the golden positive strategy includes:

[0044] Calculate the group diversity:

[0045]

[0046] where Var(t) is the variance of the current population; d is the dimension of the decision variable x; represents the j-th dimension position of the i-th black-winged kite in the t-th iteration; represents the j-th dimension sample center of the population position in the t-th iteration;

[0047]

[0048] where, H t (x) represents the information entropy of the random variable x in the t-th iteration; and represent the number of individuals and the probability of individuals falling into the i-th subspace of the solution space in the t-th generation, respectively; Q is the number of independent subspaces of the solution space;

[0049]

[0050] where, are the normalized variance and information entropy, respectively; Div(t) is the diversity of the group in the t-th iteration;

[0051] Update the predation behavior, migration behavior, and step size coefficient of the golden positive strategy:

[0052]

[0053] Among them, n(t) is the value of variable n at the t-th iteration, and its minimum and maximum values are n min and n max ; Div(t) is the diversity of the group in the t-th iteration;

[0054] m(t) = (2 - (t / T) 2 ) × r + C(0,1) × (1 - r) #(19)

[0055] where C(0, 1) is a random number generated from the Cauchy distribution, and m(t) is the migration behavior;

[0056]

[0057] where c(t) is the step size coefficient of the golden positive strategy.

[0058] The beneficial effects of the present invention are as follows:

[0059] The method for identifying the constitutive model parameters based on the improved black-winged kite algorithm of the present invention can effectively solve the problems of low accuracy, low efficiency, and difficulties in practical engineering applications existing in the previous manual calibration process;

[0060] By introducing a loss function related to fatigue life into the objective function, not only the calibration difficulty of damage parameters with high sensitivity is greatly reduced, but also the identification accuracy is improved;

[0061] By integrating Latin hypercube sampling, reverse learning strategy, diversity-driven adaptive strategy, and golden sine strategy, the problems of slow convergence speed, low convergence accuracy, and easy entrapment in local optimal solutions of the traditional black-winged kite algorithm can be effectively solved, thereby improving the identification accuracy of model parameters. BRIEF DESCRIPTION OF THE DRAWINGS

[0062] In order to more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the following will briefly introduce the drawings required in the embodiments. Obviously, the drawings in the following description are only some embodiments of the present invention. For those of ordinary skill in the art, other drawings can be obtained based on these drawings without creative efforts.

[0063] Figure 1 It is a schematic flowchart of the method for identifying the viscoplastic constitutive model parameters based on the multi-strategy fusion black-winged kite algorithm according to the embodiment of the present invention;

[0064] Figure 2 It is an evolution curve of the objective function value during the evolution process according to the embodiment of the present invention;

[0065] Figure 3The comparison diagram of the stress-strain hysteresis loop and cyclic stress response between the test results and simulation results of 2.25CrMoV in the embodiments of the present invention under low-cycle fatigue loading at a temperature of 455°C and strain amplitudes of ±0.4%, ±0.5%, and ±0.7%.

[0066] Figure 4 The comparison diagram of the stress-strain hysteresis loop and cyclic stress response between the test results and simulation results of 2.25CrMoV in the embodiments of the present invention under creep-fatigue loading at a temperature of 455°C, strain amplitudes of ±0.4%, ±0.5%, and ±0.7%, and a tensile hold time of 60 s.

[0067] Figure 5 The comparison diagram of the predicted fatigue life and experimental fatigue life of 2.25CrMoV in the embodiments of the present invention under low-cycle fatigue and creep-fatigue (hold time 60 s) loading at a temperature of 455°C and a strain range of ±0.4% to ±0.7%. Detailed implementation manners

[0068] Next, the technical solutions in the embodiments of the present invention will be clearly and completely described in conjunction with the accompanying drawings in the embodiments of the present invention. Obviously, the described embodiments are only a part of the embodiments of the present invention, rather than all the embodiments. All other embodiments obtained by those of ordinary skill in the art based on the embodiments of the present invention without creative efforts shall fall within the protection scope of the present invention.

[0069] To make the above objects, features, and advantages of the present invention more obvious and understandable, the present invention will be further described in detail below in conjunction with the accompanying drawings and specific implementation manners.

[0070] As Figure 1 shown, this embodiment proposes a parameter identification method for a viscoplastic constitutive model based on a fused multi-strategy black-winged kite algorithm, including the following steps:

[0071] Step S1: This embodiment adopts an improved damage-coupled viscoplastic constitutive model; specifically, based on the transient softening modulus, relaxation factor, static recovery, fatigue-creep interaction damage model, and the traditional Chaboche viscoplastic constitutive model framework, this embodiment constructs an improved damage-coupled viscoplastic constitutive model and determines the model parameters to be identified.

[0072] The improved damage-coupled viscoplastic constitutive model; as shown in Equations (1)-(12):

[0073] Master equation:

[0074] ε = ε e + ε in #(1)

[0075]

[0076] Each kinematic hardening rule consists of four terms, which are, from left to right: the linear hardening term, the dynamic recovery term, the static recovery term, and the damage rate term, as follows:

[0077]

[0078] φ(p,q) = φ ∞ (q) + [1 - φ ∞ (q)]·e -ω(q)p + κ(q)p#(7)

[0079]

[0080] The isotropic hardening rule for coupled damage is as follows:

[0081]

[0082] The kinematic hardening parameters are cyclically updated with the strain range as follows:

[0083]

[0084] The damage equation is:

[0085]

[0086] where ε, ε e , ε in are the total strain, elastic strain, and inelastic strain, respectively; I is the second-order unit tensor; is the rate of the plastic strain multiplier; is the cumulative inelastic strain rate; σ and α are the Cauchy stress tensor and back stress tensor, respectively; σ′ and α' are the deviatoric stress tensor and deviatoric back stress tensor, respectively; and are the total damage rate, fatigue damage rate, and creep damage rate, respectively; δ is the second-order transient softening modulus; φ(p,q) is the relaxation factor related to the cumulative inelastic strain and the maximum inelastic strain amplitude; R is the isotropic hardening variable; q is the radius of the strain memory surface; R v is the multiaxiality coefficient; σ hyd and σ eq are the hydrostatic pressure and equivalent stress, respectively. This model has a total of 29 material parameters, including 24 scalar parameters: ν, E, σ y0 , K, n c , γ r , m c , Q s , b, H, η, D crit , Ω, βf , r f , λ, β c , r c . Specifically, v is the Poisson's ratio, usually taken as 0.3; E is the elastic modulus; σ y0 is the initial yield stress; K and n c are material parameters describing viscous deformation; and are the linear hardening term and the dynamic recovery term coefficient obtained from the stable cycle number respectively; γ r and m c are material parameters controlling the static recovery amount and the recovery rate respectively; Q s and b are the asymptotic value of R and the rate of its evolution respectively, and H is the linear softening modulus describing the stable softening stage of the material; η is the coefficient characterizing progressive memory, usually set to 0.5; D crit , Ω, β f and r f are fatigue damage model parameters; λ, β c and r c are creep damage model parameters. In addition, there are 5 vector parameters: I kin , S kin , R kin , δ0 and V, where I kin , S kin and R kin are third-order vector parameters composed of material parameters controlling the evolution of φ ∞ (q), ω(q) and κ(q) with q; and δ0 and V are the initial value of δ and the rate of its evolution to its asymptotic value (two-dimensional unit column vector [1,1] T ) respectively. Under uniaxial conditions, the model parameters to be identified can be selected as: Its boundary conditions are shown in Table 1.

[0087] Table 1. Boundary conditions of the constitutive model parameters of 25CrMoV at 455℃

[0088]

[0089]

[0090] Step S2: Based on the improved constitutive model and the stress-strain data set within the full life cycle under low-cycle fatigue and creep-fatigue interaction conditions at different strain amplitudes, a single-objective optimization model is established by using the weighted method:

[0091]

[0092] subject to: lb ≤ x ≤ ub

[0093] In the formula, and are the simulated values and the corresponding observed values of each optimization objective respectively; M is the total number of objective functions (loss functions), and the optimization objectives include: maximum / minimum stress, stress-strain relationship, stress relaxation, and fatigue life; N i is the total number of data sets of the i-th objective; O ij is the total number of sampling points of the j-th data set of the i-th objective; w i is the weight coefficient used to adjust the contribution of each objective, which are set to 0.25 (maximum / minimum stress), 0.25 (stress-strain relationship), 0.3 (stress relaxation), and 0.2 (fatigue life) respectively; ζ is an arbitrarily small constant used to avoid division by zero; lb and ub are the lower and upper boundaries of the decision variable x (model parameters to be identified). In this embodiment, using the low-cycle fatigue data of 2.25CrMoV at a temperature of 455°C, strain amplitudes of ±0.5% and ±0.7%, and creep-fatigue data with a tensile hold time of 60 s in the strain ranges of ±0.5% and ±0.7%, a single-objective optimization model is established.

[0094] The stress-strain data during the entire life cycle is obtained through low-cycle fatigue experiments.

[0095] Step S3, based on the above single-objective optimization model, use the black-winged kite algorithm integrating multiple strategies to inversely solve the model parameters to be identified, so as to obtain the optimal constitutive model parameters.

[0096] Specifically, step S3 is as follows:

[0097] S301. Set the algorithm parameters. Set the population size N = 30, the maximum number of iterations T = 30, the probability threshold P = 0.9 for the black-winged kite predation behavior selection, the parameter n min = 2 and n max = 8 for controlling the adaptive parameter n(t) of the predation behavior, and the parameter ξ = 1e-5 for avoiding invalid golden sine search.

[0098] S302. Initialize the population using the symmetric Latin hypercube sampling and reverse learning strategy. The specific process is as follows: First, initialize the positions of the black-winged kites using the symmetric Latin hypercube sampling; then, perform reverse learning on the initial individuals according to Equation (14); next, calculate the fitness values of the initial individuals and the reverse individuals; finally, use the elite strategy to screen N elite individuals from the combination of the initial individuals and the reverse individuals to construct the initial population;

[0099]

[0100] Wherein, i represents the number of the black-winged kite individual; j represents the j-th dimension of the decision variable; is the initial individual X obtained by symmetric Latin hypercube sampling (i,j) the offspring obtained by performing opposition-based learning; r is a random number between 0 and 1;

[0101] S303. Update the step coefficients n(t), m(t), and c(t) of the predation behavior, migration behavior, and golden positive strategy according to the group diversity. Among them, the diversity Div(t) is defined as the average of the normalized information entropy and the normalized variance, and is calculated by formulas (15)-(17); n(t), m(t), and c(t) are updated by (18)-(20) in sequence.

[0102]

[0103] Wherein, Var(t) is the variance of the current population; d is the dimension of the decision variable x; represents the j-th dimension position of the i-th black-winged kite in the t-th iteration; represents the sample center of the j-th dimension of the population position in the t-th iteration.

[0104]

[0105] Wherein, H t (x) represents the information entropy of the random variable x in the t-th iteration; and respectively represent the number of individuals in the i-th subspace of the solution space of the t-th generation and the probability that the individuals fall into this space; Q is the number of independent subspaces of the solution space, usually set to N.

[0106]

[0107] Wherein, are the normalized variance and information entropy respectively; Div(t) is the diversity of the group in the t-th iteration, and its value range is from 0 to 1. The higher the value, the higher the diversity.

[0108]

[0109] Wherein, n(t) is the value of the variable n in the t-th iteration, and its minimum and maximum values are n min and n max ; Div(t) is the diversity of the group in the t-th iteration. The higher the diversity value of the group, the higher the value of n(t), thereby enhancing the global exploration of the algorithm, and vice versa;

[0110] m(t) = (2 - (t / T) 2 ) × r + C(0,1) × (1 - r) #(19)

[0111] where \(C(0, 1)\) is a random number generated from the Cauchy distribution; \(m(t)\) starts from a high initial value to get rid of local optima and decreases in subsequent iterations to refine the search;

[0112]

[0113] where \(c(t)\) is designed to decrease non - linearly with iterations while allowing the incorporation of evolutionary feedback. At the initial stage of iteration or when the diversity is high, a larger step size is adopted to avoid premature local convergence; while at the later stage of iteration or when the group diversity is low, a smaller step size is adopted to maintain the mechanism of getting rid of local optima and refine the search at the same time; \(\xi\) is an arbitrarily small integer to avoid invalid search.

[0114] S304. Update the individual position according to the predation behavior model. The predation behavior mathematical model of the black - winged kite is shown in Equation (21):

[0115]

[0116] where is the position of the \(i\) - th black - winged kite in the \(j\) - th dimension at the \(t\) - th iteration; \(n(t)\) is the adaptive step size controlling the predation behavior, as shown in Equation (18).

[0117] S305. Update the individual position according to the migration behavior model. The migration behavior mathematical model of the black - winged kite is shown in Equation (22):

[0118]

[0119] where is the position of the leader in the \(j\) - th dimension at the \(t\) - th iteration, that is, the optimal solution position of the current \(j\) - th dimension; \(F\) i is the fitness value of the current black - winged kite; \(F\) ri is the fitness value of a random position; \(m(t)\) is the adaptive step size controlling the predation behavior, as shown in Equation (19).

[0120] S306. Perturb the position \(X\) best of the current optimal black - winged kite individual according to the golden sine strategy, and update the position of the worst black - winged kite individual using the greedy strategy, as shown in Equations (23) and (24):

[0121]

[0122] where is the position of the \(j\) - th dimension of the offspring generated by the golden sine strategy at the \(t\) - th iteration; ​is the position of the j-th dimension of the current optimal black-winged kite individual; R1 and R2 are random numbers within the ranges of [0, 2π] and [0, π] respectively; x1 and x2 are constants obtained by integrating the golden section numbers: x1 = -π + (1 - τ) × 2π, x2 = -π + 2π × τ, where the golden interface number: θ(t) is the step size coefficient, as shown in Equation (20).

[0123]

[0124] In the formula, and are respectively the position and fitness value of the current worst black-winged kite individual; and are respectively the position and fitness value of the individual obtained by the current golden sine strategy;

[0125] S307. Update the position X best and fitness value F best , as shown in Equation (25):

[0126]

[0127] S308. Determine whether the maximum number of iterations is reached. If t > T, output the position X best and fitness value F best , otherwise, continue to execute S303.

[0128] The technical feature of this embodiment is to identify the constitutive model parameters through a black-winged kite algorithm that fuses multiple strategies. The position and fitness value of the black-winged kite individual are divided into the viscoplastic constitutive model parameters and the function value (i.e., fitness) of the objective function in the single-objective optimization model. The position of the optimal individual is the optimal viscoplastic constitutive model parameter.

[0129] Finally, according to the parameter value ranges listed in Table 1, the objective function F(x) was inverted by using the black-winged kite algorithm that fuses multiple strategies, and the identification results shown in Table 2 were obtained. Figure 2 The evolution curve of the objective function value during the evolution process is shown. Analyzing this curve, it can be seen that the model parameter identification method based on the black-winged kite algorithm that fuses multiple strategies proposed by the present invention not only has high accuracy in identifying model parameters, but also has a fast convergence speed, which fully verifies the effectiveness of the proposed model and the efficiency and reliability of the parameter identification method.

[0130] Table 2 Parameter identification results of the proposed model for 2.25CrMoV at a temperature of 455 °C

[0131]

[0132] By comparing and analyzing the low-cycle fatigue and creep-fatigue test data and simulation data of 2.25CrMoV under different strain amplitudes, such as Figure 3 and Figure 4 shown, it is not difficult to find that there is good consistency between the test data and the simulation data, which fully verifies the ability of the proposed constitutive model to describe the complex behaviors of 2.25CrMoV, such as continuous cyclic softening, transient Bauschinger effect, strain-range memory effect, and decelerated stress relaxation. It should be noted that even for the test cases not involved in parameter identification, such as the low-cycle fatigue and creep-fatigue experiments with a strain amplitude of ±0.4%, the proposed model also shows good consistency. In addition, as Figure 5 shown, by comparing the predicted life and the experimental life under different low-cycle fatigue and creep-fatigue conditions, it is not difficult to find that all the predicted lives fall within the 1.25-fold error band. The above results consistently show that the proposed model is robust, not only accurately reproducing the cyclic deformation behavior of the material, but also achieving accurate prediction of the fatigue life. In addition, the excellent fatigue life prediction performance further confirms that incorporating the damage function related to fatigue life into the objective function is an effective strategy for accurately calibrating the damage parameters.

[0133] The embodiments described above are only descriptions of the preferred embodiments of the present invention, and do not limit the scope of the present invention. Without departing from the design spirit of the present invention, various deformations and improvements made by those of ordinary skill in the art to the technical solutions of the present invention shall fall within the protection scope determined by the claims of the present invention.

Claims

1. A method for identifying parameters of a viscoplastic constitutive model based on a fusion multi-strategy black kite algorithm, characterized in that: include: Integrate multiple factors to construct an improved damage-coupled viscoplastic model and determine the model parameters to be identified; wherein the multiple factors include: transient softening modulus, relaxation factor, static recovery, fatigue-creep interactive damage model and traditional Chaboche viscoplastic constitutive framework; Based on the improved damage-coupled viscoplastic model, a single-objective optimization model is constructed by using a weighted method; Based on the single-objective optimization model, the Black Kite algorithm that integrates the initialization strategy based on symmetric Latin hypercube sampling and reverse learning, the diversity-driven adaptive strategy and the golden sine strategy is used to inversely solve the model parameters to be identified and obtain the optimal constitutive model parameters.

2. The method for identifying parameters of a viscoplastic constitutive model based on a fusion multi-strategy black kite algorithm according to claim 1, characterized in that: The improved damage-coupled viscoplastic model includes: The main governing equation is: e=e e +e in #(1) Kinematic hardening rules: Isotropic hardening rules for coupled damage: Cyclic update of the kinematic hardening parameters over the strain range: Damage equation: Among them, ε, ε e , ε in are total strain, elastic strain, and inelastic strain respectively; I is the second-order unit tensor; ν is Poisson's ratio; E is the elastic modulus; σ y0 is the initial yield stress; K and n c is the material parameter describing the viscous deformation; is the rate of the plastic strain multiplier; is the cumulative inelastic strain rate; σ and α are the Cauchy stress tensor and back stress tensor, respectively; f y is the Von-Mises yield function; σ′ and α′ are the deviatoric stress tensor and the anterior stress tensor, respectively; is the rate of change of the i-th back stress component; is the linear hardening term obtained from the stable cycles, is the dynamic recovery coefficient obtained from the stable cycle; γ r and m c are the material parameters that control the static recovery amount and recovery rate, respectively; φ(p,q) is the relaxation factor related to the accumulated inelastic strain and the maximum inelastic strain amplitude; q is the radius of the strain memory surface; φ ∞ (q), ω(q) and κ(q) are the variables that control the memory surface radius q, and their evolution law is determined by the third-order material parameter I kin , S kin and R kin control; Schur product operator; δ i is the i-th component of the second-order transient softening modulus δ; δ0 and V are the initial value of δ and the rate of evolution to its asymptotic value, respectively; R is the isotropic hardening variable; Q s and b are the asymptotic value of R and its evolution rate, respectively; H is the linear softening modulus describing the stable softening stage of the material; D, and are total damage, total damage rate, fatigue damage rate and creep damage rate; R v is the multiaxial coefficient; σ hyd and σ eq are hydrostatic pressure and equivalent stress respectively; D crit ,Ω,β f and r f are fatigue damage model parameters; λ, β c and r c is the creep damage model parameter.

3. The method for identifying parameters of a viscoplastic constitutive model based on a fusion multi-strategy black kite algorithm according to claim 1, characterized in that: The model parameters to be identified include: elastic modulus, initial yield stress, material parameters describing viscous deformation, linear hardening terms and dynamic recovery term coefficients obtained from stable cycles, material parameters controlling static recovery amount and recovery rate, asymptotic values ​​of various isotropic hardening variables R and their evolution rates, linear softening modulus describing the stable softening stage of the material, fatigue damage model parameters, creep damage model parameters, and vector parameters.

4. The method for identifying parameters of a viscoplastic constitutive model based on a fusion multi-strategy black kite algorithm according to claim 1, characterized in that: The single-objective optimization model is: in, and are the simulated values ​​and corresponding observed values ​​of each optimization target; M is the total number of objective functions, and the optimization targets include: maximum / minimum stress, stress-strain relationship, stress relaxation, and fatigue life; N i is the total number of data sets for the i-th target; O ij is the total number of sampling points of the jth data set of the i-th target; w i is the weight coefficient used to adjust the contribution of each objective; ζ is an arbitrarily small constant used to avoid zero division; lb and ub are the lower and upper bounds of the model parameters to be identified, respectively.

5. The method for identifying parameters of a viscoplastic constitutive model based on a fusion multi-strategy black kite algorithm according to claim 4 is characterized in that: Using the Black Kite algorithm integrating multiple strategies, the inversion solution of the model parameters to be identified includes: Setting algorithm parameters; wherein the algorithm parameters include: population number, maximum number of iterations, probability threshold of black kite predation behavior selection, parameters for controlling predation behavior adaptive parameters, and parameters for avoiding invalid golden sine search; Symmetric Latin hypercube sampling and reverse learning strategy are used to initialize the population; wherein, initializing the population refers to initializing the parameters of the viscoplastic constitutive model; Update the predation behavior, migration behavior and step length coefficient of the golden positive strategy according to the group diversity; Update individual positions and fitness values ​​according to the predation behavior model and the objective function in the single-objective optimization model; Update individual positions and fitness values ​​according to the migration behavior model and the objective function in the single-objective optimization model; According to the golden sine strategy, the position X of the current optimal black-winged kite individual best Perturb and use greedy strategy to update the position of the worst black kite individual; among them, the position of the current best black kite individual X best Refers to the optimal viscoplastic constitutive model parameters Update the position X of the optimal black-winged kite individual best And the fitness value F best ; Determine whether the maximum number of iterations has been reached. If t>T, output the location X of the optimal solution. best And the fitness value F best , otherwise, continue to update the predation behavior, migration behavior and step length coefficient of the golden positive strategy according to the group diversity.

6. The method for identifying parameters of a viscoplastic constitutive model based on a fusion multi-strategy black kite algorithm according to claim 5, characterized in that: Initializing the population using symmetric Latin hypercube sampling and reverse learning strategy includes: Initialize the position of the black-winged kite using symmetric Latin hypercube sampling; Conduct reverse learning on the initial individuals; Calculate the fitness values ​​of the initial individuals and reverse individuals; The elite strategy is used to select N elite individuals from the set of initial individuals and reverse individuals to construct the initial population.

7. The method for identifying parameters of a viscoplastic constitutive model based on a fusion multi-strategy black kite algorithm according to claim 5, characterized in that: The step length coefficients for updating predation behavior, migration behavior, and golden positive strategy according to group diversity include: Calculate group diversity: Among them, Var(t) is the variance of the current population; d is the dimension of the decision variable x; represents the j-th dimension position of the i-th black-winged kite in the t-th iteration; represents the sample center of the jth dimension of the population position in the tth iteration; Among them, H t (x) represents the information entropy of the random variable x in the tth iteration; and They represent the number of individuals in the i-th subspace of the solution space of the t-th generation and the probability that an individual falls into the space; Q is the number of independent subspaces of the solution space; in, are the normalized variance and information entropy respectively; Div(t) is the diversity of the group in the tth iteration; Update the predation behavior n(t), migration behavior m(t) and the step coefficient c(t) of the golden sine strategy: Among them, n(t) is the value of variable n at the tth iteration, and its minimum and maximum values ​​are n min and n max ; Div(t) is the diversity of the group in the tth iteration; m(t)=(2-(t / T) 2 )×r+C(0,1)×(1-r)#(19) Among them, C(0,1) is a random number generated in the Cauchy distribution, and m(t) is the migration behavior; Among them, c(t) is the step coefficient of the golden positive strategy.

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