Modeling method of TC4 titanium alloy high-precision thermoplastic constitutive model

Abstract

The invention discloses a modeling method of a TC4 titanium alloy high-precision thermoplastic constitutive model, and belongs to the field of TC4 titanium alloy thin-wall part thermoplastic forming numerical simulation. The method comprises the following steps: firstly, obtaining an engineering stress-strain curve under different loading conditions, converting the engineering stress-strain curve into a real stress-strain curve, establishing a corrected Johnson-Cook constitutive model, and obtaining an initial parameter of the constitutive model; secondly, defining an objective function, a decision variable and a feasible region of an optimization problem by taking the precision of the constitutive model as a reference; thirdly, initial parameters of a sparrow search algorithm are set, an initial population is generated, the positions of a discoverer, a following person and a warning person are updated, and then the population of the next generation is improved; and finally, checking whether the target function value of the next-generation population reaches the target precision or not to obtain parameters of a new constitutive model, and establishing an optimized Johnson-Cook correction constitutive model. According to the constitutive model modeling method, prediction precision, calculation cost and fitting difficulty are considered, and the model precision problem caused by a traditional method can be solved.

Description

Technical Field

[0001] The present invention belongs to the field of numerical simulation of thermoplastic forming of TC4 titanium alloy thin-walled parts, and relates to a modeling method and application of a high-precision thermoplastic constitutive model for TC4 titanium alloy. Background Art

[0002] TC4 titanium alloy has the following excellent material properties: (1) low density and high specific strength, which can significantly reduce the weight of structural parts and contribute to the lightweight and miniaturization of structures; (2) low thermal conductivity, which can slow down the heat transfer inside the structure and protect internal precision components; (3) fatigue resistance and corrosion resistance, which can withstand harsh working environments and meet the high-strength service requirements, effectively improving the reliability of weapons and equipment. Therefore, its structural parts are widely used in fields such as automobiles, aerospace, military, and medical devices, such as: lightweight frames for automobile bodies, thermal insulation layers for rocket engines, thin-walled plates for aircraft, and rudder wings for missiles. However, due to problems such as high deformation resistance, severe springback, and local fracture at room temperature, the cold forming effect of TC4 titanium alloy is not good, so thermoplastic forming processes such as hot pressing, hot gas pressure forming, and superplastic forming are often used.

[0003] During the thermoplastic forming process of TC4 titanium alloy, its forming effect is closely related to the thermoplastic deformation behavior, and this deformation behavior is affected by temperature and strain rate. Therefore, in order to accurately predict the thermoplastic forming effect of titanium alloy through simulation analysis, it is necessary to carry out high-temperature mechanical property tests of materials and establish a high-precision thermoplastic constitutive model for process parameters such as forming temperature and strain rate to accurately describe the plastic deformation behavior of TC4 titanium alloy under different working conditions.

[0004] At present, although the constitutive models of TC4 titanium alloy have been greatly developed, such as the improved Arrhenius-type constitutive model and the Johnson-Cook constitutive model, etc., due to the limitations of the number of test samples and the constitutive model parameter fitting method, their prediction accuracy still does not meet the high-precision requirements of thermoplastic forming numerical simulation analysis. Therefore, providing a TC4 titanium alloy thermoplastic constitutive model that takes into account prediction accuracy, calculation cost, and fitting difficulty has important engineering application value for future high-precision thermoplastic forming numerical simulation analysis. Summary of the Invention

[0005] Aiming at the above-mentioned deficiencies of the existing constitutive models, the purpose of the present invention is to provide a modeling method for a high-precision thermoplastic constitutive model of TC4 titanium alloy that takes into account prediction accuracy, calculation cost, and fitting difficulty, so as to solve the problem of low prediction accuracy of thermoplastic forming numerical simulation of titanium alloy.

[0006] To achieve the above purpose, the present invention adopts the following technical solutions:

[0007] A modeling method for a high-precision thermoplastic constitutive model of TC4 titanium alloy, comprising the following steps:

[0008] First step, conduct high-temperature tensile tests on TC4 titanium alloy under different temperatures and strain rates to obtain engineering stress-strain curves under different loading conditions.

[0009] Second step, based on the conversion formulas between engineering stress, engineering strain, true stress, and true strain, convert the engineering stress-strain curve into a true stress-strain curve to be used as sample data for establishing a modified Johnson-Cook constitutive model.

[0010] Furthermore, in the second step, the conversion formulas are as follows:

[0011]

[0012] where, σ t , ε t are true stress and true strain respectively; σ e , ε e are engineering stress and engineering strain respectively; for the symbol ±, - represents the compression condition, and + represents the tensile condition.

[0013] Third step, based on the true stress-strain curve obtained in the second step, establish a modified Johnson-Cook constitutive model to obtain the initial parameters of the constitutive model.

[0014] Furthermore, in the third step, the modified Johnson-Cook constitutive model is as follows:

[0015]

[0016] where, σ is the stress; the first term on the right side of the equal sign is the strain-related term, ε is the strain, A, B1, and B2 are second-order polynomial coefficients used to simulate stress values under different strain conditions; the second term on the right side of the equal sign is the strain rate-related term, C is the strain rate sensitivity coefficient, is the reference strain rate, defined as where is the strain rate under the current condition, is the reference strain rate, generally taking the minimum strain rate in the test; the third term on the right side of the equal sign is the strain rate and temperature coupling term, λ1, λ2 are coupling term coefficients, T is the temperature under the current condition, T r is the reference temperature, generally taking the lowest temperature in the test.

[0017] In the fourth step, based on the error between the predicted stress and the experimental stress of the modified Johnson-Cook constitutive model under the same working conditions, that is, based on the accuracy of the constitutive model, the objective function, decision variables, and feasible region of the optimization problem are defined.

[0018] Furthermore, in the fourth step, the objective function of the optimization problem is as follows:

[0019]

[0020] where n is the total number of sample points used to fit the constitutive model, y i is the experimental stress value, and p i is the stress value predicted by the constitutive model.

[0021] Furthermore, in the fourth step, the decision variables of the optimization problem are as follows:

[0022] x = [A B1 B2 C λ1 λ2]

[0023] where x is the decision variable; A, B1, B2, C, λ1, and λ2 are the matrix elements of the decision variable x, and their meanings are the same as those in the modified Johnson-Cook constitutive model.

[0024] Furthermore, in the fourth step, the feasible region of the optimization problem is as follows:

[0025] x ∈ [-2|x0|, +2|x0|]

[0026] where x is the decision variable; x0 is the numerical value of the constitutive model parameters A, B1, B2, C, λ1, and λ2 in the third step.

[0027] In the fifth step, based on the improved method of the optimization algorithm, a sparrow search algorithm with chaotic initialization, reverse learning, and mutation improvement is developed.

[0028] Furthermore, in the fifth step, the improved method of the optimization algorithm includes but is not limited to the chaotic initialization improvement strategy, mutation improvement strategy, and reverse learning strategy.

[0029] In the sixth step, the initial parameters of the sparrow search algorithm are set.

[0030] Furthermore, in the sixth step, the initial parameters of the sparrow search algorithm are the population size, maximum number of iterations, proportion of discoverers in the total population, proportion of followers in the total population, and safety threshold.

[0031] In the seventh step, based on the Logistic-Tent chaotic function, the initial population of the sparrow search algorithm is generated.

[0032] Further, in the seventh step, the Logistic-Tent chaotic function formula is as follows:

[0033]

[0034] where t is the number of iterations; x t+1 is the position at the (t + 1)-th iteration; r is a parameter controlling the chaotic behavior, r ∈ (0, 4); x t is the position at the t-th iteration; the symbol mod1 represents taking the remainder of the previous formula divided by 1.

[0035] Eighth step, update the positions of the discoverers, followers, and scouts in the sparrow search algorithm.

[0036] Further, in the eighth step, the position update formula for the discoverers is as follows:

[0037]

[0038] where represents the value of the j-th dimension of the i-th sparrow at the t-th iteration; α is a random number, α ∈ (0, 1]; iter max is a constant representing the maximum number of iterations; Q is a random number following a normal distribution; L is a row vector with all elements being 1.

[0039] Further, in the eighth step, the position update formula for the followers is as follows:

[0040]

[0041] where x worst represents the globally worst position in the current iteration; x p represents the optimal position within the discoverers in the current iteration; A is a row vector with elements randomly assigned 1 or -1, where,

[0042] A + = A t (AA t ) -1 .

[0043] Further, in the eighth step, the position update formula for the scouts is as follows:

[0044]

[0045] where x best represents the globally optimal position in the current iteration; β is a step size control parameter, which is a random number with a mean of 0, a variance of 1, and following a normal distribution; K is a random number, K ∈ [-1, 1]; ε is the minimum constant to prevent division by zero error, which is 1×10 in the embodiments of the present invention-50 ; f i represents the sparrow x i of the objective function value, f g represents the objective function value of the global optimal solution at the current iteration number, f w represents the objective function value of the global worst solution at the current iteration number.

[0046] Step 9, based on the fast random reverse learning strategy, generate the next generation of population according to the opposite population of the contemporary population.

[0047] Furthermore, in the said Step 9, the formula of the fast random reverse learning is as follows:

[0048]

[0049] where, is the reverse solution of the i-th sparrow; α is a random number, α ∈ (0, 1].

[0050] Step 10, based on the differential evolution strategy, improve the weak solutions of the next generation of population.

[0051] Furthermore, in the said Step 10, the formula of the differential evolution strategy is as follows:

[0052] x i = x best + F·(x1 - x2)

[0053] where, x1 and x2 are two randomly selected individuals at the current iteration number.

[0054] Step 11, check whether the objective function value of the next generation of population reaches the target accuracy. If the target accuracy is not reached, return to Step 8 to update the positions of the discoverer, follower and vigilant in the sparrow search algorithm based on the next generation of population. If the target accuracy is reached, proceed to the next step.

[0055] Step 12, based on the optimal solution of the next generation of population in Step 10, obtain the parameters of the new modified Johnson-Cook constitutive model.

[0056] Step 13, based on the updated constitutive model parameters in Step 12, establish the optimized Johnson-Cook modified constitutive model, and then the high-precision thermoplastic constitutive model of TC4 titanium alloy that meets the accuracy requirements can be obtained.

[0057] The present invention has the following beneficial effects:

[0058] (1) By conducting high-temperature tensile tests on TC4 titanium alloy under thermoplastic forming temperature and strain rate conditions, the true stress-strain curves under different working conditions are obtained; based on the test data, a modified Johnson-Cook constitutive model is established, the objective function, decision variables and feasible domain of the optimization problem are defined, and the parameters of the constitutive model are optimized by using the sparrow search algorithm improved by chaotic initialization, reverse learning and mutation; based on the optimal solution of the constitutive model parameters, a high-precision thermoplastic constitutive model of TC4 titanium alloy is established.

[0059] (2) On the basis of the development of the existing constitutive model, the sparrow search algorithm improved by chaotic initialization, reverse learning and mutation is used to globally optimize the parameters of the constitutive model, forming a constitutive model modeling method that takes into account prediction accuracy, calculation cost and fitting difficulty, and solves the model accuracy problem caused by the limitations of the number of test samples and parameter fitting methods of the previous thermoplastic constitutive model of TC4 titanium alloy. Description of the Drawings

[0060] Figure 1 It is a flowchart of a high-precision thermoplastic constitutive model of TC4 titanium alloy constructed based on the embodiments of the present invention.

[0061] Figure 2 It is the true stress-strain curve obtained by conducting high-temperature tensile tests on TC4 titanium alloy under the conditions of a temperature range of 973K to 1123K and a strain rate range of 0.01s -1 ~1s -1 ; among them Figure 2 (a) is the true stress-strain curve diagram of TC4 titanium alloy under the conditions of a temperature of 973K and a strain rate of 0.01s -1 ~1s -1 ; Figure 2 (b) is the true stress-strain curve diagram of TC4 titanium alloy under the conditions of a temperature of 1023K and a strain rate of 0.01s -1 ~1s -1 ; Figure 2 (c) is the true stress-strain curve diagram of TC4 titanium alloy under the conditions of a temperature of 1073K and a strain rate of 0.01s -1 ~1s -1 ; Figure 2 (d) is the true stress-strain curve diagram of TC4 titanium alloy under the conditions of a temperature of 1123K and a strain rate of 0.01s -1 ~1s -1 ;

[0062] Figure 3 It is the comparison result of the predicted values and the test curves of Example 1 and Comparative Example 1; among them Figure 3 (a) is at a temperature of 973K and a strain rate of 0.01s-1 ~1 s -1 Comparison diagrams of the predicted values and test curves of Example 1 and Comparative Example 1 under the conditions; Figure 3 (b) is the comparison diagram of the predicted values and test curves of Example 1 and Comparative Example 1 under the conditions of a temperature of 1023 K and a strain rate of 0.01 s -1 ~1 s -1 Comparison diagrams of the predicted values and test curves of Example 1 and Comparative Example 1 under the conditions; Figure 3 (c) is the comparison diagram of the predicted values and test curves of Example 1 and Comparative Example 1 under the conditions of a temperature of 1073 K and a strain rate of 0.01 s -1 ~1 s -1 Comparison diagrams of the predicted values and test curves of Example 1 and Comparative Example 1 under the conditions; Figure 3 (d) is the comparison diagram of the predicted values and test curves of Example 1 and Comparative Example 1 under the conditions of a temperature of 1123 K and a strain rate of 0.01 s -1 ~1 s -1 Comparison diagrams of the predicted values and test curves of Example 1 and Comparative Example 1 under the conditions. Specific implementation manners

[0063] To make the objectives, solutions and beneficial effects of the present invention clearer, the following will further describe this specific implementation manner in combination with the accompanying drawings, Example 1 and Comparative Example 1. It should be understood that Example 1 described herein is only used to explain this application and is not used to limit the application.

[0064] The following will describe in detail the specific implementation of the present invention in combination with the accompanying drawings, Example 1 and Comparative Example 1.

[0065] Example 1:

[0066] As Figure 1 shown, a modeling method for a high-precision thermoplastic constitutive model of TC4 titanium alloy, the specific implementation steps include:

[0067] The first step is to conduct high-temperature tensile tests on TC4 titanium alloy under the conditions of a temperature range of 973 K to 1123 K and a strain rate range of 0.01 s -1 ~1 s -1 to obtain engineering stress-strain curves under different loading conditions;

[0068] Specifically, in the first step of Example 1, the high-temperature tensile test of TC4 titanium alloy is carried out on an electro-hydraulic servo dynamic and static universal testing machine equipped with a high-temperature furnace.

[0069] The second step is to convert the engineering stress-strain curve into a true stress-strain curve based on the conversion formulas of engineering stress, engineering strain, true stress, and true strain, so as to be used as the sample data for establishing a modified Johnson-Cook constitutive model.

[0070] Specifically, in the second step of Example 1, the conversion formulas are as follows:

[0071]

[0072] Among them, σ t , ε t are the true stress and true strain respectively; σ e , ε e are the engineering stress and engineering strain respectively; for the symbol ±, - represents the compression condition and + represents the tensile condition.

[0073] Specifically, in the second step of the first embodiment, the true stress-strain curve of TC4 titanium alloy under the temperature range of 973K to 1123K and the strain rate range of 0.01s -1 to 1s -1 is as shown in Figure 2 , where Figure 2 (a) is the true stress-strain curve diagram of TC4 titanium alloy under the conditions of temperature 973K and strain rate 0.01s -1 to 1s -1 ; Figure 2 (b) is the true stress-strain curve diagram of TC4 titanium alloy under the conditions of temperature 1023K and strain rate 0.01s -1 to 1s -1 ; Figure 2 (c) is the true stress-strain curve diagram of TC4 titanium alloy under the conditions of temperature 1073K and strain rate 0.01s -1 to 1s -1 ; Figure 2 (d) is the true stress-strain curve diagram of TC4 titanium alloy under the conditions of temperature 1123K and strain rate 0.01s -1 to 1s -1 .

[0074] In the third step, based on the true stress-strain curve obtained in the second step, a modified Johnson-Cook constitutive model is established to obtain the initial parameters of the constitutive model.

[0075] Specifically, in the third step of the first embodiment, the established modified Johnson-Cook constitutive model is as follows:

[0076]

[0077] Among them, σ is the stress value predicted by the constitutive model; ε is the strain; is the reference strain rate, defined as where is the strain rate under the current condition, is the reference strain rate, generally taking the minimum strain rate in the test; T is the temperature under the current condition, T r is the reference temperature, generally taking the lowest temperature in the test.

[0078] In the fourth step, based on the error between the predicted stress and the experimental stress of the modified Johnson-Cook constitutive model under the same working conditions, that is, based on the accuracy of the constitutive model, the objective function, decision variables, and feasible region of the optimization problem are defined.

[0079] Specifically, in the fourth step of Embodiment 1, the objective function of the optimization problem is as follows:

[0080]

[0081] where n is the total number of sample points used to fit the constitutive model, y i is the experimental stress value, and p i is the stress value predicted by the constitutive model.

[0082] Specifically, in the fourth step of Embodiment 1, the decision variables and feasible region of the optimization problem are as follows:

[0083] x = [A B1 B2 C λ1 λ2]

[0084] A ∈ [-496.8746, +496.8746]

[0085] B1 ∈ [-78.2294, +78.2294]

[0086] B2 ∈ [-1058.8736, +1058.8736]

[0087] C ∈ [-0.5402, +0.5402]

[0088] λ1 ∈ [-0.01480, +0.01480]

[0089] λ2 ∈ [-0.0009958, +0.0009958]

[0090] where x is the decision variable; A, B1, B2, C, λ1, and λ2 are the matrix elements of the decision variable x, and their meanings are the same as those in the modified Johnson-Cook constitutive model.

[0091] In the fifth step, based on the improved method of the optimization algorithm, a sparrow search algorithm with chaotic initialization, reverse learning, and mutation improvement is developed.

[0092] Specifically, in the fifth step of Embodiment 1, the improved method of the optimization algorithm includes, but is not limited to, chaotic initialization improvement strategy, mutation improvement strategy, and reverse learning strategy.

[0093] In the sixth step, the initial parameters of the sparrow search algorithm are set.

[0094] Specifically, in the sixth step of the first embodiment, the parameters of the sparrow search algorithm are shown in Table 1:

[0095] Table 1 Parameter settings of the sparrow search algorithm

[0096]

[0097]

[0098] In the seventh step, an initial population of the sparrow search algorithm is generated based on the Logistic-Tent chaotic function.

[0099] Specifically, in the seventh step of the first embodiment, the Logistic-Tent chaotic function formula is as follows:

[0100]

[0101] where t is the number of iterations; x t+1 is the position at the (t + 1)-th iteration; r is a parameter controlling the chaotic behavior, r ∈ (0, 4); x t is the position at the t-th iteration; the symbol mod1 represents taking the remainder of the previous formula divided by 1.

[0102] In the eighth step, the positions of the discoverers, followers, and vigilant ones in the sparrow search algorithm are updated.

[0103] Specifically, in the eighth step of the first embodiment, the position update formula for the discoverers is as follows:

[0104]

[0105] where represents the value of the j-th dimension of the i-th sparrow at the t-th iteration; α is a random number, α ∈ (0, 1]; iter max is a constant representing the maximum number of iterations; Q is a random number following a normal distribution; L is a row vector with all elements being 1.

[0106] Specifically, in the eighth step of the first embodiment, the position update formula for the followers is as follows:

[0107]

[0108] where x worst represents the globally worst position in the current iteration; x p represents the optimal position within the discoverers in the current iteration; A is a row vector with elements randomly assigned 1 or -1, where

[0109] A + = At (AA t ) -1 。

[0110] Specifically, in the eighth step of the first embodiment, the position update formula of the vigilant is as follows:

[0111]

[0112] where x best represents the global optimal position in the current iteration; β is the step size control parameter, which is a random number with a mean of 0, a variance of 1, and follows a normal distribution; K is a random number, K ∈ [-1, 1]; ε is the minimum constant to prevent division by zero error, which is 1×10 -50 in the embodiments of the present invention; f i represents the objective function value of the sparrow x i , f g represents the objective function value of the global optimal solution in the current iteration, and f w represents the objective function value of the global worst solution in the current iteration.

[0113] In the ninth step, based on the fast random reverse learning strategy, the next generation of population is generated according to the opposite population of the current generation of population.

[0114] Specifically, in the ninth step of the first embodiment, the formula of the fast random reverse learning is as follows:

[0115]

[0116] where is the reverse solution of the i-th sparrow; α is a random number, α ∈ (0, 1].

[0117] In the tenth step, based on the differential evolution strategy, the weak solutions of the next generation of population are improved.

[0118] Specifically, in the tenth step of the first embodiment, the formula of the differential evolution strategy is as follows:

[0119] x i = x best + F·(x1 - x2)

[0120] where x1 and x2 are two randomly selected individuals in the current iteration.

[0121] In the eleventh step, it is checked whether the objective function value of the next generation of population reaches the target accuracy. If the target accuracy is not reached, return to the eighth step to update the positions of the discoverer, follower, and vigilant in the sparrow search algorithm based on the next generation of population. If the target accuracy is reached, proceed to the next step.

[0122] Step 12: Based on the optimal solution of the next-generation population in Step 10, obtain the new and modified Johnson-Cook constitutive model parameters.

[0123] Step 13: Based on the updated constitutive model parameters in Step 12, establish an optimized Johnson-Cook modified constitutive model, and then a high-precision thermoplastic constitutive model of TC4 titanium alloy that meets the accuracy requirements can be obtained.

[0124] Specifically, in Step 13 of Embodiment 1, the formula of the TC4 high-precision thermoplastic constitutive model is as follows:

[0125]

[0126] Comparative Example 1:

[0127] The specific implementation steps of Comparative Example 1 are the same as the first three specific implementation steps of Embodiment 1, as follows:

[0128] Step 1: Conduct high-temperature tensile tests on TC4 titanium alloy under the conditions of a temperature range of 973K to 1123K and a strain rate range of 0.01s -1 ~1s -1 to obtain engineering stress-strain curves under different loading conditions;

[0129] Specifically, in Step 1 of Comparative Example 1, the high-temperature tensile test of TC4 titanium alloy is carried out on an electro-hydraulic servo dynamic and static universal testing machine equipped with a high-temperature furnace.

[0130] Step 2: Based on the conversion formulas of engineering stress, engineering strain, true stress, and true strain, convert the engineering stress-strain curve into a true stress-strain curve to be used as sample data for establishing a modified Johnson-Cook constitutive model.

[0131] Specifically, in Step 2 of Comparative Example 1, the conversion formulas are as follows:

[0132]

[0133] Among them, σ t and ε t are true stress and true strain respectively; σ e and ε e are engineering stress and engineering strain respectively; for the symbol ±, - represents the compression condition, and + represents the tensile condition.

[0134] Step 3: Based on the true stress-strain curve obtained in Step 2, establish a modified Johnson-Cook constitutive model to obtain the initial parameters of the constitutive model.

[0135] Specifically, in the third step of Comparative Example 1, the established modified Johnson-Cook constitutive model is as follows:

[0136]

[0137] where σ is the stress value predicted by the constitutive model; ε is the strain; is the reference strain rate, defined as where, is the strain rate under the current working condition, is the reference strain rate, generally taking the minimum strain rate in the test; T is the temperature under the current working condition, T r is the reference temperature, generally taking the lowest temperature in the test.

[0138] As Figure 3 shown, comparing the predicted stress values of Example 1, the predicted values of Comparative Example 1, and the true stress values obtained from the high-temperature tensile test under the temperature range of 973K to 1123K and the strain rate range of 0.01s -1 to 1s -1 conditions, where Figure 3 (a) is the comparison diagram of the predicted values of Example 1 and Comparative Example 1 and the test curve under the conditions of temperature 973K and strain rate 0.01s -1 to 1s -1 conditions; Figure 3 (b) is the comparison diagram of the predicted values of Example 1 and Comparative Example 1 and the test curve under the conditions of temperature 1023K and strain rate 0.01s -1 to 1s -1 conditions; Figure 3 (c) is the comparison diagram of the predicted values of Example 1 and Comparative Example 1 and the test curve under the conditions of temperature 1073K and strain rate 0.01s -1 to 1s -1 conditions; Figure 3 (d) is the comparison diagram of the predicted values of Example 1 and Comparative Example 1 and the test curve under the conditions of temperature 1123K and strain rate 0.01s -1 to 1s -1 conditions. It can be seen that the predicted stress values of Example 1 are in better agreement with the test curve. Among them, the average relative error between the predicted values of Comparative Example 1 and the true stress values of the test is 6.31%, while the average relative error between the predicted values of Example 1 of the present invention and the true stress values of the test is 5.12%. Compared with Comparative Example 1, the error value is reduced by 1.19%, which shows the high efficiency of the present invention.

[0139] The above-described Embodiment 1 is only a specific implementation manner of the present application. Although the present invention has been described in detail with reference to Embodiment 1, those skilled in the art should understand that within the technical scope disclosed in the present application, changes and substitutions that can be easily thought of are still within the protection scope of the present invention.

Claims

1. A modeling method for a high-precision thermoplastic constitutive model of TC4 titanium alloy, characterized in that It includes the following steps: In the first step, conduct high-temperature tensile tests on TC4 titanium alloy under different temperatures and strain rates to obtain engineering stress-strain curves under different loading conditions. In the second step, based on the conversion formulas between engineering stress, engineering strain, true stress, and true strain, convert the engineering stress-strain curve obtained in the first step into a true stress-strain curve to be used as sample data for establishing a modified Johnson-Cook constitutive model. In the third step, based on the true stress-strain curve obtained in the second step, establish a modified Johnson-Cook constitutive model to obtain the initial parameters of the constitutive model. In the fourth step, taking the error between the predicted stress and the test stress of the modified Johnson-Cook constitutive model under the same working conditions, that is, taking the accuracy of the constitutive model as the benchmark, define the objective function, decision variables, and feasible domain of the optimization problem. In the fifth step, based on the improvement method of the optimization algorithm, develop a sparrow search algorithm with chaotic initialization, reverse learning, and mutation improvement. In the sixth step, set the initial parameters of the sparrow search algorithm, where the initial parameters are the population size, the maximum number of iterations, the proportion of discoverers in the total population, the proportion of followers in the total population, and the safety threshold. In the seventh step, generate the initial population of the sparrow search algorithm based on the Logistic-Tent chaotic function. In the eighth step, update the positions of the discoverers, followers, and scouts in the sparrow search algorithm. In the ninth step, based on the fast random reverse learning strategy, generate the next generation population according to the opposite population of the current generation population. In the tenth step, based on the differential evolution strategy, improve the weak solutions of the next generation population. In the eleventh step, check whether the objective function value of the next generation population reaches the target accuracy. If the target accuracy is not reached, return to the eighth step and update the positions of the discoverers, followers, and scouts in the sparrow search algorithm based on the next generation population; if the target accuracy is reached, proceed to the next step. In the twelfth step, based on the optimal solution of the next generation population in the tenth step, obtain the parameters of the new modified Johnson-Cook constitutive model. In the thirteenth step, based on the updated constitutive model parameters in the twelfth step, establish an optimized Johnson-Cook modified constitutive model, and then a high-precision thermoplastic constitutive model of TC4 titanium alloy that meets the accuracy requirements can be obtained.

2. The modeling method of a high-precision thermoplastic constitutive model for TC4 titanium alloy according to claim 1, characterized in that In the second step, the conversion formulas are as follows: Among them, σ t and ε t are the true stress and true strain respectively; σ e and ε e are the engineering stress and engineering strain respectively; for the symbol ±, - represents the compression condition and + represents the tension condition.

3. The modeling method of a high-precision thermoplastic constitutive model for TC4 titanium alloy according to claim 1, characterized in that, In the third step, the modified Johnson-Cook constitutive model is as follows: Among them, σ is the stress; the first term on the right side of the equal sign is the strain-related term, ε is the strain, and A, B1, and B2 are the coefficients of the second-order polynomial, which are used to simulate the stress values under different strain conditions; the second term on the right side of the equal sign is the strain rate-related term, C is the strain rate sensitivity coefficient, is the reference strain rate, defined as where is the strain rate under the current working condition, is the reference strain rate, taking the minimum strain rate in the experiment; the third term on the right side of the equal sign is the coupling term of the strain rate and temperature, λ1 and λ2 are the coupling term coefficients, T is the temperature under the current working condition, T r is the reference temperature, taking the lowest temperature in the experiment.

4. The modeling method of a high-precision thermoplastic constitutive model for TC4 titanium alloy according to claim 1, characterized in that In the fourth step: The objective function of the optimization problem is as follows: where n is the total number of sample points used to fit the constitutive model, y i is the stress value of the test, p i is the stress value predicted by the constitutive model; The decision variables of the optimization problem are as follows: x = [A B1 B2 C λ1 λ2] (4) Where x is the decision variable; A, B1, B2, C, λ1, and λ2 are the matrix elements of the decision variable x, and their meanings are the same as those in the modified Johnson-Cook constitutive model. The feasible domain of the optimization problem is as follows: x ∈ [-2|x0|, +2|x0|] (5) Where x is the decision variable; x0 is the numerical value of the constitutive model parameters A, B1, B2, C, λ1, and λ2 in the third step.

5. A modeling method for a high-precision thermoplastic constitutive model of TC4 titanium alloy according to claim 1, characterized in that In the fifth step, the improvement methods of the optimization algorithm include but are not limited to the chaos initialization improvement strategy, the mutation improvement strategy, and the opposition-based learning strategy.

6. The modeling method of a high-precision thermoplastic constitutive model for TC4 titanium alloy according to claim 1, characterized in that, In the seventh step, the formula of the Logistic-Tent chaos function is as follows: where t is the number of iterations; x t+1 is the position at the (t + 1)-th iteration; r is a parameter controlling the chaotic behavior, r ∈ (0, 4); x t is the position at the t-th iteration; the symbol mod1 represents taking the remainder of the previous formula divided by 1.

7. A modeling method for a high-precision thermoplastic constitutive model of TC4 titanium alloy according to claim 1, characterized in that In the eighth step: The position update formula of the discoverer is as follows: Among them, represents the value of the j-th dimension of the i-th sparrow at the t-th iteration; α is a random number, α ∈ (0, 1]; iter max is a constant representing the maximum number of iterations; Q is a random number following a normal distribution; L is a row vector with all elements being 1; The position update formula of the follower is as follows: Among them, x worst represents the globally worst position in the current iteration; x p represents the optimal position within the discoverer in the current iteration; A is a row vector with elements randomly assigned 1 or -1, where, A + = A t (AA t ) -1 ; The position update formula of the vigilant is as follows: Among them, x best represents the global optimal position in the current iteration; β is the step size control parameter, which is a random number with a mean of 0, a variance of 1, and follows a normal distribution; K is a random number, K ∈ [-1, 1]; ε is the minimum constant to prevent division by zero error, which is 1×10 -50 in the embodiment of the present invention; f i represents the objective function value of the sparrow x i , f g represents the objective function value of the global optimal solution in the current iteration, and f w represents the objective function value of the global worst solution in the current iteration.

8. A modeling method for a high-precision thermoplastic constitutive model of TC4 titanium alloy according to claim 1, characterized in that In the ninth step, the formula of the fast random opposition-based learning is as follows: Among them, is the reverse solution of the i-th sparrow; α is a random number, α ∈ (0, 1].

9. The modeling method of a high-precision thermoplastic constitutive model for TC4 titanium alloy according to claim 1, characterized in that, In the tenth step, the differential evolution strategy formula is as follows: x i = x best + F·(x1 - x2) (11) Where x1 and x2 are two individuals randomly selected in the current iteration.

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