Material mechanical parameter identification method based on interval optimization and indentation test

Abstract

The present invention discloses a material mechanical parameter identification method based on interval optimization and indentation testing, which specifically comprises the following steps: Step 1: performing multiple Berkovich indentation tests on the metal material to be tested, obtaining load and displacement curves of multiple loading processes of the nanoindentation test of the tested material, and obtaining the upper and lower limits of the loading curvature C; Step 2: establishing a design space for the material plasticity parameters, and establishing a simulated indentation displacement snapshot matrix X. sim Step 3: Establish an artificial neural network including an input layer, two hidden layers, and an output layer connected in sequence, and optimize the hyperparameters of the established artificial neural network; Step 4: Establish an uncertain optimization problem; Step 5: Based on the interval optimization and interval order relationship of the minimization problem, the uncertain optimization is converted into a deterministic optimization, and a two-layer genetic algorithm nested solution method is used to solve the uncertain optimization problem. The method of the present invention reduces the cost of parameter identification calculation and improves the efficiency of numerical calculation.

Description

Technical Field

[0001] The present invention belongs to the technical field of material plastic mechanical property testing methods, and particularly relates to a material mechanical parameter identification method based on interval optimization and indentation testing. Background Art

[0002] Measuring the plastic mechanical properties of materials has been a long-standing research topic. Traditional methods for measuring these parameters typically rely on multiple uniaxial tension / compression tests. However, these destructive tests require the preparation of test specimens of a specific shape prior to measurement, which is time-consuming and unsuitable for measuring the plastic mechanical properties of materials with limited volumes or in-service components. Therefore, finding a sample-saving, time-saving, and labor-saving experimental method for measuring these parameters is crucial.

[0003] In recent years, instrumented indentation testing technology has greatly facilitated the experimental testing of the plastic mechanical properties of metal materials. Compared with conventional tensile tests, the indentation test method is simpler and more flexible. Moreover, this test method can be applied to many occasions where the uniaxial tensile test method cannot be applied, which greatly makes up for the shortcomings of conventional test methods. Due to the above advantages of the indentation test method, it has gradually received special attention in the field of material performance testing research and has become a hot topic in international academic research. With the in-depth application of finite element simulation technology in the study of indentation elastic-plastic contact deformation, it has become possible to use indentation experiments combined with certain mathematical methods to infer the plastic mechanical properties of the tested material. In 2017, De Bono DM et al. (De Bono DM, London T, Baker M, et al. A robust inverse analysis method to estimate the local tensile properties of heterogeneous materials from nano-indentation data [J]. International Journal of Mechanical Sciences, 2017, 123: 162-176.) performed inverse analysis on experimental data with perturbations on welded structures, taking into account the impact of nanoindentation experimental perturbations on the robustness of the identification results.

[0004] In previous work, the experimental data used to measure material properties was a single indentation load-displacement curve or the average of multiple indentation load-displacement curves. This can lead to errors in the recognition process due to factors such as the uneven structure of the material being tested and inaccurate experimental testing. Furthermore, averaging the load-displacement curves of indentation experiments, if the indentation test exhibits a biased distribution, can result in the average not being at or near the peak of the biased distribution, thus impacting recognition accuracy. Summary of the Invention

[0005] The purpose of the present invention is to provide a material mechanical parameter identification method based on interval optimization and indentation testing, which solves the problem that the existing technology directly uses the indentation test load-displacement curve or the average value of the indentation test load-displacement curve and other methods to identify the plastic mechanical properties of the tested material without considering the uncertainty of the experiment, and the problem that a large-scale iterative finite element simulation calculation process is required in the original material property identification.

[0006] The technical solution adopted by the present invention is a material mechanical parameter identification method based on interval optimization and indentation testing, which is specifically implemented according to the following steps:

[0007] Step 1: Perform multiple Berkovich indentation tests on the metal material to be tested, obtain the load-displacement curves of multiple loading processes of the nanoindentation test of the material to be tested, and fit the loading curvature C according to Kick's law to obtain the upper and lower limits of the loading curvature C;

[0008] Step 2: Based on the Hollomon hardening law, establish the design space of the material plastic parameters, carry out the Berkovich indentation finite element simulation, and establish the simulation indentation displacement snapshot matrix X sim ;

[0009] Step 3: Establish an artificial neural network, which includes an input layer, two hidden layers, and an output layer connected in sequence. The output layer is the indentation profile data predicted by the artificial neural network. Based on the artificial neural network, a functional relationship between material performance parameters and indentation profile is established. The Bayesian optimization algorithm in machine learning is used to optimize the hyperparameters of the established artificial neural network.

[0010] Step 4: Establish an uncertain optimization problem;

[0011] Step 5: Based on interval optimization and minimization problem interval order relation ≤ cw, further transforming the uncertain optimization into deterministic optimization, and adopting the double-layer genetic algorithm nesting solution method to solve the uncertainty optimization problem. The inner nested genetic algorithm uncertain parameter is the loading curvature, and the outer genetic algorithm is used to solve the material tensile performance parameter, so that the tensile performance parameter yield stress σ of the tested material can be obtained. y and identification results of the strain hardening exponent n.

[0012] The present invention is also characterized in that

[0013] The specific implementation of step 1 is as follows:

[0014] Step 1.1: Polish the surface of the metal material to be tested, and conduct a Berkovich indentation test using an indenter and the metal material to be tested. The Berkovich indentation test is performed on an instrumented indentation test device, with the loading mode being load-controlled. During the loading process, a snapshot of the load-displacement curve of the indentation test is obtained. The snapshot of the load-displacement curve of the indentation test is represented by a vector X. exp =[x exp1 ,x exp2 ,…,x expp ] in the form of X exp ∈R m×p , where p represents the number of indentation tests; x expp is the displacement snapshot in the load-displacement curve during the pth indentation experiment. It is expressed in the form of , where m represents the dimension of the displacement snapshot of the experimental curve;

[0015] Step 1.2: Using the load-displacement curve during the indentation experiment, according to Kick's law, the loading curvature C is obtained according to C = [C 1 ,C 2 ,…,C p ]∈[C L ,C R ]; where p represents the number of indentation tests; C L Indicates the lower limit of loading curvature; C R Indicates the upper limit of the loading curvature.

[0016] The specific implementation of step 2 is as follows:

[0017] Step 2.1: Establish the design space of material plastic parameters based on the Hollomon hardening law, where the Hollomon hardening law is expressed as:

[0018]

[0019] Among them, σ is stress; E is elastic modulus; ε is strain; σ yis the yield stress; n is the strain hardening exponent; ε y is the yield strain;

[0020] Step 2.2, establish the finite element simulation of cone indentation, carry out a series of finite element simulations of cone indentation according to the design space of material plastic parameters; simulate the load-displacement curve displacement snapshot matrix X during the loading process of the indentation experiment sim Expressed as: X sim =[x sim1 ,x sim2 ,...,x simN ], where X sim ∈R m×N , N represents the number of material parameter combinations used for indentation simulation in the material parameter design space, m represents the dimension of the displacement snapshot of the simulation experiment curve; the simulation profile snapshot vector X ximi is the parameter combination corresponding to the i-th material obtained by finite element simulation; represents the Hollomon hardening law parameter, and Load snapshot matrix P in the load-displacement curve during the simulated indentation experiment loading process sim Expressed as: Among them, P sim ∈R m×1 , the vector contains the values is the sequence quantity of the indentation test load snapshot.

[0021] In step 3, the material tensile performance parameter σ y The relationship between n and the indentation profile is:

[0022]

[0023] Among them, the matrix Y pre The displacement snapshot of the load-displacement curve during the indentation test predicted by the artificial neural network; the matrices W1, W2, and W3 are the weight coefficient matrices of the 1st, 2nd, and 3rd layer neural networks respectively; the matrices b1 and b2 are the bias matrices of the 1st and 2nd layer neural networks respectively, which are column vectors; the matrix W represents the tensile performance parameter σ y and the row vector of n; σ(x) is the activation function of the third layer neural network, which is a linear function; The activation function of the first and second layers of the artificial neural network is the Sigmoid function.

[0024] In step 4, a deterministic optimization problem is established, which is expressed as:

[0025]

[0026] Where, the value range of W is Ω m; C is the curvature of the uncertain vector loading; h is the displacement snapshot of the indentation experiment loading process with respect to the uncertain vector C, which is a column vector, and h(C)=C(P sim ) 2 ; C L and C R They are the lower and upper limits of the loading curvature of the load-displacement curve of the indentation experiment, respectively.

[0027] In step 5:

[0028] Minimization problem interval order relation ≤ cw , which is expressed as:

[0029]

[0030] Establish a deterministic optimization problem, which is expressed as:

[0031]

[0032] Where, f d is the multi-objective evaluation function; 0≤β≤1 is the multi-objective weight coefficient; ξ is the guarantee f c (X)+ξ and f w (X)+ξ is a non-negative parameter; φ and ψ are multi-objective regularization factors; σ ymin and σ ymax Represents the yield stress σ of the database material y The minimum and maximum values ​​of n min and n max Indicates the minimum and maximum values ​​of the strain hardening exponent n of the materials in the established database.

[0033] The beneficial effects of the present invention are:

[0034] (1) The method of the present invention uses the load-displacement curve obtained by the indentation test to obtain the tensile performance parameters of the metal material, which can effectively avoid the tedious process of specimen preparation in the traditional tensile test process and avoid the problem of material damage and waste. At the same time, it can also be extended to the performance testing of in-service parts.

[0035] (2) The method of the present invention establishes a direct and effective association between the indentation profile snapshot and the material properties based on the artificial neural network in machine learning. By inputting the material performance parameters, the simulated data of the load-displacement curve of the material indentation experiment can be obtained, avoiding the large-scale iterative finite element simulation calculation process in the original material performance identification, reducing the parameter identification calculation cost, and improving the efficiency of numerical calculation. Bayesian optimization is also used to optimize the artificial neural network hyperparameters, avoiding the errors introduced in the identification process due to the predicted indentation curve, which leads to inaccurate identification results, thereby improving the recognition accuracy.

[0036] (3) The method of the present invention takes into account the existence of uncertainty in the indentation experiment, avoiding the introduction of errors due to the uncertainty of the experiment, which leads to uncertainty in the recognition results. The uncertain optimization problem is converted into a deterministic problem through interval optimization, and is solved through a double-layer genetic algorithm nesting, which reduces the error in the recognition results caused by the uncertainty of the experiment and improves the recognition accuracy.

[0037] (4) The method of the present invention solves the problem in the prior art of directly using other methods such as the indentation test load-displacement curve or the average value of the indentation test load-displacement curve to identify the plastic mechanical properties of the tested material without considering the uncertainty of the experiment, and the need for a large-scale iterative finite element simulation calculation process in the original material property identification. BRIEF DESCRIPTION OF THE DRAWINGS

[0038] Figure 1 is a flow chart of the method of the present invention;

[0039] Figure 2 This is the indentation test model under cone indentation loading;

[0040] Figure 3 This is a snapshot of the load-displacement curve of the 2024-T3 aluminum alloy material under a 300 mN load in Example 1 of the present invention, represented by X exp ;

[0041] Figure 4 This is a finite element model for one quarter of the indentation simulation in Example 1 of the present invention;

[0042] Figure 5 The training performance of the artificial neural network model established in Example 1 of the present invention;

[0043] Figure 6 The fitting effect and correlation coefficient between the actual output value of the artificial neural network model established in Example 1 of the present invention and the training set;

[0044] Figure 7 The fitting effect and correlation coefficient of the actual output value of the artificial neural network model established in Example 1 of the present invention and the validation set;

[0045] Figure 8 The fitting effect and correlation coefficient between the actual output value of the artificial neural network model established in Example 1 of the present invention and the test set;

[0046] Figure 9 The fitting effect and correlation coefficient of the actual output value of the artificial neural network model established in Example 1 of the present invention and the entire set;

[0047] Figure 10This is a comparison chart of the output value of the artificial neural network model established in Example 1 of the present invention and the actual output value.

[0048] Figure: 1. Indenter, 2. Metal material to be tested, 3. Finite element model of the indenter, 4. Finite element model of 2024-T3 aluminum alloy. DETAILED DESCRIPTION

[0049] The present invention will be described in detail below with reference to the accompanying drawings and specific embodiments.

[0050] The present invention provides a material mechanical parameter identification method based on interval optimization and indentation testing, such as Figure 1 , including the following steps:

[0051] Step 1: Perform multiple Berkovich indentation tests on the metal material to be tested, obtain the load-displacement curves of multiple loading processes of the nanoindentation test of the material to be tested, and fit the loading curvature C according to Kick's law to obtain the upper and lower limits of the loading curvature C;

[0052] The specific implementation of step 1 is as follows:

[0053] Step 1.1: Polish the surface of the metal material to be tested, such as Figure 2 The Berkovich indentation test is performed using an indenter 1 and a metal material 2 to be tested. The Berkovich indentation test is performed on an instrumented indentation test device using a load-controlled loading mode. During the loading process, a snapshot of the load-displacement curve of the indentation test is obtained. The snapshot of the load-displacement curve of the indentation test is represented by the vector X exp =[x exp1 ,x exp2 ,…,x expp ] in the form of X exp ∈R m×p Where p represents the number of indentation tests; x expp is the displacement snapshot in the load-displacement curve during the pth indentation experiment. It is expressed in the form of , where m represents the dimension of the displacement snapshot of the experimental curve.

[0054] Step 1.2: Using the load-displacement curve during the indentation experiment, according to Kick's law, the loading curvature C is obtained according to C = [C 1 ,C 2 ,…,C p ]∈[C L ,C R ]; where p represents the number of indentation tests; C L Indicates the lower limit of loading curvature; C R Indicates the upper limit of the loading curvature.

[0055] Step 2: Based on the Hollomon hardening law, establish the design space of the material plastic parameters, carry out a series of Berkovich indentation finite element simulations, and establish the simulation indentation displacement snapshot matrix X sim .

[0056] The specific implementation of step 2 is as follows:

[0057] Step 2.1: Establish the design space of material plastic parameters based on the Hollomon hardening law. The Hollomon hardening law is expressed as:

[0058]

[0059] Among them, σ is stress; E is elastic modulus; ε is strain; σ y is the yield stress; n is the strain hardening exponent; ε y is the yield strain.

[0060] Step 2.2: Establish a finite element simulation of cone indentation. Based on the design space of the material plasticity parameters, carry out a series of finite element simulations of cone indentation. Load-displacement curve displacement snapshot matrix X during the loading process of the simulated indentation experiment sim Expressed as: X sim =[x sim1 ,x sim2 ,...,x simN ]. Among them, X sim ∈R m×N , N represents the number of material parameter combinations used for indentation simulation in the material parameter design space, and m represents the dimension of the displacement snapshot of the simulation experiment curve. Therefore, the simulation profile snapshot vector X ximi is the parameter combination corresponding to the i-th material obtained by finite element simulation. represents the Hollomon hardening law parameter, and Load snapshot matrix P in the load-displacement curve during the simulated indentation experiment loading process sim Expressed as: Among them, P sim ∈R m×1 , the vector contains the values is the sequence quantity of the indentation test load snapshot.

[0061] Step 3: Build an artificial neural network consisting of an input layer, two hidden layers, and an output layer. The output layer contains the predicted indentation profile data. Based on the artificial neural network, a functional relationship between material performance parameters and indentation profiles is established. The hyperparameters of the established artificial neural network are optimized using a Bayesian optimization algorithm from machine learning.

[0062] Material tensile performance parameter σ y The relationship between n and the indentation profile is:

[0063]

[0064] Among them, the matrix Y pre The displacement snapshot of the load-displacement curve during the indentation test predicted by the artificial neural network; the matrices W1, W2, and W3 are the weight coefficient matrices of the 1st, 2nd, and 3rd layer neural networks respectively; the matrices b1 and b2 are the bias matrices of the 1st and 2nd layer neural networks respectively, which are column vectors; the matrix W represents the tensile performance parameter σ y and the row vector of n; σ(x) is the activation function of the third layer neural network, which is a linear function; The activation function of the first and second layers of the artificial neural network is the Sigmoid function.

[0065] Step 4: Establish the uncertain optimization problem, which is expressed as:

[0066]

[0067] Where, the value range of W is Ω m ; C is the curvature of the uncertain vector loading; h is the displacement snapshot of the indentation experiment loading process with respect to the uncertain vector C, which is a column vector, and h(C)=C(P sim ) 2 ; C L and C R They are the lower and upper limits of the loading curvature of the load-displacement curve of the indentation experiment, respectively.

[0068] Step 5: Based on interval optimization and minimization problem interval order relation ≤ cw , further transforming the uncertain optimization into deterministic optimization, and adopting the double-layer genetic algorithm nesting solution method to solve the uncertainty optimization problem. The inner nested genetic algorithm uncertain parameter is the loading curvature, and the outer genetic algorithm is used to solve the material tensile performance parameter, so that the tensile performance parameter yield stress σ of the tested material can be obtained. y and identification results of the strain hardening exponent n.

[0069] Minimization problem interval order relation ≤ cw , which is expressed as:

[0070]

[0071] Establish a deterministic optimization problem, which is expressed as:

[0072]

[0073] Where, f d is the multi-objective evaluation function; 0≤β≤1 is the multi-objective weight coefficient; ξ is the guarantee f c (X)+ξ and f w (X)+ξ is a non-negative parameter; φ and ψ are multi-objective regularization factors; σ ymin and σ ymax Represents the yield stress σ of the database material y The minimum and maximum values ​​of n min and n max Indicates the minimum and maximum values ​​of the strain hardening exponent n of the materials in the established database.

[0074] The effects of the method of the present invention are further illustrated below by means of specific examples.

[0075] Example 1

[0076] Step 1, such as Figure 2 , which is the indentation test under Berkovich indentation loading. The surface of 2024-T3 aluminum alloy material was polished and the Berkovich indentation test was carried out. The Berkovich indentation test was carried out on an instrumented indentation test equipment, and the loading mode was load control mode. Figure 3 In order to obtain the experimental data of the load-displacement curve during the loading process, the load-displacement curve snapshot was fitted by Kick's law to obtain the loading curvature snapshot and its upper and lower limits. The upper and lower limits of the loading curvature obtained were 41.60 GPa and 34.93 GPa, respectively.

[0077] Step 2, such as Figure 4 , is the finite element simulation model of the conical indenter. The finite element model 3 of the indenter is regarded as a deformable body, the elastic modulus is set to 1141GPa, and the Poisson's ratio is 0.07. A large number of conical indentation finite element simulations are carried out within the given material plasticity parameter range to obtain the displacement snapshot matrix X during the indentation loading process. sim The calculation range of the material plasticity parameters set in the finite element model 4 of 2024-T3 aluminum alloy is 320MPa≤σ y ≤440MPa, with an interval of 20MPa, 0.1≤n≤0.19, with an interval of 0.015. The elastic modulus of the aluminum alloy is assumed to be a known quantity and is taken as 70.354GPa.

[0078] Step 3: If Figure 5 , is the training performance of the artificial neural network. It can be seen from the figure that the trained artificial neural network has good performance; Figure 6-9, is the fitting effect and correlation coefficient of the actual output value of the trained two-parameter artificial neural network with the training set, validation set, test set and the entire set. The correlation coefficients R are 0.98883, 0.98428, 0.0.95492 and 0.98813 respectively, all reaching above 0.9. Therefore, it can be seen that the trained two-parameter artificial neural network model has a good fitting effect and can make good predictions for the simulation model. Figure 10 , which compares the output values ​​of the trained artificial neural network model with the actual output values. The artificial neural network consists of an input layer, two hidden layers, and an output layer. The output layer contains the displacement data of the load-displacement curve predicted by the artificial neural network during the simulated indentation loading process. Based on the artificial neural network, a functional relationship between material performance parameters and the displacement of the load-displacement curve during loading is established.

[0079] Material tensile performance parameter σ y The relationship between n and the load-displacement curve during the indentation test is as follows:

[0080]

[0081] Among them, the matrix Y pre is a snapshot of the displacement during the loading process of the indentation experiment predicted by the artificial neural network; matrices W1, W2, and W3 are the weight coefficient matrices of the 1st, 2nd, and 3rd layer neural networks respectively; matrices b1 and b2 are the bias matrices of the 1st and 2nd layer neural networks respectively, which are column vectors; matrix W represents the tensile performance parameter σ y and the row vector of n; σ(x) is the activation function of the third layer neural network, which is a linear function; The activation function of the first and second layers of the artificial neural network is the Sigmoid function.

[0082] The Bayesian optimization algorithm in machine learning is used to optimize the hyperparameters of the established artificial neural network.

[0083] Step 4: Establish the uncertain optimization problem, which is expressed as:

[0084]

[0085] Where, the value range of W is Ω m ; C is the curvature of the uncertain vector loading; h is the displacement snapshot of the indentation experiment loading process with respect to the uncertain vector C, which is a column vector, and h(C)=C(P sim ) 2 ; C L and C R They are the lower and upper limits of the loading curvature of the load-displacement curve of the indentation experiment, respectively.

[0086] Step 5: Based on interval optimization and interval order relationship ≤ cw , further transforming the uncertain optimization into deterministic optimization, and adopting the double-layer genetic algorithm nesting solution method to solve the uncertainty optimization problem. The inner nested genetic algorithm uncertain parameter is the loading curvature, and the outer genetic algorithm is used to solve the material tensile performance parameter, so that the tensile performance parameter yield stress σ of the tested material can be obtained. y , and identification results of the strain hardening exponent n.

[0087] Minimize the interval order relation of the optimization problem ≤ cw , which is expressed as:

[0088]

[0089] Establish a deterministic optimization problem, which is expressed as:

[0090]

[0091] Where, f d is the multi-objective evaluation function; 0≤β≤1 is the multi-objective weight coefficient; ξ is the guarantee f c (X)+ξ and f w (X)+ξ is a non-negative parameter; φ and ψ are multi-objective regularization factors; σ ymin and σ ymax Represents the yield stress σ of the database material y The minimum and maximum values ​​of n min and n max Indicates the minimum and maximum values ​​of the hardening exponent n of the material in the established database.

[0092] The above uncertain optimization problem is solved by using a nested double-layer genetic algorithm solution method, and the yield stress σ of the tensile performance parameter of the tested material can be obtained. y and identification results of the strain hardening exponent n.

[0093] Tensile tests were conducted on 2024-T3 aluminum alloy, and the tensile properties of the material were obtained by fitting the Hollomon hardening law. The tensile properties of the material obtained from the tensile test were compared with those obtained by this method. Table 1 shows the uniaxial tensile plastic properties of the 2024-T3 aluminum alloy obtained by fitting the Hollomon hardening law. Table 2 shows the comparison of the uniaxial tensile properties of the 2024-T3 aluminum alloy with the indentation test results.

[0094] Table 1 Uniaxial properties of 2024-T3 aluminum alloy obtained by fitting the Hollomon hardening law

[0095]

[0096] Table 2 Comparison of uniaxial tensile performance parameters and indentation test results of 2024-T3 aluminum alloy

[0097]

[0098] By analyzing the uniaxial tensile performance parameters of 2024-T3 aluminum alloy in Table 2 and comparing them with the tensile performance parameters identified according to the method proposed in the present invention, the following conclusions can be drawn:

[0099] 1) The tensile performance parameters of the 2024-T3 aluminum alloy identified by the method of the present invention are highly accurate, with very small errors compared with the uniaxial test, and are in very good agreement with the expected results.

[0100] 2) In the parameter identification modeling, the method of the present invention takes into account the experimental uncertainty in the form of intervals, which is more in line with the essential properties of the problem of identifying material parameters by the indentation method, and the recognition results are more reliable.

[0101] 3) When identifying material plasticity parameters, the method of the present invention replaces large-scale finite element simulation with an optimized neural network, which reduces the cost of parameter identification calculation and improves the efficiency of numerical calculation.

Claims

1. A material mechanical parameter identification method based on interval optimization and indentation testing, characterized in that: Please follow the steps below to implement: Step 1: Perform multiple Berkovich indentation tests on the metal material to be tested, obtain the load-displacement curves of multiple loading processes of the nanoindentation test of the material to be tested, and fit the loading curvature C according to Kick's law to obtain the upper and lower limits of the loading curvature C; Step 2: Based on the Hollomon hardening law, establish the design space of the material plastic parameters, carry out the Berkovich indentation finite element simulation, and establish the simulation indentation displacement snapshot matrix X sim ; Step 3: Establish an artificial neural network including an input layer, two hidden layers, and an output layer connected in sequence. The output layer is the indentation profile data predicted by the artificial neural network. Establish a functional relationship between material performance parameters and indentation profile, and optimize the established artificial neural network hyperparameters. Step 4: Establish an uncertain optimization problem; Step 5: Based on interval optimization and minimization problem interval order relation ≤ cw , further transforming the uncertain optimization into deterministic optimization, and using the nested solution method of the double-layer genetic algorithm to solve the uncertain optimization problem, thus obtaining the tensile performance parameter yield stress σ of the tested material y and identification results of the strain hardening exponent n.

2. The material mechanical parameter identification method based on interval optimization and indentation testing according to claim 1 is characterized in that: The specific implementation of step 1 is as follows: Step 1.1: The surface of the metal material to be tested (2) is polished, and a Berkovich indentation test is performed using the indenter (1) and the metal material to be tested (2); the Berkovich indentation test is performed on an instrumented indentation test device, and the loading mode is a load control mode; during the loading process of the indenter, a snapshot of the load-displacement curve of the indentation test is obtained; the snapshot of the load-displacement curve of the indentation test is represented by a vector X exp =[x exp1 ,x exp2 ,…,x expp ] in the form of X exp ∈R m×p , where p represents the number of indentation tests; x expp is the displacement snapshot in the load-displacement curve during the pth indentation experiment. It is expressed in the form of , where m represents the dimension of the displacement snapshot of the experimental curve; Step 1.2: Using the load-displacement curve during the indentation experiment, according to Kick's law, the loading curvature C is obtained according to C = [C 1 ,C 2 ,…,C p ]∈[C L ,C R ]; where p represents the number of indentation tests; C L Indicates the lower limit of loading curvature; C R Indicates the upper limit of the loading curvature.

3. The material mechanical parameter identification method based on interval optimization and indentation testing according to claim 1 is characterized in that: The specific implementation of step 2 is as follows: Step 2.1: Establish the design space of material plastic parameters based on the Hollomon hardening law, where the Hollomon hardening law is expressed as: Among them, σ is stress; E is elastic modulus; ε is strain; σ y is the yield stress; n is the strain hardening exponent; ε y is the yield strain; Step 2.2, establish the finite element simulation of cone indentation, carry out a series of finite element simulations of cone indentation according to the design space of material plastic parameters; simulate the load-displacement curve displacement snapshot matrix X during the loading process of the indentation experiment sim Expressed as: X sim =[x sim1 ,x sim2 ,...,x simN ], where X sim ∈R m×N , N represents the number of material parameter combinations used for indentation simulation in the material parameter design space, m represents the dimension of the displacement snapshot of the simulation experiment curve; the simulation profile snapshot vector X ximi is the parameter combination corresponding to the i-th material obtained by finite element simulation; represents the Hollomon hardening law parameter, and Load snapshot matrix P in the load-displacement curve during the simulated indentation experiment loading process sim Expressed as: Among them, P sim ∈R m×1 , the vector contains the values is the sequence quantity of the indentation test load snapshot.

4. The material mechanical parameter identification method based on interval optimization and indentation testing according to claim 1 is characterized in that: In step 3, the material tensile performance parameter σ y The relationship between n and the indentation profile is: Among them, the matrix Y pre The displacement snapshot of the load-displacement curve during the indentation test predicted by the artificial neural network; the matrices W1, W2, and W3 are the weight coefficient matrices of the 1st, 2nd, and 3rd layer neural networks respectively; the matrices b1 and b2 are the bias matrices of the 1st and 2nd layer neural networks respectively, which are column vectors; the matrix W represents the tensile performance parameter σ y and the row vector of n; σ(x) is the activation function of the third layer neural network, which is a linear function; The activation function of the first and second layers of the artificial neural network is the Sigmoid function.

5. The material mechanical parameter identification method based on interval optimization and indentation testing according to claim 1 is characterized in that: In step 4, a deterministic optimization problem is established, which is expressed as: Where, the value range of W is Ω m ; C is the curvature of the uncertain vector loading; h is the displacement snapshot of the indentation experiment loading process with respect to the uncertain vector C, which is a column vector, and h(C)=C(P sim ) 2 ; C L and C R They are the lower and upper limits of the loading curvature of the load-displacement curve of the indentation experiment, respectively.

6. The material mechanical parameter identification method based on interval optimization and indentation testing according to claim 1 is characterized in that: In step 5: Minimization problem interval order relation ≤ cw , which is expressed as: Establish a deterministic optimization problem, which is expressed as: Where, f d is the multi-objective evaluation function; 0≤β≤1 is the multi-objective weight coefficient; ξ is the guarantee f c (X)+ξ and f w (X)+ξ is a non-negative parameter; φ and ψ are multi-objective regularization factors; σ ymin and σ ymax Represents the yield stress σ of the database material y The minimum and maximum values ​​of n min and n max Indicates the minimum and maximum values ​​of the strain hardening exponent n of the materials in the established database.

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