Method for determining parameters of anisotropic yield criterion of high-strength steel sheet

Abstract

The present application relates to a kind of high-strength steel sheet anisotropic yield criterion parameter determination method, belong to metal material mechanics performance detection and characterization method technical field.The technical scheme of the present application is: obtain three tensile directions plastic strain ratio, and three tensile directions engineering strain and engineering stress data;Remove the data after the maximum engineering stress in engineering strain and engineering stress data, and convert into plastic strain and true stress data;Calculate Barlat89 yield criterion parameter, define stress error;Through optimization algorithm iterative calculation, realize stress error minimization;Solve Barlat89 yield criterion parameter, obtain optimized equation.The present application is simple and effective, accurately characterizes high-strength steel anisotropy, does not need to carry out CAE iterative optimization, and the yield criterion formed can be used for forming simulation, strength and collision simulation analysis etc., to provide technical data for automobile CAE simulation.

Description

Technical Field

[0001] This invention relates to a method for determining the parameters of the anisotropic yield criterion for high-strength steel thin plates, belonging to the technical field of mechanical property testing and characterization methods for metallic materials. Background Technology

[0002] High-strength automotive steel exhibits anisotropic properties due to its rolling process, and yield criteria such as Barlat 89 and Hill 90 are typically used to describe it. Yield criterion parameters are generally obtained by measuring material parameters through tensile testing and then calculating them. For example, in the Barlat 89 model, tensile tests are first conducted at 0°, 45°, and 90° to the rolling direction to obtain the yield strength in the 0° direction and the plastic strain ratios r0, r45, and r90 in the three directions. Then, the model parameters are calculated. During the tensile process, the plastic strain ratio is obtained by measuring the displacement of the transverse and longitudinal extensometers. Because there are errors in the measured r values ​​in the three tensile directions, the calculated yield criterion parameters will also have errors, causing the model to not accurately characterize the yield stress in the three directions. Summary of the Invention

[0003] The purpose of this invention is to provide a method for determining the anisotropic yield criterion parameters of high-strength steel thin plates. By optimizing the r-value of high-strength steel, more accurate yield criterion parameters are obtained, which more accurately characterize the stress in the three directions. This method can be used for forming simulation, strength and collision simulation analysis, etc., providing technical data for automotive CAE simulation and effectively solving the above-mentioned problems existing in the background technology.

[0004] The technical solution of this invention is: a method for determining the parameters of anisotropic yield criterion for high-strength steel thin plates, comprising the following steps:

[0005] (1) Tensile tests were conducted on high-strength steel in three directions to obtain the plastic strain ratios in the three tensile directions. and , as well as engineering strain and engineering stress data in three tensile directions;

[0006] (2) Remove the data after the maximum engineering stress from the engineering strain and engineering stress data, and convert them into plastic strain and true stress data, then select... ≥0.2%, obtain the corresponding True stress at a point , and ;

[0007] (3) Calculate the Barlat89 yield criterion parameters, whose anisotropy parameters a, c, h, and p are derived from... , and Calculated;

[0008] (4) Calculate the yield stress in the tensile directions at 45° and 90° using the yield criterion. , Define stress error: ;

[0009] (5) and As optimization variables, they are respectively denoted as and The optimal solution is obtained through iterative calculation using an optimization algorithm. and To minimize stress error;

[0010] (6) Using r0, and Solve for the Barlat89 yield criterion parameters to obtain the optimized parameters. equation;

[0011] (7) Finite element simulation of tension in three directions, the material yield criterion is obtained in step (6). The equations are compared with the experimental and simulation results of the stress-strain curves to verify the effectiveness of the model.

[0012] In step (2), the engineering stress is converted into the actual stress using formula (Ⅰ), and the engineering strain is converted into the actual plastic strain using formula (Ⅱ):

[0013] (I)

[0014] (II)

[0015] In the formula: This represents the actual stress, in MPa. This represents true plastic strain, in mm / mm. Engineering stress, unit MPa; For engineering strain, the unit is mm / mm; This is the elastic modulus, expressed in MPa.

[0016] In step (3), under plane stress, the Barlat 89 yield criterion is given by formula (Ⅲ), and its anisotropy parameters a, c, h, and p are derived from... , , The values ​​of a, c, and h are calculated using formulas (Ⅳ), (Ⅴ), and (Ⅵ), respectively. The parameter p is solved using an iterative algorithm. The x value is obtained by solving formula (Ⅶ) using an iterative algorithm, and the p value is calculated using formula (Ⅷ).

[0017] ,

[0018] in It is the yield strength. , (III)

[0019] (IV)

[0020] (V)

[0021] (VI)

[0022] 0 (VII)

[0023] (VIII).

[0024] In step (4), the equations are solved and the results are calculated according to formulas (IX) and (X). and The stress error is defined by formula (XI):

[0025] (IX)

[0026] (X)

[0027] (XI).

[0028] The beneficial effects of this invention are: by optimizing the r-value of high-strength steel, more accurate yield criterion parameters are obtained, and the stress in the three directions is more accurately characterized. It can be used for forming simulation, strength and collision simulation analysis, etc., providing technical data for automotive CAE simulation. Attached Figure Description

[0029] Figure 1 This is a comparison chart of the experimental and simulation results of the stress-strain curves in an embodiment of the present invention. Detailed Implementation

[0030] To make the purpose, technical solutions, and advantages of the invention's embodiments clearer, the technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the embodiments described are only a small part of the embodiments of the present invention, not all of them. All other embodiments obtained by those skilled in the art based on the embodiments of the present invention without creative effort are within the protection scope of the present invention.

[0031] A method for determining the parameters of anisotropic yield criterion for high-strength steel thin plates includes the following steps:

[0032] (1) Tensile tests were conducted on high-strength steel in three directions to obtain the plastic strain ratios in the three tensile directions. and , as well as engineering strain and engineering stress data in three tensile directions;

[0033] (2) Remove the data after the maximum engineering stress from the engineering strain and engineering stress data, and convert them into plastic strain and true stress data, then select... ≥0.2%, obtain the corresponding True stress at a point , and ;

[0034] (3) Calculate the Barlat89 yield criterion parameters, whose anisotropy parameters a, c, h, and p are derived from... , and Calculated;

[0035] (4) Calculate the yield stress in the tensile directions at 45° and 90° using the yield criterion. , Define stress error: ;

[0036] (5) and As optimization variables, they are respectively denoted as and The optimal solution is obtained through iterative calculation using an optimization algorithm. and To minimize stress error;

[0037] (6) Using r0, and Solve for the Barlat89 yield criterion parameters to obtain the optimized parameters. equation;

[0038] (7) Finite element simulation of tension in three directions, the material yield criterion is obtained in step (6). The equations are compared with the experimental and simulation results of the stress-strain curves to verify the effectiveness of the model.

[0039] In step (2), the engineering stress is converted into the actual stress using formula (Ⅰ), and the engineering strain is converted into the actual plastic strain using formula (Ⅱ):

[0040] (I)

[0041] (II)

[0042] In the formula: This represents the actual stress, in MPa. This represents true plastic strain, in mm / mm. Engineering stress, unit MPa; For engineering strain, the unit is mm / mm; This is the elastic modulus, expressed in MPa.

[0043] In step (3), under plane stress, the Barlat 89 yield criterion is given by formula (Ⅲ), and its anisotropy parameters a, c, h, and p are derived from... , , The values ​​of a, c, and h are calculated using formulas (Ⅳ), (Ⅴ), and (Ⅵ), respectively. The parameter p is solved using an iterative algorithm. The x value is obtained by solving formula (Ⅶ) using an iterative algorithm, and the p value is calculated using formula (Ⅷ).

[0044] ,

[0045] in It is the yield strength. , (III)

[0046] (IV)

[0047] (V)

[0048] (VI)

[0049] 0 (VII)

[0050] (VIII).

[0051] In step (4), the equations are solved and the results are calculated according to formulas (IX) and (X). and The stress error is defined by formula (XI):

[0052] (IX)

[0053] (X)

[0054] (XI).

[0055] In practical applications, this invention includes the following steps:

[0056] (1) High-strength steel is processed into uniaxial tensile specimens, with the specimen direction at angles of 0°, 45°, and 90° to the rolling direction, respectively. Tensile tests are performed on the 0° tensile specimens using a tensile testing machine to obtain... The values ​​of engineering strain and stress in the 0° tensile direction were obtained, and tensile tests were conducted on 45° tensile specimens using a tensile testing machine to obtain... The values ​​of engineering strain and stress in the 45° tensile direction were obtained, and tensile tests were conducted on 90° tensile specimens using a tensile testing machine to obtain... Values ​​and engineering strain and stress data in the 90° tensile direction.

[0057] (2) Remove the data after the maximum engineering stress from the engineering strain and engineering stress data. Use formula (I) to convert the engineering stress into the true stress, and use formula (II) to convert the engineering strain into the true plastic strain. Select ≥0.2%, respectively obtaining the corresponding tensile directions at 0°, 45°, and 90°. True stress at a point , , .

[0058] (I),

[0059] (II);

[0060] In the formula: This represents the actual stress, in MPa. This represents true plastic strain, in mm / mm. For engineering stress, the unit is MPa. For engineering strain, the unit is mm / mm; This is the elastic modulus, in MPa, with a value of 210000MPa.

[0061] (3) Utilization , , Fitting the parameters of the Barlat 89 yield criterion. Under plane stress, the Barlat 89 yield criterion is given by formula (Ⅲ). 1) First, calculate the model parameter a using formula (Ⅳ); 2) Second, calculate the model parameter c using formula (Ⅴ); 3) Third, calculate the model parameter h using formula (Ⅵ); 4) Finally, solve equation (Ⅶ) using an iterative algorithm to obtain the value of x, and then calculate the value of p using formula (Ⅷ). Through the above steps, all parameters of formula (Ⅲ) for the Barlat 89 yield criterion are obtained.

[0062] ,

[0063] in It is the yield strength. , (III)

[0064] (IV)

[0065] (V)

[0066] (VI)

[0067] 0 (VII)

[0068] (VIII)

[0069] (4) Calculate the yield stress in the 45° and 90° tensile directions using the Barlat 89 yield criterion obtained in step (3). , Based on the characteristics of the stress components in the 45° tensile direction, formula (IX) can be derived from the Barlat 89 yield criterion formula (III). Solving formula (IX) yields... Based on the characteristics of the stress components in the 90° tensile direction, formula (X) can be derived from the Barlat 89 yield criterion formula (III). Solving formula (X) yields... The result obtained by solving the Barlat 89 yield criterion , With the results of the experiment , Compare the results and calculate the stress error according to formula (XI).

[0070] (IX)

[0071] (X)

[0072] (XI)

[0073] (5) Following steps (3)-(4), through , The parameters of the Barlat 89 yield criterion were obtained, and the yield stresses in the tensile directions at 45° and 90° were calculated based on this model. , The stress error was calculated. , As an optimization variable, let it be denoted as , The optimal solution is obtained through iterative calculation using an optimization algorithm. , This minimizes the stress error. Constraints can be added based on the experimental error (r value), for example: > > , > > .

[0074] (6) Following step (3), using r0, , Fit the parameters of the Barlat89 yield criterion to obtain the optimized result. equation.

[0075] (7) Verification by tensile tests in three directions, using the results obtained in step (6). The equations were used to conduct finite element simulations of tensile stresses in the 0°, 45°, and 90° directions. The experimental and simulation results of stress-strain curves were compared to verify the effectiveness of the model.

[0076] Example:

[0077] The following explanation uses high-strength steel HC820 / 1180DPD+Z as an example.

[0078] (1) High-strength steel HC820 / 1180DPD+Z was processed into tensile specimens in three directions: 0°, 45°, and 90°. The gauge length of the specimens was 50 mm, and the width of the parallel section of the specimens was 10 mm. Tensile tests were performed using a tensile testing machine to obtain... , Record the engineering strain and stress data; the tensile test curves are shown below. Figure 1 As shown.

[0079] (2) Remove the data after the maximum engineering stress from the engineering strain and engineering stress data. Use formula (I) to convert the engineering stress into the true stress, and use formula (II), where E is taken as 210000MPa, to convert the engineering strain into plastic strain; select =4%, and the actual stress corresponding to 4% plastic strain in the tensile directions at 0°, 45°, and 90° were obtained respectively. , , =1341.5 .

[0080] (3) Utilization , , Fitting the parameters of the Barlat 89 yield criterion. 1) First, calculate the model parameter a=1.13 using formula (Ⅳ); 2) Second, calculate the model parameter c=0.87 using formula (Ⅴ); 3) Third, calculate the model parameter h=0.96 using formula (Ⅵ); 4) Finally, solve equation (Ⅶ) using an iterative algorithm to obtain x=1.07, and calculate p=1.07 using formula (Ⅷ). Through the above, all parameters of formula (Ⅲ) for the Barlat 89 yield criterion are obtained.

[0081] (4) Based on the characteristics of the stress components in the 45° tensile direction, formula (IX) can be derived from the Barlat 89 yield criterion formula (Ⅲ). By solving formula (IX), we can obtain... =1256.6MPa. Based on the characteristics of the stress components in the 90° tensile direction, formula (X) can be derived from the Barlat 89 yield criterion formula (III). Solving formula (X) yields... 1369.0 MPa. Obtained by solving the Barlat 89 yield criterion. , With the results obtained from the experiment , By comparison, the stress error was calculated according to formula (XI) as error = 26.5MPa.

[0082] (5) An optimization algorithm was written based on the Python language, and the algorithm was improved. , As an optimization variable, let it be denoted as , Add constraints: > > , > > The optimal solution is obtained by iteratively calculating steps (3) and (4) using a quasi-Newton method optimization algorithm. , The final stress error is 0.

[0083] (6) Following the method in step (3), using r0, , Fitting the parameters of the Barlat 89 yield criterion yields all the parameters of the model: a=1.14; c=0.86; h=0.98; p=1.10, thus obtaining the optimized model. equation.

[0084] (7) Establish a tensile test simulation model using finite element simulation software, and perform tensile test simulation in three directions. Select two nodes with an initial distance equal to the gauge length as virtual extensometers. The material yield criterion is obtained in step (6). The equation is then calculated, and the tensile load F-virtual extensometer displacement s curve of the specimen cross-section is output, and converted into a stress-strain curve. Finally, the model's effectiveness is verified by comparing the experimental and simulation results of the stress-strain curves in the 0°, 45°, and 90° directions. Figure 1 It can be seen that the simulation results of the stress-strain curves in the 0°, 45° and 90° directions are basically consistent with the experimental results, and the agreement is very good.

Claims

1. A method for determining the parameters of anisotropic yield criterion for high-strength steel thin plates, characterized in that... Includes the following steps: (1) Tensile tests were conducted on high-strength steel in three directions to obtain the plastic strain ratios in the three tensile directions. and , as well as engineering strain and engineering stress data in three tensile directions; (2) Remove the data after the maximum engineering stress from the engineering strain and engineering stress data, and convert them into plastic strain and true stress data, then select... ≥0.2%, obtain the corresponding True stress at a point , and ; (3) Calculate the Barlat89 yield criterion parameters, whose anisotropy parameters a, c, h, and p are derived from... , and Calculated; (4) Calculate the yield stress in the tensile directions at 45° and 90° using the yield criterion. , Define stress error: ; (5) and As optimization variables, they are respectively denoted as and The optimal solution is obtained through iterative calculation using an optimization algorithm. and To minimize stress error; (6) Using r0, and Solve for the Barlat89 yield criterion parameters to obtain the optimized parameters. equation; (7) Finite element simulation of tension in three directions, the material yield criterion is obtained in step (6). The equations were compared with the experimental and simulation results of the stress-strain curves to verify the effectiveness of the model. In step (2), the engineering stress is converted into the actual stress using formula (Ⅰ), and the engineering strain is converted into the actual plastic strain using formula (Ⅱ): （Ⅰ） （Ⅱ） In the formula: This represents the actual stress, in MPa. This represents true plastic strain, in mm / mm. Engineering stress, unit MPa; For engineering strain, the unit is mm / mm; This is the elastic modulus, expressed in MPa.

2. The method for determining the parameters of the anisotropic yield criterion for high-strength steel thin plates according to claim 1, characterized in that: In step (3), under plane stress, the Barlat 89 yield criterion is given by formula (Ⅲ), and its anisotropy parameters a, c, h, and p are derived from... , , The values ​​of a, c, and h are calculated using formulas (Ⅳ), (Ⅴ), and (Ⅵ), respectively. The parameter p is solved using an iterative algorithm. The x value is obtained by solving formula (Ⅶ) using an iterative algorithm, and the p value is calculated using formula (Ⅷ). ， in It is the yield strength. , (III) （Ⅳ） （Ⅴ） （Ⅵ） 0 （Ⅶ） （Ⅷ）。 3. The method for determining the parameters of the anisotropic yield criterion for high-strength steel thin plates according to claim 1, characterized in that: In step (4), the equations are solved and the results are calculated according to formulas (IX) and (X). and The stress error is defined by formula (XI): （Ⅸ） （Ⅹ） （Ⅺ）。

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