Material forming limit prediction method

Abstract

The invention relates to a material forming limit prediction method, and belongs to the technical field of mechanical behavior simulation prediction methods. According to the technical scheme, a nonlinear forming limit test is carried out by adopting a proportional loading and two-stage proportional loading method, and test data are collected and calculated; forming limit strain under the two-stage loading condition is calculated, and model parameter optimization is carried out; calculating limit strain by inputting different pre-strain stage loading path parameters phi 1, pre-strain parameters E0 and two-stage loading path parameters phi 2, and constructing a neural network model training data set; constructing a neural network model, and carrying out training testing; and predicting the nonlinear forming limit of the plate. According to the method, on the basis of the two-stage loading test, the advantages of the M-K, the failure criterion theoretical model method and the machine learning method are effectively combined, formability prediction analysis of the plate under the complex nonlinear forming condition is achieved, and meanwhile prediction reliability and efficiency are guaranteed.

Description

Technical Field

[0001] The present invention relates to a method for predicting the forming limit of a material, and belongs to the technical field of mechanical behavior simulation and prediction methods. Background Art

[0002] In addition to being affected by the organizational structure, the formability of sheet metal is closely related to the forming path of the sheet metal. With the increasing demand for automotive lightweighting, advanced forming technologies such as roll stamping, roll pressing, hot stamping, hot gas bulging, and integrated forming have been gradually applied and popularized in the forming of automotive high-strength steel components. Nonlinear path loading exists in the forming processes such as stamping and roll pressing of sheet metal. The conventional forming limit diagram (FLD) has been widely used in the evaluation and prediction analysis of sheet metal formability. However, since the FLD is established based on the linear loading test method, there will be a large deviation when it is used to analyze and predict the sheet metal forming under complex nonlinear loading paths. At the same time, the forming process personnel usually rely on a semi-empirical method for die trial debugging, which will result in setting the safety margin too high or too low, leading to problems such as material waste.

[0003] In order to improve the reliability and efficiency of the formability evaluation of sheet metal in industrial design and production, it is necessary to provide a method for predicting the forming limit of sheet metal under nonlinear loading paths. Since the experiment of the forming limit of a specific non-proportional loading path is both challenging and costly, the development of a theoretical method to achieve the forming limit prediction will greatly reduce the cost. The M-K model is one of the most widely used models for predicting the forming limit of thin-walled metals. The M-K model can consider the influence of strain path changes, the normal stress and shear stress through the thickness, and can be combined with anisotropic yield criteria and hardening laws. Some research works have applied the M-K model to predict the forming limit of aluminum alloy and high-strength steel materials under nonlinear loading conditions. However, the M-K model is sensitive to the geometric defect size, and the calculation process is affected by the iterative method. If the initial value is set unreasonably, the calculation may not converge. The data-driven method based on machine learning tools is increasingly used in the research of material mechanical behavior. The machine learning method can conveniently and quickly describe the nonlinear behavior of materials. However, the method of establishing a machine learning prediction model solely based on data depends on a large amount of sample data and high data quality. Therefore, combining the physical model with the machine learning model to describe the forming performance of materials is more applicable to complex loading paths than the pure data-driven method, and can be further integrated and applied to commercial software packages. Summary of the Invention

[0004] The object of the present invention is to provide a method for predicting the forming limit of materials. Based on the two-stage loading test, the advantages of the M-K, failure criterion theoretical model method and machine learning method are effectively combined to realize the prediction and analysis of the formability of sheet materials under complex non-linear forming conditions, while ensuring the prediction reliability and efficiency, and effectively solving the above problems existing in the background technology.

[0005] The technical solution of the present invention is: a method for predicting the forming limit of materials, comprising the following steps:

[0006] (1) Adopt the proportional loading and two-stage proportional loading methods to conduct non-linear forming limit tests, conduct anisotropic tensile property tests, conduct DIC fracture failure tests under different stress triaxialities during pre-strain loading, and collect and calculate test data;

[0007] (2) Adopt the improved M-K theoretical model or combine the failure criterion model to calculate the forming limit strain under the two-stage loading condition, and optimize the model parameters using the test data in step (1);

[0008] (3) By inputting different pre-strain stage loading path parameters Pre-strain parameter E0 and two-stage loading path parameters Calculate the limit strain and construct the training data set of the neural network model;

[0009] (4) Construct a neural network model and conduct training and testing;

[0010] (5) Apply the neural network model passed the test to predict the non-linear forming limit of the sheet material.

[0011] In the above step (1), the test data includes pre-strain stage loading path parameters Pre-strain parameter E0, two-stage loading path parameters Limit major strain ε1, limit minor strain ε2, strain hardening index n, strain strengthening coefficient K, anisotropy parameter R, and the corresponding cumulative instability strain and cumulative fracture strain under different stress triaxialities;

[0012] Loading path parameters Are represented by the stress ratio α 、 Strain ratio β or Indicated; the pre-strain parameter E0 is represented by the following formula (1), (2) or (3). Formula (1) is applicable to the isotropic model, formula (2) is applicable to the anisotropic model, and formula (3) is the polar coordinate model; the loading path parameter And the pre-strain parameter E0 are not limited to the above representation forms

[0013]

[0014] In step (2), the improved M-K theoretical model considers the stress in the thickness direction, uses the Newton-Raphson iteration method for programming calculation, and continuously corrects the material hardening model parameters K, n, the initial thickness non-uniformity f0, and the ultimate damage judgment condition through an optimization method to reduce the error between the model calculation result and the test result; the ultimate damage judgment condition selects formula (4) or formula (5); in formula (4), dε1 b is the main strain increment in the groove in the M-K model groove theory, and dε1 a is the main strain increment outside the groove, and the initial value of the ultimate damage judgment parameter D is 10; formula (5) is the damage judgment condition combined with the fracture failure criterion model, and ε f The expression options include but are not limited to the MMC criterion model and the Lou-Huh criterion model, and their expressions are formula (6) and formula (7) respectively. In the formulas, A, C1, C2, and C3 are material model parameters, μ is the Lode parameter, and η is the stress triaxiality

[0015]

[0016] In step (3), the programming calculation method is adopted in the construction process of the neural network model training data set, and the data set has no less than 1000 sample data.

[0017] In step (4), the neural network model is not limited to the backpropagation neural network model, and the number of neural networks in the hidden layer is greater than or equal to 7.

[0018] The described two-stage linear loading test method and calculation method can be extended and applied to multi-stage linear loading and non-linear loading processes.

[0019] The beneficial effects of the present invention are as follows: Based on the two-stage loading test, the advantages of the M-K, failure criterion theoretical model method and the machine learning method are effectively combined, realizing the formability prediction and analysis of the sheet under complex non-linear forming conditions, and at the same time ensuring the prediction reliability and efficiency. Description of the Drawings

[0020] Figure 1 is the flowchart of the method of the present invention;

[0021] Figure 2 is the accuracy result of the neural network model in the embodiment of the present invention Figure 1 ;

[0022] Figure 3 is the accuracy result of the neural network model in the embodiment of the present invention Figure 2 ;

[0023] Figure 4 is the accuracy result of the neural network model in the embodiment of the present invention Figure 3 ;

[0024] Figure 5 are the accuracy results of the neural network model in the embodiments of the present invention Figure 4 ;

[0025] Figure 6 is the correlation coefficient graph of the forming limit prediction data and the experimental test data in the embodiments of the present invention;

[0026] Figure 7 is the prediction result graph of the forming limit diagram under the non - linear path in the embodiments of the present invention. Detailed implementation manners

[0027] In order to make the objectives, technical solutions and advantages of the embodiments of the invention clearer, the technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings in the embodiments. Obviously, the described embodiments are only a small part of the embodiments of the present invention, rather than all the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those of ordinary skill in the art without creative efforts shall fall within the protection scope of the present invention.

[0028] A method for predicting the forming limit of a material, comprising the following steps:

[0029] (1) Conduct non - linear forming limit tests using proportional loading and two - stage proportional loading methods, conduct anisotropic tensile property tests, conduct DIC fracture failure tests under different stress triaxialities during pre - strain loading, and collect and calculate test data;

[0030] (2) Use an improved M - K theory model or a combined failure criterion model to calculate the forming limit strain under two - stage loading conditions, and optimize the model parameters using the test data in step (1);

[0031] (3) By inputting different pre - strain stage loading path parameters pre - strain parameter E0 and two - stage loading path parameters calculate the limit strain and construct a training data set for the neural network model;

[0032] (4) Construct a neural network model and conduct training and testing;

[0033] (5) Apply the neural network model that has passed the test to predict the non - linear forming limit of the sheet metal.

[0034] In the said step (1), the test data includes pre - strain stage loading path parameters pre - strain parameter E0, two - stage loading path parameters The ultimate principal strain ε1, the ultimate secondary strain ε2, the strain hardening index n, the strain strengthening coefficient K, the anisotropy parameter R, and the corresponding cumulative instability strain and cumulative fracture strain under different stress triaxialities;

[0035] Loading path parameters Using the stress ratio α 、 The strain ratio β or Represented; the pre-strain parameter E0 is represented by the following formula (1), (2) or (3). Formula (1) is applicable to the isotropic model, formula (2) is applicable to the anisotropic model, and formula (3) is the polar coordinate model; the loading path parameters And the pre-strain parameter E0 is not limited to the above representation form

[0036]

[0037]

[0038] In the said step (2), the improved M-K theory model considers the stress in the thickness direction, uses the Newton-Raphson iteration method for programming calculation, and continuously corrects the material hardening model parameters K, n, the initial thickness non-uniformity f0 and the ultimate damage judgment condition through an optimization method to reduce the error between the model calculation result and the test result; the ultimate damage judgment condition selects formula (4) or formula (5); in formula (4), dε1 b Is the main strain increment in the groove in the M-K model groove theory, dε1 a Is the main strain increment outside the groove, and the initial value of the ultimate damage judgment parameter D is 10; formula (5) is the damage judgment condition combined with the fracture failure criterion model, and the expression of ε f The expression is optional but not limited to the MMC criterion model and the Lou-Huh criterion model, and their expressions are formula (6) and formula (7) respectively. In the formulas, A, C1, C2, and C3 are material model parameters, μ is the Lode parameter, and η is the stress triaxiality

[0039]

[0040] In the said step (3), the construction process of the neural network model training data set adopts a programming calculation method, and the data set has no less than 1000 samples.

[0041] In the said step (4), the neural network model is not limited to the backpropagation neural network model, and the number of hidden layer neural networks is greater than or equal to 7.

[0042] The said two-stage linear loading test method and calculation method can be extended and applied to multi-stage linear loading and non-linear loading processes.

[0043] In practical applications, the present invention provides a method for predicting the forming limit of sheet metal based on a neural network model and a physical model, which includes the following steps:

[0044] Step 1: Take the high-strength dual-phase steel DP780 sheet as the test research object, and adopt a two-stage proportional loading method, that is, conduct 3% and 6% unidirectional pre-strain and biaxial pre-strain loading respectively, and then carry out the forming limit strain test to obtain the loading path parameters (stress ratio α1) and pre-strain parameters of the two-stage loading path (stress ratio α2), the ultimate major strain ε1, and the ultimate minor strain ε2;

[0045] Conduct anisotropic tensile property tests to obtain the strain hardening index n, the strain strengthening coefficient K, and the anisotropy parameter R;

[0046] Conduct fracture failure tests under pre-strain loading. The specimen types include but are not limited to tensile-shear specimens, R5-notch specimens, R15-notch specimens, center-hole specimens, and Erichsen cupping specimens. Apply the DIC method to obtain the cumulative instability strain and cumulative fracture strain corresponding to specimens with different stress triaxialities.

[0047] Step 2: Combine the improved M-K theory model and the Lou-Huh failure criterion model to calculate the forming limit strain under two-stage loading conditions, and use the forming limit test data in Step 1 for model parameter optimization analysis. The improved M-K theory model considers the stress in the thickness direction, and uses the Newton-Raphson iteration method for programming calculation. The material hardening model parameters K, n, the initial thickness non-uniformity f0, and the ultimate damage determination condition are continuously corrected through an optimization method to reduce the error between the model calculation result and the test result. The ultimate damage determination condition is

[0048] Table 1 Partial model parameters of DP780 material

[0049] Material K n <![CDATA[f0]]> R C1 C2 C3 DP780 1247 0.1393 0.99 0.90 13.91 1.86 1.41

[0050] Step 3: Based on the optimized physical model in Step 2, use the programming calculation method to calculate the ultimate strain under different pre-strain stage stress ratios α1 (range 0 - 1), pre-strain parameters E0 (range 0 - 0.1), and two-stage loading stage stress ratios α2 (range 0 - 1), construct a neural network model training dataset, and generate 1320 data samples.

[0051] Step 4: Construct a backpropagation neural network model with input parameters α1, E0, and α2, an output layer of ultimate principal strain ε1 and ultimate secondary strain ε2, and 10 neural networks in the hidden layer. Use the data obtained in Step 3 for training and testing, with 70% for model training and 30% for verification and testing. As Figures 2 to 5 , the training accuracy result R of the model is ≥ 0.99.

[0052] Step 5: Use the neural network model that passed the test in Step 4 to predict the non-linear forming limit of DP780 sheet metal. As Figure 6 , the correlation coefficient between the prediction result and the test result is 0.91748. As Figure 7 , form the prediction result graph of the forming limit diagram under the non-linear path of DP780 material.

Claims

1. A method for predicting the forming limit of a material, characterized in that The steps include: (1) Conduct non-linear forming limit tests using proportional loading and two-stage proportional loading methods, conduct anisotropic tensile property tests, conduct DIC fracture failure tests under different stress triaxialities with pre-strain loading, and collect and calculate test data; (2) Use the improved M-K theoretical model or a combined failure criterion model to calculate the forming limit strain under two-stage loading conditions, and optimize the model parameters using the test data in step (1); (3) By inputting different pre-strain stage loading path parameters Pre-strain parameter E0 and two-stage loading path parameters Calculate the ultimate strain and construct a neural network model training dataset; (4) Construct a neural network model and conduct training and testing; (5) Apply the neural network model that has passed the test to predict the non-linear forming limit of the sheet metal.

2. The material forming limit prediction method according to claim 1, characterized in that: In the step (1), the test data includes the loading path parameters in the pre-strain stage pre-strain parameter E0, two-stage loading path parameters ultimate principal strain ε1, ultimate secondary strain ε2, strain hardening index n, strain strengthening coefficient K, anisotropy parameter R, and the corresponding cumulative instability strain and cumulative fracture strain under different stress triaxialities; Loading path parameter Using stress ratio α 、 Strain ratio β or Indicated; the pre-strain parameter E0 is expressed by the following formula (1), (2) or (3), formula (1) is applicable to the isotropic model, formula (2) is applicable to the anisotropic model, and formula (3) is the polar coordinate model; the loading path parameter And the pre-strain parameter E0 is not limited to the above representation form 3. A method for predicting the forming limit of a material according to claim 1, characterized in that: In the step (2), the improved M-K theoretical model takes into account the stress in the thickness direction, and is programmed and calculated by the Newton-Raphson iteration method. The material hardening model parameters K, n, the initial thickness non-uniformity f0 and the ultimate damage judgment condition are continuously corrected by an optimization method to reduce the error between the model calculation result and the test result; the ultimate damage judgment condition selects formula (4) or formula (5); in formula (4), dε1 b is the main strain increment in the groove in the M-K model groove theory, and dε1 a is the main strain increment outside the groove. The initial value of the ultimate damage judgment parameter D is 10; formula (5) is the damage judgment condition combined with the fracture failure criterion model. The expression of ε f can be selected but is not limited to the MMC criterion model and the Lou-Huh criterion model. Their expressions are formula (6) and formula (7) respectively. In the formulas, A, C1, C2 and C3 are material model parameters, μ is the Lode parameter, and η is the stress triaxiality 4. The material forming limit prediction method according to claim 1, characterized in that: In step (3), the process of constructing the training data set of the neural network model uses a programming calculation method, and the data set has no less than 1000 samples.

5. A method for predicting the forming limit of a material according to claim 1, characterized in that: In step (4), the neural network model is not limited to the backpropagation neural network model, and the number of neurons in the hidden layer is greater than or equal to 7.

6. A method for predicting the forming limit of a material according to claim 1, characterized in that: The two-stage linear loading test method and calculation method can be extended and applied to multi-stage linear loading and non-linear loading processes.

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