A method for fitting a hardening curve of a metallic material

Abstract

The application discloses a metal material hardening curve fitting method, which comprises the following steps: S1, performing a unidirectional tensile test on the material to obtain a force-displacement curve and an engineering stress-strain curve of the test; S2, calculating a true stress-plastic strain curve of the material based on data points before a peak point of the engineering stress-strain curve and taking the true stress-plastic strain curve as a first part of the hardening curve; S3, fitting an epitaxial hardening curve to obtain a second part of the hardening curve; S4, combining the first part and the second part; S5, establishing a finite element model and performing simulation calculation to obtain a simulated force-displacement curve; S6, comparing the simulated force-displacement curve with the force-displacement curve of the test, if the error between the two is within a set threshold, then the hardening curve of S4 is taken as the hardening curve of the material; if the error between the two is not within the set threshold, then returning to S3 to optimize the parameter value until the error is within the set threshold. While improving the fitting precision, the convenience of fitting is also improved.

Description

Technical Field

[0001] This invention relates to the field of finite element simulation analysis technology, specifically to a method for fitting hardening curves of metallic materials. Background Technology

[0002] When simulating large deformations of metal components, such as in collision analysis and forming analysis, the hardening curve of the material under large strain conditions is required. The stress-strain curve of a material is generally obtained through uniaxial tensile testing: first, the force-displacement curve of the gauge length of the specimen is obtained through uniaxial tensile testing; then, the engineering stress-strain data is calculated based on the force-displacement data and the specimen's geometry; finally, the true stress, true strain, and plastic strain are obtained by converting the engineering stress-strain data. This method relies on the premise that the stress and strain of the specimen are uniformly distributed along the gauge length during the tensile process. However, for ductile metals, necking occurs when stretched to a relatively large strain. After necking, the stress and strain of the specimen along the gauge length are not uniformly distributed. Therefore, the stress-strain curve of the material after necking cannot be directly obtained through testing, making it difficult to obtain the hardening curve of the metal material under large strain conditions.

[0003] CN111339703A discloses a virtual prediction method for the hardening behavior of materials under large strain conditions, and provides a method for obtaining hardening curves under large strain conditions. This method uses a commonly used hardening curve formula to fit the stress-strain curve of an experiment, and artificially adds data points during the fitting process to adjust the fitting results. Then, it adjusts the artificially added data points based on the comparison between finite element simulation results and uniaxial tensile test results, thereby optimizing the fitting results. However, this method uses the same formula to characterize the entire hardening curve during the fitting process, resulting in a relatively small adjustable range and thus limited fitting accuracy. Furthermore, different empirical formulas produce varying fitting effects, and the fitting formula can only be selected based on experience. Therefore, this method may require multiple trials to determine a suitable fitting formula, causing inconvenience in use. Therefore, it is necessary to develop new methods to improve fitting accuracy and ease of use. Summary of the Invention

[0004] The purpose of this invention is to provide a method for fitting the hardening curve of metallic materials. The true stress-plastic strain curve before necking, obtained by uniaxial tensile test, is used as the first part of the hardening curve, while the second part of the hardening curve is obtained by extrapolation using the Hartley and Srinivasan formula. This method improves both the fitting accuracy and the convenience of fitting.

[0005] The method for fitting the hardening curve of metallic materials according to the present invention includes the following steps:

[0006] S1, Perform a uniaxial tensile test on the material to obtain the force-displacement curve and the engineering stress-strain curve;

[0007] S2, based on data points before the peak point of the engineering stress-strain curve, calculates the true stress-plastic strain curve of the material and uses the true stress-plastic strain curve as the first part of the hardening curve;

[0008] S3. Fit and extrapolate the true stress-plastic strain curve to obtain the second part of the hardening curve. Generate m strain points between the strain ε1 at the end of the first part of the hardening curve and the preset strain value ε2 at the end of the second part of the hardening curve. Then, the i-th strain point is calculated using the Hartley and Srinivasan formula. Corresponding stress The calculated data points As the second part of the hardening curve, i = 1, 2, ..., m;

[0009] S4, combine the first part and the second part to obtain the hardening curve;

[0010] S5. Establish the finite element model of the tensile specimen used in the uniaxial tensile test in S1, and use the hardening curve obtained in S4 for simulation calculation to obtain the simulated force-displacement curve.

[0011] S6. Compare the simulated force-displacement curve with the experimental force-displacement curve. If the error between the two is within the set threshold, then use the hardening curve of S4 as the hardening curve of the material. If the error between the two is not within the set threshold, return to S3 and optimize the parameter values ​​in the Hartley and Srinivasan formula until the error between the simulated force-displacement curve and the experimental force-displacement curve is within the set threshold.

[0012] Furthermore, the Hartley and Srinivasan formula in S3 is as follows: In the formula:

[0013] ε0=(ε2(h1 / h2) 1 / (n-1) -ε1) / (1-(h1 / h2) 1 / (n-1) ),

[0014] σ0=σ1-(ε0+ε1)h1 / n,

[0015] k = (σ1 - σ0) / (ε0 + ε1) n ;

[0016] ε1 is the strain at the end point of the first part of the hardening curve, σ1 is the stress at the end point of the first part of the hardening curve, and h1 is the slope at the end point of the first part of the hardening curve; ε2 is the preset value of the strain at the end point of the second part of the hardening curve, 1≤ε2≤2; h2 is the preset value of the slope at the end point of the second part of the hardening curve, 0<h2<h1; n is a constant, 0<n<1.

[0017] Further, if the error between the simulated force-displacement curve and the tested force-displacement curve in S6 is not within the set threshold, h2 and n in the Hartley and Srinivasan formula are adjusted until the error between the simulated force-displacement curve and the tested force-displacement curve is within the set threshold.

[0018] Further, in S2, the true stress and true strain of the material are calculated according to a conversion formula, the true stress-plastic strain curve of the material is calculated through a plastic strain calculation formula, and the X-axis of the first point of the true stress-plastic strain curve is zeroized.

[0019] Further, the calculation formula for the true stress σ is: σ=σ nom (1+ε nom ), the calculation formula for the true strain ε is: ε=ln(1+ε nom ), the plastic strain ε p The calculation formula of is: ε p =ε-σ / E, where E is the elastic modulus.

[0020] Further, in S2, if the number of data points before the peak point of the engineering stress-strain curve is less than 25, the calculated true stress-plastic strain curve of the material is taken as the first part of the hardening curve; if the number of data points before the peak point of the engineering stress-strain curve is ≥25, the calculated true stress-plastic strain curve of the material is compressed to reduce the number of data points, and then taken as the first part of the hardening curve.

[0021] Further, the value range of m in S3 is 10 to 20.

[0022] Compared with the prior art, the present invention has the following beneficial effects.

[0023] 1. The method provided by this invention uses the stress-plastic strain curve before necking obtained by uniaxial tensile testing as the first part of the hardening curve. Compared with traditional fitting methods, it eliminates errors caused by fitting, ensuring that the first part of the hardening curve accurately describes the hardening behavior of the material before necking. The second part of the hardening curve is extended using a formula based on the first part of the curve. At this point, only the accuracy of the hardening curve after necking needs to be considered, reducing the overall fitting difficulty of the hardening curve and improving both fitting accuracy and convenience.

[0024] 2. This invention optimizes the fitting effect of the second part of the hardening curve by adjusting the values ​​of h2 or n. h2 is the slope of the second part of the hardening curve at its endpoint. The smaller h2 is, the smaller the slope of the hardening curve at its endpoint, and the "softer" the material appears. When the simulated force-displacement curve is higher than the experimental force-displacement curve, the value of h2 is reduced to optimize the result, and vice versa. n is a constant, ranging from 0 to 1, used to determine the shape of the extrapolation curve. The closer n is to 1, the closer the extrapolation curve is to a straight line. When n is close to 0, the transition at the junction of the two parts of the hardening curve is smoother. The value of n should not be too large. When adjusting h2 can no longer optimize the result, the value of n is adjusted to optimize the simulated force-displacement curve result, making the simulated force-displacement curve closer to the experimental force-displacement curve. Attached Figure Description

[0025] Figure 1 This is a schematic flowchart of the metal material hardening curve fitting method described in this invention;

[0026] Figure 2 This is a schematic diagram of the force-displacement curves of three uniaxial tensile tests on the material to be tested according to the present invention;

[0027] Figure 3 These are schematic diagrams of engineering stress-strain curves and actual stress-strain curves;

[0028] Figure 4 This is a schematic diagram of the actual stress-plastic strain curve obtained from the conversion;

[0029] Figure 5 This is a schematic diagram of the finite element model of a uniaxial tensile test.

[0030] Figure 6 These are the actual stress-plastic strain curves obtained from four different sets of fitting parameters;

[0031] Figure 7 A comparison graph showing the force-displacement curves obtained from simulation using different fitting parameters and the experimental force-displacement curves;

[0032] Figure 8A comparison of the simulated force-displacement curve and the experimental force-displacement curve for solidifying the epitaxial fitting parameters. Detailed Implementation

[0033] To make the objectives, technical solutions, and advantages of this invention clearer, the technical solutions of the embodiments of this invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of this invention, and not all embodiments. Based on the embodiments of this invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of this invention.

[0034] See Figure 1 The method for fitting the hardening curve of metallic materials, as shown, includes the following steps:

[0035] S1, Three repeated uniaxial tensile tests were performed on the material to obtain the force-displacement curves for the three tests. See [link / reference]. Figure 2 The force-displacement curves of Experiment 1, Experiment 2 and Experiment 3 are basically consistent, which verifies the consistency of the uniaxial tensile test and eliminates the possibility of deviation in the fitting results due to problems with the uniaxial tensile test device and the tensile specimen itself.

[0036] See Figure 3 The solid line in the figure represents the engineering stress-strain curve of the material during the first test.

[0037] S2, based on data points before the peak point of the engineering stress-strain curve, calculates the material's true stress-plastic strain curve and uses it as the first part of the hardening curve. Specifically: Extract data points before the peak point of the engineering stress-strain curve obtained in S1, calculate the material's true stress-plastic strain curve using the plastic strain calculation formula, and then normalize the X-axis of the first point of the true stress-plastic strain curve to zero.

[0038] The formula for calculating the actual stress σ is: σ = σ nom (1+ε nom );

[0039] The formula for calculating the actual strain ε is: ε=ln(1+ε nom );

[0040] Plastic strain ε p The formula for calculating ε is: p = ε - σ / E, where E is the elastic modulus. nom ε represents engineering stress. nom It indicates engineering strain.

[0041] See Figure 3 The dashed line in the figure shows the calculated true stress-true strain curve of the material during Experiment 1. The true stress-plastic strain curve can be found in [reference needed]. Figure 4 .

[0042] The initial stress-plastic strain curve contains 104 data points. The number of data points is ≥25. The calculated true stress-plastic strain curve of the material is compressed, and only 11 data points are retained after compression, which greatly reduces the number of data points. The calculation result is then used as the first part of the hardening curve.

[0043] The compression processing method is as follows: the initial stress-plastic strain curve is divided into 10 segments according to stress, and the stress difference between the start point and the end point of each segment is equal. That is, based on the stress value of the first data point and the stress value of the last data point of the initial stress-plastic strain curve and the number of segments, the stress difference between the start point and the end point of each segment is determined. Then, the data points of the two ends of each segment are retained, and the remaining data points are removed.

[0044] S3, based on the calculation results of S2, the strain at the end of the first part of the hardening curve is ε1 = 0.1225, the stress at the end of the first part of the hardening curve is σ1 = 649.4 MPa, the slope at the end of the first part of the hardening curve is h1 = 746.2 MPa, and the preset strain value at the end of the second part of the hardening curve is set to ε2 = 2. The parameters of the first set of fitting extrapolation are set to n = 0.4 and h2 = 600.

[0045] The calculation yielded:

[0046] ε0=(ε2(h1 / h2) 1 / (n-1) -ε1) / (1-(h1 / h2) 1 / (n-1) =4.16;

[0047] σ0=σ1-(ε0+ε1)h1 / n=-7342.3;

[0048] k = (σ1 - σ0) / (ε0 + ε1) n =4465.8.

[0049] Fifteen strain points are generated between the strain ε1 at the end of the first part of the hardening curve and the preset strain value ε2 at the end of the second part of the hardening curve. Then, the i-th strain point can be calculated using the Hartley and Srinivasan formula. Corresponding stress The calculated data points As the second part of the hardening curve, i = 1, 2, ..., 15.

[0050] The Hartley and Srinivasan formula is:

[0051] S4, combine the first part and the second part to obtain the hardening curve;

[0052] S5, see S5. Figure 5 A finite element model of the tensile specimen used in the uniaxial tensile test in S1 was established, and the hardening curve obtained in S4 was used for simulation calculation to obtain the simulated force-displacement curve.

[0053] S6, see S6. Figure 7 By comparing the simulated force-displacement curves and the experimental force-displacement curves, the simulated force-displacement curves of the first group are higher than the experimental force-displacement curves after the peak point, indicating that the parameters set for the fitting extrapolation are too "rigid", so the value of h2 needs to be reduced.

[0054] Set h2 = 200 and repeat steps S3 to S6. The resulting hardening curve can be found in [reference needed]. Figure 6 The curves marked "Group 2" are simulated force-displacement curves obtained from the simulation calculations. Figure 7 The curves marked "Group 2" in the middle.

[0055] Based on the comparison results, continue to adjust the value of h2 or n. See Table 1 for specific adjustment values.

[0056] Table 1. Numerical values ​​of parameter adjustment process for fitted extrapolation.

[0057] Group 1 600 0.4 4.16 -7342.3 4465.8 Group 2 200 0.4 0.113 210.2574 783.24 Group 3 160 0.4 0.0337 358.0033 612.39 Group 4 160 0.2 0.1982 -547.145 1502.3

[0058] The hardening curves for groups three and four are shown in [reference 1]. Figure 6 The curves labeled "Group 3" and "Group 4" are the simulated force-displacement curves obtained from the simulation calculations. Figure 7 The curves are labeled "Group 3" and "Group 4".

[0059] Finally, when h2 = 160 and n = 0.2, see [reference needed]. Figure 8 The force-displacement curve obtained from the simulation is very close to the force-displacement curve of the experiment, so the result at this time is used as the final result output.

[0060] from Figure 8 The results show that the hardening curve obtained by fitting can achieve a high degree of agreement between the simulated force-displacement curve and the experimental force-displacement curve, indicating that the method provided by this invention can accurately fit the hardening behavior of materials under large strain conditions. Table 1 shows that a good fitting effect can be obtained by appropriately adjusting the values ​​of the fitting extrapolation parameters h2 or n during the fitting process, making the fitting process simple.

[0061] The above description is merely a preferred embodiment of this application and is not intended to limit this application. Any modifications, equivalent substitutions, and improvements made within the spirit and principles of this application should be included within the protection scope of this application.

Claims

1. A method for fitting hardening curves of metallic materials, characterized in that, Includes the following steps: S1, Perform a uniaxial tensile test on the material to obtain the force-displacement curve and the engineering stress-strain curve; S2, based on data points before the peak point of the engineering stress-strain curve, calculates the true stress-plastic strain curve of the material and uses the true stress-plastic strain curve as the first part of the hardening curve; The true stress and true strain of the material are calculated according to the conversion formula. The true stress-plastic strain curve of the material is calculated through the plastic strain calculation formula, and the first point of the true stress-plastic strain curve is zeroed out on the X-axis. The actual stress The calculation formula is: The actual strain The calculation formula is: Plastic strain The calculation formula is: E is the elastic modulus, where, Indicates engineering stress, Indicates engineering strain; S3, by fitting and extrapolating the true stress-plastic strain curve, the second part of the hardening curve is obtained, and the strain at the end of the first part of the hardening curve is... The strain preset value at the end of the second part of the hardening curve. m strain points are generated between them Then, the i-th strain point is calculated using the Hartley and Srinivasan formula. Corresponding stress The calculated data points ( , As the second part of the hardening curve, i = 1, 2, ..., m; the Hartley and Srinivasan formula is... In the formula: ， ， ； The strain is the end point of the first part of the hardening curve. Let h1 be the stress at the end of the first part of the hardening curve, and h1 be the slope at the end of the first part of the hardening curve. The strain preset value at the end of the second part of the hardening curve, 1≤ ≤2; h2 is the preset slope value of the endpoint of the second part of the hardening curve, 0<h2<h1; n is a constant, 0<n<1; S4, combine the first part and the second part to obtain the hardening curve; S5. Establish the finite element model of the tensile specimen used in the uniaxial tensile test in S1, and use the hardening curve obtained in S4 for simulation calculation to obtain the simulated force-displacement curve. S6. Compare the simulated force-displacement curve with the experimental force-displacement curve. If the error between the two is within the set threshold, then use the hardening curve of S4 as the hardening curve of the material. If the error between the two is not within the set threshold, return to S3 and optimize h2 and n in the Hartley and Srinivasan formula until the error between the simulated force-displacement curve and the experimental force-displacement curve is within the set threshold.

2. The method for fitting the hardening curve of metallic materials according to claim 1, characterized in that: In S2, if the number of data points before the peak point of the engineering stress-strain curve is less than 25, the calculated true stress-plastic strain curve of the material is used as the first part of the hardening curve; if the number of data points before the peak point of the engineering stress-strain curve is greater than or equal to 25, the calculated true stress-plastic strain curve of the material is compressed to reduce the number of data points and then used as the first part of the hardening curve.

3. The method for fitting hardening curves of metallic materials according to claim 1, characterized in that: In S3, the value of m ranges from 10 to 20.

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