Construction method of high-strength steel stress-strain constitutive model
Patent Information
- Application Number
- CN202411788854.0
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Filing Date
- 2024-12-06
- Publication Date
- 2025-04-11
AI Technical Summary
然而对于先进高强钢DP钢、MS钢等产品，n值在塑性阶段变化较大，swift和Ludwik本构方程表征精度不高
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Figure CN119808361A_ABST
Abstract
Description
Technical Field
[0001] The invention belongs to the field of metal material mechanical property detection and characterization, in particular to a method for constructing a stress-strain constitutive model of high-strength steel. Background Art
[0002] The stress-strain curve of automobile sheet material represents the hardening of the material as the yield stress increases with strain during the plastic deformation stage. To characterize the relationship between stress and strain, researchers have created a variety of constitutive equations, including the Swift equation: T =K(ε P +ε0) n , Ludwik equation: σ T =σ0+K(ε P ) n . The above equation assumes that stress and strain are in a power exponential relationship, and the power exponent n value remains consistent throughout the plastic deformation stage. For automotive sheet products such as ultra-low carbon IF steel, the n value changes very little during the plastic deformation stage, and this equation can well characterize the stress-strain relationship of ultra-low carbon IF steel products. However, for advanced high-strength steel products such as DP steel and MS steel, the n value changes greatly during the plastic stage, and the Swift and Ludwik constitutive equations are not accurate enough. Summary of the invention
[0003] The technical problem to be solved by the present invention is to provide a method for constructing a stress-strain constitutive model of high-strength steel.
[0004] In order to solve the above technical problems, the technical solution adopted by the present invention includes the following steps:
[0005] (1) Conduct tensile tests on high-strength steel to obtain engineering strain and engineering stress data;
[0006] (2) Use formula (I) to convert engineering stress into true stress, and use formula (II) to convert engineering strain into true plastic strain;
[0007] σ T =σ(1+e) (I),
[0008] ε P =ln(1+e)-σ T / 21000-0.002 (Ⅱ);
[0009] Where: T is the true stress, unit: MPa; ε P is the true plastic strain, unit 1, unit mm; σ is the engineering stress, unit MPa, e is the engineering strain, unit 1;
[0010] (3) The true stress and true plastic strain data are fitted using a piecewise function, with the segmentation point being εc ;
[0011] The true plastic strain ε P <ε c The data of: The constitutive equation described in formula (III) is used for fitting.
[0012] σ T =K(ε P +ε0) n (III),
[0013] Where K is the coefficient to be fitted, unit MPa; ε0, n are the coefficients to be fitted, unit 1; the values of K, ε0, and n are obtained by fitting using the least squares method;
[0014] The true plastic strain ε P ≥ε c The data of: The constitutive equation described in formula (III) is used for fitting.
[0015]
[0016] Where K1 is the coefficient to be fitted, unit MPa, a, b are the coefficients to be fitted, unit 1; the values of K1, a and b are obtained by least squares fitting;
[0017] (4) Through the above steps, the stress-strain constitutive model of the high-strength steel is obtained;
[0018] True plastic strain ε P <ε c When , the constitutive model is: T =K(ε P +ε0) n ;
[0019] True plastic strain ε P ≥ε c When , the constitutive model is: T =K1ε P (a-bln(εP)) .
[0020] Furthermore, in step (1), the data after the maximum engineering stress is removed.
[0021] Furthermore, in step (2), data with true plastic strain less than 0 are removed.
[0022] Furthermore, in step (3), ε c The value range is 0.005~0.025.
[0023] The beneficial effect of adopting the above technical solution is that: by studying the strain hardening law of high-strength steel, it is found that the strain hardening exponent n of high-strength steel is not constant during the plastic deformation stage, and the logarithmic stress and logarithmic strain are not a simple linear relationship, but a quadratic function relationship. The present invention innovatively constructs a new constitutive model based on the strain hardening characteristics of high-strength steel, and accurately characterizes the constitutive relationship of the stress-strain curve by adopting a piecewise fitting method, which has the characteristics of high characterization accuracy, and the constitutive model fitting goodness is greater than 0.9999. The constitutive model obtained by the present invention can be directly used for forming simulation, strength simulation analysis, etc., and is particularly suitable for advanced high-strength steel and advanced high-strength steel for automotive plates, such as DP steel and MS steel, to provide technical data for the development of new automobile models. BRIEF DESCRIPTION OF THE DRAWINGS
[0024] The present invention will be further described in detail below in conjunction with the accompanying drawings and specific embodiments.
[0025] Figure 1 It is a schematic diagram of the engineering stress-strain curve of HC550 / 980DP described in Example 1;
[0026] Figure 2 It is a schematic diagram of the true stress and true plastic strain curve of HC550 / 980DP described in Example 1;
[0027] Figure 3 is a schematic diagram of the constitutive model curve of HC550 / 980DP described in Example 1;
[0028] Figure 4 It is a schematic diagram of the engineering stress-strain curve of HC420 / 780DP described in Example 2;
[0029] Figure 5 It is a schematic diagram of the true stress and true plastic strain curve of HC420 / 780DP described in Example 2;
[0030] Figure 6 is a schematic diagram of the constitutive model curve of HC420 / 780DP described in Example 2;
[0031] Figure 7 is a schematic diagram of the engineering stress-strain curve of MS1180 described in Example 3;
[0032] Figure 8 is a schematic diagram of the true stress and true plastic strain curve of MS1180 described in Example 3;
[0033] Fig. 9 This is a schematic diagram of the MS1180 constitutive model curve described in Example 3. DETAILED DESCRIPTION
[0034] The construction method of this high-strength steel stress-strain constitutive model adopts the following steps:
[0035] (1) High-strength steel is processed into mechanical properties tensile specimens, and the specimen sizes are P5, P6 and P7 specimens in GB / T 228.1 "Metallic materials tensile test Part 1: Room temperature test method". The tensile test is carried out using a tensile testing machine, and the data of engineering strain e and engineering stress σ are recorded. The data after removing the maximum engineering stress can also be further constructed to construct the engineering stress-strain curve.
[0036] (2) Use formula (I) to convert engineering stress into true stress σ T , using formula (Ⅱ) to convert engineering strain into true plastic strain ε P , and remove the true plastic strain ε P Data less than 0 can also be further constructed into true stress and true plastic strain curves;
[0037] σ T =σ(1+e) (I),
[0038] ε P =ln(1+e)-σ T / 21000-0.002 (Ⅱ);
[0039] Where: T is the true stress, unit: MPa; ε P is the true plastic strain, unit 1; σ is the engineering stress, unit MPa, e is the engineering strain, unit 1;
[0040] (3) The true stress and true plastic strain data obtained in step (2) are fitted using a piecewise function, with the segmentation point being ε c , ε c The value range is 0.005~0.025;
[0041] The true plastic strain ε P <ε c Data: Swift constitutive equation is used for fitting. The fitting constitutive equation is as described in formula (III).
[0042] σ T =K(ε P +ε0) n (III),
[0043] Where K is the coefficient to be fitted, unit MPa; ε0, n are the coefficients to be fitted, unit 1; the values of K, ε0, and n are obtained by fitting using the least squares method;
[0044] The true plastic strain ε P ≥ε c The data of: The constitutive equation described in formula (III) is used for fitting.
[0045] σ T =K1ε P (a-bln(εP)) (IV),
[0046] Where K1 is the coefficient to be fitted, unit MPa, a, b are the coefficients to be fitted, unit 1; the values of K1, a and b are obtained by least squares fitting;
[0047] (4) Through the above steps, the stress-strain constitutive model of the high-strength steel is obtained;
[0048] True plastic strain ε P <ε c When , the constitutive model is as described in formula (A):
[0049] σ T =K(ε P +ε0) n (A);
[0050] True plastic strain ε P ≥ε c When , the constitutive model is as described in formula (B):
[0051] σ T =K1ε P (a-bln(εP)) (B).
[0052] (5) The ε c A number of scattered values are selected within the value range and substituted into the stress-strain constitutive model of high-strength steel, the goodness of fit is calculated, and the constitutive model corresponding to the highest goodness of fit is selected as the stress-strain constitutive model of the high-strength steel.
[0053] Example 1: The method for constructing the stress-strain constitutive model of high-strength steel is described by taking advanced high-strength steel HC550 / 980DP as an example.
[0054] (1) The advanced high-strength steel HC550 / 90DP for automobile plates was processed into mechanical properties tensile specimens. The specimen size adopted the P5 specimen in GB / T 228.1 "Tensile test of metallic materials Part 1: Room temperature test method". The tensile test was carried out using a tensile testing machine, and the engineering strain and engineering stress data were recorded. The data after the maximum engineering stress was removed; thus, the engineering stress-strain curve of HC550 / 980DP was obtained, as shown in Figure 1 shown.
[0055] (2) Using the formula σ T =σ(1+e) Convert engineering stress into real stress, using the formula ε P =ln(1+e)-σ T / 21000-0.002Convert engineering strain into true plastic strain; and remove true plastic strain ε P Data less than 0. Thus, the true stress and true plastic strain curve of HC550 / 980DP is obtained, such as Figure 2 shown.
[0056] (3) The true stress-strain curve obtained in step 2 is fitted in sections, with the section points being ε c , ε c The value range is 0.005~0.025; in this example, ε c The values are taken as 0.005, 0.01, and 0.025 respectively for implementation.
[0057] (3.1)ε c =0.005:
[0058] For the true plastic strain ε P The data in the range of <0.005 were fitted by the least square method, and the constitutive equation was σ T =K(ε P +ε0) n Through the least squares fitting method, we get K = 1789.96MPa, ε0 = 0.00143, n = 0.153. For the true plastic strain ε P For data ≥0.005, the constitutive equation is used Fitting was performed and K1 = 1280.46 MPa, a = 0.0224, b = 0.0117 were obtained by least squares fitting. The goodness of fit was calculated to be 0.99993.
[0059] (3.2)ε c =0.01:
[0060] For the true plastic strain ε P The data in the range of <0.01 were fitted by the least square method, and the constitutive equation was σ T =K(ε P +ε0) n Through the least squares fitting, we get K = 1756.78 MPa, ε0 = 0.00135, and n = 0.149. For the true plastic strain ε P For data ≥0.01, the constitutive equation is used Fitting was performed and K1 = 1251.87 MPa, a = 0.0087, b = 0.0137 were obtained by least squares fitting. The goodness of fit was calculated to be 0.99999.
[0061] (3)ε c =0.025:
[0062] For the true plastic strain εP The data in the range of <0.025 are fitted by the least square method, and the constitutive equation is σ T =K(ε P +ε0) n Through the least squares fitting, we get K = 1675.67 MPa, ε0 = 0.00108, n = 0.138. For the true plastic strain ε P For data ≥0.025, the constitutive equation is used Fitting was performed and K1 = 1283.70 MPa, a = 0.0252, b = 0.0110 were obtained by least squares fitting. The goodness of fit was calculated to be 0.99988.
[0063] (4) Through the above steps, the stress-strain constitutive model of high-strength steel for automobile plates was obtained:
[0064] (4.1)ε c =0.005:
[0065]
[0066] The goodness of fit of this equation is 0.99993, and the degree of fit is very high.
[0067] (4.2)ε c =0.01:
[0068]
[0069] The goodness of fit of this equation is 0.99999, and the degree of fit is very high.
[0070] (4.3)ε c =0.025:
[0071]
[0072] The goodness of fit of this equation is 0.99988, and the degree of fit is very high.
[0073] (5) From the goodness of fit results, ε c In the range of 0.005 to 0.025 (0.005, 0.01, 0.025), good fitting results can be obtained. c = 0.01. The true stress true plastic strain curve obtained in step (2) and ε c = 0.01 constitutive model curve drawing chart see Figure 3 .
[0074] Example 2: The method for constructing the stress-strain constitutive model of high-strength steel is described by taking advanced high-strength steel HC420 / 780DP as an example.
[0075] (1) The advanced high-strength steel HC420 / 780DP for automobile plates was processed into mechanical properties tensile specimens. The specimen size adopted the P5 specimen in GB / T 228.1 "Tensile test of metallic materials Part 1: Room temperature test method". The tensile test was carried out using a tensile testing machine, and the engineering strain and engineering stress data were recorded. The data after the maximum engineering stress was removed. Thus, the engineering stress-strain curve of HC420 / 780DP was obtained, as shown in Figure 4 shown.
[0076] (2) Using the formula σ T =σ(1+e) to convert engineering stress into real stress, using the formula ε P =ln(1+e)-σ T / 21000-0.002 Convert engineering strain to true plastic strain. And remove the true plastic strain ε P Data less than 0. Thus, the true stress and true plastic strain curve of HC420 / 780DP is obtained, such as Figure 5 shown.
[0077] (3) The true stress-strain curve obtained in step (2) is fitted in segments, with the segmentation points being ε c , ε c The value range is 0.005~0.025. c The values are taken as 0.005, 0.02, and 0.025 respectively for implementation.
[0078] (3.1)ε c =0.005:
[0079] For the true plastic strain ε P The data in the range of <0.005 were fitted by the least square method, and the constitutive equation was σ T =K(ε P +ε0) n The values of K, ε0 and n obtained by least squares fitting are 1568.24MPa, 0.00139 and 0.190 respectively. For the true plastic strain ε P For data ≥0.005, the constitutive equation is used The fitting was performed and the parameters K1, a, and b were obtained by least squares fitting, which were 1180.68 MPa, 0.0374, and 0.0182, respectively. The goodness of fit was calculated to be 0.99966.
[0080] (3.2)ε c =0.02:
[0081] For the true plastic strain ε P The data in the range of <0.01 were fitted by the least square method, and the constitutive equation was σT =K(ε P +ε0) n The values of K, ε0 and n obtained by least squares fitting are 1769.14MPa, 0.00197 and 0.218 respectively. For the true plastic strain ε P For data ≥0.01, the constitutive equation is used The fitting was performed and the parameters K1, a, and b were obtained by least square fitting, which were 1118.74 MPa, 0.0000, and 0.0245, respectively. The goodness of fit was calculated to be 0.99994.
[0082] (3.3)ε c =0.025:
[0083] For the true plastic strain ε P The data in the range of <0.025 are fitted by the least square method, and the constitutive equation is σ T =K(ε P +ε0) n The values of K, ε0 and n obtained by least squares fitting are 1747.44MPa, 0.00189 and 0.215 respectively. For the true plastic strain ε P For data ≥0.025, the constitutive equation is used The fitting was performed and the parameters K1, a, and b were obtained by least squares fitting, which were 1121.00 MPa, 0.0015, and 0.0242, respectively. The goodness of fit was calculated to be 0.99930.
[0084] (4) Through the above steps, the stress-strain constitutive model of high-strength steel for automobile plates was obtained:
[0085] (4.1)ε c =0.005:
[0086]
[0087] The goodness of fit of this equation is 0.99993, and the degree of fit is very high.
[0088] (4.2)ε c =0.02:
[0089]
[0090] The goodness of fit of this equation is 0.99999, and the degree of fit is very high.
[0091] (4.3)ε c =0.025:
[0092]
[0093] The goodness of fit of this equation is 0.99988, and the degree of fit is very high.
[0094] 4) From the goodness of fit results, ε c In the range of 0.005 to 0.025 (0.005, 0.02, 0.025), good fitting results can be obtained. c = 0.02. The true stress true plastic strain curve obtained in step (2) and ε c = 0.02 constitutive model curve plot chart, see Figure 6 .
[0095] Example 3: The method for constructing the stress-strain constitutive model of high-strength steel is described by taking advanced high-strength steel MS1180 as an example.
[0096] (1) Advanced high-strength steel MS1180 for automobile plates was processed into mechanical properties tensile specimens. The specimen size adopted the P7 specimen in GB / T228.1 "Metallic Materials Tensile Test Part 1: Room Temperature Test Method". The tensile test was carried out using a tensile testing machine, and the engineering strain and engineering stress data were recorded, and the data after the maximum engineering stress was removed. The engineering stress-strain curve of MS1180 was obtained. Figure 7 shown.
[0097] (2) Using the formula σ T =σ(1+e) Convert engineering stress into real stress, using the formula ε P =ln(1+e)-σ T / 21000-0.002 Convert engineering strain to true plastic strain. And remove the true plastic strain ε P The data is less than 0. Thus, the true stress and true plastic strain curve of MS1180 is obtained. Figure 8 shown.
[0098] (3) The true stress-strain curve obtained in step (2) is fitted in segments, with the segmentation points being ε c , ε c The value range is 0.005~0.025. c The values are taken as 0.005, 0.01 and 0.02 respectively for implementation.
[0099] (3.1)ε c =0.005:
[0100] For the true plastic strain ε P The data in the range of <0.005 were fitted by the least square method, and the constitutive equation was σ T =K(ε P +ε0) nThe values of K, ε0 and n obtained by least squares fitting are 1670.80MPa, 0.00123 and 0.064 respectively. For the true plastic strain ε P For data ≥0.005, the constitutive equation σ T =K1ε P (a-bln(εP)) The fitting was performed and the parameters K1, a, and b were obtained by least squares fitting, which were 1378.94 MPa, 0.0000, and 0.0048, respectively. The goodness of fit was calculated to be 0.99990.
[0101] (3.2)ε c =0.01:
[0102] For the true plastic strain ε P The data in the range of <0.01 were fitted by the least square method, and the constitutive equation was σ T =K(ε P +ε0) n The values of K, ε0 and n obtained by least squares fitting are 1625.30MPa, 0.00100 and 0.059 respectively. For the true plastic strain ε P ≥0.01, using the constitutive equation σ T =K1ε P (a-bln(εP)) The fitting was performed and the parameters K1, a, and b were obtained by least squares fitting, which were 1376.55 MPa, 0.0000, and 0.0047, respectively. The goodness of fit was calculated to be 0.99987.
[0103] (3.3)ε c =0.02:
[0104] For the true plastic strain ε P The data in the range of <0.02 were fitted by the least square method, and the constitutive equation was σ T =K(ε P +ε0) n The values of K, ε0 and n obtained by least squares fitting are 1564.88MPa, 0.00064 and 0.051 respectively. For the true plastic strain ε P For data ≥0.02, the constitutive equation σ T =K1ε P (a-bln(εP)) The fitting was performed and the parameters K1, a, and b were obtained by least squares fitting, which were 1371.52 MPa, 0.0000, and 0.0044, respectively. The goodness of fit was calculated to be 0.99864.
[0105] (4) Through the above steps, the stress-strain constitutive model of high-strength steel for automobile plates was obtained:
[0106] (4.1)ε c =0.005:
[0107]
[0108] The goodness of fit of this equation is 0.99990, which means the degree of fit is very high.
[0109] (4.2)ε c =0.01:
[0110]
[0111] The goodness of fit of this equation is 0.99987, and the degree of fit is very high.
[0112] (4.3)ε c =0.02:
[0113]
[0114] The goodness of fit of this equation is 0.99864, which means the degree of fit is very high.
[0115] 4) From the goodness of fit results, ε c In the range of 0.005-0.025 (0.005, 0.01, 0.02), good fitting results can be obtained. c = 0.005 and 0.01. The true stress true plastic strain curve obtained in step (2) and ε c = 0.005 constitutive model curve plot chart, see Fig. 9 .
Claims
1. A method for constructing a stress-strain constitutive model of high-strength steel, characterized in that: The steps include: (1) Conduct tensile tests on high-strength steel to obtain engineering strain and engineering stress data; (2) Use formula (I) to convert engineering stress into true stress, and use formula (II) to convert engineering strain into true plastic strain; s T =σ(1+e) (Ⅰ), e P =ln(1+e)-σ T / 21000-0.002 (Ⅱ); Where: T is the true stress, unit: MPa; ε P is the true plastic strain, unit 1, unit mm; σ is the engineering stress, unit MPa, e is the engineering strain, unit 1; (3) The true stress and true plastic strain data are fitted using a piecewise function, with the segmentation point being ε c ; The true plastic strain ε P <ε c The data of: The constitutive equation described in formula (III) is used for fitting. s T =K(e P +ε0) n (III), Where K is the coefficient to be fitted, unit MPa; ε0, n are the coefficients to be fitted, unit 1; the values of K, ε0, and n are obtained by fitting using the least squares method; The true plastic strain ε P ≥ε c The data of: The constitutive equation described in formula (III) is used for fitting. Where K1 is the coefficient to be fitted, unit MPa, a, b are the coefficients to be fitted, unit 1; the values of K1, a and b are obtained by least squares fitting; (4) Through the above steps, the stress-strain constitutive model of the high-strength steel is obtained; True plastic strain ε P <ε c When , the constitutive model is: T =K(ε P +ε0) n ; True plastic strain ε P ≥ε c When , the constitutive model is:
2. The method for constructing a stress-strain constitutive model of high-strength steel according to claim 1, characterized in that: The step (1) is to remove the data after the maximum engineering stress.
3. The method for constructing a stress-strain constitutive model of high-strength steel according to claim 1, characterized in that: The step (2) removes data whose true plastic strain is less than 0.
4. A method for constructing a stress-strain constitutive model of high-strength steel according to claim 1, 2 or 3, characterized in that: In step (3), ε c The value range is 0.005~0.025.