A parameter calibration method based on Hill48 yield criterion of metal pipe

Abstract

The application provides a Hill48 yield criterion parameter calibration method based on metal pipes, wherein the axial yield stress sigma0 is obtained through an axial tensile test, the circumferential yield stress sigma is obtained through a circumferential tensile test, the axial yield stress sigma of a plane strain state is obtained through a plane strain state tensile test, the values of Hill48 yield criterion parameters F, G and H are obtained by substituting sigma0, sigma and sigma into an equation group, the value of Hill48 yield criterion parameter N is inversely calculated based on a GA genetic optimization algorithm through the axial tensile test and finite element simulation, and the accurate calibration of the Hill48 yield criterion parameters F, G, H and N is completed. 90 p 90 p The method can provide accurate parameters for metal pipe plastic forming process simulation, and further more accurately simulate plastic deformation behaviors of the metal pipe in a bending process, including wall thickness change rate, cross section distortion and springback and the like.​​​

Description

TECHNICAL FIELD

[0001] The application belongs to the technical field of mechanical property testing of metal materials, and particularly relates to a Hill48 yield criterion parameter calibration method based on metal pipes. BACKGROUND

[0002] Metal pipes are widely used in the fields of aerospace, shipbuilding, automobile, building, instruments and meters, etc. due to their advantages of light weight, high strength and toughness, high shock absorption capacity and excellent forming performance. The metal pipes are usually processed through a plastic forming process before use. Defects such as cracking, wrinkling and springback may occur in the plastic forming process, resulting in product scrap. Therefore, it is necessary to predict whether defects will occur in the plastic forming process of the metal pipes before processing, so as to optimize the plastic forming process parameters. The finite element simulation technology is widely used in simulating the plastic forming process of metal pipes due to its high precision and high efficiency. However, the simulation precision is highly dependent on the yield criterion. Therefore, accurate calibration of the yield criterion parameters is crucial to improving the simulation result precision.

[0003] Most of the production processes of metal pipes are rolling, extrusion and drawing, which causes the pipes to exhibit anisotropy in the plastic forming process. Therefore, the Hill48 yield criterion is generally selected to describe the plastic deformation behavior of the pipes. The traditional method for calibrating the Hill48 yield criterion parameters for metal pipes is to select the parameters of the same material plate to replace the parameters of the pipes, or to flatten the pipes and then use the calibration method for the plate to calibrate the parameters. However, plastic deformation may occur in the flattening process of the pipes, which affects the accuracy of the parameters. Therefore, the parameters obtained by the above two methods cannot reflect the true parameters of the pipes. Therefore, how to accurately and effectively calibrate the Hill48 yield criterion parameters for metal pipes is a technical problem to be solved at present. SUMMARY

[0004] In order to solve the above technical problems, the application provides a Hill48 yield criterion parameter calibration method based on metal pipes, which comprises the following steps:

[0005] (1) Perform an axial tensile test on the metal pipe to obtain a load-displacement curve and an engineering stress-engineering strain curve. Convert the engineering stress-engineering strain curve into a true stress-true strain curve by using formulas 1) and 2), and take the stress when the plastic deformation is 0.2% as the yield stress. Obtain the axial yield stress σ0 from the true stress-true strain curve;

[0006] σ = s (1 + e) 1)

[0007] ε = ln (1 + e) 2)

[0008] wherein σ is the true stress, ε is the true strain, s is the engineering stress, and e is the engineering strain.

[0009] (2) Perform the hoop tensile test of the metal pipe, and obtain the true stress-true strain curve and the hoop yield stress σ 90 ;

[0010] (3) Place a cylindrical mandrel inside the metal pipe, and perform the plane strain state tensile test, and obtain the true stress-true strain curve and the plane strain state axial yield stress σ p , in the process of the plane strain state tensile test, since the strain increment of the sample in the circumferential direction is zero, formula 3) can be obtained:

[0011] 2(F+H)σ q -2Hσ p =0 3)

[0012] Taking the axial yield stress σ0 obtained in step (1) as the reference equivalent stress, formulas 4), 5) and 6) can be obtained:

[0013]

[0014]

[0015]

[0016] Wherein, F, G, H, N are Hill48 yield criterion parameters, σ p is the plane strain state axial yield stress, σ q is the plane strain state hoop yield stress;

[0017] (4) Substitute the values of the axial yield stress σ0 obtained in step (1), the hoop yield stress σ 90 obtained in step (2), and the plane strain state axial yield stress σ p obtained in step (3) into formulas 3), 4), 5), 6), and obtain the values of Hill48 yield criterion parameters F, G, H and the plane strain state hoop yield stress σ q by solving the equation set;

[0018] (5) Input the values of Hill48 yield criterion parameters F, G, H and the value of the simulation parameter Z obtained in step (4) into the finite element simulation software to perform axial tensile simulation, the value range of Z is 0.1-3.0, select m groups of Z values between 0.1-3.0, wherein m is a natural number between 30-200, obtain m groups of simulation load displacement curves by simulation, compare the m groups of simulation load displacement curves with the load displacement curve obtained in step (1) respectively, and then based on the GA genetic optimization algorithm, back-calculate the value of the parameter N in the Hill48 yield criterion.

[0019] Further, the Hill48 yield criterion parameter calibration method based on metal pipes is applied to the simulation of wall thickness change rate, cross-section distortion or springback in the material plastic forming process.

[0020] Further, the metal pipe is steel, aluminum alloy or magnesium alloy.

[0021] The beneficial effects of the present application are:

[0022] (1) The present application proposes a Hill48 yield criterion parameter calibration method based on metal pipes. Compared with the traditional method, the sample keeps the original circular shape of the metal pipe during the performance test without plastic deformation affecting the test results, so more accurate parameters can be obtained. All tests are tensile tests, which are simple and feasible to operate.

[0023] (2) The Hill48 yield criterion parameter calibration method based on metal pipes proposed by the present application can accurately obtain the parameters F, G, H and N in the Hill48 yield criterion, providing accurate parameters for the simulation of the metal pipe plastic forming process, and further more accurately simulating the plastic deformation behavior of the metal pipe in the bending process, including wall thickness change rate, cross-section distortion or springback, etc., to improve the accuracy of the simulation results.

[0024] (3) The Hill48 yield criterion parameter calibration method based on metal pipes proposed by the present application is suitable for steel, aluminum alloy, magnesium alloy and other metal pipes.

[0025] (4) Compared with the experimental test results, the error of the simulation results of the present application is controlled within 2%, among which the simulation load displacement curve has high consistency with the experimental data, and the error range is 0.1-2%. BRIEF DESCRIPTION OF DRAWINGS

[0026] Figure 1 The axial tensile test engineering stress-engineering strain curve and true stress-true strain curve comparison chart in step (1) of Example 1;

[0027] Figure 2 The hoop tensile test engineering stress-engineering strain curve and true stress-true strain curve comparison chart in step (2) of Example 1;

[0028] Figure 3 The plane strain state tensile test engineering stress-engineering strain curve and true stress-true strain curve comparison chart in step (3) of Example 1;

[0029] Figure 4 The axial tensile finite element model in step (6) of Example 1;

[0030] Figure 5For axial stretching test in example 1 step (6) and comparison chart of simulated load displacement curve;

[0031] Figure 6 For Hill 48 yield criterion parameter calibration method flow chart based on metal pipe. DETAILED DESCRIPTION

[0032] The application is further described below in conjunction with specific embodiments and drawings.

[0033] Example 1

[0034] (1) Taking 304 stainless steel pipe as an example, the outer diameter of the pipe is 25 mm and the wall thickness is 1.5 mm. First, axial tensile test of the metal pipe is carried out to obtain load displacement curve and engineering stress-engineering strain curve. Engineering stress-engineering strain curve is converted into true stress-true strain curve by formula 1) and 2), Figure 1 For comparison chart of axial tensile test engineering stress-engineering strain curve and true stress-true strain curve, the stress when plastic deformation is 0.2% is taken as yield stress, and axial yield stress σ0=265.46 MPa is obtained from true stress-true strain curve.

[0035] σ=s(1+e) 1)

[0036] ε=ln(1+e) 2)

[0037] Wherein, σ is true stress, ε is true strain, s is engineering stress, and e is engineering strain;

[0038] (2) Metal pipe hoop tensile test is carried out, and true stress-true strain curve and circumferential yield stress σ 90 =284.59 MPa, Figure 2 For comparison chart of hoop tensile test engineering stress-engineering strain curve and true stress-true strain curve;

[0039] (3) A cylindrical mandrel is placed inside the metal pipe, and plane strain state tensile test is carried out. True stress-true strain curve and plane strain state axial yield stress σ p =273.23 MPa, Figure 3 For comparison chart of plane strain state tensile test engineering stress-engineering strain curve and true stress-true strain curve.

[0040] During the plane strain state tensile test, since the strain increment in the circumferential direction of the sample is zero, formula 3) can be obtained:

[0041] 3(F+H)σ q -2Hσ ρ =0 3)

[0042] The axial yield stress σ0obtained in step (1) is taken as a reference equivalent stress, and formulas 4), 5) and 6) are obtained:

[0043]

[0044]

[0045]

[0046] wherein F, G, H, N are Hill48yield criterion parameters, σ p is the axial yield stress in the plane strain state, σ q is the circumferential yield stress in the plane strain state;

[0047] (4) The axial yield stress σ0=265.46 MPa obtained in step (1), the circumferential yield stress σ 90 =284.59 MPa obtained in step (2), and the axial yield stress σ p =273.23 MPa obtained in step (3) are substituted into formulas 3), 4), 5), 6), and the Hill48yield criterion parameters F=0.6492, G=0.7791, H=0.2209 and the circumferential yield stress σ q =69.37 MPa in the plane strain state are obtained by solving the equation set;

[0048] (5) The values of the Hill48yield criterion parameters F, G, H obtained in step (4) and the value of the simulation parameter Z are input into the finite element simulation software for axial tensile simulation, the value range of Z is 0.1-3.0, 60 values are uniformly taken between 0.1-3.0, 60 groups of simulated load displacement curves are obtained through simulation, and the 60 groups of simulated load displacement curves are compared with the load displacement curve obtained in step (1), and then the value of the Hill48yield criterion parameter N is inversely solved based on the GA genetic optimization algorithm;

[0049] The Hill48yield criterion parameters F, G, H, N are calibrated through steps (4) and (5), as shown in Table 1;

[0050] Table 1 Hill48yield criterion parameters of 304 stainless steel pipe

[0051]

[0052] (6) The values of the Hill48yield criterion parameters F, G, H, N obtained in step (5) are input into the finite element simulation software for axial tensile simulation, and the finite element model is as shown in Figure 4The output analog load displacement curve is shown, and is plotted together with the load displacement curve obtained in step (1) for comparison. Figure 5 From the comparison, it can be seen from Figure 5 The simulation load displacement curve based on the Hill48 yield criterion parameters determined by the technical scheme of the application and the experimental load displacement curve are basically coincided, with an error of 0.1-0.5%, which proves the accuracy and effectiveness of the technical scheme of the application.

[0053] Example 2

[0054] (1) Taking AA6022 aluminum alloy pipe as an example, the pipe has an outer diameter of 25 mm and a wall thickness of 1.5 mm. First, axial tensile test of the metal pipe is performed to obtain a load displacement curve and an engineering stress-engineering strain curve. The engineering stress-engineering strain curve is converted into a true stress-true strain curve by formula 1) and 2), and the stress at a plastic deformation of 0.2% is taken as a yield stress. The axial yield stress σ0 is obtained from the true stress-true strain curve, and is 138.35 MPa.

[0055] σ = s (1 + e) 1)

[0056] ε = ln (1 + e) 2)

[0057] Wherein, σ is the true stress, ε is the true strain, s is the engineering stress, and e is the engineering strain;

[0058] (2) The metal pipe is subjected to circumferential tensile test, and the true stress-true strain curve and the circumferential yield stress σ 90 = 149.16 MPa are obtained according to the method of step (1).

[0059] (3) A cylindrical mandrel is placed inside the metal pipe, and the plane strain state tensile test is performed. The true stress-true strain curve and the plane strain state axial yield stress σ p = 143.57 MPa are obtained according to the method of step (1).

[0060] During the plane strain state tensile test, since the strain increment in the circumferential direction of the sample is zero, formula 3) can be obtained:

[0061] 2 (F + H) σ q - 2Hσ p = 0 3)

[0062] Taking the axial yield stress σ0 obtained in step (1) as a reference equivalent stress, formulas 4), 5) and 6) can be obtained:

[0063]

[0064]

[0065]

[0066] wherein F, G, H, N are Hill48 yield criterion parameters, σ p is the axial yield stress in plane strain state, σ q is the circumferential yield stress in plane strain state;

[0067] (4) the axial yield stress σ 0 = 138.35 MPa obtained in step (1), the circumferential yield stress σ 90 = 149.16 MPa obtained in step (2) and the axial yield stress σ p = 143.57 MPa obtained in step (3) are substituted into formulas 3), 4), 5), 6), and by solving the equation group, the Hill48 yield criterion parameters F = 0.6125, G = 0.7522, H = 0.2478 and the circumferential yield stress σ q = 41.35 MPa in plane strain state are obtained;

[0068] (5) the values of the Hill48 yield criterion parameters F, G, H obtained in step (4) and the value of the simulation parameter Z are input into the finite element simulation software for axial tensile simulation, the value range of Z is 0.1-3.0, 80 values are uniformly taken between 0.1-3.0, 80 groups of simulation load displacement curves are obtained through simulation, the 80 groups of simulation load displacement curves are compared with the load displacement curve obtained in step (1) respectively, and then the value of the Hill48 yield criterion parameter N is inversely solved based on the GA genetic optimization algorithm;

[0069] The Hill48 yield criterion parameters F, G, H, N are calibrated through steps (4) and (5), as shown in Table 2;

[0070] Table 2 Hill48 yield criterion parameters of AA6022 aluminum alloy pipe

[0071]

[0072] (6) the values of the Hill48 yield criterion parameters F, G, H, N obtained in step (5) are input into the finite element simulation software for axial tensile simulation, the simulation load displacement curve is output, and compared with the load displacement curve obtained in step (1), the simulation load displacement curve based on the Hill48 yield criterion parameters determined by the technical scheme of the present application and the experimental load displacement curve basically coincide, with an error of 0.2-0.8%, which proves the accuracy and effectiveness of the technical scheme of the present application.

[0073] Example 3

[0074] (1) Taking AZ31 magnesium alloy tube as an example, the outer diameter of the tube is 25 mm and the wall thickness is 1.5 mm. Firstly, axial tensile test of the metal tube is carried out to obtain load-displacement curve and engineering stress-engineering strain curve. The engineering stress-engineering strain curve is converted into true stress-true strain curve by formula 1) and 2), and the stress when the plastic deformation is 0.2% is taken as the yield stress. The axial yield stress σ0=130.45 MPa is obtained from the true stress-true strain curve.

[0075] σ=s(1+e) 1)

[0076] ε=ln(1+e) 2)

[0077] Wherein, σ is true stress, ε is true strain, s is engineering stress, and e is engineering strain;

[0078] (2) The circumferential tensile test of the metal tube is carried out, and the true stress-true strain curve and the circumferential yield stress σ 90 =142.39 MPa are obtained according to the method of step (1).

[0079] (3) A cylindrical mandrel is placed inside the metal tube, and the plane strain state tensile test is carried out. The true stress-true strain curve and the plane strain state axial yield stress σ p =133.76 MPa are obtained according to the method of step (1).

[0080] During the plane strain state tensile test, since the strain increment of the sample in the circumferential direction is zero, formula 3) can be obtained:

[0081] 2(F+H)σ q -2Hσ p =0 3)

[0082] The axial yield stress σ0obtained in step (1) is taken as the reference equivalent stress, and formulas 4), 5) and 6) can be obtained:

[0083]

[0084]

[0085]

[0086] Wherein, F, G, H and N are Hill48 yield criterion parameters, σ p is the plane strain state axial yield stress, and σ q is the plane strain state circumferential yield stress.

[0087] (4) The axial yield stress σ0=130.45 MPa obtained in step (1) and the circumferential yield stress σ 90= 142.39 MPa and the axial yield stress σ of the plane strain state obtained in step (3) p = 133.76 MPa Substituting into formulae 3), 4), 5), 6), the Hill48 yield criterion parameters F = 0.6368, G = 0.7975, H = 0.2025 and the circumferential yield stress σ of the plane strain state are obtained by solving the equation set q = 32.27 MPa

[0088] (5) The values of the Hill48 yield criterion parameters F, G, H and the value of the simulation parameter Z obtained in step (4) are input into the finite element simulation software for axial tensile simulation, the value range of Z is 0.1-3.0, 100 values are uniformly taken between 0.1-3.0, 100 groups of simulated load displacement curves are obtained by simulation, 100 groups of simulated load displacement curves are compared with the load displacement curve obtained in step (1) respectively, and then the value of the Hill48 yield criterion parameter N is inversely solved based on the GA genetic optimization algorithm;

[0089] The calibration of the Hill48 yield criterion parameters F, G, H and N is completed through step (4) and step (5), as shown in Table 3;

[0090] Table 3 Hill48 yield criterion parameters of AZ31 magnesium alloy pipe

[0091]

[0092] (6) The values of the Hill48 yield criterion parameters F, G, H and N obtained in step (5) are input into the finite element simulation software for axial tensile simulation, the simulated load displacement curve is output, and compared with the load displacement curve obtained in step (1), the simulated load displacement curve based on the Hill48 yield criterion parameters determined by the technical scheme of the present application and the experimental load displacement curve are basically coincided, the error is 0.15-0.58%, which proves the accuracy and effectiveness of the technical scheme of the present application.

Claims

1. A method for calibrating the Hill 48 yield criterion parameters based on metal pipes, characterized in that: It includes the following steps: (1) Conduct axial tensile tests on metal pipes to obtain load-displacement curves and engineering stress-engineering strain curves. Convert the engineering stress-engineering strain curves into true stress-true strain curves using formulas 1) and 2). Use the stress when the plastic deformation is 0.2% as the yield stress. Obtain the axial yield stress σ0 from the true stress-true strain curve. σ=s(1+e) 1) ε=ln(1+e) 2) Where σ is the true stress, ε is the true strain, s is the engineering stress, and e is the engineering strain; (2) Conduct a circumferential tensile test on the metal pipe and obtain the true stress-true strain curve and circumferential yield stress σ according to the method in step (1). 90 ; (3) Place a cylindrical mandrel inside the metal tube and conduct a plane strain tensile test. Obtain the true stress-true strain curve and the axial yield stress σ in the plane strain state according to the method in step (1). p During a plane strain tensile test, since the strain increment in the circumferential direction of the specimen is zero, we can obtain formula 3): 3） Using the axial yield stress σ0 obtained in step (1) as the reference equivalent stress, we can obtain formulas 4), 5), and 6). 4） 5） 6） Where F, G, H, and N are the Hill48 yield criterion parameters, σ p For the axial yield stress under plane strain state, σ q The circumferential yield stress is in the plane strain state. (4) The axial yield stress σ0 obtained in step (1) and the circumferential yield stress σ0 obtained in step (2) are... 90 and the axial yield stress σ in the plane strain state obtained in step (3) p Substituting the values ​​into formulas 3), 4), 5), and 6), the values ​​of the Hill48 yield criterion parameters F, G, and H, as well as the circumferential yield stress σ under plane strain state, are obtained by solving the system of equations. q The value; (5) Input the values ​​of Hill48 yield criterion parameters F, G, and H obtained in step (4) and the value of simulation parameter Z into the finite element simulation software for axial tension simulation. The value of Z is in the range of 0.1-3.

0. Select m sets of Z values ​​between 0.1 and 3.0, where m is a natural number between 30 and 200. A total of m sets of simulated load-displacement curves are obtained through simulation. Compare the m sets of simulated load-displacement curves with the load-displacement curves obtained in step (1), and then use the GA genetic optimization algorithm to reverse calculate the value of parameter N in the Hill48 yield criterion.

2. The method for calibrating the Hill 48 yield criterion parameters based on metal tubing according to claim 1, characterized in that: The metal pipe is made of steel, aluminum alloy, or magnesium alloy.

3. The method for calibrating the Hill 48 yield criterion parameters based on metal tubing according to claim 1, characterized in that: Application of Hill 48 Yield Criterion Parameter Calibration Method Based on Metal Tubes in Springback Simulation During Material Plastic Forming Processes.

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