CN115641928A - Hill48 yield criterion parameter calibration method based on metal pipe - Google Patents
Hill48 yield criterion parameter calibration method based on metal pipe Download PDFInfo
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Abstract
The invention provides a method for calibrating Hill48 yield criterion parameters based on a metal pipe, which comprises the steps of firstly obtaining axial yield stress sigma through an axial tensile test 0 Obtaining a circumferential yield stress sigma through a hoop tensile test 90 Obtaining the axial yield stress sigma of the plane strain state through a plane strain state tensile test p Then will σ 0 、σ 90 、σ p Substituting into the system of equations to obtain the value of Hill48 yield criterion parameter F, G, H,and then combining an axial tension test with finite element simulation, reversely calculating the value of the yield criterion parameter N of the Hill48 based on a GA genetic optimization algorithm, and finishing the accurate calibration of the yield criterion parameter F, G, H, N of the Hill 48. The method can provide accurate parameters for the simulation of the plastic forming process of the metal pipe, so as to more accurately simulate the plastic deformation behavior of the metal pipe in the bending process, including wall thickness change rate, section distortion, rebound and the like.
Description
Technical Field
The invention belongs to the technical field of mechanical property testing of metal materials, and particularly relates to a method for calibrating a Hill48 yield criterion parameter based on a metal pipe.
Background
The metal pipe has the advantages of light weight, high strength and toughness, high shock absorption capacity, excellent forming performance and the like, and is widely applied to the fields of aerospace, ships, automobiles, buildings, instruments and meters and the like.
Because the production process of most metal pipes is a rolling, extruding, drawing and other method, the pipes present anisotropy in the plastic forming process, the Hill48 yield criterion is generally selected to describe the plastic deformation behavior of the pipes, and the traditional method for calibrating Hill48 yield criterion parameters of the metal pipes is to select parameters of plates made of the same material to replace the parameters of the pipes or to calibrate the parameters by adopting a plate calibration method after the pipes are flattened, but the pipes are subjected to plastic deformation in the flattening process to influence the accuracy of the parameters, so the parameters obtained by the two methods cannot reflect the real parameters of the pipes, and therefore, how to accurately and effectively calibrate the Hill48 yield criterion parameters for the metal pipes is a technical problem to be solved urgently at present.
Disclosure of Invention
In order to solve the technical problem, the invention provides a method for calibrating Hill48 yield criterion parameters based on a metal pipe, which comprises the following steps:
(1) Performing an axial tensile test on the metal pipe to obtain a load displacement curve and an engineering stress-engineering strain curve, converting the engineering stress-engineering strain curve into a true stress-true strain curve by formulas 1) and 2), taking the stress when the plastic deformation is 0.2% as the yield stress, and obtaining the axial yield stress sigma from the true stress-true strain curve 0 ；
σ＝s(1+e) 1)
ε＝ln(1+e) 2)
Wherein, sigma is true stress, epsilon is true strain, s is engineering stress, and e is engineering strain;
(2) Performing a hoop tensile test on the metal pipe, and obtaining a true stress-true strain curve and a circumferential yield stress sigma according to the method in the step (1) 90 ；
(3) Placing a cylindrical mandrel in the metal pipe, performing a plane strain state tensile test, and obtaining a true stress-true strain curve and a plane strain state axial yield stress sigma according to the method in the step (1) p In the process of the plane strain state tensile test, as the strain increment of the sample in the circumferential direction is zero, the formula 3 can be obtained):
2(F+H)σ q -2Hσ p ＝0 3)
subjecting the axial yield stress sigma obtained in the step (1) to 0 As a reference equivalent stress, equations 4), 5), and 6) can be obtained:
wherein F, G, H, N is a parameter of Hill48 yield criterion, sigma p Axial yield stress in plane strain state, σ q Circumferential yield stress in a plane strain state;
(4) Subjecting the axial yield stress sigma obtained in the step (1) to 0 The circumferential yield stress sigma obtained in the step (2) 90 And the axial yield stress sigma of the plane strain state obtained in the step (3) p Substituting the values of (3), 4), 5), 6), obtaining the value of the Hill48 yield criterion parameter F, G, H and the circumferential yield stress sigma of the plane strain state by solving the equation system q A value of (d);
(5) Inputting the value of the yield criterion parameter F, G, H of the Hill48 obtained in the step (4) and the value of the simulation parameter Z into finite element simulation software for axial tensile simulation, wherein the value range of Z is 0.1-3.0, selecting m groups of Z values between 0.1-3.0, wherein m is a natural number between 30-200, obtaining m groups of simulation load displacement curves through simulation, comparing the m groups of simulation load displacement curves with the load displacement curves obtained in the step (1) respectively, and then reversely calculating the value of the parameter N in the yield criterion of the Hill48 based on a GA genetic optimization algorithm.
Further, the method is applied to the field of simulation of wall thickness change rate, section distortion or rebound in the plastic forming process of materials based on the Hill48 yield criterion parameter calibration method of the metal pipe.
Further, the metal pipe is steel, aluminum alloy or magnesium alloy.
The invention has the beneficial effects that:
(1) Compared with the traditional method, the method for calibrating the parameters of the Hill48 yield criterion based on the metal pipe has the advantages that the original arc shape of the metal pipe is kept in a test sample in the performance detection process, the detection result is not influenced by plastic deformation, more accurate parameters can be obtained, all tests are tensile tests, and the method is simple and feasible to operate.
(2) The method for calibrating the parameters of the Hill48 yield criterion based on the metal pipe can accurately obtain the parameters F, G, H and N in the Hill48 yield criterion, provides accurate parameters for the simulation of the plastic forming process of the metal pipe, further more accurately simulates the plastic deformation behavior of the metal pipe in the bending process, including the wall thickness change rate, the section distortion or the rebound and the like, and improves the accuracy of the simulation result.
(3) The method for calibrating the Hill48 yield criterion parameters based on the metal pipes is suitable for the metal pipes of steel, aluminum alloy, magnesium alloy and the like.
(4) Compared with the experimental test result, the error of the simulation result is controlled within 2%, wherein the fit degree of the simulation load displacement curve and the experimental data is higher, and the error range is 0.1-2%.
Drawings
FIG. 1 is a graph comparing an engineering stress-engineering strain curve and a true stress-true strain curve in an axial tensile test in step (1) of example 1;
FIG. 2 is a comparison graph of the hoop tensile test engineering stress-engineering strain curve and the true stress-true strain curve in step (2) of example 1;
FIG. 3 is a graph comparing the engineering stress-engineering strain curve and the true stress-true strain curve of the tensile test in the plane strain state in step (3) of example 1;
FIG. 4 is an axial tension finite element model in step (6) of example 1;
FIG. 5 is a graph comparing the axial tensile test and the simulated load displacement curve in step (6) of example 1;
FIG. 6 is a flow chart of a method for calibrating parameters based on the Hill48 yield criterion of metal pipes.
Detailed Description
The invention is further described with reference to the following specific embodiments and the accompanying drawings.
Example 1
(1) Taking a 304 stainless steel pipe as an example, the outer diameter of the pipe is 25mm, the wall thickness is 1.5mm, firstly, the axial tensile test of the metal pipe is carried out 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 through formulas 1) and 2), the graph of figure 1 is a comparison graph of the engineering stress-engineering strain curve and the true stress-true strain curve of the axial tensile test, the stress when the plastic deformation is 0.2 percent is taken as the yield stress, and the axial yield stress sigma is obtained from the true stress-true strain curve 0 ＝265.46MPa。
σ＝s(1+e) 1)
ε＝ln(1+e) 2)
Wherein σ is true stress, ε is true strain, s is engineering stress, and e is engineering strain;
(2) Performing a hoop tensile test on the metal pipe, and obtaining a true stress-true strain curve and a circumferential yield stress sigma according to the method in the step (1) 90 =284.59MPa, fig. 2 is a comparison graph of hoop tensile test engineering stress-engineering strain curve and true stress-true strain curve;
(3) Placing a cylindrical mandrel in the metal pipe, performing a plane strain state tensile test, and obtaining a true stress-true strain curve and a plane strain state axial yield stress sigma according to the method in the step (1) p =273.23MPa, fig. 3 is a graph comparing the engineering stress-engineering strain curve and the true stress-true strain curve of the tensile test in the plane strain state.
In the plane strain state tensile test process, since the strain increment of the sample in the circumferential direction is zero, formula 3 can be obtained):
3(F+H)σ q -2Hσ ρ ＝0 3)
subjecting the axial yield stress sigma obtained in the step (1) to 0 As a reference equivalent stress, canEquations 4), 5) and 6):
wherein F, G, H, N is a parameter of Hill48 yield criterion, sigma p Axial yield stress in plane strain state, σ q Circumferential yield stress in a plane strain state;
(4) Subjecting the axial yield stress sigma obtained in the step (1) to 0 =265.46MPa, circumferential yield stress σ obtained in step (2) 90 =284.59MPa and the in-plane strain state axial yield stress sigma obtained in step (3) p =273.23MPa into equation 3), 4), 5), 6), hill48 yield criterion parameters F =0.6492, G =0.7791, H =0.2209 and plane strain state circumferential yield stress σ are obtained by solving equation system q ＝69.37MPa；
(5) Inputting the value of the yield criterion parameter F, G, H of the Hill48 obtained in the step (4) and the value of the simulation parameter Z into finite element simulation software for axial tensile simulation, wherein the value range of Z is 0.1-3.0, 60 values of Z are uniformly selected between 0.1-3.0, 60 groups of simulation load displacement curves are obtained through simulation, and after the 60 groups of simulation load displacement curves are respectively compared with the load displacement curve obtained in the step (1), the value of the yield criterion parameter N of the Hill48 is reversely solved based on a GA genetic optimization algorithm;
completing the calibration of the Hill48 yield criterion parameter F, G, H, N through the step (4) and the step (5), as shown in Table 1;
TABLE 1 Hill48 yield criterion parameters for 304 stainless steel pipes
(6) Inputting the value of the yield criterion parameter F, G, H, N of Hill48 obtained in the step (5) into finite element simulation software for axial tensile simulation, outputting a simulated load displacement curve by a finite element model as shown in FIG. 4, and drawing the simulated load displacement curve and the load displacement curve obtained in the step (1) in FIG. 5 for comparison, wherein as can be seen from FIG. 5, the simulated load displacement curve of the yield criterion parameter of Hill48 determined based on the technical scheme of the invention is basically coincident with the experimental load displacement curve, the error is 0.1-0.5%, and the accuracy and the effectiveness of the technical scheme of the invention are proved.
Example 2
(1) Taking AA6022 aluminum alloy pipe as an example, the outer diameter of the pipe is 25mm, the wall thickness is 1.5mm, firstly, the axial tensile test of the metal pipe is carried out 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 through formulas 1) and 2), the stress when the plastic deformation is 0.2 percent is taken as the yield stress, and the axial yield stress sigma is obtained from the true stress-true strain curve 0 ＝138.35MPa。
σ＝s(1+e) 1)
ε＝ln(1+e) 2)
Wherein σ is true stress, ε is true strain, s is engineering stress, and e is engineering strain;
(2) Performing a hoop tensile test on the metal pipe, and obtaining a true stress-true strain curve and a circumferential yield stress sigma according to the method in the step (1) 90 ＝149.16MPa；
(3) Placing a cylindrical mandrel in the metal pipe, performing a plane strain state tensile test, and obtaining a true stress-true strain curve and a plane strain state axial yield stress sigma according to the method in the step (1) p ＝143.57MPa。
In the plane strain state tensile test process, since the strain increment of the sample in the circumferential direction is zero, formula 3 can be obtained):
2(F+H)σ q -2Hσ p ＝0 3)
subjecting the axial yield stress sigma obtained in the step (1) to 0 As a reference equivalent stress, equations 4), 5), and 6) can be obtained:
wherein F, G, H, N is a parameter of Hill48 yield criterion, sigma p Axial yield stress in plane strain state, σ q Circumferential yield stress in a plane strain state;
(4) Subjecting the axial yield stress sigma obtained in the step (1) to 0 =138.35MPa, circumferential yield stress σ obtained in step (2) 90 =149.16MPa and axial yield stress sigma in plane strain state obtained in step (3) p =143.57MPa into equations 3), 4), 5), 6), the Hill48 yield criterion parameter F =0.6125, G =0.7522, H =0.2478 and the plane strain state circumferential yield stress σ is obtained by solving the system of equations q ＝41.35MPa；
(5) Inputting the value of the yield criterion parameter F, G, H of the Hill48 obtained in the step (4) and the value of the simulation parameter Z into finite element simulation software for axial tensile simulation, wherein the value range of Z is 0.1-3.0, and Z is uniformly 80 values between 0.1-3.0, obtaining 80 groups of simulation load displacement curves through simulation, respectively comparing the 80 groups of simulation load displacement curves with the load displacement curve obtained in the step (1), and reversely calculating the value of the yield criterion parameter N of the Hill48 based on a GA genetic optimization algorithm;
completing the calibration of the Hill48 yield criterion parameter F, G, H, N through the step (4) and the step (5), as shown in Table 2;
TABLE 2 AA6022 aluminum alloy tubes Hill48 yield criterion parameters
(6) Inputting the value of the yield criterion parameter F, G, H, N of Hill48 obtained in the step (5) into finite element simulation software for axial tensile simulation, outputting a simulated load displacement curve, comparing the simulated load displacement curve with the load displacement curve obtained in the step (1), determining that the simulated load displacement curve of the yield criterion parameter of Hill48 is basically coincident with the experimental load displacement curve based on the technical scheme of the invention, wherein the error is 0.2-0.8%, and the accuracy and the effectiveness of the technical scheme of the invention are proved.
Example 3
(1) Taking an AZ31 magnesium alloy pipe as an example, the outer diameter of the pipe is 25mm, the wall thickness is 1.5mm, firstly, an axial tensile test of the metal pipe is carried out 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 through formulas 1) and 2), the stress when the plastic deformation is 0.2 percent is taken as the yield stress, and the axial yield stress sigma is obtained from the true stress-true strain curve 0 ＝130.45MPa。
σ＝s(1+e) 1)
ε＝ln(1+e) 2)
Wherein σ is true stress, ε is true strain, s is engineering stress, and e is engineering strain;
(2) Performing a hoop tensile test on the metal pipe, and obtaining a true stress-true strain curve and a circumferential yield stress sigma according to the method in the step (1) 90 ＝142.39MPa；
(3) Placing a cylindrical mandrel in the metal pipe, performing a plane strain state tensile test, and obtaining a true stress-true strain curve and a plane strain state axial yield stress sigma according to the method in the step (1) p ＝133.76MPa。
In the plane strain state tensile test process, since the strain increment of the sample in the circumferential direction is zero, formula 3 can be obtained):
2(F+H)σ q -2Hσ p ＝0 3)
subjecting the axial yield stress sigma obtained in the step (1) to 0 As a reference equivalent stress, canEquations 4), 5) and 6):
wherein F, G, H, N is a parameter of Hill48 yield criterion, sigma p Axial yield stress in plane strain state, σ q Circumferential yield stress in a plane strain state;
(4) Subjecting the axial yield stress sigma obtained in the step (1) to 0 =130.45MPa, circumferential yield stress σ obtained in step (2) 90 =142.39MPa and the in-plane strain state axial yield stress sigma obtained in step (3) p =133.76MPa into equations 3), 4), 5), 6), the Hill48 yield criterion parameters F =0.6368, G =0.7975, H =0.2025 and the plane strain state circumferential yield stress σ are obtained by solving the system of equations q ＝32.27MPa；
(5) Inputting the value of the yield criterion parameter F, G, H of the Hill48 obtained in the step (4) and the value of the simulation parameter Z into finite element simulation software for axial tensile simulation, wherein the value range of Z is 0.1-3.0, the Z is 100 values uniformly between 0.1-3.0, 100 groups of simulation load displacement curves are obtained through simulation, the 100 groups of simulation load displacement curves are respectively compared with the load displacement curve obtained in the step (1), and then the value of the yield criterion parameter N of the Hill48 is reversely obtained based on a GA genetic optimization algorithm;
the calibration of the Hill48 yield criterion parameter F, G, H, N is completed through the steps (4) and (5), and is shown in the table 3;
TABLE 3 Hill48 yield criterion parameters for AZ31 magnesium alloy pipes
(6) Inputting the value of the yield criterion parameter F, G, H, N of Hill48 obtained in the step (5) into finite element simulation software for axial tensile simulation, outputting a simulated load displacement curve, and comparing the simulated load displacement curve with the load displacement curve obtained in the step (1), wherein the simulated load displacement curve of the yield criterion parameter of Hill48 determined based on the technical scheme of the invention is basically superposed with the experimental load displacement curve, and the error is 0.15-0.58%, so that the accuracy and the effectiveness of the technical scheme of the invention are proved.
Claims (3)
1. A Hill48 yield criterion parameter calibration method based on metal pipes is characterized by comprising the following steps: it comprises the following steps:
(1) Performing an axial tensile test on the metal pipe to obtain a load displacement curve and an engineering stress-engineering strain curve, converting the engineering stress-engineering strain curve into a true stress-true strain curve by formulas 1) and 2), taking the stress when the plastic deformation is 0.2% as the yield stress, and obtaining the axial yield stress sigma from the true stress-true strain curve 0 ；
σ＝s(1+e) 1)
ε＝ln(1+e) 2)
Wherein σ is true stress, ε is true strain, s is engineering stress, and e is engineering strain;
(2) Performing a hoop tensile test on the metal pipe, and obtaining a true stress-true strain curve and a circumferential yield stress sigma according to the method in the step (1) 90 ；
(3) Placing a cylindrical mandrel in the metal pipe, performing a plane strain state tensile test, and obtaining a true stress-true strain curve and a plane strain state axial yield stress sigma according to the method in the step (1) p In the process of the plane strain state tensile test, as the strain increment of the sample in the circumferential direction is zero, the formula 3 can be obtained):
2(F+H)σ q -2Hσ p ＝0 3)
subjecting the axial yield stress sigma obtained in the step (1) to 0 As a reference equivalent stress, equations 4), 5), and 6) can be obtained:
wherein F, G, H, N is a parameter of Hill48 yield criterion, sigma p Axial yield stress in plane strain state, σ q Circumferential yield stress in a plane strain state;
(4) Subjecting the axial yield stress sigma obtained in the step (1) to 0 The circumferential yield stress sigma obtained in the step (2) 90 And the axial yield stress sigma of the plane strain state obtained in the step (3) p Substituting the values of (3), 4), 5), 6), obtaining the value of the Hill48 yield criterion parameter F, G, H and the circumferential yield stress sigma of the plane strain state by solving the equation system q A value of (d);
(5) Inputting the value of the yield criterion parameter F, G, H of the Hill48 obtained in the step (4) and the value of the simulation parameter Z into finite element simulation software for axial tensile simulation, wherein the value range of Z is 0.1-3.0, selecting m groups of Z values between 0.1-3.0, wherein m is a natural number between 30-200, obtaining m groups of simulation load displacement curves through simulation, respectively comparing the m groups of simulation load displacement curves with the load displacement curves obtained in the step (1), and reversely calculating the value of the parameter N in the yield criterion of the Hill48 based on a GA genetic optimization algorithm.
2. The method for calibrating the parameters of the Hill48 yield criterion based on the metal pipe as claimed in claim 1, wherein: the metal pipe is steel, aluminum alloy or magnesium alloy.
3. The method for calibrating the parameters of the Hill48 yield criterion based on the metal pipe as claimed in claim 1, wherein: the method is applied to the field of simulation of wall thickness change rate, section distortion or rebound in the plastic forming process of materials based on the Hill48 yield criterion parameter calibration method of the metal pipe.
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